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This paper proposes a new quantitative precipitation estimation (QPE) technique to provide accurate rainfall estimates in complex terrain, where conventional QPE has limitations. The operational radar QPE in Taiwan is mainly based on the simplified relationship between radar reflectivity Z and rain rate R [R(Z) relation] and only utilizes the single-point lowest available echo to estimate rain rates, leading to low accuracy in complex terrain. Here, we conduct QPE using deep learning that extracts features from 3D radar reflectivities to address the above issues. Convolutional neural networks (CNN) are used to analyze contoured frequency by altitude diagrams (CFADs) to generate the QPE. CNN models are trained on existing rain gauges in northern and eastern Taiwan with the 3-yr data during 2015–17 and validated and tested using 2018 data. The weights of heavy rains (≥10 mm h−1) are increased in the model loss calculation to handle the unbalanced rainfall data and improve accuracy. Results show that the CNN outperforms the R(Z) relation based on the 2018 rain gauge data. Furthermore, this research proposes methods to conduct 2D gridded QPE at every pixel by blending estimates from various trained CNN models. Verification based on independent rain gauges shows that the CNN QPE solves the underestimation of the R(Z) relation in mountainous areas. Case studies are presented to visualize the results, showing that the CNN QPE generates better small-scale rainfall features and more accurate precipitation information. This deep learning QPE technique may be helpful for the disaster prevention of small-scale flash floods in complex terrain. [ABSTRACT FROM AUTHOR]

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]

Machine learning algorithms are trained on a 10-yr archive of composite weather radar images in the Swiss Alps to nowcast precipitation growth and decay in the next few hours in moving coordinates (Lagrangian frame). The hypothesis of this study is that growth and decay is more predictable in mountainous regions, which represent a potential source of practical predictability by machine learning methods. In this paper, artificial neural networks (ANN) are employed to learn the complex nonlinear dependence relating the growth and decay to the input predictors, which are geographical location, mesoscale motion vectors, freezing level height, and time of the day. The average long-term growth and decay patterns are effectively reproduced by the ANN, which allows exploring their climatology for any combination of predictors. Due to the low intrinsic predictability of growth and decay, its prediction in real time is more challenging, but is substantially improved when adding persistence information to the predictors, more precisely the growth and decay and precipitation intensity in the immediate past. The improvement is considerable in mountainous regions, where, depending on flow direction, the root-mean-square error of ANN predictions can be 20%–30% lower compared with persistence. Because large uncertainty is associated with precipitation forecasting, deterministic machine learning predictions should be coupled with a model for the predictive uncertainty. Therefore, we consider a probabilistic perspective by estimating prediction intervals based on a combination of quantile decision trees and ANNs. The probabilistic framework is an attempt to address the problem of conditional bias, which often characterizes deterministic machine learning predictions obtained by error minimization. [ABSTRACT FROM AUTHOR]

The stability and accuracy of weather radar reflectivity calibration are imperative for quantitative applications, such as rainfall estimation, severe weather monitoring and nowcasting, and assimilation in numerical weather prediction models. Various radar calibration and monitoring techniques have been developed, but only recently have integrated approaches been proposed, that is, using different calibration techniques in combination. In this paper the following three techniques are used: 1) ground clutter monitoring, 2) comparisons with spaceborne radars, and 3) the self-consistency of polarimetric variables. These techniques are applied to a C-band polarimetric radar (CPOL) located in the Australian tropics since 1998. The ground clutter monitoring technique is applied to each radar volumetric scan and provides a means to reliably detect changes in calibration, relative to a baseline. It is remarkably stable to within a standard deviation of 0.1 dB. To obtain an absolute calibration value, CPOL observations are compared to spaceborne radars on board TRMM and GPM using a volume-matching technique. Using an iterative procedure and stable calibration periods identified by the ground echoes technique, we improve the accuracy of this technique to about 1 dB. Finally, we review the self-consistency technique and constrain its assumptions using results from the hybrid TRMM–GPM and ground echo technique. Small changes in the self-consistency parameterization can lead to 5 dB of variation in the reflectivity calibration. We find that the drop-shape model of Brandes et al. with a standard deviation of the canting angle of 12° best matches our dataset. [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]

The Keys Area Microphysics Project (KAMP), conducted as part of NASA’s Fourth Convective and Moisture Experiment (CAMEX-4) in the lower Keys area, deployed a number of ground radars and four arrays of rain gauge and disdrometer clusters. Among the various instruments is an X-band dual-polarization Doppler radar on wheels (XPOL), contributed by the University of Connecticut. XPOL was used to retrieve rainfall rate and raindrop size distribution (DSD) parameters to be used in support of KAMP science objectives. This paper presents the XPOL measurements in KAMP and the algorithm developed for attenuation correction and estimation of DSD model parameters. XPOL observations include the horizontal polarization reflectivity ZH, differential reflectivity ZDR, and differential phase shift ΦDP. Here, ZH and ZDR were determined to be positively biased by 3 and 0.3 dB, respectively. A technique was also applied to filter noise and correct for potential phase folding in ΦDP profiles. The XPOL attenuation correction uses parameterizations that relate the path-integrated specific (differential) attenuation along a radar ray to the filtered-ΦDP (specific attenuation) profile. Attenuation-corrected ZH and specific differential phase shift (derived from filtered ΦDP profiles) data are then used to derive two parameters of the normalized gamma DSD model, that is, intercept (Nw) and mean drop diameter (D0). The third parameter (shape parameter μ) is calculated using a constrained μ–Λ relationship derived from the measured raindrop spectra. The XPOL attenuation correction is evaluated using coincidental nonattenuated reflectivity fields from the Key West Weather Surveillance Radar-1988 Doppler (WSR-88D), while the DSD parameter retrievals are statistically assessed using DSD parameters calculated from the measured raindrop spectra. Statistics show that XPOL DSD parameter estimation is consistent with independent observations. XPOL estimates of water content and Nw are also shown to be consistent with corresponding retrievals from matched ER-2 Doppler radar (EDOP) profiling observations from the 19 September airborne campaign. Results shown in this paper strengthen the applicability of X-band dual-polarization high resolution observations in cloud modeling and precipitation remote sensing studies. [ABSTRACT FROM AUTHOR]

In this two-part paper, a correction for rain attenuation of radar reflectivity (ZH) and differential reflectivity (ZDR) at the X-band wavelength is presented. The correction algorithm that is used is based on the self-consistent method with constraints proposed by Bringi et al., which was originally developed and evaluated for C-band polarimetric radar data. The self-consistent method is modified for the X-band frequency and is applied to radar measurements made with the multiparameter radar at the X-band wavelength (MP-X) operated by the National Research Institute for Earth Science and Disaster Prevention (NIED) in Japan. In this paper, characteristic properties of relations among polarimetric variables, such as AH–KDP, ADP–AH, AH–ZH, and ZDR–ZH, that are required in the correction methodology are presented for the frequency of the MP-X radar (9.375 GHz), based on scattering simulations using drop spectra measured by disdrometers at the surface. The scattering simulations were performed under conditions of three different temperatures and three different relations for drop shapes, in order to consider variability of polarimetric variables for these conditions. For the X-band wavelength, the AH–KDP and ADP–AH relations can be assumed to be nearly linear. The coefficient α of the AH–KDP relation varies over a wide range from 0.139 to 0.335 dB (°)-1 with a mean value of 0.254 dB (°)-1. The coefficient γ of the ADP–AH relation varies from 0.114 to 0.174, with a mean value of 0.139. The exponent b of the AH–ZH relation does not depend on drop shapes and is almost constant for a given temperature (about 0.78 at the temperature of 15°C). The ZDR–ZH relation depends primarily on drop shape, and does not vary with temperature. [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]

In this paper, statistical properties of rainfall are derived from 14 years of Tropical Rainfall Measuring Mission data to optimize the use of flight hours for the upcoming High Altitude Ice Crystals (HAIC)/High Ice Water Content (HIWC) program. This program aims to investigate the convective processes responsible for the generation of the high ice water content that has been recognized as a threat to civil aviation. The probability that convective cells are conducive to HIWC is also further investigated using three years of C-band polarimetric radar data. Further insights into the variability of convective rainfall and favorable conditions for HIWC are also gained using two different methods to characterize the large-scale atmospheric conditions around Darwin, Australia (the Madden-Julian oscillation and the Darwin atmospheric regimes), and the underlying surface type (oceanic vs continental). The main results from the climatology relevant to flight-plan decision making are (i) convective cells conducive to HIWC should be found close to Darwin, (ii) at least 90% of convective cells are conducive to HIWC at 10- and 12-km flight levels, (iii) multiple flights per day in favorable large-scale conditions will be needed so as to utilize the 150 project flight hours, (iv) the largest numbers of HIWC radar pixels are found around 0300 and 1500 local time, and (v) to fulfill the requirement to fly 90 h in oceanic convection and 60 h in or around continental convection, a minimum 'acceptable' size of the convective area has been derived and should serve as a guideline for flight-decision purposes. [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]

Because of its extensive quality control procedures and uniform space-time grid, the NCEP Stage IV merged Weather Surveillance Radar-1988 Doppler (WSR-88D) radar and surface rain gauge dataset is often considered to be the best long-term gridded dataset of precipitation observations covering the contiguous United States. Stage IV accumulations are employed in a variety of applications, and while the WSR-88D systems are well suited for observing heavy rain events that are likely to affect flooding, limitations in surface radar and gauge measurements can result in missed precipitation, especially near topography and in the western United States. This paper compares hourly Stage IV observations of precipitation occurrence to collocated observations from the 94-GHz CloudSat Cloud Profiling Radar, which provides excellent sensitivity to light and frozen precipitation. Statistics from 4 yr of comparisons show that the CloudSat observes precipitation considerably more frequently than the Stage IV dataset, especially in northern states where frozen precipitation is prevalent in the cold season. The skill of Stage IV for precipitation detection is found to decline rapidly when the near-surface air temperature falls below 0°C. As a result, agreement between Stage IV and CloudSat tends to be best in the southeast, where radar coverage is good and moderate-to-heavy liquid precipitation dominates. Stage IV and CloudSat precipitation detection characteristics are documented for each of the individual river forecast centers that contribute to the Stage IV dataset to provide guidance regarding potential sampling biases that may impact hydrologic applications. [ABSTRACT FROM AUTHOR]

This paper presents new methods for rainfall estimation from X-band dual-polarization radar observations along with advanced techniques for quality control, hydrometeor classification, and estimation of specific differential phase. Data collected from the Hydrometeorology Testbed (HMT) in orographic terrain of California are used to demonstrate the methodology. The quality control and hydrometeor classification are specifically developed for X-band applications, which use a 'fuzzy logic' technique constructed from the magnitude of the copolar correlation coefficient and the texture of differential propagation phase. In addition, an improved specific differential phase retrieval and rainfall estimation method are also applied. The specific differential phase estimation is done for both the melting region and rain region, where it uses a conventional filtering method for the melting region and a self-consistency-based method that distributes the total differential phase consistent with the reflectivity factor for the rain region. Based on the specific differential phase, rainfall estimations were computed using data obtained from the NOAA polarimetric X-band radar for hydrometeorology (HYDROX) and evaluated using HMT rain gauge observations. The results show that the methodology works well at capturing the high-frequency rainfall variations for the events analyzed herein and can be useful for mountainous terrain applications. [ABSTRACT FROM AUTHOR]

A novel, rapid-scanning, X-band (3-cm wavelength), polarimetric (RaXPol), mobile radar was developed for severe-weather research. The radar employs a 2.4-m-diameter dual-polarized parabolic dish antenna on a high-speed pedestal capable of rotating the antenna at 180° s−1. The radar can complete a 10-elevation-step volume scan in about 20 s, while maintaining a 180-record-per-second data rate. The transmitter employs a 20-kW peak-power traveling wave tube amplifier that can generate pulse compression and frequency-hopping waveforms. Frequency hopping permits the acquisition of many more independent samples possible than without frequency hopping, making it possible to scan much more rapidly than conventional radars. Standard data products include vertically and horizontally polarized equivalent radar reflectivity factor, Doppler velocity mean and standard deviation, copolar cross-correlation coefficient, and differential phase. This paper describes the radar system and illustrates the capabilities of the radar through selected analyses of data collected in the U.S. central plains during the 2011 spring tornado season. Also noted are opportunities for experimenting with different signal-processing techniques to reduce beam smearing, increase sensitivity, and improve range resolution. [ABSTRACT FROM AUTHOR]

A stochastic method to disaggregate rain rate fields into drop size distribution (DSD) fields is proposed. It is based on a previously presented DSD simulator that has been modified to take into account prescribed block-averaged rain rate values at a coarser scale. The integral quantity used to drive the disaggregation process can be the rain rate, the radar reflectivity, or any variable directly related to the DSD. The proposed method is illustrated and qualitatively evaluated using radar rain rate data provided by MeteoSwiss for two rain events of very contrasted type (stratiform versus convective). The evaluation shows that both types of rainfall are correctly disaggregated, although the general agreement in terms of rain rate distributions, intermittency, and space-time structures is much better for the stratiform case. Possible extensions and generalizations of the technique (e.g., using radar reflectivities at two different frequencies or polarizations to drive the disaggregation process) are discussed at the end of the paper. [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 describes the cubic spline–based operational system for the generation of the Tropical Rainfall Measuring Mission (TRMM) 1-min rain-rate product 2A-56 from tipping-bucket (TB) gauge measurements. A simulated TB gauge from a Joss–Waldvogel disdrometer is employed to evaluate the errors of the TB rain-rate estimation. These errors are very sensitive to the time scale of rain rates. One-minute rain rates suffer substantial errors, especially at low rain rates. When 1-min rain rates are averaged over 4–7-min intervals or longer, the errors dramatically reduce. Estimated lower rain rates are sensitive to the event definition whereas the higher rates are not. The median relative absolute errors are about 22% and 32% for 1-min rain rates higher and lower than 3 mm h-1, respectively. These errors decrease to 5% and 14% when rain rates are used at the 7-min scale. The radar reflectivity–rain-rate distributions drawn from the large amount of 7-min rain rates and radar reflectivity data are mostly insensitive to the event definition. The time shift due to inaccurate clocks can also cause rain-rate estimation errors, which increase with the shifted time length. Finally, some recommendations are proposed for possible improvements of rainfall measurements and rain-rate estimations. [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]

Simultaneous transmission and reception of horizontally and vertically polarized waves is a preferable choice technique for dual-polarization weather radar. One of the consequences of such a choice is possible cross-coupling between orthogonally polarized waves. Cross-coupling depends on depolarizing properties of propagation media, and it is usually negligible in rain because the net mean canting angle of raindrops is close to zero. Snow crystals at the tops of thunderstorm clouds are often canted in the presence of strong electric fields and produce noticeable cross-coupling between radar signals at horizontal and vertical polarizations if both signals are transmitted and received simultaneously. As a result, peculiar-looking radial signatures of differential reflectivity ZDR and differential phase ΦDP are commonly observed in the crystal regions of thunderstorms. The paper presents examples of strong depolarization in oriented crystals from the data collected by the polarimetric prototype of the Weather Surveillance Radar-1988 Doppler (WSR-88D) and a theoretical model that explains the results of measurements. It is shown that the sign and magnitude of the ZDR and ΦDP signatures strongly depend on the orientation of crystals and a system differential phase on transmission. [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]

The instruments on the Tropical Rainfall Measuring Mission (TRMM) satellite have been observing storms as well as rainfall since December 1997. This paper shows the results of a systematic search through seven full years of the TRMM database to find indicators of uncommonly intense storms. These include strong (> 40 dBZ) radar echoes extending to great heights, high lightning flash rates, and very low brightness temperatures at 37 and 85 GHz. These are used as proxy variables, indicating powerful convective updrafts. The main physical principles supporting this assertion involve the effects of such updrafts in producing and lofting large ice particles high into the storm, where TRMM's radar easily detects them near storm top. TRMM's passive microwave radiometer detects the large integrated ice water path as very low brightness temperatures, while high lightning flash rates are a physically related but instrumentally independent indicator. The geographical locations of these very intense convective storms demonstrate strong regional preferences for certain land areas while they are extremely rare over tropical oceans. Favored locations include the south-central United States, southeast South America, and equatorial Africa. Other regions have extreme storms mainly in specific seasons, such as the Sahel, the Indian subcontinent, and northern Australia. Because intense storms are distributed quite differently from rainfall, these maps provide some new metrics for global models, if they are to simulate the type of convection as a component of our climate system. [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]

A procedure for estimating radar rainfall in real time consists of three main steps: 1) the measurement of reflectivity and removal of known sources of errors, 2) the conversion of the reflectivity to a rainfall rate (Z–R conversion), and 3) the adjustment of the mean field bias as assessed using a rain gauge network. Error correction is associated with the first two steps and incorporates removing erroneous measurements and correcting biases in the Z–R conversion. This paper investigates the relative importance of error correction and the mean field bias–adjustment processes. In addition to the correction for ground clutter, the bright band, and hail, the two error correction strategies considered here are 1) a scale transformation function to remove range-dependent bias in measured reflectivity resulting from an increase in observation volume with range, and 2) the classification of storm types to account for the variation in Z–R relationships for convective and stratiform rainfall. The mean field bias is removed using two alternatives: 1) estimation of the bias at each time step based on the sample of observations available, and 2) use of a Kalman filter to estimate the bias under assumptions of a Markovian dependence structure. A 7-month record of radar and rain gauge rainfall for Sydney, Australia, were used in this study. The results show a stepwise decrease in the root-mean-square error (rmse) of radar rainfall with added levels of error correction using either of the two mean field bias–adjustment methods considered in our study. It was found that although the effects of the two error correction strategies were small compared to bias adjustment, they do form an important step of radar-rainfall estimation. [ABSTRACT FROM AUTHOR]

The vertical distribution of Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR)-observed precipitation reflectivity and their mirror image (MI) reflectivity are outlined in this paper. The purpose of this study is to investigate the possibility and the limitation of the MI method, which can be used to estimate rain attenuation. Because the MI returns are attenuated much more greatly than the direct image returns, and also because the MI return is affected by the surface reflection and surface scattering, the MI returns are much smaller and more complex than the direct image (DI) returns. However, because the MI returns might be contaminated by the surface or contributed by bistatic scattering near the surface, there are many strong mirror returns between the surface and below surface at 1 km. The ratio of detectable MI return pixels to detected DI return pixels depends on rain rate, target height, and storm height. In addition, differences also exist between the convective and stratiform rain. The reason for this might be because the difference of the surface cross section and the difference of the storm height between the two types of rainfall. Furthermore, the direct and the mirror returns for a 35-GHz radar are also estimated. The virtue of the MI method of the Ka-band radar may reside in expanding the dynamic range of the MI method from 4–30 to 0.6–30 mm h-1. [ABSTRACT FROM AUTHOR]

In this paper, the attenuation-correction methodology presented in Part I is applied to radar measurements observed by the multiparameter radar at the X-band wavelength (MP-X) of the National Research Institute for Earth Science and Disaster Prevention (NIED), and is evaluated by comparison with scattering simulations using ground-based disdrometer data. Further, effects of attenuation on the estimation of rainfall amounts and drop size distribution parameters are also investigated. The joint variability of the corrected reflectivity and differential reflectivity show good agreement with scattering simulations. In addition, specific attenuation and differential attenuation, which are derived in the correction procedure, show good agreement with scattering simulations. In addition, a composite rainfall-rate algorithm is proposed and evaluated by comparison with eight gauges. The radar-rainfall estimates from the uncorrected (or observed) ZH produce severe underestimation, even at short ranges from the radar and for stratiform rain events. On the contrary, the reflectivity-based rainfall estimates from the attenuation-corrected ZH does not show such severe underestimation and does show better agreement with rain gauge measurements. More accurate rainfall amounts can be obtained from a simple composite algorithm based on specific differential phase KDP, with the R(ZH_cor) estimates being used for low rainfall rates (KDP ≤ 0.3° km-1 or ZH_cor ≤ 35 dBZ). This improvement in accuracy of rainfall estimation based on KDP is a result of the insensitivity of the rainfall algorithm to natural variations of drop size distributions (DSDs). The ZH, ZDR, and KDP data are also used to infer the parameters (median volume diameter D0 and normalized intercept parameter Nw) of a normalized gamma DSD. The retrieval of D0 and Nw from the corrected radar data show good agreement with those from disdrometer data in terms of the respective relative frequency histograms. The results of this study demonstrate that high-quality hydrometeorological information on rain events such as rainfall amounts and DSDs can be derived from X-band polarimetric radars. [ABSTRACT FROM AUTHOR]

In this paper a sea surface radar echo spectral analysis technique to correct for the rainfall velocity error caused by radar-pointing uncertainty is presented. The correction procedure is quite straightforward when the radar is observing a homogeneous rainfall field. When nonuniform beam filling (NUBF) occurs and attenuating frequencies are used, however, additional steps are necessary in order to correctly estimate the antenna-pointing direction. This new technique relies on the application of the combined frequency–time (CFT) algorithm to correct for uneven attenuation effects on the observed sea surface Doppler spectrum. The performance of this correction technique was evaluated by a Monte Carlo simulation of the Doppler precipitation radar backscatter from high-resolution 3D rain fields (either generated by a cloud resolving numerical model or retrieved from airborne radar measurements). The results show that the antenna-pointing-induced error can, indeed, be reduced by the proposed technique in order to achieve 1 m s-1 accuracy on rainfall vertical velocity estimates. [ABSTRACT FROM AUTHOR]

Rain radar measures instantaneous spatial-average rainfall, while conventional rain gauges directly measure point rainfall with low temporal resolution. Thus differences in the resolution of the sensors create difficulties for rain radar validation, especially for spaceborne rain radar. Accordingly, rainfall measurement by microwave link has been proposed for several decades, as it estimates instantaneous path-average rainfall. Thus it is expected that the microwave link rain gauge will overcome, at least partly, the problems in the rain radar validation, toward which a 50-GHz band microwave link [the path-averaged rain gauge (PRG)] was developed that has been in operation since September 2000. In this paper, the authors show the potential of the PRG system by a simple model and rainfall comparison with a disdrometer and a tipping-bucket rain gauge. Differences observed by the instruments were within 15% (within 10% in half of the cases) during actual rain events in 2003. This confirmed that the PRG system displayed good performance as a rain gauge. Finally, the possibility of the PRG system being applied for spaceborne rain radar validation is considered. [ABSTRACT FROM AUTHOR]

The advent of Internet-2 and effective data compression techniques facilitates the economic transmission of base-level radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) network to users in real time. The native radar spherical coordinate system and large volume of data make the radar data processing a nontrivial task, especially when data from several radars are required to produce composite radar products. This paper investigates several approaches to remapping and combining multiple-radar reflectivity fields onto a unified 3D Cartesian grid with high spatial (≤1 km) and temporal (≤5 min) resolutions. The purpose of the study is to find an analysis approach that retains physical characteristics of the raw reflectivity data with minimum smoothing or introduction of analysis artifacts. Moreover, the approach needs to be highly efficient computationally for potential operational applications. The appropriate analysis can provide users with high-resolution reflectivity data that preserve the important features of the raw data, but in a manageable size with the advantage of a Cartesian coordinate system. Various interpolation schemes were evaluated and the results are presented here. It was found that a scheme combining a nearest-neighbor mapping on the range and azimuth plane and a linear interpolation in the elevation direction provides an efficient analysis scheme that retains high-resolution structure comparable to the raw data. A vertical interpolation is suited for analyses of convective-type echoes, while vertical and horizontal interpolations are needed for analyses of stratiform echoes, especially when large vertical reflectivity gradients exist. An automated brightband identification scheme is used to recognize stratiform echoes. When mosaicking multiple radars onto a common grid, a distance-weighted mean scheme can smooth possible discontinuities among radars due to calibration differences and can provide spatially consistent reflectivity mosaics. These schemes are computationally efficient due to their mathematical simplicity. Therefore, the 3D multiradar mosaic scheme can serve as a good candidate for providing high-spatial- and high-temporal-resolution base-level radar data in a Cartesian framework in real time. [ABSTRACT FROM AUTHOR]

This paper presents a method to correct for the range-dependent bias in radar reflectivity that is a result of partial beam filling and of the increase in observation volume with range. The scaling behavior of reflectivity fields as a function of range from the radar was explored in this study. It was found that a simple scaling paradigm was applicable, and a scale transformation function was proposed to ensure uniformity in the probability distributions of reflectivity at both near and far range. The scaling exponents of the power-law transformation function were estimated using a 6-month sequence of reflectivity maps in a Cartesian grid and two sets of instantaneous reflectivity maps in polar coordinates from 1° C-band and 1.6° S-band radars at Sydney, Australia. The averaging process that transforms the instantaneous polar reflectivity into the hourly Cartesian grid data leads to a lower scaling exponent of the hourly Cartesian reflectivity data compared with the instantaneous plan precipitation indicator (PPI) polar data. The scaling exponents for the hourly Cartesian case, the instantaneous polar case using the 1° C-band radar, and the instantaneous polar case using the 1.6° S-band radar data were estimated as 0.024, 0.10, and 0.22, respectively. [ABSTRACT FROM AUTHOR]

The Kwajalein, Marshall Islands, Tropical Rainfall Measuring Mission (TRMM) ground validation radar has provided a multiyear three-dimensional radar dataset at an oceanic site. Extensive rain gauge networks are not feasible over the ocean and, hence, are not available to aid in calibrating the radar or determining a conversion from reflectivity to rain rate. This paper describes methods used to ensure the calibration and allow the computation of quantitative rain maps from the radar data without the aid of rain gauges. Calibration adjustments are made by comparison with the TRMM satelliteborne precipitation radar. The additional steps required to convert the calibrated reflectivity to rain maps are the following: correction for the vertical profile of reflectivity below the lowest elevation angle using climatological convective and stratiform reflectivity profiles; conversion of reflectivity (Z) to rain rate (R) with a relationship based on disdrometer data collected at Kwajalein, and a gap-filling estimate. The time series of rain maps computed by these procedures include low, best, and high estimates to frame the estimated overall uncertainty in the radar rain estimation. The greatest uncertainty of the rain maps lies in the calibration of the radar (±30%). The estimation of the low-altitude vertical profile of reflectivity is also a major uncertainty (±15%). The Z–R and data-gap uncertainties are relatively minor (±5% or less). These uncertainties help to prioritize the issues that need to be addressed to improve quantitative rainfall mapping over the ocean and provide useful bounds when comparing radar-derived rain estimates with other remotely sensed measures of oceanic rain (such as from satellite passive microwave sensors). [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]

The paper presents a rainfall estimation technique based on algorithms that couple, along a radar ray, profiles of horizontal polarization reflectivity (Z[sub H] ), differential reflectivity (Z[sub DR] ), and differential propagation phase shift (Φ[sub DP] ) from X-band polarimetric radar measurements. Based on in situ raindrop size distribution (DSD) data and using a three-parameter “normalized” gamma DSD model, relationships are derived that correct X-band reflectivity profiles for specific and differential attenuation, while simultaneously retrieving variations of the normalized intercept DSD parameter (N[sub w] ). The algorithm employs an iterative scheme to intrinsically account for raindrop oblateness variations from equilibrium condition. The study is facilitated from a field experiment conducted in the period October–November 2001 in Iowa City, Iowa, where observations from X-band dual-polarization mobile radar (XPOL) were collected simultaneously with high-resolution in situ disdrometer and rain-gauge rainfall measurements. The observed rainfall events ranged in intensity from moderate stratiform precipitation to high-intensity (>50 mm h[sup -1] ) convective rain cells. The XPOL measurements were tested for calibration, noise, and physical consistency using corresponding radar parameters derived from coincidentally measured raindrop spectra. Retrievals of N[sub w] from the attenuation correction scheme are shown to be unbiased and consistent with N[sub w] values calculated from independent raindrop spectra. The attenuation correction based only on profiles of reflectivity measurements is shown to diverge significantly from the corresponding polarimetric-based corrections. Several rain retrieval algorithms were investigated using matched pairs of instantaneous high-resolution XPOL observations with rain rates from 3-min-averaged raindrop spectra at close range (∼5 km) and rain-gauge measurements from further ranges (∼10 km). It is shown that combining along-a-ray (corrected Z[sub H] , Z[sub DR] , and specific differential phase shift) values gets the best performance in rainfall estimation with about 40% (53%) relative standard deviation in the radar–disdrometer (radar–gauge) differences. The case-tuned reflectivity–rainfall rate (Z–R) relationship gives about 65% (73%) relative standard deviation for the same differences. The systematic error is shown to be low (∼3% overestimation) and nearly independent of rainfall intensity for the multiparameter algorithm, while for the standard Z–R it varied from 10% underestimation to 3% overestimation. [ABSTRACT FROM AUTHOR]

Radar and rain gauge observations collected in coastal mountains during the California Land-Falling Jets Experiment (CALJET) are used to diagnose the bulk physical properties of rainfall during a wet winter season (January–March 1998). Three rainfall types were clearly distinguishable by differences in their vertical profiles of radar reflectivity and Doppler vertical velocity: nonbright band, bright band, and hybrid (seeder–feeder). The contribution of each rainfall type to the total rainfall observed at the radar site (1841 mm) was determined by a new, objective algorithm. While hybrid rain occurred most often, nonbrightband rain (NBB rain) contributed significantly (28%) to the total. This paper focuses on characterizing NBB rain because of the need to document this key physical process and because of its impact on Weather Surveillance Radar-1988 Doppler (WSR-88D) precipitation surveillance capabilities. NBB rain is a quasi-steady, shallow rain process that does not exhibit a radar bright band, that occurs largely beneath the melting level, and that can produce rain rates exceeding 20 mm h[sup -1] . Composite vertical profiles were produced for NBB rain using 1417 samples and brightband rain using 5061 samples. Although the mean rain rate for each composite was 3.95 mm h[sup -1] , at all altitudes NBB rain had systematically weaker equivalent radar reflectivity (e.g., 20.5 dBZ[sub e] vs 28.5 dBZ[sub e] at 263 m above ground level) and much smaller Doppler vertical fall velocities (e.g., 2.25 m s[sup -1] vs 6.25 m s[sup -1] at 263 m) than did brightband rain. The reflectivity–rain-rate (Z–R) relationship for NBB rain (Z = 1.2R[sup 1.8] ) differs significantly from that of brightband/hybrid rain (Z = 207R[sup 1.1] ). The meteorological context in which NBB rain occurred is described through case studies and seasonal statistics. NBB rain occurred in a wide variety of positions relative to frontal zones within land-falling storms, but... [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]

The Marseilles Hydrometeorological Experiment has been designed to improve rainfall measurement techniques over the space scales and timescales useful for urban hydrology applications. Among other sensors, an X-band light configuration weather radar system was set up near the city. The main objective of the present paper is to test the feasibility of using mountain return to correct rain attenuation effects, an application of the well-known 'surface reference technique' developed for spaceborne radar configurations. The radar siting and scan procedures were defined so as to obtain both (i) rain reflectivity measurements free of ground detection over a large domain and (ii) strong mountain return for the path-integrated attenuation (PIA) estimation in a reduced azimuthal sector. The so-called PIA constraint equation is proposed to relate the measured rain reflectivity profile in one direction to the corresponding mountain PIA. A study of this equation for the 23 September 1993 rain event provides valuable information concerning (i) the parameterization of the radar data processing and (ii) the comparison of various models proposed for the estimation of the mountain and blind-range PIAs. Three attenuation correction algorithms, already proposed in the literature, are then reviewed. Two of them make direct use of the mountain PIA, while the other is a modified version of the well-known Hitschfeld and Bordan algorithm. A consistency test between the various sources of rainfall data available for the considered rain event is presented. First, disdrometer drop size distribution measurements are modeled and used to derive the (Z, k, R) relations required for radar data processing. Then, a validation procedure is used to test the effectiveness of the attenuation correction algorithms by comparison with rain gauge measurements. The performance characteristics of the three algorithms are basically equivalent--a result to be considered with respect to the (...). [ABSTRACT FROM AUTHOR]