Investigating synergies between weather radar data and mesoscale model output

Transcription

1 Department of Meteorology University of Reading Investigating synergies between weather radar data and mesoscale model output Marion Petra Mittermaier A thesis submitted for the degree of Doctor of Philosophy December 3

2 Declaration I confirm that this is my own work and the use of all material from other sources has been properly and fully acknowledged. i

3 Abstract Rainfall estimates from weather radar provide the most important real-time information regarding the spatial and temporal distribution of precipitation. During flooding situations, radar-rainfall fields are crucial ingredients for nowcasts of precipitation up to three hours ahead. In this thesis, current and future prospects for synergistic relationships between weather radar data and mesoscale model output from the Unified Model (UM) have been explored to improve rainfall estimates from radar measurements when the radar is sampling in the ice. The use of model freezing level forecast heights in the UK operational vertical profile of reflectivity (VPR) correction scheme was validated using a novel cloud radar technique. Results from a one-year analysis show that the model forecast heights have a rms error of 147 m, well within the sensitivity limit for the correction to be effective. Falling ice and snow are susceptible to wind drift, leading to displacement errors of up to 3 km between where the radar measures and where the rain falls at the surface. A wind-drift correction method using mesoscale model forecast wind profiles is presented. The correction produces a large improvement in the placement of surface rainfall, reducing errors to 15 5% of their original values. This change in placement is more than enough to move precipitation from one catchment to another. For the first time the UM ice water content (IWC) was evaluated in precipitating clouds, and was found to be in good correspondence to observations. It was also found that spinup errors for model moisture variables such as IWC is appreciable for forecast lead times of less than four hours. Radar data resolution effects have an impact on data quality and the accuracy of derived products. An analysis of the requirements for the UK radar network showed that an oversampling scan strategy would have a positive impact on radar-rainfall products. ii

4 Acknowledgements I would like to express my thanks to my supervisor, Anthony Illingworth. His suggestions always challenged me and his insight humbled me. A special thanks must also go to Robin Hogan for his unstinting practical support, ideas, listening and most of all, for propping up a flagging morale! His encouragement got me through. I also want to express my gratitude to the Met Office for the funding support and to my project managers: Malcolm Kitchen, Dawn Harrison and Alison Smith for their input and interest. My thanks also go Ewan O Connor for his Matlab how-to, Rich Forbes and Pete Clark for valuable insights into the Unified Model, Peter Panagi for processing and providing me with all the 3-D model data. I d like to thank RAL for the radar data. Although it hasn t been an easy three years, for several reasons, I shall carry away with me fond memories of the department: great people, great facilities and there were some great times. Thanks to all the wonderful people at Reading Vineyard, the house group support and the many many prayers. My list of thanks would not be complete without mentioning my mother, she has been a pillar of strength all my life. Thanks for always believing in me, always encouraging me, always picking up the pieces and putting me back together again, even from afar! iii

5 iv The Cloud I am the daughter of the Earth and Water, And the nursling of the Sky; I pass through the pores of the ocean and shores; I change, but cannot die. For after the rain when with never a stain The pavilion of Heaven is bare, And the winds and sunbeams with their convex gleams Build up the blue dome of the air, I silently laugh at my cenotaph, And out of the caverns of rain, Like a child from the womb, like a ghost from the tomb, I arise and unbuild it again. Percy Bysshe Shelley

6 Contents 1 Introduction Importance of accurate rainfall estimates and forecasts Principles of radar The weather radar equation Drop size distributions Estimating rainfall rate from radar measurements The vertical reflectivity profile Overview of the Met Office Unified Model Current state of synergy Thesis outline Evaluation of Unified Model freezing level forecasts 19.1 Background Vertical profile correction techniques Use of profile derived from multiple elevation radar data Use of standard vertical profile and mesoscale model temperatures.3 Derivation of the step height from cloud radar data Derivation of temperature profiles from model data Results of the radar and model comparison Overall performance evaluation Comparison with Met Office continuous radiosonde validation results Frontal events and associated timing errors The presence of a deep isothermal layer at or near C Degradation of forecasts with increasing lead times Discussion and implications Using mesocale model winds for correcting wind-drift 37 v

7 CONTENTS vi 3.1 Introduction A theoretical model of fall streak geometry Justification of use of model winds and temperatures Comparison to radar-derived Doppler wind profiles A model climatology of wind speed and shear Model vertical temperature structure Observed displacements Optimum parameters for use in fall streak model Fall speed Sensitivity to the height of the generating level A case study in the vertical plane Case study in plan view Implications for Vertical Profiles of Reflectivity Discussion and conclusions Evaluating Unified Model ice water content Introduction Estimating ice water content from observed radar reflectivity Empirical relationships Model particle size distributions Retrieving model ice water content from radar reflectivity Sensitivity analysis Data description Radar scans Model output fields Errors and uncertainties Validating model ice water content Summary and conclusions Predicting the vertical profile of reflectivity in the ice Background Data Method Calculating reflectivity from model IWC

8 CONTENTS vii 5.3. Creating radar hourly mean vertical profiles Model spin-up effects A comparison of model-derived and radar VPRs Comparison of mean profiles at the hourly time scale Comparison of global mean profiles Assessing predictive skill Conclusions Investigating radar vertical sampling resolution Background Motivation High resolution radar data Description Beam geometry and range effects Method outline Pre-analysis steps Freezing level analysis Significant echo height distribution Scan sequence selection Studying the effects of oversampling Sequence design and selection Steps 1 and : Convolution and resampling Steps 3 and 4: Interpolation and error analysis Error analysis for current and future potential UK scan sequences Sequence design and selection Resampling and interpolation Error analysis Discussion and concluding remarks Conclusions and further work Summary of results Validating the Unified Model variables Use of model forecast variables for correcting radar-rainfall estimates

9 CONTENTS viii Possibilities for assimilation of radar parameters Further remarks Future work References 145

10 CHAPTER ONE Introduction 1.1 Importance of accurate rainfall estimates and forecasts The spatial and temporal distribution of precipitation, from the catchment to the global scale, is important because of the many links of precipitation to clouds, radiation, the water balance, different types of droughts and floods. Climate is important because it drives the weather. In the reports compiled by the Intergovernmental Panel on Climate Change (IPCC), Folland et al. (1) and Arnell et al. (1) list the impacts of climate change. The number of extreme events such as droughts and floods, is expected to increase and affect a larger proportion of the world population. Both an increase in the number of water-stressed regions on the one hand, and more flood-prone regions on the other, has an impact on disease and insurance. The challenge for governments lies in minimizing and mitigating the loss of life and property. Continued accurate monitoring of precipitation in particular is vital, not only because floods are high-impact weather events, but also to detect the climate change response. The distribution of precipitation in space and time is highly variable, intermittent and probably the most chaotic in behaviour of all atmospheric parameters (Fritsch et al., 1998). For a flash flood to occur it must rain heavily over a localized area, but the antecedent conditions and the general characteristics of the run-off surface also play an 1

11 CHAPTER 1: Introduction important role. For a flood in general, it must rain moderately and persistently over a long period of time. Let s consider the different means of measuring and forecasting such events. The traditional means of measuring precipitation is the rain or snow gauge. Besides the sampling errors associated with the small instrument apertures, siting, wind-effects, instrument and human error, a gauge s ability to represent the rainfall distribution accurately depends on the type of rainfall. For convective rainfall, even if the gauge spacing were 1 km, convective cells can rain between the gauges, with the gauges themselves registering no rainfall at all (e.g. Mittermaier and Terblanche, ). This is the appeal of areal rainfall estimation, inferring precipitation from radar and satellite measurements. Radar especially can provide detailed observations of the structure and movement of precipitation at high update rates. However areal estimates are still compared and evaluated against gauge measurements. Seed et al. (1996) state that gauges themselves have 5 1% errors but that they are useful in removing biases in radar-rainfall estimates. Validation of areatype measurements or estimates, such as radar, satellite and model precipitation against point measurements is problematic, as there are clear issues regarding the representativity of gauge measurements (Fritsch et al., 1998). Weather radar provides a qualitatively accurate representation of the location and intensity of precipitation. Although weather radar have inherent system errors (Section 1..1), most of the error in Quantitative Precipitation Estimates (QPE) is associated with the process whereby rainfall is inferred from radar measurements (Section 1..3) as precipitation is not measured directly. Weather radar can also not predict where the convective outbreaks will occur (unless they are sensitive enough, and measure the Doppler radial wind field for the detection of convergence boundaries), but once the convection has been triggered they can provide useful information about the distribution of precipitation and latent heat in the domain. Accurate observations and measurements are required to produce a skillful forecast, regardless of lead time. The generation of nowcasts in the zero to six hour range from the

12 CHAPTER 1: Introduction 3 extrapolation or Lagrangian advection of radar-rainfall fields (e.g. Hill and Browning, 1979; Golding, ; Germann and Zawadzki, ) has been shown to be successful for large-scale systems such as frontal bands with a persistence of greater than six hours or so. Nowcasts of convection are typically useful for no more than 3 minutes because of the rapid evolution of the rainfall field (Wilson et al., 1998). Operational mesoscale models such as the UK Met Office Unified Model (UM) are as yet unable to resolve convection explicitly. Convection is therefore a subgrid scale process and is parameterized. It is therefore difficult for the mesoscale model to get the onset, placement and intensity of convection correct. This is most often because the large-scale dynamics of the flow in the model does not support convection. Model precipitation forecasts in the short- to mid-ranges also depend on an accurate description of the initial state. A detailed description of the three-dimensional moisture distribution is required (Zhang and Fritsch, 1986). In addition information about the forcing that leads to condensation and latent heat release are vital for producing accurate forecasts. Although model precipitation forecasts are increasing in skill, forecasts of large totals at forecast ranges beyond 3 days are still poor (e.g. Buizza et al., 1999). For models such as the UM, the earliest new forecast available is typically four hours old. This implies there is a need to extrapolate the observations and gradually blend in the output from mesoscale models to effect a smooth transition for the longer forecast lead times. The UK Met Office Nimrod system is an example of an automated precipitation nowcasting framework that blends radar rainfall, gauge data, satellite images and UM mesoscale output fields to produce very short range forecasts of up to 6 hours (Golding, 1998). The quantification of error characteristics is one of the major outstanding issues for assimilating radar variables into numerical models. The errors themselves do not preclude the use of data, but lack of knowledge about their magnitude does (Collier, 1).

13 CHAPTER 1: Introduction 4 To date there have been several reasons why the hydrological community has been reluctant to use radar-rainfall estimates for more than qualitative purposes. Hydrological models, especially lumped models, are typically initialized with point values (a gauge) for a catchment, and very few have been developed to cope with the true spatial variability of precipitation over a catchment. The advent of distributed models, where each sub-catchment can be initialized separately, is making this possible. Most hydrological models also require long climatological time series of rainfall, and many radar networks have not been in existence long enough and archiving data for this to be feasible. The hydrological community has focused its efforts on simulating the space-time characteristics of radar-rainfall fields to generate believable time series of pseudo radar data to advance the hydrological modelling development effort (e.g. Pegram and Clothier, 1a,b). Lastly, but arguably the largest obstacle, just like for assimilation of radar data into numerical weather prediction (NWP) models, the lack of error statistics, and the large observed variability in the errors is confounding efforts to input radar-derived rainfall into hydrological run-off or design storm models (Jordan et al., ). In an effort to reduce radar-rainfall errors, there are other data sources to use beside a rain gauge, such as model output fields of temperature and ice water content, which are currently under-utilized. There is the potential and the need to combine them to get optimal use. Model output fields are invaluable in observation-sparse regions; they are spatially gridded (unlike observations) and temporally frequent, more so than many observations. Potential disadvantages are mainly due forecast time errors, although less so at short forecast lead times. In the following sections of this chapter, the principles of radar will be described. This will be followed by a brief description of the model, the idea of synergy and a thesis outline.

14 CHAPTER 1: Introduction 5 1. Principles of radar A weather radar emits pulses of microwaves of a given length and frequency, which scatter from distributed targets such as hydrometeors within clouds. The strength of the return is proportional to the sixth power of the diameter of the particles. Operational radars around the world today are generally also Dopplerized, so that the radial wind field as well as the intensity of the return can be retrieved The weather radar equation The equation that describes the received power from a distributed weather target (Probert- Jones, 196) is given by: P r = π3 P t g θ φ h K D 6 i 14 ln λ r (1.1) where P r P t g θ φ h K D i λ r received power transmitted power antenna gain (by condensing P t into a narrow beam) horizontal beamwidth (typically 1 for operational radars) vertical beamwidth (typically 1 for operational radars) pulse length dielectric factor, constant for rain (.93) but varies for ice diameter of scatters wavelength (mostly 5 or 1 cm for operational radars, also 3 cm) distance of the sample volume from the radar The summation is over a unit volume. Eq. 1. can be re-written as P r = C K Z r (1.) where C is the radar constant, and Z the radar reflectivity factor. Eq. 1. is valid if:

15 CHAPTER 1: Introduction 6 The precipitation particles are homogeneous dielectric spheres, with diameters small compared to the wavelength. The particles are spread throughout the contributing region (or else we should introduce a beam filling factor ψ). The reflectivity factor Z is uniform throughout the contributing region as strong gradients introduce errors. The main lobe is adequately described by the Gaussian function. Attenuation over the propagation path between the radar and the target is negligible. Multiple scattering is negligible. The incident and back-scattered waves are linearly polarized at the same polarization. The reflectivity factor Z, usually just referred to as reflectivity by radar meteorologists (and also the convention here), is defined as the sixth power of the diameter summed over all hydrometeors in a unit volume, Z[mm 6 m 3 ] = K.93 N(D) D6 dd (1.3) where.93 is the value of the dielectric factor for liquid water. Due to the magnitudes of Z, it is expressed in logarithmic units, dbz: Z[dBZ] = 1 log 1 (Z[mm 6 m 3 ]). (1.4) Since the abovementioned assumptions are quite frequently violated we introduce an equivalent reflectivity factor, Z e. We essentially use a water-equivalent value as we assume K =.93. It is important to note that for Rayleigh scatterers (small when compared to the wavelength), Z = Z e. Effectively the radar observes P r, and we interpret the return as that from small spherical drops. A comprehensive review of radar system-related errors is given by Joss and Waldvogel (199). These include beam blocking, wavelength-dependent responses such as attenuation (the weakening of the signal by the presence of atmospheric gases and particulates

16 CHAPTER 1: Introduction 7 such as cloud droplets, rain, hail and snow), radome-wetting, ground clutter and anomalous propagation (beam bending by the atmospheric density stratification). One problem could be partial beam filling. This causes an under-estimation of the precipitation echo by as much as a factor of or 3 db, with this error increasing with range. For this reason a non-dimensional beam filling factor ψ can be introduced. The actual value of ψ is seldom known. The most serious problems from partial beam filling result in estimating storm dimensions especially the echo top height. Radar system errors can be minimized through: favourable radar location, with minimal beam blocking at close range; the radar wavelength, beam width, and receiver sensitivity are suited for the intended use and purpose; the radar hardware being in good working order and well calibrated; corrections for anomalous propagation and attenuation are applied. 1.. Drop size distributions Ulbrich (1983) proposed a general gamma distribution to describe the drop size distribution (DSD), with µ varying between -3 and 8. The equation reduces to the traditional Marshall-Palmer (M-P) exponential distribution (Marshall and Palmer, 1948) for µ =. The number of drops N(D) between diameter D and D+dD are defined by N(D) = N D µ exp( Λ D), (1.5) where N is the intercept, µ governs the shape of the distribution, and Λ the slope of the distribution. For most applications the M-P exponential distribution (µ = ) is still used where N is assumed to be 8 m 3.mm 1. More recently it has been shown by Illingworth and Blackman () that a normalized three-parameter gamma distribution ought

17 CHAPTER 1: Introduction 8 to be used, where the three variables N, D and µ are independent and provide information about the number concentration, mean size and spectral shape. The M-P exponential distribution has by definition an infinite maximum diameter and needs to be truncated. The mean size is sensitive to the truncation value. The gamma function introduces a natural truncation for µ greater than. Another advantage of the gamma function is that it captures the relationships between the higher-order moments used for radar-rainfall estimation more accurately. From the definition in Eq. 1.5 a cloud s total water mass per unit volume is M = πρ w 6 N(D) D 3 dd, (1.6) where ρ w is the density of liquid water (1 3 kg.m 3 ). Similarly the ice water content can be computed using IWC = π 6 ρ(d) N(D) D 3 dd, (1.7) where the density ρ, is now the density of ice. To solve Eqs. 1.6 and 1.7 the general formula D k 1 exp( ΛD) = Γ(k) Λ k (1.8) can be used, where for integer values of k, Γ(k) = (k 1)!. Eq. 1.6 then becomes: M = π ρ w N Λ 4. (1.9) The median volume diameter D is defined such that half the water is contained in the drops larger than D. Eq. 1.6 can be used to solve for D which is (3.67+µ)/Λ. Eq. 1.5 and other equations pertaining to the DSD are often expressed in terms of D as it is a physical attribute that is easily identified. If the DSD is known then the rainfall rate R can also be computed, in still air, using a diameter-dependent terminal fall speed w t : R = πρ w 6 w t (D) N(D) D 3 dd. (1.1)

18 CHAPTER 1: Introduction 9 It can be seen that the common ingredient in Eqs is the size distribution as a function of diameter, and this links all the parameters such as IWC, Z and R together. If a M-P exponential distribution is used to investigate the effect of the sixth power, it can be deduced that it is the few large particles that contribute the most to Z, even if the small diameter drops are more numerous. So even if the Λ and N parameters are poor estimates at the small diameter end of the spectrum, so long as they accurately describe the diameters that strongly contribute, the error in Z will be small Estimating rainfall rate from radar measurements In this section different methods for calculating rainfall rate from radar reflectivity measurements are reviewed. Empirically derived power-law Z-R relationships of the form Z = ar b are still the most widely-used method for deriving rainfall rates from radar measurements. The coefficient and exponent are determined from an exponential regression fit between radar reflectivity and rain rates derived from DSDs measured typically by disdrometers. The Marshall- Palmer relationship (1948) Z = R 1.6 is still the benchmark equation. The assumptions regarding DSDs that N is constant however are violated within similar climatic regions, in successive events in the same region and even within different parts of the same precipitating system, explaining why there are more than 6 quoted relationships in Battan (1973). Other methods such as the area-time-integral (ATI) (Doneaud et al., 1984) and the Probability Matching Method (PMM) (Rosenfeld et al., 1993, 1994) are non-parametric and independent of Z-R relations. The PMM method assumes that the distributions of radarderived and gauge-derived rain rates can be matched because the probability density function (PDF) of the two distributions is identical. The method is also free of spatial and temporal constraints, unlike the others. The idea of linking PDFs will be explored in this

19 CHAPTER 1: Introduction 1 thesis, but in a different context. The error statistics of radar-rainfall estimates have not improved much in the last twenty years, with errors up to a factor of or 3 still common (Illingworth, 3). These same figures were quoted by Joss and Waldvogel (199) and Wilson and Brandes (1979). Dual-polarization radars offer a larger variety of parameters, providing additional information about the shape (and size) of hydrometeors. For some time now using dualpolarization parameters such as the differential reflectivity Z DR and specific differential phase shift K DP have been touted as the means of getting better rainfall estimates (Seliga and Bringi, 1976; Sachidananda and Zrnić, 1987; Illingworth and Caylor, 1989) but thus far this has been shown on research radars only. The differential reflectivity is defined as the ratio of the power returned in the horizontal plane Z h to that returned in the vertical plane Z v : Z DR = 1 log 1 (Z h / Z v ). (1.11) Z DR can be used to detect mean particle shape, especially in the rain as rain drops are oblate and the horizontal wave has a longer path through the rain drop than the vertical wave, implying that the horizontal return will be greater. Empirical relationships that make use of both Z and Z DR require that the Z DR can be retrieved to within. db and Z calibrated to within 1 db. Z DR is high in bright band, low in the ice and is usually db in hail. Specific differential phase shift K DP is defined as the rate of change of the differential phase φ DP where φ DP = φ v φ h. It increases monotonically with range and the values are small. The velocity of the horizontal wave travelling through a region containing oblate rain drops should be less than the velocity of the vertically polarized wave. The phase of the horizontal wave φ h will progressively lag behind the phase of the vertical wave φ v. It means that φ DP increases with range, so K DP should be positive and should

20 CHAPTER 1: Introduction 11 increase with rainfall rate R. Empirical relationships of the form R = akdp b have been proposed by Sachidananda and Zrnić (1987) and the relationship appears almost linear. It is not affected by attenuation or hail and is independent of absolute calibration. However φ DP errors must be within 1 (in reality about 3 ) and the signal is noisy. Ryzhkov and Zrnić (1995, 1996) have also suggested R Z DR K DP relationships. More recently Illingworth and Blackman () proposed a new equation for calculating R that in the absence of hail and attenuation should provide R accurate to within 5% provided that Z DR can be retrieved to within. db and Z calibrated to within 1 db. The disadvantages with many of the polarization parameters is therefore the level of accuracy required in terms of calibration for the parameters to be useful, which is feasible on research-calibre radars, but so far not for operational radar because of the prohibitive costs. Goddard et al. (1994) have shown that Z, Z DR and K DP are not independent in the rain; Z and K DP scale with the number concentration, implying that their ratio will be independent, as is Z DR. This redundancy means that Z can be calibrated to within.5 db (1%). This is the technique used to calibrate the Rutherford Appleton Laboratory (RAL) S-band radar at Chilbolton, southern England. The data from this radar are used extensively throughout this thesis. As precipitation in the UK is predominantly stratiform, empirical Z-R relationships still remain the method of choice for converting radar reflectivity to rainfall rate. To improve accuracy, polarization methods represent the way forward for radars in the UK, with an investigation into the use of combined Z Z DR methods currently in progress (Thompson and Illingworth, 3). The key feature of this work is the use of area-averaged relationships to overcome the expected large errors in Z DR for operational systems, which would normally render the method no better than the Z-R relationships currently in use. Implicit in the discussion just presented is that measurements are made in the rain. Unfor-

21 CHAPTER 1: Introduction 1 tunately polarization parameters hold no advantage to improving surface rainfall estimates when measurements are made in the ice. The fact that a radar doesn t always sample in the rain is addressed next The vertical reflectivity profile In Fig. 1.1 various factors that contribute to the accuracy of radar-rainfall estimates, or lack thereof, are shown. Height Vertical U Profile of FALL STREAK Reflectivity * (VPR) T vapour deposition * * * * ** * ICE * ICE o ** * * aggregation SNOW C * ** ** * * * *** **** * * * * melting BRIGHTBAND melting RAIN Height RAIN droplet break up * * cloud top BEAM BROADENS WITH RANGE ** * * cloud base o C Reflectivity (dbz) RADAR Distance from the radar VPR Figure 1.1: Schematic showing various microphysical processes, the bright band and the beam broadening with distance from the radar. Convective and stratiform rainfall areas are characterized by distinctly different microphysical processes. This dicussion has been limited to stratiform rainfall areas. Stratiform areas are marked by gentle uplift, a stratification of hydrometeor-type and generally large regions of light to moderate intensity precipitation (e.g. Houze, 1993). Vapour deposition and at warmer temperatures aggregation are the main contributors to particle growth. Ice crystals become sticky as they fall and approach temperatures T near zero. They clump together to form large snow flakes. If the freezing level is some distance above the ground, the snow flakes melt, with the large drops being hydrodynamically unstable and breaking up, producing rain. At low levels, the rain may be subject to orographic growth or evaporation. On rare occasions, double bright bands may also be seen. The horizontal wind U tends to increase with height so that falling ice is advected and subjected to the vertical

22 CHAPTER 1: Introduction 13 shear of the horizontal wind as it falls. This means that the point where it finally reaches the ground can be quite a distance from where it began to fall, the so-called wind-drift effect. This produces fall streaks that can be observed by radar (Marshall, 1953). The radar beam broadens and is progressively further away from the surface as the distance from the radar increases. Ideally, for rainfall estimation we wish to sample close to the ground in the rain. Factor of to 3 errors are common (e.g. Joss and Waldvogel, 199), which is why Z-R relationships are usually implemented together with gauge adjustment factors (e.g. Golding, ), such as in Nimrod. The radar response mirrors the microphysical processes. Snow flake diameters are large and when melting often coated with a thin film of water, making them more reflective than ice and appear like rain. The melting process manifests itself as the radar bright band, which leads to a large and sudden increase in the radar reflectivity, and a potentially large over-estimate in surface rainfall rate if left uncorrected. Below the bright band in the rain, the reflectivity decreases. In the UK pioneering work done by Smith (1986) provided one of the first VPR correction schemes. Today Nimrod (Kitchen et al., 1994) makes use of a template describing the vertical profile of reflectivity (VPR). The mesoscale model freezing level forecast is used to determine where in height the template should be applied to successfully retrieve realistic surface rain rates. In the ice above the bright band, the K is up to five times lower and the diameter of the particles is small, therefore the reflectivities in the ice are low, making the direct retrieval of realistic surface rainfall rates from the ice more difficult, but not futile, as Fabry et al. (199) have stated. From a VPR point of view, this is seen as the sharp decrease in reflectivity immediately above the freezing level. Whereas the problem of retrieving surface rainfall rates from measurements in the ice may in most instances only be necessary at long ranges from the radar, at high latitudes and during the cold season the surface temperatures may be zero or below zero so that no sampling in the rain is possible. The low reflectivities in the ice pre-determine that

23 CHAPTER 1: Introduction 14 the surface rainfall rates will be under-estimated leading to large errors when compared to surface measurements from rain gauges. It has however also been demonstrated that snowfall can be measured as accurately at the surface as rainfall. There are two other aspects regarding radar measurements in the ice that compound the errors, the large variability of reflectivity (e.g. Joss and Waldvogel, 199), and wind effects (Doviak and Zrnić, 1993). The lack of radar measurements in the ice could also contribute to the errors as the variability can not be adequately resolved. The work presented in this thesis explores new ways of improving the rainfall rates derived from radar measurements in the ice. 1.3 Overview of the Met Office Unified Model Although the current operational version of the Met Office Unified Model (UM) is now non-hydrostatic, the UM output used in this thesis is based on the quasi-hydrostatic dynamics and has a full suite of parameterization schemes representing diabatic processes (Cullen, 1993). It uses a bulk microphysics scheme (Wilson and Ballard, 1999) with water vapour, cloud liquid water and cloud ice the only prognostic variables. It represents transfer processes described by equations for ice nucleation and growth (deposition, riming), evaporation, droplet capture, accretion and autoconversion of cloud liquid water to rain. Operationally, the Met Office runs the Unified Model in two configurations. The global model has a horizontal resolution of.83 longitude and.56 latitude giving an approximate resolution of 6 km in mid-latitudes. The global model is used to provide boundary conditions to the mesoscale model which is a regional model centered on the UK. This model has a resolution of.11 latitude by.11, which is approximately 1 km, and runs with a rotated North Pole to obtain a more uniform horizontal resolution over the UK. Both the global and mesoscale models have 35 levels in the vertical. The global model is run twice daily to produce forecasts for up to 6 days (144 hours)

24 CHAPTER 1: Introduction 15 ahead. These main runs are initialized with data valid at : and 1: UT. The mesoscale model is run four times a day at data times :, 6:, 1: and 18: UT. It uses observations 9 minutes before and after the data time and produces forecasts for up to 48 hours ahead. For research analysis purposes model output is typically at an hourly time step. 1.4 Current state of synergy Synergy is defined in the concise Oxford dictionary as the interaction or cooperation of two or more organizations, substances or other agents to produce a combined effect that is greater than the sum of the separate parts. The COST 75 final report (Collier, 1) states that the combinations of radar with NWP, radar in NWP and NWP in radar all have important contributions to make. Radar data is important for model verification and validation. Cloud radar data is especially useful for validating microphysics parameterizations (Mace et al., 1998; Hogan et al., 1). Multiparameter radar data are also being used because of the hydrometeortyping that can be achieved (Brown and Swann, 1997). Yet the process of validation does not combine the radar data and model output fields, they are simply compared. Figure 1. gives a schematic of ways in which radar data can be ingested into NWP and how NWP output can be combined with radar data. The schematic is by no means exhaustive, but includes some of the aspects that will be discussed in this thesis. The solid-line ellipses indicate current synergies already in place, the dashed-ellipses contain potential future synergies. If we first consider radar in NWP, then it has already been shown that the assimilation of radar-derived surface rain rates from the Nimrod system (Golding, ) into the UM via a latent heat nudging scheme is beneficial (Jones and Macpherson, 1997; Anderson et al., ).

25 CHAPTER 1: Introduction 16 MODEL Use model freezing level forecasts to correct for the bright band Direct assimilation for radar surface rainfall rates The Loop Using the model winds to correct for observed wind drift in the ice 3 D assimilation of radar derived ice water content Use the model ice water content to predict the slope of the VPR in the ice Assimilation of radar surface rain rates via a latent heat nudging scheme (Jones and Macpherson, 1997) RADAR Figure 1.: Schematic showing the interaction and feedback loop between the UM and the operational radar data. Solid ellipses indicate those synergistic relationships already in operation. Dashed ellipses indicate some of the possible future synergies. Generally mesoscale models now have a fine enough spatial resolution (1 1 km) and four-dimensional variational data assimilation (4DVAR) required for the assimilation of time-series variables such as radar data which has a high spatial and temporal resolution. The challenge for models is how to cope with information about the placement and the intensity of precipitation when the model atmospheric state does not support it (Rogers et al., ). One way of possibly improving forecasts in the short-term forecast range is through the assimilation of radar rainfall fields (e.g. Rogers et al., ; Guo et al., ). Other possibilities include the assimilation of radar-derived wind fields (Snyder and Zhang, 3), and the direct assimilation of radar-derived ice water content (IWC). The latter depends strongly on whether the radar scan strategy will provide sufficient measurements in the ice. It is a closed feedback loop because already the UM mesoscale freezing level forecast heights are used by Nimrod for VPR-correcting the radar data (Harrison et al., ). Further possibilities for achieving better rainfall rate estimates from measurements in the ice include: using the mesoscale model wind fields to correct for the advection and shear that ice is subjected to as it falls. Another would be the use of the model IWC fields to predict the shape of the VPR ahead of time, which might enable the

26 CHAPTER 1: Introduction 17 optimization of the template used for correction. Both the latter options will be explored in later chapters. 1.5 Thesis outline The work presented in this thesis can be divided into two parts: firstly the evaluation of existing synergistic relationships, and secondly the exploration of new synergistic relationships, their strengths and weaknesses, and feasabiliy for implementation in an operational context. As an integral part, the issue of data resolution and impact of errors has also been studied. The scope of the thesis is constrained to show the potential of new techniques, not their implementation and testing. The purpose of this chapter has been to introduce general key concepts and methods for the intepretation and processing of radar data, including a review of both current and future prospects. A brief description of the UM was also included. Background material of particular relevance is given as part of the following chapters themselves. In Chapter we shall begin by evaluating one of the current synergistic relationships that exists between radar and model, namely the use of UM forecast freezing level heights in the Nimrod VPR correction scheme. Chapters 3 to 5 are devoted to investigating previously untried synergies, which also includes an evaluation component testing whether the model parameter is good enough to use in a downstream application. Firstly, the model winds are investigated to use in a wind-drift correction scheme. Then the model ice water content is evaluated within precipitating clouds. The predictive skill of using vertical profiles derived from model ice water content is then investigated. Ultimately, the hardware and software of a radar system determine the resolution of the data that are being collected for product generation. In Chapter 6 the issue of radar data

27 CHAPTER 1: Introduction 18 resolution, and how it can be optimized given the underlying constraints of the radar system, are investigated. Concluding remarks and comments regarding future work and the potential for the techniques and methods introduced in the other chapters are presented in Chapter 7.

28 CHAPTER TWO Evaluation of Unified Model freezing level forecasts.1 Background One of the largest contributions to the errors in deriving rainfall rate (R) from observed radar reflectivity (Z) arises from the vertical profile of radar reflectivity (VPR) and in particular the layer of enhanced reflectivity associated with melting snow. The height of the radar beam above the ground increases with range so that if the bright band is, say, at 1 km, then at short ranges the beam should only sample raindrops, but at longer ranges the beam samples the melting layer and the enhanced values of the Z leads to a large overestimate of the rainfall. At longer ranges the overestimation due to the bright band may cancel out the underestimation due to beam broadening and smoothing, possibly giving the right answer for the wrong reasons. If at longer ranges the beam samples in the ice above the bright band, the rainfall is underestimated. If accurate surface rain rates are to be made with operational radar networks then a correction scheme for the VPR is essential. Two quite different approaches have been proposed: 1. A vertical profile is derived by analysing the three dimensional radar reflectivity 19

29 CHAPTER : Evaluation of Unified Model freezing level forecasts and this profile is used to correct observed values of Z at a given height to yield a rainfall rate at the ground.. A standard high resolution vertical profile is used for correction with the height of the top of the bright band set by the height of the C wet-bulb temperature T w (WBZ) derived from an operational forecast model. One example of the first approach is summarized in Sánchez-Diezma et al. (); indeed Sánchez-Diezma et al. (1999) suggest that the height of the bright band derived from the radar data could be used to improve the temperature structure of an operational model. The second approach using the temperature from the model to fix the height of the bright band has been adopted by the UK Met Office, and is described in Kitchen et al. (1994) and Harrison et al. (). In this chapter we address the fundamental question as to whether current mesoscale models have the required m accuracy in the representation of the vertical structure of temperature to be of use in radar bright band correction schemes, suggested by sensitivity tests done by Kitchen et al. (1994). This is achieved by comparing, over a one-year period, the height of the step in reflectivity observed with an accuracy of 6 m using a vertically pointing cloud radar, with the height of WBZ in the operational analyses and forecasts of the ECMWF (European Centre for Medium Range Forecasts) and Met Office Unified mesoscale model (UM). The aims are to establish: the error characteristics of the C isotherm in the operational forecast models and whether it is better for VPR correction schemes to derive the height of the bright band from multiple-elevation radar scans or from an operational forecast model.

30 CHAPTER : Evaluation of Unified Model freezing level forecasts 1. Vertical profile correction techniques..1 Use of profile derived from multiple elevation radar data Germann and Joss () provide a comprehensive summary of the various methods for deriving an average vertical profile from radar observations taken at different elevation angles. One question that arises is the optimum scale in space and time for deriving an average profile. If the averaging over space and time is too great then there is little advantage over a climatological mean, but on the other hand if the averaging is too small then the derived profile is not representative enough. For example Vignal et al. () derived a mean profile from an hourly average over a 7 km radius cylinder (area 15 km ) using the different elevation scans of the Swiss radar network. They found a mean fractional standard error for the six-hourly rain gauge totals of 5% compared to 44% without any profile correction. When they used a more local profile as suggested by Andrieu et al. (1995a,b) and averaged over an area of 4 km, this error was reduced to 3%, an improvement of only %. The system being implemented operationally in Switzerland, uses a profile averaged over 7 km weighted with an exponentially decaying function which has a time constant varying from 5 minutes when the volume is full of precipitation to more than 3 hours when 1% of the volume is filled with precipitation. Sánchez-Diezma et al. () considered the idealized situation when the true vertical profile of radar reflectivity was constant out to a range of 15 km, and computed the profiles which would be observed with an operational radar as a function of range, scanning at various elevations. In such an idealized situation they estimated that the bright band could be estimated to within an accuracy of 3 5 m out to a range of 7 km. In reality this performance can not be achieved because rainfall is never constant over such a large area. Vignal and Krajewski (1) report on two different VPR correction schemes (a mean and a local VPR derived from multi-elevation data), both brought about significant im-

31 CHAPTER : Evaluation of Unified Model freezing level forecasts provements but with computationally serious shortcomings as far as being considered for operational real-time application. Therefore currently no vertical profile correction scheme is applied to the NEXRAD data (J. Keeler, personal communication)... Use of standard vertical profile and mesoscale model temperatures.3 km Zb Z Figure.1: The standard profile template that is used for VPR correction (after Kitchen et al. (1994)). It is an average profile compiled from three years high resolution data collected with 3 GHz Chilbolton radar. The second approach for vertical profile correction involves using a standard VPR together with a bright band height that is derived from the temperature structure predicted by an operational model. The method adopted by the Met Office as described by Kitchen et al. (1994) uses this technique and is based on the standard vertical profile in Fig..1, which has been derived from 11 days of rainfall over three years of high resolution vertical scans taken with the.8 beamwidth radar at Chilbolton. In this profile the background reflectivity in the rain, Z b, is constant, the bright band enhancement occurs over a depth of 7 m, and then Z decreases with height above the bright band. In the bright band Z rises linearly for 35 m by Z and then falls linearly back to Z b over the

32 CHAPTER : Evaluation of Unified Model freezing level forecasts 3 next 35 m, where Z (in mm 6 m 3 ) is given by: log Z = 1.4 logz b.44 (.1) so that the enhancement for a Z b of, 3 and 4 dbz (equivalent to rainfall rates of.65,.7 and 11.5 mm.h 1 using the Marshall-Palmer relationship) would be 5.4, 8.7 and 1 dbz, respectively. Above the bright band the cloud top is inferred from the infrared satellite temperatures, to be a height of 1,, 3 or a maximum of 4 km above the bright band peak and the reflectivity in dbz is linearly reduced to zero. The correction procedure is as follows: 1. The standard VPR in Fig..1 is shifted in height so that the top of the bright band coincides with the height of the WBZ from the model.. The VPR is scaled in magnitude (with accompanying changes to the bright band enhancement), so that when the the profile is multiplied by the operational radar beam pattern at the appropriate height, the radar reflectivity matches the observed value. 3. The best estimate of the rainfall rate at the ground is given by the value of Z b of the scaled profile. Given that Hardaker et al. (1995) also found that VPR correction was most sensitive to the height of the C isotherm Table.1 assesses the impact of height errors on the VPR correction scheme s ability to remove the effects of the bright band for the profile in Fig..1 and a Gaussian beamwidth having a two-way half-power beamwidth of 1 appropriate for the Met Office radar network. The calculations were done for a bright band enhancement of 8.7 db (a surface rain rate of.7 mm.h 1 ). If no correction is applied then at a range of 4 km the peak error in the inferred ground-based reflectivity is 93% and the errors exceed 5% for a 13 m range in beam heights. Applying the VPR correction algorithm, but with the bright band height wrong by 5 m leads to negligible

33 CHAPTER : Evaluation of Unified Model freezing level forecasts 4 Table.1: Peak errors at 4 and 8 km in inferred ground-based reflectivity for a bright band peak enhancement of 8.7 db and the height range for the centre of the radar beam over which the reflectivity error exceeds 5%. at 4 km at 8 km Peak error Range>5% Peak error Range>5% (a) No correction applied 93% 13 m 197% 8 m (b) Correction applied but with 5 m WBZ height error 67% 98 m 177% 13 m but with m WBZ height error 54% m <3% improvement in rainfall estimates, whereas an inaccuracy of m in the bright band height leads to a peak error in the inferred reflectivity in the rain of less than 6%. This confirms Kitchen et al. s statement that the algorithm requires the height of the bright band to be known to within m. Another advantage of this correction scheme is that it is applied over each 5 km x 5 km area of every low level radar scan, thus avoiding all the difficulties that arise for volumetric scans in choosing an appropriate scale in space and time over which the average profile is derived; these scales could also vary with precipitation type and geographic location. The algorithm is suppressed, however, when the value of Z exceeds 3 dbz at a height of 1.5 km above the freezing level. An analysis by Smyth and Illingworth (1998) has shown this threshold to be a reliable indicator that no bright band is present, presumably associated with the high density graupel in convective cells. Harrison et al. () found that over a twelve-month period the average reduction in the root-mean-square (rms) difference between the hourly gauge accumulations and the corresponding radar-estimated accumulations was approximately 3%. The rms differences were still a factor of two, as is expected for representativeness sampling errors if hourly totals are estimated with a 5 km resolution every 15 minutes (Kitchen and Blackall, 199). According to Kitchen and Blackall these representativeness errors would be reduced to about 5% if or 5 minute

34 CHAPTER : Evaluation of Unified Model freezing level forecasts 5 sampling with a spatial resolution of 3 km were used for the hourly totals; with this sampling the true impact of the VPR correction scheme could be quantified more accurately. An evaluation of the radar precipitation estimates by Kitchen and Harrison (1) has shown that the tractable (i.e. non-sampling related) error in the ratio of the hourly gauge to radar rainfall ratio has been reduced by 5% through the introduction of their VPR correction methods. A similar vertical profile correction scheme is used in France (Chèze et al., 1998). Rather surprisingly, Kitchen (1997) found no improvement in the bright band correction scheme when the higher elevation beams were included (via a penalty function), presumably because of the variability in the profile in the ice above the bright band, thus supporting the assertion of Fabry et al. (199) that beyond the range where the radar horizon intercepts the freezing level any attempt to obtain quantitative rainfall estimates is futile..3 Derivation of the step height from cloud radar data From all available data collected by the vertically pointing 94 GHz Galileo cloud radar at Chilbolton in southern England (51.14 N and 1.44 W) between 1 May 1999 to 3 April, 435 condensed hours were associated with rain rates exceeding.48 mm.h 1. Of this number 189 hours (43%) had VPRs with detectable melting level heights. Another 35% of the hours were very shallow rain or showery elements, leaving about % of the hours which were more convective with no bright band detected. Surface rain rates associated with individual bright band profiles were found up to mm.h 1, although the majority are less than 5 mm.h 1. The radar provided time series of vertical reflectivity profiles at 6 m range resolution every 3 seconds with a minimum range of 5 m. Typical vertical profiles from the 3 GHz and 94 GHz Chilbolton radars are plotted in Fig... The 6-dB step in the 94 GHz vertical profile indicates the onset of melting. The more

35 CHAPTER : Evaluation of Unified Model freezing level forecasts 6 Figure.: Typical vertical profiles sampling a stratiform rainfall area as seen at 3 and 94 GHz. Note that the 94 GHz data has not been calibrated, typical values in the rain are 17 dbz. This does not affect the shape of the profile. gradual rise in Z at 3 GHz (1 cm) is caused by the finite time it takes for the snow flakes to acquire a sufficient liquid water coating so that the dielectric factor, K, rises from the value of dry ice to that of liquid water. The fall in Z below the bright band is caused by the decreasing size and concentration of drops as they melt, the break up of large drops and increasing terminal velocities. The thickness of the liquid water shell required for a change in K is wavelength dependent and becomes very small at 94 GHz (Meneghini and Kozu, 199). This accounts for the observed 6-dB step within one range gate. At these high frequencies Mie scattering and attenuation is responsible for much lower values of Z, and also explains why the 94 GHz VPR is less sensitive to changes in the size of melting particles when a spectrum of sizes is present. Accordingly we can identify the 6-dB jump occurring within one gate as the height at which melting starts and T w reaches C. White et al. () derive the height of the bright band by searching vertical profiles of Doppler velocity from a 915 MHz Doppler wind profiler from the bottom up for a change in velocity of 1.5 m.s 1 over a distance of 1 m. We have tested this technique with the 94 GHz Doppler data, and find that the change in velocity is typically spread over 18

36 CHAPTER : Evaluation of Unified Model freezing level forecasts 7 3 m, and is offset by as much as 4 m below the step in reflectivity which occurs when the particles become wet. Presumably they need to fall this distance to melt sufficiently so that the terminal velocity increases. As discussed in the previous section a 4 m offset in determining the bright band height is not acceptable Normalized height (km) wrt bright band height dbz Relative frequncy of occurrence Figure.3: A contoured-frequency-by-altitude diagram (CFAD) of the vertical profile structure for 4 October 1999, relative to the freezing level height. Contours are at.1 intervals. The vertical structure of reflectivity can also be summarized in the form of contouredfrequency-by-altitude diagrams or CFADs, as a function of height relative to the bright band height of each profile, as described by for example Yuter and Houze (1995). Figure.3 shows the CFAD for all the identified profiles on 4 October Again the step transition showing the onset of melting under stratiform conditions is clearly evident and very sharp, indicating that the WBZ can be determined to within 6 m or one range gate. The maximum rain rate did not exceed 5 mm.h 1. A vertical profile was only included in the analysis if the near-ground reflectivity was greater than 1 dbz, the corresponding 3-second rain rate from a drop-counting gauge exceeded the detection threshold of.48 mm.h 1 and a step in the VPR in the vicinity of the WBZ height. The hourly heights were calculated as the mean of the 1 3-second profiles. A 5% data threshold was imposed, so that only hours with more than 6 3-

37 CHAPTER : Evaluation of Unified Model freezing level forecasts 8 second profiles were included for analysis. The technique is completely independent of radar calibration or attenuation by rain..4 Derivation of temperature profiles from model data Wet-bulb temperature profiles were derived from the relative humidity fields for both the ECMWF and UM forecasts. During the period in question the ECMWF model had a horizontal grid resolution of 6 km with 5 vertical levels (after 13 October 1999 the horizontal resolution changed to 5 km and 6 vertical levels). There is one run each day at midday, with forecasts being produced hourly from t+1h to t+36h (midnight to midnight). The mesoscale version of the UM had a grid resolution of around 15 km with 35 vertical levels and was initialized every 6 hours. The t+h to t+5h forecasts were used for most of this analysis. Hourly forecasts are available out to t+36h. At heights between.5 and 3 km, model layer depths range between 17 to 5 m, but before 13 October 1999 ECMWF layer depths had less resolution below km. Because temperature profiles are often quite complicated, linear interpolation was found to be most reliable. Experiments carried out with more complex fits did not yield significantly different heights for the interpolated values. The algorithm extracts the height at which T w first rises to C when one searches downwards. Two parameters were derived from the interpolated model profiles to study the height and temperature errors: (i) WBZ and (ii) T w at the observed step height of radar reflectivity..5 Results of the radar and model comparison This study investigated: The model errors of WBZ heights to establish whether using the model heights is the optimum approach. The performance of the model in predicting changes in WBZ heights, such as the mean error in the timing of frontal passages.

38 CHAPTER : Evaluation of Unified Model freezing level forecasts 9 The performance of the model in predicting isothermal layers at or near C. The formation of deep or double bright bands could have an impact on the effectiveness of the VPR correction scheme. Degradation of the UM forecast over a 36-hour lead period..5.1 Overall performance evaluation.5 UM.5 ECMWF RMS= mean= RMS= mean= Relative frequency of occurrence Relative frequency of occurrence (a) Height error (km) (b) Height error (km) Figure.4: Histograms of the height differences between (a) the UM t+ to t+5 h forecast, (b) the ECMWF t+1h to t+36h WBZ heights and the observed radar heights. Histograms of the relative frequency of occurrence of height differences (radar model) with respect to the WBZ for a sample of 189 hours obtained during the 1-month period are given in Fig..4(a) for the UM and Fig..4(b) for ECMWF. The rms error for the UM for the t+h to t+5h values is 147 m with a bias of only 15 m below the observed height. The ECMWF profiles have a rms error of 316 m with a bias of 58 m above the observed bright band height; but of course this increase may be because the ECMWF time series is a t+1h to t+36h forecast. When the same period is considered for the UM forecast, the rms error is 5 m with a bias of 95 m above the observed height. It is important to notice the encouraging lack of outliers in the error distribution for the UM, with no occasions of differences above 4 m. The hourly differences exceeding 8 m for the ECMWF error analysis are due to a single case where the model failed to predict the development of a deep isothermal layer.

39 CHAPTER : Evaluation of Unified Model freezing level forecasts 3.5. Comparison with Met Office continuous radiosonde validation results The Met Office continually monitor the model vertical temperature structure by comparisons with radiosonde data, over the whole model domain. The rms errors of 17 m (D. Forrester, personal communication) for the period April to June 1 are very similar to those reported in Fig..4(a). The radiosonde data are not truly independent however; they are themselves assimilated into the model, causing the errors at observational locations to be lower as the model and observations are being forced to agree here. In addition the validation is performed over the whole domain every 1 hours, whereas the radar comparisons reported here are confined to rainfall events which may be expected to be more error prone, often associated with fronts and changes in temperature..5.3 Frontal events and associated timing errors The passage of a front is typically associated with significant changes in the vertical temperature profile and also the freezing level height. It might well be thought that the occurrence of timing errors would cause frequent errors in the bright band correction scheme. An example of such a rapid change in the height of the freezing level is displayed in Fig..5. Note that gaps in the radar time series occur when the radar is not vertically pointing but in scanning mode (at this time the radar was mounted on the side of the 3 GHz radar antenna dish at Chilbolton). The radar observations show that the freezing level dropped about 8 m in the space of 4 hours. The model WBZ heights tracked this change with considerable accuracy. For this particular front the model showed no significant timing errors. To obtain a more global view, a simple analysis of the timing errors is presented here. Frontal events accompanied by temperature changes were isolated by searching the hourly time series for a change exceeding 5 m in 3 hours. In this way, 6 events were identified.

40 31 1 Height (km) R (mm/h) CHAPTER : Evaluation of Unified Model freezing level forecasts Height (km) 4 dbz RADAR ECMWF UM Time (hours) Figure.5: The daily 3-second time series of radar (uncalibrated), rain-gauge rain rates, hourly radar freezing levels and model forecasts for December The model timing was then assessed based on an analysis of trends by matching the peaks and the periods of increase and decrease on an event-by-event basis. For three of the events no timing errors can be inferred. Two of the events however had substantial errors of between 3 and 8 hours, yet these errors were more associated with a difference in the rate of change in temperature rather than an outright model timing error. Only one event could be described to have a combination of model timing error and a difference in the rate of change in the height of the freezing level. The worst forecast was for the frontal passage on 11 December 1999 as shown in Fig..6. The model predicted a steady fall in temperature starting at 4: UT, whereas the radar observations indicated a much greater rate of decrease starting at 1: UT. The model error at this time was more than 4 m, one of the worst performances in the data set considered. Fortunately it would appear that such events are rare and generally shortlived, affecting only 1 or % of rainfall cases and we conclude that errors due to poorly

41 CHAPTER : Evaluation of Unified Model freezing level forecasts UM radar Height (km) Time (hours) Figure.6: Hourly radar observed freezing level heights and model forecast WBZ heights for 11 December predicted frontal passages are not serious..5.4 The presence of a deep isothermal layer at or near C The performance of a model in predicting isothermal layers is very important. For several hours on 3 April the UM was accurately predicting the presence of a deep isothermal layer which cooled throughout the day until its temperature fluctuated about C. The ECMWF WBZ was eventually 8 m lower than the UM WBZ height, and, more significantly the ECMWF forecast showed no sign of any isothermal layers through the day. An isothermal layer at or around the C isotherm would imply that the bright band would be deeper than usual, as the melting in this layer is retarded. The 3-panel plot in Fig..7 indicates the well defined melting level step. Note the gradual decrease in the ECMWF WBZ height to near ground level as the day progressed. The large errors from this poor forecast would lead to a poor performance of the bright band correction scheme, and emphasize the importance of using the current analysis and 6h forecast scheme rather than the longer lead times of the daily ECMWF forecast.

42 33 1 Height (km) R (mm/h) CHAPTER : Evaluation of Unified Model freezing level forecasts Height (km) 4 dbz RADAR ECMWF UM Time (hours) Figure.7: The daily 3-second time series of radar (uncalibrated), rain-gauge rain rates, hourly radar freezing levels and model forecasts for 3 April, a case with an isothermal layer at C..5.5 Degradation of forecasts with increasing lead times The performance of the UM as a function of forecast lead time up to 36 hours is shown in Fig..8. Whereas it is useful to evaluate the bright band correction scheme performance in terms of height errors, for the model s vertical temperature structure it is more convenient to express the errors in terms of temperature, so the value of Tw at the bright band height is plotted. It is encouraging to see that the bias stays fairly constant around.15 C, but the rms error increases from.7 C to 1.4 C after t+36h, so half the error is introduced at initialization time. For the ECMWF forecast lead times of t+1h to t+36h, the UM forecast for the same lead time suggests an average error of 1. C 7% higher than t+h to t+5h. Accordingly we conclude that the larger rms errors of 316 m for the ECMWF scheme rather than 147 m for the UM arise because of the longer lead times and the lower horizontal resolution of the ECMWF forecast. This is confirmed by the comparison of ECMWF model temperatures with observations over Europe and the Northern

43 CHAPTER : Evaluation of Unified Model freezing level forecasts 34 Hemisphere for the last six months of 1 (J.-F. Mahfouf, personal communication), which have an rms analysis error at 7 mb of C and C at t+4h, and are very similar to Fig..8 for the UM. The Met Office continuous validation using sondes yield a worsening in the rms error from 17 m at t+h to 7 m at t+48h (D. Forrester, personal communication), which is consistent with the data in Fig..8 and suggest that the temperature errors within precipitation are no worse than those for all conditions. 1.5 r.m.s.e. bias Temperature error (degrees) Forecast lead time (hours) Figure.8: Summary of the temperature differences between the T w at the observed bright band height and the T w C isotherm for the different forecast lead times of the UM. These results suggest that if the initial analysis error could be further reduced, a significant improvement could be brought about for the entire forecast lead time..6 Discussion and implications A one year analysis of 189 hours of rainfall over the UK has revealed that the rms error of the UM t+h to t+5h forecasts of the WBZ during rainfall is 147 m with a bias of 15 m. The model was able to track changes in bright band heights which sometimes changed as much as 5 1 m in 4 hours with good accuracy, although the % of occasions in which the errors reached their maximum value of 4 m were associated with frontal timing errors. For forecasts from t+3h to t+36h the rms error was doubled. These

44 CHAPTER : Evaluation of Unified Model freezing level forecasts 35 errors compare well with those obtained from the sonde comparisons for all weather conditions, rather than the radar comparisons which were only during precipitation, even though sonde data are not independent as they are used in the model analysis. The performance of the ECMWF model over Europe and the Northern Hemisphere is similar when consideration is given to the longer forecast lead time and the degraded model resolution with an rms error of 316 m for t+1h to t+36h forecast. On one occasion during the 189 hours of comparisons an isothermal layer at least 8 m deep developed and persisted during 4 hours of rainfall. This layer and the height of the WBZ was accurately captured by the UM, but the ECMWF model, with its longer lead time, failed to predict it, and this event was responsible for the worst errors of 8 m for the ECMWF model comparison. The results can be compared with the idealized accuracy of 3 to 5 m obtained from the simulation study of Sánchez-Diezma et al. (). This simulation assumed: (1) the bright band was at the same height and was the same shape at all distances out to 1 km; () a uniform rainfall rate and identical profiles regardless of range; and (3) that the profile was sampled by a 1 beamwidth radar at 4 elevations. These simulated accuracies appear to be rather worse than those of the operational forecast models. A comparison of one hour s data at elevations of widespread stratiform rain with an independent estimate of the bright band height from a UHF vertically pointing radar, found that the height of the bright band was relatively stable, but beyond 8 km it could not be detected. The advantage of using the model temperature field is that it always provides a bright band height, and is not limited to rather unusual conditions when rainfall is continuous over a large distance. Our analysis in the UK demonstrates that the mesoscale version of the UM with 1 km resolution run every 6 hours with hourly forecasts from t+h to t+6h provides sufficiently accurate temperatures, as does the ECMWF model over the Northern Hemisphere for similar lead times. Germann and Joss () suggest that over the Alps the height of the melting layer varies both in space (air masses following the terrain) and time (temperature fronts), and that to use this temperature information in a correction scheme, a model

45 CHAPTER : Evaluation of Unified Model freezing level forecasts 36 resolution of 3 minutes and 1 km would be required. It would be interesting to see results of radar comparisons with the ECMWF model temperature data in Switzerland and other parts of the world, but it appears that, in the UK at least, the errors in the operational forecast height of the WBZ from t+h to t+6h are within the bounds of m listed by Kitchen et al. (1994), and that the model-predicted height of the bright band height is more accurate than the height derived from the multiple elevation radar data themselves. We conclude that operational forecast models can provide the height of the bright band with an rms error of 15 m. If this model height is used in conjunction with an appropriately scaled and shifted standard VPR then it should lead to improved estimates of rainfall rates at the ground. If the error in the bright band height reaches 5 m then this technique will not lead to improved rainfall rates at the ground, however, such large errors were not observed. An alternative method of deriving bright band heights has been proposed which involves the use of volumetric radar scans averaged over an area, but at present it is not clear that such an approach can yield the required m accuracy in the inferred bright band height. 1 1 See Mittermaier M.P. and Illingworth, A.J. (3): Comparison of model-derived and radar-observed freezing level heights: Implications for vertical reflectivity profile correction schemes, Quart. Jour. Roy. Meteorol. Soc., 18,

46 CHAPTER THREE Using mesocale model winds for correcting wind-drift 3.1 Introduction Operational radars around the world share a common objective in producing as accurate an estimate of the spatial distribution of precipitation as possible. There are several errors associated with radar-rainfall estimation (e.g. Joss and Waldvogel, 199), and it is acknowledged that the largest source of error is associated with the observed variability of vertical profiles of reflectivity (VPR). Most VPR correction schemes assume that any correction to the reflectivity observed aloft applies to the rainfall rate on the ground below this point, but in reality any wind will cause the position of the precipitation on the ground to be displaced. At middle and high latitudes the radar beam will frequently be sampling the ice. Because the terminal velocity of ice is so much lower than that of rain drops, the ice will be particularly prone to wind drift problems. Marshall (1953) explained the parabolic shape of vertical fall streaks as revealed in radar range-height-indicator (RHI) scans in terms of ice particles falling with constant terminal velocity through a region of constant wind shear, with the pattern itself moving horizontally with the speed of the wind at the height of the generating level. Fabry (1993) suggested that the shape of the fall steak and its displacement as the particles fell from the 37

47 CHAPTER 3: Using mesocale model winds for correcting wind-drift 38 level of one plan-position-indicator (PPI) scan to a lower PPI could be used to infer the vertical profile of wind, and showed examples where the wind could ideally be estimated to about.5 m.s 1. In this chapter we suggest an inverse approach, whereby the profiles of vertical winds held in a mesoscale forecast model are used to predict where an echo from ice particles which is detected by the radar at some height above the ground would actually fall to ground. The wind-drift effect is most important for ice precipitation. For rain the advection distances are small. When comparing radar estimates of precipitation rates with gauge measurements, Harrold et al. (1974) found an improvement if the rain was moved with a wind speed estimated from two anemometers and nearby radiosonde ascent. Typical movements were about 1 km, as the rain fell at an assumed velocity of 5 m.s 1 to ground from the height of the radar beam (5 m). Dalezios and Kouwen (199) found similar distances for wind-drift of the rain. Although such movements are important for gauge calibrations, they are not so important for an operational radar which produces rainfall estimates with a resolution of 1 km for use in hydrology. Collier (1999) also studied how accuracy at different horizontal resolutions was affected by wind drift and suggested that the wind profile type was important in determining the error. Fabry et al. (1994) concluded that wind-drift in rain was unimportant for resolutions greater than 5 km. The situation for ice is quite different. If we consider ice which is being detected by the radar km above the bright band and is falling at 1 m.s 1, then the displacement can easily become 4 km; such a distance is now very significant in hydrology. It is important to distinguish between wind-drift as seen by a radar RHI and a PPI. The RHI provides a snapshot, and will reveal the shape of the fall streak which is controlled by the wind shear; analysis of such RHIs is useful in judging if model winds are sufficiently accurate for explaining the shape of the fall streaks. Operationally the problem is rather different. The challenge is to consider the lowest level PPI available, and to predict where the precipitation will hit the ground. The shape of the fall streak, controlled by the wind shear, is important, but in addition the horizontal displacement of the fall streak while the

48 CHAPTER 3: Using mesocale model winds for correcting wind-drift 39 particles fall to ground, which is a function of the horizontal wind at the generating level, must also be considered. In reality the two components are often of similar magnitude. The UK state-of-the-art VPR correction scheme (Kitchen et al., 1994) uses a standard vertical profile where the bright band depth is 7 m, and the peak is 35 m below the top which is set to the height where the model wet-bulb temperature T w is C. The magnitude of the high resolution profile is then scaled to produce the observed reflectivity when the profile is multiplied by the appropriate radar beamwidth, and the best estimate of the rain at the ground is read off from the scaled profile. This Chapter extends this philosophy of using the model temperature to fix the bright band height, to the use of the model winds to predict wind drift. Figure 3.1 shows a range-height-indicator (RHI) scan of nimbostratus with fall streaks on 18 August at 13:4 UT. Regions of rain and ice, the vertical wind profile, the freezing level (FL) and dotted lines for two vertical cross sections are indicated. For 7 VPR1 VPR 4 6 u EL 35 Height (km) FL ice EL rain Range (km) x dbz Figure 3.1: RHI scan for 13:4 UT on 18 August measured by the 1 cm radar at Chilbolton, southern England, showing fall streaks and how radar beams EL 1 and EL intersect the freezing level (FL) and the fall streaks at different ranges. Downward arrows indicate the surface placement of radar estimates. A displacement error is shown as x. Also shown are idealized VPRs extracted at two locations, VPR 1 and VPR. radar-rainfall estimation the ideal case would be when the lowest elevation beam samples in the rain, never intersecting the bright band within the maximum radar range, like

49 CHAPTER 3: Using mesocale model winds for correcting wind-drift 4 EL 1. Now suppose EL is the lowest beam, with a bright band near the ground. Then the beam would be sampling in the ice at most ranges. With the presence of shear in the vertical wind profile, sampling at the radar beam height will lead to progressively larger discrepancies between the range where the radar measures and where it is raining at the ground, as shown by the arrows. Furthermore, the presence of fall streaks leads to different VPR shapes. VPR 1 is an idealized profile more typical of stratiform rain with a rapid decrease in the reflectivity above the bright band. VPR on the other hand would indicate an increase in the reflectivity higher up, as the top of the next fall streak element is intersected by the radar beam. We therefore hypothesize that some of the observed variability in VPRs is due to wind effects. Panagi et al. (1) report on comparisons between wind profiler data from various locations around the UK and Europe and Unified Model (UM) wind profiles. Regardless of whether the data were assimilated or not most of the profiles showed that the rms errors below 4 km height are less than 1 m.s 1. Turton et al. (1994) state that the model-derived wind profiles are preferable to radiosonde profiles once 3 hours has elapsed since the sonde launch. Sondes are launched only every 6 or 1 hours at a few locations, so we conclude that the model winds which are available at every grid point every hour are the best source of wind data. In this chapter we explore a new radar-model synergy, by proposing the use of UM mesoscale model forecast winds to correct for wind drift of falling ice and snow above the freezing level. First, in Section 3. an equation for calculating displacements using the model winds is presented. A comparison between model and radar-derived wind profiles is given in Section 3.3 to establish whether the model winds are indeed good enough to use. In Section 3.4 the magnitude of observed displacements in RHIs are investigated. The fall speed and generating level sensitivity to height errors are discussed next in Section 3.5. Sections 3.6 and 3.7 then present two case studies where the method is applied in the vertical plane and plan view. Section 3.8 outlines potential implications on the variability of VPRs. A discussion and conclusion follows in Section 3.9.

50 CHAPTER 3: Using mesocale model winds for correcting wind-drift A theoretical model of fall streak geometry To devise a method, the following assumptions, adapted from those made by Dalezios and Kouwen (199), are made: i. The fall speed w of the ice, is constant. ii. The wind profile is linear between the generating level height and the bright band, implying constant vertical shear. We take the approach that natural uncertainties in the fall speed and generating level height do not justify a more complex model. A schematic introducing the fall streak geometry is given in Fig. 3.. The vertical shear of the horizontal wind, S x is calculated for the layer between two reference heights, the freezing level (FL) (h = ) and a fall streak source region or generating height, h t. The height that precipitation has fallen from h t is denoted as h f, with a corresponding zonal displacement x f. u t Generating level h f h Radar sampling location h t h u x x f Freezing Level (FL) x t Figure 3.: Fall streak geometry showing the linear wind profile that is assumed in height, giving constant shear. The height of the generating level is denoted as h t, which is the where the maximum horizontal displacement x t occurs. At any given height, h relative to the freezing level (FL, h = ), the distance x can be calculated. Similar to the approach of Marshall (1953), the time to fall a distance h f from h t is h f /w. In this time the fall streak has moved zonally a distance (u t h f )/w, where u t is the wind

51 CHAPTER 3: Using mesocale model winds for correcting wind-drift 4 at the generating level height. As the zonal shear S x is assumed constant, the horizontal displacement is determined by the average zonal velocity that it experiences as it falls a distance h f, which is u t S x h f. (3.1) Therefore the zonal displacement relative to the new position of the source region at the generating level is x f = S x h f w, (3.) showing that the shear controls the shape of the fall streak and the absolute horizontal velocity is irrelevant. From the figure, h = h t h f and x = x t x f. The maximum displacement occurs when the radar samples at the generating level height, where h f = so that h t = h: x t = S x h t w, (3.3) and to know the displacement of precipitation sampled at any height h between h t and h =, we substitute x and h to get x = S x w ) (h h t h ; (3.4) similarly for meridional displacement y with shear S y. Given the assumptions, the displacements, x and y at any given height above the freezing level can then be calculated using Eq. 3.4, indicating a parabolic fall streak shape. The magnitude of the displacement scales linearly with the shear S and inversely with fall speed, w. Operationally direct measurements of the fall speed w are not available. Similarly the height of the generating level will not be directly observed due to the way in which operational radars scan. Using the radar data itself might seem like the optimal solution, but determining the generating level objectively, even when RHI data are available, is difficult. The fall streak geometry seen in RHIs is a snapshot whereas operationally precipitation sampled at a height is affected by shear and advection before it reaches the

52 CHAPTER 3: Using mesocale model winds for correcting wind-drift 43 ground. We therefore investigate whether it is valid to assume a constant fall speed and use the mesoscale model temperatures (as we have confidence in them) for determining the generating level height. 3.3 Justification of use of model winds and temperatures In order to use the model winds we first need to ensure that they are accurate enough for our purposes. Turton et al. (1994) and Panagi et al. (1) have reported on validation of model winds using radiosondes and wind profilers. Alternatively, wind profiles derived from Doppler radar are here used as an independent source for comparison Comparison to radar-derived Doppler wind profiles The radar data were collected using the 3 GHz radar situated at Chilbolton in southern England (51.14 N and 1.44 W). The large 5 m antenna affords a beamwidth of.8. Both RHI and PPI data at 3 m range resolution were used. Vertical sampling occurs at.1. elevation steps, between 3 elevation. PPIs have.5 resolution in azimuth. An earth curvature correction was applied. Several events between March 1999 and November were studied. For the current work, single-column model wind profiles from the version of the UM (1 km horizontal grid spacing) for the Chilbolton grid reference were compared to vertical profiles of wind derived from the horizontal component of the radial Doppler wind. Fig. 3.3 shows such a comparison for one RHI scan with the along-rhi component of the hourly (t+h) model wind forecast. Forecasts are in the t+h to t+5h range. Despite the discrepancies in vertical and temporal resolution between the radar and model data, the comparison is remarkably good. The plane-perpendicular profile is also shown for reference.

53 CHAPTER 3: Using mesocale model winds for correcting wind-drift Model Model normal Doppler Height (km) Wind speed (m.s 1 ) Figure 3.3: Wind profiles derived from the horizontal component of RHI Doppler winds for 13:4 UT on 18 August and the hourly model forecast. The plane-perpendicular model wind profile is also shown. The comparison can be taken one step further and several scans within the same hour can be evaluated, and also other hourly forecasts on other days. Figure 3.4 shows the comparison of the mean layer winds for 34 scans, spanning 6 days between August and November, and representing 1 hourly forecasts. As the aim is to evaluate the lowermid-tropospheric winds, the top of the layer was here defined to be the model level closest to 4 km, the bottom being the model level closest to the freezing level. The mean layer wind calculated from Fig. 3.3 is but one of the data points on this graph. This suggests a good correspondence between model and radar-measured winds for a spectrum of weather systems, with a correlation of.94, but a mean error of.67 m.s 1 which is larger than the 1 m.s 1 quoted by Panagi et al..

54 CHAPTER 3: Using mesocale model winds for correcting wind-drift <u model > (m.s 1 ) <u > (m.s 1 ) rad Figure 3.4: Plot of the mean layer winds as determined from the model, against the mean layer wind calculated from Doppler velocity data. A 1:1 line has been added for reference. The correlation is.94. It can therefore be concluded that the model winds are good enough to use for wind-drift correction of radar data with errors of 1 m.s 1. Furthermore, the last assumption in the method can now be added: iii. Model wind profiles are sufficient and accurate enough to use A model climatology of wind speed and shear The 34 RHI scans included in this study are useful for conceptualization, testing and validation. But the data set is insufficient to say, determine the range of displacements and the conditions that lead to them. This is because of the requirement that for RHIs the radar samples along the mean wind direction with little variation in wind direction with height. To capture this range of displacements a two-and-a-half year time series of UM single column forecasts for the Chilbolton grid reference (mid-1999 to end 1) was analyzed to determine the distributions of wind speed and shear. The results are shown in Fig. 3.5, obtained by considering the same layer between the freezing level and the model level nearest 4 km.

55 CHAPTER 3: Using mesocale model winds for correcting wind-drift 46 Frequency Shear (s 1 ) Frequency Mean wind speed (m.s 1 ) Figure 3.5: Two-and-a-half year model climatology of shear and mean wind speed. Ninety percent of the data have a shear between and s 1, and average layer winds are between 3 and 4.5 m.s 1, and a mean of 1 m.s 1. From a correction point of view it is useful to know whether the shear scales with the magnitude of the wind. Fig. 3.6 shows the contoured distribution of wind speed and shear. It shows that there is no clear relationship between the two and that high winds are not a prerequisite for strong shear, with typical values of 5 1 m.s 1 and. s 1. So, a layer depth of.5 km, a shear of. s 1 and a fall speed w of 1 m.s 1 yields a maximum fall streak displacement of 6.5 km. Advection at 1 m.s 1 would add another 5 km. 7 x Shear (s 1 ) Mean wind speed (m.s 1 ) %.5 Figure 3.6: Contoured distribution of mean layer winds and layer shear from the model climatology. Contours are at every.5% between.5 5%.

56 CHAPTER 3: Using mesocale model winds for correcting wind-drift Model vertical temperature structure In Chapter it was shown that the UM mesoscale forecasts of the vertical temperature structure is good with freezing levels within 147 m for a one-year comparison to vertically-pointing cloud radar data. The study showed that heights can be derived with confidence from the model temperatures. 3.4 Observed displacements The slope of fall streaks and displacements can be calculated from RHI data using a radar-only approach by using the concept of lagged correlations in space. The generating level is defined as the height where fall streaks originate, which can be subjectively determined from RHI data, but would not be obvious from operational PPIs. Data series at constant heights are extracted from an RHI, one located in the rain, which is the reference. The other heights, located in the ice, are spaced 5 m apart. A range of heights is required because if a fall streak exists, it should intersect at least one of these heights, the maximum displacement determined by the convergence of the correlation traces from different heights. For correlation the data series were converted to linear Z space to assist in identifying the fall streak peaks in the ice. This was done to increase the difference in magnitude between reflectivities in the fall streak and the background. Maximum displacement would be associated with the radar measuring at the top of the fall streak. An example of such correlation traces is given in Fig The correlations were calculated between a reference series in the rain at 1 km and a sequence at heights from.5 5 km in the ice, 5 m apart. In this case the traces converge at a displacement of km at a height of 5 km. The method does provide an independent quantitative means of calculating radar-only displacements, not affected by the assumptions made in this paper, providing the means for comparison to the model-calculated values discussed in Section 3.6.

57 CHAPTER 3: Using mesocale model winds for correcting wind-drift 48 (a) (b) (c) Correlation Height (km) Height (km) Range (km) 6 5 v dbz o Range (km) 1.5 km 3 km 3.5 km 4 km 4.5 km 5 km Range (km) Figure 3.7: RHI for 13:31 UT on 18 August showing (a) reflectivity and (b) Doppler winds (m.s 1 ), positive away from the radar. Also shown are distance correlation traces (c). Each trace represents the correlation between two constant-height data series, one at 1 km below the bright band and the others heights between.5 5 km. 3.5 Optimum parameters for use in fall streak model Fall speed From Eq. 3.4, the fall speed is a key parameter. For stratiform rain, the region up to km above the bright band is typically dominated by aggregates of ice and snow. Fall speeds of around 1 m.s 1 are typical (e.g. Locatelli and Hobbs, 1974). Empirical relationships linking radar reflectivity and fall speed have been derived for rain and snow (e.g Sauvageot, 198) but these have been disputed, mainly because the accuracy depends on precipitation type.

58 CHAPTER 3: Using mesocale model winds for correcting wind-drift 49 The fall speed can also be investigated using the RHI data in an exploratory manner to see how they compare to those quoted in the literature. Displacements can be calculated using the measured shear in the layer from the radial Doppler winds and a range of fall speeds between.5 5 m.s 1. A variation on the correlation method described in Section 3.4 can be used to determine the fall speed associated with the peak in the correlation trace. For this purpose 5 carefully selected RHIs, aligned with the wind, were used. Only two constant-height series were extracted, one below the bright band in the rain, the other at the generating level height. The horizontal displacement of the fall streaks is typically 1 15 km. An example correlation trace is shown in Fig. 3.8, suggesting a fall speed of.95 m.s 1. Peaks for the 5 cases are 1.±.1 m.s 1, suggesting that a constant fall speed of 1 m.s 1 is appropriate. 1 Correlation trace for 1::1 on 9 October.9 Correlation coefficient Fall speed (m.s 1 ) Figure 3.8: Correlation trace between a series in the rain at 1.8 km and the other at the observed generating level of 4.5 km using a range of fall speeds for the RHI at 1: UT on 9 October Sensitivity to the height of the generating level The other key parameter in determining the displacement is the height of the generating level. Knowing the depth of the layer between the generating level and the freezing level is crucial, but is difficult to determine, even from RHI scans. Some proxy for this height needs to be found that will capture the average behaviour. An analysis of the hourly

59 CHAPTER 3: Using mesocale model winds for correcting wind-drift 5 model wet-bulb temperatures associated with the observed generating level heights for the scans in this study have a mean of C and a standard deviation of 1.7 C. The mean observed layer depth calculated from the RHI scans used in this analysis is.6 km. Can the -15 C wet-bulb temperature be used as a proxy for the generating level height so as to calculate the layer over which the correction is to be applied? To test this on a longer time scale, an analysis of the same two-and-a-half year model time series described in Section 3.3(b) gives the mean layer depth between the -15 C and C wet-bulb temperature isotherm heights as.8±.5 km, representing the seasonal fluctuation. If we consider that on average the generating level is.8 km above the freezing level and the beam is sampling at km above the freezing level, then for a mean shear of. s 1 and a fall speed of 1 m.s 1 the displacement is 7. km. Changing the generating level by m would lead to a fractional displacement of about 11%, to which one should add % error due to uncertainties in the fall speed w, making a total error of 3%. Finally when calculating actual displacements one must also add the advection of the echo pattern: A mean horizontal wind speed of 1 m.s 1 contributes an additional km with a % error for uncertainties in the fall speed w. Combining the effects of wind shear and advection leads to a typical wind drift of 7 km with an error of %. This can be expressed as follows: Err(Displacement) = Err(advection) + Err(shear) = ( km ± %) + (7. km ± 3%) = ( ± 4 km) + (7. ± 1.6 km) = 7. ± 4.3 km = 7. km ± 16% This applies if it is assumed that the errors are independent. To test the -15 C T w, the mean ratio of the calculated values using Eq. 3.4 to the radaronly displacements calculated in Section 3.4 for the 5 RHI scans is 1.19, suggesting that a 19% over-correction is made. This is comparable to the 3% shear-only error calculated above. A direct comparison of the correlation and calculated displacements

60 CHAPTER 3: Using mesocale model winds for correcting wind-drift 51 gives a slope of 1.3, nearly one-to-one with a root-mean-squared-difference (rmsd) of 7 km. If the radar-derived shear (from the Doppler velocity) is used in Eq. 3.4 the same slope is obtained but with an rmsd 1.3 km. Another way of analyzing the error would be to use the observed correlation distances from Section 3.4 and inverted versions of Eq. 3.4, either with the radar-derived shear, to calculate the mean fall speed for the 5 RHI scans, or assuming a constant fall speed (1 m.s 1 ) to calculate the mean shear. This tests how well the different assumed values perform and the robustness of the formula. The mean fall speed is.9±.51 m.s 1 comparing well to those determined earlier, and the mean shear is.6±.3 s 1 which compares well to the mean observed value of.7±. s 1. The displacements obtained in two very different ways appear to agree well, validating the assumptions. This error analysis is not ideal as the alignment of the wind with respect to the RHI direction will contribute to the error. This is however irrelevant for operational or PPI scans. 3.6 A case study in the vertical plane When applying the technique in the vertical plane, the largest difficulty is motion through the plane. Therefore to apply the technique to RHIs, scans must be found where the wind speed can change with height but the direction is constant, i.e. unidirectional speed shear. Therefore we specify that the component of the forecast model wind perpendicular to the RHI must be small (less than half) compared to the magnitude of the plane-parallel wind component, and this must be the case for the entire depth of the layer that the correction is to be applied to. In Fig. 3.1 one of the four remaining RHIs for 18 August at 13:4 UT at 5 azimuth that meets the above criteria is shown. A strong bright band with fall streaks is evident. This is a relatively low shear case with the shear calculated from the radar data was.15 s 1 and the model shear calculated from a t+h forecast was.17 s 1. A constant fall speed of 1 m.s 1 was used. Fall streak geometries and displacements calculated using Eq. 3.4, based on the height that precipitation has fallen

61 CHAPTER 3: Using mesocale model winds for correcting wind-drift 5 from observed generating level are superimposed as black dashed and solid lines. Displacements of between 7 1 km were calculated for layer depths of km. This corresponds well with the lagged-correlation displacement of 7 km. The shape and displacements are captured well by the calculations, suggesting that the constant fall speed, shear and single-column assumptions are sufficient o Height (km) Range (km) dbz 1 Figure 3.9: RHI for 18 August at 13:4 UT at 5 showing clear fall streaks. Fall streak trajectories calculated using Eq. 3.4 are superimposed. The two fall streaks were produced using two different generating level heights, with the layer depth.9 and 3.7 km. The magnitude of the calculated displacements is dependent on the generating level height which for the RHI data is a priori information. From the radar measurements, depending on the reflectivity threshold that is used, a mean generating level height of 5.5 km for the scan seems appropriate.

62 CHAPTER 3: Using mesocale model winds for correcting wind-drift Case study in plan view All operational radars collect data in volume mode, as a sequence of plan-positionindicators (PPI), one of the purposes being the calculation of radar-rainfall estimates. Although studying the vertical plane using RHIs is instructive and a proof of concept, the method must be applicable in plan-view. The RHIs provide a snapshot of the sheardependent fall streak trajectories, but for the PPI sequence the advection of the echo by the horizontal wind during the time taken for the precipitation to fall must be added, as is the case for operational data. The displacements are range-dependent because the magnitude depends on the height of the beam above the freezing level, which increases with distance from the radar. To keep the idea of the layer between the generating and freezing levels, corrections are only applied for heights falling within the layer interval. The PPI sequences analyzed are for 3 March Prior to May 1999, no UM data were available, so the European Centre for Medium Range Forecasting (ECMWF) model forecast for the Chilbolton grid location was used instead. Fig. 3.1 (a) shows the vertical wind and temperature profiles for 1: UT (t+4h) and 13: UT (t+5h), and (b) shows the hodograph of the horizontal wind at 1: UT. There are no significant changes between the two hourly forecasts. The freezing level is just below km and the wind speed is increasing with height. The hodograph was approximately unidirectional, so the shear is mostly due to the change in the strength of the wind with height. Both the radar-only analysis of an RHI as described in Section 3.4 and applying Eq. 3.4 gives displacements of 3 km when precipitation falls from the generating level. An aspect not addressed thus far is the issue of spatial scales. The UK Met Office produces radar-rainfall fields at three different resolutions. The national composite is at 5 by 5 km, but there are also by km and 1 by 1 km products produced for individual radars, primarily for hydrological applications. One of the main objectives besides devising a

63 CHAPTER 3: Using mesocale model winds for correcting wind-drift (a) v (b) (c) Height (km) u Height (km) C v wind (m.s 1 ) Speed (m.s 1 ) 1 1 Temperature ( C) u wind (m.s 1 ) Figure 3.1: ECMWF wind (a) and temperature (b) profiles for 1: UT (t+4h) and 13: UT on 3 March 1999 for Chilbolton grid location. The hodograph for 1: UT (c) shows that the wind shear is unidirectional. method for applying a wind-drift correction is determining the magnitude of the correction in relation to the product resolution. To illustrate the method, and for validation purposes the correction is applied at ranges where.5 data are also available below the bright band, in the rain. Figure 3.11 shows the uncorrected and corrected sector scans at.5 on 3 March 1999 at 11:4 UT, together with the.5 sector scan PPI at 11:44 UT, as 1, and 5 km contoured fields of rain rate, R. Only areas of potential overlap are shown for each field. A simple VPR slope correction was applied to both uncorrected and corrected.5 by applying a 3 db.km 1 reflectivity lapse rate as a function of height. This was calculated from the scan itself. A system advection correction, to account for the time difference between the scans at the two elevations, was also applied. The maximum rain rate was of the order of 1.8 mm.h 1. This is therefore a low rain-rate event but for the UK, a rather typical example. The uncorrected.5 PPI shows no rain in the area coincident with the.5 rain area. After the application of the fall streak (up to 8.7 km) and advection (1.6 km for 1 s scan separation) correction the rain area is now in the same place, especially the position of the closed 1.6 mm.h 1 contour at 1 km north, 4 km west. Note that the advection correction would be up to 3 km for operational radar precipitation estimation. The pattern is evident at all spatial resolutions, implying that the correction has made a positive impact at all these scales.

64 CHAPTER 3: Using mesocale model winds for correcting wind-drift 55 Uncorrected.5 o PPI Corrected.5 o PPI.5 o PPI km S km S km S km W mm.h 1 (a) km W km W Uncorrected.5 o PPI Corrected.5 o PPI.5 o PPI km S km S km S km W mm.h 1 (b) km W km W Uncorrected.5 o PPI Corrected.5 o PPI.5 o PPI km S km S km S km W mm.h 1 (c) km W km W Figure 3.11: Uncorrected and wind-drift corrected.5 PPIs and the.5 counterpart as (a) 1 km, (b) km and (c) 5 km averages of rainfall rate. Contour intervals are at. mm.h 1 between. 1.6 mm.h 1.

65 CHAPTER 3: Using mesocale model winds for correcting wind-drift 56 A standard technique for evaluating the positioning of rainfall in precipitation forecasts from models is the use of rain-rate thresholds and binary maps, combined with a contingency table and various skill scores (e.g. Mason, 3). This approach was applied here to evaluate the effect that the correction has had on the positioning of the rainfall. To compile the contingency table all the pixels for the.5 PPI above a pre-determined threshold are set to 1 (else ), and similarly for both the uncorrected and corrected.5 PPIs. The area of overlap at that rain-rate threshold is then determined, and the pixels counted depending on whether it is a hit, a miss, a false alarm, or a correct rejection. This is shown in Fig Two measures derived from a contingency table were used to evaluate the success of the wind-drift correction, the bias and the equitable threat score (ETS) given in Eqs 3.5 and 3.6. The ETS is also known as the Gilbert s skill score. The bias in this context is the ratio of the number of observed occurrences at.5 to the number of observed occurrences at.5. A bias of 1 would imply that the correct number of forecasts are made when compared to the actual observations. The ETS takes the hits that would have occurred purely by chance into account. Observed at.5deg Observed at.5deg EVENT yes no Total yes a no Total c ("hit") ("miss") b d ("false alarm") ("correct rejection") a + c b + d a + b c + d a+b+c+d=n Figure 3.1: Schematic of a contingency table showing the meaning of each of the values. ETS = B = a + b a + c a a + b + c ( ) (a+c)(a+b) N ( (a+c)(a+b) N (3.5) ) (3.6) The bias and ETS for three PPI sequences on 3 March 1999 of.5 and.5 including the example in Fig are plotted as a function of rain-rate thresholds ( mm.h 1 ) in Fig Specifically, the uncorrected-to-.5 and the corrected-to-.5 are plotted for the 1, and 5 km resolution fields. As the bias is always less than 1, there is always an under-estimate in the observed occurrences at.5, both for the uncorrected and corrected fields. The absolute value of the bias is affected by the lapse rate used to correct the VPR. The bias for the corrected field

66 CHAPTER 3: Using mesocale model winds for correcting wind-drift Bias (a) 1 km C. 1 km UC km C.1 km UC 5 km C 5 km UC Threshold rain rate (mm.h 1 ).4 1 km C 1 km UC km C km UC 5 km C 5 km UC Equitable Threat Score (ETS). (b) Threshold rain rate (mm.h 1 ) Figure 3.13: The corrected (C) and uncorrected (UC) bias (a) and equitable threat score (ETS) (b) at all spatial scales and for different rain rate thresholds, from.3 to 1.3 mm.h 1. is better (closer to 1) with an improvement in the bias for rain rates greater 1 mm.h 1, which is unusual in the forecast validation context where the skill of predicting more intense events often decreases. The ETS measures the accuracy of the estimate, i.e. how many hits are matched. Again the ETS for the corrected field is better at all rain-rate thresholds. This substantiates in a quantitative manner the improvement that can be seen from visual inspection, in the placement of precipitation, at all spatial scales.

67 CHAPTER 3: Using mesocale model winds for correcting wind-drift Implications for Vertical Profiles of Reflectivity Conventionally, VPRs are extracted as truly vertical profiles for the purposes of defining the shape of the VPR and VPR correction. We define a fall streak profile of reflectivity or FSPR, which is extracted along a fall-streak path using the model wind shear and the parabolic fall streak geometry model. Figure 3.14 shows the mean FSPRs and VPRs extracted from four 5 km range intervals from the RHI shown in Fig To avoid the bright band zone, profiles were calculated between km. We find that most average FSPRs exhibit a significantly smaller decrease reflectivity with height, particularly in the 1 5 km above the bright band, when compared to the more familiar decrease of reflectivity with height of the VPRs. The average VPRs for 4 45 km and 5 55 km (with respect to surface range) are examples as shown in Fig. 3.1 where the higher reflectivities of the generating level source region are intersected. This can still happen for FSPRs, e.g. for 4 45 km above 5 km, because the generating level was not optimally defined for this interval. This behaviour is also found between fall streaks in regions of lower reflectivity, but the higher reflectivities are more relevant for radar-rainfall estimation. Even more important than the mean profiles is the spread or variability. This is shown in Fig where the standard deviation of normalized VPRs and FSPRs (with respect to reflectivity in the rain) in db is plotted against absolute height, above the bright band, extracted from the RHI shown in Fig The values for the profiles extracted along the calculated fall streak geometry have lower standard deviations at all heights with differences in the spread of up to db between the VPRs and FSPRs. The normalized mean profiles are almost identical, as ought to be expected over the entire RHI.

68 CHAPTER 3: Using mesocale model winds for correcting wind-drift 59 Height (km) km Reflectivity (dbz) Height (km) FSPR VPR km Reflectivity (dbz) Height (km) Height (km) km Reflectivity (dbz) km Reflectivity (dbz) Figure 3.14: Example of VPRs and FSPRs for 5 km range intervals, for the RHI in Fig. 6.1 for 18 August, 13:4 UT. 5.5 FSPR VPR 5 Height (km) Standard Deviation to the normalized profiles (db) Figure 3.15: Comparison of the standard deviations of normalized (with respect to reflectivity in the rain) VPRs and FSPRs for the RHI shown in Fig. 6.1 on 18 August 13:4 UT, plotted against absolute height. These differences would suggest that some of the observed variability is because the wind effect has not been taken into account. The rapid decrease of reflectivity in the ice is

69 CHAPTER 3: Using mesocale model winds for correcting wind-drift 6 delayed to above the generating level height with FSPRs displaying higher reflectivities. 3.9 Discussion and conclusions Observational evidence shows that vertical shear of the horizontal wind can cause displacements in the positioning of surface rainfall derived from radar measurements in the ice of 1 km. Advection by the horizontal wind can also be a significant effect. Comparisons of the model wind profiles to wind profiles derived from the radial Doppler winds show good correspondence, suggesting that using the model winds for a wind-drift correction scheme is feasible. A method using a single-column wind profile forecast from the UM mesoscale version together with assumptions of a linear wind profile, a constant fall speed and a constant temperature of the generating level has been proposed. It has been shown it can reproduce observed displacements due to vertical shear of the horizontal wind and improve the ground placement of radar-derived precipitation, as indicated by the better bias and skill scores. The use of a constant 1 m.s 1 fall speed in calculations appears adequate. Corrections are applied to a layer between the freezing level and a generating level height which coincides with the top of the fall streak. As the generating level may not be directly observed operationally, the -15 C wet-bulb temperature derived from the model was considered for use instead of an observed generating level height. It has been shown that it yields layer depths of the right magnitude so that the height of the -15 C wet-bulb temperature isotherm can be considered an adequate proxy. Calculated displacements are sensitive to this layer depth, which is on average.8 km. The displacement error could, in theory, be corrected to within 15 %, although more realistic figures would suggest that the correction is possible to within 5%. Vertical profiles of reflectivity extracted along calculated fall-streak paths (FSPRs) show

70 CHAPTER 3: Using mesocale model winds for correcting wind-drift 61 a lower spread than ordinary VPRs, suggesting that at least some of the variability in the observed VPRs is due to wind effects aloft. Some FSPRs exhibit an almost constant reflectivity with height, more reminiscent of convective profiles. This is significant for VPR correction schemes and calculating lapse rates of reflectivity in ice. We suggest that the method be implemented and tested operationally, especially the use of proxy values for critical parameters that can not be directly measured, such as the generating level height. More data, perhaps RHIs (with the constraints as described) will need to be collected and analyzed to evaluate the effect on VPRs, and whether it justifies a change to the operational VPR correction scheme. 1 1 Mittermaier, M.P., R.J. Hogan and A.J. Illingworth, 3. Using mesocale model winds for correcting wind-drift errors in radar estimates of surface rainfall. Accepted by Quart. Jour. Roy. Met. Soc., 1 December 3

71 CHAPTER FOUR Evaluating Unified Model ice water content 4.1 Introduction Clouds dominate the Earth s energy budget and are fundamental to the water cycle. They simultaneously cool the Earth through reflectance and warm the atmosphere by absorbing and re-emitting thermal radiation from the surface and lower atmosphere. Therefore both short-wave and long-wave parts of the radiation budget are sensitive not only to the presence but also the vertical distribution of clouds (Matrosov, 1997). This in turn determines the net global radiation at the top of the atmosphere and at the surface (Heymsfield and Platt, 1984). The size distribution and number concentration of ice and liquid particles in the atmosphere is of great importance, not only for precipitation but also radiative processes (Ryan, 1996). Ice water content (IWC) in climate models varies over an order of magnitude (Stephens et al., ). Since it was found that particle distributions play a major role in determining the model climate (e.g. Stephens et al., 199; Gregory and Morris, 1996), water content is now a prognostic variable in most numerical weather prediction (NWP) models, and is fundamental to predicting cloud evolution and other properties of clouds, especially for forecasting precipitation. Traditionally particle size and mass distributions (PSD) have been derived from aircraft 6

72 CHAPTER 4: Evaluating Unified Model ice water content 63 in situ measurements (e.g. Brown and Francis, 1995; McFarquhar and Heymsfield, 1996; Mitchell, 1996; Matrosov, 1997; Heymsfield et al., ). Cloud radar has also been used to infer ice crystal sizes and IWC from radar reflectivity (Hogan et al., ; Brown et al., 1995). This has led to the planning of satellite missions, placing active instruments such as cloud radar in space (e.g. CloudSat: Stephens et al., ), which aim to map the global distribution of clouds and most importantly, provide profiles of cloud properties such as IWC. Ice particle spectra have been observed to behave systematically with temperature, with the largest change occurring between -5 and -4 C (Heymsfield and Platt, 1984). Atlas et al. (1995) refer to the large changes in the particle sizes from day to day and cloud to cloud. Matrosov (1997) observes that this variability is less for larger reflectivities. Nevertheless observed IWC can vary by four orders of magnitude for individual profiles with the bulk in the range of.1 1 g.m 3 for non-precipitating clouds. Recent observational evidence (Heymsfield et al., ) and cloud resolving model simulations (Sassen et al., ) show that the particle spectra become narrower (with smaller mean sizes) as the temperatures get colder, being broadest near cloud base. Ou and Liou (1995) also derived a relationship between ice crystal size and temperature based on the data presented by Heymsfield and Platt (1984). This temperature-dependent size is used in the ice parameterization scheme of the ECMWF model. Although empirically-derived power law relationships linking observed IWC from in-situ measurements to radar reflectivity are the accepted means of deriving IWC from radar reflectivity, Atlas et al. (1995) and Sassen et al. () warn of the limitations, mainly because the relationships do not capture the observed temperature dependence that leads to large errors in retrieved IWC (e.g. Sassen and Liao, 1996). Ryan (1996) in his review points out that the slope of the distribution is a simple function of temperature, and appears to be independent of geographical location, whereas the relationship between the intercept N and temperature is less systematic, with observed local variations. Liu and Illingworth () attempted to rectify this by introducing a suite of IWC-Z relationships applicable

73 CHAPTER 4: Evaluating Unified Model ice water content 64 for different temperature intervals, which effectively incorporates the observed decrease in ice particle size with falling temperature. Their method encountered problems when attempting to reconcile IWC at the temperature boundaries. More recently Hogan (3) has devised a method for deriving a single relationship that incorporates the temperature dependence. In the Unified Model (UM), ice water mixing ratio, as a prognostic variable, is advected around the model domain, representing the wind drift effect in an explicit manner. Transfer calculations between the different moisture variables are performed at every model level from the top down with any water content converted to precipitation falling straight through the layers below to the surface. In recent years several validation studies on the representation of clouds and related variables in models using cloud radar have been conducted (Mace et al., 1998; Hogan et al., 1; Forbes, ; Brooks, 3; Hogan and Illingworth, 3). Most of these have focused on cirrus and other non-precipitating clouds. For instance, recently Brooks (3) presented results of a one-year validation study of the UM and ECMWF model nonprecipitating cloud variables using vertically pointing cloud radar data (a cloud radar is not suited for the study of precipitating clouds because of the frequency-dependent response to particle size), showing that non-precipitating clouds in the UM are generally in good correspondence with observations at temperatures colder than -1 C. At warmer temperatures almost twice as much ice is present. Forbes () deduced similar findings from several case studies. Before attempting to use the model IWC in any synergistic relationship for improving weather radar estimates of surface rainfall rates, the soundness of the model IWC within precipitating clouds, needs to be verified. So how well does the UM represent ice within precipitating clouds? In this chapter 3 GHz high-resolution weather radar data for several frontal rain bands will be used to evaluate model IWC. Two new methods for retrieving IWC from radar reflectivity Z are discussed and compared in Section 4.. The UM internal model assumptions for density, size and temperature dependence are investigated to determine how sensitive the retrieval is to

74 CHAPTER 4: Evaluating Unified Model ice water content 65 these assumptions. Section 4.3 introduces the radar data used for validation and the model data to be validated. A brief discussion on errors and uncertainties is given in Section 4.4. The results of the validation in terms of the means and distributions are given in Section 4.5. A summary and conclusions follow in Section Estimating ice water content from observed radar reflectivity In this section two new methods for converting radar reflectivity Z to IWC will be discussed. The first, using a temperature-dependent empirically-derived power-law relationship (Hogan, 3); the second, using the UM parameterization equations of the precipitation scheme (Wilson and Ballard, 1999). With the second method we seek to explore how well the model parameterization equations and the constants used represent what is observed Empirical relationships As mentioned in Section 4.1, the use of empirically derived power laws is the conventional approach for converting radar measurements to IWC, the relationships derived from aircraft in-situ measurements. Sassen et al. () test several Z-IWC relationships to find that they suffer because the inherent temperature dependence is ignored. This was also pointed out by Atlas et al. (1995). Liu and Illingworth () attempted to address this by deriving a suite of Z-IWC relationships, each equation valid for a specified temperature interval. The problem with this approach were the discontinuities that arose at the temperature interval boundaries. Hogan (3) has developed a new three-way regression technique for deriving a single IWC-T -Z relationship that incorporates the temperature dependence. Both Liu and Illingworth () and Hogan (3) used the EUCREX aircraft data set (Brown et al., 1995) together with the Brown and Francis (1995) density

75 CHAPTER 4: Evaluating Unified Model ice water content 66 relationship: ρ[g.cm 3 ] =.7D[mm] 1.1. (4.1) The method is illustrated in Fig (a) 1 (b) Ice water content (g.m 3 ) Ice water content (g.m 3 ) Radar reflectivity factor (dbz) Radar reflectivity factor (dbz) C C C C C C C 5.. C.. 15 C C C 5.. C log (IWC[g m 3 ]) =.635 Z[dBZ].31 T[ C] (c) IWC/Z.635 [m 1 (mm 6 m 3 ).635 ] Data Linear mean Logarithmic mean Fit to linear mean Temperature T ( C) Figure 4.1: Deriving a three-way regression relationship from the EUCREX data. (a) Radar reflectivity vs IWC, colour-coded to indicate the different temperature intervals as shown in the legend; (b) regression relationships for each of the temperature intervals (solid) and redrawn relationships with a constant median slope for each interval (dashed); (c) means and a regression fit of the ratio of IWC-to-Z against temperature. The standard deviation to the linear mean (red-dashed) is also shown (after Hogan (3)). In (a) the 3 GHz radar reflectivity Z is plotted against IWC, colour-coded according to temperature into 5 C temperature intervals as shown in the legend, between -6 and C. Regression lines are calculated for each of these temperature intervals. These are the dashed lines in (b). It can be seen that the slopes of the regression lines vary. The next step is to calculate a median slope for all the different temperature intervals (.635). The

76 CHAPTER 4: Evaluating Unified Model ice water content 67 solid lines in (b) represent the relationships for each temperature interval using the median slope, i.e. their slope is the same. The variability of IWC as a function of temperature is now clear, as the magnitude for a given Z varies by an order of magnitude over a C temperature range. In (c) the ratio of the IWC to the reflectivity Z, raised to the power of the median slope, is plotted against temperature. The grey points represent the distribution of ratios at each temperature. The means (logarithmic and linear) and standard deviations (red-dashed) of the ratios are calculated and have been plotted. As a last step a regression fit is obtained from the (ratio, T ) pairs to give the slope and an expression for the temperature dependence, plotted in black. In this manner the temperature dependence has been built into the retrieval process. The EUCREX IWC-T -Z relationship, expressed in logarithmic terms, is given by Eq. 4., and will be used for validating the model IWC in Section 4.5. log 1 (IWC [g.m 3 ]) =.635 Z [dbz].31 T [ C] 1.83 (4.) 4.. Model particle size distributions The PSD used in the UM microphysics parameterization scheme is an inverse-exponential distribution function (Eq. 4.3) as reported in Wilson and Ballard (1999), from now on referred to as WB99. It is also dependent on temperature such that the mean particles are smaller at lower temperatures, in line with observations. This can be considered as an implicit way of parameterizing aggregation, but particles can also increase in size through vapour deposition as vapour density increases with temperature. In the WB99 scheme the number concentration N(D) of particles between diameters D and D+dD is given by N(D) = N e.1 T e Λ D = N(T)e ΛD, (4.3) where N = 1 6 m 4, D is the equivolume diameter in metres and T the temperature in degrees Celsius. The ice particle mass, in kilogram, is defined by: m(d) = a D b, (4.4)

77 CHAPTER 4: Evaluating Unified Model ice water content 68 where a is.69 kg m and b is. This provides an inverse relationship between the particle diameter and the density, if spherical particles are assumed, given by: ρ(d) = (6a / π) D 1 =.13 D 1 [kg.m 3 ]. (4.5) Note that this density is about twice that of Brown and Francis (1995) in Eq The fall speed (in m.s 1 ) of an ice particle given an air density of 1 kg.m 3 is parameterized as v(d) = c D.57, (4.6) where c is 5. m.473 s 1. Figure 4. shows the behaviour of the equations in the WB99 scheme. The mass (referenced with respect to the left ordinate) and fall speed (referenced with respect to the right ordinate) are plotted as a function of diameter D. Forbes () in his study also reported on the UM s moist bias and how this, combined with probably too low fall speeds and possibly too large particles at critical temperatures, results in the evaporation depth scale being approximately twice the observed depth from cloud radar. x Mass (g) 1..8 Fall speed 1..8 Fall speed (m.s 1 ).4.4 Mass Diameter (mm) Figure 4.: Behaviour of the WB99 scheme for mass and fall speed. Mass is referenced to the left y-axis, the fall speed to the right y-axis. Currently the model mass is parabolic with respect to D, whereas the fall speed has an approximately square-root dependence on D; a mm diameter particle has a fall speed of 1 m.s 1.

78 CHAPTER 4: Evaluating Unified Model ice water content Retrieving model ice water content from radar reflectivity This discussion is linked to the introduction given in Section 1.. of Chapter 1. The radar reflectivity Z is defined as Z = K.93 N(D) D6 dd [mm 6 m 3 ], (4.7) where K is the dielectric factor of an ice-air mixture. For solid ice with a density of.917 g.cm 3, K i is.176. From Debye s theory, a K for a unit density can be approximated, so that K = K i (ρ/ρ i ) =.9ρ [g.cm 3 ]. This value of K enables the use of the melted diameter of an ice particle, regardless of its density, to compute the reflectivity, provided the particles are Rayleigh scatterers (e.g. Mason, 1971). For a given radar reflectivity and temperature T, the slope of the PSD, Λ, can be determined by the expression for N(D), substituted into Eq. 4.7, expressing K as a function of density and integrating to give: Λ = ( C N(T) a Z )1 5, (4.8) where C = 118 (.9/.93) Γ(5) (ρ i π/6) (4.9) The IWC can be calculated by integrating Eq. 4.3 appropriately weighted IWC = N(T) a Λ 3 [g.m 3 ]. (4.1) Eqs. 4.8 and 4.1 can be combined to yield the following analytical expression: IWC = N(T).4 a. Z.6. (4.11) This can be expressed in log-space, as a function of temperature T and Z only: log 1 IWC =.6 Z[dBZ].1 T[ C] (4.1)

79 CHAPTER 4: Evaluating Unified Model ice water content 7 The log-form of the equation allows for the direct comparison to the EUCREX relationship in Eq. 4.. It also facilitates the implementation of other density relationships via the coefficients a and b in Eq Furthermore a generalized version of Eq and 4.1 can be derived, IWC = Q(b) N(T) 1 m a 1 m Z m, (4.13) and log 1 IWC = m log (1.1Z ) + (1 m) [log N.1T/ ln1] + (1 m) log a + log Q where m = (b + 1)/(b + 1) and the constant Q(b) is given by (4.14) [ ] 1 18 m (.9/.93) Γ(b + 1) Q(b) = 1 Γ(b + 1). (4.15) (ρ i π/6) We can now investigate the behaviour of the WB99 equations, determining the robustness, or sensitivity to changes in the assumptions, and whether (and how) the scheme may be improved in the future. Using the coefficients obtained from observations (Eq. 4.) is an effective way of testing the parameterization equations. Eqs. 4.8 and 4.1 could also be inverted and used in the opposite direction, i.e. calculating the slope from model IWC, and then calculating a pseudo reflectivity. This is done in the next chapter Sensitivity analysis Eq has four coefficients to modify: the coefficient and power in the mass relationship, a and b, the intercept of the PSD, N, and the coefficient that determines the temperature dependence,.1 (Eq. 4.11).

80 CHAPTER 4: Evaluating Unified Model ice water content 71 Direct comparison between the EUCREX Eq. 4. and the WB99 version given by Eq. 4.1 shows they are remarkably similar, but there are slight differences. The temperature (and N dependence) coefficient is slightly too small (by 1%), the constant term (also linked to N ) is too large (by 3%), hinting at the fact that N in the model is too small, and the Z-coefficient or slope is slightly less. Most notably the density relationships assumed are different. Here we assume that the EUCREX relationship is the truth and forms the basis of comparison. Purely analytically, a halving of a through the use of, say, the Brown and Francis (1995) density relationship (Eq. 4.1) implies that (a/). gives 1.15, not a significant increase. The power 1.9, is also not significantly different from b which is for the WB99 scheme. The exponents, through m, will therefore not change significantly. The largest potential impact could lie with a change in N where a doubling or a trebling of N would lead to a factor 1.3 and 1.55 increase respectively. We therefore expect the model equations to be relatively insensitive to the density assumption but possibly responsive to changes in N. Findings such as those of Forbes () would suggest that the particle sizes at critical temperatures are not in line with observations, and a change in the temperature dependence coefficient will be investigated. Testing the density assumption In the WB99 scheme a D assumption is made for mass which leads to a D 1 density dependence. Many mass-diameter laws can be found in the literature. Mitchell (1996) presents a comprehensive list of mass relationships for different ice crystal habits. Here the relationship suggested by Brown and Francis (1995) (Eq. 4.1) is used for consistency as it was also used to process the EUCREX dataset; the coefficients of the mass relationship are now a =.35 and b = 1.9. Eq becomes IWC = N(T).3958 a.83 Z.64, (4.16)

81 CHAPTER 4: Evaluating Unified Model ice water content 7 where it can be seen that the powers have changed, but only marginally. This can be expressed in log-space as log 1 IWC =.64 Z[dBZ].1 T[ C] (4.17) By forcing the density assumptions for the two methods to be the same, the Z-coefficient is now very close to the EUCREX coefficient and the constant is also closer to the EU- CREX value. The remaining differences in the relationships are now due to the magnitude of N and the temperature dependence, which are totally independent and can be explored further. Although there are other density-size relationships in the literature with very different exponents (e.g by Francis et al. (1998)), recently Gaussiat and Illingworth (3) presented evidence from dual-wavelength Doppler radar measurements that an exponent of the order of -1 is the most appropriate. Testing the temperature dependence The.1 coefficient in Eq. 4.3 appears rather mysteriously with little explanation where it comes from, both in WB99 and Cox (1988), yet it does determine the magnitude of the temperature dependence and seemed worthy of investigation. The difference in the temperature terms results in around 35% difference in retrieved IWC at -3 C, and about % difference at -6 C, although very little data are available at this temperature. The.1 is the reciprocal of 8.18, which can be traced back as the slope of the regression between temperature and the N parameter in a paper by Houze et al. (1979), not even being explicitly mentioned in the paper itself. The particle spectra used for the fit in the Houze et al. paper were measured by aircraft-mounted probes sampling various frontal rainbands. Attempting to reproduce the results, the data points were re-digitized manually (and only approximately) and these are plotted in Fig Although not an exact match, it serves a useful purpose for studying the effect of changing the coefficient. From the plot it can be seen that N decreases toward warmer temperatures corresponding

82 CHAPTER 4: Evaluating Unified Model ice water content 73 to narrow spectra at colder temperatures, the spectra broadening at warmer temperatures. 1 N * =.1345 T ln N 17 N * =.85 T R = N * =.1 T R = Temperature ( o C) Figure 4.3: Plot reproducing Fig. 4 in Houze et al. (1979) to show the change of N with temperature. The derived slope of the regression (dashed line) was 8.18, which leads to the.1 constant. A regression coefficient of -.66 is quoted. Also shown in red is the best fit to the re-digitized data, and the line obtained by deriving the temperature dependence and N (intercept) from the EUCREX coefficients (blue dashed). Figure 4.3 shows several possible regression fits, one forcing the slope to 8.18 as in the paper. The linear regression on the re-digitized data could not reproduce the 8.18 slope or the.66 regression coefficient, probably because it is only an approximation. The regression may also have been calculated in a different way, bearing in mind that there are several ways the regression could have been obtained, yielding different results. For the re-digitized data, the best fit gives a slope of.85 with an R of.56. This line was also added to the figure. Ryan (1996) in his review also shows the same relationship (HHHP) in Fig. 4.4 from Houze et al. (1979). From the figure it is clear that N varies substantially with temperature and from study to study with the Houze et al. (1979) value being at the lower end in terms of magnitude.

83 CHAPTER 4: Evaluating Unified Model ice water content 74 Figure 4.4: Fig. 9 from the Ryan (1996) paper which shows the temperature dependence of N as observed by several different authors. The HHHP line is the relationship from Houze et al. (1979). Given the coefficients of the EUCREX equation shown in Eq. 4., potentially more appropriate values for the temperature dependence constant and N can be derived, using the generalized equation Eq Evaluating the temperature dependent term in the EU- CREX equation yields a new slope of.1345 instead of the original.1. Evaluating the constant terms for the EUCREX equation yields an N of m 4. This is substantially different from the current values. This modified relationship has also been added to Fig. 4.3, illustrating the regression effect where a different approach may lead to a completely different outcome. With the.1345 temperature dependence coefficient and N equal to m 4, the EUCREX and WB99 equations are now the same except for the small difference in the Z-coefficient. The differences in the relationships and the effect of changing the density relationship are summarized in Fig The Z to IWC relationship is shown for consecutive temperature intervals, similar to Fig The solid lines in (a) and (b) represent the WB99 equation as described in Eq The dashed lines in (a) show the EUCREX

84 CHAPTER 4: Evaluating Unified Model ice water content 75 Eq. 4., showing that for the same Z, the IWC is about twice the WB99 value. The dotted lines in (b) show the impact of changing the density relationship (Eq. 4.17). There is only a small impact, as discussed, with the differences slightly greater at colder temperatures. Ice water content (g.m 3 ) C C C 3.. C.. 1 C 1.. C WB99 Eq 4.1 EUCREX Eq. 4. Ice water content (g.m 3 ) C C C 3.. C.. 1 C 1.. C WB99 Eq 4.1 WB99 with changed ρ in Eq (a) Radar reflectivity (dbz) (b) Radar reflectivity (dbz) Figure 4.5: Radar reflectivity against IWC for consecutive temperature intervals, following the same approach as illustrated in Fig The solid lines in (a) and (b) represent the behaviour of the WB99 Eq In (a) the dashed lines represent the EUCREX Eq. 4. whereas in (b) the dotted lines represent the WB99 equation with the modified density relationship as given by Eq Data description Radar scans To investigate precipitating clouds, a non-attenuating wavelength radar such as the 3 GHz (1 cm) radar situated at Chilbolton in southern England needs to be used. The data are in the form of Range-Height-Indicators (RHIs) with 3 m horizontal resolution, sampling at.1. elevation steps, between 3 elevation. An earth curvature correction was applied. Two different scanning strategies were used for data collection: around-theclock sampling at 3 azimuthal intervals, and two fixed azimuths in the south-eastern quadrant only. Eight events spanning the period from August to December were considered, providing 39 hours of concurrent model and radar data.

85 CHAPTER 4: Evaluating Unified Model ice water content Model output fields Depending on the scan strategy as described in Section 4.3.1, two different model domains were used. For around-the-clock scanning a model sub-domain encompassing the entire radar domain was used (15 by 15 model grid boxes). When the scanning was concentrated in the south-east quadrant, then a smaller domain of 8 by 8 model grid boxes was used. Model grid boxes at this latitude are between 1 15 km and there are 35 model levels in the vertical. As the main interest is precipitating clouds, the model instantaneous rain rate at the ground had to be non-zero to ensure that a model column was associated with rain. A maximum of 64 or 5 profiles can therefore be produced. Full 3-D UM mesoscale forecast fields between t6-t11h of temperature, pressure, humidity and ice water mixing ratio were used, together with -D fields of surface instantaneous rain rate to identify raining model columns. 4.4 Errors and uncertainties The radar calibration error for the 3 GHz radar at Chilbolton is around.5 db (Goddard et al., 1994) which is much better than most cloud radars, for which it is 1.5 db. For quantitative studies this is a huge advantage. The largest area of uncertainty for both methods of calculating IWC from Z and the model itself is the mass-size relationship. Hollow non-spherical ice particles may scatter and attenuate microwaves about the same as solid ice particles of the same mass (Sassen and Liao, 1996). Recent evidence presented by Gaussiat and Illingworth (3) suggests that an exponent in the vicinity of -1 is appropriate, i.e. what is used in the UM is in line with observations. The results in the preceding sections have shown that changing the density relationship may not contribute greatly to scattering, but the smaller particles are important for radiation calculations and optical extinction.

86 CHAPTER 4: Evaluating Unified Model ice water content 77 The other component to this discussion on errors is the use of a higher moment, radar reflectivity (Z D 6 ), skewed to the larger particles, to retrieve lesser moments such as the mass (D 3 ) or the optical extinction (related to area D ). The mean size of the PSDs has a large impact on these relationships. The factor of two increase due to the change in N and the slope of Z is due to the PSD deviating from exponential. Observational random errors for EUCREX are 4% (Brown and Francis, 1995). Liu and Illingworth () state that the inclusion of temperature into the retrieval can reduce the errors to within 5%. 4.5 Validating model ice water content IWC was calculated for each RHI, firstly using the EUCREX IWC-T -Z relationship Eq. 4. and secondly, using the WB99 Eqs or the log-form Eq The radar IWC was averaged into 1 km range bins to correspond to the horizontal model resolution. In height, averages were calculated to correspond to the vertical model level spacing, which is roughly 3 m. At low levels model levels are closer together. For comparison mean hourly distributions or probability density functions (PDF) and mean profiles were compiled. Figure 4.6 shows the mean and fractional standard deviation (standard deviation divided by the mean) profiles of radar-derived and model IWC, as a function of temperature. In (a) the correspondence between the model and radar profiles between -3 and -1 C is remarkable. IWC in precipitating clouds is larger than values quoted from studies of nonprecipitating clouds, with values greater than.1 g.m 3 for temperatures warmer than - C. This is in line with findings reported by Brooks (3) and Forbes () for nonprecipitating clouds. At temperatures colder than -5 C, the model has more IWC, in the mean. This may be mostly because the radar sensitivity is -17 dbz at 1 km, decreasing

87 CHAPTER 4: Evaluating Unified Model ice water content 78 to -7 dbz at 3 km, which implies that the retrieval would under-estimate IWC less than. g.m 3 at -5 C. As a result radar-derived IWC at temperatures colder than -5 C is not likely to be an accurate representation. On the other hand, using the WB99 equations to convert Z to IWC leads to a significant under-estimation at all temperatures, by as much as a factor of two, as was found from the equations comparison shown in Fig This is in line with findings of the sensitivity analysis results given in Section Figure 4.6: Mean and fractional standard deviation profiles of hourly IWC a function of temperature. Observed radar reflectivity values were converted to IWC using the temperature-dependent EUCREX IWC- T -Z relationship Eq. 4. and the WB99 equations Eqs The IWC-equivalent radar sensitivity at 1 km (17 dbz) is plotted as a dashed line in (a). The fractional standard deviation in (b) shows that the model IWC has the smaller spread, increasing slightly with colder temperatures. As the model is more diffusive than reality, one would expect the model to have a lower spread. The spread calculated for the radarderived IWC is much larger, but similar for both retrieval equations. Radar sensitivity at temperatures around -5 C results in the sudden large increase in spread. It is also useful to consider the hour-to-hour variability in the hourly model and radar IWC means. To investigate this the root-mean-squared difference between the hourly mean radar-derived and the model IWC was calculated and is plotted in Fig.4.7. It can be seen that the hourly spread is largest near the melting level and up to -1 C, decreas-

88 CHAPTER 4: Evaluating Unified Model ice water content 79 ing steadily at colder temperatures. This is in keeping with IWC values being largest at warmer temperatures, and as this study also evaluates the IWC in a spatial sense, the horizontal variability in IWC fields (McFarquhar and Heymsfield, 1996). 6 Hour to hour root mean square difference (rmsd) 5 Temperature ( C) Radar(Eucrex) Model Radar(WB99) Model rmsd in IWC (g.m 3 ) Figure 4.7: The hour-to-hour root-mean-squared difference (rmsd) between the radar-derived IWC and the model values. Figure 4.8 shows the PDFs, stratified by temperature, for the same profiles shown in Fig The model appears to have too few occurrences of IWC less than.5.8 g.m 3 at temperatures warmer than -3 C, and also too few occurrences of large IWC, at all temperatures. We speculate that this may be because the overall spread of the model IWC values is low. The radar sensitivity again accounts for the reversal in order of PDFs at low IWC, especially noticeable at temperatures less than -45 C. These results are consistent and complementary to those obtained by Brooks (3) and Forbes () for non-precipitating clouds as described in Section 4.1. This study explores the higher IWC in the tail of the distribution which could not be resolved using cloud radar. 4.6 Summary and conclusions Thirty-nine hours of high-resolution radar data and hourly model time series were used in the study. Two methods for converting radar reflectivity Z to IWC were tested and

89 CHAPTER 4: Evaluating Unified Model ice water content 8 1 IWC distribution for 15 < T < C 1 IWC distribution for 3 < T < 15 C 1 1 Frequency 1 4 Frequency IWC distribution for 45 < T < 3 C 1 IWC distribution for 6 < T < 45 C Model Radar Eucrex 1 1 Frequency 1 4 Frequency Ice water content (g.m 3 ) Figure 4.8: PDFs of IWC as a function of temperature, plotted on a log-log scale, for the mean profiles shown in Fig compared, one the accepted approach using a temperature-dependent empirical relationship linking IWC to Z; the other making use of the equations in the UM parameterization scheme. Considering the two methods equations analytically, sensitivity tests showed that although the effect of changing the mass relationship appears small, N in the model PSD appears to be about half of what it ought to be. The combined effect of changing all four modifiable coefficients to be in line with observations brings the WB99 and EUCREX equations into close agreement, with N contributing the largest change.

90 CHAPTER 4: Evaluating Unified Model ice water content 81 It was found that the mean model IWC for precipitating clouds is comparable to observations with standard deviations of the same order of magnitude as the mean values. The model IWC compared remarkably well to the EUCREX values, although the PDFs differ. This is consistent with findings by others such as Brooks (3) and Forbes () which studied non-precipitating clouds. As both these studies used the same EUCREX data and density assumptions, the results presented in this Chapter can be considered as an extension to previous findings, now covering both precipitating and non-precipitating clouds. Using the WB99 equations shows that radar IWC is under-estimated at all temperatures, when compared to the model. Results from the analytical inspection of the equation suggest that changes to N and the temperature assumption would produce improvements. We conclude that the representation of IWC within precipitating clouds in the UM is within the spread of retrieved IWC from radar observations. This suggests that if a weather radar were to scan to higher elevations, the measurements of Z in the ice could be converted to IWC and assimilated into the model, improving the initial distribution of IWC. Scan strategy will be examined further in Chapter 6. The good correspondence also suggests that synergistic relationships using model IWC, such as will be explored in the next Chapter, are a possibility.

91 CHAPTER FIVE Predicting the vertical profile of reflectivity in the ice 5.1 Background The most frequent source of error for radar estimates of rainfall is associated with the large observed variability of vertical profiles of reflectivity (VPR), especially in the ice, above the melting layer. Here similar values of reflectivity factor can be associated with a range of rain rates at the ground. This was also the theme of Chapter 3. During widespread stratiform rain, weather radars sample three distinct regions, in the rain itself (most ideal), in the bright band (leading to an over-estimation in the rain rate if not corrected for), and above the bright band in the ice, the region of precipitation overshoot. Collier (1986) and Joss and Waldvogel (199) pointed out that precipitation overshoot is of particular concern at middle and high latitudes during the winter months when the freezing level is near the ground and a radar samples in the ice, virtually at all ranges. In the UK, the vast majority of rainfall comes from melting ice particles. In Chapter 3 the impact of wind drift on falling ice was investigated, the results suggesting that at least some of the observed variability in the VPRs in the ice is due to wind drift effects, and can be corrected for. This is important, especially in the UK context as Kitchen (1997) pointed out that the UK operational radar network spacing determines 8

92 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 83 that the lowest elevation angle is centred higher than 1 km above mean sea level (AMSL) for most of the land area covered, and 5% of the area has the beam centred above 3 km, making the issue of sampling in the ice a critical one to resolve. The VPR correction scheme used in the UK (Kitchen et al., 1994) involves using a standard VPR template together with a bright-band height that is derived from the temperature structure predicted by the operational mesoscale version of the Unified Model (UM). This was described in detail in Chapter. With the current scheme, the echo top is estimated from infrared satellite imagery, up to a maximum of 4 km depth above the freezing level. Could the model three-dimensional distribution of ice water content (IWC) give a better indication of how shallow or deep an echo will be? Could it provide a decision mechanism for tuning the depth of the template used for VPR correction? Do the derived profiles encompass sufficient variation to make such a decision mechanism feasible? The hypothesis to test is that while the actual model rain rate might be wrong on a particular occasion, the physics that makes the VPR steeper or shallower on that occasion (such as the humidity profile or aggregation) may be present in the model, and it may be possible to exploit this for the interpretation and processing of the radar data. In the previous chapter, it was established that model IWC agrees with the mean from the observations for the temperature range of interest here, the km above the freezing level (FL), up to about -15 to -1 C. Here, model output fields from the mesoscale version of the Unified Model (UM) and high-resolution radar data, as described in Section 4.3, have been studied to investigate the feasibility of converting model IWC to reflectivity. Pseudo VPRs can then be constructed to see whether they can be used for predicting the observed behaviour, the aim being to implement a decision-making structure for determining the depth of the precipitating layer more accurately. In the following section the data will again be briefly described. In Section 5.3 the equa-

93 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 84 tion used for converting model IWC to a radar reflectivity is given. This is the inverse of the relationship given in Chapter 4. Two methods for constructing vertical profiles from the radar data are also described. Section 5.4 investigates the spin-up effects that were discovered for short forecast lead times. The results of the IWC-to-Z conversion and predictability of VPRs are discussed in Section 5.5. Concluding remarks follow in Section Data The same eight events introduced in Chapter 4 are used, providing a total of 39 hours for comparison. This was an exceptionally wet period for the British Isles, with extensive flooding over many parts. It is worth mentioning again that a maximum of 64 or 5 model vertical profiles can be used to calculate hourly mean profiles of, in this case, reflectivity. The analysis was done using the range-height-indicator (RHI) data, but some plan-position-indicator (PPI) data are also available for spatial comparison. For example, Fig. 5.1(a) shows a PPI for 9: UT on 18 August from the radar, and (b) shows the t+9h forecast of the surface reflectivity for the same time. Note that the model domain covers the entire radar area, but that the radar in this instance only scanned the western half. Also it must be remembered that the radar is an instantaneous representation whereas the model field represents the hour as a whole. The overall correspondence in terms of placement is good but note that peak derived reflectivities for the model are lower when compared to the observed reflectivities given in Fig. 5.1(a), as should be expected given the resolution differences between radar and model.

94 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 85 6 (a) Distance S N (km) Distance W (km) dbz (b) Distance S N (km) Distance W E (km) dbz 1 Figure 5.1: Surface fields of reflectivity for 9: UT on 9 October as (a) a PPI from the Chilbolton radar and (b) the t+9h UM forecast instantaneous surface rain rate converted to reflectivity using the Marshall-Palmer relationship. It is shown with an average Cartesian grid with the radar location indicated by the circle in the model domain. The coastline has also been included for reference.

95 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice Method Calculating reflectivity from model IWC In the previous chapter it was established that although using the Wilson and Ballard (1999) scheme underestimated IWC, the retrieval is well-behaved and consistent. Equation 4.11 in Chapter 4 gives the means of retrieving IWC from radar reflectivity (Z), using the Wilson and Ballard (1999) scheme. The equations can also be inverted and applied in the opposite direction: converting model IWC to a pseudo reflectivity, as: ] Z[dBZ] = 1 log [ N(T) /3 a 1/3 IWC 5/3. (5.1) 5.3. Creating radar hourly mean vertical profiles In Chapter 3 it was shown that the reflectivity within fall streaks is relatively constant with height, behaving more like typical profiles for convection, suggesting that at least some of the variability of VPRs in the ice is due to wind drift. In an attempt to correct for wind-drift effects when constructing VPRs from RHI data, cumulative probability density functions (CDF) at each model level height representing an interval corresponding to the difference between successive model level heights centred on the model level heights, were compiled. This provides VPRs with a vertical spacing of around 3 m, as the model level spacing increases with increasing height. The method is based on the assumption that a given percentile of surface reflectivities is paired with the same percentile of each of the upper-level CDFs in the ice, the CDFs compiled from all the radar RHIs over an hour and the hourly model forecast domain. Ideally RHIs representing several different directions are required in an hour to ensure both the parallel and tangential directions are sampled.

96 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 87 This then is the hypothesis: We define Z sfc as the surface reflectivity with F(Z sfc ) its cumulative probability distribution function (CDF). Similarly the reflectivity in the ice at height h, Z h, has a CDF G h (Z h ). Then the reflectivity in the ice Z h is associated with a surface reflectivity Z sfc by the same value of the CDF. The approach is shown schematically in Fig. 5.. Referring to Fig. 5. the steps are then: 1 F(Z sfc ) G h (Z h ) 3 Z sfc Z h Figure 5.: Schematic of the cumulative density function (CDF) approach of constructing VPRs. The numbers correspond to the steps described in the text. 1. Extract the probability of occurrence F(Z sfc ) of a selected range of surface reflectivities, e.g. 5 dbz.. This probability of occurrence of surface reflectivities is assumed to be the same for all subsequent levels so that F(Z sfc ) = G h (Z h ). (5.) 3. In this manner the corresponding percentile of reflectivities Z h associated with an interval of surface reflectivity values Z sfc can be retrieved via Z h = G 1 h [F(Z sfc)]. (5.3)

97 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 88 A mean value for the corresponding interval can be calculated for each height h, and a profile constructed. Mean profiles were constructed for four 5-dB intensity near ground reflectivity categories, spanning the range between 4 dbz. This new method of extracting profiles which attempts to compensate for wind-drift effects was compared with the conventional method of simply extracting vertically aligned profiles, binned and averaged according to the same four near-ground reflectivity intervals between 4 dbz. Standard deviations were calculated at each level with the CDF standard deviation effectively constrained by the range of Z h at every height. In this manner, a series of hourly profiles for both radar and model were compiled for analysis. 5.4 Model spin-up effects At the moment, IWC is not adjusted at initialization in the UM, so it will take the value that it has from the previous model run as a background field. The assimilation will add in water vapour and temperature increments over a number of time steps, and these will adjust IWC using the microphysics scheme throughout the period of the assimilation, but the IWC itself is not nudged towards any particular value. The effect of forecast lead time was examined by grouping forecasts into 6-hourly windows. For each 6-hourly mean, the window was shifted, by replacing the oldest with the newest forecast, t-t5h, t1-t6h, t-t7h,..., t6-t11h. All the IWC profiles within the mesoscale domain corresponding to the maximum Chilbolton radar coverage (9 km radius) associated with model precipitation at the ground, were included. Figure 5.3 shows the change in IWC with forecast lead time. The standard deviations are of the same order of magnitude as the mean values themselves. There is an increase in the mean IWC with forecast lead time (factor of to 3 over 6 hours) at temperatures warmer than -4 C and an increase in the spread of IWC at

98 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 89 temperatures warmer than - C. At colder temperatures the standard deviation decreases for older forecasts t t5h t3 t8h t6 t11h Temperature ( o C) 3 5 Temperature ( o C) (a) Mean IWC (g.m 3 ) 5 (b) std. dev. IWC (g.m 3 ) Figure 5.3: The evolution of the mean and standard deviation IWC profiles for three six-hourly forecast windows, t-t5h, t3-t8h and t6-t11h. The t6-t11h results shown here are the same as in Fig. 4.6 in Chapter 4. However, the impact of spin-up is more apparent in the derived pseudo reflectivity profiles for different forecast lead times. Figure 5.4 shows all the model-derived profiles binned by six different model rainfall intensities at the ground. Part (a) shows the profiles derived from forecasts in the t-t5h forecast range, and part (b) for the forecasts falling in the t6-t11h forecast range. Profiles are referenced with respect to the freezing level. All the hourly forecasts for the same day are the same colour. In particular there are large changes in the profiles for 18 August (pink) and 15 September (purple). Especially noticable is the increase in the range of reflectivities between the different forecast runs, and the stabilization of the profiles, especially for Z between 35 4 dbz. Whereas there appears to be continuity between the model surface instantaneous rain rate and the model IWC for the profiles in t6-t11h forecast range, this does not always appear to be the case for the t-t5h profiles. Overall the scatter evident in Fig. 5.4(a) is much reduced in (b). This is somewhat counter-

99 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 9 (a) 6 Model t t5 hourly mean profiles 6 (b) 6 Model t6 t11 hourly mean profiles Z [15,) 4 Z [,5) 4 Z [15,) 4 Z [,5) Height (km) Z [5,3) 4 Z [3,35) 4 Height (km) Z [5,3) 4 Z [3,35) Z [35,4) 4 Z [4,45) 4 Z [35,4) 4 Z [4,45) 4 Reflectivity (dbz) Reflectivity (dbz) Figure 5.4: Model pseudo reflectivity profiles for six different near-surface reflectivity intervals (corresponding to different rainfall rate intensities) from (a) forecasts in the t-t5h range and (b) forecasts in the t6-t11h range. All the hourly forecasts for the same day are the same colour. intuitive to the findings for IWC shown in Fig. 5.3 where the spread in IWC increases from t-t5h to t6-t11h. The reversal can be explained by the fact that the mean IWC shown in Fig. 5.3 was not separated into different intensity categories. The higher mean IWC for t6-t11h forecasts ensures that higher reflectivities can be deduced, and the larger spread in IWC for t6-t11h forecasts at temperatures warmer than - C provides a wider range of reflectivities within the first -3 km above the freezing level, increasing the frequency of occurrence of profiles for all categories. One of the key intervals (in terms of frequency of occurrence) is the 5 3 dbz category, which corresponds to a surface rain rate of 1 3 mm.h 1. Figure 5.5 shows how the standard deviation of reflectivity of the profiles, in db, for a given surface rain rate interval decreases with forecast lead time, averaged over all heights above the melting layer. This is a net decrease because the decrease in spread at colder temperatures is greater than the increase at warm temperatures.

100 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice Standard deviation (db) t t5 t3 t8 t4 t9 t6 t11 6 hr forecast window Figure 5.5: The mean (in height) standard deviation of model-derived reflectivity in db as a function of forecast lead time for surface rain rate intensities of 1 3 mm.h 1. From the plot it can be seen that the spread is halved between t-t5h to t6-t11h. The change from t3-t8h to t4-t9h, and from t4-t9h to t6-t11h suggests that the forecast hours that contributed most to the spread have been removed, implying that forecasts from t+4h are essentially free of spin-up. However, it is worth noting that all the forecasts in the t6-t11h range are from the previous model run. It would therefore appear to be better to use forecasts from the previous run for any applications involving model IWC. So to conclude, significant differences in the derived model VPRs from model runs six hours apart, seemed to suggest that spin-up effects in the cloud water content fields were appreciable. Forecasts at shorter lead times (up to t+5h) had lower IWC and therefore lower Z values on average. As Z IWC (5/3), higher IWC and greater scatter for forecasts in the t6 11h range implies higher Z and a wider range of values. Spin-up effects can be considered negligible from t+4h onwards. It is therefore fortuitous that Nimrod applications make use of the forecasts with lead times of four hours or longer, given the time it takes to generate the new forecast from initialization.

101 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice A comparison of model-derived and radar VPRs Comparison of mean profiles at the hourly time scale An example of mean profiles for one individual hour for the four surface reflectivity intervals is given in Fig. 5.6, and refers to the same hour shown in Fig Part (a) shows the mean and standard deviation of the radar profiles extracted using the new method of CDFs, whereas the radar profiles in (b) were extracted conventionally. The model profiles in (a) and (b) are the same. Standard deviations are shown as dashed lines for the radar and error bars for the model profiles. By definition, the spread of the radar profiles in (a) is much reduced, and there are differences in the slope of the radar profiles in (a) and (b). Note the good correspondence for the t6-t11h forecasts for all categories. In particular the CDF and model profiles are a good match between 3 5 km, whereas the conventional VPRs appear to be better matched for the higher near-ground reflectivities greater than 5 dbz. The t-t5h profiles are also shown to indicate the effect of spin-up. Only the lowest reflectivity category has a model pseudo reflectivity profile, and clearly there is little ice near the freezing level. This is because the model had no surface instantaneous rain rates larger than 1 mm.h 1, perhaps because the model has not spun up enough precipitation. This may also be an example of where forecast timing errors worsened with shorter forecast lead times.

102 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 93 (a) (b) Z Z Height (km) 1 Z [,5) Z [5,3) 4 8 Height (km) 1 Z [,5) Z [5,3) Z [3,35) 1 Z [35,4) 4 4 dbz Radar * UM t t5 x UM t6 t11 1 Z [3,35) 1 Z [35,4) 4 4 dbz Radar * UM t t5 x UM t6 t11 Figure 5.6: Example of an individual hour s mean profiles of reflectivity for the radar and the model t+9h (red) and t+3h (blue) forecasts at 9: UT on 18 August, also showing standard deviations as dashed lines for the radar and error bars for the model: (a) shows radar profiles constructed using CDFs and (b) shows radar profiles extracted conventionally. The model profiles in (a) and (b) are the same Comparison of global mean profiles To calculate the so-called global mean profiles, two measures of quality control were imposed. For inclusion in the calculation at least 1% of the maximum possible model profiles for each hour had to be associated with a non-zero rain rate at the surface, and the calculated spread (standard deviation) of dbz at any height, had to be less than half the mean value, i.e. for a mean value of dbz, the spread had to be less than 1 db. Imposing these restrictions the initial 39 hours are reduced to 9. These remaining 9 hours were used to calculate global mean profiles, shown in Figs. 5.7 and 5.8 for both methods; (a) gives the radar profiles for each of the categories. The standard deviations with height are shown in (b), giving a measure of spread. The model mean profiles are given in Fig. 5.8(c) and the model standard deviations in Fig. 5.8(d). Profiles are referenced to the freezing level.

103 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 94 Height relative to FL (km) Z [,5) Z [5,3) Z [3,35) Z [35,4) (a) Radar Reflectivity (dbz) Height relative to FL (km) Radar (b) Standard deviation (db) Figure 5.7: Global mean (a) and standard deviation (b) profiles of reflectivity obtained from 9 hours of radar data for the four near-ground reflectivity categories. The profiles were extracted in the conventional manner. Height relative to FL (km) Z [,5) Z [5,3) Z [3,35) Z [35,4) (a) Radar Reflectivity (dbz) Height relative to FL (km) Radar (b) Standard deviation (db) Height relative to FL (km) Z [,5) Z [5,3) Z [3,35) Z [35,4) (c) Model Reflectivity (dbz) Height relative to FL (km) Model (d) Standard deviation (db) Figure 5.8: Same as Fig. 5.7 but now the radar profiles were constructed using the CDFs. Parts (c) and (d) show show the model mean and standard deviation profiles for the four intensity categories.

104 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 95 First we compare the global mean radar profiles in Figs. 5.7 and 5.8(a). The main difference between them is the separation between the four different categories with height. At km above the FL only 4 db separates the global mean profiles of the four groups of conventionally extracted profiles. For the CDF global mean profiles this separation is 1 db. The CDF mean values are also larger; for example at 1.5 km above the FL the CDF mean value for the 35-4 dbz surface category is 5 dbz, whereas the conventional profile value is dbz. The cloud top and associated cloud depth above the FL can be defined in terms of the height where the profile drops below a set threshold, e.g. dbz. For the CDF mean profiles in Fig. 5.8(a), it is clear that the cloud depth is a function of surface reflectivity, where a greater surface Z is associated with a deeper cloud. This is not the case for the conventional profiles in Fig. 5.7 where all categories have almost the same vertical extent, crossing the dbz line at 4.5 km. Importantly, the lapse rates (which define the shape) of the CDF mean profiles in Fig. 5.8(a) for each of the categories is similar, whereas the lapse rate of the conventional mean profiles in Fig. 5.7(a) changes from category to category, so the profiles converge. Next we consider the differences in the spread between the two methods in Figs. 5.7 and 5.8(b). Overall the spread is lower with a difference in spread of up to 4 db between the two methods of constructing mean profiles. For the less intense categories the spread of the CDF mean profiles is about 1 db greater at 1 km above the FL. Lastly, we consider the differences between radar and model mean and standard deviation profiles in Fig The shape of the model-derived profiles is different to the shape of the observed radar VPRs, the model-profile shape being distinctly convex. Although the model-surface Z values (not shown here) are in the same intensity categories as the radar, the model categories, though distinct, are lower and closer together. They are distinct up to 3 km above the FL. One of the key questions is whether the model can predict different profiles at different

105 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 96 times. The spread in the radar mean profiles for both methods increases with increasing intensity (Figs. 5.7(b) and 5.8(b)). The radar spread is about twice that of the model, which is around 3 db, as seen in Fig. 5.8(c). Therefore, the model must be predicting different profiles, even though the spread of the model profiles for forecasts in the t6-t11h range is quite similar regardless of the intensity category, and from hour to hour. At this point, it is worth digressing to discuss lapse rates of reflectivity in the ice and aspects linking this to the template used in the Nimrod operational VPR correction scheme (Kitchen et al., 1994). In the scheme, Z is linearly reduced to zero at cloud top (CT,) and a maximum cloud depth of 4 km above the freezing level is allowed. Table 5.1 gives a summary of the mean lapse rates in intervals corresponding to the Nimrod templates of different depths. The templates are referenced with respect to where the wet-bulb temperature is zero (WBZ), which comes from the UM mesoscale model (see Chapter ). Note that the lapse rate in the first 65 m above where the wet-bulb temperature is zero (WBZ) is the greatest for the shallowest cloud. Table 5.1: Mean lapse rates (db.km 1 ) derived for Nimrod templates with different cloud depths (CD) up to a maximum of 4 km. The WBZ is at 1.5 km and the bright band peak is another 35 m below. Height above WBZ CD < 1 km CD < km CD < 3 km CD < 4 km..65 km km km km Fig. 5.9 shows the operational template shapes associated with different cloud depths and four different surface reflectivities representing the four categories used in the analysis. The WBZ is at 1.5 km, with the brightband peak another 35 m below. It becomes apparent from the figure that although the peak of the reflectivity in the bright band changes, the lapse rate specified by the template is only a function of cloud top height and is independent of surface reflectivity.

106 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice Height (km) Reflectivity (dbz) Figure 5.9: The Kitchen et al. (1994) templates for different cloud top (CT) heights. The templates are referenced in height with respect to the WBZ. The profile is constructed from a maximum of four reference points in the ice above (WBZ), namely 65, 165 and 65 m and 365 m, yielding layer depths of 65 and 1 m. Solid lines have one reference point, dashed lines two, dot-dashed lines three, and dotted lines four reference points. For VPR correction and for typical elevation angles, the gradients of interest are in the first two kilometres above the WBZ. Gradients or lapse rates are sensitive to the intervals they are calculated over, so it would seem sensible to calculate lapse rates from the radar profiles at a higher spatial resolution, say 1 m. This analysis was performed at 1 m, but it turns out that the average trends calculated from 1 m and 3 m resolution are the same. Figure 5.1 shows both the CDF and conventionally constructed 1 m global mean profiles for the four categories, referenced to the WBZ height.

107 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice Z [,5) Z [5,3) Z [3,35) Z [35,4) 4 CDF profiles Height (km) 3 1 Conventional profiles Reflectivity (dbz) Figure 5.1: High-resolution (1 m) global mean profiles calculated for the four near-surface intensity categories. Both the CDF and conventionally constructed profiles are shown. As noted before, the two methods yield very different profiles, both in shape, extent of the bright band and intensity. The lapse rates calculated from the CDF and conventional mean profiles shown in Fig. 5.1 are listed in Tables 5. and 5.3 respectively. Table 5.: Mean lapse rates (db.km 1 ) derived from the CDF mean profiles, calculated over the same height ranges as the Nimrod templates. Height above FL Z [,5) Z [5,3) Z [3,35) Z [35,4)..65 km km km km As CDF mean profile depths appear to scale with surface reflectivity, the highest lapse rates in the first 65 m above the WBZ are also associated with the most intense surface reflectivity. This behaviour is mirrored to a degree by the conventional mean profiles with slight differences in the actual magnitude. For the m interval the conventional lapse rates are greater.

108 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 99 Table 5.3: Mean lapse rates (db.km 1 ) derived from the conventional mean profiles, calculated over the same height ranges as the Nimrod templates. Height above FL Z [,5) Z [5,3) Z [3,35) Z [35,4)..65 km km km km When comparing the Nimrod lapse rates in Table 5.1 to those listed in Table 5. and if we were to assume that the surface Z and the cloud top height are indeed linked, then the template lapse rates listed in Table 5.1 for the first 65 m above the WBZ are the other way around; the trend is reversed. This is in line with findings by Hardaker et al. (1995) based on microphysical model results simulating the melting layer and the VPR. Even if the assumption that the cloud top height and surface rain rate intensity are linked is not made (i.e. Table 5.3), then the trend in the Nimrod template lapse rates is still reversed, and above 65 m the template lapse rates are typically around half of those observed. So what conclusion can be drawn from this? The CDF profiles for the different surface reflectivity categories are similar enough that a single profile, independent of the surface reflectivity could be derived. This verifies the independence of the Nimrod template from surface reflectivity. The CDF profiles are also implying that higher reflectivities (by 8 1 db in the first kilometre above the WBZ) are needed, in the ice, for a given surface rainfall rate to occur Assessing predictive skill One of the outcomes of this study thus far is that the global mean profiles of the model and radar observations are distinct as a function of reflectivity (or rain rate) at the ground, and that model mean profiles do vary so there may be some skill in predicting the VPR.

109 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 1 The question now is whether a deviation from these global mean profiles on an hourly time scale can be used as a decision mechanism, for instance for estimating the depth of the profile. Rather than attempt to find differences in the slopes of the profiles (which can be very noisy), a trends approach was tried. Given operational scanning constraints in the UK (radar scanning only up to 4 elevation or less) the main region of interest can be defined as the -km layer immediately above the bright band. The aim here was to establish if when the radar hourly profile values, Z r, in this km layer above the bright band are larger than the global radar mean, µ r ; whether the hourly model profile values in the same - km layer, Z m, validating at that time are also larger than the global model mean µ m. Each of the 9 hours were evaluated in this way using a contingency table expressed as probabilities, a standard tool for model forecast verification (Murphy and Winkler, 1987). This is shown schematically in Fig Part (a) gives the physical behaviour in terms of the contingency table, and (b) describes the numerical interpretation, where a and d are the successes/hits, and b and c the failures/false alarms. Here the successes are interpreted as the correct identification of the VPR trend and the failures as an incorrect identification of the trend. The contingency table for the comparison of each of the intensity categories for all values within the km layer above the freezing level is given in Table 5.4. The largest values per intensity category are highlighted in bold. Note that all categories have higher correct identifications where Z r µ r and Z m µ m, but the same is not true for all categories in the opposite sense. Various indicators and scores used to evaluate skill can then be calculated, or follow naturally from the contingency table itself. For this analysis not all would be meaningful. Two that are useful are the success rate S defined as the ratio of the successes to the total and is given in Eq S = a + d N. (5.4)

110 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 11 (a) EVENT Z r < µ r Z r >= µ r Radar Model Radar Model Z m < µ m FL FL Radar Model Radar Model Z m >= µ m FL FL (b) EVENT Z r < µ r Z r >= µ r Total < Z m µ m a ("hit") b ("miss") a + b Z m >= µ m c ("miss") d ("hit") c + d Total a + c b + d a+b+c+d=n (adapted from Stephenson () ) Figure 5.11: Schematic of the physical interpretation of the entries in the contingency table used in this study in (a) and the numerical equivalent in (b). Another useful measure of skill for this study is the odds ratio or log odds ratio devised by Stephenson () and given by Eq It is independent of any biases that may be present. Positive values, especially larger than 1, show skill. Negative values suggest a random forecast. ln θ = ln a + ln d lnb ln c (5.5) A standard error ɛ for the log odds can also be calculated using Eq ɛ = ( 1 a + 1 b + 1 c + 1 )1 d (5.6)

111 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 1 Table 5.4: Contingency table validating the predictability for the km layer above the bright band. Both the counts and the probabilities, in brackets, are listed. Z r < µ r Z r µ r Total Z m < µ m Z [, 5) 46 (.16) 37 (.13) 83 (.3) Z [5, 3) 48 (.18) 6 (.3) 11 (.41) Z [3, 35) 31 (.18) 13 (.8) 44 (.6) Z [35, 4) 1 (.13) 13 (.14) 5 (.7) Z m µ m Z [, 5) 81 (.9) 111 (.4) 19 (.7) Z [5, 3) 7 (.7) 86 (.3) 158 (.59) Z [3, 35) 57 (.33) 69 (.41) 16 (.74) Z [35, 4) 6 (.8) 4 (.45) 68 (.73) Z [, 5) 17 (.46) 148 (.54) 75 (1.) Total Z [5, 3) 1 (.45) 148 (.55) 68 (1.) Z [3, 35) 88 (.5) 8 (.48) 17 (1.) Z [35, 4) 38 (.41) 55 (.59) 93 (1.) Table 5.5: Selected measures of skill for the predicted profile trends. Intervals with Category S ln θ ± ɛ Z [, 5).57.53±.6 Z [5, 3).5 -.8±.5 Z [3, 35) ±.38 Z [35, 4).58.4±.47 The abovementioned measures of skill for this data set are listed in Table 5.5. Values of S greater than.5 with a positive log-odds ratio are given in bold. Only the category Z [3, 35) has a log-odds ratio above 1, although two other categories have positive log-odds ratios. The error ɛ is greater than the skill score itself for Z [35, 4), although it still has a high success rate. The Z [5, 3) category, that corresponds to a rain rate of 1 4 mm h 1 shows no skill. So the most interesting conclusion to be drawn from Table 5.5 is that some categories have more discriminatory skill than others. At first glance this appears discouraging as a large percentage of rain rates fall in the 5 35 dbz ( mm h 1 ) range.

112 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 13 3 Z [,5) 3 Z [5,3) (Z m µ m )/σ m 1 1 (Z m µ m )/σ m r= (Z µ )/σ r r r r= (Z µ )/σ r r r 3 Z [3,35) 3 Z [35,4) (Z m µ m )/σ m 1 1 (Z m µ m )/σ m r= (Z µ )/σ r r r r= (Z µ )/σ r r r 1 3 Figure 5.1: Normalized radar-to-model plot for the four intensity categories at 1 km above the freezing level. Correlation coefficients are also shown. To investigate the issue of spread further, it is helpful to normalize all the radar and model values by subtracting their mean values and dividing by their standard deviations. A plot of radar versus model normalized values at 1 km layer above the FL is given in Fig. 5.1, and at km above the FL in Fig The correlations overall are low with two high skill categories Z [, 5) and Z [35, 4) (Table 5.5) between.6 and.8. The other categories, Z [5, 3) and Z [3, 35) have correlations between -.3 and.15. The results are consistent between 1 and km, and with the contingency table results, except the Z [3, 35) category which had the highest log-odds ratio and high success rate, but only intermediate correlations. This highlights the fact that the two results need

113 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 14 not necessarily be the same because capturing the trend, and predicting the magnitude correctly are two separate aspects. 3 Z [,5) 3 Z [5,3) (Z m µ m )/σ m 1 1 (Z m µ m )/σ m 1 1 r= (Z µ )/σ r r r 3 r= (Z µ )/σ r r r 3 3 Z [3,35) 3 Z [35,4) (Z m µ m )/σ m 1 1 (Z m µ m )/σ m 1 1 r= (Z µ )/σ r r r 3 r= (Z µ )/σ r r r 3 Figure 5.13: Same as for Fig. 5.1 but at km above the freezing level. 5.6 Conclusions The current Met Office operational vertical profile correction scheme uses one template that is scaled in depth according to cloud top obtained from infrared satellite imagery, up to a maximum depth of 4 km in the ice, at which point it has been linearly reduced to zero. In the previous sections, possible improvements to the determination of cloud depth

114 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 15 and the associated reflectivity lapse rate were investigated. VPRs were constructed from mesoscale IWC fields and tested for possible use in this context. Initially all thirty-nine hours of high-resolution radar data and hourly model time series were used in the study. Model forecasts in the t-t11h range were considered. It was found that spin-up effects are an issue for forecast lead times of up to four hours, and it is suggested that for cloud water content and related parameters such as cloud fraction (Brooks, 3), forecasts from the previous model run (i.e. t+6h and older), should be used for applications. Although individual hourly comparisons between radar and model profiles in the fourintensity categories can be quite good (such as in Fig. 5.6), the shape of the model VPRs was found to be more convex, compared to observations with pseudo reflectivities derived from the model too low in magnitude. Mean radar profiles were obtained in two ways. A new method of constructing VPRs through the use of CDFs was compared to the conventional method. This was done in an attempt to respond to the findings of Chapter 3, which showed that wind effects apparently increase the variability of VPRs. Mean global profiles for 9 hours suggest that reflectivity values are higher for CDF profiles and that the slope remains relatively constant with height. This is true for all four intensity categories. The spread of the CDF profiles is less, suggesting that this method can indeed emulate the observed differences between whether the wind-drift effect is taken into account or not. Furthermore the global CDF profiles for the different intensity categories were associated with distinct cloud depths. The lapse rates applicable operationally in the Nimrod VPR correction scheme are independent of the surface reflectivity. This independence can be substantiated as the CDF profiles for the four surface reflectivity categories are very similar in shape, and could be condensed into one shape. Given a maximum beam elevation of between.5 and 4 for UK network radars, VPR correction is only applicable within the first km above the WBZ. This study has found that for more intense stratiform rain, the lapse rate in the

115 CHAPTER 5: Predicting the vertical profile of reflectivity in the ice 16 1 km above the WBZ is greater than for lighter stratiform rain and that there appears to be a link between cloud depth above the WBZ and the reflectivity in the rain. Hardaker et al. (1995) also found that the surface rainfall rate and the bright band intensity were related. Lapse rates for the Nimrod template on the other hand are greatest for the shallowest cloud depth, a trend that is opposite to that observed. Overall it was found that the template lapse rates in the 65 m above the WBZ are approximately half those observed. There appears to be a small amount of skill in using the model forecast profiles as an indicator of what slope can be expected in the ice. Specifically, there is skill for VPRs associated with near-ground reflectivities of 5 dbz (light possibly more shallow than normal precipitating systems), and 35 4 dbz (heavier possibly deeper than normal vertical extent). In the future, implementing this method to assist with determining cloud depth might perhaps improve the representation of very light (< 1 mm.h 1 ) and heavy (> 6 mm.h 1 ) precipitation. Further tests over longer time series and future improvements to the model are needed to be done to establish long-term skill and the feasibility of such an approach operationally. At present the lack of skill is prohibitive for implementation. The results also suggest that a wind-drift correction is likely to be a more effective modification.

116 CHAPTER SIX Investigating radar vertical sampling resolution 6.1 Background If the sole purpose of collecting and processing radar data were obtaining surface estimates of precipitation, then scanning at one elevation as close to the ground as possible (without contaminating the signal with clutter) would be the solution. However, as radars also give important information regarding the vertical structure of the precipitation, scanning occurs at several elevations, to produce vertical profiles of reflectivity (VPR). The resolution in the vertical largely determines how well this structure is resolved and represented. The scan strategy and other fundamental characteristics of the radar system determine this vertical resolution. Multiple elevation data are essential for: determining the shape of the VPR, forming the basis for VPR correction schemes which correct for melting effects and ice, assisting in the discrimination between stratiform and convective precipitation processes, determining the development stage that a thunderstorm is in and related echo tops, and deriving Doppler wind fields. In the future, ice water content calculated from radar reflectivity in the ice could even be assimilated into numerical weather prediction models. This challenge of providing adequate information for downstream applications and users of radar 17

117 CHAPTER 6: Investigating radar vertical sampling resolution 18 data is one shared by all operational radar networks. The questions that are repeatedly asked are: How close to the horizon can be scanned to get reasonable data, given ground clutter suppression capabilities and blocking? How much areal coverage is needed at a given height and how high should the maximum elevation be to reduce the cone of silence (the region above the radar where no data are collected due to the scan geometry)? How many elevations are required to get satisfactory vertical resolution? This is dependent on the storm characteristics that need to be resolved and the nature of the VPR. Fundamentally all the above are a function of the underlying climatic regime, radar location relative to the terrain and also system specifications or more often limitations. Harrold et al. (1974) state that hilly terrain is the most important contributor to errors in radarrainfall estimates, even in the UK. Westrick et al. (1999) discuss the blocking problems of the NEXRAD radars along the west coast of the United States. Precipitation there tends to be shallow and stratiform. Heavy rainfall events occur mainly during the cool season. Due to severe blocking only about 5% of the land region has coverage at altitudes less than 4 km above sea level (ASL) which during critical times in the cool season can mean no coverage at all in the rain. One solution for radars sited higher than the surrounding area is to use a or negative base scan (i.e. scan down to heights at or below the radar site height). The other more costly solution is the installation of more radars. Similarly Brown et al. () also show improvements using negative base scan elevation angles and suggest the implementation of such for the designated NEXRAD mountaintop radar sites. Many radar applications are weather driven, determining the need for VPR corrections, or hail and severe weather detection (tornadoes and aviation hazards such as microbursts).

118 CHAPTER 6: Investigating radar vertical sampling resolution 19 Brown et al. () assess the scanning strategies used by the US WSR-88Ds for detection of tall convective storms at long ranges, being particularly interested in the cloud-top height. They also tested new scan sequences, searching for ways of improving current identified weaknesses and suggest how the temporal and vertical resolution of the radar can be improved. Temporal resolution can be improved by increasing the antenna rotation speed, whilst maintaining acceptable levels of accuracy for velocity and reflectivity measurements. Increased flexibility in time could also be achieved by terminating a volume scan if two successive elevations detect no significant echoes, or to maintain a basic consistency from scan to scan, not before a specific elevation has been reached. Furthermore, improved vertical resolution can be achieved by increasing the maximum elevation and calculating a scan sequence where low elevation angles are close together at long ranges, and maintaining the same height interval between successive elevations at close range, for the higher elevation angles, referred to here as optimized scanning. An interlaced scanning strategy was first proposed by Vasiloff et al. (1987). Their study found that by increasing the elevation step to twice its normal value and starting every other scan at the second step of a 5-minute sequence, a pair of.5 minute sequences are produced that could halve the wind shear warning time for WSR-88Ds (important at airports) compared to the non-interlaced strategy. The evaluation of storm characteristics was not found to be detrimentally affected. The interlaced strategy is now also implemented on the Swiss radar network and the Czech Republic (Novák and Kráčmar, ). The Canadian National Radar Network (Joe and Lapczak, ) and South African networks (Terblanche, 1997; Terblanche et al., 1999), both use more than 1 elevations scanning up to between 4 and 45 with rapid update times of the order of 5 minutes. 6. Motivation The UK radar network consists of 11 C-band radars with a 1 beamwidth. One of two standard 4-elevation scan strategies is used. Both complete a base scan at.5 but one

119 CHAPTER 6: Investigating radar vertical sampling resolution 11 scans up to.5, with some oversampling, the other to 4 ; with no oversampling. Of the 11 radars in the network, six use the scan sequence up to.5, the other 5 scan up to 4, amongst these is the Chenies radar that covers the Greater London region. On-site processing includes clutter removal, attenuation correction, conversion to rain rate, spatial averaging and conversion to Cartesian co-ordinates (Harrison et al., ). Recently all the processing that used to be performed on-site, is now also being done centrally at the Met Office Headquarters. Here radar data are also combined to produce and 5 km Cartesian composites over the UK. Nimrod is an automated precipitation nowcasting framework that makes use of radar rainfall, gauge data, satellite images and Unified Model mesoscale version (UM) output to produce very short range forecasts of up to 6 hours (Golding, 1998). Centrally, radar data are further processed within the Nimrod framework. Corrupt images are removed and fields are corrected for anomalous propagation and the vertical profile of reflectivity (Kitchen et al., 1994). Gauge adjustments are applied (Harrison et al., ). The one weakness of the VPR correction scheme discussed by Kitchen et al. (1994) is the assumption of a climatological profile (lapse rate of reflectivity) between the freezing level and the cloud top. For radar-rainfall measurement only the lowest elevation is considered and the multi-beam radar data are not utilized. An echo-top is determined from satellite IR cloud top measurements but the vertical extent of the VPR is limited to 4 km above the bright band. Kitchen (1997) introduced the use of a penalty function to minimize the differences between the observed values and a template through iteration. Application of this algorithm to operational data only produced better results than the method using just the base scan elevation, under so-called atypical conditions, where the profile in the ice differs significantly from the climatological one. Currently the Kitchen et al. (1994) scheme is used operationally except for the few pixels where the higher elevations detect reflectivities exceeding 3 dbz 1.5 km above the general level of the bright band and the profile is flagged as convective, so no correction is applied. According to Smyth and Illingworth (1998), reflectivities exceeding 3 dbz at 1.5 km above the bright band indicate the presence of graupel rather than snow.

120 CHAPTER 6: Investigating radar vertical sampling resolution 111 Nimrod produces its 6h forecasts by extrapolating current conditions and trends in such a way as to preserve the defining features such as the rainfall area. This works well for frontal precipitation but not so for convection. GANDOLF is an automated convective rainfall nowcasting and early warning system that makes use of raw multi-beam radar data, with only minimal corrections applied. Otherwise Nimrod is the primary data source. It uses a conceptual model of thunderstorm evolution in an object-oriented precipitation model (Pierce et al., ). One of its features is its rapid update time, especially useful for urban hydrology. One of the identified weaknesses is the lack of information on cloud depth and cloud top from the radar data due to the low maximum elevation used. The main aims of the present study are to: 1. Investigate the benefits, if any, of oversampling on data quality, most notably the potential error reduction of near-ground reflectivities.. Investigate the benefits, if any, of scanning to elevations greater than 4 given local UK conditions. Or conversely put, what are the elevation requirements in terms of observed echo distributions in the UK. 3. Quantify the information content that is gained by doubling the number of elevations, by comparing three proposed 8-elevation sequences with specific reference to the potential impact on the operational VPR correction scheme in determining VPR shape. Plans for upgrades to the UK radar network include doubling the number of elevations from four to eight. Better ground clutter suppression algorithms also enable the use of a lower base scan than before (Sugier et al., ). Based on the results appropriate to the UK described by Kitchen (1997), more elevations sampling at larger heights should be beneficial for the Nimrod VPR correction scheme, and also for applications such as GANDOLF. A method has been developed to address the UK radar network scan strategy issue. The method however has a wider applicability as factors such as the underlying

121 CHAPTER 6: Investigating radar vertical sampling resolution 11 climate are also considered. It provides a structured, objective and quantitative means for decision making. In Section 6.3, the high-resolution data used in this chapter are described. Also discussed is the height requirement for radar data to achieve the optimum information content derived from the high-resolution radar data. Section 6.3 also covers aspects regarding beam geometry and range effects. Section 6.4 outlines the methodology. Section 6.5 then proceeds to show the pre-analysis steps that enable scan sequence design and selection. The effect of oversampling is considered in Section 6.6. The current and various potential future UK scan sequences are compared in Section 6.7. Both Sections 6.6 and 6.7 use high-resolution range-height-indicator (RHI) data. Concluding remarks and recommendations can be found in Section High resolution radar data Description A database of 981 RHI scans sampling nine events between August and December has been used in this study. The data were collected using the 3 GHz dual-polarization Doppler weather radar located at Chilbolton (51.14 N and 1.44 W), southern England. The 5 m antenna provides a.8 beamwidth. Typically the RHI scans have.1. elevation steps between 3. Data are collected to a range of 9 km with a 3 m range resolution. Figure 6.1 shows a typical RHI from the database. It is worth noting the level of fine structure that is detectable with such high sampling capabilities. Only VPRs with reflectivities greater than 1 dbz at the lowest level of a particular scan sequence were considered, in the analysis described in Sections 6.6 and 6.7, chiefly because the main focus here is on rainfall. This 1-dBZ threshold was chosen as it corresponds to a rainfall rate of. mm.h 1 using the Marshall-Palmer relationship (Marshall

122 CHAPTER 6: Investigating radar vertical sampling resolution High resolution RHI on November at 9:13 UT Height (km) Range (km) dbz 1 Figure 6.1: Example of a high resolution RHI for November at 9:13 UT showing radar reflectivity factor. and Palmer, 1948) and all values exceeding this threshold shall be referred to here as significant reflectivities. A further requirement was for this 1 dbz to be measured in the rain, below the freezing level. To do this, freezing level heights from the mesoscale version of the Unified Model (UM) were used. In this manner only drizzle or rain-producing profiles with low-level reflectivities sampled in the rain were included for analysis Beam geometry and range effects We first consider beam broadening effects as a function of range. To illustrate this effect consider an idealized VPR template with a constant reflectivity of dbz in the rain, a bright band 7 m deep with a peak reflectivity of 8.75 dbz, and a constant reflectivity lapse rate of 3 db.km 1 above the bright band. It has values every 1 m in height and is shown in Fig. 6.. To simulate the sampling that would be achieved by the operational Met Office radars, this profile template is convolved with a Gaussian beamwidth having a twoway full-power effective beamwidth of 1, and the resulting VPRs at, 4, 6 and 8 km are shown. Pure beam broadening effects cause the 7 m bright band to be smeared out to around 88, 15, 164 and 1 m at, 4, 6 and 8 km respectively with the peak reflectivity also reduced by up to 4.8 db. From the template, an uncontaminated sample

123 CHAPTER 6: Investigating radar vertical sampling resolution 114 in the rain ( db) can be obtained just 35 m below the bright-peak, but due to the beam being smeared out this distance has increased to m below the peak to obtain the same uncontaminated sample. This implies that the radar needs to sample at least 1 km below the bright band peak in the rain to get an uncontaminated sample Ideal km 4 km 6 km 8 km Height (km) Reflectivity factor (dbz) Figure 6.: The Nimrod VPR template convolved with a 1 beam at, 4, 6 and 8 km range showing beam broadening effects. Figure 6. was compiled with a 3 db.km 1 slope above the bright band. Convolution with the beam pattern also introduces a constant positive bias to the resulting reflectivities above the bright band in the ice but the magnitude is dependent on the steepness of the lapse rate of reflectivity. This bias is shown in Fig. 6.3, as a function of range and for three lapse rates: 3, 6 and 9 db.km 1. Steeper slopes imply a larger positive bias at progressively closer ranges. This increase appears to be nearly linear with range for smaller lapse rates, but the increase becomes increasingly non-linear as the lapse rate increases. For small lapse rates the effect is negligible, with biases <.15 db, but large lapse rates will exacerbate any vertical sampling problem in the 1 km immediately above the bright band and must be considered when analyzing results. The idealized profiles in Fig. 6. are very high resolution (1 m), but resampling at selected heights corresponding to a few elevations, and reconstructing the profiles using

124 CHAPTER 6: Investigating radar vertical sampling resolution db.km 1 6 db.km 1 9 db.km 1.5 Bias (db) Range (km) Figure 6.3: Biases introduced in the ice due to beam pattern convolution as a function of range and VPR slope. these few values will introduce differences between the original and the reconstructed one. The differences will depend on where the resampling is performed in height, and also on the range. 6.4 Method outline Central to the idea of this methodology is that the underlying radar climatology of rainfall should determine the requirements. This also determines generally what the users want. This in turn leads to the definition of the concept of information content: how much does the radar data tell us about the rainfall at the ground and the vertical structure. The pre-analysis steps are as follows: i. Analyze the seasonal fluctuation of the freezing level height. (Section 6.5.1) ii. Determine the vertical echo distribution, and make an assessment of the information content. Decide on what will yield a satisfactory level of information con-

125 CHAPTER 6: Investigating radar vertical sampling resolution 116 tent.(section 6.5.) iii. Based on (i) and (ii), select the base scan, and the maximum elevation required to meet the specified information content and the number of elevation steps.(section 6.5.3) iv. Design the different scan strategies to be compared. (Sections and 6.7.1) Given the scan sequences as determined in (iv) the analysis can proceed according to the following four steps: Step 1: Convolve the high-resolution data with the operational beamwidth. Step : Resample using the sequences in (iv). Step 3: Linearly interpolate the resampled data back to the high-resolution grid. Step 4: Perform an error analysis to see how the operational radar can reproduce the main features of the high-resolution VPR. These steps are discussed in Sections 6.6 and Pre-analysis steps Freezing level analysis The seasonal fluctuation of the freezing level relevant at a given location ought to be considered to get a true reflection of the maximum height that needs to be sampled. To illustrate the issue, seasonal freezing level heights (where the wet-bulb temperature is zero) were calculated from the single-column output of the mesoscale version of the UM over Chilbolton for the year, and are represented as histograms in Fig These freezing level heights are used in the operational Nimrod VPR correction scheme (Harrison et al., ). The use of the model freezing level height in the operational VPR

126 CHAPTER 6: Investigating radar vertical sampling resolution 117 correction scheme is evaluated in Chapter (Mittermaier and Illingworth, 3). It is not clear that the freezing level height forecast from other models and other parts of the world will be as good and this result should not be generalized unless a thorough study with the model and local conditions has been made. Considering the distributions in Fig. 6.4 shows that if at least km sampling above the freezing level is to be achieved for the discrimination between brightband and non-brightband events (Smyth and Illingworth, 1998), a minimum height of 5 km for coverage ought to be considered for Chilbolton and surroundings..5 DJF Wetbulb Zero Height Mean = 1. km.5 MAM Wetbulb Zero Height Mean = 1. km.. Frequency.15.1 Frequency Height (km) 1 3 Height (km).5 JJA Wetbulb Zero Height Mean =. km.5 SON Wetbulb Zero Height Mean = 1.7 km.4. Frequency.3. Frequency Height (km) 1 3 Height (km) Figure 6.4: Seasonal distributions of freezing level heights for December-January-February (DJF), March- April-May (MAM), June-July-August (JJA) and September-October-November (SON) from the UM t+h to t+5h forecasts for. Whereas a rather short time series has been presented here for one model grid box, Collier (1976) presents a freezing level climatology during rainfall for the British Isles Significant echo height distribution The echo distribution in the vertical was analyzed using the RHI database. This was done to determine up to which height radar coverage is required to capture the most important

127 CHAPTER 6: Investigating radar vertical sampling resolution 118 features and the maximum elevation that is required to provide this coverage. Cumulative distributions of the frequency of occurrence of significant reflectivities ( 1 dbz in the rain) were calculated. These distributions, shown in Fig. 6.5, are presented in two ways, first as a distribution in height and then also as a function of elevation angle. The data are reduced to 1 km range bins and either 5 m height bins from 9 km, or.5 elevation bins from 3. At least 9% of significant reflectivities appear to be found below 4 km at all ranges up to 9 km from (a). From (b) it can be seen that to achieve this 9% level of coverage at km, an elevation of 15 is required. This requirement does decrease rapidly with range and elevations less than 5 are sufficient for ranges greater than 6 km to achieve the same 9% margin. Given the wide spectrum of data included in this data set, a suggested maximum height of 5 km would come close to including most reflectivities of relevance, for VPR related applications. Height (km) (a) 9% Cumulative frequency F(dBZ > 1) Elevation angle (Degrees) 3 (b) Range (km) Figure 6.5: Cumulative distributions of the frequency of occurrence of echoes in the RHI database exceeding 1 dbz as a function of height in (a) and as a function of elevation in (b). Contours are every.1 between and Scan sequence selection In the UK, for the most part beam blocking by the topography is not problematic, although some sites such as Hameldon Hill suffer from excessive clutter. For the most part low base scan angles are possible, especially when implemented together with an effective clutter suppression technique (Sugier et al., ). Climatologically the precipitation systems are also shallow and predominantly stratiform. Ray paths of selected elevations up to 5

128 CHAPTER 6: Investigating radar vertical sampling resolution 119 calculated using an earth curvature correction are plotted in Fig. 6.6 to a range of 15 km. If coverage up to, say, 5 km were required then for a maximum elevation of 4 this is only possible at ranges greater than 6 km. For a maximum elevation of.5 this is only achievable beyond 1 km from the radar. Yet the.5 base scan is below 1 km to 7 km, below km to 11 km, and below 3 km above ground level (AGL) up to 15 km range. Depending on the height of the freezing level, there is the possibility of sampling in the rain to considerable ranges from the radar. It could then be argued that information at 5 km is not important for precipitation estimation. It depends how valuable detailed information on the VPR in the ice above the bright is considered to be. 6 5 o 4 o.5 o o o Height (km) 3.5 o Range (km) Figure 6.6: Change in beam height with range for given elevations. Base scan So how low can base scan elevation be to be useful? Simple theoretical calculations by Smith (1998), neglecting surface properties and multiple propagation effects suggest that a base scan elevation of.3 times the beamwidth provides near-optimum sensitivity with acceptable levels of degradation in reflectivity. Critically, ground clutter suppression capabilities and beam occultation must then still be superimposed to get the best possible

129 CHAPTER 6: Investigating radar vertical sampling resolution 1 base scan elevation for a particular site. For the UK radars, the nominal beamwidth is 1. Based on the theoretical calculations by Smith (1998), this would imply a theoretical lower limit of.33 as base scan. However, half the operational beamwidth is.5 and setting base scan to.33 would result in a significant portion of the beam intersecting the ground. Even at Chilbolton, with a beamwidth of.8, elevations less than or equal to.33 suffer from ground clutter and obscuration. As base scan is operationally already at.5, the lowest possible empiricallydetermined new base scan is.4, which would be lower than what is used now but avoid power losses and clutter due to excessive ground intersections. This is still a site-specific parameter and must be empirically determined for each radar location. Maximum required elevation To assess the impact of increasing the maximum elevation angle on radar areal coverage, consider Fig Based on observational evidence Smyth and Illingworth (1998) showed that it is desirable to sample up to a height of at least km above the bright-band height to distinguish between the ice processes, and whether the VPRs are convective or stratiform, an important consideration when attempting to estimate surface rainfall rate. Aggregation gives a strong signature in the 1 km above the bright band for stratiform VPRs. The figure shows the fraction of radar area that is covered within a range of 8 km from the radar given four different maximum elevations,.5, 4, 8 and 16. Therefore, if the freezing level were at 1 km AGL, then km coverage above the bright-band height means the radar needs to sample to 3 km, so for a maximum elevation of.5 and a maximum range of 8 km, only 6% of the radar area would be sampled. With a 4 maximum elevation 71% of the radar area is sampled. For 8 the area increases to 93%, and for 16 98% of the area at 3 km is sampled. Notice that the incremental increases in coverage grow smaller as the maximum elevation increases.

130 CHAPTER 6: Investigating radar vertical sampling resolution 11 Bright band height + km (km) o 4. o 8. o 16. o Max. elev Max. range = 8 km (solid) Fraction of radar area Figure 6.7: Radar coverage dependence on maximum elevation. 6.6 Studying the effects of oversampling Sequence design and selection One way of studying the effect of oversampling, is to nest several equally-spaced scan sequences spanning the same elevation interval. Starting with a coarse sequence (effectively undersampling), each of the other sequences is nested, providing progressively finer resolution data, until a resolution near that of the Chilbolton radar of.8 is reached. For this analysis the minimum and maximum elevations of the interval were.5 and 4.5. This elevation interval was then sampled at.33,.5,.67, 1, 1.33 and degrees producing sequences of length 13, 9, 7, 5, 4 and 3. Operationally, equally-spaced elevation steps are only useful for increments smaller than or equal to the beamwidth, at which point the overlap between consecutive beams ceases to exist and gaps or data voids are created, where the radar is not sampling. This is illustrated in Fig 6.8.

131 CHAPTER 6: Investigating radar vertical sampling resolution 1 (a) (b) Figure 6.8: Schematic showing the scan sequence for (a) the three-angle sequence sampling every and (b) the thirteen-angle sequence sampling every.33. In both, the shaded areas represent the region the radar is sampling Steps 1 and : Convolution and resampling The database of RHIs described in Section 6.3 was subjected to the four-step analysis outlined in Section 6.4. The high-resolution RHIs were convolved with a 1 beamwidth Gaussian beam pattern (Step 1), and then resampled (Step ) according to the sequences outlined in Section 6.6.1, to investigate the effect of oversampling the same elevation angle interval Steps 3 and 4: Interpolation and error analysis By linearly interpolating the resampled profiles (Step 3) back onto the original highresolution heights, error statistics can be calculated (Step 4). As all sequences are sampling the same height ranges at various resolutions, it is possible to calculate the mean root-mean-squared difference (rmsd ) in height, as a function of constant elevation angle separation, and for different horizontal ranges from the radar. This is plotted in Fig The 95th percentile rmsd is also plotted as an indication of the maximum error. The graph yields some surprising results. It would appear that oversampling at.33 as