Revised versions of previous passive microwave land rainfall algorithms are developed for the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), the Special Sensor Microwave/Imager (SSM/I), and the new Advanced Microwave Sounding Radiometer-Earth Observing System (EOS) (AMSR-E). The relationships between rainfall rate and 85 GHz brightness temperature are recalibrated with respect to previous algorithms using collocated TMI and TRMM Precipitation Radar (PR) data. Another new feature is a procedure to estimate the probability of convective rainfall, as convective/stratiform classification can reduce the ambiguity of possible rainfall rates for a given brightness temperature. These modifications essentially eliminate the global high bias found in studies [e.g., McCollum et al., 2000; Kummerow et al., 2001] of previous versions of the SSM/I and TMI algorithms. However, many regional and seasonal biases still exist, and these are identified. The applicability of the new features to the other microwave sensors is studied using SSM/I data, and a correction is developed to account for the differences in footprint resolution between the TMI and SSM/I. The AMSR-E algorithm is the same as the TMI, as the footprint resolutions and frequencies of these instruments are very similar. The TMI algorithm will be used in the land portion of the official version 6 TMI instantaneous rainfall rate product, to be released in 2003, while the AMSR algorithm will be used in a similar manner for future AMSR-E products.
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 The primary source of microwave satellite data for rainfall estimation from the late 1980s to the late 1990s was the SSM/I data from the Defense Meteorological Satellite Program satellites. At the time of this writing, microwave data were available from additional sensors on board other satellite platforms. Among these are the TMI, the Advanced Microwave Sounding Unit (AMSU) on board NOAA K-L-M polar orbiting satellites (currently on NOAA-15 and NOAA-16), and the AMSR-E, launched on board the Earth Observing System (EOS) Aqua satellite in May 2002 (AMSR will also be on board the upcoming ADEOS-II satellite). In comparison with the SSM/I, these new sensors have in general better spatial resolution and a wider range of measurement frequencies, which provides the potential for more accuracy in satellite rainfall estimation.
 Microwave satellite rainfall estimates are produced at different spatial and temporal scales for different purposes. The algorithms here produce instantaneous rainfall rate estimates associated with each 85 GHz microwave footprint. The frequencies and approximate instantaneous fields of view (IFOV) of the TMI are shown in Table 1.
Table 1. TMI Instrument Parameters
Center Frequency, GHz
IFOV, km × km
63 × 37
30 × 18
23 × 18
16 × 9
7 × 5
 These rainfall rates can be used in numerical weather prediction for model verification and data assimilation, and for hydrologic applications such as flood forecasting. For more climatological scales, over ocean, many projects, e.g., the Global Precipitation Climatology Project (GPCP) [Huffman et al. 1997], TRMM, and Aqua AMSR-E, use the algorithm of Wilheit et al.  that was designed specifically for monthly rainfall rates over 5° × 5° grid boxes. Over land we simply average the instantaneous pixel estimates to the appropriate scales. These lower-resolution products are aimed more toward climate monitoring and diagnostics, as well as GCM validation.
 The microwave properties of land and ocean surfaces are different, so microwave land and ocean rainfall algorithms are based on different physical principles. In general, land algorithms utilize the scattering due to cloud ice, and the associated reduction of brightness temperatures, observed at higher frequency channels during rain events to estimate rainfall rates over land. Many microwave land algorithms have been developed since microwave data became prevalent with the SSM/I and later the TMI; a commonly used SSM/I algorithm for several years has been the Ferraro  NOAA/NESDIS algorithm. Some of the more recent ones are described by Conner and Petty , Prabhakara et al. , Grecu and Anagnostou , and Bauer et al. [2001a]. Some of the many ocean algorithms are Petty , Kummerow et al. , and Bauer et al. [2001b].
 These other microwave land rainfall algorithms use more sophisticated physics than the empirical NOAA/NESDIS algorithm. Prabhakara et al. , Grecu and Anagnostou , and Bauer et al. [2001a] all utilize the TRMM PR in complex ways to calibrate the TMI rainfall predictors. However, the first two of these algorithms still essentially rely on the global application of a rainfall rate (RR) versus 85 GHz brightness temperature (TB) relationship, using the 85 GHz scattering signature as the basis for the rainfall estimate. Here we do use some of the new concepts from these algorithms, however. Bauer et al. [2001a] use information from additional channels, accounting for the background land surface temperatures, to isolate the multichannel brightness temperature signature response to rainfall. While this method shows promise, evaluation of a similar algorithm of Conner and Petty  indicated that the other microwave algorithms tested, including the NOAA/NESDIS algorithm, had similar performance. In terms of older algorithms, the algorithm intercomparison project AIP-3 found that the algorithms using similar instruments for estimation over similar surfaces, including microwave land algorithms utilizing scattering, tend to perform similarly, while the differences between classes are significant [Ebert et al., 1996].
 So at this point in time, we feel that we still don't have conclusive evidence to completely change the basic structure of the algorithm we have been using. The microwave land rainfall estimates still essentially come down to the rain/no-rain screening, developed extensively for version 5 [Kummerow et al., 2001], and the rainfall rate to brightness temperature relationship. The empirical Ferraro  NOAA/NESDIS algorithm has been used for many years for different weather and climate applications (including operational use at the U.S. Navy's Fleet Numerical and Oceanography Center since 1995) and is considered reliable. We are continuing to base our official algorithms on this well-understood algorithm and to make incremental changes to previous versions so that the user community can continue to use our algorithms with confidence and understanding of the concept of the algorithm.
 We are recalibrating the algorithm with PR data and including some of the more sophisticated physics, namely convective/stratiform estimation procedures, to keep our algorithm in line with the current state of the field. But the primary objective of this updated algorithm is to eliminate the high bias in tropical rainfall found in the NOAA/NESDIS SSM/I algorithm [McCollum et al., 2000] and the Version 5 TMI algorithm [Kummerow et al., 2001] relative to rain gauges. Kummerow et al.  found an overall high bias of 19% for TMI Version 5 land rainfall estimates in comparison with gauges, primarily from overestimation in the tropics. McCollum et al.  also found overestimation by the GPCP SSM/I algorithm over the tropics, particularly in equatorial Africa.
2. Data and Prior Algorithms
 TRMM Precipitation Radar (PR) data were taken from the TRMM 3G68Land product (http://tsdis.gsfc.nasa.gov/trmmopen/index.html), which among other parameters contains the mean PR instantaneous surface rain rate estimates and convective rainfall percentage estimates. These estimates are calculated from all the PR pixels (∼4.4 km resolution) within each 0.1° grid box containing PR data for Africa and South America; each continent is in a different file. It also contains the observation time for each box so that the coincident TMI pixels can be found in the TMI orbital, instantaneous brightness temperature product (1B11 in TRMM nomenclature). These TMI brightness temperatures can be compared with the associated PR rain rates and convective percentage estimates.
 The microwave rain rate estimates are calculated for each 7 km by 5 km 85 GHz TMI pixel, and because any 85 GHz pixel is smaller than a 0.1° (∼10 km) grid box, the PR rainfall and convective percentage estimates include areas outside the matched 85 GHz TMI footprint. We attempt to reduce the sampling error by using only those 0.1° grid boxes containing the center of only one 85 GHz TMI pixel, as a 0.1° grid box may contain from 1 to 5 TMI pixels depending on the sampling pattern. However, additional sampling error occurs because of the parallax effect between the high-frequency microwave signal contribution caused by cloud ice at higher altitudes and the radar-estimated surface rainfall [Bauer et al., 2001a] and the use of the other lower-resolution frequencies in the algorithm that have resolution greater than 0.1°. Bauer et al. [2001a] show that the mean shift due to parallax is several km, while Hong et al.  showed that for tilted convective systems, the 85 GHz signal can be shifted as much as 100 km from the liquid precipitation in the column. In addition, some of the microwave convection predictors use adjacent 85 GHz microwave pixels so that again there is naturally smoothing in all the variables of interest.
 Thus we assume that the bias introduced by sampling of the 0.1° grid box by the TMI footprint is negligible compared to all the other sources of uncertainty for the sake of convenience of using the 3G68Land product for TMI/PR match-ups. 4 GB of PR data products per day are reduced to 0.02 GB/day by using this product as opposed to the general PR product, named 2A25 in the TRMM nomenclature. If only surface rainfall rate and convective percentage are desired, the 3G68Land product is very advantageous from a computational standpoint. The product was first created on the request of individual researchers, who were interested in the largest landmasses of Africa and South America. Due to its convenience, it has perhaps now become more widely used than the associated PR and TMI products from which it is derived (Erich Stocker, personal communication).
 The GPROF algorithm calculates instantaneous rainfall rate estimates from the weighted average of rainfall rates from different vertical hydrometeor profiles created from numerical cloud models, primarily the Goddard Cumulus Ensemble model of Tao and Simpson . Radiative transfer calculations for the frequencies and resolutions of a particular satellite are done to produce a library of vertical profiles with the associated brightness temperatures. The profiles used for estimation are chosen and given weights based on the proximity of the observed microwave radiances to those of the library of profiles [Kummerow et al., 1996]. Then in addition to a surface rainfall estimate, the estimated profiles can be used to estimate latent heating profiles for model assimilation [Olson et al., 1999].
 The physical basis of the GPROF algorithm is most useful over oceans, where the low and predictable oceanic emissivity results in information about both ice and liquid hydrometeors over the range of microwave frequencies. The high and variable emissivity of the land surface makes the information from the lower frequency channels ambiguous, so the ice scattering at higher frequencies is currently the most useful way to estimate rainfall over land. However, the GPROF framework can be used to reproduce empirically determined rainfall rate estimates by choosing a database containing only those profiles having the relationship between rainfall rate and scattering as a desired empirical relationship.
 The use of the GPROF framework has a minor effect on the rainfall estimates of the previous (Version 5) algorithm and the one (Version 6) described here. It does provide vertical hydrometeor distributions that can be used for latent heating estimation, although they have not yet been validated over land and their errors are assumed to be quite high. The use of GPROF in this version is a starting point for future versions that will attempt to use physical principles as in the ocean algorithm to improve the rainfall estimates and produce better vertical hydrometeor distributions so that the latent heating estimates will improve.
 The version 5 (V5) TMI instantaneous rainfall rate algorithm (2A12 product in TRMM nomenclature [Kummerow et al., 2001]) was created to produce rain rate estimates similar to those of the Ferraro  NOAA/NESDIS algorithm. This was done by selecting from the entire library of cloud model output (∼3000–4000 profiles) a profile database for the SSM/I algorithm comprised of 30 profiles with similar rainfall rate versus 22 GHz minus 85 GHz vertically polarized brightness temperature differences (TB22V - TB85V) as in the NOAA/NESDIS algorithm. These 30 profiles span the range of possible rain rates. In the V5 algorithm, TB22V - TB85V is used as the only profile selection criterion, in contrast to matching multiple frequencies as in the GPROF ocean algorithm. This procedure can be used to force the GPROF to reproduce any relationship between rainfall rate and brightness temperature, as long as the profiles with that relationship can be found in the original cloud model output database and span the range of possible rain rates and brightness temperatures. We created the corresponding TMI database by calculating the brightness temperatures for those hydrometeor profiles, accounting for the differences in frequencies and resolutions between the TMI and SSM/I.
3. Algorithm Development
 Prior to 1998, calibration of the rainfall rate (RR) to brightness temperature (TB) relationship was usually done using ground-based radar-rainfall estimates, often calibrated with rain gauges. The main disadvantage of this method is that the fraction of land with well-calibrated radar coverage is low [McCollum et al., 2002], so the relationship determined from ground radars may not even be applicable at the location of the radars, let alone to other regions and climates. With the launch of TRMM, there has been a continuous record of coincident spaceborne radar rainfall estimates and microwave TB's covering the tropics available for RR calibration. In addition, these collocated (with the spatial matching limitations discussed earlier) data can be used to calibrate relationships between PR-estimated convective rainfall percentage and microwave convective rainfall predictors. While PR rainfall rate estimates have their own errors [Kummerow et al., 2000], we assume the PR's ability to detect raindrops directly makes it's estimates much better than the indirect estimates of the land algorithm so that we are justified in using PR to calibrate microwave algorithms.
3.1. Convective/Stratiform Estimation
 For each TMI pixel corresponding to a 0.1° grid box of the PR product, several convective rainfall predictors were extracted and tested for their utility in estimating the convective percentage estimated by the PR. These methods are taken from previous work and will be described briefly here.
The first method is spatial standard deviation (STDEV), as in the work of Grecu and Anagnostou . This is based on the principle that the TB85 field for convective rainfall is spatially inhomogeneous due to the cloud ice in the isolated convective updrafts. Due to the irregular spacing of TMI footprints (∼4.6 km along scan and ∼14 km along track) the standard deviation was calculated from 7 pixels along scan and 3 along track to reduce directional bias. In addition, the closely related variability index (VI) of Anagnostou and Kummerow , defined as the mean absolute difference between a pixel and it's surrounding pixels, was tested. We use TB85V, although the horizontally polarized brightness temperature (TB85H) could have been used instead to give similar results.
The second method is brightness temperature minima as developed by Prabhakara et al. ; this method will be abbreviated here as PIWD. Convective cores should result in the lowest TB's over a region because of the increased scattering. They developed a detailed method of identifying TB minima and assigning convective rainfall to radius of 10 km around a minimum, corresponding to the typical size of a thunderstorm. Their method was implemented and used to classify a pixel as convective or stratiform. Another measure of the minimum, the VC of Hong et al.  was tested. The VC is defined as the TB difference between the center pixel and the averaged value of the surrounding pixels. Finally, the VM, also used by Hong et al. , is the maximum 85 GHz depression from each of the surrounding pixels.
The third method is polarization. Olson et al.  based their method on the concept first proposed by Spencer et al.  that the difference (POL) between the vertical and horizontal polarizations at 85 GHz is less in convective than stratiform rain. This is presumably due to a preferred orientation of ice particles from gravity in stratiform rain, whereas convective updrafts would result in a more uniform distribution of orientations. In addition, Olson et al.  developed a normalized polarization difference (NPOL) after finding that normalizing the 85 GHz polarization difference by the mean of TB85V and TB85H leads to better classifications.
The fourth method is brightness temperatures. Grecu and Anagnostou  found that the product of the TB37V and TB85V is a good predictor of rainfall, and thus possibly a good predictor of convection. We include the other channels as well, as they also could have predictive capability.
 For each TMI pixel corresponding to a 0.1° box, the quantities above were computed. These variables were used as predictor variables in a stepwise linear regression procedure [Draper and Smith, 1981], with the PR convective percentage as the dependent variable. Stepwise approaches are used to build regression models from large numbers of variables that may be correlated with one another, using statistical testing to prohibit the addition of redundant (collinear) variables to the model. Data from October and November 2000 from both Africa and South America were used separately. The concept of testing several convective predictors was taken from Grecu and Anagnostou , who used a neural network approach to determine a predictive relationship between convective percentage and several predictor variables.
 In each of the four (October and November for Africa and South America) stepwise procedures, the STDEV parameter was chosen first, i.e., this parameter explains the most variance (around 17%) in the estimate of PR convective percentage. The next three variables chosen were also the same in all four models; POL was chosen second, PIWD third, and TB10V fourth. It's interesting that TB10V was chosen fourth all four times, as it's practically unaffected by the atmosphere, but it is related to surface temperature and emissivity. We hypothesize it is included because convection occurs more over warmer surfaces. The order of selection of variables 5–7 were mixed in the four runs but the variables were essentially the same: TB37V (or 37H), TB85V (or 85H), and NPOL. These 7 variables explain around 26% of the variance. The stepwise procedure selected 9 more variables in each case, but the increase in explained variance was small so these variables were not included in the model.
 The regression coefficients for each variable were chosen from the October 2000 South America model, as these coefficients were typical of those of the other three models. The final equation for the estimator of PR convective percentage, named the convective percentage index (CPI), is:
 This equation explains only about 26% of the variance, so there is large random error that could cause algorithm errors when the convective percentage estimate is far from correct. Thus we apply the convective predictor in a more conservative way that reduces the variance (frequency of extreme estimates) of the convection estimate. The CPI was calculated with the original data set and used to calculate the empirical probability of convective rain (P(C)), based on the PR estimates, as a function of the index. A line was fit to these data, as shown in Figure 1, yielding the following equation to convert the convective percentage estimate to a probability of convective rain:
 Upper and lower limits of 0.85 and 0.03, respectively, are given to P(C) based on Figure 1, meaning, the data show that we can never be certain in our estimates. Also shown in Figure 1 are the corresponding index values of the STDEV parameter alone to show that the additional terms in (1) produce an index with a greater dynamic range, so that we can be more certain of our extreme estimates using all the predictors.
 The convective probability is used to estimate RR as a function of TB85V in the following equation:
 The use of (3) eliminates the preferred rainfall rates found in the official V5 products that occurred from choosing the closest GPROF profile to the satellite brightness temperatures but only using 30 profiles close to the NOAA/NESDIS rainfall versus scattering relationship.
3.2. Rainfall Rate Estimation and Other Modifications of Previous Versions
 The convective (RRconv(TB85V)) and stratiform (RRstrat(TB85V)) rain rate functions were also determined from collocated TMI and PR data. The data were grouped to the nearest integral value of TB85V, and the mean PR RR for each bin was determined for both convective and stratiform classifications. This procedure is shown schematically in Figure 2.
 To use the results in the GPROF framework, we found those profiles having similar relationships between RR and TB85V; Figure 3 shows the results for the new convective and stratiform calibrations, as well as the NESDIS scattering index (SI) based calibration of the Version 5 algorithm. Note the large difference between convective (dotted line) and stratiform (long- and short-dashed line) RR's for a given TB85V from the PR/TMI match-ups; this is why an estimate of the convective versus stratiform nature of the rainfall can reduce uncertainty in the RR estimate significantly. Also included are the GPROF profile data (points). We show later that there is more stratiform than convective rainfall in the data, giving mean P(C) values in the range of 0.3 in (3). This produces estimated rainfall rates closer to the stratiform line, which is more in the vicinity of the Version 5 estimates for the frequently occurring low rates. Thus the difference in estimates from version 5 to version 6 will only be significant when the CPI gives enough information for the convective or stratiform RR to be given high weight, and at the high rain rates, which are infrequent and have high uncertainty.
Figure 4 shows the rain rate versus TB85V relationship from three different months of PR/TMI match-ups for both continents, and these mean relationships are relatively similar between the different data subsets, although the data diverge for the less sampled, colder brightness temperatures. The relationship between rain rate and TB85V scattering is dependent on climate regime over scales smaller than continental [Mohr et al., 1999; Petersen et al., 2001], so averaging over entire continents, which includes several different climate regimes, may reduce the variability. Similarly, averaging may cause the results to be similar for different months from the same continent by mixing climate regimes. Future versions will attempt to identify climate regimes so that different relationships between rainfall and brightness temperatures may be accounted for, but for simplicity and to be more conservative, this version still uses one global relationship based on Figure 4.
 In addition to rainfall rate estimation, another important aspect of microwave algorithms is the criteria used to distinguish raining from nonraining areas. Kummerow et convectiveal.  describes updates to these criteria originally developed by Grody , but one important addition was made for this Version 6 algorithm. The PR data were used to choose a TB85H brightness temperature threshold of 270 K, as this threshold was found to produce similar rain areas for the TMI and PR. However, owing to (1) the weighting of the convective and stratiform rain rates using (3); (2) the somewhat high convective rain rates for TB85V; and (3) our conservative probability estimation method that doesn't estimate extremes, the convective rain rate receives enough weight to limit the lowest rain rates to around 1 mm/h. Neither this nor probably any other microwave rainfall algorithm can estimate rainfall rates of less than 1 mm/h with much confidence, although new radiometers such as AMSU-B are showing potential using a new, higher frequency of 183 GHz. Again, we are conservative in our approach and don't make the attempt with our TMI algorithm.
 Assuming the PR rain rates have the same accuracy as ground-based radar rainfall estimates, PR-based calibration is superior to previous ones that used RR to TB relationships from limited ground-based radars. However, we recognize that the PR surface rainfall rates algorithms are still under development [Kummerow et al., 2000] and are not assuming these estimates as “truth”, only as a tool to calibrate the microwave algorithm. If the comparisons with rain gauges show bias, then the previous calibration will have to be adjusted.
4.1. Comparisons With PR Calibration Data Set
 The proposed Version 6 (V6) TMI rain estimates resulting from the new profiles and (3) were first compared with the PR estimates to check whether the estimates are unbiased with respect to the PR rainfall. The TMI/PR data from Oct. 2000 through February 2001 were used again to compare rainfall estimates. Table 2 shows that for these sample data the new (V6) algorithm is nearly unbiased with respect to the PR.
Table 2. Mean Daily Rainfall Estimate for October 2000 Through February 2001
South America, mm/d
 In addition to bias, it is useful to know whether the new algorithm produces better rain rate estimates as a result of the convective estimation procedure. The South America data for October 2000 through February 2001 were used to evaluate the skill of the algorithm over the range of possible rain rates using the Heidke Skill Score (HSS), as shown in Figure 5. We compute the HSS using the same, variable threshold for the TMI and PR data to evaluate the correspondence of rain areas from PR and TMI above the specified threshold as shown on the x axis.
 To determine whether the improvement in HSS is only due to the bias reduction shown in Table 2, the HSS for a bias-corrected V5 algorithm (obtained by multiplying each rain rate by the PR/V5 ratio from Table 2) is also shown. Over all but the highest, infrequently occurring rain rates >30 mm/h, there is improved skill in estimation of the rain areas above the specified PR thresholds.
Figure 6 extends the Heidke Skill Score analysis to two dimensions, as in the work of Conner and Petty . The shift of the major axis of highest HSS indicates the dependence of the bias on the rainfall rate. Relative to PR, the V6 TMI algorithm slightly overestimates the frequently occurring low rainfall rates, while it significantly underestimates the infrequently higher rainfall rates. This behavior is as expected; we have less confidence in the TMI estimates relative to PR so we are more conservative in attempting to estimate extreme rainfall rates on both ends.
4.2. Case Studies With Independent Data Sets
 We also looked at several case studies to observe the performance of the algorithm on the pixel scale, an example of which is shown in Figure 7. The strength of the Prabhakara et al.  algorithm is it's ability to depict the small-scale structure of convective storms, and we chose the case study of their Figure 5, an event over the southern United States, to test and compare our algorithm. They compared their estimates with PR and the TMI Version 4 algorithm, which was significantly improved with our version 5 [Kummerow et al., 2001]. The shapes of our TMI rainfall patterns compare very well with the PR surface rainfall; the Version 6 algorithm appears to further sharpen the gradients within the convective cells in comparison to Version 5, although the gradients don't appear quite as sharp as those of Prabhakara et al. . Figure 8 shows a comparison of the probability of convection estimated from the algorithm and that estimated by PR, and the two compare well. The high-resolution TRMM PR classification product used for Figure 8 (the 3G68Land product is only for Africa and South America) has an index used to classify the certainty of the estimate of convection. The higher the value of the index, the more certain the convection.
 The rainfall rate histograms (Figure 9) corresponding to the Figure 7 scenes show that the nonsmooth Version 5 histogram, due to assignment of the closest GPROF profile from Figure 3, has been eliminated. The more smooth histograms result from weighting profiles within the convective/stratiform class, as in the traditional GPROF algorithm of Kummerow et al. , and then the further weighting by convective/stratiform probabilities in (3). The Version 6 algorithm shows the desired reduction in mean rainfall rate that will be observed in many subsequent results.
 In contrast, an example from a heavy rainfall case 1 April 2002, over South America shows relatively poor correspondence between PR and TMI (Figure 10). There is even a problem with the rain/no-rain screening procedure; in this case TB22V reached sufficiently low values to cause the algorithm to estimate a possible ice-covered surface, but with not enough certainty to say either way so no estimate is made for these pixels.
 Comparisons with the NCEP merged hourly radar/gauge product and rain gauges are shown in Figures 11 and 12. The TMI estimate is considered to be instantaneous so there will be some temporal collocation errors. Figure 11 compares a TMI estimate taken at ∼1Z on 28 May 2002, with the hourly estimate for 1–2 Z the same day. This comparison indicates that even despite the temporal mismatch, the microwave algorithm has the potential of working very well. The quantitative comparison statistics with the radar/gauge product, with both aggregated to a common 1/6° grid, is given in Table 3. The data are from the pixels where at least one of the three products has nonzero rain. The high bias is reduced somewhat (the mean radar/gauge estimate for these pixels is 1.9 mm/h), but the correlation is slightly worse for V6.
Table 3. Comparison of Satellite Estimates With Hourly Radar/Gauge Estimates (Mean = 1.9 mm/h) for All 1/6° Pixels (Total = 1321) Where at Least One of the Products Has Nonzero Rain (28 May 2002 Case)
 A more typical case is shown in Figure 12, which compares the TMI estimate from ∼9:40 Z with the gauge/radar estimate for 9–10 Z. The rain area estimated by microwave is not as distinct and the rainfall around 33N, 102W was almost missed. These case studies don't indicate significant differences between V5 and V6 on the instantaneous scale; as mentioned before the major objective was to reduce the global high bias found in previous studies. Table 4 shows virtually identical correlations and the reduction in the high bias compared to a radar/gauge mean of 2.4 mm/h.
Table 4. Comparison of Satellite Estimates With Hourly Radar/Gauge Estimates (Mean = 2.4 mm/h) for All 1/6° Pixels (Total of 839) Where at Least One of the Products Has Nonzero Rain (30 March 2002 Case)
4.3. Large-Scale Comparisons With GPCP Estimates
 The PR rain rate algorithm is still undergoing significant changes from one version to the next, so calibration to the PR will not necessarily produce globally unbiased estimates. The best test of the bias of the TMI algorithm is a long-term comparison with the GPCP monthly rainfall product, as this product uses rain gauge data with extensive quality control to reduce the satellite bias over land. It is reasonable to assume that the relationship between RR and TB varies regionally, so it is useful to plot zonal means to observe the variation of bias with climate. Figure 13 displays the zonal rainfall profiles for the three rainfall products. The overall global means are shown in Table 5.
Table 5. Global Land Mean Rainfall Estimates for 1998–2000
Mean Rainfall, mm/month
 Overall, the V6 algorithm is relatively unbiased with respect to the GPCP, but it is far from unbiased on regional scales due to the nonconstant relationship between rainfall rate and scattering. There is an overestimate in equatorial latitudes balanced by an underestimation in northern midlatitudes. The overestimation of equatorial rainfall, which is reduced from that of V5, could be from reasons ranging from thermodynamics [Petersen and Rutledge, 2001], different ice particle size distributions [Bennartz and Petty, 2001] from more vigorous convection, to enhanced evaporation and aerosols over equatorial Africa [McCollum et al., 2000].
 One source of the underestimation in the northern midlatitudes is from the late-summer months, as shown in the zonal plot from July 1998–2000 in Figure 14. Upon inspection of global maps from these months, the severe underestimation occurs for the landfalling Indian monsoon. This is illustrated in the image of global rainfall for July 2000 in Figure 15. This might be expected, as maritime air masses produce less ice and consequently less scattering than storms evolving over land [Nesbitt et al., 2000] producing the same surface rainfall.
 Quantitative results from different cases are shown in Table 6 and there are many items to discuss. On an annual basis, the highest mean monthly estimates are from South America, so the degree of bias over South America will be more related to the global bias than that from other regions, and not surprisingly V6 is relatively unbiased there. The bias is also small over Africa and Australia. Figure 15 illustrates the underestimation of the Indian monsoon, which is reflected in Table 6 for estimates in Asia. North American data were used to illustrate the differences that can occur based on season. There is tremendous overestimation during the summer months, but underestimation during winter. All of these results suggest that regimes with more convective rainfall with substantial cloud ice lead to overestimation, while the more stratiform regimes containing less cloud ice result in underestimation. These results make sense from a physical standpoint.
Table 6. Subdivision of Global Land Rainfall Estimates for 1998–2000
Case Rainfall, mm/month
North America JJA
North America DJF
 Another important point is that all these results were for TRMM data, so the estimates were limited to the latitudes between 37.5°S and 37.5°N. The underestimation for the North American winter months suggests that there are probably more problems outside of the TRMM latitudes. To further investigate these latitudes, we need to use the algorithm with other data, namely, SSM/I.
5. Application to Other Sensors
 Several basic changes were necessary for implementation to SSM/I. First, we chose profiles from the profile database using SSM/I frequencies and resolutions for the radiative transfer calculations. We selected the profiles to match the RR versus TB85V relationships determined from the collocated PR and TMI data. The SSM/I profiles (not shown) are in the vicinity of the TMI profiles of Figure 3 and within the cluster of lines of Figure 4. The only major difference is that the highest RR in the SSM/I profiles is ∼35 mm/h, compared to ∼50 mm/h for TMI due to the lower SSM/I resolution.
 The other basic adaptations to the SSM/I were in the convective predictors. We applied the V6 TMI algorithm using the same convective probability estimation index (1) to SSM/I data and found that the zonal profiles of estimated P(C) were lower than those from the TMI, presumably due to differences in resolution and spatial sampling pattern between the two sensors. With all other factors the same, this would lead to lower RRs.
 It's not surprising that the TMI-derived convective probability estimator (1) does not work for SSM/I, but due to the lack of collocated SSM/I and PR data we could not simply recalibrate the relationship. So we used the best convection estimator, STDEV, from (1) and the quantitative results of Anagnostou and Kummerow . They used surface radars in different climate regimes to estimate convective/stratiform rainfall type, and calculated probabilities of convective, stratiform, and mixed classification for different values of their VI, which has similar magnitude as STDEV. We use the following approximations to their results:
where P(C)ssmi, P(S)ssmi and P(M)ssmi are the probabilities of convective, stratiform, and mixed rainfall classifications. The values for P(M) are around 0.2 over the range of STDEV, as in the work of Anagnostou and Kummerow . The SSM/I rainfall estimate is calculated as:
where the convective and stratiform rain rates are similar to those for the TMI in (3) and the RRmixed rain rates are taken from the mean rain rate versus 85V relationship (SI data and SI-fit profiles in Figure 3) that doesn't distinguish between convective and stratiform.
 One other issue concerning the adaptation from TMI to SSM/I is the 85H no-rain threshold. Using the 270 K TMI threshold, the SSM/I rain area is smaller than the TMI rain area, again due to resolution differences. With it's larger footprint, the SSM/I can observe low rainfall rates at a higher brightness temperature due to the nonraining areas within the footprint, so the no-rain threshold was increased to 280 K as this was found to give similar rain areas as the TMI.
 The resulting comparison between SSM/I and TMI estimates is shown in Figure 16. To illustrate the effect of the time of day sampled, the estimates from the two SSM/I satellites are shown separately. The F13 SSM/I satellite observes more rainfall due to it's local observing times of approximately 6:30 am/pm, closer to the afternoon diurnal maximum in convective zones, in comparison with the approximate 8:30 am/pm F14 observing times. The same trends in SSM/I and TMI-estimated rainfall and convective probabilities are observed, although the SSM/I estimates higher probabilities for high latitudes.
 As with the TMI zonal profiles, the SSM/I performance becomes worse at higher latitudes where there is less convective rainfall. The SSM/I estimates are compared with GPCP estimates for the higher latitudes of North America for January 2002 in Figure 17. The obvious feature in this plot is that the SSM/I estimates no rainfall in the north, while the GPCP estimates precipitation everywhere. This is an important difference of the algorithms: the Global Precipitation Climatology Project includes snowfall, whereas our rainfall algorithm only estimates liquid precipitation. We do not have a method to estimate precipitation over frozen surfaces such as snow, so we make the assumption that if the surface is identified as frozen, there is no liquid precipitation. So our rainfall algorithm becomes less effective as the regimes move from convective to stratiform, and we do not attempt to make estimates over surfaces estimated as frozen; rainfall estimates of zero are given to these areas.
 The AMSR has similar resolution as the TMI, so the RR versus TB calibration for TMI should be applicable to AMSR. However, the 85 GHz sampling strategy is different, so the convective probabilities may differ. It is difficult to predict whether this will bias the rainfall rate estimates; this will require further study when the AMSR data become available. The first official AMSR-E algorithm, submitted to the software team in 2002, is nearly identical to the TMI Version 6 algorithm described here, so the first set of AMSR-E products should have similar results.
6. Discussion of Limitations
 The previous sections have pointed out difficulties of the algorithm and they will be reiterated here. The main difficulty is simply in the microwave remote sensing physics over land; the best proxy for surface rainfall that can be detected is cloud ice, and the brightness temperature depression due to cloud ice is highly variable due to the ice particle size distribution. Bennartz and Petty  estimate this leads to variability ranging over a factor of 6–7 in the amount of microwave scattering for a given surface rain rate.
 In addition to this variability, which may only cause second order (errors in addition to bias) errors, one global calibration results in biases dependent upon many factors. The results presented here concur with McCollum et al. , who combined their results with other validation studies to conclude that microwave land algorithms overestimate in convectively-active regimes, especially those with less water vapor. Conversely, the algorithms underestimate in more stratiform, maritime regimes, simply because there is much less cloud ice in these regimes. Finally, the rainfall is estimated as zero over surfaces estimated as frozen, such as snow or ice. With respect to the high spatial resolution, instantaneous estimates, the TMI algorithm (and probably the associated microwave algorithms) overestimates the light rainfall and overestimates heavy rainfall relative to the PR.
 Other limitations mentioned earlier result from attempting to make high-resolution estimates. The spatial parallax effect discussed by Bauer et al. [2001a] and Hong et al.  makes it difficult to identify rainfall to within several km on the surface based on the scattering signature by the cloud. This also applies in time; there must be some offset between the time the ice is observed in the cloud and the time the rain reaches the ground; this is a topic for future investigations. Due to these many limitations, this algorithm takes a more conservative approach with the goal of providing unbiased estimates on the long-term, global scale, so naturally there relative unbiasedness for the tropics where the most rainfall occurs.
7. Summary, Conclusions, and Future Work
 A new revision of the microwave land rainfall algorithm has been made for the official products of the TMI and AMSR-E instruments, and a similar revision has been made for SSM/I data. The major improvement of this algorithm over previous versions is the elimination of the global high bias with respect to gauges. This is done using coincident TMI and PR data to derive relationships between RR and TB85V for both convective and stratiform rain. In addition, the PR-estimated convective percentage is used to calibrate the relationship between the probability of convection and microwave predictors of convection. The resulting rainfall estimates compare quite well with GPCP estimates, which are considered to be the most unbiased global rainfall estimates as they use high-quality gauge estimates.
 After slight modifications to account for different resolutions and sampling patterns, the algorithm was applied to SSM/I data to produce similar rain estimates. With the launch of AMSR on the Aqua satellite, we will also be able to test the TMI algorithm using AMSR data. The experience with these three microwave instruments will be used in support of the upcoming Global Precipitation Measurement (GPM) mission, so that the data from several different satellites and microwave sensors will be merged into a global product made up of unbiased estimates with respect to one another.
 As mentioned previously, a value of the GPROF framework is that vertical hydrometeor profiles are estimated instead of only rain rates. For version 7, we will use the estimated convective/stratiform characteristics to select profiles so that the latent heating estimates will be improved. Another future advantage of the GPROF framework will be in uncertainty estimation. We plan to create a more diversified library of profiles similar to the observed variability, so that the retrieval uncertainty will be related to the uncertainty in matching profiles to the observed brightness temperatures. So while we are not yet utilizing the many of the opportunities of the GPROF framework in this version, we do have the algorithm in this format for future upgrades.
 The first author was supported by NASA Grant S-87398-F. We are grateful to the three anonymous reviewers for the extremely helpful comments.