Comparing rain retrievals from GPROF with ECMWF 1D-Var products

Authors


Abstract

Both the Goddard Profiling Algorithm (GPROF) and European Centre for Medium-Range Weather Forecasts (ECMWF) one-dimensional + four-dimensional variational analysis (1D+4D-Var) rainfall retrievals are inversion algorithms based on Bayes' theorem. Differences stem primarily from the a priori information. The GPROF uses an observationally generated a priori database whereas ECMWF 1D-Var uses the model forecast first guess (FG) fields. The relative similarity in the two approaches means that comparisons can shed light on the differences that are produced by the a priori information. Case studies have found that differences can be classified into four categories based upon the agreement in the brightness temperatures (Tbs) and in the microphysical properties of cloud water path (CWP) and rainwater path (RWP) space. A category of special interest is when both retrievals converge to similar Tb through minimization procedures but produce different CWP and RWP. The similarity in Tb can be attributed to comparable total water path (TWP) between the two retrievals while the disagreement in the microphysics is caused by their different degrees of constraint of the cloud/rain ratio by the observations. This situation occurs frequently and takes up 46.9% in the 1 month 1D-Var retrievals examined. The two retrievals produce similar spatial patterns but with different magnitude. The allocation of a large amount of CWP in the 1D-Var retrieval seems to be related to the stratiform portion of rain, which is produced by the large-scale condensation scheme. To attain better-constrained cloud/rain ratios and improved retrieval quality, this study suggests the implementation of higher microwave frequency channels in the 1D-Var algorithm. Copyright © 2012 Royal Meteorological Society

1. Introduction

Accurate rainfall measurements over the oceans are crucial for many applications and microwave radiometers provide physically reasonable rainfall estimates due to the direct interaction of the radiation with water in the rain column. The multichannel inversion type algorithms invert the observed radiances simultaneously to retrieve the rain parameters using physical forward/inverse modelling. The Goddard Profiling Algorithm (GPROF; Kummerow et al., 2001) approach has been utilized for the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), Special Sensor Microwave Imager (SSM/I) and Advanced Microwave Scanning Radiometer—Earth Observing System (AMSR-E) and served as a prototype for a single retrieval approach. The European Centre for Medium-Range Weather Forecasts (ECMWF) in the meantime has begun assimilating radiances corresponding to raining scenes using the Bauer et al. (2001, 2006a) radiative transfer and a retrieval algorithm referred to as 1D+4D-Var (Bauer et al., 2006b, 2006c). Both algorithms are based on Bayes' theorem but vary in the implementation process such as a priori information, usage of frequencies and algorithm formulation. The most recent version of GPROF relies on an observationally generated database of precipitation profiles that uses a combination of active and passive microwave sensors (Kummerow et al., 2011). This database constitutes a pseudo-observational microphysics space that defines the cloud/rainwater path ratios that have been observed using the active–passive microwave combination flying on TRMM.

These ‘observations’ are compared with the ECMWF results. Generally, there are two approaches to perform the comparisons between observations and models: the ‘satellite-to-model’ approach and the ‘model-to-satellite’ approach. In the first approach, retrievals are performed to convert satellite observations to model output variables (e.g., Zhou et al., 2007; Geer et al., 2008). In the second approach, observation operators such as radiative transfer models (RTMs) are used to simulate observed radiances or Tbs from the model variables (e.g., Panegrossi et al., 1998; Chevallier and Bauer, 2003; Matsui et al., 2009). However, both approaches ultimately lead to comparing either rainfall or radiance maps where the comparison in radiance space has the advantage that at least the observations are very accurately known. In conducting this research, we seek to better understand the microphysical properties that lead to differences in the GPROF and ECMWF rainfall, particularly for cases where both methods successfully minimize the differences between the model and the observed Tb. Detailed descriptions of the GPROF and 1D-Var algorithms are provided in section 2. Comparisons between them using case studies are depicted in section 3, while the physical understanding and statistical analyses of the differences are examined and analyzed in section 4, followed by a summary and conclusion in section 5.

2. The GPROF a priori database and 1D-Var retrieval algorithm

2.1. The GPROF rainfall algorithm

The GPROF is a Bayesian retrieval scheme that is currently used operationally for radiometers such as TMI, SSM/I and AMSR-E. The GPROF aims to retrieve the instantaneous rainfall and the rainfall vertical structure from the satellite microwave observations. The original algorithm is described in Kummerow et al. (1996) and was further extended to include the latent heating estimation (Olson et al., 1999).

Rainfall retrieval from passive microwave radiances is an ill-conditioned inverse problem in the sense that the total information content of the observations is less than the independent variables within raining clouds that must be retrieved. Therefore, there is no unique solution that can be obtained without introducing prior knowledge and the derived solution may even be non-optimal. The Bayesian theorem provides a rigorous mathematical formulation to introduce this a priori knowledge. Following Bayes' formulation, the probability of observing a particular hydrometeor profile R, given the observed brightness temperature vector Tb can be written as:

equation image(1)

where Pr(R) is the probability of observing a certain rain profile R and Pr(Tb|R) is the probability of observing Tb given a particular rain profile R.

Older versions of GPROF used cloud resolving models (CRMs) to define Pr(R). Pr(Tb|R) in those versions of GPROF was calculated from the CRM output using a radiative transfer model (RTM). More details of the CRMs and the RTM applied in GPROF are described in Kummerow et al. (2001). In practice, the available sets of CRM simulations constituted the assumed a priori probability of finding a particular profile R, in nature. In the retrieval process, given an observed Tb, profiles in the database that have consistent simulated Tb will be selected and weighted to give the expected value that is considered to be the ‘best’ estimate. With x representing the vector of all the physical quantities to be retrieved, the expected value of x is given by:

equation image(2)

where xi represents all model simulated profiles in the database, y0 represents the observation vector, H(xi) is the simulated observation vector corresponding to profile xi with H representing the observation operator, R and Q are the observation and model error covariance matrices respectively, and A is the normalization factor that is a scalar constant. For further descriptive details relating to the retrieval process see Kummerow et al. (1996, 2001).

This algorithm has undergone many improvements over the years. Examples include an improved freezing level over oceans to reduce the artificially high rainfall at high latitudes, improved convective–stratiform discrimination to significantly decrease the precipitation in stratiform areas, especially in areas far from convection, including melting layers in the RTM (Bauer, 2001), and use of an improved rainfall relationship over land (Kummerow et al., 2001). Recently, an important improvement consisted of replacing the original CRM-based database with an observationally generated database (Kummerow et al., 2011). The choice of database is very important because it is assumed that the database accurately represents the true probability of observed situations.

2.2. Observationally generated GPROF a priori database

The traditional databases generated by CRM simulations suffered from issues including the correctness and completeness issues described in Kummerow et al. (2006). To avoid these shortcomings, an observationally generated database of precipitation profiles has been constructed using the combination of active and passive microwave sensors (i.e., the precipitation radar (PR) and theTMI on board the TRMM satellite; Kummerow et al., 1998).

One year of TRMM observations of TMI and PR from 1 June 1999 to 31 May 2000 generated approximately 62 million data entries and were used to build the database. The TRMM operational PR algorithm (TRMM 2A25, V6) was used as the starting point. When PR indicated no rain, an optimal estimation procedure was used to retrieve non-raining geophysical parameters including surface wind, total precipitable water (TPW) and cloud liquid water path (LWP) from the TMI observations (Elsaesser and Kummerow, 2008). The sea-surface temperature (SST) is specified from the Reynolds weekly climatology (Reynolds et al., 2002). When PR indicates rain, the TRMM 2A25 rainfall profiles are used as the first guess. The SST and wind speed are interpolated from the neighbouring non-raining fields. Cloud water, water vapour and profiles of rain and ice hydrometeors are obtained by matching radar profiles to CRM. When matched, CRM hydrometeor profiles are used. This step is important in that the CRM provides a first guess for cloud liquid and cloud ice water content that are not sensed directly by the PR. The RTMs (Kummerow, 1993) are used to compute the simulated Tbs from these hydrometeors and the resulting Tbs are compared with coincident TMI observations. Comparisons are accumulated as a function of SST and TPW at 1 K and 1 mm intervals. Where disagreements at 19 and 85 GHz vertically polarized Tbs occurred, an adjustment procedure was performed by first adding rainwater that is below the detection threshold of the PR. If the addition of light rain did not correct mean biases, the adjustment procedure then focused on rain-drop size distributions and ice density to match the modelled and observed Tb. The adjusted profiles are then adopted for the database construction. Complete details of the procedure, which is only summarized here, can be found in Kummerow et al. (2011). The 1 yr pseudo-observed microphysical database will be used to evaluate the modelled microphysics. It should be noted here that because the PR is sensitive primarily to precipitation whereas TMI is sensitive primarily to TWP, there is good reason to assume that the rain and cloud water amounts may, to the first order, be representative of observed clouds.

2.3. The ECMWF 1D+4D-Var algorithm

The ECMWF 1D+4D-Var algorithm has been operational since June 2005 (Bauer et al., 2006b, 2006c; Geer et al., 2008) over cloudy and rainy SSM/I observations and may be considered as an intermediate step towards the direct 4D-Var assimilation of all-sky microwave radiances, which was made operational in March 2009 (Bauer et al., 2010; Geer et al., 2010). The 1D+4D-Var algorithm includes two parts: the 1D-Var that includes an optimal estimation procedure to retrieve the microphysical properties and TPW from SSM/I radiance observations, and the 4D-Var analysis (Rabier et al., 2000) that assimilates the TPW as a pseudo-observation. The observation operator includes three components: a convection scheme (Lopez and Moreau, 2005) that represents subgrid-scale processes and treats convection types defined as shallow, mid-level and deep convection in a unified way; a large-scale condensation scheme (Tompkins and Janisková, 2004) that uses the convective detrainment prescribed by the convection model with a similar precipitation generation formulation; and a multiple-scattering radiative-transfer model RTTOV-SCATT (Bauer et al., 2006a) with scattering calculated using the delta-Eddington approach. The advantage of the 1D-Var over ordinary variational retrievals is that it uses the same background state, background errors and moist physics package as the 4D-Var (Bauer et al., 2010). Therefore, its a priori information (short-range forecast) is more accurate than the statistical climatology as it contains information about physically important features such as fronts, inversions and the tropopause heights. Using 1D-Var allows an extra step of quality control before assimilating radiances into 4D-Var (Bauer et al., 2010). An important aspect of the 1D-Var retrieval is that the control vector consists of temperature and humidity profiles as well as surface windspeed. Cloud and precipitation are calculated from the moist physics parametrizations before running a radiative transfer scheme. The optimization is thus constrained by the models, the observations and the background fields for temperature, moisture and windspeed with associated errors and not by model background cloud/precipitation fields and their errors.

The processing of rain-affected SSM/I Tbs used in 1D-Var retrieval involves several steps including: removing the scan-position-dependent biases known to affect SSM/I, a pre-screening process including a land surface and sea-ice check, a check for valid Tb observations, and the screening of clear-sky observations not to be treated in the retrieval. A check for cloud liquid water and precipitation presence is applied that is based on a cloud identification algorithm (Karstens et al., 1994) and the polarization signal at 37 GHz. A check of excessive falling snow in the 1D-Var first guess (FG) profile is also performed to avoid unreliable radiative transfer simulations in such conditions (Geer et al., 2008). Then the bias correction is performed that is a correction of systematic differences between observed and simulated Tbs (Bauer et al., 2006b).

In general, it is not uncommon for simulations to have large biases compared with the observations, and it is crucial to correct these biases for achieving good assimilation results. A multiple linear regression between FG departures (observation minus FG) and FG TWP, surface wind speed and column rain amount is performed to predict the biases in the 1D+4D-Var system. The bias correction is then applied to the observation Tbs to make them less biased with respect to the 1D-Var FG prior to the assimilation (Geer et al., 2008). The bias correction is applied to the 19 GHz vertical polarization channel (shortened as 19 V hereafter), 19 GHz horizontal polarization channel (shortened as 19H hereafter) and 22 V.

The bias correction scheme may not be proper for cloudy observations because of the usage of an asymmetric predictor (Geer and Bauer, 2011) that is the FG rain amount in the 1D+4D-Var system. Some biases are very large, and they may be due to errors in the structure and intensity of forecast cloud and rain, but may also be due to displacement errors. The largest error might be coming from the improper cloud overlap scheme (Geer et al., 2009) in which assumptions regarding the subgrid-scale cloud variability are made. These are known as beam filling biases in the satellite community.

The model forecast provides the FG fields including temperature profiles, water vapour profiles, surface fields, which include latent heat and sensible heat fluxes, and wind stress. These FG fields all serve as inputs to the convection scheme that in turn produces detrained convective cloud water, and rain and snow fluxes. Together with the FG fields and the detrained cloud water, the large-scale condensation scheme produces cloud-cover fraction and models the clouds and precipitation when they are formed by model-resolved processes. Using the thermodynamic and hydrometeor information generated above, the multiple-scattering microwave RTM is used to calculate the simulated radiances.

In a variational retrieval, the optimal estimation of a state vector x is acquired by minimization of a cost function using the a priori information from the FG. The cost function J is defined as:

equation image(3)

where J is the cost function, x is the state vector, containing vertical profiles of temperature and specific humidity on 91 model levels in this case, xb is the a priori state vector acquired from model simulation,y0 is the observation vector, H stands for the observation operator that maps geophysical space to observational space, B is the background error covariance matrix, R is the observation error covariance matrix, which includes both the observation error and the errors originating from observation operators.

The first term is the fit of the solution to the background estimate of the atmospheric state weighted inversely by the background error covariance B. The second term is the fit of the solution to the measured radiances y0 weighted inversely by the measurement error covariance R. The solution obtained is optimal in that it fits the a priori (or background) information and measured radiances respecting the uncertainty in both.

The 1D-Var produces outputs including vertical profiles of humidity, temperature, cloud and precipitation. The TPW derived from the retrieved humidity profile is assimilated in the main 4D-Var analysis (Rabier et al., 2000). It should be noted that the 1D+4D-Var algorithm is affected by a sampling bias, which comes from applying 1D+4D-Var when the observations are cloudy or rainy, but not when the FG is rainy or cloudy and the observations are clear (Geer et al., 2008).

3. Case studies

When comparing the GPROF retrieval in Eq. (2) and the 1D+4D-Var assimilation in Eq. (3), it can be seen that these two methods are very similar in the sense that they are both performing underconstrained retrievals given the observations. Both methods use a priori information. The primary differences are: (i) the GPROF retrieval is constrained by the observation database consisting of PR/TMI observations and CRM simulations, while 1D-Var retrieval is constrained by the ECMWF model's FG and the 1D cloud model; (ii) the x to be minimized in GPROF represents the microphysics profiles, while in 1D-Var it represents the thermodynamic profiles; and (iii) in GPROF there is no assumption about the a priori probability density function (PDF) of possible solutions as the PDF is empirically derived, whereas in 1D-Var the PDF is in terms of the probabilities of departures from the FG thermodynamic profiles, and these departures are assumed to be Gaussian-distributed. In this section, detailed comparisons of the retrievals are made utilizing case studies.

3.1. Data

Data collected within a 12-h window extending from 0900 to 2100 UTC on 30 September 2007 are used in this case study. The data are based on a T511 run using the default configuration of cycle 35r1 of the Integrated Forecasting System (IFS) and include 6619 1D-Var retrievals over the ocean between 60°S and 60°N. The product consists of SSM/I Tb vectors, thermodynamic profiles, and microphysical profiles of cloud liquid water, cloud ice water, rain flux and snow flux at 91 levels for both the FG and the analysis generated in the 1D-Var observation operator. Figure 1 shows SSM/I 19 V Tb for 30 September 2007, and all the pixels that are used in the assimilation. Over the ocean, the background is radiometrically cold due to its low emissivities. Emissions from water vapour, clouds and rain will increase the 19-GHz Tb and therefore appear warmer against the background (Chevallier and Bauer, 2003).

Figure 1.

(a) SSM/I 19 V Tb between 0900 to 2100 UTC on 30 September 2007. (b) 19 V Tb pixels used in the 1D+4D-Var assimilation. The box centred at 120°W and 10°N includes the area for further investigation.

A 10° by 10° area at 115°W, 125°W and 5°N, 15°N, as shown by the box in Figure 1(b), was selected for the case study. Pixels from this area are expanded in Figure 2. Two representative pixels are chosen to include a variable range of Tb values for case studies, as illustrated in Figure 2.

Figure 2.

Observed Tbs at 19 V within the area of interest. The pixels chosen for case studies are illustrated.

3.2. The GPROF a priori database and 1D-Var retrieval comparisons

In the 1D-Var retrieval algorithm, only the lower frequency channels including 19 V, 19H and 22 V are used. The higher frequencies are not used due to the non-Gaussian shape of the histogram of FG departures, the complexity of nonlinearity in the RTM and the sensitivity to surface emissivity modelling biases (Bauer et al., 2006b). Accordingly, the observation vector y0 in Eq. (2) was modified to include only those three channels in the GPROF retrieval as well. Given an observation Tb vector y0, each entry in the a priori database xi within the TPW and SST ranges (TPW is defined by the 1D-Var analysis field and SST is defined by climatology) is assigned a weighting based on the closeness between the simulated Tb vector H(xi) and the observation Tb vector y0. From Eq. (2), the weighting for entry xi can be expressed as:

equation image(4)

where j is the channel number. Gaussian error distribution is assumed and Rj and Qj are the diagonal values of the error covariance matrices (off-diagonal elements are not taken into account because it is assumed that the errors of different channels are uncorrelated).

Equation (4) indicates that more similar Tb vectors will receive larger weight. It will be assigned a greater weight in the final solution than a pixel with Tbs that differ significantly. All the possible solutions defined by the database within given TPW and SST ranges are considered by using the normalized weighting to produce a statistically averaged GPROF retrieval. The entry that produces the closest Tb vector is called the ‘GPROF maximum likelihood’, which has the highest probability of being the solution. Comparisons between GPROF retrieval and 1D-Var retrieval are made for all of the selected pixels, and the results for pixels 1 and 2 as shown in Figure 2 are discussed below.

3.2.1. Pixel 1

Given TPW and SST, the grey envelope in Figure 3 represents the range of selected a priori database profiles with respect to CWP and RWP for the retrieval of this pixel using a cut-off weighting of 0.01. A cut-off weight of 0.01 as defined in Eq. (4) is used to eliminate entries that are too dissimilar to the observations. The relationship between CWP, RWP and Ice Water Path (IWP) is considered separately. The basic envelope constitutes a pseudo-observation space (i.e., for a given three-channel Tb vector, this is what PR/TMI considers to be possible) to evaluate the 1D-Var retrieved microphysics. The CWP and RWP values for the GPROF retrieval, GPROF maximum likelihood, 1D-Var FG and 1D-Var analysis are all shown in the figure. Corresponding rain rates are 6.527 mm h−1 for GPROF retrieval, 1.889 mm h−1 for FG and 5.111 mm h−1 for analysis. This pixel has a strong rain signal indicated by its high 19 V Tb (see Figure 2).

Figure 3.

The GPROF retrieval weighting contour as a function of CWP and RWP, overlain by the 1D-Var FG water paths (black triangle), 1D-Var analysis water paths (red triangle), GPROF weighted/retrieved water paths (asterisk) and GPROF maximum weighted water paths (red circle) for pixel 1. The rain rate for each retrieval is shown in the upper left box.

The goal of the 1D-Var retrieval is to adjust the temperature and moisture (and cloud and precipitation) profiles to minimize the difference between the simulated and observed Tb vectors under the constraints of the background field and the background error covariance matrix, as shown in Eq. (3). Table 1 shows the comparison of Tb departures from the observation of the GPROF maximum likelihood, 1D-Var FG and 1D-Var analysis. For ECMWF, the departures are bias-corrected. For example, FG Tb departure is defined as:

equation image(5)

where bi is the bias correction. Analysis departure is defined similarly.

Table 1. Bias corrected Tb departures at channel 19 V, 19 H and 22 V for GPROF maximum likelihood entry, ECMWF 1D-Var FG and ECMWF 1D-Var analysis solution.
Tb departures (K)19 V19 H22 V
GPROF maximum likelihood departures−0.041 0.9120.843
ECMWF 1D-Var FG departures30.44857.7849.600
ECMWF 1D-Var analysis departures 9.19019.0112.200

Figure 3 demonstrates that the selected GPROF database for the observed Tb vector contains profiles with RWP ranging from 500 g m−2 to 5000 g m−2 and CWP ranging up to 700 g m−2. The closest Tb match from the GPROF database produces less than a 1 K bias from the observation for all channels, as shown in Table 1. From Table 1 it can also be seen that the 1D-Var FG has overwhelmingly large Tb departures from the observation. This means that the FG profile does not match observations particularly well. The prominent positive Tb biases in the FG indicate that the modelled liquid water must be increased in the analysis to increase the emission. Figure 3 shows that the FG solution resides outside the observation-based envelope, which is considered to be all the possible observed solutions defined by the database. The FG has a CWP that is too large and a RWP that is too small. The small RWP corresponds to a smaller retrieved rain rate (1.889 mm h−1) compared with the GPROF retrieval (6.527 mm h−1). To produce realistic cloud ranges defined by the database, the CWP needs to be reduced and RWP needs to be increased. After the 1D-Var retrieval, the bias-corrected Tb departures are greatly reduced from 30.448 K, 57.784 K, and 9.600 K to 9.190 K, 19.011 K and 2.200 K, respectively for channels 19 V, 19H and 22 V, and the retrieval has also managed to adjust the microphysics to produce a better Tb match to the observation although the departures remain larger than those from GPROF. However, Figure 3 shows that besides adding in some rainwater, the analysis cloud liquid water is moving away from the GPROF. The GPROF produces more rain than cloud and 1D-Var produces more cloud than rain at each level.

The two retrievals for pixel 1 differ primarily in the CWP/RWP ratios. This can also be attributed to the underconstrained nature of the retrieval problem and their non-unique solutions. Even though the analysis rain rate of 5.111 mm h−1 is closer to the GPROF retrieval, and the Tb departures are greatly reduced, the cloud/rain ratio is significantly different from what was ever observed by PR/TMI. In 1D-Var, the microphysics are generated by the linearized moist physics scheme run at a single point and a single time step, with thermodynamic profiles as inputs. Although producing a similar rain rate, the difference in the CWP/RWP points to issues in other aspects, especially with the linearized moist physics scheme that deserves further investigation and improvement. In this case, GPROF and 1D-Var analysis have large differences, but it may be argued that the analysis did not quite converge on the observed Tb. As such, these differences may not be very meaningful.

3.2.2. Pixel 2

For pixel 2, the rain rates are 0.364, 4.477 and 1.244 mm h−1, respectively, for GPROF, 1D-Var FG and analysis. The analysis rain rate is reduced from FG and moves closer to the GPROF retrieval. The FG has large negative Tb biases for all channels, as seen in Table 2, indicating too much emission from liquid compared with the observation. Figure 4 shows that the FG CWP and RWP are approximately 2300 and 900 g m−2 and significantly outside GPROF's envelope range of 300 and 600 g m−2.

Figure 4.

Same as in Figure 3 except for pixel 2.

Table 2. Same as in Table 1 except for pixel 2.
Tb departures (K)19 V19 H22 V
GPROF maximum likelihood departures −0.191 −1.105−0.222
ECMWF 1D-Var FG departures−13.212−23.246−4.788
ECMWF 1D-Var analysis departures −0.684 0.603−1.809

After the 1D-Var, the analysis reduces the Tb departures to substantially lower values by reducing both cloud and rainwater. The analysis RWP is brought into the database range while the analysis CWP is still several times larger than the maximum value of GPROF's envelope. In other words, although the minimization process is successful in matching the Tb vectors, the CWP/RWP ratio is highly biased with an extremely large CWP value (1620 g m−2). As the minimization process is trying to produce a simulated Tb vector that is close to the bias-corrected observed Tb vector instead of the real Tb, large bias corrections may cause 1D-Var to produce biased microphysics with respect to the one observed. Also, the analysis IWP of 180 g m−2 is larger than the GPROF IWP of 60 g m−2, which will increase the scattering slightly and therefore reduce the Tbs in the analysis. In this case, both GPROF and 1D-Var reach similar results to Tb, while at the same time having very different cloud and rainwater solutions.

4. Statistical analysis

4.1. Data

The ECMWF Cycle 35r1 was operational from 30 September 2008 to 10 March 2009. One month of 1D+4D-Var data from October 2008 were extracted from the operational ECMWF analysis to perform further statistical analysis. Cloudy and rainy observations were assimilated into the 4D-Var system and only 1D-Var retrievals that converge and pass the ‘excess snow’ check from SSM/I on Defense Meteorological Satellite Program (DMSP) F-13 are analyzed. For each pixel, the data include stratiform surface precipitation flux, convective precipitation flux, total column water vapour, water paths of rain, snow, cloud and ice, SSM/I observed Tb vector, simulated Tb vector and bias corrections for both the FG and analysis. The data represent a later version of the assimilation used in the case studies.

4.2. Cloud and rain partitioning

Figure 5 shows that the two retrievals produce cloud and rain at similar locations while the TWP retrieval is much larger in 1D-Var than in GPROF. It can be seen from Figure 6 that both 1D-Var FG and 1D-Var analysis retrievals produce overwhelmingly larger cloud percentages compared with GPROF. Quality control and linearization of 1D-Var do not account for the large discrepancies. The little difference between Figure 6(b) and 6(c) indicates that the cloud/rain ratio is not being changed by the observations in the 1D-Var but instead is completely controlled by the moist physics. However, the two algorithms produce similar spatial patterns although with different magnitude (note that the scales are different).

Figure 5.

(a) The GPROF retrieved and (b) 1D-Var retrieved TWP map for October 2008. The data are 1° by 1° binned monthly mean.

Figure 6.

(a) The GPROF retrieved cloud/(cloud + rain) map for October 2008. (b) 1D-Var FG and (c) 1D-Var analysis cloud/(cloud + rain) map for the same month. The data are 1° by 1° binned monthly mean and four selected regimes are enclosed in boxes.

Microwave observations are sensitive to TWP and precipitation. Low frequency microwave channels almost penetrate all clouds, hence they can provide a direct measurement of TWP after considering the dependency on the cloud temperature (Liu and Curry, 1993; Lin and Rossow, 1994; Greenwald et al., 1995). However, assumptions have to be made regarding the cloud water and rainwater partitioning, which cannot be determined by microwave observations alone because cloud water and rainwater present very similar radiative effects at these microwave frequencies. Sensitivity of the assumptions on the retrieval of the cloud liquid water path was explored in O'Dell et al. (2008). Due to the current limitations of ECMWF 1D-Var, only channel 19 V, 19 H and 22 V could be used. Given the close spacing of these microwave channels, generally speaking one can only hope to retrieve information about attenuation due to total cloud and precipitation and attenuation due to water vapour from 22 GHz, which is at the centre of the water vapour absorption band. Independent Mie scattering information needs to be brought in so as to separate cloud from precipitation attenuation, and therefore improve the partition.

4.3. Impact of higher frequencies on constraining the cloud/rain ratio

At the lower microwave frequencies (e.g., 19 V, 19 H and 22 V), cloud droplets belong to the Rayleigh scattering regime in which absorption/emission dominates and scattering is only a minor effect. Raindrops begin to fall in the Mie regime—particularly for larger rainfall rates. With higher frequencies such as 37 and 85 GHz, cloud droplets still belong to the Rayleigh scattering regime, but the absorption and scattering process increase more rapidly in the Mie regime due to increased size parameters. It is therefore possible to differentiate these two hydrometeor species with information from these higher frequency channels.

Forward model uncertainties also increase somewhat at higher frequencies. Elsaesser and Kummerow (2008) used values of 1.45, 1.87, 1.46, 1.50, 2.38, 2.15 and 3.54 K for 19 V, 19 H, 22 V, 37 V, 37 H, 85 V and 85 H, respectively. To perform the sensitivity of using higher frequency channels on the cloud/rain ratio change, three channel combination schemes are evaluated. The three-channel case uses 19 V, 19 H and 22 V; the five-channel case uses 19 V, 19 H, 22 V, 37 V and 37 H; and the seven-channel case uses 19 V, 19 H, 22 V, 37 V, 37 H, 85 V and 85 H. Several raining cases are examined below. For each case, rainwater and cloud water are converted between each other by redistributing the water content at each level while holding TWP constant. A ratio increment is defined with negative values to indicate that rainwater was redistributed to the cloud water category while positive values convert cloud water to rainwater. For instance, −60% means that 60% of the rainwater at each layer is removed and redistributed as cloud. If the changes are less than the Tb uncertainty values for all the channels used, the microphysical change is considered too small to be detected by these channels. Otherwise, if the Tb change goes beyond the uncertainty value for any channel, the microphysics change is detectable. Several representative profiles of different raining scenarios that produce surface rain rates of 0.05, 0.52, 1.00, 5.09, 10.06 and 21.15 mm h−1 are used to explore the impact of adding high frequency channels, shown in Figure 7, and the results are summarized in Table 3.

Figure 7.

Six representative hydrometeor profiles for the case studies.

Table 3. Sensitivity tests of different channel combinations to the cloud/rain ratios for all six raining cases.
CaseRain rate (mm h−1)Channel combinationRain to cloud detection threshold (%)Channel ChannelCloud to rain detection threshold (%)Channel
1 0.053 channelNone+4119 H
  5 channelNone+1737 H
  7 channelNone+1737 H
2 0.523 channel−5919 H+1219 H
  5 channel−2437 H +737 H
  7 channel−2437 H +737 H
3 1.003 channel−2619 H+2119 H
  5 channel−1437 H+1237 H
  7 channel−1437 H+1237 H
4 5.093 channel −419 H+3619 H
  5 channel −419 H+3619 H
  7 channel −419 H+2585 V
510.063 channel −719 H+8522 V
  5 channel −719 H+2937 V
  7 channel −719 H+1985 V
621.153 channel−3619 HNone
  5 channel −437 V+4437 V
  7 channel −285 V+3085 V

4.3.1. Case 1

Case 1 rains at only 0.05 mm h−1 with a CWP of 210 g m−2 and a RWP of 20 g m−2. As a result, even when all the rainwater is converted to cloud water, the Tb changes are still within the uncertainty ranges for all the seven channels. However, when cloud water is converted to rainwater, Tbs increase for 19, 22 and 37 GHz due to the increased emission efficiency from cloud to rain. The Tbs decrease for 85 GHz due to increased Mie scattering caused by rain drops as well as decreased emission from elevated weighting functions that are associated with lower temperatures. Considering differences between the cloud and rain profiles, the positive and negative ratio increment regimes are discussed separately. Qualitatively, converting rainwater to cloud water cannot be detected because of the small amount of rainwater for this case even if all the seven channels are used. When cloud water is converted to rainwater, a sensitivity of +41% ratio increment is found for three channel combinations, with channel 19 H first detecting the difference. When 37 GHz is used, the detectable ratio increment moves up to +17% at channel 37 H, but when 85 GHz is added the sensitivity remains at 17%. In this very light rain case, adding 37 GHz is beneficial to separate cloud from rain for the retrieval because the emission/absorption efficiency of water increases with microwave frequency. However, further adding 85 GHz is not useful in this respect because the Tb uncertainty range of 85 GHz masks the signal.

4.3.2. Case 2

Profiles and sensitivity results for case 2 are displayed in Figure 7 and Table 3. This profile includes 330 g m−2 of CWP and 70 g m−2 of RWP. By moving from three channels to five channels and then to seven channels, the detectable ratio increment of converting rainwater to cloud water moves from −59% (the detection channel is at 19 H, shortened as ‘at 19 H’ hereafter) to −24% (at 37 H) to −24% (at 37 H), and the detectable ratio increment of converting cloud water to rainwater improves from +12% (at 19 H) to +7% (at 37 H) to +7% (at 37 H). For this drizzle case (0.52 mm h−1), adding 37 GHz improves the sensitivity significantly whereas adding 85 GHz does not further improve the result. The increased sensitivity at 85 GHz is once again masked by the greater uncertainty in these channels. Scattering is still relatively unimportant for this profile.

4.3.3. Case 3

The rain rate increases to 1 mm h−1 in this case, which contains more rainwater with less cloud water compared with case 2 as seen in Figure 7. The detectable ratio increment of converting rainwater to cloud water moves from −26% (at 19 H) to −14% (at 37 H) to −14% (at 37 H), and converting cloud water to rainwater improves from +21% (at 19 H) to +12% (at 37 H) to +12% (at 37 H). As the rain rate is still relatively small, the results match case 2.

4.3.4. Case 4

Case 4 rains at 5.09 mm h−1. With the increased rain content, the detection sensitivity of converting rain to cloud further increases from previous cases. The detectable ratio increment is held constant at −4% for all channel combinations because 19 H sets the strongest constraint. When rain is converted to cloud, channels 19 H, 19 V and 22 V decrease monotonically due to the decreased emission efficiency of the clouds, whereas the sensitivity to channels 37 H, 37 V, 85 H and 85 V increases at first due to decreased scattering from rain drops and then it decreases. When cloud water is converted to rainwater, the detectable ratio increment moves from +36% (at 19 H) to +36% (at 19 H) to +25% (at 85 V). In this scenario, 19 V, 19 H and 22 V increases with an increased emission signal from more rain, while 37 H, 37 V, 85 H and 85 V decreases with an increased scattering signal from rain. For 37 GHz, increased scattering and increased emission cancel each other out in providing higher sensitivity. The 85 GHz channel is beneficial in constraining the cloud/rain ratio in this case.

4.3.5. Case 5

Snow and graupel particles start to appear in this case, as seen in Figure 7. The existence of these ice particles masks some of the sensitivity to cloud water and rainwater changes. The sensitivity mark is held constant at −7% because 19 H again sets the strongest constraint for all channel combinations when rain is converted to cloud. In the other direction, the detectable ratio increment moves from +85% (at 22 V) to +29% (at 37 V) to +19% (at 85 V). In this large rain case (10.06 mm h−1), both 37 and 85 GHz bring more sensitivity for differentiating cloud and rain.

4.3.6. Case 6

In this intense raining case (21.15 mm h−1) that contains large amounts of snow and graupel lying above the liquid layer, the sensitivity moves from −36% (at 19 H) to −4% (at 37 V) to −2% (at 85 V), and from no signal to +44% (at 37 V) to +30% (at 85 V). When rain is converted to cloud, Tbs at all frequencies increase in the beginning due to decreased scattering followed by a decrease due to decreased emission from cloud. The sensitivity to the cloud/rain ratio is enhanced by adding in 37 GHz and further enhanced by the incorporation of 85 GHz. It is worthwhile to note that these tests are based on theoretical sensitivity studies in which the ice contents are fixed. In reality, 85 GHz is more sensitive to ice instead of the cloud/rain ratios. It is therefore difficult to detect these ratios without prior knowledge of the ice.

From the case studies above, it is found that higher frequency channels are able to constrain the cloud/rain ratio with increased sensitivity. However, 37 GHz is sufficient for drizzle cases (≤ 1 mm h−1) and 85 GHz is beneficial for large rain rate cases (≥ 5 mm h−1) due to the increased scattering signal from raindrops. It is therefore helpful to include the higher frequency channels into the retrieval to improve the cloud and rain differentiation. These sensitivity tests disregard variations in other parameters, such as TPW and surface wind speed, which could still lead to ambiguities even if the higher frequency channels are added.

4.4. Categorization and microphysics biases

4.4.1. Categorization

Generalized from the pixel-by-pixel comparisons in section 3, differences between the GPROF and 1D-Var retrievals can be categorized into four scenarios: (i) Tbs match within given uncertainty ranges and the cloud water/rainwater paths are in general agreement defined as the analysis being within the observational envelope (examples of this were not presented in the examined scene). This category includes the cases in which the 1D-Var retrieval produces CWP/RWP ratios that are observationally possible; (ii) Tbs match but the CWP/RWP ratios do not (e.g., pixel 2). This category includes the cases in which the 1D-Var retrieval successfully matches the observation but allocates microphysical properties that are not observed in the PR/TMI database; (iii) Tbs do not match and microphysics do not match either (e.g., pixel 1). This category includes the cases in which the liquid species of rain and clouds match but the rest such as ice species do not, which contribute to the unmatched Tbs; and (iv) Tbs do not match while the investigated microphysics properties do match (examples of this were not presented in the examined scene). Among these, category 2 is of special interest because in this category, the optimal estimation procedure successfully minimizes the cost function, yet the cloud does not converge to a solution that is similar or even allowed in the GPROF algorithm; in other words, the retrieval results are biased even when the retrieval is successful. Now two compelling questions become: How often does this condition occur? And, what are the microphysical biases in this category? This section strives to answer these questions.

The GPROF Bayesian retrieval is performed over each 1D-Var pixel utilizing the analyzed 1D-Var TPW and SST to ensure consistency between model and retrieval. This process is equivalent to assigning weights to qualified entries within the given SST and TPW ranges from the observationally constrained a priori database. To avoid using entries in the higher latitude out of the TMI orbit range that have colder SSTs, the comparisons are constrained to 40°S and 40°N. Comparisons between GPROF and 1D-Var retrievals are classified into four categories based on the Tb and microphysical agreement.

The GPROF retrievals use estimated uncertainties in each of the channels; 1.45 K, 1.87 K and 1.46 K at 19 V, 19 H and 22 V, respectively, to assign weights to individual profiles (Elsaesser and Kummerow, 2008). The same values are used to determine if the 1D-Var method has converged as well. If the 1D-Var values differ by more than the stated Tb, the pixel is deemed not to have converged for the analysis.

The microphysical properties to be examined in this study include the RWP and CWP. To determine whether the 1D-Var retrieved RWP and CWP are within the database envelope that was described in section 3 for each pixel, a procedure is defined as follows and an example is shown in Figure 8. First, if the 1D-Var RWP is outside of the GPROF envelope, the microphysics are considered unmatched. Otherwise, the 1D-Var RWP's 20% uncertainty values are calculated, which is illustrated with dashed lines in Figure 8(a). The database's CWP distribution within this RWP range is determined. With reference to the distribution's weighted mean value (weighting is determined by Eq. (4) in section 3), the distribution's 95% ranges (95% is equivalent to the 2σ range in the Gaussian distribution) on both sides are calculated. This bound is illustrated in Figure 8(b). If the 1D-Var CWP falls outside of the 95% range, the microphysics is considered to be unmatched. Otherwise, when both the 1D-Var analysis CWP and RWP fall within the allowed ranges, the microphysics is considered to be matched, implying that the 1D-Var retrieved microphysics falls within the range of values that GPROF deems possible.

Figure 8.

Illustration of the procedure to define the match of microphysics. (a) Same as in Figure 3 with the dash lines showing the 20% RWP variability range. (b) The CWP distribution within the 20% RWP range. Dashed line represents the location of the weighted mean CWP and sold lines mark the 95% boundary on both sides.

Based on whether the Tbs and/or microphysics match, each pixel in the one-month period is assigned to one of the four categories. The percentage of each category is 40.7%, 46.9%, 4.5% and 7.9%, as shown in Table 4. It is worthwhile to note that category 2 takes up 46.9% of all of the retrievals. In this scenario, the variational method works successfully to minimize the cost function with respect to the Tbs, but does not converge to the ‘observed’ microphysical properties from the cloud schemes. The incorrect properties, especially the rain structures, will inevitably have an impact on the rain retrieval results.

Table 4. Percentage of each category in the database.
PercentageTb s match (%)Tb s do not match (%)
RWP and CWP matchCategory 1: 40.7Category 3: 4.5
RWP and CWP do not matchCategory 2: 46.9Category 4: 7.9

4.4.2. Microphysics bias in category 2

This section explores the nature of the microphysical biases between GPROF and 1D-Var. It also tries to ascertain if these biases are consistent and universal or have a dependence on the regional meteorology.

4.4.2.1. Global microphysics bias

The bias is first explored using the whole month's global data between 40°N and 40°S. The ratio of 1D-Var over GPROF retrieved CWP as a function of RWP is plotted in Figure 9. Consistent with Figure 6, the prominent feature of Figure 9(b) is that a very large percentage of the category 2 entries in the database produce much larger CWP in the 1D-Var analysis than in GPROF for pixels with rain rates greater than 1 mm h−1. Table 5 shows the percentages of different CWP and RWP ratio ranges for category 2. It can be seen that only 2.87% of the retrievals can be considered comparable in both CWP and RWP; in 79.6% of the time, 1D-Var produces less than half the GPROF-retrieved RWP (in 93.6% of the time, 1D-Var retrieval produces smaller RWP than GPROF retrieval), and in 34.0% of the time, 1D-Var produces more than two times of GPROF-retrieved CWP. Removing the impact of drizzle cases that produce very large ratios, only cases where the GPROF-retrieved surface rain rate is greater than 1 mm h−1 are kept for analysis and the percentages are shown in parentheses in Table 5. For 90.6% of the time, 1D-Var retrieved CWP is at least two times that of the GPROF retrieval. It is clear that large discrepancies exist between the two retrieval algorithms in allocating the water content between different liquid hydrometeor species, i.e., cloud water and rainwater. The ratio is directly responsible for the unmatched microphysical properties in category 2. In GPROF retrievals, the rainwater estimate is driven by PR retrievals and the cloud water estimate is driven by CRM simulations but constrained by the PR and TMI observations. In the case of 1D-Var retrievals, both are the result of microphysical parametrizations that are used in the minimization and are linked by common hydrological processes in clouds and convection.

Figure 9.

Normalized frequency contour of CWP ratio over RWP ratio for category 2 with (a) all rain rates and (b) rain rate ≥ 1 mm h−1. The contour intervals for panel (a) are 1e-5, 1e-4, 1e-3 and 1e-2. The contour intervals for panel (b) are 0.0005, 0.001, 0.0015, and 0.002.

Table 5. Percentage of cases in category 2 with different CWP and RWP ratio ranges. Values in parentheses are the percentages for GPROF surface rain rate ≥ 1 mm h−1.
PercentageCWP ratio0.5 ≤ CWP ratioCWP ratio
 < 0.5 (%)≤ 2.0 (%)> 2.0 (%)
RWP ratio < 0.520.50 (0.0141.96% (0.01)17.14 (18.17)
0.5 ≤ RWP ratio ≤ 2.0 0.56 (0.12) 2.87% (9.30)15.59 (71.35)
RWP ratio > 2.0 0.06 (0.01) 0.09% (0.01) 1.24 (1.04)

4.4.2.2. Regional differences

To explore the regional dependence, four representative regions associated with different meteorological regimes are selected based on the difference in cloud water/rainwater ratios. As shown in Figure 6, the four specific regions are:

  • Regime 1 (10°S, 30°S and 100°W, 70°W) is the Southeast Pacific regime, which is identified as the region with relatively low SST, low total precipitable water and frequent stratocumulus and trade cumulus occurrence. The abundance of clouds with relatively low rain efficiency associated with the subsidence of air in the high pressure system in these clouds cause high cloud/rain ratios.

  • Regime 2 (0°N, 10°N and 120°E, 180°E) is the West Pacific regime associated with higher SSTs in the warm pool and high relative humidity that provide a favourable environment for tropical convections. This regime shows the lowest cloud/rain ratio.

  • Regime 3 (0°N, 15°N and 140°W, 100°W) is the East Pacific regime. Regime 3 has a relatively lower cloud/rain ratio compared with regime 2. Berg et al. (2002) investigated the differences of the storm systems between the East and West Pacific and found that the storms over the East Pacific have shallower clouds with warmer cloud tops, larger proportion of stratiform rain, less ice for similar amounts of rainwater and lower melting layers.

  • Regime 4 (30°N, 40°N and 120°E, 180°E) is the Northern Hemisphere storm track regime. This regime is generally associated with mid-level convection within the mid-latitude frontal storms. This regime may also be influenced by the increased aerosol concentration that will increase the ratio of cloud water to rainwater (Berg et al., 2008).

The CWP/RWP ratios that are not observed in the GPROF database differ systematically across the four regimes. Percentage of category 2 is 41.4% in the Southeast Pacific regime, 58.2% in the West Pacific regime, 73.1% in the East Pacific regime, and 46.0% in the storm track regime.

The frequency contours of CWP versus RWP for category 2 in each regime of both GPROF and 1D-Var are shown in Figure 10. Regime 1 is characterized by small RWP and little correlation between CWP and RWP. This is consistent with the relatively small rain rates in the stratocumulus and trade cumulus within this regime. For GPROF, the relationships of CWP versus RWP are similar for regimes 2, 3 and 4 at a RWP range of up to 100 g m−2. At higher RWP values, the amount of CWP needed per amount of RWP is highest at regime 2 and lowest at regime 4. This is found to be associated with the stratiform portion within each regime. In stratiform rain, GPROF consistently retrieves very little cloud water. The relative larger portion of stratiform clouds in regime 3 compared with regime 2 is consistent with Berg et al. (2002). On the other hand, the 1D-Var retrieved CWP is much larger than the GPROF retrieved CWP for the same amount of RWP for all regimes. A ‘convective fraction’ parameter is defined for 1D-Var as the ratio of convective rain to total rain produced by the cumulus parametrization and the large-scale condensation scheme. It appears that in 1D-Var, the CWP/RWP ratio is related to the convective fraction with smaller convective fractions producing larger CWP for the same amount of RWP. This indicates that larger CWP in 1D-Var is produced by the stratiform rain in the large-scale parametrization. In other words, in cases of small convective fractions, a stratus-type cloud topped by a convective plume was produced by the ECMWF cloud schemes. This suggests some physical inconsistency between the convective scheme and the large-scale parametrization. However, it is worthwhile to note that there exist large uncertainties on the modelling of stratiform areas by CRMs (Varble et al., 2011).

Figure 10.

Normalized frequency contour of CWP over RWP in category 2 for all four regimes in GPROF (left-hand column), 1D-Var retrieval (middle column) and convective 1D-Var retrieval pixels with convective fractions that are greater than 80% (right-hand column). Rows 1 to 4 represent regimes 1 to 4, respectively.

If the cases with larger convective fractions (> 80%) are selected out, their ratios fall closer to those of GPROF, as shown in the right-hand columnof Figure 10. It is worthwhile to note here that the definition of ‘stratiform’ is not equivalent in GPROF and 1D-Var. Regardless of the detailed differences, all regimes contain a consistently different distribution of cloud water and rainwater in the 1D-Var algorithm when compared with GPROF.

4.4.2.3. Discussion

The previous section shows that GPROF and the 1D-Var solutions tended to differ quite dramatically in their CWP and, to a lesser extent, in their RWP, despite matching the observed Tb. This is examined further below.

For each pixel, the TWP distribution of the possible solutions in the GPROF database is calculated. Similar to Figure 8, the boundary values of the 95% range on each side of the weighted mean TWP is determined. If the 1D-Var analyzed TWP falls within this range, it is 95% probable that the analysis TWP is within the GPROF observed TWP solutions. For the global dataset, it is found that in category 2, although the cloud and rain microphysics do not match, 83.8% of the 1D-Var analysis pixels fall within the 95% ranges of GPROF solutions. Specifically, the TWP match ratio takes 93.1%, 90.9%, 96.7% and 80.8%, respectively, for the four selected regimes above. The smaller percentage in regime 4 compared with the other three regimes could potentially be caused by a larger portion of ice hydrometeors in the included storms. This is consistent with the expectation, and together with the larger amount of cloud liquid water, it is clear that although 1D-Var finds comparable TWP in order to match the Tbs, it allocates different amounts of cloud water and rainwater relative to the GPROF solution. As suggested in section 4.3, by using more higher frequency channels, less ambiguity in CWP/RWP partitioning is expected from both GPROF and 1D-Var.

5. Summary and conclusion

GPROF and 1D-Var rainfall retrievals are compared, as they are both inversion algorithms based on Bayes' theorem aimed at reproducing the observations given available a priori information. The PR/TMI combination does allow the combined algorithm to partition the cloud water and rainwater. The GPROF utilizes an observationally generated database from PR/TMI whereas 1D-Var uses the ECMWF model forecast FG field of temperature and moisture for a priori information. The state vector to be solved in the minimization procedure includes microphysical profiles in GPROF and thermodynamic profiles in the 1D-Var. Retrieved microphysical properties for 1D-Var are outputs from the moist physics schemes given the retrieved temperature and humidity profiles and other model variables as inputs. However, 1D-Var makes use of an imperfect moist physics parameterization, which must also be linearized for assimilation purposes. The moist physics controls the ratio of cloud to rain in the 1D-Var retrievals, but this ratio is much higher than observed in the GPROF database, i.e., modelled cloud amounts are excessive as a fraction of rain amounts. The cloud water and rainwater partitioning in the 1D-Var model is therefore evaluated using the GPROF a priori database in this study.

Comparisons are first made using case studies of raining pixels extracted from 12 h data on 30 September 2007. Differences between the two retrieval algorithms can be categorized into four categories based upon their agreements on three-channel Tbs and on their CWP/RWP ratios. Among the four categories, category 2 defines the scenario when Tbs agree when microphysics do not. This is the category in which the retrieval is successful at reproducing the Tbs but the retrieved cloud and rain properties were not observed by PR/TMI. From statistical analysis using 1 month's global retrievals in October 2008, it is found that category 2 occurs as often as 46.9% of all the 1D-Var retrievals. The agreement in Tbs is due to the comparable retrieved TPW between the two algorithms to match the same observation signals, whereas the microphysical discrepancy is found specifically to be due to the difference in allocating the TWP between CWP and RWP. The dependence of the bias on regional variability is explored by selecting four regimes including the Southeast Pacific regime, the West Pacific regime, the East Pacific regime, and the Northern Hemisphere storm track regime. It was found that although all regimes share the same issue of improper distribution of cloud water and rainwater within the 1D-Var cloud scheme, the two retrievals produce similar spatial patterns. The dependence of the ratio on spatial variability is found to be related to the portion of stratiform rain, although the definition of stratiform is not equivalent in these two algorithms. Therefore, subject to being further validated to the observations, this work suggests the large-scale parametrization needs to be modified to represent the observed cloud/rain ratio.

This work explores solutions to improve the cloud/rain ratio in the 1D-Var retrieval using several representative raining cases that have a wide range of rain intensities. It is found that the implementation of higher microwave frequency channels is beneficial to better constrain the ratio due to increased sensitivity at these frequencies in differentiating cloud water from rainwater. Including 37 GHz is sufficient for drizzle cases (≤ 1 mm h−1) while adding in 85 GHz has a greater impact for larger rain rate cases (≥ 5 mm h−1). Therefore, to improve the retrieval quality we suggest that higher frequencies be added to the 1D-Var's three-channel retrieval algorithm. The comparisons between GPROF and 1D-Var can also be applied to other inversion algorithms.

Acknowledgements

This work was supported by the NASA Precipitation Measurement Missions (PMM) under Contract No. NNX10AI48G. The authors are very grateful to two anonymous reviewers for valuable suggestions that greatly helped to improve the paper.

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