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- Author or Editor: Witold F. Krajewski x
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Abstract
A statistical framework for climatological Z–R parameter estimation is developed and simulation experiments are conducted to examine sampling properties of the estimators. Both parametric and nonparametric models are considered. For parametric models, it is shown that Z–R parameters can be estimated by maximum likelihood, a procedure with optimal large sample properties. A general nonparametric framework for climatological Z–R estimation is also developed. Nonparametric procedures are attractive because of their flexibility in dealing with certain types of measurement errors common to radar data. Simulation experiments show that even under favorable assumptions on error characteristics of radar and raingages, large datasets are required to obtain accurate Z–R parameter estimates. Another important conclusion is that estimation results are generally quite sensitive to radar and raingage measurement thresholds. For fixed sample size, the simulation results can be used to provide quantitative assessments of the accuracy of Z–R model parameter estimates. These results are particular useful for error analysis of precipitation products that are derived using climatological Z–R relations. One example is the large-area rainfall estimates derived using the height-area rainfall threshold (HART) technique.
Abstract
A statistical framework for climatological Z–R parameter estimation is developed and simulation experiments are conducted to examine sampling properties of the estimators. Both parametric and nonparametric models are considered. For parametric models, it is shown that Z–R parameters can be estimated by maximum likelihood, a procedure with optimal large sample properties. A general nonparametric framework for climatological Z–R estimation is also developed. Nonparametric procedures are attractive because of their flexibility in dealing with certain types of measurement errors common to radar data. Simulation experiments show that even under favorable assumptions on error characteristics of radar and raingages, large datasets are required to obtain accurate Z–R parameter estimates. Another important conclusion is that estimation results are generally quite sensitive to radar and raingage measurement thresholds. For fixed sample size, the simulation results can be used to provide quantitative assessments of the accuracy of Z–R model parameter estimates. These results are particular useful for error analysis of precipitation products that are derived using climatological Z–R relations. One example is the large-area rainfall estimates derived using the height-area rainfall threshold (HART) technique.
Abstract
In this paper procedures are developed for estimating the mean field bias of radar rainfall estimates. Mean field bias is modeled as a random process that varies not only from storm to storm but also over the course of a storm. State estimates of mean field bias are based on hourly raingage data and hourly accumulations of radar rainfall estimates. The procedures are developed for the precipitation processing systems used with products of the Next Generation Weather Radar (NEXRAD) system. To implement the state estimation procedures, parameters of the bias model must be specified. Likelihood-based procedures are developed for estimating these parameters. A simulation experiment is carried out to assess performance of the parameter estimation procedure. Convergence of parameter estimators is rapid for the cases studied, with data from approximately 25 storms providing parameter estimates of acceptable accuracy. The state estimation procedures are applied to radar and raingage data from the 27 May 1987 storm, which was centered near the NSSL radar in Norman, Oklahoma. The results highlight dependence of the state estimation problem on the parameter estimation problem.
Abstract
In this paper procedures are developed for estimating the mean field bias of radar rainfall estimates. Mean field bias is modeled as a random process that varies not only from storm to storm but also over the course of a storm. State estimates of mean field bias are based on hourly raingage data and hourly accumulations of radar rainfall estimates. The procedures are developed for the precipitation processing systems used with products of the Next Generation Weather Radar (NEXRAD) system. To implement the state estimation procedures, parameters of the bias model must be specified. Likelihood-based procedures are developed for estimating these parameters. A simulation experiment is carried out to assess performance of the parameter estimation procedure. Convergence of parameter estimators is rapid for the cases studied, with data from approximately 25 storms providing parameter estimates of acceptable accuracy. The state estimation procedures are applied to radar and raingage data from the 27 May 1987 storm, which was centered near the NSSL radar in Norman, Oklahoma. The results highlight dependence of the state estimation problem on the parameter estimation problem.
Abstract
Efforts to validate the Tropical Rainfall Measuring Mission (TRMM) space-based rainfall products have encountered many difficulties and challenges. Of particular concern is the quality of the ground-based radar products—the main tool for validation analysis. This issue is addressed by analyzing the uncertainty in the maps of rain rate provided by the ground-validation radar. To look closely at factors that contribute to the uncertain performance of the radar products, this study uses high-quality rainfall observations from several surface sensors deployed during the Texas and Florida Underflights (TEFLUN-B) field experiment in central Florida during the summer of 1998. A statistical analysis of the radar estimates is performed by comparison with a high-density rain gauge cluster. The approach followed in the current analysis accounts for the recognized effect of rainfall's spatial variability in order to assess its contribution to radar differences from independent reference observations. The study provides uncertainty quantification of the radar estimates based on classification into light and heavy rain types. The methodology and the reported results should help in future studies that use radar-rainfall products to validate the various TRMM products, or in any other relevant hydrological applications.
Abstract
Efforts to validate the Tropical Rainfall Measuring Mission (TRMM) space-based rainfall products have encountered many difficulties and challenges. Of particular concern is the quality of the ground-based radar products—the main tool for validation analysis. This issue is addressed by analyzing the uncertainty in the maps of rain rate provided by the ground-validation radar. To look closely at factors that contribute to the uncertain performance of the radar products, this study uses high-quality rainfall observations from several surface sensors deployed during the Texas and Florida Underflights (TEFLUN-B) field experiment in central Florida during the summer of 1998. A statistical analysis of the radar estimates is performed by comparison with a high-density rain gauge cluster. The approach followed in the current analysis accounts for the recognized effect of rainfall's spatial variability in order to assess its contribution to radar differences from independent reference observations. The study provides uncertainty quantification of the radar estimates based on classification into light and heavy rain types. The methodology and the reported results should help in future studies that use radar-rainfall products to validate the various TRMM products, or in any other relevant hydrological applications.
Abstract
A simple, analytically tractable model of the radar–rain gauge rainfall observational process, including measurement errors, is presented. The model is applied to study properties of different reflectivity–rainfall (Z–R) relationships estimated from radar and rain gauge data. Three common Z–R adjustment schemes are considered: direct and reverse nonlinear regression, and the probability matching method. The three techniques result in quite different formulas for the estimated Z–R relationships. All three also are different from the intrinsic Z–R of the model and depend strongly on the assumed observational uncertainties. The results explain, to a degree, the diversity of Z–R relationships encountered in the literature. They also suggest that development of new tools that account for the uncertainties is necessary to separate the observational and natural causes of the Z–R variability.
Abstract
A simple, analytically tractable model of the radar–rain gauge rainfall observational process, including measurement errors, is presented. The model is applied to study properties of different reflectivity–rainfall (Z–R) relationships estimated from radar and rain gauge data. Three common Z–R adjustment schemes are considered: direct and reverse nonlinear regression, and the probability matching method. The three techniques result in quite different formulas for the estimated Z–R relationships. All three also are different from the intrinsic Z–R of the model and depend strongly on the assumed observational uncertainties. The results explain, to a degree, the diversity of Z–R relationships encountered in the literature. They also suggest that development of new tools that account for the uncertainties is necessary to separate the observational and natural causes of the Z–R variability.
Abstract
It is well acknowledged that there are large uncertainties associated with the operational quantitative precipitation estimates produced by the U.S. national network of the Weather Surveillance Radar-1988 Doppler (WSR-88D). These errors result from the measurement principles, parameter estimation, and the not fully understood physical processes. Even though comprehensive quantitative evaluation of the total radar-rainfall uncertainties has been the object of earlier studies, an open question remains concerning how the error model results are affected by parameter values and correction setups in the radar-rainfall algorithms. This study focuses on the effects of different exponents in the reflectivity–rainfall (Z–R) relation [Marshall–Palmer, default Next Generation Weather Radar (NEXRAD), and tropical] and the impact of an anomalous propagation removal algorithm. To address this issue, the authors apply an empirically based model in which the relation between true rainfall and radar rainfall could be described as the product of a systematic distortion function and a random component. Additionally, they extend the error model to describe the radar-rainfall uncertainties in an additive form. This approach is fully empirically based, and rain gauge measurements are considered as an approximation of the true rainfall. The proposed results are based on a large sample (6 yr) of data from the Oklahoma City radar (KTLX) and processed through the Hydro-NEXRAD software system. The radar data are complemented with the corresponding rain gauge observations from the Oklahoma Mesonet and the Agricultural Research Service Micronet.
Abstract
It is well acknowledged that there are large uncertainties associated with the operational quantitative precipitation estimates produced by the U.S. national network of the Weather Surveillance Radar-1988 Doppler (WSR-88D). These errors result from the measurement principles, parameter estimation, and the not fully understood physical processes. Even though comprehensive quantitative evaluation of the total radar-rainfall uncertainties has been the object of earlier studies, an open question remains concerning how the error model results are affected by parameter values and correction setups in the radar-rainfall algorithms. This study focuses on the effects of different exponents in the reflectivity–rainfall (Z–R) relation [Marshall–Palmer, default Next Generation Weather Radar (NEXRAD), and tropical] and the impact of an anomalous propagation removal algorithm. To address this issue, the authors apply an empirically based model in which the relation between true rainfall and radar rainfall could be described as the product of a systematic distortion function and a random component. Additionally, they extend the error model to describe the radar-rainfall uncertainties in an additive form. This approach is fully empirically based, and rain gauge measurements are considered as an approximation of the true rainfall. The proposed results are based on a large sample (6 yr) of data from the Oklahoma City radar (KTLX) and processed through the Hydro-NEXRAD software system. The radar data are complemented with the corresponding rain gauge observations from the Oklahoma Mesonet and the Agricultural Research Service Micronet.
Abstract
This study explores the scale effects of radar rainfall accumulation fields generated using the new super-resolution level II radar reflectivity data acquired by the Next Generation Weather Radar (NEXRAD) network of the Weather Surveillance Radar-1988 Doppler (WSR-88D) weather radars. Eleven months (May 2008–August 2009, exclusive of winter months) of high-density rain gauge network data are used to describe the uncertainty structure of radar rainfall and rain gauge representativeness with respect to five spatial scales (0.5, 1, 2, 4, and 8 km). While both uncertainties of gauge representativeness and radar rainfall show simple scaling behavior, the uncertainty of radar rainfall is characterized by an almost 3 times greater standard error at higher temporal and spatial resolutions (15 min and 0.5 km) than at lower resolutions (1 h and 8 km). These results may have implications for error propagation through distributed hydrologic models that require high-resolution rainfall input. Another interesting result of the study is that uncertainty obtained by averaging rainfall products produced from the super-resolution reflectivity data is slightly lower at smaller scales than the uncertainty of the corresponding resolution products produced using averaged (recombined) reflectivity data.
Abstract
This study explores the scale effects of radar rainfall accumulation fields generated using the new super-resolution level II radar reflectivity data acquired by the Next Generation Weather Radar (NEXRAD) network of the Weather Surveillance Radar-1988 Doppler (WSR-88D) weather radars. Eleven months (May 2008–August 2009, exclusive of winter months) of high-density rain gauge network data are used to describe the uncertainty structure of radar rainfall and rain gauge representativeness with respect to five spatial scales (0.5, 1, 2, 4, and 8 km). While both uncertainties of gauge representativeness and radar rainfall show simple scaling behavior, the uncertainty of radar rainfall is characterized by an almost 3 times greater standard error at higher temporal and spatial resolutions (15 min and 0.5 km) than at lower resolutions (1 h and 8 km). These results may have implications for error propagation through distributed hydrologic models that require high-resolution rainfall input. Another interesting result of the study is that uncertainty obtained by averaging rainfall products produced from the super-resolution reflectivity data is slightly lower at smaller scales than the uncertainty of the corresponding resolution products produced using averaged (recombined) reflectivity data.
Abstract
The vertical variability of reflectivity is an important source of error that affects estimations of rainfall quantity by radar. This error can be reduced if the vertical profile of reflectivity (VPR) is known. Different methods are available to determine VPR based on volume-scan radar data. Two such methods were tested. The first, used in the Swiss Meteorological Service, estimates a mean VPR directly from volumetric radar data collected close to the radar. The second method takes into account the spatial variability of reflectivity and relies on solving an inverse problem in determination of the local profile. To test these methods, two years of archived level-II radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) located in Tulsa, Oklahoma, and the corresponding rain gauge observations from the Oklahoma Mesonet were used. The results, obtained by comparing rain estimates from radar data corrected for the VPR influence with rain gauge observations, show the benefits of the methods—and also their limitations. The performance of the two methods is similar, but the inverse method consistently provides better results. However, for use in operational environments, it would require substantially more computational resources than the first method.
Abstract
The vertical variability of reflectivity is an important source of error that affects estimations of rainfall quantity by radar. This error can be reduced if the vertical profile of reflectivity (VPR) is known. Different methods are available to determine VPR based on volume-scan radar data. Two such methods were tested. The first, used in the Swiss Meteorological Service, estimates a mean VPR directly from volumetric radar data collected close to the radar. The second method takes into account the spatial variability of reflectivity and relies on solving an inverse problem in determination of the local profile. To test these methods, two years of archived level-II radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) located in Tulsa, Oklahoma, and the corresponding rain gauge observations from the Oklahoma Mesonet were used. The results, obtained by comparing rain estimates from radar data corrected for the VPR influence with rain gauge observations, show the benefits of the methods—and also their limitations. The performance of the two methods is similar, but the inverse method consistently provides better results. However, for use in operational environments, it would require substantially more computational resources than the first method.
Abstract
To detect anomalous propagation echoes in radar data, an automated procedure based on a neural network classification scheme has been developed. Earlier results had indicated that algorithms used to detect anomalous propagation must be calibrated before they can be applied to new sites. Developing a calibration dataset is typically laborious as it involves a human expert. To eliminate this problem, an efficient methodology of calibrating and validating neural network–based detection is proposed. Using volume scan radar reflectivity data from two WSR-88D locations, the authors demonstrate that the procedure can be calibrated easily and applied successfully to different sites.
Abstract
To detect anomalous propagation echoes in radar data, an automated procedure based on a neural network classification scheme has been developed. Earlier results had indicated that algorithms used to detect anomalous propagation must be calibrated before they can be applied to new sites. Developing a calibration dataset is typically laborious as it involves a human expert. To eliminate this problem, an efficient methodology of calibrating and validating neural network–based detection is proposed. Using volume scan radar reflectivity data from two WSR-88D locations, the authors demonstrate that the procedure can be calibrated easily and applied successfully to different sites.
Abstract
A method of detecting anomalous propagation echo in volume scan radar reflectivity data is evaluated. The method is based on a neural network approach and is suitable for operational implementation. It performs a classification of the base scan data on a pixel-by-pixel basis into two classes: rain and no rain. The results of applying the method to a large sample of Weather Surveillance Radar-1988 Doppler (WSR-88D) level II archive data are described. The data consist of over 10 000 volume scans collected in 1994 and 1995 by the Tulsa, Oklahoma, WSR-88D. The evaluation includes analyses based on radar data only and on various comparisons of radar and rain gauge data. The rain gauge data are from the Oklahoma Mesonet. The results clearly show the effectiveness of the procedure as indicated by reduced bias in rainfall accumulation and improved behavior in other statistics.
Abstract
A method of detecting anomalous propagation echo in volume scan radar reflectivity data is evaluated. The method is based on a neural network approach and is suitable for operational implementation. It performs a classification of the base scan data on a pixel-by-pixel basis into two classes: rain and no rain. The results of applying the method to a large sample of Weather Surveillance Radar-1988 Doppler (WSR-88D) level II archive data are described. The data consist of over 10 000 volume scans collected in 1994 and 1995 by the Tulsa, Oklahoma, WSR-88D. The evaluation includes analyses based on radar data only and on various comparisons of radar and rain gauge data. The rain gauge data are from the Oklahoma Mesonet. The results clearly show the effectiveness of the procedure as indicated by reduced bias in rainfall accumulation and improved behavior in other statistics.
Abstract
The relationship between monthly mean area-averaged rainfall and monthly mean fractional rainfall occurrence is used to develop a new method of open ocean rainfall estimation. This method uses acoustic sensors attached to drifting buoys to sample rainfall occurrence in space and time. The fractional rainfall occurrences measured by the sensors are used in a linear relationship to estimate monthly rainfall averaged over large (i.e., 2.5° × 2.5°) areas. This estimation method is tested for different scenarios using a stochastic model. Results support the feasibility of this new rainfall estimation scheme. Simulations show that the existing density of drifting buoys is inadequate, but densities around 10 times the existing density will give correlation coefficients between estimated and true rainfall around 0.55. Estimates obtained with this method may be used to calibrate and/or validate the satellite-based methods of open ocean rainfall.
Abstract
The relationship between monthly mean area-averaged rainfall and monthly mean fractional rainfall occurrence is used to develop a new method of open ocean rainfall estimation. This method uses acoustic sensors attached to drifting buoys to sample rainfall occurrence in space and time. The fractional rainfall occurrences measured by the sensors are used in a linear relationship to estimate monthly rainfall averaged over large (i.e., 2.5° × 2.5°) areas. This estimation method is tested for different scenarios using a stochastic model. Results support the feasibility of this new rainfall estimation scheme. Simulations show that the existing density of drifting buoys is inadequate, but densities around 10 times the existing density will give correlation coefficients between estimated and true rainfall around 0.55. Estimates obtained with this method may be used to calibrate and/or validate the satellite-based methods of open ocean rainfall.
