Rain Rate Retrieval Research Articles

The Varying Response of Microwave Signatures to Different Types of Overland Rainfall Found over the Korean Peninsula

Abstract The Tropical Rainfall Measuring Mission (TRMM) precipitation radar and ground rain measurements were used to investigate the performance of the TRMM Microwave Imager (TMI) land algorithm. In particular, data from a dense network of rain gauges being operated over the Korean Peninsula were utilized. To retrieve information related to the rainfall rate over land, the TRMM land algorithm relies mainly on brightness temperature TB depression at vertically polarized 85(V) GHz because of scattering by ice particles. It refers to the relationships between 85(V)-GHz TBs and rain rates in its predefined database. By comparing the TMI rain rates with the surface rain gauge and TRMM radar measurements, it was found that there are a variety of relationships between 85(V)-GHz TBs and rainfall rates resulting from the various types of precipitating clouds. The TMI land algorithm, therefore, could not resolve some raining clouds such as warm clouds as well as cold clouds having small amounts of ice particles above the rain layer. The rainfall amounts for those missed rain events are significant. As a result, rain rates produced by the land algorithm show systematic biases, which are a function of raining cloud types. Meanwhile, it is found that the 37-GHz TMI channels contain additional information on surface rain; the uncertainties in retrieving rain rates from TBs at TMI frequencies can be reduced up to 11% if all polarized 37- and 85-GHz TBs are used as predictors.

A Rain-Rate Retrieval Algorithm for Attenuated Radar Measurements

Abstract A dynamic regularization scheme for rain-rate retrievals from attenuated radar measurements is presented. Most regularization techniques, including the optimal estimation method, use the state-space parameters to regularize the problem, which will always lead to a bias in the solution. To avoid this problem the authors introduce an evolutionary regularization technique, which is based on the spatial derivative of the measured reflectivity profile and allows for a bias-free global solution. The regularization strength is determined by the quadratic eigenvalue solution using the regularized total least squares method. With the new method, the authors perform a retrieval of rain-rate profiles from simulated measurements of a nadir-pointing W-band (94 GHz) radar, in a configuration similar to the cloud radar employed on CloudSat. The simulations assume that multiple scattering is negligible and only liquid hydrometeors are taken into account. The authors compare the results of this method with the outcome of an optimal estimation method and demonstrate that their method is superior in terms of reliability, correlation coefficient, and dispersion to the optimal estimation method for layers experiencing high values of attenuation; therefore, the a priori bias typical for optimal estimation solutions is avoided.

Evidence of Rainfall Signatures on X-Band Synthetic Aperture Radar Imagery Over Land

Five spaceborne X-band synthetic aperture radars (X-SARs) are nowadays operating, and several more will be launched in the coming years. These X-SAR sensors, able to image the Earth's surface at metric resolution, may provide a unique opportunity to measure rainfall over land with spatial resolution of about a few hundred meters due to the moving-target degradation effects. This work is devoted to experimentally demonstrate this X-SAR capability, which can also be exploited to correct synthetic aperture radar (SAR) imagery for rainfall attenuation effects. Several case studies, selected from TerraSAR-X (TSX) overpasses over Europe and the southern U.S. in 2008, are qualitatively analyzed in terms of rainfall signatures. Visual validation of these rainfall SAR signatures is carried out by using available data from ground-based weather radars. A detailed data analysis for the case study of Hurricane ¿Gustav¿ on September 2, 2008, is carried out to assess a quantitative correlation among X-SAR response and near-surface precipitation rain rate. Two simplified empirical inversion algorithms, based on statistical regression and probability matching, are developed to retrieve rain rate from TSX cross-track ground-range measurements. The TSX-retrieved rain fields are compared to those estimated from the Next Generation Weather Radar (NEXRAD) in Mobile (Alabama, U.S.), showing a root-mean-square error less than 15 mm/h and a correlation of about 0.7.

SHAPE SLOPE PARAMETER DISTRIBUTION MODELLING OF ELECTROMAGNETIC SCATTERING BY RAIN DROPS

Gamma model parameters using 2nd, 3rd and 4th moments are calculated from the drop size data of Singapore. The gamma model is simplifled into two parameter model by flnding a relation between the shape and slope parameters, and ⁄. Due to the poor correlation found between and ⁄, the drop size data is flltered based on their rain rates before a good correlation between the two parameters can be found. The -⁄ relations are then fltted for the difierent ranges of rain rate flltering. Scatter plots of and ⁄ are plotted with constant median volume diameter (D0) lines. The -⁄ relations for the difierent rain types for the tropical island of Singapore are proposed and compared with the -⁄ relations from three other countries of difierent climatic zones. T-Matrix calculations are performed to flnd the polarimetric variables at S-band by using the gamma DSD calculated from the Singapore's drop size data. The calculated difierential re∞ectivity and horizontal re∞ectivity are used along with the best -⁄ relations to flnd the gamma model parameters. The retrieved rain rate using polarimetric variables is compared with the distrometer's measured rain rate. Results show a good agreement between the retrieved rain rate and the measured rain rate. Therefore, the proposed shape slope relationship is found to be suitable for rain rate retrieval.

SEVIRI rainfall retrieval and validation using weather radar observations

This paper presents and validates a new algorithm to detect precipitating clouds and estimate rain rates from cloud physical properties retrieved from the Spinning Enhanced Visible and Infrared Imager (SEVIRI). The precipitation properties (PP) algorithm uses information on cloud condensed water path (CWP), particle effective radius, and cloud thermodynamic phase to detect precipitating clouds, while information on CWP and cloud top height is used to estimate rain rates. An independent data set of weather radar data is used to determine the optimum settings of the PP algorithm and calibrated it. For a 2‐month period, the ability of SEVIRI to discriminate precipitating from nonprecipitating clouds is evaluated using weather radar over the Netherlands. In addition, weather radar and rain gauge observations are used to validate the SEVIRI retrievals of rain rate and accumulated rainfall across the entire study area and period. During the observation period, the spatial extents of precipitation over the study area from SEVIRI and weather radar are highly correlated (correlation ≈ 0.90), while weaker correlations (correlation ≈ 0.63) are found between the spatially mean rain rate retrievals from these instruments. The combined use of information on CWP, cloud thermodynamic phase, and particle size for the detection of precipitation results in an increase in explained variance (∼10%) and decrease in false alarms (∼15%), as compared to detection methods that are solely based on a threshold CWP. At a pixel level, the SEVIRI retrievals have an acceptable accuracy (bias) of about 0.1 mm h−1 and a precision (standard error) of about 0.8 mm h−1. It is argued that parts of the differences are caused by collocation errors and parallax shifts in the SEVIRI data and by irregularities in the weather radar data. In future studies we intend to exploit the observations of the European weather radar network Operational Programme for the Exchange of Weather Radar Information (OPERA) and extend this study to the entirety of Europe.

Rainfall retrieval over Indian land and oceanic regions from SSM/I microwave data

Present study focuses on the estimation of rainfall over Indian land and oceanic regions from the Special Sensor Microwave/Imager (SSM/I) on the Defense Meteorological Satellite Program (DMSP) F-13. Based on the measurements at 19.35, 22.235 and 85.5 GHz channels of SSM/I Satellite, scattering index (SI) has been developed for the Indian land and oceanic regions separately. These scattering indices were co-located against rainfall from Precipitation Radar (PR) onboard Tropical Rainfall Measuring Mission (TRMM) to develop a new regional relationship between the SI and the rain rate for the Indian land and oceanic regions. A non-linear fit between the rain rate and the SI is established for rain measurement. In order to have confidence in our method, we have also estimated rainfall using the global rainfall and scattering index relationship developed by Ferraro and Marks [Ferraro, R.R., Marks, G.F. The development of SSM/I rain rate retrieval algorithms using ground based radar measurements. J. Atmos. Ocean. Technol. 12, 755–770, 1995]. The validation with the rain-gauge shows that the present scheme is able to retrieve rainfall with better accuracy than that of Ferraro and Marks (1995). Further intercomparison with TRMM-2A12 and validation with rain-gauges rainfall showed that the present algorithm is able to retrieve the rainfall with reasonably good accuracy.

An Algorithm for Real-Time Rainfall Rate Estimation by Using Polarimetric Radar: RIME

Abstract Polarimetric radars provide measurements that describe the shape and dimensions of hydrometeors and are unaffected by calibration, attenuation, and the presence of ice. These measurements can potentially lead to a more detailed description of hydrometeors and to an improvement in quantitative rainfall rate estimation. The authors present an algorithm that exploits polarimetric measures for rain-rate estimation and investigate its application in a real-time framework by using measurements from the C-band polarimetric radar at Monte Settepani in Savona, Italy. It is based on a flowchart decision tree that allows the use of the best rain-rate retrieval algorithm, depending on the value of polarimetric variables. The methodology was applied to a real-time framework for more than a year, and the results were presented for all the significant events observed during the test period. To evaluate the performance of the algorithm, a comparison was made with rain gauge observation from a dense regional network. The performances of the algorithm were compared with those obtained by standard operational Z–R formulations to evaluate the benefit of this approach for operational applications.

Quantitative Precipitation Estimation over Ocean Using Bayesian Approach from Microwave Observations during the Typhoon Season

We have developed a new Bayesian approach to retrieve oceanic rain rate from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), with an emphasis on typhoon cases in the West Pacific. Retrieved rain rates are validated with measurements of rain gauges located on Japanese islands. To demonstrate improvement, retrievals are also compared with those from the TRMM/Precipitation Radar (PR), the Goddard Profiling Algorithm (GPROF), and a multi-channel linear regression statistical method (MLRS). We have found that qualitatively, all methods retrieved similar horizontal distributions in terms of locations of eyes and rain bands of typhoons. Quantitatively, our new Bayesian retrievals have the best linearity and the smallest root mean square (RMS) error against rain gauge data for 16 typhoon overpasses in 2004. The correlation coefficient and RMS of our retrievals are 0.95 and ~2 mm hr-1, respectively. In particular, at heavy rain rates, our Bayesian retrievals outperform those retrieved from GPROF and MLRS. Overall, the new Bayesian approach accurately retrieves surface rain rate for typhoon cases. Accurate rain rate estimates from this method can be assimilated in models to improve forecast and prevent potential damages in Taiwan during typhoon seasons.

An Evaluation of Over-Land Rain Rate Estimates by the GSMaP and GPROF Algorithms: The Role of Lower-Frequency Channels

This paper presents an evaluation of over-land rain-rate estimates by both the Global Satellite Mapping of Precipitation (GSMaP) algorithm and the standard (GPROF) algorithm for the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), by comparing them with estimates by the standard algorithm for TRMM Precipitation Radar (PR). This study has the following advantages over previous studies: (1) the errors in rain-rate estimates are decomposed into those caused by rain/no-rain classification and those caused by rain-rate retrieval, (2) the quantitative effects of bright band height (BBH) and land surface physical temperature on retrieval are evaluated; and (3) the role of lower frequency channels (37.0 GHz and lower) for retrieval is investigated. GSMaP yields monthly average and zonal mean rain-rate estimates close to those estimated by the standard algorithm for PR, as it refers to a database produced with PR data. However, GSMaP and GPROF overestimate (underestimate) rain rates for tall (shallow), stratiform (convective), and evening (morning) rainfall. Dependence on storm height (SH) is unavoidable as long as the algorithm relies on the scattering signal caused by solid precipitation for higher frequency channels (85.5 GHz). Lower frequency channels are secondarily used in some algorithms to mitigate the above bias characteristics to some degree. In GSMaP Version 4.7, the severe overestimation seen in GSMaP Version 4.5 when SH is higher than 10 km is mitigated by using 37.0 GHz observations as a scattering signal. The following are indicated for stratiform rainfall with a bright band (SRBB). While the rain-rate estimates are negatively dependent on BBH in GSMaP, the use of 21.3 GHz and 10.7 GHz observations resulted in the cancellation of the dependence on the BBH in GPROF. Although lower-frequency observations are subject to variation in land surface physical temperature, no significant effects of land surface physical temperature on the rain-rate estimates were observed in this study. To improve over-land rain-rate estimates, it is important to make the most effective use of lower-frequency observations.

An Interpretation of TRMM Radar Observations of Shallow Convection with a Rain Cell Model

Observations of shallow, isolated convection from the Precipitation Radar (PR) aboard the Tropical Rainfall Measuring Mission (TRMM) observatory were compared with simulations from a rain cell model to examine effects of sub-resolution scale convection on space-borne radar observations. A large sample of shallow isolated convection was obtained from PR data over the central Pacific Intertropical Convergence Zone. Storm top heights, ranged from 1000 to 3750 m, with a mode at 1500 m. A secondary classification was made to identify 3 classes with progressively smaller spatial scales: groups of rainy fields-of-view (FOVs), rainy FOVs with one neighboring rainy FOV, and solitary rainy FOVs. Smaller spatial scales were associated with shallower storms and lower radar reflectivity (dBZ) values. The solitary class was the focus of the modeling comparison. The first objective of the modeling exercise was to explore the possibility that information on the horizontal scale and rain rate intensity of sub-resolution shallow convection could be extracted from the PR observations by finding an optimal fit between simulated and observed dBZ distributions. The height and diameter of simulated rain cells were linked by assuming an average aspect ratio of one. Simulated and observed probability distributions of dBZ were compared for two modes of rain cell variability: a fixed aspect ratio with variable cell dBZ, and a fixed cell dBZ with variable aspect ratio. Both modes resulted in excellent comparisons with observed distributions. The second modeling objective was to compare rain rates from the simulated “ground truth” and simulated “retrieved” rain rates, and to determine the effective sampling area of the modeled FOV. In general, simulated retrieved rain rates had a positive bias, as expected from the non-linear Z-R relation. However, more complex patterns of potential negative biases were evident, depending on the size and intensity of modeled rain cells.

Comparison of TRMM Rain-Rate Retrievals in Tropical Cyclones

Rain rates from four algorithms are examined in tropical cyclones (TCs). Old and new versions of the Remote Sensing Systems (RSS) rain estimates (RSS V03 and RSS V04) are compared with the standard version 6 TMI 2A12 and PR 2A25 algorithms, after averaging those down to the 0.25° scale used by RSS. RSS V03 produces more rain by a factor of two than the others, frequently assigning rain rates up to 25 mm h-1 (which is an internal limit for that product). Among the three current algorithms, PR 2A25 produces the most rain when averaged over a 0 to 100 km radius in hurricanes. This results from PR 2A25 assigning much higher grid-scale rain rates (up to 100 mm h-1) in the small fraction of grid boxes having heaviest rain. TMI 2A12 has the least rain, assigning moderate rain rates (5 mm h-1) to more grid boxes than the other products. The differences between algorithms are greatest for the inner regions of Category 3 to 5 hurricanes. In weaker TCs, or further away from the TC center, the three current algorithms tend to agree on mean rain rate. However, they arrive at these areal means from completely different distributions of grid-scale rain rates. PR 2A25 gets a greater fraction of its rain from grid boxes having high rain rates, with little contribution from the light and moderate rain rates. RSS V04 gets much of its rain from grid boxes with 10 mm h-1. TMI 2A12 gets less rain around 10 mm h-1, but balances that with greater contributions both from the occasional higher (15 mm h-1) and more common lower (5 mm h-1) rain rates. At the 0.25° scale, the TMI-based products are better correlated with each other than with PR 2A25. The RSS products are better correlated with PR 2A25 than TMI 2A12 is. All the correlations increase when more zero-rain or light-rain grid boxes are included (i.e., the weaker TCs or greater distances from the center).

Advanced Rain/No-Rain Classification Methods for Microwave Radiometer Observations over Land

Abstract Seto et al. developed rain/no-rain classification (RNC) methods over land for the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). In this study, the methods are modified for application to other microwave radiometers. The previous methods match TMI observations with TRMM precipitation radar (PR) observations, classify the TMI pixels into rain pixels and no-rain pixels, and then statistically summarize the observed brightness temperature at the no-rain pixels into a land surface brightness temperature database. In the modified methods, the probability distribution of brightness temperature under no-rain conditions is derived from unclassified TMI pixels without the use of PR. A test with the TMI shows that the modified (PR independent) methods are better than the RNC method developed for the Goddard profiling algorithm (GPROF; the standard algorithm for the TMI) while they are slightly poorer than corresponding previous (PR dependent) methods. M2d, one of the PR-independent methods, is applied to observations from the Advanced Microwave Scanning Radiometer for Earth Observing Satellite (AMSR-E), is evaluated for a matchup case with PR, and is evaluated for 1 yr with a rain gauge dataset in Japan. M2d is incorporated into a retrieval algorithm developed by the Global Satellite Mapping of Precipitation project to be applied for the AMSR-E. In latitudes above 30°N, the rain-rate retrieval is compared with a rain gauge dataset by the Global Precipitation Climatology Center. Without a snow mask, a large amount of false rainfall due to snow contamination occurs. Therefore, a simple snow mask using the 23.8-GHz channel is applied and the threshold of the mask is optimized. Between 30° and 60°N, the optimized snow mask forces the miss of an estimated 10% of the total rainfall.

Characterization of warm season convective systems over US in terms of Cloud to Ground lightning, cloud kinematics, and precipitation

Convective systems are tracked for two summer months over the continental USA and their properties at different stages of life are investigated in terms of Cloud to Ground (CG) lightning flashes, cloud kinematics, and precipitation. The study employs lightning data from the National Lightning Detection Network (NLDN) along with 1/2-hourly satellite Infrared observations, and hourly rainfall accumulation fields from the nationwide WSR-88D radar network. Results show strong dependence of the amount of CG lightning flashes with the stage of the storm's life cycle. The highest number of CG lightning flashes and highest area expansion rates are also seen to be during the growth stage of the systems. The stronger the lightning density, or cloud top area expansion rate, of the storms at their initiation stage is the longer is shown to be their life duration. The average rainfall yield per flash in the growing, mature and dissipation stages of storms with duration greater than 4 h is 4.7, 12.5 and 8.5 10 7 kg, respectively. The temporal evolution of the storms' area and CG flash rate are shown to correlate well with the evolution of rainfall parameters, such as storm's rainfall yield (m 3), conditional mean rainfall rate, and the fraction of rain area. The consideration of the kinematics and CG lightning flashes of convective systems and the knowledge of their life cycle stage demonstrate a potential for drawing information useful in rain rate retrievals and their variability.

An Artificial-Neural-Network-Based Integrated Regional Model for Rain Retrieval Over Land and Ocean

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> An integrated regional model is proposed for rain-rate retrievals over land/ocean from the brightness temperature (Tb) values of the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI). The polarization-corrected temperature <formula formulatype="inline"><tex>$(\hbox{PCT}_{85})$</tex></formula> calculated from the 85.5-GHz channels is also considered as one of the inputs along with the nine channel Tb values. This model is applicable over the region between <formula formulatype="inline"><tex>$0^{\circ}{-}30^{\circ}\ \hbox{N}$</tex> </formula> and <formula formulatype="inline"><tex>$65^{\circ}{-}100^{\circ}\ \hbox{E}$</tex></formula>. For this purpose, an artificial neural network is utilized. The collocated precipitation radar (PR) near-surface rain rates as given by a 2A25 data product is considered as a target value. The methodology consists of the separation of land and ocean pixels, the separation of stratiform and convective pixels over land/ocean, and the selection of important features (inputs) for the multilayer perceptron network by the feature selection technique for each group. For the separation of land/ocean pixels, the Tb values of the 10.65-GHz vertical channel are utilized. The <formula formulatype="inline"> <tex>$\hbox{PCT}_{85}$</tex></formula> values are utilized to separate the stratiform and convective pixels both over land and ocean. The rain retrieval from the developed model is validated with TRMM PR. Overall result shows the better agreement of the model-retrieved rain rate with the PR observation compared to the TMI (2A12) rain rate particularly over land. The rain retrieved from the developed model is further validated with Doppler weather radar. A reasonably good agreement is observed between these two estimations. </para>

Development of precipitation retrievals at millimeter and sub‐millimeter wavelengths for geostationary satellites

We study the potential of millimeter and sub‐millimeter wavelengths for precipitation retrieval from geostationary sensors based on mesoscale cloud modeling and radiative transfer computation. Hydrometeor profiles simulated with the Meso‐NH cloud resolving model for five European midlatitude situations are used to compute the brightness temperatures at frequencies from 23.8 to 875 GHz with the Atmospheric Transmission at Microwaves (ATM). Performances of both rain detection and rain rate retrieval are analyzed for different frequency sets, over ocean and land separately, and compared to the user requirements. The performances of a frequency set such as that already planned for geostationary satellites (with channels in the O2 lines at 50, 118, and 424 GHz, and in the H2O lines at 183, 325, 380 GHz) satisfy the requirements for Numerical Weather Prediction and NoWCasting in terms of rain detection as well as for rain rate retrieval above 1 mm/h. Suppressing the 50 GHz O2 channels does not seriously degrade the performances, except for rain rate below 1 mm/h, and, in addition, limits the spatial resolution problem from a geostationary orbit. Adding the thermal infrared observations has a limited impact. The retrieval of other hydrometeor quantities (cloud, ice) is also tested as well as the possibility to retrieve rain and the other hydrometeor profiles. These theoretical results are evaluated at close‐to‐millimeter wavelengths with coincident AMSU‐B and radar observations (BALTEX and CAMRa). The results are degraded with respect to the theory, as expected, but are consistent with the observations.

Water vapor, cloud liquid water paths, and rain rates over northern high latitude open seas

Data from the Special Sensor Microwave Imager (SSMI; years 1987–2006), Advanced Microwave Scanning Radiometer, and a surface‐based radiometer at Barrow, Alaska are examined for insights into the behavior of water vapor, cloud liquid water and rainrates over the northern high latitude seas. We evaluated two separate sets of retrievals, and achieved the best results through combining one that contained explicit monthly mean sea ice fractions with the Wentz V6 water vapor path (WVP), cloud liquid water path (LWP), and rainrate (RR) retrievals. The water vapor path retrieval shows no sensitivity to a proxy for sub‐pixel sea ice presence, while the liquid water path retrievals are sensitive to sea ice presence during summertime but otherwise the Wentz internal sea‐ice screening appears effective. The rainrate retrieval is highly sensitive to any sea ice during all seasons. The seasonal cycle and 1987–2006 time trends are examined. The WVP annual cycle has an amplitude of ∼1 cm at all locations, approximately double a broad winter minimum, with a July maximum phasing that is consistent with a continental influence. Little change occurs between January and April in WVP and LWP. The springtime LWP increase usually occurs in tandem with the WVP increase and slightly lags the falltime WVP decrease. The maximum lag occurs over the northern Pacific, where the maximum LWP occurs in August, one month later than over the northern Atlantic, and is correlated to an August precipitation maximum. The strongest SSMI‐derived trend is an increase in wintertime moisture south of Greenland, with wintertime LWP increases in the Labrador Sea. North of the Bering Strait, where much of the recent summer and autumn sea ice loss has occurred, the autumn WVP and LWP increased from 1989 to 2001 with a subsequent LWP decrease in recent years. The recent decline appears linked to a decrease in cyclone activity. Winter and spring LWP increases from 2002 to the present are noted in the surface‐based data set from Barrow, Alaska. Over the Barents Sea, where much of the recent winter sea ice loss has occurred, winter WVP and LWP have increased over the past decade. A comparison to National Center for Atmospheric Research Community Atmospheric Model Version 3.5 values finds modeled WVPs are slightly underestimated but the amplitude of the annual cycle is similar to that observed. Modeled winter LWPs slightly exceed those measured while the modeled summer LWPs exceed by a factor of two those observed (which are more likely to be positively biased also). The modeled rainrates are similar to retrieved values in the north Pacific, and exceed retrieved values by approximately a factor of 2 in the northeast Atlantic.

Retrieval of Raindrop Size Distribution from Simulated Dual-Frequency Radar Measurements

Abstract Observations of raindrop size distributions (DSDs) have validated the use of three-parameter distribution functions in representing the observed spectra. However, dual-frequency radar measurements are limited to retrieving two independent parameters of the DSD, thus requiring a constraint on a three-parameter distribution. In this study, disdrometer observations from a variety of climate regions are employed to develop constraints on the gamma distribution that are optimized for dual-frequency radar rainfall retrievals. These observations are composited by reflectivity, and then gamma parameters are fit to the composites. The results show considerable variability in shape parameter between regions and within a region at different reflectivities. Most notable is that oceanic regions exhibit maxima in shape parameter at 13.6-GHz reflectivities between 40 and 50 dBZ, in contrast to continental regions. The shape parameter and slope parameter of all composite DSDs are poorly correlated. Thus, constraints of a constant shape parameter or shape parameter–slope parameter relationship are inadequate to represent the observed variability. However, the shape and slope parameters are highly correlated at a given reflectivity. Constraints of a fixed shape parameter and relationships between a shape parameter m and slope parameter Λ, both of which are given as functions of 13.6-GHz reflectivity, are applied to retrieve rain rate, liquid water content, and mean mass diameter from the composites. The m–Λ relationships perform best at high reflectivity (dBZ13.6 &amp;gt; 35), whereas the fixed shape parameter generally results in lower error at medium and low reflectivities (dBZ13.6 &amp;lt; 35). All calculations have been made under the assumption that the reflectivity measurements have been corrected for attenuation.

A Method to Estimate Rain Rate over Tropical Oceans with the TRMM Microwave Imager Radiometer

In this preliminary study, we have developed a method to retrieve rain rate on a scale of 20 km from the brightness temperatures measured by the TRMM microwave imaging radiometer (TMI) over the tropical oceans, using the estimates of rain rate RPR made by the TRMM Precipitation Radar (PR) as a benchmark. The purpose of this study is to demonstrate with a limited amount of PR and TMI data the feasibility of improving the TRMM operational rain retrieval method V6 over the tropical oceans. This study utilizes the TMI-measured brightness temperatures T19H, T37H, and T85H of horizontally polarized microwave radiances at 19, 37 and 85 GHz, respectively, to deduce a salient non-linear parameter ξ that is highly correlated with RPR over the oceans. Two additional parameters generated from TMI data, ω and γ, add significant amounts of rain information to our retrieval method. The parameter &omega is based on T19V and T21V, the brightness temperatures measured by TMI for vertically polarized microwave radiances at 19 and 21 GHz respectively. This parameter takes advantage of the independent information contained in T21V. The parameter Γ depends on the average horizontal gradient of the TMI-measured T85V (vertically-polarized 85 GHz radiance) in a 20 km footprint. Initially our TMI rain retrieval algorithm is tuned with the help of RPR for seven cases of 2° × 3° area over tropical oceans. Then it is applied to 13 other independent tropical ocean cases. For these independent cases, the rain rate R* estimated from our method correlates better with RPR than the rain rate RV6 retrieved from the present TMI V6 operational retrieval method. On a 20 km scale, the correlation between RPR and R* is better by about 6% compared to that between RPR and RV6. The slope of the regression line between the rain rates RPR and RV6 is about 0.5. With respect to RPR, the rain rate RV6 retrieved from operational V6 method tends to underestimate high rain rates and overestimate low rain rates. The slope of the regression line between RPR and the rain rate R* retrieved with our method is about 0.8, another indication of the improvement of R* over RV6. In addition, the area average rain rate on a scale of 2° × 3° deduced from our method agrees better with that of PR by about 7%.

How TRMM precipitation radar and microwave imager retrieved rain rates differ

Analysis of the collocated rain retrievals from Tropical Rainfall Measuring Mission's precipitation radar and microwave radiometer reveals that their difference depends on the intensity and the type of rain – the radiometer‐derived rain rates vary from higher to lower than the radar‐derived ones as rain rate or convective fraction increases. To better understand how this difference occurs, the relations between the two leading EOFs (Empirical Orthogonal Functions) of the observed brightness temperatures and the radiometer‐ or radar‐derived rain rates were examined for convective, mixed and non‐convective rain categories. In all types of rain, the two EOFs respond to the variation of the radiometer‐ and radar‐derived rain rates in a similar fashion in low rain rates, while they respond quite differently in high rain rates.

Impact of Uncertainty in the Drop Size Distribution on Oceanic Rainfall Retrievals From Passive Microwave Observations

The variability of the drop size distribution (DSD) is one of the factors that must be considered in understanding the uncertainties in the retrieval of oceanic precipitation from passive microwave observations. Here, we have used observations from the Precipitation Radar on the Tropical Rainfall Measuring Mission spacecraft to infer the relationship between the DSD and the rain rate and the variability in this relationship. The impact on passive microwave rain rate retrievals varies with frequency and rain rate. The total uncertainty for a given pixel can be slightly larger than 10% at the low end (ca. 10 GHz) of frequencies commonly used for this purpose and smaller at higher frequencies (up to 37 GHz). Since the error is not totally random, averaging many pixels, as in a monthly rainfall total, should roughly halve this uncertainty. The uncertainty may be lower at rain rates less than about 30 mm/h, but the lack of sensitivity of the surface reference technique to low rain rates makes it impossible to tell from the present data set.