Lessons learnt from the operational 1D+4D-Var assimilation of rain- and cloud-affected SSM/I observations at ECMWF

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1 QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY Q. J. R. Meteorol. Soc. 134: (28) Published online in Wiley InterScience ( DOI: 1.12/qj.34 Lessons learnt from the operational 1D+4D-Var assimilation of rain- and cloud-affected SSM/I observations at ECMWF Alan J. Geer*, Peter Bauer and Philippe Lopez European Centre for Medium-Range Weather Forecasts, Reading, UK ABSTRACT: Rain- and cloud-affected Special Sensor Microwave/Imager (SSM/I) observations are assimilated operationally at the European Centre for Medium-Range Weather Forecasts (ECMWF). The four-dimensional variational analysis (4D-Var) assimilates total column water vapour (TCWV) derived from one-dimensional variational retrievals (1D-Var). From the SSM/I radiances, 1D-Var retrieves surface wind and the vertical profiles of temperature, humidity, cloud and precipitation. The main shortcoming of the 1D+4D-Var technique is that, of all this information, only TCWV gets into the 4D-Var analysis. More information could be used: the rainwater path agrees well, in an instantaneous comparison, with observations from the precipitation radar on the Tropical Rainfall Measuring Mission. There are other issues, however: the simplified moist physics operators used in 1D-Var produce roughly twice the observed amount of rain, but the problem is masked by a sampling bias, which comes from applying 1D+4D-Var when the observations are cloudy or rainy, but not when the first guess is rainy or cloudy and the observations are clear. The shortcomings of 1D+4D-Var will be addressed by moving to a direct 4D-Var assimilation which includes all SSM/I observations, whether clear, cloudy or rainy, in the same stream. Copyright c 28 Royal Meteorological Society KEY WORDS precipitation; numerical weather prediction; microwave radiance; satellite Received 19 March 28; Revised 9 July 28; Accepted 11 July Introduction In terms of both modelling and observations, it is perhaps in the area of clouds and precipitation that numerical weather prediction (NWP) is least well developed. The quality of weather forecasts has been substantially improved in recent decades by making better use of satellite data, especially in the Southern Hemisphere and over the ocean where other observations are scarce (e.g. Bouttier and Kelly, 21; Uppala et al., 25). However, satellite observations are still rarely used in areas of precipitation and heavy cloud, in part because radiative transfer simulations are more difficult in these regions. Additionally, rain and cloud processes take place on much smaller scales than the typical global model grid box of 25 to 6 km in size, and cannot be modelled to the same accuracy as clear-sky atmospheric dynamics. A final difficulty is that data assimilation techniques work best with processes that are nearly linear; rain and cloud processes, such as the sudden onset of convection, can be far from this. In the hope of improving forecasts, NWP centres are trying to improve the use of satellite observations in cloudy and rainy areas (e.g. Andersson et al., 25). One approach, known as cloud clearing, is to make best use of temperature and humidity information in clearsky areas, while removing the effects of cloud. Examples include the technique of McMillin and Dean (1982), *Correspondence to: Alan J. Geer, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, UK. alan.geer@ecmwf.int which derives the clear signal in areas of scattered cloud, and that of Pavelin et al. (28), which infers information above cloud tops. Cloud clearing is important in the infrared (IR) where as few as 5% of observations can be free from the radiative influence of clouds (McNally and Watts, 23). In contrast, microwave observations are less sensitive to cloud and can be used in a greater range of situations without considering the radiative effect of cloud. This greater coverage, especially in active weather systems, helps substantially improve forecasts (e.g. English et al., 2). A second approach could be considered true rain and cloud assimilation. Observations sensitive to precipitation and cloud are assimilated directly, with the modelled cloud and precipitation fields changing during the assimilation procedure so as to bring the model closer to the observations. The European Centre for Medium-Range Weather Forecasts (ECMWF) has assimilated cloud- and precipitation-affected Special Sensor Microwave/Imager (SSM/I) radiance observations since 25. As shorthand in this paper, we will refer to this as rainy SSM/I assimilation. SSM/I observations are sensitive to surface properties, total column water vapour (TCWV), cloud ice and water, rain and frozen precipitation. Given the SSM/I radiances and a first guess (FG) from the model, a one-dimensional variational retrieval (1D-Var) determines surface winds and vertical profiles of humidity, temperature, cloud and precipitation. The TCWV is derived from the retrieved humidity profile and assimilated in the main four-dimensional variational (4D-Var) analysis (Rabier Copyright c 28 Royal Meteorological Society

2 1514 A. J. GEER ET AL. et al., 2); this approach is referred to as 1D+4D-Var. We aim to have a true rain and cloud assimilation system but, as we will see, there is still work to be done to fully achieve that. The use of rainy and cloudy SSM/I observations at ECMWF is the result of much research. Typically, a precursor to assimilation is to simulate radiances from the model and compare them to their observed equivalents. Using cloudy and rainy radiative transfer to simulate SSM/I observations in all weather conditions, Chevallier and Bauer (23) found excessive modelled rain and cloud amounts in the Tropics. Separately, simplified moist physics operators were being developed (together with their tangent-linear and adjoint versions) for use in the linearised part or inner loop of the main 4D- Var assimilation. These need to be consistent with the nonlinear operators used in the full model, but should also have a smoother, less nonlinear behaviour. As a further simplification, clouds are treated diagnostically rather than prognostically. Cloud and rain amounts can be diagnosed from the temperature and moisture profile plus some surface parameters, which makes the simplified operators easy to use in 1D-Var retrievals. Early experiments made 1D-Var retrievals of temperature and moisture from satellite-retrieved rainfall rates (e.g. Marecal and Mahfouf, 2) and directly from satellite radiances (e.g. Moreau et al., 24). Experiments were also made to assimilate the products of the 1D-Var retrievals, using the 1D+4D-Var technique (Marécal and Mahfouf, 22, 23). These focused on local case-studies (such as single hurricanes) and periods of at most 15 days, so their results will have had little statistical significance. However, they did demonstrate the potential for operational assimilation of rainrelated measurements, and established 1D+4D-Var as a robust technique for using rain observations and coping with the nonlinearity of the moist physics operators. With improved simplified moist physics operators (Tompkins and Janisková, 24; Lopez and Moreau, 25) and microwave radiative transfer in the presence of scattering (Bauer et al., 26c), operational assimilation of rain- and cloud-affected SSM/I observations started in June 25 (Bauer et al., 26a,b). Efforts to assimilate cloud and precipitation observations are of course not unique to ECMWF. The Meteorological Service of Canada are starting to experiment with 1D-Var retrievals from SSM/I (Deblonde et al., 27). More generally, Errico et al. (27) provide references to many different approaches, which typically assimilate derived products, such as precipitation rate, rather than radiances. Only a few of these experimental approaches have been made operational (e.g. Treadon et al., 22; Tsuyuki et al., 22). Recently, Kelly et al. (28) tested the impact of rainy SSM/I assimilation on operational forecasts at ECMWF. They used a set of observing system experiments (OSEs), including a baseline in which only in situ observations and a single satellite temperature sounder were assimilated, and a control in which the full set of operational observations was assimilated. When the rainy SSM/I observations were removed from the control system, the result was a small degradation in the skill of humidity forecasts, indicating that the rainy assimilation provides a small positive contribution. The global observing system contains much redundancy and it is unusual to see a big change in forecast skill when only one observation type is removed. It is only when many other observations have already been removed, such as in the baseline system, that adding or removing an observation type makes significant changes in forecast skill. Hence, when the rainy SSM/I observations were added to the baseline system, accuracy of forecasts improved by about one day s lead time in the Tropics. Importantly, it was not just relative humidity forecasts which improved, but also the wind forecasts, despite the fact that, in rainy SSM/I assimilation, only a TCWV pseudo-observation is assimilated in 4D-Var. Impacts were limited to the region 3 Nto3 S in the experiments with the full observing system, but extended from 5 Nto5 S in the baseline experiments (Figure 5a of Kelly et al., 28). These results help justify the use of rainy SSM/I assimilation. The purpose of this paper is to describe what we have learnt after two years of operational rainy SSM/I assimilation. It covers the highlights from a much longer internal technical report (Geer et al., 27), as well as some further experiments and analysis. We want to answer questions such as: Does the 1D+4D-Var technique work well enough? Does it actually improve analysed cloud and rain? How exactly does rainy SSM/I assimilation provide the forecast improvements shown by Kelly et al. (28)? Compared to many earlier studies of 1D+4D-Var, we can examine the effects globally, and can study longer periods. We show that there are a number of areas where the current technique could be improved. Most of these problems should be overcome once we move to a direct 4D-Var assimilation of rainy SSM/I observations, which is already in testing. 2. Method 2.1. NWP system The experiments in this paper are representative of the operational system at ECMWF, but have some modifications (including a slightly lower resolution) that are described in section 2.3. The closest operational version is cycle 32r2, which was used from from June to November 27. This produced routine global analyses and 1-day forecasts from an assimilation system based on an atmospheric model with a semi-lagrangian, spectral formulation. The model had 91 levels from the surface to an altitude of 8 km, and a T799 horizontal resolution, corresponding to about 25 km (see for documentation on earlier model versions; documentation on the later versions is not yet available). Global analyses of wind, temperature, surface pressure, humidity and ozone were produced twice daily using 4D-Var (Rabier et al., 2) with a 12-hour time window. The forecasts themselves Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

3 LESSONS LEARNT FROM 1D+4D-VAR RAIN ASSIMILATION 1515 were initialised from a subsequent 6-hour time window analysis that enabled an early delivery to customers (Haseler, 24). The analysis included in situ conventional data, satellite radiances from polar orbiters (mainly from the microwave sounding instruments AMSU-A, AMSU-B and MHS, and the infrared sounder AIRS), geostationary radiances, satellite-derived atmospheric motion vectors and surface winds from scatterometers. SSM/I radiances were assimilated, over oceans only, in two separate streams. An estimate of rain and cloud was made directly from the observed radiances. Observations identified as clear sky were assimilated as radiances directly in 4D-Var, and are referred to as clear in this paper; those identified as cloud- and rain-affected were assimilated using the 1D+4D-Var procedure described in the next section, and are referred to as rainy. No observation was used simultaneously in both streams D+4D-Var rain assimilation The initial operational implementation of 1D+4D-Var for SSM/I assimilation is described by Bauer et al. (26a,b). The version examined here, including some minor upgrades, is described by Geer et al. (27). The procedure starts with a 1D-Var retrieval at each model grid point where there is a rainy or cloudy SSM/I observation available. In the rainy stream, only SSM/I channels 19v, 19h and 22v are used, and only at latitudes between 6 N and 6 S. (Here, the channel number indicates the nearest frequency in GHz and the letter v indicates vertical polarisation and h horizontal polarisation.) The retrieval makes a best estimate of the state of a single column of the atmosphere at the observation point, by combining the observed SSM/I radiances with an a priori (or background) taken from the FG forecast of the 4D-Var assimilation, which includes surface parameters (such as skin temperature and surface wind speed) and the temperature and moisture profile. The mathematical basis of the 1D-Var is identical to that of the 4D-Var (e.g. Rodgers, 2), but we distinguish the two in this paper by describing the 1D-Var step as a retrieval, and the 4D-Var step as an analysis. The weighting between observations and the background profile is determined by the observation and background-error covariances. Background-error covariances for temperature and moisture are the same as those used in the 4D-Var analysis. Observation errors are considered to be uncorrelated and are set to 3 K, 6 K, and 3 K respectively for channels 19v, 19h and 22v. Bauer et al. (26a) justify these values using the Hollingsworth and Lönnberg (1986) method. The observation errors account not just for the instrumental error but also that coming from the forward models, which is thought to be the largest part. The 1D-Var control vector contains only the humidity and temperature profiles and the surface wind components. Other surface parameters are held fixed. The control vector is varied, using an iterative quasi-newtonian procedure (Gilbert and Lemaréchal, 1989), until the best estimate solution is found. At each iteration, the vertical profile of cloud and precipitation is derived from the temperature and moisture profile (plus some surface parameters) using simplified moist physics operators for convection (Lopez and Moreau, 25) and large-scale condensation (Tompkins and Janisková, 24). These are the same operators used in the linearised parts of the 4D- Var minimisation. SSM/I radiances are calculated using a fast radiative transfer code (RTTOV-SCATT, Bauer et al., 26c) which takes into account the absorption, emission and scattering effects of cloud particles, raindrops and frozen hydrometeors. The SSM/I radiances do not contain enough information to unambiguously reconstruct the full atmospheric and surface state and, unlike a typical satellite retrieval, the 1D-Var retrieval depends strongly upon the model s FG. In practice, the technique is able to produce a retrieval that matches the SSM/I observations very closely (Figure 7 of Bauer et al., 26a). In contrast to the way other observations are used, there is no interpolation of model fields to the observation point. When temperature and humidity profiles are interpolated to a location and cloud and rain is diagnosed using the simplified moist physics operators, the results may be very different to those from an interpolation of cloud and rain to that location. This discrepancy comes paticularly from the convection scheme, which is very sensitive to details of the vertical profile. Since interpolation is not done, a 1D-Var retrieval is only made when an observation is available within a radius of 7 km or 1 km from a grid point centre (for resolutions T799 or T511 respectively). This distance is substantially smaller than the 7 km by km resolution of the SSM/I channels used. Bias correction is crucial to getting good results from data assimilation. Before being assimilated, observed radiances from SSM/I are corrected to make them less biased with respect to the 1D-Var FG. Bias is modelled using a multiple linear regression between FG departures (i.e. observation minus FG) and FG TCWV, surface wind speed, and column rain amount. Approximately 5% of rainy observations are removed for quality control reasons during 1D-Var, mostly when the ratio of frozen precipitation to liquid precipitation is too high, and thus might compromise the quality of radiative transfer simulations, or when the 1D-Var minimisation failed to converge sufficiently. Geer et al. (27, Figure 4 and discussion) provide further details. The ability to apply such stringent quality controls is one of the advantages of the 1D+4D-Var technique. From the 1D-Var retrieval, a TCWV pseudoobservation is derived and then assimilated in the main 4D-Var analysis. It is assumed to be representative of the nearest model grid point and again no interpolation is done. A spatial thinning is applied, so that around 2 pseudo-observations are finally assimilated into 4D-Var in each 12-hour window. The TCWV pseudo-observations are thought to be relatively unbiased compared to the 4D-Var FG, so they are not bias corrected. However, this paper later finds that improved bias corrections are needed. Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

4 1516 A. J. GEER ET AL Experiments The conclusions of this paper are representative of all versions of the ECMWF system that have included 1D+4D-Var assimilation of rainy SSM/I radiances. To be precise, however, our experiments are based on cycle 32r1 of the ECMWF system, but with additional improvements to 1D+4D-Var rain assimilation that were not introduced operationally until cycle 32r3. Cycle 32r1 was never used operationally but cycle 32r2 was, and this was extremely similar except for some mostly technical modifications. (This is the version described in section 2.1.) To save computer resources, the horizontal resolution has been reduced to T511, rather than the full operational resolution of T799. The operational vertical resolution of 91 levels has been retained. For simplicity, only the 12-hour time window analyses are done (the early delivery 6-hour analyses and forecasts mentioned in section 2.1 are not done). The most recent versions of the operational system have included data from other similar microwave imagers (e.g. the Tropical Microwave Imager, TMI, and the Advanced Microwave Scanning Radiometer EOS, AMSR-E), but none of these are included here; the only microwave imager data used in these experiments come from SSM/I. Table I summarises the experiments. Experiment RAIN assimilates rainy SSM/I observations and is representative of the operational NWP system. Experiment NORAIN is identical except that the rainy SSM/I observations are removed. These experiments were run for the month of February 27, taking initial conditions from the operational analyses for 12 UTC on 31 January 27. Though it is common to exclude an initial period during which the experiment might be spinning up, our results are based on the entire month, as the spin-up is insignificant here. We prefer to maximise the amount of data available by keeping the whole period. Two further experiments were run for a single 4D-Var assimilation window, centred on 12 UTC on 28 February 27. They were started from the UTC analyses of the RAIN experiment. NORAIN28 turns off the assimilation of rainy SSM/I observations and NOSSMI28 turns off both rainy and clear SSM/I observations. While the two main experiments were intended to show the effect of the rainy SSM/I assimilation on mean fields, these two short experiments are used to isolate the instantaneous effect of the observations on analysed TCWV during a single 4D-Var minimisation, which can only be done if the FG is the same in each experiment. 3. Results 3.1. Quality of 1D-Var rain retrievals Except for a few limited case-studies, none of the original papers on the 1D+4D-Var technique validated 1D-Var rainfall retrievals by comparison to independent observations. We remedy that deficiency here by comparing to 2A25 rain retrievals from the precipitation radar (PR) on the Tropical Rainfall Measuring Mission (TRMM; Kummerow et al., 1998; Iguchi et al., 2). Though surface rain rates are of most interest to humans, neither PR nor SSM/I has direct sensitivity to this parameter. PR measures the vertical profile of the radar reflectivity factor (Z; e.g. Petty, 26), which can only be converted into a rain rate by making assumptions about the drop-size distribution and fall speeds of the rain. However, it is possible to avoid making any assumption about fall speeds if Z is instead converted into rainwater content, given in kg m 3. As shown by Masunaga et al. (22), who compared PR to TMI, it is thus more accurate to make comparisons between radar and passive microwave measurements in terms of water content. Masunaga et al. (22) note that PR has some sensitivity to large ice particles above the freezing level, but show that this sensitivity is small. We also tested this sensitivity in our comparisons by removing or including the part of the PR precipitation column above the freezing level, but our results were not significantly affected. Hence, for this comparison, we assume that PR sees only rain. The rain information content in the SSM/I measurements, roughly speaking, is the vertical integral of water content, i.e. the rainwater path (RWP), measured in kg m 2. In 1D-Var, rain rate (used in the moist physics) is converted to rainwater content (used in the radiative transfer) by making assumptions about fall speeds and the drop-size distribution. Once again it is best to look at rainwater content to avoid incorporating these assumptions into the comparison. Overall, the most representative and accurate comparison between PR and 1D-Var retrievals will be in terms of the RWP. Because the Equator-crossing time of TRMM s orbit varies from day to day, it is possible to make colocations between SSM/I and PR within a few minutes in time (7.5 minutes is the limit used here) and with an exact match in space. Each day, such colocations are found at only a small range of latitudes, but these latitudes change day by day, and over the month of February 27, we build up colocations at all longitudes, and all latitudes between 36.4 S and 36.4 N. Orbital crossings are more Table I. Experiment summary. Experiment SSM/I observations Initialised Dates in ECMWF ID Rainy Clear from February 27 RAIN On On Operations 1 28 evu6 NORAIN Off On Operations 1 28 evxp NORAIN28 Off On RAIN 12 UTC 28 ey1h NOSSMI28 Off Off RAIN 12 UTC 28 ey24 Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

5 LESSONS LEARNT FROM 1D+4D-VAR RAIN ASSIMILATION 1517 frequent in the extratropics, so in the sample used here, only 4% of colocations come from latitudes smaller than 2. The horizontal resolution of PR is 5 km. For the 1D- Var retrievals we cannot be so precise. We could consider either the resolution of SSM/I, which is 7 km by km for the 19 GHz channels, or that of the model grid point, which is representative of the FG, and is roughly 4 km by 4 km at T511 in the RAIN experiment. For our comparison we chose to average all PR measurements within a 25 km radius of the centre point of the SSM/I observation. We consider only colocations where there are more than 1 available PR observations. Changing the radius to either 12.5 km or 5 km affects the number of successful colocations but does not significantly change the following results. Over February 27 there were 236 colocations where RWP was greater than 1 4 kg m 2 in both PR and 1D-Var retrievals. Figure 1 shows a scatterplot of the results. There is little agreement between PR and the 1D-Var FG, but there is quite substantial agreement between PR and the 1D-Var retrievals, especially for the higher rainfall amounts (RWP >.1 kg m 2 ). At the lower rainfall amounts, 1D-Var shows more rain than PR. Table II quantifies the agreement between 1D-Var and PR in terms of the Pearson correlation coefficient. There is a small improvement between 1D-Var FG and retrieval when the calculations are done in terms of the logarithm of RWP, as displayed in Figure 1. However, if RWP is treated linearly, which emphasises the higher rain amounts, there is a substantial increase in correlation. A big factor in the lack of agreement at smaller rain rates is likely to be the lack of sensitivity of PR to small rain amounts. In areas of relatively uniform frontal rainfall, PR may lose sensitivity to RWPs as high as.1 kg m 2. (Assuming a horizontally uniform, 4 km thick layer of rain at the minimum rain rate observed by PR,.5 mm h 1, and converting rain rate to water content using the formula of Appendix B in Geer et al., 27.) Table II also shows the results if done in terms of surface rain rate (see also Figure 21 of Geer et al., 27), for rain rates > 1 4 mm h 1. Here, the agreement Table II. Correlation coefficients between PR and 1D-Var. Rainwater path Surface rain rate Sample FG Retrieval FG Retrieval log (RWP) RWP FG = first guess RWP = rainwater path between 1D-Var and PR is slightly less good, confirming our earlier discussion on information content. In Geer et al. (27), we had not yet realised that it would be better to examine RWP rather than surface rain. Hence, we can now be more confident of the quality of 1D-Var rain retrievals than we were in that report. Instantaneous comparisons of rainfall amounts from different sensors are always difficult, and it helps if the two sensors use the same measurement principle (e.g. ground-based versus space-borne radar; Schumacher and Houze, 2) or if the comparison is done with careful consideration of the spatial and temporal representativity of each instrument (e.g. ground-based radar versus rain gauge; Le Bouar et al., 21). To our knowledge, instantaneous comparisons between satellite passive microwave retrievals and other observation types are often unsuccessful and rarely presented in the literature. More typically, monthly means are compared (e.g. Masunaga et al., 22). In this context, the good agreement between 1D-Var and PR is extremely encouraging. We have validated the 1D-Var rain retrievals at RWPs greater than.1 kg m 2, but this has also thrown down a challenge: in order to demonstrate a true improvement in rain in our 4D-Var analyses and forecasts, nothing short of an improved instantaneous agreement with independent observations is acceptable. However, as the next section explains, we are not yet at that stage Transfer of information from 1D-Var to 4D-Var Remember that, although 1D-Var retrieves surface wind and vertical profiles of moisture, temperature, cloud and (a) (b) 1D-Var rainwater path [kg m -2 ] D-Var rainwater path [kg m -2 ] PR rainwater path [kg m -2 ] PR rainwater path [kg m -2 ] Figure 1. 1D-Var rainwater path from the RAIN experiment: (a) first guess and (b) retrieval, against retrievals from Precipitation Radar (PR) on TRMM. Note that PR starts to lose sensitivity to rain amounts below.1 kg m 2. Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

6 1518 A. J. GEER ET AL. precipitation, only a TCWV pseudo-observation is passed into 4D-Var. Early studies with 1D+4D-Var demonstrated the potential to improve rain in the 4D-Var analyses, despite the fact that rain is not directly assimilated (Marécal and Mahfouf, 22). To investigate if rain is improved in our system, Figure 2 examines increments in 4D-Var at the SSM/I observation locations, versus those in 1D-Var, for the RAIN experiment. We look at the integrated columns (or paths) of water vapour (TCWV), cloud liquid water (LWP) and rain (RWP), all in kg m 2. The sample consists of all rainy SSM/I observations assimilated in 4D-Var for the month of February 27. Increments in 1D-Var come purely from the SSM/I observations. Increments in 4D-Var come not just from the TCWV pseudo-observations but from all other assimilated observations. Where the 1D-Var and 4D-Var increments agree, it cannot necessarily be attributed to the 1D-Var observations alone. However, where the 1D-Var and 4D-Var increments differ, this is a clear indication that the information retrieved in 1D-Var is not getting into 4D-Var. Figure 2(a) shows that 1D-Var TCWV increments are strongly correlated with increments in 4D-Var, which suggests that for TCWV, 1D+4D-Var is working well. In contrast, 1D-Var increments in rain appear to show absolutely no correlation with those in 4D-Var (Figure 2(b)). The previous section has shown that the 1D-Var increments in RWP (on a linear scale at least, as shown here) contain real information. However, we cannot expect the TCWV pseudo-observation to magically recreate this rainfall when assimilated in 4D-Var. Rain in the 4D-Var system is generated using nonlinear moist physics operators and must be consistent with the full 12-hour forecast trajectory and other observations. In 1D-Var, rain is constrained only by the SSM/I observations and the FG. Though it is possible that the TCWV pseudo observation could make improvements to 4D-Var analysed rain, for example in a mean sense, there is clearly no instantaneous improvement at the observation points. Figure 2(c) shows there are encouraging hints of a correlation in cloud increments. Where 1D-Var significantly reduces cloud, in many cases 4D-Var does too. This should perhaps be expected given the direct link between relative humidity and large-scale cloud formation. But apart from the minor improvement in 4D-Var analysed cloud, it is clear that we are not yet successfully assimilating the SSM/I rain or cloud information. What we have is a system that makes best use of TCWV information in cloudy and rainy areas. However, in contrast to the cloud clearing approach outlined in the introduction (e.g. Pavelin et al., 28), our approach does incorporate some cloud and rain information into the 4D-Var analyses, since the assimilated TCWV pseudo-observation has been constrained by the moist physics operators in 1D-Var, with the result that it is consistent with the observed rain and cloud. The difficulty is in transferring the retrieved rain and cloud into 4D-Var. We already noted that the 4D-Var increments in Figure 2 could be influenced by many other observations apart from rainy SSM/I. For a single 12-hour assimilation window, in experiment NORAIN28 we removed rainy SSM/I observations, and in experiment NOSSMI28 we removed all SSM/I (both clear and rainy). SSM/I provides the only direct observation of lower tropospheric moisture over the oceans in our system (e.g. Andersson et al., 27), but Figure 3 shows SSM/I causes only small changes in the instantaneous TCWV increments in 4D-Var. The additional information that SSM/I provides is in the scatter about the 1:1 line on the plot. This is responsible for the small improvements in relative humidity and wind forecast skill in the Tropics that SSM/I assimilation brings in the context of the full observing system (Kelly et al., 28). But to a first approximation, the rest of the observing system is already generating TCWV increments similar to those retrieved by 1D-Var, even in rainy areas where we might have expected few observations to be available. These increments need not necessarily come from humidity-sensitive observations. Given, for example, the link between areas of high TCWV and moisture convergence and transport, both in the Intertropical Convergence Zone (ITCZ) and at midlatitudes (e.g. Bao et al., 26), increments in TCWV could have come from observations such as sea-surface winds and atmospheric motion vectors, as well as from (a) 15 (b) 1.5 (c) 4D-Var increments in TCWV [kgm -2 ] D-Var increments in rain [kgm -2 ] D-Var increments in cloud [kgm -2 ] D-Var increments in TCWV [kgm -2 ] D-Var increments in rain [kgm -2 ] D-Var increments in cloud [kgm -2 ] Figure 2. 2D histograms of increments (analysis or retrieval minus FG) at rainy SSM/I observation points in 4D-Var against those in 1D-Var: (a) TCWV, (b) rainwater path, and (c) cloud liquid water path. The sample is all successful 1D-Var observations for February 27 in the RAIN experiment, and the 1:1 line is overplotted. Contours are in logarithmic steps, starting from the outermost contour: 3, 1, 32, 1, 316, etc. Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

7 LESSONS LEARNT FROM 1D+4D-VAR RAIN ASSIMILATION 1519 (a) TCWV increment (RAIN) [kg m -2 ] (b) TCWV increment (NORAIN28) [kg m -2 ] TCWV increment (NORAIN28) [kg m -2 ] TCWV increment (NOSSMI28) [kg m -2 ] Figure 3. 2D histograms of TCWV increments in 4D-Var (analysis minus first guess) at rainy SSM/I observation points: (a) Increments from the RAIN experiment plotted against those from the NORAIN28 experiment, and (b) increments from the NORAIN28 experiment plotted against those from the NOSSMI28 experiment. The sample is from 9 UTC to 21 UTC on 28 February. Other details are as Figure 2. wind increments generated by temperature-sensitive radiance observations such as AMSU-A. In summary, we have seen that in 1D+4D-Var we only use the TCWV information content of rainy SSM/I observations. We see that TCWV is already well constrained by the rest of the observing system, which helps understand the results of Kelly et al. (28). It is the rain and cloud information content of rainy SSM/I observations that is unique. The challenge remains to use this information to directly improve analysed rain and cloud, and we hope, improve forecasts. This could come from assimilating the 1D-Var retrieved profiles of precipitation, cloud, temperature and moisture into 4D-Var. However, there would be problems with excessive data volumes, and correlated observation errors, which our assimilation system is not designed to handle. Even if these issues were avoided by, for example, assimilating just the integrated column amounts of rain, cloud and water vapour, there remains the problem that the retrievals have already been influenced by the FG. The same problem long ago led to NWP centres abandoning the assimilation of retrieved temperature profiles in favour of direct assimilation. Hence, the best use of the rainy SSM/I observations would also be with a direct 4D-Var assimilation Bias and sampling in rainy and cloudy skies Mean effects in 1D-Var and 4D-Var Figure 4 summarises the mean impact of rainy SSM/I assimilation on the analyses. It is derived from our experiments RAIN and NORAIN (Table I) but the features are very consistent with the figures shown by Bauer et al. (26a,b) using an earlier version of the system in a different season. Figure 4(a) shows the monthly mean of channel 19v FG departures for the 1D-Var retrievals. Departures are defined as bias-corrected observation minus first guess (OBS FG), and are given as a brightness temperature. (Brightness temperature is simply a scalar multiple of radiance at microwave frequencies, where the Rayleigh- Jeans approximation is valid; e.g. Petty, 26.) Departures in channel 19h are similar (not shown) but are smaller for channel 22v (not shown), which is more sensitive to TCWV and less sensitive to rain and cloud than channels 19v and 19h. Even with bias correction, monthly mean 19v departures range from roughly 4 K to +4 K. These biases are investigated in more depth in section 3.3.2: we show that negative departures are associated with excess rain in the FG; these biases particularly show up in the ITCZ, South Pacific convergence zone (SPCZ) and midlatitude storm tracks. Figure 4(b) shows the monthly mean of the FG departure of TCWV pseudo-observations presented to 4D-Var. We have meaned the FG departure percentages, so that the figure shows 1 n (OBS i FG i ), n FG i i= which tends to emphasise increments in dry areas, compared to an absolute measure, because in dry areas the denominator gets very small. Since the 1D-Var retrieval starts from the 4D-Var FG, the panel shows, equivalently, the mean TCWV increments made by the 1D-Var retrieval. The patterns of moistening and drying clearly come from the residual brightness temperature biases going into the 1D-Var retrieval (Figure 4(a)). Figure 4(c) shows the mean TCWV difference between RAIN and NORAIN analyses. The patterns of moistening and drying are similar to those seen in the FG departures (Figure 4(b)), but with a much greater tendency towards drying. Only the subtropical oceanic high pressure regions show any moistening. When interpreting these figures we should bear in mind that Figure 4(b) is representative of a dynamic equilibrium between the forecast model, which tends to diverge away from the analysis over 12 hours, and the observation increments, which bring it back again. Figure 4(c) meanwhile shows the difference in that equilibrium between experiments Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

8 152 A. J. GEER ET AL. 19v FG departure in 1D-Var [K] (a) TCWV FG departure in 4D-Var [%] TCWV at 4D-Var analysis [%] (c) Change in TCWV [%] or in Tb [K] (b) TCWV at T+24 forecast [%] (d) Figure 4. February 27 mean in boxes: (a) Channel 19v brightness temperature departure (obs minus 1D-Var FG) for successful 1D-Var retrievals; (b) Departure of 1D-Var TCWV pseudo-observations in 4D-Var (1 {obs minus FG}/FG); (c) TCWV differences between RAIN and NORAIN analyses (1 {RAIN minus NORAIN}/RAIN); (d) is as (c) but for T+24 forecasts. c 28 Royal Meteorological Society Copyright Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

9 LESSONS LEARNT FROM 1D+4D-VAR RAIN ASSIMILATION with and without rainy assimilation. This indicates that, despite our efforts towards bias correction, the rainy SSM/I observations still have a slight dry bias compared to other humidity observations and compared to the model itself. Figure 4(d) shows the difference between RAIN and NORAIN forecasts after 24 hours, showing that the patterns of moistening and drying are maintained into the forecasts, even if the magnitudes have reduced Understanding FG biases in 1D-Var Figure 5 attempts to explain the biases in 1D-Var. To reduce data volumes in the graphics software, it is based on only 1 days from the full month duration of - 1D bias corrected, successful retrievals (a) D rainy (b) (c) D rainy and clear (d) D rainy and clear Mean FG departure [K] Figure 5. Mean of channel 19v first guess departures (obs minus FG) in bins for the period 1 to 1 February 27, from experiment RAIN: (a) For all successful 1D-Var retrievals (by definition rainy ), based on the bias-corrected 1D-Var FG; (b) for all rainy observations, successful or not, and based on the 1D-Var FG before bias correction; (c) as (b) but including all observations ( clear and rainy ); (d) is as (c) but from the 4D-Var FG. c 28 Royal Meteorological Society Copyright Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

10 1522 A. J. GEER ET AL. experiment RAIN. Figure 5(a) shows mean channel 19v departures; these are very similar to the monthly mean shown in Figure 4(a). In fact, the features we describe here are common to all periods we have investigated, in different seasons and in different ECMWF versions. Also, very similar results can be drawn from studying the other cloud- and rain-sensitive SSM/I channels. Figure 5(b) examines the 19v FG departures before bias correction. The negative biases are even larger. This shows that our bias correction scheme has been successful in removing at least some of the bias. Large negative departures are associated with the ITCZ, the SPCZ, the warm pool region, and at 2 S, 65 E, which was the location of typhoon Dora for much of the period shown. Negative biases mean that FG brightness temperatures are too high. Higher channel 19v brightness temperatures come from higher amounts of cloud or rain. It is clear that there is a bias towards excessive rain or cloud in the 1D-Var FG. As explained in more detail in the next section, Figure 5(b) contains a sampling bias. In the current 1D+4D- Var system, the selection of rainy cases is purely determined by the observations. Cases when the FG is cloudy or rainy, but the observation is clear, go through the clear assimilation stream. It would be more correct to include these cases in our comparison. Figure 5(c) shows mean FG 19v departures when all clear and rainy observations are included in the sample. Note that in contrast to the operational clear stream, here we have generated FG brightness temperatures using the 1D-Var moist physics operators, along with cloud and rain radiative transfer. As might be imagined, the negative bias becomes even larger. We now have a true picture of the size (in brightness temperature) of the bias towards excess cloud or rain in the 1D-Var FG. Figure 5(d) shows 19v FG departures specially generated from 4D-Var using cloudy and rainy radiative transfer. Here, rain and cloud amounts come from the full nonlinear moist physics included in the global model. The bias is substantially reduced compared to 1D-Var. Figure 6 compares zonal mean monthly mean RWP over oceans from the 1D-Var FG, the 4D-Var FG, and from 2A25 rain retrievals from the precipitation radar on TRMM. We see that the 1D-Var FG produces excessive amounts of rain, explaining the large brightness temperature biases compared to SSM/I. The 4D-Var FG is much more realistic, though there still appears to be a bias towards excess rain, consistent with the SSM/I comparisons (Figure 5(d)). Though we should be cautious in claiming that 4D-Var rain is biased, we can be sure that the 1D-Var FG is unrealistically high. During initial testing, the simplified convection scheme produced similar rain amounts to the nonlinear full physics (Lopez and Moreau, 25). Certain minor changes were made afterwards, with the aim of increasing linearity in the 1D- Var and 4D-Var minimisations, but these actually caused a large change to diagnosed rain amounts. The problem was not noticed in rainy SSM/I assimilation until now, as its effect on FG departures was compensated by the sampling bias which is exemplified by Figures 5(b) and (c). Monthly mean rain over ocean [kg m -2 ] Latitude Figure 6. Zonal mean February 27 mean rainwater path (kg m 2 ) from experiment RAIN, over oceans only, from the 1D-Var first guess (solid), the 4D-Var first guess (dashed) and TRMM PR 2A25 (dotdashed) Identification of cloud and rain Before exploring the sampling bias in more detail, we need to explain the simple tests used to identify cloud and rain in the SSM/I observations, and thus separate the clear and rainy assimilation streams. Cloud is identified using a regression algorithm derived by Karstens et al. (1994): LWP = ln (28 TB 22v ) ln (28 TB 37v ) (1) Here, LW P is the cloud liquid water path in kg m 2,and TB x indicates the brightness temperature (K) in channel x. Here, we define cloud as LW P >.1 kg m 2. Rain is identified using the polarisation difference between the 37 Ghz channels, with rain corresponding to TB 37v TB 37h < 4 K. The polarisation difference is widely used in microwave sensing (e.g. Petty, 1994). It works on the principle that microwave emissions from the sea surface are strongly polarised, but that cloud and rain emission and scattering are not. The more cloud and rain in the optical path to the satellite, the less will the polarisation difference of the sea surface be seen. Observations are sent through the rainy path if either cloud or rain is identified. It would be expected that rain occurs only when there is cloud, but in practice a small fraction of observations are identified as rain without cloud. This highlights the fact that these tests are only approximate and ignore the true number of factors influencing the radiances. Looking at non-rainy situations, and ignoring the influence of the vertical distribution of water vapour and cloud, SSM/I brightness temperatures are affected by at least four different independently varying factors: LWP, TCWV, sea surface temperature and wind speed (e.g. Karstens et al., 1994). However it is still not mathematically possible to retrieve four independent pieces of information from the two channels used in the LWP regression, so surface variations must Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj

11 LESSONS LEARNT FROM 1D+4D-VAR RAIN ASSIMILATION 1523 affect these retrievals to some degree. However, the regression is still useful, because TCWV and LWP effects are dominant Rain and cloud sampling As well as using the simple rain and cloud tests on SSM/I observations, we can also apply them to the 1D- Var FG. However, because of relatively large mean biases between FG and observations, particularly in channel 22v (Figure 7 of Bauer et al., 26a) the LWP regression of Karstens et al. (1994) does not work properly when applied to the 1D-Var FGs. Our solution is to apply the bias corrections in the opposite sense to normal, i.e. to correct the 1D-Var FG to the observations before applying the rain and cloud tests. We can now use contingency tables to compare binary forecasts of rain and cloud to SSM/I observations. This has two aims: first, to further explain the sampling bias we noted in the previous section, and second, to assess the quality of rain and cloud distributions in the model FG. Table III gives a contingency table for rain, identified when the polarisation difference between channels 37v and 37h is less than 4 K. The full set of all clear and rainy SSM/I observations from experiment RAIN, from 1 1 February 27, is broken down into four categories. Frequencies and mean FG departures (without bias correction) are given for each category. Where FG and observation both agree that rain exists, that is described as a hit. When only the FG sees rain, that is a false alarm. When only the observation sees rain, that is a miss. When both agree that there is no rain, that is a correct negative. Wilks (26) provides more information on contingency tables. In Table III, only 6.4% of observations show rain. However, 6.9% of all FGs are false alarms, and there are very few misses (only 1.9%): this shows that rain occurrence is excessively widespread in the FG. The large negative departures in the hit and false alarm categories ( 5.1 K and 12.7 K) suggest that rain is also too intense in the 1D-Var FG. All this is consistent with the large bias between 1D-Var FG and PR (Figure 6). Table IV gives a contingency table for cloud over a threshold of.1 kg m 2, retrieved using the LWP regression. Though this regression has its limitations, the Table III. Contingency table analysis of rain forecasts versus observations, along with mean channel 19v departures (obs. minus FG before bias correction) for each category. Sample is observations from 1 to 1 February 27. Threat score:.34; Bias: Fraction Departure (%) (K) a. Hit b. False alarm c. Miss d. Correct negative a + c a + b + c Table IV. As Table III but for cloud forecasts. Threat score:.49; Bias: Fraction Departure (%) (K) a. Hit b. False alarm c. Miss d. Correct negative a + c a + b + c errors should affect both FG and observation equally. This assumes that external factors, such as the state of the sea surface, are similar in both the FG and in the real world that the observation sees. This is not an unreasonable assumption; for example, errors in the FG sea surface wind speed in the ECMWF system are thought to be no larger than 2 m s 1. However, if this assumption fails, the result will simply be to produce additional false alarms and misses. The combined set of hits and misses in Table IV, i.e. those 44.6% of points where the observations show cloud by this measure, is essentially what passes through the rainy SSM/I assimilation stream. As explained, the 19.2% of false alarms are currently going through the clear assimilation path. This has a number of consequences. FG departures are large and negative in this category. By ignoring this category, we have historically underestimated the size of FG departures in the 1D-Var FG. Mean 1D-Var FG departures are only.9 K in the rainy path (see the row marked a+c) but are really 2.3 K if the false alarms are considered properly (see the row marked a+b+c). If we were to pass the false alarms through the rainy assimilation stream, this would actually help to correct them in the analyses; by ignoring the presence of rain and cloud in the FG in the clear assimilation path, the FG is not properly corrected. Note that Deblonde et al. (27) have successfully avoided our mistake by applying 1D-Var to all hits, misses and false alarms. However, by our measures, only 36.1% of observations are clear in both observations and FG. We might as well do away with the distinction between clear and rainy altogether. Our conclusion is that clear and rainy streams are best merged into a single, direct 4D-Var assimilation. Some simple indicators of the quality of forecasts are the threat score (TS), defined using the labels from the tables as TS = a/(a + b + c) and the bias, B = (a + b)/(a + c). The best possible TS is one, and the worst is zero. When B is one, that indicates unbiased forecasts. Comparing the numbers listed in the captions to the tables, we see that cloud is much better forecast than rain, in terms of both smaller biases and better threat scores. The low threat score of.34 for rain is an indicator that the 12-hour FG forecast has difficulty placing rain in the right place and at the right time; the score of.49 for cloud indicates that the forecast agrees more often Copyright c 28 Royal Meteorological Society Q. J. R. Meteorol. Soc. 134: (28) DOI: 1.12/qj