Retrieving stratocumulus drizzle parameters using Doppler radar and lidar

Transcription

1 Retrieving stratocumulus drizzle parameters using Doppler radar and lidar EWAN J. O CONNOR, ROBIN J. OGAN AND ANTONY J. ILLINGWORT Department of Meteorology, University of Reading, United Kingdom Submitted to J. Appl. Meteorol., July 3 ABSTRACT Stratocumulus is one of the most common cloud types globally with a profound effect on the Earth s radiation budget, and the drizzle process is fundamental in understanding the evolution of these boundary-layer clouds. In this paper a combination of 9-Gz Doppler radar and backscatter lidar is used to investigate the microphysical properties of drizzle falling below the base of stratocumulus clouds. The ratio of the radar to lidar backscatter power is proportional to the fourth power of mean size so potentially can provide an accurate size estimate. Information about the shape of the drop size distribution is then inferred from the Doppler spectral width. The algorithm estimates vertical profiles of drizzle parameters such as liquid water content, liquid water flux and vertical air velocity, assuming that the drizzle size spectrum may be represented by a gamma distribution. The depletion timescale of cloud liquid water through the drizzle process can be estimated when the liquid water path of the cloud is available from microwave radiometers and our observations suggest that this timescale varies from a few days in light drizzle to a few hours in strong drizzle events. We have used both radar and lidar observations from Chilbolton, and aircraft size spectra taken during the Atlantic Stratocumulus Transition Experiment, to derive the following power law relationship between liquid water flux (LWF) in g m s and radar reflectivity () in mm 6 m 3 : LWF This is valid for frequencies up to 9 Gz and therefore would allow a forthcoming spaceborne radar to measure liquid water flux around the globe to within a factor of two for values of above db.. Introduction Boundary-layer clouds are one of the most significant components of the shortwave radiation budget of the Earth (Ramanathan et al., 989; arrison et al., 99) and the accurate representation of such clouds in numerical models is crucial for understanding climate (Slingo and Slingo, 99; Jones et al., 99). Observations (Miller et al., 998; Albrecht, 989) and modelling studies (Albrecht, 993; Wood, ) have shown that drizzle is important principally because it is involved in determining the cloud lifetime and evolution. The drizzle process may also have implications for the radiative properties of such clouds (Feingold et al., 996, 997) through alteration of the cloud droplet spectra. For the purposes of this paper, we define drizzle as water droplets greater than 5 m in diameter (e.g. French et al., ) which may or may not evaporate before reaching the surface, rather than the m in the American Meteorological Society glossary (959). Previous ground-based Doppler radar techniques for measuring rain and drizzle droplets have attempted to exploit the direct relationship between terminal fall velocity and droplet size. By assuming a model for the droplet size distribution, such as lognormal or gamma, the radar reflectivity factor, mean Doppler velocity and Doppler spectral width can be used to estimate the number concentration and mean size of the drops (Atlas et al., 973; Frisch et al., 995). owever, an ambiguity arises because the measured mean Doppler velocity has a significant contri- Corresponding author address: Department of Meteorology, Earley Gate, PO Box 3, Reading RG6 6BB, United Kingdom. e.j.oconnor@reading.ac.uk. bution from the vertical velocity of the air. Wakasugi et al. (986) proposed that clear air Doppler radar provided the necessary air velocity information and Gossard (988), using a 95 Mz wind profiler, also demonstrated that it is possible to separate the clear air return from the drizzle return and thus obtain the vertical air velocity directly. Millimeter-wave cloud radars have the necessary sensitivity and narrow beamwidth to measure the Doppler spectrum of the smaller drizzle droplets of interest but are no longer sensitive to the clear air return, so a method of estimating the vertical air velocity accurately by some other means is required as the terminal velocity of the drizzle droplets is comparable to the expected updrafts and downdrafts. The airborne Wyoming Cloud Radar aboard the University of Wyoming King Air uses the aircraft inertial navigation system to attempt to correct for the vertical air velocity (Vali et al., 998; Galloway et al., 999; French et al., ) but this is of course not possible from the ground. In addition to measuring the mean velocity and spectral width, Doppler radars are able to measure the full spectrum of velocities within the radar sample volume. It is therefore possible, in principle, to separate the cloud droplet component of the spectrum (droplets less than 5 m in diameter) from the drizzle component (Gossard et al., 997; Babb et al., 999). The terminal fall velocity of these cloud droplets is typically only a few cm s, so that they can be considered as tracers of the air motion and the air velocity can be inferred. owever, due to the sixth power dependence of the radar return on droplet diameter, the echo from the cloud mode tends to be much smaller than that of the drizzle, and only a small amount of turbulence is sufficient to smear the Doppler spectrum

2 so that the narrow cloud peak is lost in the larger drizzle mode. In this paper we combine the Doppler radar measurements with those of a backscatter lidar to retrieve the crucial drizzle parameters. The lidar backscatter signal is approximately proportional to the second power of the diameter so the ratio of the radar to lidar backscatter power is a very sensitive function of mean size (Intrieri et al., 993). Once the size is known, concentration and higher moments of the distribution can be derived from the observed radar reflectivity, which depends on the assumed size distribution. owever, the technique may only be applied in the drizzle below cloud base as the lidar beam is strongly attenuated as soon as it penetrates the cloud. In drizzle there is minimal attenuation of the lidar and radar signals and cloud base is always well defined by the lidar, but cannot be detected using the radar echo which is dominated by the drizzle droplets. The inferred drizzle droplet concentration and mean size are refined further by using the Doppler spectral width to infer the shape of the droplet size distribution. We also correct the observed Doppler spectral width for turbulence by calculating the standard deviation of the measured mean velocities and assuming a 5 3 power law for the vertical velocity spectrum. We then calculate bulk parameters such as drizzle liquid water content and liquid water flux, and if total liquid water path is available from microwave radiometers, the timescale for the depletion of cloud water by drizzle may be estimated. The absolute value of the mean Doppler velocity is not used in the retrieval of the drizzle droplet size distribution but we are able to calculate the theoretical Doppler velocity that would be measured in still air for the derived size distribution. The difference between this and the actual Doppler velocity therefore yields the air vertical velocity. A useful validation for the technique is that over a few hours the mean of this inferred air velocity should be zero providing there are no topographical effects. The instrumentation used in this paper is described in section. In section 3, the theoretical basis for the technique is explained in detail. The parameters that are available from the radar and lidar are presented, as are any necessary assumptions. The expected accurracy and possible shortcomings of the technique are discussed in section. In sections 5 and 6 results are presented from two case studies undertaken at Chilbolton and a relationship between radar reflectivity and liquid water flux is proposed in section 7.. Instrumentation The radar used in the first case study was the zenithpointing 9 Gz Galileo radar located at Chilbolton in Southern England. It is of the conventional pulsed type with a pulse width of.5 s, a beamwidth of.5 and is operated with a range resolution of 6 m and a PRF of 65 z, yielding a folding velocity of 5 m s. The first three moments of the Doppler spectrum are calculated from the average of thirty 56-point FFTs (fast fourier transforms) which gives a temporal resolution of.5 s. The estimated sensitivity is 5 db at km. It has been calibrated to within.5 db by comparison with the 3 Gz radar at Chilbolton which itself has been calibrated to better than.5 db using the non-independence of its polarimetric parameters (Goddard et al., 99). The radar used in the second case study was the zenithpointing 35 Gz Rabelais radar, on loan from the University of Toulouse. It is of the conventional pulsed type with a pulse width of.33 s, a beamwidth of., a PRF of 35 z, has a folding velocity of 6 m s and was sampled every 75 m. It has been calibrated to within.5 db by comparison with the 3 Gz radar at Chilbolton in the same manner as the 9 Gz Galileo radar and the estimated sensitivity is db at km. Situated close to the radar during both case studies was a zenith-pointing Vaisala CT75K ceilometer consisting of an InGaAs diode laser operating at 95 nm with a divergence of.75 mrad and a field of view of.66 mrad (both half angle). It is a fully automated system which produces averaged profiles every 3 s with a range resolution of 3 m. Calibration of the lidar to within 5% is achieved using the technique described by O Connor et al. (). 3. Theory a. Measured parameters A Doppler radar commonly measures the first three moments of the Doppler spectrum which, in principle, contain the information required to derive the parameters of a three-parameter droplet size distribution (Frisch et al., 995). owever, although the radar reflectivity is directly related to the droplet size distribution alone, the Doppler velocity and Doppler spectral width may have significant contributions from the air motion as well. The radar reflectivity factor for spherical liquid water droplets at frequency f, is defined as f K f T K f n D D 6 f D d D () where K f T is the dielectric factor of liquid water at temperature T, K f is the dielectric factor of liquid water at C, n D d D is the number concentration of water droplets with diameters between D and D d D, and f D is the Mie/Rayleigh backscatter ratio. The ratio of dielectric factors present in () ensures that radars of different wavelengths will all measure the same for a C cloud containing Rayleigh-scattering liquid water droplets. The dielectric constant varies with temperature at 9 and 35 Gz and is calculated using the empirical formula given by Liebe et al. (989).

3 The mean Doppler velocity,, measured by a zenithpointing Doppler radar is the sum of the vertical air motion,, and the mean -weighted droplet terminal fall velocity, d: d d () n D D 6 D f D d D n D D 6 f D d D In this paper we adopt the convention that velocity is positive away from the radar. Beard (976) provided semiempirical formulae for calculating the terminal velocity of individual water droplets, D. The radar Doppler spectral width,, is the - weighted standard deviation of velocities within the pulse volume. In the absence of turbulence a distribution of droplets will have an intrinsic Doppler variance due to the range of terminal velocities given by D!" d d n D D 6 f D d D n D D 6 () f D d D Broadening of the spectrum can occur if the droplets experience additional random motion due to turbulence and for a vertically pointing radar with finite beamwidth there is a contribution from the component of the horizontal wind along the beam. If it is assumed that the sources of spectral broadening are independent of one another, the observed spectral variance,, is the sum of the variances from each source (Doviak and rnić, 993) such that (3) d # b $ t (5) where b is the contribution due to finite beamwidth and t is the contribution from air turbulence. We are interested in d so we need to estimate b and t and remove them. The value of b, assuming a circularly symmetric Gaussian pattern, is given by (Doviak and rnić, 993) b U% ln (6) where % is the one-way, half-power beamwidth of the radar antenna in radians and U is the horizontal wind. For a typical wind speed (U m s ) in the boundary layer, b 3 m s for the 9 Gz Galileo radar. Kollias et al. () estimated the turbulence in fairweather cumuli by assuming that t in (5) was the dominant contribution. We follow the method of Bouniol et al. (3), where it is assumed that turbulence is a homogeneous and isotropic process of energy dissipation. The Kolmogorov hypothesis then states that the statistical representation of the turbulent energy spectrum S k is given by S k a& ' 3 k 5' 3 (7) log (vertical velocity spectral energy) k l k s k λ log (horizontal wavenumber) FIG. : Theoretical turbulent spectrum plotted on a log-log scale where the dark shaded area is the turbulent energy affecting the radar in second and the light grey area is the turbulent energy measured over 3 seconds. where a is the universal Kolmogorov constant, & is the dissipation rate and k is the wavenumber which can be related to a length scale, L, by k () L. The turbulent contribution to the spectral width is then t ks k* S k dk (8) 3 a& ' 3 k+ ' 3 k ' 3 s (9) 3 a & ' 3 L ' 3 s L+ ' 3 () ( where k+ (, L+ is the smallest scale probed by the Doppler radar (L+ is half the radar wavelength) and k s (, L s corresponding to the scattering volume dimension which also includes large eddies travelling through the sampling volume within the dwell time ( second) for the radar. For a beamwidth of 5 and no wind, L s is about 9 m at km whereas L+ is.6 mm and the impact of L+ appears negligible. The cut-off for the turbulent kinetic energy spectrum in the viscous sub-range may be at larger scales than the smallest scale probed by the Doppler radar but, even if the cut off is at cm, the second term in () is only 5% of the first term and L+ can be ignored. The difficulty with this technique using the observed Doppler width,, for a one second dwell is that we cannot separate the d and t components in (5). We now follow Bouniol et al. (3) and consider a new parameter,.-, which is the variance of the individual mean Doppler velocities measured each second, computed over 3 seconds, and show that.- is dominated by turbulence and can be used to estimate the t component of the one second Doppler variance in (5) which can be subtracted so that d can be derived. Figure displays the theoretical turbulent energy spectrum as a function of wavenumber and the two in- 3

4 ; Ratio of σ t to σ v km km km 3 km 3 5 orizontal wind speed, U (m s ) FIG. : Theoretical ratio of / t to / as a function of horizontal wind speed for a beamwidth of 53 at various altitudes. tegrals that relate to - and t, where we assume the turbulent contribution dominates.- and is given by - kl ks 3 a S k dk () & ( ' 3 L l ' 3 L s ' 3 () where k l (, L l and relates to the large eddies travelling through the sampling volume during the averaging time. If we take the ratio of () to () we have t.- The length scale is given by, L s ' 3 L l ' 3 L s ' 3 L Ut z sin % (3) () where t is the observation time and z is the height in m. For an averaging time of 3 seconds the second term in () can often be ignored and L l Ut. For L s, t is second and the correction for the beamwidth is necessary for low U. The theoretical ratio of t to - is displayed in Fig. and shows the effect of the beamwidth correction at low wind speeds. It also shows that for low altitudes and horizontal winds greater than about m s the ratio is close to. so that for the Galileo radar at a height of km the contribution of turbulence to on a second timescale is estimated as t - (5) The horizontal winds from the Met Office mesoscale model are generally accurate to - m s (Panagi et al., ) so, in this study, we have used the model winds and Fig. to provide a more precise estimate of the turbulent contribution. The equations (7-5) are based on the assumption that the length scales of turbulent eddies being probed by the Doppler radar lie within the inertial subrange of the turbulence spectrum and that - is dominated by turbulence rather than any coherent fluctuations in droplet terminal velocity. These assumptions have been shown to be valid by Bouniol et al. (3) who observed that, in drizzle, the value of & derived from - is independent of the integration time. The lidar extinction coefficient, (in m ), is defined as ( n D D d D (6) where it is assumed that the lidar wavelength is small compared to the particle size and the geometric optics approximation can be applied. The relationship between and the lidar backscatter coefficient, 5 (in m sr ), is described by S5! (7) where S (in sr) is termed the lidar ratio and varies with wavelength and droplet size. Raman lidars (Ansmann et al., 99) and high spectral resolution lidars (Grund and Eloranta, 99) can measure directly but most lidars measure only the attenuated backscatter coefficient 5,6 which is related to the true backscatter coefficient, 5, by 5 6 z 57 z exp z 8 z6 dz6 (8) Generally, the attenuation in drizzle is small ( 9 5 km ) and therefore can be retrieved from (7) and (8) without experiencing instability, providing S can be estimated with sufficient accuracy. The estimation of S using Mie theory is described below. b. Drizzle parameters We now have three independent measurables,, and from which to derive the three parameters (N W, D and ) describing the droplet size distribution, n D, which we assume can be represented by a normalised gamma distribution of the form n D N W f : D D exp [3 67 ] D D (9) where N W is the concentration normalised so that the liquid water content is independent of, D is the median equivolumetric diameter, distribution and f represents the shape of the () where ; denotes the gamma function. For a value of, (9) reduces to the familiar inverse-exponential distribution.

5 ; ; Mie to Rayleigh ratio, γ µ =. µ = µ = 5 µ = Median volume diameter, D (µm) FIG. 3: Theoretical Mie-to-Rayleigh ratio, <>=, at 9 Gz (black) and 35 Gz (grey) for gamma distributions of droplet sizes with different values of? at 3 C. If we initially assume Rayleigh scattering so that f D in () and that, in the absence of attenuation, the lidar extinction coefficient can be obtained from the observed lidar backscatter, then we can take the ratio of to defined in terms of (9) to remove the dependence on N W f and obtain as a first approximation ( D 6@ : : exp [3A 67@ : ]D D exp [3A 67@ : ]D D d D () d D where the slight variation of the dielectric factor with temperature in () has been accounted for by using the temperature profile obtained from observations (radiosondes) or numerical operational forecast models. Integration over all sizes yields ( D () and the potential accuracy of the technique is illustrated by the fourth power dependence of the radar/lidar ratio on D, which results in the relative error in retrieved size being much less than the error in the input parameters and, and any small errors due to the truncation ratio of the gamma function (Ulbrich and Atlas, 998) will be similarly reduced to negligible levels. At high frequencies the Rayleigh scattering assumption can only strictly be applied when dealing with individual cloud and drizzle droplets smaller than around 3 m at 9 Gz and mm at 35 Gz. Since we are considering size distributions whose droplets are spherical (droplets are not significantly aspherical until they are a few millimetres in diameter) and have a well defined refractive index, their backscattering properties can be determined accurately using Mie scattering theory by including the factor f D from () in (). For the purposes of this paper we define 6 to describe this departure from pure Rayleigh scattering in terms of distributions of droplet sizes rather than for single droplets (i.e. Mie 6 Rayleigh ). Figure 3 shows theoretical values of 6 at 9 and 35 Gz as a function of D and. For D 9 m, 6B D to within % at C for all, but at larger sizes Mie scattering effects become significant and, for certain sizes, Mie scattering is stronger than the Rayleigh scattering assumption due to the influence of the resonance region described by van de ulst (957). The temperature profile obtained from observations or an operational forecast model is used to account for the small temperature dependence of 6. Intrinsic Doppler spectral width, σ d (ms ). µ = µ = µ = 5 µ =. Median volume diameter, D (µm) FIG. : Intrinsic Doppler spectral width, / d, at 9 Gz for gamma distributions of droplet sizes with different values of? at 3 C. Intrinsic Doppler spectral width, σ d (ms ). µ = µ = µ = 5 µ =. Median volume diameter, D (µm) FIG. 5: Intrinsic Doppler spectral width, / d, at 35 Gz for gamma distributions of droplet sizes with different values of? at 3 C. Figures and 5 display theoretical values of d as a 5

6 ; ; D G function of median volume diameter for various values of at 9 and 35 Gz. These show the smooth transition from the Stokes regime, where d C D for the terminal fall velocity of droplets 9 6 m, to a more linear regime. Mie scattering effects are again noticeable when D m. It can be seen that d varies by about a factor of two between and, allowing retrieval of from after it has been corrected for turbulence and any horizontal winds using (6). The relationship between lidar extinction and backscatter in stratocumulus clouds and drizzle can also be derived using Mie theory. The value of the lidar backscatter coefficient oscillates wildly with size for individual droplets but once a realistic spectrum of droplet sizes is present these oscillations are smoothed out (O Connor et al., ). Figure 6 displays the 95 nm extinction-to-backscatter ratio, S, as a function of D and. Our computations show that the change in visible refractive index is negligible for the range of temperatures expected. For droplet median diameters ranging from Extinction to backscatter ratio, S (sr) µ = µ = µ = 5 µ = Median volume diameter, D (µm) FIG. 6: Theoretical lidar ratio, S, at 95 nm as a function of D for gamma distributions of droplet sizes with different values of?. to 5 m the value of S D is almost constant with a value of 8 8 sr. Typical droplet diameters for stratocumulus with significant liquid water content (Miles et al., ) lie between 8 and m. It is this feature of stratocumulus clouds that can be used to calibrate the lidar (O Connor et al., ). The median diameter of the droplet size distribution for drizzle droplets falling below the cloud (D D 5 m) lie in the range where S D can no longer be assumed constant and needs to be taken into account. c. Algorithm Equation can now be written as 5 ( 7 3 S D 6E D 3 67 D (3) where S and 6 are functions of and D ( 6 also varies very slightly with temperature), and are implemented as look-up tables. A first estimate of D can be found by assuming a value of in (3). This estimate can then be refined iteratively by comparing the observed spectral width (corrected for turbulence) with that calculated using (), adjusting to agree with observations and recomputing D until convergence. Once D and are established, N W is derived from observed. Now that we have derived the three parameters, N W, D and that define n D, d can be calculated independently of the mean Doppler velocity, using (3), and the vertical air motion can be inferred. The drizzle liquid water content (LWC d and the drizzle liquid water flux (LWF d ) are defined as follows; ( LWC d F l 6 ( LWF d F l 6 n D D 3 d D () n D D 3 D d D (5) where F l is the density of liquid water. If we can estimate how much liquid water is in the cloud and the rate at which drizzle is leaving the cloud, then the timescale for cloud liquid water depletion by drizzle is given by LWP LWF d (6) where LWP is the total liquid water path (i.e. cloud plus drizzle) obtained from coincident radiometers and LWF d is the liquid water flux immediately below cloud base.. Error analysis In this section we estimate the error in the retrieval of D, drizzle liquid water content, drizzle liquid water flux and vertical air velocity. We first assume that the shape of the droplet size distribution (i.e. the value of in Eq. ) is known and the droplets are Rayleigh scattering with respect to the radar. If we integrate the appropriately weighted gamma function over the drop size distribution then we have C N W D 7 (7) 5 C N W D 3 (8) LWC d C N W D (9) LWF d C N W D 5 (3) d C D (3) where it has been assumed that for LWF d, the terminal velocity distribution D in (5) is adequately represented by C D. The weak functional dependence on is addressed later. 6

7 I The random error in can be expressed, in linear space, as (3) M I where M I is the number of equivalent independent samples, given by Doviak and rnić (993): M I G d( J (33) where is the spectral width, G d the dwell time and J the radar wavelength. In this paper the radar data are averaged over 3 seconds to match the temporal resolution of the lidar data. With a typical spectral width of 5 m s, the random error in is about db, or.5%, at 9 Gz and close to db, or %, at 35 Gz. A larger systematic error may be present due to the difficulty of accurately calibrating a radar of this wavelength. We estimate the accuracy of the calibration to be around.5 db (ogan et al., 3) or %. The lidar is a commercial instrument and the errors are difficult to determine. owever, the signal to noise ratio is good at low altitudes and the lidar has been calibrated to within 5% using the technique described by O Connor et al. () so that we estimate the error in lidar backscatter, 5, for individual rays to be about %. From (), if S is constant, D C K5) ' but for drizzle the factor S D from (3) should also be included; the slope of the curves in Fig. 6 for D D m indicates this can be approximated by S C D A 5 so that D C L5M 7 (3) The fractional error in the median volume diameter is then D D 7 (35) so that if the fractional error in is about % and the fractional error in 5 is about %, the relative error in D is about % when is known. For the drizzle liquid water content, LWC d C N W D, which can be written as LWC d C D 3 or LWC d C ' 7 5 6' 7 and the fractional error, LWC d LWC d 7 6 (36) is about %. Considering the drizzle liquid water flux, LWF d C N W D 5, which can be written as LWF d C D or LWF d C 3' 7 5 ' 7, the fractional error is given by LWF d LWF d 7 3 (37) and is about 8%. The -weighted droplet terminal velocity, d, is proportional to D according to (3) and will therefore have the same error characteristics as D with a relative error of %. If D is very low, then the contribution of drops falling in the Stoke s regime could lead to d C D, and a consequent error in d of %. The mean Doppler velocity is measured directly by the radar and the error in is better than the bin width of the Doppler spectrum produced by the FFT as part of the coherent processing algorithm. For the Galileo radar the velocity resolution is on the order of cm s. The error in the vertical air velocity is given by d (38) and as is so low, the error in is the same magnitude as the error in d. The Doppler spectral width contains the information about the shape of the droplet size distribution. Figures and 5 show that estimating the value of to within one element of the sequence,, 5,, requires that d can be obtained to within 3%. In principle, the Doppler spectral width,, can be measured to much better than 3%, but the error in deriving d depends on the relative size of the other contributing terms to plus their associated error. It was shown in section 3 that b is typically a few cm s and can be neglected. We observe that typical values of M- in drizzle are of the order m s so from (5) the estimated value of t is about m s. From Figs. and 5, the terminal velocity component of the Doppler width, d, is above m s once D D m, and so the turbulent correction is less than 5%. Consequently, we should be able to distinguish changes in from to, to 5 or 5 to quite easily for D D m and obtain an indication of the value of for D D 5 m. The effect of these changes in can be derived by an appropriately weighted integration of the normalised gamma function (9) to give the dependence in equations (7-3), and reveals that these step changes in lead to a change in D and LWF d of about 7% and minimal change in the liquid water content. ence we conclude that, for the instrument errors considered, the overall error in D and is about %, LWC d about % and LWF d about %. These errors are valid provided that, at 9 Gz, D is less than around 5 m, and at 35 Gz, D is less than around mm. 5. September Case Study We now apply the technique described in section 3 to data taken by the Galileo Doppler radar and the Vaisala lidar ceilometer at Chilbolton. Figure 7 shows 3 hours of data taken on the morning of September during typical stratocumulus conditions with appreciable drizzle falling beneath the base of the cloud. Panel (a) shows 7

8 eight (km) eight (km) eight (km) eight (km) (a) Chilbolton 9 Gz Galileo radar Radar Reflectivity Factor (b) Chilbolton 95nm CT75K Lidar Ceilometer Attenuated backscatter coefficient (c) Chilbolton 9 Gz Galileo radar Mean Doppler Velocity (d) Chilbolton 9 Gz Galileo radar Doppler Spectral Width 5:3 6: 6:3 7: 7:3 8: 8:3 Time (UTC) ms sr m db ms FIG. 7: Observed variables for September. Time-height plots of (a) radar reflectivity factor, (b) attenuated lidar backscatter, (c) radar Doppler velocity (positive away from the radar) and (d) radar Doppler spectral width. The black line in each panel indicates cloud base derived from the lidar. radar reflectivity,, and panel (b) coincident attenuated lidar backscatter 5,6. The lidar shows a prominent cloud base at all times, while the radar appears unable to discriminate between drizzle in cloud and drizzle falling beneath the cloud. Cloud base remains relatively constant at.5 km with occasional departures to km which may indicate pannus, and cloud top appears constant for long periods with a typical cloud depth of 35 m. The radar reflectivity is dependent on the sixth power of the diameter and so the larger, but far less numerous, drizzle droplets in cloud and below cloud dominate the radar return even though their liquid water content is neglible compared to that of the small but numerous cloud droplets. This also explains why, in regions where it is not drizzling (such as before 5: and after 8: UTC), cloud base is detected by the lidar but not the radar as it is not so sensitive to the small cloud droplets. Reflectivity values reach db both in cloud and below cloud while 5,6 values reach 5 N 5 sr m below cloud and jump rapidly to 5 6 D N sr m when penetrating the cloud. The drizzle evaporates completely before reaching the ground. The background lidar signal of 6 sr m is due to boundary layer aerosol. The radar Doppler velocity, displayed in panel (c), shows a large variation in the velocity of the drizzle, ranging from 5 to m s, and the pattern of velocities is characterized by narrow fall streaks, indicating the stongly inhomogeneous nature of drizzle. These streaks usually coincide with the increases seen in radar reflectivity and lidar backscatter below cloud. Within the cloud the velocities are generally of a smaller magnitude and decrease towards cloud top where they are close to m s. Cloud droplets have terminal velocities of only a few cm s and as the drizzle droplets grow a corresponding increase in terminal fall velocity is observed. The Doppler spectral width, depicted in panel (d), is also characterized by streaks which coincide with the increases in radar reflectivity and lidar backscatter below cloud. The high values seen just prior to 7: UTC coincide with the strong negative values in the Doppler velocity. The derived microphysical parameters are displayed in Fig. 8. Panel (a) shows D, the median volume diameter of the derived drizzle droplet size distribution, varying from m to 5 m, similar sizes to those found by Vali et al. (998). The value of which describes the shape of the size distribution is shown in panel (b). The derived distributions are consistently broad although 8

9 eight (km) eight (km) eight (km) eight (km) (a) Drizzle Median Diameter (b) Drizzle Shape Parameter (c) Drizzle Liquid Water Content (d) Drizzle Liquid Water Flux 5:3 6: 6:3 7: 7:3 8: 8:3 Time (UTC) g m 3 µm g m s FIG. 8: Drizzle parameters derived from the radar and lidar for September : (a) median diameter D, (b) shape parameter?, (c) liquid water content and (d) liquid water flux. eight (km) (a) U (ms ) (b) Estimated air velocity, w Distance (km) w (ms ) Velocity (ms ).5.5 (c) Correlation Distance (km) 3 5 LWF (g m s ) FIG. 9: (a) orizontal wind speed, U, taken from sondes at Larkhill at 5 (solid) and (dashed) on September. (b) Time series of vertical air velocity, O, for a selected region (7 to 78 UTC) is shown with an aspect ratio of 3: (horizontal:vertical). Velocity is positive away from the radar. Cloud top as measured by the radar is shown by the black line. (c) Time series showing correlation of vertical air velocity, O, (black) and drizzle liquid water flux, LWF d, (red) at an altitude of 7 m for the same region as in (b). 9

10 there are occasions when much narrower distributions are observed (i.e higher values of ), particularly between and towards the base of the drizzle streaks. Preferential evaporation of the smaller drizzle droplets is a possible explanation. Liquid water content values (panel c) reach g m 3 and liquid water flux values (panel d) reach g m s ( 7 mm hr ) which are consistent with Vali et al. (998) who found maximum drizzle rates of.- mm hr. The background vertical air velocity,, can be estimated using () and (3) and the derived up and downdrafts reach m s with an error of up to m s. Radiosonde ascents at Larkhill (5 km to the west of Chilbolton) were available for 5: UTC and : UTC and were indicative of a decoupled cloud layer capped by a strong inversion at about km and a boundary layer reaching km below a transition layer which remained in place throughout the day. The mean horizontal wind measured by the radiosondes (Fig. 9a) at cloud level has been used to transform the time axis into a length scale and a section of (from 7: to 7:8 UTC) is shown in Fig. 9b. Wind shear is present below cloud and manifests itself by causing the drizzle streaks to fall at a significant angle to the vertical, up to.5 km in the horizontal for a km fall in the vertical. There is a strong impression of a cellular structure which, if it extended through the whole boundary layer, had horizontal-vertical aspect ratios ranging from : to 3: but if confined to the cloud layer had horizontal-vertical aspect ratios of : to 6:. The cloud top and base remain relatively constant throughout this period. A time series of and LWF d at 7 m are depicted together in Fig. 9c to show that an increase in drizzle liquid water flux is seen in the vicinity of updrafts. The mean vertical velocity during this period is m s and considering the error in this is not significantly different from zero. Thus far topography has been neglected and around Chilbolton the ground slopes up to m over a distance of km (a gradient of %). A steady horizontal airflow of m s could give rise to a vertical motion of m s. 6. October 998 Case Study An opportunity to estimate the drizzle depletion timescale occured during the Cloud Lidar and Radar Experiment, CLARE 98 (ESA, 999), at Chilbolton in October 998 using data from the 35 Gz Rabelais radar and Vaisala CT75K ceilometer. Estimates of LWP from microwave radiometers at.3, 3.8 and 3.7 Gz were provided by the Technical University of Eindhoven, Netherlands. The 35 Gz Rabelais did not measure Doppler spectral width during this period and so a constant value of for n D was used when estimating D, LWC d and LWF d. This seems a reasonable assumption based on the values obtained on September and any error in deriving values based on this assumption is not expected to significantly alter the results, as explained in section. For instance, if 5 when it has been assumed that, then LWF d is in error by only % whereas the depletion timescale varies over orders of magnitude. With no mean Doppler velocity available, it was not possible to estimate the vertical air velocity. Figure shows two hours of data taken on the morning of October 998. Panel (a) shows radar reflectivity factor,, and cloud base derived from the lidar is superimposed. Panel (b) shows attenuated lidar backscatter and, as in the previous case, the cloud base is prominent in the lidar data but not in the radar data. Again, wind shear was present and affected the angle at which the drizzle fell although it does not appear to have been as strong within cloud. The cloud top remained constant at about.5 km while the cloud base had more variation and cloud depth ranged from m to 8 m. The drizzle completely evaporated before reaching the ground. The derived microphysical parameters are shown in Fig.. Values of D (panel a) reach 3 m in the strong drizzle streaks near 8: UTC with LWC d values reaching g m 3 (panel b) and LWF d values reaching 5 g m s (panel c). Values of the total column liquid water path, LWP, obtained from the microwave radiometers, range from - 3 g m which are typical of stratocumulus (Greenwald et al., 995) and distinct increases in cloud LWP correlate well with the strong drizzle streaks and associated increases in drizzle LWP. Comparison of the cloud LWP with the liquid water path of the drizzle in panel d indicates the relative partitioning of liquid water between cloud mode and drizzle mode; the drizzle LWP is often two orders of magnitude lower than the cloud LWP in light drizzle. This confirms that the drizzle LWP makes a negligible contribution to the total LWP measured by the radiometer which is dominated by the cloud. The value of G derived using (6) is shown in panel e and varies from several days for the weaker drizzle to two hours in the stronger drizzle events (the period after 7:35 UTC). The scatter in G matches the inherent variable nature of drizzle. 7. Relation between drizzle flux and radar reflectivity factor Observed values of radar reflectivity factor versus derived values of drizzle flux, LWF d, are plotted together with the line of best fit and its standard deviation, in Fig. for the 9 Gz case on September, and in Fig. 3 for the 35 Gz case on October 998. The fits for the two cases agree quite well and we suggest that the power law relationship derived from the September case; LWF 9 3 N 6 A 69 (39)

11 eight (km) eight (km) (a) 35 Gz Rabelais radar Radar Reflectivity Factor (b) Chilbolton 95nm CT75K Lidar Ceilometer Attenuated backscatter coefficient 6: 6:3 7: 7:3 8: Time (UTC) db sr m FIG. : Observed variables for October 998: (a) radar reflectivity factor and (b) attenuated lidar backscatter. The black line indicates cloud base derived from the lidar. LWP (gm ) eight (km) eight (km) eight (km) 5 (a) Drizzle Median Diameter (b) Drizzle Liquid Water Content (c) Drizzle Liquid Water Flux (d) Liquid water path LWP cloud LWP drizzle x µm g m 3 g m s τ (hrs) 3 (e) Depletion timescale 6: 6:3 7: 7:3 8: Time (hrs) FIG. : Drizzle parameters derived from radar, lidar and microwave radiometer for October 998: (a) median diameter D, (b) liquid water content, (c) liquid water flux, (d) liquid water path and (e) drizzle depletion timescale.

12 3 log (LWF[kg m s ]) =.6889[dB] Liquid water flux (kg m s ) Liquid water flux (kg m s ) v (m s ) Radar reflectivity factor (db) 8 3 Radar reflectivity factor (db) FIG. : Drizzle liquid water flux and radar reflectivity values derived for the 9 Gz case on September with mean (solid) and P standard deviation (dashed) fits to the data. Liquid water flux (kg m s ) log (LWF[kg m s ]) =.763[dB].85 3 Radar reflectivity factor (db) FIG. 3: Drizzle liquid water flux and radar reflectivity values derived for the 35 Gz case on October 998 with mean (solid) and P standard deviation (dashed) fits to the data. where LWF is in kg m s and has units of mm 6 m 3, would, from the scatter in Fig., allow LWF to be measured to within a factor of two from alone. This is similar to the relationship derived for the th October 998 case, where the shape of the size distribution was not known, and implies that the relationship is also valid at 35 Gz. It has been proposed that spaceborne radar will be able to retrieve liquid water content by using a -LWC relationship that also incorporates visible optical depth when available (Austin and Stephens, ; Stephens et al., ). This may be possible in drizzle-free clouds but ignores the fact that drizzle can dominate, especially in marine stratocumulus, while having a negligible impact on the liquid water content (Fox and Illingworth, 997), so a -LWC relationship should be limited to nonprecipitating liquid water clouds (Papatsoris, 99). A -LWF relationship is likewise limited to precipitating liquid water clouds, i.e. those that contain drizzle but, FIG. : Liquid water flux and radar reflectivity calculated from FSSP and DC size spectra measured by the Met Office C-3 during ASTEX. The shading of each point indicates the -weighted mean terminal velocity calculated from the spectra. Liquid water flux (kg m s ) log (LWF[kg m s ]) =.673[dB].75 3 Radar reflectivity factor (db) FIG. 5: Liquid water flux and radar reflectivity values calculated from FSSP and DC size spectra measured by the Met Office C-3 during ASTEX with thick lines indicating mean (solid) and P standard deviation (dashed) fits to the data. To remove pure cloud droplet spectra, only values with a -weighted mean terminal velocity greater than m s are plotted and considered for the regression fit. since the presence of drizzle droplets greatly enhances the reflectivity, these are the clouds that are easily detected by a spaceborne cloud radar (Fox and Illingworth, 997) whereas the reflectivity of non-precipitating liquid water clouds will usually be below the detection limit. No direct in situ validation was available for the radar studies in this paper, so, for the purposes of comparison, we have looked at aircraft observations of particle size spectra taken during the Atlantic Stratocumulus Transition Experiment (ASTEX) (Albrecht et al., 995). Figure shows drizzle flux, LWF d, versus radar reflectivity factor,, calculated from second averages of the size distributions obtained by the Forward Scattering Spectrometer Probe (FSSP) and the D cloud probe (DC) aboard the Met Office C-3 aircraft. It should be noted that the ASTEX data include events both in and below

13 cloud and the large scatter is due to the presence of both small cloud droplets and larger drizzle droplets. Any direct fit to the data will be biased by the high number of spectra containing cloud droplets only. owever, the -weighted mean terminal velocity, d, calculated from second averages of the size spectra using the formulae given by Beard (976), and indicated by the shading of each point in Fig., provides an objective means of separating the cloud and drizzle components so that a comparison can be made with the values of LWF d derived from the radar/lidar technique. Potentially, the velocity information in Fig. could be used by a Dopplerised spaceborne radar, such as that proposed for EarthCARE (ESA, ), to discriminate between drizzle and cloud. Figure 5 shows drizzle flux versus radar reflectivity factor calculated from the ASTEX data, for the drizzle component only, obtained by selecting the spectra with d D m s. The -LWF d relationship that is derived from the drizzle component of the data is relatively insensitive to the value of d chosen as the threshold. The fit derived from the ASTEX data is reasonably consistent with those in Figs. and 3 which are derived from below cloud base only. The bias of the ASTEX fit is probably due to the fact that some mixed drizzle and cloud droplet spectra have been included, and also because the aircraft probes provided a poor sample of the low concentration of the larger drizzle droplets. The 3 s averaging of the radar and lidar data corresponds to a horizontal distance of approximately 3 m, assuming a typical horizontal wind speed of m s, and 6 m in the vertical. The AS- TEX data were averaged over s, which corresponds to a horizontal distance of approximately km, and was regarded as the shortest averaging period that would provide enough drizzle sized drops to form representative drizzle droplet spectra. This may account for the larger spread seen in Fig. 5, compared to Figs. and 3, since longer averaging periods may have produced better spectra but would have encompassed regions with markedly different drizzle rates and concentrations. These plots show that a future spaceborne radar will be able to make much more accurate measurements of liquid water flux than liquid water content for values of above db, where the radar reflectivity and liquid water flux is dominated by drizzle droplets and the liquid water content is dominated by cloud droplets. For lower values of, an ambiguity may arise in deriving liquid water flux or liquid water content, because both cloud and drizzle droplets can make a significant contribution to and liquid water flux; the ambiguity could be removed if the radar had a Doppler capability as envisaged for Earth- CARE. 8. Conclusion A technique has been demonstrated that uses the inherent sensitivity of radar/lidar synergy with zenith pointing radar and lidar to provide continuous measurements of drizzle. The technique only requires temporal averaging for matching the two data streams, thus 3 second temporal timescale (and smaller) is possible. This allows detection of the cellular structure and investigation of the inhomogeneities present in drizzle. An advantage of the technique is that there is no reliance on the mean Doppler velocity to obtain the droplet size distribution, in contrast to existing radar-only techniques. It has the potential to retrieve vertical profiles of D, drizzle LWC and drizzle LWF below cloud base to within 5-% with the assumption that a gamma function fits the size distribution, and can also estimate the vertical wind and the shape parameter,, of the size distribution. The spatial scales of updrafts and downdrafts can also be derived and it was found that updrafts tended to coincide with the occurrence of the strongest drizzle streaks. This indicates that drizzle production may be enhanced by the evaporative cooling experienced below cloud which can have a feedback effect into stimulating the production of more drizzle. Vali et al. (998) also observed upward transport of drizzle drops in cloud. Observations in the first case study suggest that, except at the edges of drizzle regions, the shape parameter,, tends to be close to zero and appears to confirm the findings of Ichimura et al. (98) and Wood (), who both indicated that observations could be sufficiently well described by an exponential distribution. Therefore, the technique could be used by an un-dopplerised radar assuming a fixed value of. There also appears to be a correlation between drizzle LWP and cloud LWP in the strong drizzle regions. Previous observations have stated that there is no relationship between the two and a long timeseries of data would be required to see if this is a regular occurrence. The drizzle LWP is affected by wind shear but the timescale for depletion of liquid water is derived from values of LWF taken directly below cloud base and is unaffected. The minimum value for this timescale is about hours; more observations need to be made to link this timescale to other meteorological parameters. The presence of drizzle droplets enhances the reflectivity of liquid water clouds sufficiently so that they can be detected by a spaceborne cloud radar and, although it is not possible to retrieve the LWC of such clouds, a -LWF relationship has been shown to be robust enabling the drizzle beneath climatically important marine stratocumulus to be monitored routinely for the first time. Acknowledgements We thank the Radiocommunications Research Unit at the Rutherford Appleton Laboratory, enri Sauvageot (University of Toulouse, France), Phil Brown (Met Office) and Suzanne Jongen (Technical University of Eindhoven, Netherlands) for providing the data. The Galileo radar 3

14 was developed for the European Space Agency (ESA) by Officine Galileo, the Rutherford Appleton Laboratory and the University of Reading, under ESTEC Contract No. 568/NL/NB. This research was funded by NERC grant NER/T/S/999/5 and EU CloudNet contract EVK- CT--65. The CLARE 98 campaign was funded by ESA (grant 957/98). REFERENCES Albrecht, B. A., 989: Aerosols, cloud microphysics, and fractional cloudiness. Science, 5, 7 3. Albrecht, B. A., 993: The effects of precipitation on the thermodynamic structure of trade-wind boundary layers. J. Geophys. Res., 98, Albrecht, B. A., Bretherton, C. S., Johnson, D., Schubert, W.., and Frisch, A. S., 995: The Atlantic Stratocumulus Transition Experiment ASTEX. Bull. Amer. Meteorol. Soc., 76(6), American Meteorological Society, 959: Glossary of Meteorology. American Meteorological Society, 5 Beacon St. Boston, MA. Ansmann, A., Wandinger, U., Riebesell, M., Weitkamp, C., and Michaelis, W., 99: Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar. Appl. Opt., 3(33), Atlas, D., Srivastava, R. C., and Sekon, R. S., 973: Doppler radar characteristics of precipitation at vertical incidence. Rev. Geophys. Space Phys.,, 35. Austin, R. T. and Stephens, G. L., : Retrieval of stratus cloud microphysical parameters using millimetric radar and visible optical depth in preparation for Cloud- Sat, Part I: Algorithm formulation. J. Geophys. Res., 6, 8,33 8,. Babb, M. B., Verlinde, J., and Albrecht, B. A., 999: Retrieval of cloud microphysical quantities from 9-Gz radar Doppler power spectra. J. Atmos. Ocean. Technol., 6, Beard, K. V., 976: Terminal velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci., 33, Bouniol, D., Illingworth, A. J., and ogan, R. J., 3: Deriving turbulent kinetic energy dissipation rate within clouds using ground based 9 Ghz radar. In 3st Conference on Radar Meteorology, Seattle, USA. Amer. Meteor. Soc., Doviak, R. J. and rnić, D. S., 993: Doppler radar and weather observations. Academic Press, nd edition. ESA (European Space Agency), 999: International Workshop Proceedings, CLARE 98, Cloud Lidar And Radar Experiment, ESA WPP-7. European Space Agency, ESTEC, Nordwijk, The Netherlands. ESA (European Space Agency), : The Five Candidate Earth Explorer Core Missions - EarthCARE Earth Clouds, Aerosols and Radiation Explorer, ESA