Rain Rate Algorithm Research Articles

Modified Monthly Oceanic Rain-Rate Algorithm to Account for TRMM Boost

We provide a modified algorithm for computing Tropical Rainfall Measuring Mission (TRMM) monthly oceanic rain rates (3A11) for TRMM Microwave Imager data using the Microwave Emission Brightness Temperature Histogram (METH) technique developed by Wilheit Shin and Chiu examined changes associated with TRMM boost by adjusting the microwave brightness temperature ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> ) for the postboost data to match the preboost data. We computed a new relation between <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> and rain rate ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> ) for the postboost characteristics using the same radiative transfer model of Wilheit and modified the algorithm by providing two <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> relations for the preboost and postboost era, respectively. The modified algorithm is applied to TRMM data without <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> adjustment. Preliminary results show a significant improvement over the unmodified algorithm in terms of biases and linear trends. Their differences on the application of the METH technique to other microwave data for climate-scale rainfall are discussed.

Preliminary evaluation of polarimetric parameters from a new dual-polarization C-band weather radar in an alpine region

Abstract. The first operational weather radar with dual polarization capabilities was recently installed in Austria. The use of polarimetric radar variables rises several expectations: an increased accuracy of the rain rate estimation compared to standard Z-R relationships, a reliable use of attenuation correction methods, and finally hydrometeor classification. In this study the polarimetric variables of precipitation events are investigated and the operational quality of the parameters is discussed. For the new weather radar also several polarimetric rain rate estimators, which are based on the horizontal polarization radar reflectivity, ZH, the differential reflectivity, ZDR, and the specific differential propagation phase shift, KDP, have been tested. The rain rate estimators are further combined with an attenuation correction scheme. A comparison between radar and rain gauge indicates that ZDR based rain rate algorithms show an improvement over the traditional Z-R estimate. KDP based estimates do not provide reliable results, mainly due to the fact, that the observed KDP parameters are quite noisy. Furthermore the observed rain rates are moderate, where KDP is less significant than in heavy rain.

Superposition of the Neyman–Scott Rectangular Pulses Model and the Poisson White Noise Model for the Representation of Tropical Rain Rates

Abstract A point process model for tropical rain rates is developed through the derivation of the third moment expression for a combined point process model. The model is a superposition of a Neyman–Scott rectangular pulse model and a Poisson white noise process model. The model is scalable in the temporal dimension. The derivation of the third moment for this model allows for the inclusion of the skewness parameter, which is necessary to adequately represent rainfall intensity. Analysis of the model fit to tropical tipping-bucket rain gauge data ranging in temporal scale from five min to one day indicates that it can adequately produce synthesized rainfall having the statistical characteristics of rain rate over the range of scales tested. Of special interest is the model’s capability to accurately preserve the probability of extreme tropical rain rates at different scales. In addition to various hydrological applications, the model also has many potential uses in the field of meteorology, such as the study and development of radar rain rate algorithms for the tropics, which need to parameterize attenuation due to heavy rain.

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate from Microwave Observations

Abstract A new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) over the ocean is presented, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain-rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes’s theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance the understanding of theoretical benefits of the Bayesian approach, sensitivity analyses have been conducted based on two synthetic datasets for which the “true” conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism, but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak owing to saturation effects. It is also suggested that both the choice of the estimators and the prior information are crucial to the retrieval. In addition, the performance of the Bayesian algorithm herein is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry. Part II: Evaluation of Estimates Using Independent Data

Abstract Rainfall rate estimates from spaceborne microwave radiometers are generally accepted as reliable by a majority of the atmospheric science community. One of the Tropical Rainfall Measuring Mission (TRMM) facility rain-rate algorithms is based upon passive microwave observations from the TRMM Microwave Imager (TMI). In Part I of this series, improvements of the TMI algorithm that are required to introduce latent heating as an additional algorithm product are described. Here, estimates of surface rain rate, convective proportion, and latent heating are evaluated using independent ground-based estimates and satellite products. Instantaneous, 0.5°-resolution estimates of surface rain rate over ocean from the improved TMI algorithm are well correlated with independent radar estimates (r ∼0.88 over the Tropics), but bias reduction is the most significant improvement over earlier algorithms. The bias reduction is attributed to the greater breadth of cloud-resolving model simulations that support the improved algorithm and the more consistent and specific convective/stratiform rain separation method utilized. The bias of monthly 2.5°-resolution estimates is similarly reduced, with comparable correlations to radar estimates. Although the amount of independent latent heating data is limited, TMI-estimated latent heating profiles compare favorably with instantaneous estimates based upon dual-Doppler radar observations, and time series of surface rain-rate and heating profiles are generally consistent with those derived from rawinsonde analyses. Still, some biases in profile shape are evident, and these may be resolved with (a) additional contextual information brought to the estimation problem and/or (b) physically consistent and representative databases supporting the algorithm. A model of the random error in instantaneous 0.5°-resolution rain-rate estimates appears to be consistent with the levels of error determined from TMI comparisons with collocated radar. Error model modifications for nonraining situations will be required, however. Sampling error represents only a portion of the total error in monthly 2.5°-resolution TMI estimates; the remaining error is attributed to random and systematic algorithm errors arising from the physical inconsistency and/or nonrepresentativeness of cloud-resolving-model-simulated profiles that support the algorithm.

The Improved AMSU Rain-Rate Algorithm and Its Evaluation for a Cool Season Event in the Western United States

Abstract Rain-rate retrievals from passive microwave sensors are useful for a number of applications related to weather forecasting. For example, in the United States, such estimates are useful for offshore rainfall systems approaching land and in regions where the Weather Surveillance Radar-1988 Doppler (WSR-88D) network is inadequate. Improvements have been made to the rain-rate retrieval from the Advanced Microwave Sounding Unit (AMSU) on board the National Oceanic and Atmospheric Administration (NOAA) Polar Orbiting Environmental Satellites (POESs). The new features of the improved rain-rate algorithm include a two-stream correction of the satellite brightness temperatures at 89 and 150 GHz, cloud- and rain-type classification for better retrieval of rain rate, and removal of the two ad hoc thresholds in the ice water path (IWP) and effective diameter (De) retrieval where the scattering signals are very small. In this paper, the new algorithm has been compared to the previous NOAA operational algorithm. In particular, the better utilization of the measurements at and above 150 GHz is shown to produce improved sensitivity to light rainfall associated with winter season storm systems. This improvement is demonstrated through a wintertime case study over southern California during February 2003.

Current thrusts on TRMM and SSM/I based modeling studies on heavy rains and flooding episodes

Our research group at the Florida State University has been using a multianalysis/multimodel approach on real time for the short-range prediction of heavy rains over the tropical belt. The methodology for the construction of the superensemble forecasts follows our recent publications on this topic. Recent improvements in multianalysis/multimodel superensemble forecasts of precipitation have led to much higher skills compared to the member models. This suggested that some useful guidance for regional floods arising from heavy rains might be possible from this approach. These are 1 to 5 day forecasts where the equitable threat scores for rainfall totals in excess of 25 mm/day have been two to three times better for the superensemble compared to the best member model. This study includes forecasts using multimodels from a number of global operational centers and a multianalysis component, which is based on the FSU global spectral model that utilizes TRMM and SSM/I data sets and a number of rain rate algorithms. The differences in the analyses arise from the use of these different rain rate algorithms within physical initialization, which in turn, produces distinct differences among divergence, heating, moisture, and rain rate descriptions. A total of 11 models, of which 5 represent global operational models and 6 represent multianalysis forecasts from the FSU model initialized by different rain rate algorithms, are embedded in the multianalysis/multimodel system studied here. The TRMM and the SSM/I rainfall data sets derived from microwave instruments are key to these marked improvements of rainfall forecasts. The statistical biases of the models are determined from a multiple linear regression of these forecasts against a ‘best’ rainfall analysis field, which is based on a TRMM and SSM/I data set that utilizes rain rate algorithms recently developed at NASA Goddard. We also display a sequence of computations that illustrate a “walk-through” of a heavy rain episode. This study specifically deals with recent flood episodes over India, Bangladesh, the United States of America, Mozambique/Madagascar and the Philippines. These results compare the performance of the superensemble against the best and lowest performing model, the ensemble mean and the control experiment (that does not use any TRMM or SSM/I data sets). Overall these results show great promise over the current best models.

Real-Time Multianalysis–Multimodel Superensemble Forecasts of Precipitation Using TRMM and SSM/I Products

This paper addresses real-time precipitation forecasts from a multianalysis‐multimodel superensemble. The methodology for the construction of the superensemble forecasts follows previous recent publications on this topic. This study includes forecasts from multimodels of a number of global operational centers. A multianalysis component based on the Florida State University (FSU) global spectral model that utilizes TRMM and SSM/I datasets and a number of rain-rate algorithms is also included. The difference in the analysis arises from the use of these rain rates within physical initialization that produces distinct differences among these components in the divergence, heating, moisture, and rain-rate descriptions. A total of 11 models, of which 5 represent global operational models and 6 represent multianalysis forecasts from the FSU model initialized by different rain-rate algorithms, are included in the multianalysis‐multimodel system studied here. In this paper, ‘‘multimodel’’ refers to different models whose forecasts are being assimilated for the construction of the superensemble. ‘‘Multianalysis’’ refers to different initial analysis contributing to forecasts from the same model. The term superensemble is being used here to denote the bias-corrected forecasts based on the products derived from the multimodel and the multianalysis. The training period is covered by nearly 120 forecast experiments prior to 1 January 2000 for each of the multimodels. These are all 3-day forecasts. The statistical bias of the models is determined from multiple linear regression of these forecasts against a ‘‘best’’ rainfall analysis field that is based on TRMM and SSM/I datasets and using the rain-rate algorithms recently developed at NASA Goddard Space Flight Center. This paper discusses the results of real-time rainfall forecasts based on this system. The main results of this study are that the multianalysis‐multimodel superensemble has a much higher skill than the participating member models. The skill of this system is higher than those of the ensemble mean that assigns a weight of 1.0 to all including the poorer models and the ensemble mean of bias-removed individual models. The selective weights for the entire multianalysis‐multimodel superensemble forecast system make it superior to individual models and the above mean representations. The skill of precipitation forecasts is addressed in several ways. The skill of the superensemble-based rain rates is shown to be higher than the following: (a) individual model’s skills with and without physical initialization, (b) skill of the ensemble mean, and (c) skill of the ensemble mean of individually biasremoved models. The equitable-threat scores at many thresholds of rain are also examined for the various models and noted that for days 1‐3 of forecasts, the superensemble-based forecasts do have the highest skills. The training phase is a major component of the superensemble. Issues on optimizing the number of training days is addressed by examining training with days of high forecast skill versus training with low forecast skill, and training with the best available rain-rate datasets versus those from poor representations of rain. Finally the usefulness of superensemble forecasts of rain for providing possible guidance for flood events such as the one over Mozambique during February 2000 is shown.

Numerical weather prediction over the Eastern Caribbean using Florida State University (FSU) global and regional spectral models and multi-model/multi-analysis super-ensemble

A month-long short-range numerical weather prediction experiment using the Florida State University’s (FSU) global and regional models and the multi-model/multi-analysis super-ensemble over the Eastern Caribbean domain is presented in this paper. The paper also investigates weather prediction capabilities of FSU global and regional models by examining the root mean square errors (RMSE) for the wind and precipitation fields. Super-ensemble forecasting, a new statistical approach to weather forecasting, is used over this domain. Here, forecasts from a number of numerical models provide the input and statistical combinations of these forecasts produce the super-ensemble forecast. A similar approach is used for the precipitation field where one model using different rain rate algorithms is used to generate different model outputs. The results show that the super-ensemble method produces forecasts that are superior to those obtained from the ensemble members.

A combined microwave/infrared rain rate algorithm

A combined Microwave/Infrared Rain Rate Algorithm (MIRRA) is presented. Historically, infrared algorithms have benefited from excellent temporal sampling, but the relationship between cloud top temperature and surface rain rate is very indirect. Alternatively, passive microwave algorithms are typically more physically direct and accurate, yet the associated sensors do not provide favourable temporal sampling for daily and monthly rainfall amounts. MIRRA is an attempt to utilize the strengths of these two broad approaches to rain rate measurement from space. The algorithm has been tested and developed using data from the TOGA-COARE campaign, with shipboard radar rain rate estimates used as truth. Results indicate enhanced performance in bias, correlation and rms error for MIRRA compared with other infrared and combined algorithms at the instantaneous scale, while retaining the good performance of geostationary algorithms at daily and monthly scales.

Improving Tropical Precipitation Forecasts from a Multianalysis Superensemble

Abstract This paper utilizes forecasts from a multianalysis system to construct a superensemble of precipitation forecasts. This method partitions the computations into two time lines. The first of those is a control (or a training) period and the second is a forecast period. The multianalysis is derived from a physical initialization–based data assimilation of “observed rainfall rates.” The different members of the reanalysis are produced by using different rain-rate algorithms for physical initialization. The basic rain-rate datasets are derived from satellites’ microwave radiometers, including those from the Tropical Rainfall Measuring Mission (TRMM) satellites and the Special Sensor Microwave Imager (SSM/I) data from three current U.S. Air Force Defense Meteorological Satellite Program (DMSP) satellites. During the training period, 155 experiments were conducted to find the relationship between forecasts from the multianalysis dataset and the best “observed” estimates of daily rainfall totals. This re...

An intercomparison of hurricane forecasts using SSM/I and TRMM rain rate algorithm(s)

Three different Special Sensor Microwave Imager (SSM/I) rain rate algorithms are evaluated as a means of improving both the physical initialization and the hurricane forecast output of the Florida State University Global Spectral Model (FSU GSM). These SSM/I rain rate algorithms are known as Cal/Val, NESDIS, and GPROF 4.0. In addition the Tropical Rainfall Measuring Mission (TRMM) TMI – 2A12 rain rate algorithm is validated, and its impact on FSU GSM hurricane forecasts is also studied.

Rain rate estimation from nadir-looking TOPEX/POSEIDON microwave radiometer (TMR) for correction of radar altimetric measurements

Atmospheric liquid water, particularly in the form of rain, produces anomalies in the radar altimetric range measurements. Such features are observed as sudden large changes in radar backscatter as a means of identification. To quantify the rain that radar altimetric pulses encounter, the instantaneous rain estimation capability of the nadir looking multichannel microwave radiometer onboard the TOPEX/POSEIDON satellite is explored. The three frequency (18, 21, and 37 GHz) nadir looking TOPEX microwave radiometer (TMR) brightness temperature data are colocated with the special sensor microwave/imager (SSM/I) rain rates to find a new rain rate algorithm by regression over the Indian Sea. Among the colocated data on different spatial and temporal scales, the most restrictive criteria (<0.1/spl deg/, <1 h apart) produce the best correlations between the SSM/I estimated rain rates and the TMR brightness temperatures. The TMR measurements, colocated with SSM/I, thus presents a nontraditional usage of nadir viewing microwave radiometer data for estimation of instantaneous rainfall for correction of the radar altimetric measurements over the oceans. This equation is further used to generate monthwise-averaged global rain rate maps for the year 1993. Typical rain rate maps for two contrasting seasons for the months of January and July 1993, during the northeast and southwest monsoon, respectively, are compared with similar maps of the SSM/I rain rate. It is found that all the major features of global rainfall are picked up accurately and reproduced by the TMR-based algorithm. The mean rainfall rate thus derived (totaling a month) also is analyzed with some simultaneous atmospheric and oceanic processes in mind, which couple each other through rainfall.

An Optimal Area Approach to Intercomparing Polarimetric Radar Rain-Rate Algorithms with Gauge Data

An optimal area method is described that is used as a basis for comparing KDP-, (KDP, ZDR)-, and Zh-based estimates of rain rates with gauge-measured rain rates. The location and dimensions of an elliptically shaped optimal area within the radar scan area surrounding the gauge are determined objectively via an rms error minimization of the difference between the KDP-based radar estimate and gauge data and via use of the spatial structure of the rms difference field itself. Four convective events were analyzed with rain rates in the range of 20–120 mm h−1, with two of the events containing marble-sized hail. The analysis shows that excellent results could be achieved using KDP-based rain-rate estimators.

An Automated Neural Network Cloud Classifier for Use over Land and Ocean Surfaces

Abstract An automated neural network cloud classifier that functions over both land and ocean backgrounds is presented. Motivated by the development of a combined visible, infrared, and microwave rain-rate retrieval algorithm for use with data from the 1997 Tropical Rainfall Measuring Mission (TRMM), an automated cloud classification technique is sought to discern different types of clouds and, hence, different types of precipitating systems from Advanced Very High Resolution Radiometer (AVHRR) type imagery. When this technique is applied to TRMM visible–infrared imagery, it will allow the choice of a passive microwave rain-rate algorithm, which performs well for the observed precipitation type, theoretically increasing accuracy at the instantaneous level when compared with the use of any single microwave algorithm. A neural network classifier, selected because of the strengths of neural networks with respect to within-class variability and nonnormal cluster distributions, is developed, trained, and teste...

An intercomparison of oceanic precipitation frequencies from 10 special sensor microwave/imager rain rate algorithms and shipboard present weather reports

Oceanic precipitation frequencies produced by 10 satellite microwave algorithms submitted to the first Precipitation Intercomparison Project are compared with frequencies derived from ship reports. It is found that most algorithms yield distributions in reasonable agreement with the ship‐derived climatology at low latitudes, but the majority fail to register more than very infrequent (∼1%) precipitation at latitudes poleward of about 45°, in contrast to the much larger (∼10%) frequencies indicated by surface reports. Only two algorithms, both of which were based on the brightness temperature transformations of Petty [1994a, b], appear to approximately reproduce ship‐observed precipitation frequency patterns at both tropical and high latitudes. All 10 algorithms, however, appear to have difficulty producing realistic precipitation frequencies in the “dry” subtropical trade belts. This problem is tentatively attributed to the unique physical characteristics of precipitation in those regions.

A non‐linear algorithm for estimating three‐hourly rain rates over Amazonia from GOES/VISSR observations

Abstract Recent work has suggested that infrared window brightness temperatures can be regressed in a non‐linear formulation to estimate three‐hourly rain rates. We describe an Infrared Power law Rain rate (IPR) algorithm, which is based on such a formulation. Because it is continuous, IPR preserves the structure present in colder regions of an infrared image. In a test over Amazonia, IPR performed as well as three other infrared rain estimation techniques.

A Satellite Observational and Numerical Study of Precipitation Characteristics in Western North Atlantic Tropical Cyclones

Special Sensor Microwave/Imager (SSM/I) observations were used to examine the spatial and temporal changes of the precipitation characteristics of tropical cyclones. SSM/I observations were also combined with the results of a tropical cyclone numerical model to examine the role of inner-core diabatic heating in subsequent intensity changes of tropical cyclones. Included in the SSM/I observations were rainfall characteristics of 18 named western North Atlantic tropical cyclones between 1987 and 1989. The SSM/I rain-rate algorithm that employed the 85-GHz channel provided an analysis of the rain-rate distribution in greater detail. However, the SSM/I algorithm underestimated the rain rates when compared to in situ techniques but appeared to be comparable to the rain rates obtained from other satellite-borne passive microwave radiometers. The analysis of SSM/I observations found that more intense systems had higher rain rates, more latent heat release, and a greater contribution from heavier rain to the total tropical cyclone rainfall. In addition, regions with the heaviest rain rates were found near the center of the most intense tropical cyclones. Observational analysis from SSM/I also revealed that the greatest rain rates in the inner-core regions were found in the right half of fast-moving cyclones, while the heaviest rain rates in slow-moving tropical cyclones were found in the forward half. The combination of SSM/I observations and an interpretation of numerical model simulations revealed that the correlation between changes in the inner core diabetic heating and the subsequent intensity became greater as the tropical cyclones became more intense.

Physical initialization using SSM/I rain rates

Following our recent study on physical initialization for tropical prediction using rain rates based on outgoing long-wave radiation, the present study demonstrates a major improvement from the use of microwave radiance based rain rates. A rain rate algorithm is used on the data from a special sensor microwave instrument (SSM/1). The initialization, as before, uses a reverse surface similarity theory, a reverse cumulus parameterization algorithm and a bisection method to minimize the difference between satellite-based and the model-based outgoing long-wave radiation. These are invoked within a preforecast Newtonian relaxation phase of the initialization. These tests are carried out with a high-resolution global spectral model. The impact of the initialization on forecast is tested for a complex triple typhoon scenario over the Western Pacific Ocean during September 1987. A major impact from the inclusion of the SSM/I is demonstrated. Also addressed are the spin-up issues related to the typhoon structure and the improved water budget from the physical initialization. DOI: 10.1034/j.1600-0870.1993.t01-3-00001.x

Measuring the Global Distribution of Intense Convection over Land with Passive Microwave Radiometry

The global distribution of intense convective activity over land is shown to be measurable with satellite passive-microwave methods through a comparison of an empirical rain rate algorithm with a climatology of thunderstorm days for the months of June-August. With the 18 and 37 GHz channels of the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR), the strong volume scattering effects of precipitation can be measured. Even though a single frequency (37 GHz) is responsive to the scattering signature, two frequencies are needed to remove most of the effect that variations in thermometric temperatures and soil moisture have on the brightness temperatures. Because snow cover is also a volume scatterer of microwave energy at these microwavelengths, a discrimination procedure involving four of the SMMR channels is employed to separate the rain and snow classes, based upon their differences in average thermometric temperature.