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Partial beam blockage (PBB) correction is an indispensable step in weather radar data quality control and subsequent quantitative applications, such as precipitation estimation, especially in urban and/or complex terrain environments. This paper developed a novel PBB correction procedure based on the improved ZPHI method for attenuation correction and regional specific differential propagation phase (KDP)–reflectivity (ZH) relationship derived from in situ raindrop size distribution (DSD) measurements. The practical performance of this PBB correction technique was evaluated through comparing the spatial continuity of reflectivity measurements, the consistency between radar-measured and DSD-derived KDP and ZH relationships, as well as rainfall estimates based on R(ZH) and R(KDP). The results showed that through incorporating attenuation and PBB corrections (i) the spatial continuity of ZH measurements can effectively be enhanced; (ii) the distribution of radar-measured KDP versus ZH is more consistent with the DSD-derived KDP versus ZH; (iii) the measured ZH from a C-band radar in the PBB-affected area becomes more consistent with collocated S-band measurements, particularly in the rainstorm center area where ZH is larger than 30 dBZ; and (iv) rainfall estimates based on R(ZH) in the PBB-affected area are incrementally improved with better spatial continuity and the performance tends to be more comparable with R(KDP). [ABSTRACT FROM AUTHOR]

Compared to traditional single-polarization radar, dual-polarization radar has a number of advantages for quantitative precipitation estimation because more information about the drop size distribution and hydrometeor type can be gleaned. In this paper, an improved dual-polarization rainfall methodology is proposed, which is driven by a region-based hydrometeor classification mechanism. The objective of this study is to incorporate the spatial coherence and self-aggregation of dual-polarization observables in hydrometeor classification and to produce robust rainfall estimates for operational applications. The S-band dual-polarization data collected from the NASA Polarimetric (NPOL) radar during the GPM Iowa Flood Studies (IFloodS) ground validation field campaign are used to demonstrate and evaluate the proposed rainfall algorithm. Results show that the improved rainfall method provides better performance than a few single- and dual-polarization algorithms in previous studies. This paper also investigates the impact of radar beam broadening on various rainfall algorithms. It is found that the radar-based rainfall products are less correlated with ground disdrometer measurements as the distance from the radar increases. [ABSTRACT FROM AUTHOR]

This paper describes the assumptions, equations, and procedures of the RheaG weather generator algorithm (WGA). RheaG was conceived for the generation of robust daily meteorological time series, whether in static or transient climate conditions. Here we analyze its performance in four Iberian locations—Bilbao, Barcelona, Madrid, and Sevilla—with differentiated climate characteristics. To validate the RheaG WGA, we compared observed and generated meteorological time series' statistical properties of precipitation, maximum temperature, and minimum temperature for all four locations. We also compared observed and simulated rain events spell length probabilities in all four locations. Finally, RheaG includes two weather generation procedures: one in which monthly mean values for meteorological variables are unconstrained and one in which they are constrained according to a predefined baseline climate variability. Here, we compare the two weather generation procedures included in RheaG using the observed data from Barcelona. Our results present a high agreement in the statistical properties and the rain spell length probabilities between observed and generated meteorological time series. Our results show that RheaG accurately reproduces seasonal patterns of the observed meteorological time series for all four locations, and it is even able to differentiate two climatic seasons in Bilbao that are also present in the observed data. We find a trade-off between generation procedures in which the unconstrained procedure better reproduces the variability of monthly and yearly precipitation than the constrained one, but the constrained procedure is able to keep the same climatic signal across meteorological time series. Thus, the first procedure is more accurate, but the latter is able to maintain spatial autocorrelation among generated meteorological time series. [ABSTRACT FROM AUTHOR]

A new passive microwave rainfall retrieval algorithm for the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) that relies on an a priori database derived from matchups between TMI brightness temperatures and precipitation radar (PR)-derived surface rain rates has been developed. In addition to implementing a fairly conventional Bayesian approach to precipitation estimation, it exploits a dimensional reduction technique designed to increase the effective sample density in the database and also to improve the detectability of precipitation over problem surface types. The details of the algorithm itself are described in a companion paper. In this paper, the algorithm is validated against independent PR-TMI matchups from calendar year 2002. The validation results are benchmarked against results obtained for the same scenes from the current standard (version 7) 2A12 rainfall product for TRMM. Validation statistics considered include the biases, correlation coefficients, and root-mean-square (RMS) differences for annual precipitation totals on a 1° grid as well as two-threshold Heidke skill scores (HSS) for instantaneous (pixel level) retrievals, determined separately for each of seven surface classes, including ocean, coast, and five other basic land surface types as well as for cold (<275 K) and warm surface skin temperatures. Overall, the University of Wisconsin (UW) algorithm exhibits markedly reduced RMS error and bias in the annual total rainfall and markedly improved instantaneous skill at delineating light rain rates, especially over land and the coast. To ensure that the improved results were not due to both the training and validation data having been taken from the same calendar year, the validation of the UW algorithm is repeated using 2005 matchup data. [ABSTRACT FROM AUTHOR]

This paper presents a novel, simple method to correct reflectivity measurements of weather radars that operate in attenuation-influenced frequency bands using observations from less attenuated radar systems. In recent years radar systems operating in the X-band frequency range have been developed to provide precipitation fields for areas of special interest in high temporal (≤1 min) and spatial (≤250 m) resolution in complement to nationwide radar networks. However, X-band radars are highly influenced by attenuation. C- and S-band radars typically have coarser resolution (250 m-1 km and 5 min) but are less affected by attenuation. Correcting for attenuation effects in simple (non-Doppler) single-polarized X-band radars remains challenging and is often dependent on restriction parameters, for example, those derived from mountain returns. Therefore, these algorithms are applicable only in limited areas. The method proposed here uses measurements from C-band radars and hence can be applied in all regions covered by nationwide C- (or S-) band radar networks. First, a single scan of X-band radar measurements is used exemplary to identify advantages and disadvantages of the novel algorithm compared to a standard single radar algorithm. The performance of the correction algorithms in different types of precipitation is examined in nine case studies. The proposed method provides very promising results for each type of precipitation. Additionally, it is evaluated in a 5-month comparison with Micro Rain Radar (MRR) observations. The bias between uncorrected X-band radar and MRR data is nearly eliminated by the attenuation correction algorithm, and the RMSE is reduced by 20% while the correlation of ~0.9 between both systems remains nearly constant. [ABSTRACT FROM AUTHOR]

This paper describes improvements to the Tropical Rainfall Measurement Mission (TRMM) Microwave Imager (TMI) land rainfall algorithm in version 7 (v7) of the TRMM data products. The correlations between rain rates and TMI 85-GHz brightness temperatures (Tb) for convective and stratiform rain are generated using 7 years of collocated TMI and TRMM precipitation radar (PR) data. The TMI algorithm for estimating the convective ratio of rainfall is also modified. This paper highlights both the improvements in the v7 algorithm and the continuing problems with the land rainfall retrievals. It is demonstrated that the proposed changes to the algorithm significantly lower the overestimation by TMI globally and over large sections of central Africa and South America. Also highlighted are the problems with the 2A12 land algorithm that have not been addressed in the version 7 algorithm, such as large regional and seasonal dependence of biases in the TMI rain estimates, and potential changes to the algorithm to resolve these problems are discussed. [ABSTRACT FROM AUTHOR]

This paper extends the work of Dinku and Anagnostou overland rain retrieval algorithm for use with Special Sensor Microwave Imager (SSM/I) observations. In Dinku and Anagnostou, Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) rainfall estimates were used to calibrate TRMM Microwave Imager (TMI) retrieval. Regional differences in PR-based TMI calibration were investigated by testing the algorithm over four geographic regions, consisting of Africa, northern South America (containing the Amazon basin), the continental United States, and south Asia. In this paper the performance of Dinku and Anagnostou's technique applied on SSM/I data over three of these regions (Africa, Amazon, and South Asia) is demonstrated. Two approaches are investigated for using PR rainfall products to calibrate the algorithm parameters. In the first approach, TMI channels are remapped to the spatial resolutions of the corresponding SSM/I channels; then, PR is used to calibrate the rain retrieval on the remapped TMI data. In the second approach, the PR-based TMI algorithm calibration is performed at a coarser (0.25°) resolution. To assess the quality of algorithm estimates with respect to PR, rainfall fields derived from Dinku and Anagnostou, applied to SSM/I observations (using parameters determined from both approaches), are compared with matched (within ±15 min of the satellites' overpass time difference) PR surface rain rates. Calibration data come from the wet seasons (January–March) of 2000 and 2001. To assess the quality of the estimates with respect to PR, data from a 5-month period (December–April) of 2002, 2003, and 2004 are used. In comparison with the latest version of the Goddard profiling (GPROF) algorithm rain estimates, the current algorithm shows significant improvements in terms of both bias and random error reduction. The paper also shows that rain estimation based on TMI observations is associated with lower error statistics in comparison with the corresponding SSM/I retrievals. [ABSTRACT FROM AUTHOR]

Filtering of nonpredictable scales of precipitation can be used to improve forecast precision (rms). Previous papers have studied the scale dependence of predictability of patterns of instantaneous rainfall rate and of probabilistic forecasts. In this paper, motivated by the often localized, intermittent nature of rainfall, the wavelet transform is used to develop measures of predictability at each scale. These measures are then used to design optimal forecast filters. This method is applied to radar composites of rainfall reflectivity over much of the continental United States and is developed to be appropriate for operational forecasts of rainfall rates and raining areas. For the four precipitation events studied, the average correlation at 4-h lead time was increased from 0.50 for the original nowcasts to 0.62 with forecast filtering. This forecast filtering is incorporated into the McGill Algorithm for Precipitation Nowcasting by Lagrangian Extrapolation (MAPLE), which now includes variational echo tracking, a semi-Lagrangian advection scheme, scale-based filtering, and appropriate rescaling of the filtered nowcast fields. [ABSTRACT FROM AUTHOR]

Polarization diversity radar measurements such as reflectivity factor, differential reflectivity, and differential propagation phase are extensively used in rainfall estimation. Algorithms to estimate rainfall from polarimetric radar measurements are based on a model for the raindrop shape as a function of drop diameter. Most of the current algorithms use an equilibrium shape–size model for raindrops. Variation of the prevailing mean raindrop shapes from an assumed model has a direct impact on the accuracy of radar rainfall estimates. This paper develops composite algorithms to estimate rainfall from polarimetric radar data without an a priori assumption about the specific form of mean raindrop shape–size model such as equilibrium shape model. The accuracy of rainfall estimates is evaluated in the presence of random measurement errors as well as systematic bias errors. The composite algorithms, independent of a prespecified raindrop shape model, were applied to radar parameters simulated from disdrometer data collected over 3 months, and the corresponding rainfall estimates were found to be in good agreement with disdrometer estimates. The composite algorithms were also tested with Colorado State University CHILL radar observations of the 28 July 1997 Fort Collins (Colorado) flood event. The storm total precipitation estimates based on the composite algorithms developed in this paper were in much better agreement with rain gauge estimates in comparison with conventional algorithms. [ABSTRACT FROM AUTHOR]

The National Oceanic and Atmospheric Administration (NOAA) Geostationary Operational Environmental Satellite series R (GOES-R) will greatly expand the ability to observe the earth from geostationary orbit compared to the current-generation GOES, with more than 3 times as many spectral bands and a 75% reduction in footprint size. These enhanced capabilities are beneficial to rainfall rate estimation since they provide sensitivity to cloud-top properties such as phase and particle size that cannot be achieved using the limited channel selection of current GOES. The GOES-R rainfall rate algorithm, which is an infrared-based algorithm calibrated in real time against passive microwave rain rates, has been previously described in an algorithm theoretical basis document (ATBD); this paper describes modifications since the release of the ATBD, including a correction for evaporation of precipitation in dry regions and improved calibration updates. These improvements have been evaluated using a simplified version applicable to current-generation GOES to take advantage of the high-resolution ground validation data routinely available over the conterminous United States. Correcting for subcloud evaporation using relative humidity from a numerical model reduced false alarm rainfall by half and reduced the overall error by 35% for hourly accumulations validated against the National Centers for Environmental Prediction stage IV radar-gauge field; however, the number of missed events did increase slightly. Reducing the size of the calibration regions and increasing the training data requirements improved the consistency of the retrieved rates in time and space and reduced the overall error by an additional 4%. [ABSTRACT FROM AUTHOR]

The Goddard profiling algorithm has evolved from a pseudoparametric algorithm used in the current TRMM operational product (GPROF 2010) to a fully parametric approach used operationally in the GPM era (GPROF 2014). The fully parametric approach uses a Bayesian inversion for all surface types. The algorithm thus abandons rainfall screening procedures and instead uses the full brightness temperature vector to obtain the most likely precipitation state. This paper offers a complete description of the GPROF 2010 and GPROF 2014 algorithms and assesses the sensitivity of the algorithm to assumptions related to channel uncertainty as well as ancillary data. Uncertainties in precipitation are generally less than 1%-2% for realistic assumptions in channel uncertainties. Consistency among different radiometers is extremely good over oceans. Consistency over land is also good if the diurnal cycle is accounted for by sampling GMI product only at the time of day that different sensors operate. While accounting for only a modest amount of the total precipitation, snow-covered surfaces exhibit differences of up to 25% between sensors traceable to the availability of high-frequency (166 and 183 GHz) channels. In general, comparisons against early versions of GPM's Ku-band radar precipitation estimates are fairly consistent but absolute differences will be more carefully evaluated once GPROF 2014 is upgraded to use the full GPM-combined radar-radiometer product for its a priori database. The combined algorithm represents a physically constructed database that is consistent with both the GPM radars and the GMI observations, and thus it is the ideal basis for a Bayesian approach that can be extended to an arbitrary passive microwave sensor. [ABSTRACT FROM AUTHOR]

The predominant effect of rain on altimeter data is through the attenuation it causes of radar pulses propagating through it. Both the ERS-1 and TOPEX/Poseidon have recorded sharp decreases in the observed backscatter sigma[sup0], which have been attributed to rain events. However, the structure of rain cells and the spatial variation of rain rate can be much smaller than the altimeter footprint over which sigma[sup0] is calculated. Here an algorithm is derived to determine the rain rate and its spatial structure. This paper demonstrates that an unbiased estimator can be produced and shows the accuracy of its estimates through simulations of events of known magnitude and how the errors depend upon the accuracy of the assumptions used. Although only yielding information over a very narrow swath, rain structure and rain-rate information derived from altimetry could greatly extend records of precipitation over many areas of the oceans where little or no direct estimates exist. Routine processing of altimeter waveform data offers the prospect of a large dataset of high-resolution sections of precipitation patterns. This may be used to investigate the small-scale spatial structure of storms or in conjunction with other sensors to improve estimates of the global precipitation field. The application to real altimeter waveform data, and its validation against independent estimates of rain rate, is the subject of a forthcoming paper. [ABSTRACT FROM AUTHOR]

A variational algorithm for estimating measurement error covariance and the attenuation of X-band polarimetric radar measurements is described. It concurrently uses both the differential reflectivity ZDR and propagation phase ΦDP. The majority of the current attenuation estimation techniques use only ΦDP. A few of the ΦDP-based methods use ZDR as a constraint for verifying estimated attenuation. In this paper, a detailed observing system simulation experiment was used for evaluating the performance of the variational algorithm. The results were compared with a single-coefficient ΦDP-based method. Retrieved attenuation from the variational method is more accurate than the results from a single coefficient ΦDP-based method. Moreover, the variational method is less sensitive to measurement noise in radar observations. The variational method requires an accurate description of error covariance matrices. Relative weights between measurements and background values (i.e., mean value based on long-term DSD measurements in the variational method) are determined by their respective error covariances. Instead of using ad hoc values, error covariance matrices of background and radar measurement are statistically estimated and their spatial characteristics are studied. The estimated error covariance shows higher values in convective regions than in stratiform regions, as expected. The practical utility of the variational attenuation correction method is demonstrated using radar field measurements from the Taiwan Experimental Atmospheric Mobile-Radar (TEAM-R) during 2008's Southwest Monsoon Experiment/Terrain-Influenced Monsoon Rainfall Experiment (SoWMEX/TiMREX). The accuracy of attenuation-corrected X-band radar measurements is evaluated by comparing them with collocated S-band radar measurements. [ABSTRACT FROM AUTHOR]

This paper describes and evaluates a satellite rainfall estimation technique that combines infrared and lightning information to estimate precipitation in deep convective systems. The algorithm is developed and tested using seven years (2002-08) of TRMM measurements over the southern United States during the warm season. Lightning information is coupled with a modified IR-based convective-stratiform technique (CST) and produces a lightning-enhanced CST (CSTL). Both the CST and CSTL are then applied to the training (2002-04) and independent (2005-08) datasets. In general, this study shows significant improvement over the IR rainfall estimates (rain area, intensity, and volume) by adding lightning information. The CST and CSTL display critical skill in estimating warm-season precipitation and the performance is very stable. The CST can generally identify the heavy (convective) and light rain regions, while CSTL further identifies convective areas that are missed by CST and removes convective cores that are incorrectly defined by CST. Specifically, the CSTL improves the convective cell detection by 5% and reduces the convective false alarm rate by more than 30%. Similarly, CSTL substantially improves the CST in the overall estimate of instantaneous rainfall rates. For example, when compared with passive microwave estimates, CSTL increases the correlation coefficient by 30%, reduces the bias by 50%, and reduces RMSE by 25%. Both CST and CSTL reproduce the rain area and volume fairly accurately over a region, although both techniques show some degree of overestimation relative to radar estimates. [ABSTRACT FROM AUTHOR]

A new approach to passive microwave retrievals of precipitation is described that relies on an objective dimensional reduction procedure to filter, normalize, and decorrelate geophysical background noise while retaining the majority of radiometric information concerning precipitation. The dimensional reduction also sharply increases the effective density of any a priori database used in a Bayesian retrieval scheme. The method is applied to passive microwave data from the Tropical Rainfall Measuring Mission (TRMM), reducing the original nine channels to three 'pseudochannels' that are relatively insensitive to most background variations occurring within each of seven surface classes (one ocean plus six land and coast) for which they are defined. These pseudochannels may be used in any retrieval algorithm, including the current standard Goddard profiling algorithm (GPROF), in place of the original channels. The same methods are also under development for the Global Precipitation Measurement (GPM) Core Observatory Microwave Imager (GMI). Starting with the pseudochannel definitions, a new Bayesian algorithm for retrieving the surface rain rate is described. The algorithm uses an a priori database populated with matchups between the TRMM precipitation radar (PR) and the TRMM Microwave Imager (TMI). The explicit goal of the algorithm is to retrieve the PR-derived best estimate of the surface rain rate in portions of the TMI swath not covered by the PR. A unique feature of the new algorithm is that it provides robust posterior Bayesian probabilities of pixel-averaged rain rate exceeding various thresholds. Validation and intercomparison of the new algorithm is the subject of a companion paper. [ABSTRACT FROM AUTHOR]

This study develops a Gaussian mixture rainfall-rate estimator (GMRE) for polarimetric radar-based rainfall-rate estimation, following a general framework based on the Gaussian mixture model and Bayes least squares estimation for weather radar-based parameter estimations. The advantages of GMRE are 1) it is a minimum variance unbiased estimator; 2) it is a general estimator applicable to different rain regimes in different regions; and 3) it is flexible and may incorporate/exclude different polarimetric radar variables as inputs. This paper also discusses training the GMRE and the sensitivity of performance to mixture number. A large radar and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign is used to evaluate the GMRE approach. Results indicate that the GMRE approach can outperform existing polarimetric rainfall techniques optimized for this JPOLE dataset in terms of bias and root-mean-square error. [ABSTRACT FROM AUTHOR]

Precipitation has a high spatial variability, and thus some modeling applications require high-resolution data (<10 km). Unfortunately, in some cases, such as meteorological forecasts and future regional climate projections, only spatial averages over large areas are available. While some attention has been given to the disaggregation of mean areal precipitation estimates, the computation of a disaggregated field with a realistic spatial structure remains a difficult task. This paper describes the development of a statistical disaggregation model based on Gibbs sampling. The model disaggregates 45.6-km-resolution rainfall fields to grids with pixel sizes ranging from 3.8 to 22.8 km. The model is conceptually simple, as the algorithm is straightforward to compute with only a few parameters to estimate. The rainfall depth at each grid pixel is related to the depths of the neighboring pixels, while the spatial variability is related to the convective available potential energy (CAPE) field. The model is developed using daily rainfall data over a 40 000-km2 area located in the southeastern United States. Four-kilometer-resolution rainfall estimates obtained from NCEP's stage IV analysis were used to estimate the model parameters (2002-04) and as a reference to validate the disaggregated fields (2005/06). Results show that the model accurately simulates rainfall depths and the spatial structure of the observed field. Because the model has low computational requirements, an ensemble of disaggregated data series can be generated. [ABSTRACT FROM AUTHOR]

An improved velocity dealiasing algorithm is developed as an extension of the Next Generation Weather Radar (NEXRAD) dealiasing algorithm. The algorithm described in this paper is evaluated on selected China Next Generation Weather Radar (CINRAD) S-band radar radial velocity observations. This algorithm includes four modules for removing weak signals and determining the starting radial as a prelude to identifying and correcting aliased velocities. The proposed dealiasing algorithm was tested on 14 different weather systems, composed of typhoons, squall lines, and heavy rains. The results show that the algorithm is robust and stable for dealiasing S-band CINRAD radial velocity measurements. The performance levels for the typhoon and heavy rain cases are slightly better than for squall-line cases. [ABSTRACT FROM AUTHOR]

Part I of this series of studies developed procedures to implement the multiscale filtering algorithm for land surface hydrology and performed assimilation experiments with rainfall ensembles from a climate model. However, a most important application of the multiscale technique is to assimilate satellite-based remote sensing observations into a land surface model—and this has not been realized. This paper focuses on enabling the multiscale assimilation system to use remotely sensed precipitation data. The major challenge is the generation of a rainfall ensemble given one satellite rainfall map. An acceptable rainfall ensemble must contain a proper multiscale spatial correlation structure, and each ensemble member presents a realistic rainfall process in both space and time. A pattern-based sampling approach is proposed, in which random samples are drawn from a historical rainfall database according to the pattern of the satellite rainfall and then a cumulative distribution function matching procedure is applied to ensure the proper statistics for the pixel-level rainfall intensity. The assimilation system is applied using Tropical Rainfall Measuring Mission real-time satellite rainfall over the Red–Arkansas River basin. Results show that the ensembles so generated satisfy the requirements for spatial correlation and realism and the multiscale assimilation works reasonably well. A number of limitations also exist in applying this generation method, mainly stemming from the high dimensionality of the problem and the lack of historical records. [ABSTRACT FROM AUTHOR]

A significant scale gap between radar and in situ measurements of rainfall using rain gauges and disdrometers indicates a pressing need for improved knowledge of rainfall variability at the spatial scales below those of today's operational radar rainfall products, that is, ∼1–4 km. Lidar technology has the potential to fulfill this need, but there has been inconsistency in the literature pertaining to quantitative observations of rain using lidar. Several publications have stated that light scattering properties of raindrops could not be correlated with rain rates, while other papers have demonstrated the existence of such relationships. This note provides empirical evidence in support of the latter claim. The authors conducted a simple experiment using a near-horizontal-pointing elastic lidar to observe rain in Iowa City, Iowa, in the fall of 2005. The lidar signal was used to estimate rainfall quantities that were subsequently compared with independent estimates of the same quantities obtained from an optical disdrometer that was placed about 370 m from the lidar, ∼10 m below the lidar beam. To perform the conversion from the raw lidar signal, the authors used an optical geometry-based procedure to estimate optical extinction data. A theoretical relationship between extinction coefficients and rain rates was derived based on a theoretical drop size distribution. The parameters of the relationship were found through a best-fit procedure using lidar and disdrometer data. The results show that the lidar-derived rain rates correspond to those obtained from the optical disdrometer with a root-mean-square difference of 55%. The authors conclude that although a great deal remains to be done to improve the inversion algorithm, lidar measurements of rain are possible and warrant further studies. Lidars deployed in conjunction with disdrometers can provide high spatial (<5 m) and temporal (<1 min disdrometer, ∼1 s lidar) resolution data over a relatively long distance for rainfall measurements (1–2 km in the case of the University of Iowa lidar). [ABSTRACT FROM AUTHOR]

This paper presents a new statistical algorithm to estimate rainfall over the Amazon Basin region using the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). The algorithm relies on empirical relationships derived for different raining-type systems between coincident measurements of surface rainfall rate and 85-GHz polarization-corrected brightness temperature as observed by the precipitation radar (PR) and TMI on board the TRMM satellite. The scheme includes rain/no-rain area delineation (screening) and system-type classification routines for rain retrieval. The algorithm is validated against independent measurements of the TRMM–PR and S-band dual-polarization Doppler radar (S-Pol) surface rainfall data for two different periods. Moreover, the performance of this rainfall estimation technique is evaluated against well-known methods, namely, the TRMM-2A12 [the Goddard profiling algorithm (GPROF)], the Goddard scattering algorithm (GSCAT), and the National Environmental Satellite, Data, and Information Service (NESDIS) algorithms. The proposed algorithm shows a normalized bias of approximately 23% for both PR and S-Pol ground truth datasets and a mean error of 0.244 mm h-1 (PR) and -0.157 mm h-1 (S-Pol). For rain volume estimates using PR as reference, a correlation coefficient of 0.939 and a normalized bias of 0.039 were found. With respect to rainfall distributions and rain area comparisons, the results showed that the formulation proposed is efficient and compatible with the physics and dynamics of the observed systems over the area of interest. The performance of the other algorithms showed that GSCAT presented low normalized bias for rain areas and rain volume [0.346 (PR) and 0.361 (S-Pol)], and GPROF showed rainfall distribution similar to that of the PR and S-Pol but with a bimodal distribution. Last, the five algorithms were evaluated during the TRMM–Large-Scale Biosphere–Atmosphere Experiment in Amazonia (LBA) 1999 field campaign to verify the precipitation characteristics observed during the easterly and westerly Amazon wind flow regimes. The proposed algorithm presented a cumulative rainfall distribution similar to the observations during the easterly regime, but it underestimated for the westerly period for rainfall rates above 5 mm h-1. NESDIS1 overestimated for both wind regimes but presented the best westerly representation. NESDIS2, GSCAT, and GPROF underestimated in both regimes, but GPROF was closer to the observations during the easterly flow. [ABSTRACT FROM AUTHOR]

This paper discusses the basis for a new rainfall estimation method using geostationary infrared and visible data. The precipitation radar on board the Tropical Rainfall Measuring Mission satellite is used to train the algorithm presented (which is the basis of the estimation method) and the further intercomparison. The algorithm uses daily Geostationary Operational Environmental Satellite infrared–visible (IR–VIS) cloud classifications together with radiative and evolution properties of clouds over the life cycle of mesoscale convective systems (MCSs) in different brightness temperature (Tb) ranges. Despite recognition of the importance of the relationship between the life cycle of MCSs and the rainfall rate they produce, this relationship has not previously been quantified precisely. An empirical relationship is found between the characteristics that describe the MCSs’ life cycle and the magnitude of rainfall rate they produce. Numerous earlier studies focus on this subject using cloud-patch or pixel-based techniques; this work combines the two techniques. The algorithm performs reasonably well in the case of convective systems and also for stratiform clouds, although it tends to overestimate rainfall rates. Despite only using satellite information to initialize the algorithm, satisfactory results were obtained relative to the hydroestimator technique, which in addition to the IR information uses extra satellite data such as moisture and orographic corrections. This shows that the use of IR–VIS cloud classification and MCS properties provides a robust basis for creating a future estimation method incorporating humidity Eta field outputs for a moisture correction, digital elevation models combined with low-level moisture advection for an orographic correction, and a nighttime cloud classification. [ABSTRACT FROM AUTHOR]

The Unified Microwave Ocean Retrieval Algorithm (UMORA) simultaneously retrieves sea surface temperature, surface wind speed, columnar water vapor, columnar cloud water, and surface rain rate from a variety of passive microwave radiometers including the Special Sensor Microwave Imager (SSM/I), the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), and the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E). The rain component of UMORA explicitly parameterizes the three physical processes governing passive microwave rain retrievals: the beamfilling effect, cloud and rainwater partitioning, and effective rain layer thickness. Rain retrievals from the previous version of UMORA disagreed among different sensors and were too high in the tropics. These issues have been fixed with more realistic rain column heights and proper modeling of saturation and footprint-resolution effects in the beamfilling correction. The purpose of this paper is to describe the rain algorithm and its recent improvements and to compare UMORA retrievals with Goddard Profiling Algorithm (GPROF) and Global Precipitation Climatology Project (GPCP) rain rates. On average, TMI retrievals from UMORA agree well with GPROF; however, large differences become apparent when the instantaneous retrievals are compared on a pixel-to-pixel basis. The differences are due to fundamental algorithm differences. For example, UMORA generally retrieves higher total liquid water, but GPROF retrieves a higher surface rain rate for a given amount of total liquid water because of differences in microphysical assumptions. Comparison of UMORA SSM/I retrievals with GPCP shows similar spatial patterns, but GPCP has higher global averages because of greater amounts of precipitation in the extratropics. UMORA and GPCP have similar linear trends over the period 1988–2005 with similar spatial patterns. [ABSTRACT FROM AUTHOR]

The spectral latent heating (SLH) algorithm was developed to estimate apparent heat source (Q1) profiles for the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) in Parts I and II of this study. In this paper, the SLH algorithm is used to estimate apparent moisture sink (Q2) profiles. The procedure of Q2 retrieval is the same as that of heating retrieval except for using the Q2 profile lookup tables derived from numerical simulations of tropical cloud systems from the Tropical Ocean and Global Atmosphere (TOGA) Coupled Ocean–Atmosphere Response Experiment (COARE) utilizing a cloud-resolving model (CRM). The Q2 profiles were reconstructed from CRM-simulated parameters with the COARE table and then compared with CRM-simulated “true” Q2 profiles, which were computed directly from the water vapor equation in the model. The consistency check indicates that discrepancies between the SLH-reconstructed and CRM-simulated profiles for Q2, especially at low levels, are larger than those for Q1 and are attributable to moistening for the nonprecipitating region that SLH cannot reconstruct. Nevertheless, the SLH-reconstructed total Q2 profiles are in good agreement with the CRM-simulated ones. The SLH algorithm was applied to PR data, and the results were compared with Q2 profiles derived from the budget study. Although discrepancies between the SLH-retrieved and sounding-based profiles for Q2 for the South China Sea Monsoon Experiment (SCSMEX) are larger than those for heating, key features of the vertical profiles agree well. The SLH algorithm can also estimate differences of Q2 between the western Pacific Ocean and the Atlantic Ocean, consistent with the results from the budget study. [ABSTRACT FROM AUTHOR]

Polarization radar offers the promise of much more accurate rainfall-rate R estimates than are possible from radar reflectivity factor Z alone, not only by better characterization of the drop size distribution, but also by more reliable correction for attenuation and the identification of hail. However, practical attempts to implement retrieval algorithms have been hampered by the difficulty in coping with the inherent noise in the polarization parameters. In this paper, a variational retrieval scheme is described that overcomes these problems by employing a forward model for differential reflectivity Zdr and differential phase shift φdp and iteratively refining the coefficient a in the relationship Z = aRb such that the difference between the forward model and the measurements is minimized in a least squares sense. Two methods are used to ensure that a varies smoothly in both range and azimuth. In range, a is represented by a set of cubic-spline basis functions; in azimuth, the retrieval at one ray is used as a constraint on the next. The result of this smoothing is that the retrieval is tolerant of random errors in Zdr of up to 1 dB and in φdp of up to 5°. Correction for attenuation is achieved simply and effectively by including its effects in the forward model. If hail is present then the forward model is unable to match the observations of Zdr and φdp simultaneously. This enables a first pass of the retrieval to be used to identify the radar pixels that contain hail, followed by a second pass in which the fraction of the Z in those gates that is due to hail is retrieved, this time with the scheme being able to forward-model both Zdr and φdp accurately. The scheme is tested on S-band radar data from southern England in cases of rain, spherical hail, oblate hail, and mixtures of rain and hail. It is found to be robust and stable, even in the presence of differential phase shift on backscatter. [ABSTRACT FROM AUTHOR]

The spectral latent heating (SLH) algorithm was developed for the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) in Part I of this study. The method uses PR information [precipitation-top height (PTH), precipitation rates at the surface and melting level, and rain type] to select heating profiles from lookup tables. Heating-profile lookup tables for the three rain types—convective, shallow stratiform, and anvil rain (deep stratiform with a melting level)—were derived from numerical simulations of tropical cloud systems from the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE) utilizing a cloud-resolving model (CRM). To assess its global application to TRMM PR data, the universality of the lookup tables from the TOGA COARE simulations is examined in this paper. Heating profiles are reconstructed from CRM-simulated parameters (i.e., PTH, precipitation rates at the surface and melting level, and rain type) and are compared with the true CRM-simulated heating profiles, which are computed directly by the model thermodynamic equation. CRM-simulated data from the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE), South China Sea Monsoon Experiment (SCSMEX), and Kwajalein Experiment (KWAJEX) are used as a consistency check. The consistency check reveals discrepancies between the SLH-reconstructed and Goddard Cumulus Ensemble (GCE)-simulated heating above the melting level in the convective region and at the melting level in the stratiform region that are attributable to the TOGA COARE table. Discrepancies in the convective region are due to differences in the vertical distribution of deep convective heating due to the relative importance of liquid and ice water processes, which varies from case to case. Discrepancies in the stratiform region are due to differences in the level separating upper-level heating and lower-level cooling. Based on these results, improvements were made to the SLH algorithm. Convective heating retrieval is now separated into upper-level heating due to ice processes and lower-level heating due to liquid water processes. In the stratiform region, the heating profile is shifted up or down by matching the melting level in the TOGA COARE lookup table with the observed one. Consistency checks indicate the revised SLH algorithm performs much better for both the convective and stratiform components than does the original one. The revised SLH algorithm was applied to PR data, and the results were compared with heating profiles derived diagnostically from SCSMEX sounding data. Key features of the vertical profiles agree well—in particular, the level of maximum heating. The revised SLH algorithm was also applied to PR data for February 1998 and February 1999. The results are compared with heating profiles derived by the convective–stratiform heating (CSH) algorithm. Because observed information on precipitation depth is used in addition to precipitation type and intensity, differences between shallow and deep convection are more distinct in the SLH algorithm in comparison with the CSH algorithm. [ABSTRACT FROM AUTHOR]

Real-time rainfall monitoring in Africa is of great practical importance for operational applications in hydrology and agriculture. Satellite data have been used in this context for many years because of the lack of surface observations. This paper describes an improved artificial neural network algorithm for operational applications. The algorithm combines numerical weather model information with the satellite data. Using this algorithm, daily rainfall estimates were derived for 4 yr of the Ethiopian and Zambian main rainy seasons and were compared with two other algorithms—a multiple linear regression making use of the same information as that of the neural network and a satellite-only method. All algorithms were validated against rain gauge data. Overall, the neural network performs best, but the extent to which it does so depends on the calibration/validation protocol. The advantages of the neural network are most evident when calibration data are numerous and close in space and time to the validation data. This result emphasizes the importance of a real-time calibration system. [ABSTRACT FROM AUTHOR]

To design X-band radar systems as well as evaluate algorithm development, it is useful to have simultaneous X-band observation with and without the impact of path attenuation. One way to develop that dataset is through theoretical models. This paper presents a methodology to generate realistic range profiles of radar variables at attenuating frequencies, such as X band, for rain medium. Fundamental microphysical properties of precipitation, namely, size and shape distribution information, are used to generate realistic profiles of X band starting with S-band observation. Conditioning the simulation from S band maintains the natural distribution of rainfall microphysical parameters. Data from the Colorado State University’s University of Chicago–Illinois State Water Survey (CHILL) radar and the National Center for Atmospheric Research S-band dual-polarization Doppler radar (S-POL) are used to simulate X-band radar variables. Three procedures to simulate the radar variables and sample applications are presented. [ABSTRACT FROM AUTHOR]

This paper uses rainfall estimates retrieved from active and passive microwave data to investigate how spatially and temporally dependent algorithm biases affect the monitoring of the diurnal rainfall cycle. Microwave estimates used in this study are from the Tropical Rainfall Measuring Mission (TRMM) and include the precipitation radar (PR) near-surface (2A25), Goddard Profiling (GPROF) (2A12), and PR–TRMM Microwave Imager (TMI) (2B31) rain rates from the version 5 (v5) 3G68 product. A rainfall maximum is observed early evening over land, while oceans generally show a minimum in rainfall during the morning. Comparisons of annual and seasonal mean hourly rain rates and harmonics at both global and regional scales show significant differences between the algorithms. Relative and absolute biases over land vary according to the time of day. Clearly, these retrieval biases need accounting for, either in the physics of the algorithm or through the provision of accurate error estimates, to avoid erroneous climatic signals and the discrediting of satellite rainfall estimations. [ABSTRACT FROM AUTHOR]

While a large number of methods exist in the literature for retrieving rainfall from passive microwave brightness temperatures, little has been written about the quantitative assessment of the expected uncertainties in these rainfall products at various time and space scales. The latter is the result of two factors: sparse validation sites over most of the world’s oceans, and algorithm sensitivities to rainfall regimes that cause inconsistencies against validation data collected at different locations. To make progress in this area, a simple probabilistic algorithm is developed. The algorithm uses an a priori database constructed from the Tropical Rainfall Measuring Mission (TRMM) radar data coupled with radiative transfer computations. Unlike efforts designed to improve rainfall products, this algorithm takes a step backward in order to focus on uncertainties. In addition to inversion uncertainties, the construction of the algorithm allows errors resulting from incorrect databases, incomplete databases, and time- and space-varying databases to be examined. These are quantified. Results show that the simple algorithm reduces errors introduced by imperfect knowledge of precipitation radar (PR) rain by a factor of 4 relative to an algorithm that is tuned to the PR rainfall. Database completeness does not introduce any additional uncertainty at the global scale, while climatologically distinct space/time domains add approximately 25% uncertainty that cannot be detected by a radiometer alone. Of this value, 20% is attributed to changes in cloud morphology and microphysics, while 5% is a result of changes in the rain/no-rain thresholds. All but 2%–3% of this variability can be accounted for by considering the implicit assumptions in the algorithm. Additional uncertainties introduced by the details of the algorithm formulation are not quantified in this study because of the need for independent measurements that are beyond the scope of this paper. A validation strategy for these errors is outlined. [ABSTRACT FROM AUTHOR]

This paper evaluates and compares the ability of two different Jason-1 dual-frequency altimeter algorithms (referred as Tournadre’s and Quartly’s rain flags, respectively) to detect rain events in order to flag rain-contaminated altimeter range measurements. They are based on departures from a defined relationship between the Ku- and C-band radar cross sections observed in no-rain conditions. The algorithms’ performances were assessed via collocations of these dual-frequency-based estimates with rain rates and a rain–no-rain flag from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). The Jason-1–TMI analysis is built upon a yes–no discrimination, which is helpful in providing good insight into the altimeter rain detection flags’ efficiency through estimations of the percentages of hits, misses, false alarms, and correct negatives when compared with TMI measurements. Tournadre’s rain flag, based on a combination of altimeter and radiometer data, gives the best match with TMI estimates, compared to Quartly’s, and also has a higher sensitivity to low-intensity rainfall. [ABSTRACT FROM AUTHOR]

Recently, two physically based algorithms, the “beta” (β) method and the “constrained-gamma” method, have been proposed for retrieving the governing parameters of the gamma drop size distribution (DSD) from polarimetric radar measurements. The β method treats the drop axis ratio as a variable and computes drop shape and DSD parameters from radar reflectivity (Z), differential reflectivity (ZDR), and specific differential phase (KDP). The constrained-gamma method assumes that the axis ratio relation is fixed and computes DSD parameters from reflectivity, differential reflectivity, and an empirical relation between the DSD slope and shape parameters. In this paper, the two approaches are evaluated by comparing retrieved rain DSD parameters with disdrometer observations and examining derived fields for consistency. Error effects on the β method retrievals are analyzed. The β approach is found to be sensitive to errors in KDP and to be inconsistent with observations. Large retrieved β values are found to associate with large retrieved DSD shape parameters and small median drop diameters. The constrained-gamma DSD method provides reasonable rain DSD retrievals that agree better with disdrometer observations. [ABSTRACT FROM AUTHOR]

Attenuation in rainfall is recognized as one of the most significant limitations in rain-rate estimation from weather radar returns at X- or C-band wavelengths. This paper introduces a radar measurement correction as an inverse problem that accounts for attenuation effects in rainfall. First, a direct theoretical model, relating radar returns at attenuating wavelengths to the rainfall rates between the radar and the point of measurement, is presented. Second, the inverse algorithm used to identify rain-rate estimates from radar returns is described and its application to the attenuation correction is discussed, with the well-known characteristics of the attenuation model (i.e., instability, underdetermination, and nonlinearity) receiving particular attention. Third, a sensitivity analysis is then performed to test the influence of the raindrop size distribution, radar measurement features, and statistical parameters involved in the inverse method. The sensitivity analysis allows for establishing the application conditions of the method. Last, a preliminary evaluation of the method is provided, through simulated radar rainfall measurements and through a limited case study. Various attenuation correction methods are compared with the inverse algorithm. These methods include the standard radar reflectivity-rainfall rate algorithm and two versions of the Hitschfeld-Bordan algorithm. In the simulation exercise, various examples of rainfall field, with different characteristics, are tested. The case study confirms the utility of the proposed method and its ability to provide a robust and stable solution. The method consistently provides better results than the well-known Hitschfeld-Bordan algorithm. [ABSTRACT FROM AUTHOR]

In this paper point gauge measurements are analyzed as part of a ground truth design to validate satellite retrieval algorithms at the field-of-view spatial level (typically about 20 km). Even in the ideal case the ground and satellite measurements are fundamentally different, since the gauge can sample continuously in time but at a discrete point, while a satellite samples an area average but a snapshot in time. The design consists of comparing a sequence of pairs of measurements taken from the ground and from space. Since real rain is patchy, that is, its probability distribution has large nonzero contributions at zero rain rate, the following ground truth designs are proposed. Design 1 uses all pairs. Design 2 uses the pairs only when the field-of-view satellite average has rain. Design 3 uses the pairs only when the gauge has rain. For the nonwhite noise random field having a mixed distribution, the authors evaluate each design theoretically by deriving the ensemble mean and the mean-square error of differences between the two systems. It is found that design 3 has serious disadvantage as a ground truth design due to its large design bias. It is also shown that there is a relationship between the mean-square error of design 1 and design 2. These results generalize those presented recently by Ha and North for the Bernoulli white noise random field. The strategy developed in this study is applied to a real rain rate field. For the Global Atmospheric Program (GARP) Atlantic Tropical Experiment (GATE) data, it is found that by combining 50 data pairs (containing rain) of the satellite to the ground site, the expected error can be reduced to about 10% of the standard deviation of the fluctuations of the system alone. For the less realistic case of a white noise random field, the number of data pairs is about 100. Hence, the use of more realistic fields means that only about half as many pairs are needed to detect a 10% bias. [ABSTRACT FROM AUTHOR]

The objective of this paper is to establish a computationally efficient algorithm making use of the combination of Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and precipitation radar (PR) observations. To set up the TMI algorithm, the retrieval databases developed in Part I served as input for different inversion techniques: multistage regressions and neural networks as well as Bayesian estimators. It was found that both Bayesian and neural network techniques performed equally well against PR estimates if all TMI channels were used. However, not using the 85.5-GHz channels produced consistently better results. This confirms the conclusions from Part I. Generally, regressions performed worse; thus they seem less suited for general application due to the insufficient representation of the nonlinearities of the TB–rain rate relation. It is concluded that the databases represent the most sensitive part of rainfall algorithm development. Sensor combination was carried out by gridding PR estimates of rain liquid water content to 27 km × 44 km horizontal resolution at the center of gravity of the TMI 10.65-GHz channel weighting function. A liquid water dependent database collects common samples over the narrow swath covered by both TMI and PR. Average calibration functions are calculated, dynamically updated along the satellite track, and applied to the full TMI swath. The behavior of the calibration function was relatively stable. The TMI estimates showed a slight underestimation of rainfall at low rain liquid water contents (<0.1 g m[sup -3] ) as well as at very high rainfall intensities (>0.8 g m[sup -3] ) and excellent agreement in between. The biases were found to not depend on beam filling with a strong correlation to rain liquid water for stratiform clouds that may point to melting layer effects. The remaining standard deviations between instantaneous TMI and PR estimates after calibration may be treated as a total retriev... [ABSTRACT FROM AUTHOR]

The algorithm developed in this paper for ground-based polarimetric radars is derived from those used for the spaceborne rain radar of TRMM (Tropical Rainfall Measurement Mission)--the so-called rain profiling algorithms. The characteristic of this type of algorithm is to be nonlocal, that is, the full rain profile along the radar beam is derived from the reflectivity profile. However, to be stable such algorithms require an external constraint. In TRMM, the constraint is the total path attenuation derived from the observation of the ocean surface, which is used as a reference target. In the present algorithm, the external constraint is provided by the differential phase shift phi[subDP] between H and V polarizations. This is the reason for calling this new algorithm ZPHI. The inverse model on which ZPHI is based is a set of three power law relationships between A and Z[sube], K[subDP] and A, and R and A, respectively (A, specific attenuation; Z[sube], equivalent reflectivity; R, rainfall rate). Each of these relationships is parameterized by a 'normalized' intercept parameter of the drop size distribution N[sup*][sub0] (DSD) such as A = a[N[sup*][sub0]][sup1-b] Z[supb][sube]. In ZPHI, (retrieved by the algorithm) is assumed constant along the profile. Nevertheless, because ZPHI authorizes a segmentation of the treatment, it can deal with complex situations where two (or several) types of rain with different N[sup*][sub0] occur along the profile (e.g., as convective and stratiform rain). Also ZPHI includes a correction scheme for the backscattering effects that may affect phi[subDP] at X and C bands. A series of simulations demonstrate the capability of ZPHI to adjust to the variability of the physical characteristics of the rain (variability of N[sup*][sub0] over two decades, and of the shape parameter micro between 0 and 10), N[sup*][sub0] and to operate the rain-rate retrieval with a statistical error similar to that with a 'classic' Z--R relationship (...). [ABSTRACT FROM AUTHOR]

Three algorithm intercomparison experiments have recently been conducted as part of the Global Precipitation Climatology Project with the goal of (a) assessing the skill of current satellite rainfall algorithms, (b) understanding the differences between them, and (c) moving toward improved algorithms. The results of these experiments are summarized and intercompared in this paper. It was found that the skill of satellite rainfall algorithms depends on the regime being analyzed, with algorithms producing very good results in the tropical western Pacific and over Japan and its surrounding waters during summer, but relatively poor rainfall estimates over western Europe during late winter. Monthly rainfall was estimated most accurately by algorithms using geostationary infrared data, but algorithms using polar data [Advanced Very High Resolution Radiometer and Special Sensor Microwave/Imager (SSM/I)] were also able to produce good monthly rainfall estimates when data from two satellites were available. In most eases, SSM/I algorithms showed significantly greater skill than IR-based algorithms in estimating instantaneous rain rates. [ABSTRACT FROM AUTHOR]