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- Author or Editor: Grzegorz J. Ciach x
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Abstract
This study presents empirical analysis of the errors in tipping-bucket rain gauges that manifest themselves as random differences between closely collocated instruments. It is based on a substantial data sample from 15 collocated rain gauges. The errors are shown to be considerable and highly dependent on rainfall intensity and timescale. These dependencies are estimated using nonparametric regression. Strong dependence of the errors on the data collecting and processing strategy is also demonstrated. An analytical model and estimates of its coefficients are provided to concisely quantify the results in different scenarios. Finally, possible improvements of the accuracy and reliability of the surface rainfall measurements are discussed.
Abstract
This study presents empirical analysis of the errors in tipping-bucket rain gauges that manifest themselves as random differences between closely collocated instruments. It is based on a substantial data sample from 15 collocated rain gauges. The errors are shown to be considerable and highly dependent on rainfall intensity and timescale. These dependencies are estimated using nonparametric regression. Strong dependence of the errors on the data collecting and processing strategy is also demonstrated. An analytical model and estimates of its coefficients are provided to concisely quantify the results in different scenarios. Finally, possible improvements of the accuracy and reliability of the surface rainfall measurements are discussed.
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
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Abstract
The problem of anomalous propagation (AP) echoes in weather radar observations has become especially important now that rainfall data from fully automatic radar systems are sometimes applied in operational hydrology. Reliable automatic detection and suppression of AP echoes is one of the crucial problems in this area.
This study presents characteristics of AP patterns and the initial results of applying a statistical pattern classification method for recognition and rejection of such echoes. A classical radar (MRL-5) station operates in central Poland performing volume scanning every 10 min. Two months of hourly data (June and September of 1991) were chosen to create learning and verification samples for the AP detection algorithm. Each observation was thoroughly analyzed by an experienced radar meteorologist. The features taken into account were visually estimated local texture and overall morphology of echo pattern, vertical echo structure, time evolution (using animation), and the general synoptic information. For each 4 km × 4 km pixel of 933 observations the human classification was recorded resulting in a sample of 631 166 points with recognized echo type, 14.6% of them being AP echoes. The unsuppressed AP echo impact on monthly accumulated precipitation was 59% of the actual sum for the month of June and as much as 97% for September.
Three Bayesian discrimination functions were investigated. They differ in selection of the feature vector. This vector consisted of various local radar echo parameters: for example, maximum reflectivity, echo top, and horizontal gradients. The coefficients of the functions were calibrated using the June sample. The AP echo recognition error was about 6% for the best-performing function, when applied to an independent (September) sample, which would make the method acceptable for operational use.
Abstract
The problem of anomalous propagation (AP) echoes in weather radar observations has become especially important now that rainfall data from fully automatic radar systems are sometimes applied in operational hydrology. Reliable automatic detection and suppression of AP echoes is one of the crucial problems in this area.
This study presents characteristics of AP patterns and the initial results of applying a statistical pattern classification method for recognition and rejection of such echoes. A classical radar (MRL-5) station operates in central Poland performing volume scanning every 10 min. Two months of hourly data (June and September of 1991) were chosen to create learning and verification samples for the AP detection algorithm. Each observation was thoroughly analyzed by an experienced radar meteorologist. The features taken into account were visually estimated local texture and overall morphology of echo pattern, vertical echo structure, time evolution (using animation), and the general synoptic information. For each 4 km × 4 km pixel of 933 observations the human classification was recorded resulting in a sample of 631 166 points with recognized echo type, 14.6% of them being AP echoes. The unsuppressed AP echo impact on monthly accumulated precipitation was 59% of the actual sum for the month of June and as much as 97% for September.
Three Bayesian discrimination functions were investigated. They differ in selection of the feature vector. This vector consisted of various local radar echo parameters: for example, maximum reflectivity, echo top, and horizontal gradients. The coefficients of the functions were calibrated using the June sample. The AP echo recognition error was about 6% for the best-performing function, when applied to an independent (September) sample, which would make the method acceptable for operational use.
Abstract
This study presents the construction and calibration of a low-cost piezoelectric microprocessor impactometer designed for the field measurements of the rainfall kinetic energy (KE) flux. Its precise calibration was performed in laboratory conditions using waterdrops of different sizes and fall velocities. High-speed photography was applied to measure the velocity of each waterdrop. Although the impactometer constructed for this study is not able to measure the momentum of waterdrops, its accuracy for measuring their KE is excellent. It was found that the processing of the piezoelectric signal might determine which physical quantity is measured by different impactometers. It was also found that the distance between the waterdrop impact position and the impactometer center has a significant effect on the sensor output. A scheme to account for this effect is developed in this study, and the calibration curve for field applications of the impactometer is derived. In addition, an example comparison of the concurrent field measurements of KE flux using the impactometer and rainfall rates using a weighing rain gauge is given.
Abstract
This study presents the construction and calibration of a low-cost piezoelectric microprocessor impactometer designed for the field measurements of the rainfall kinetic energy (KE) flux. Its precise calibration was performed in laboratory conditions using waterdrops of different sizes and fall velocities. High-speed photography was applied to measure the velocity of each waterdrop. Although the impactometer constructed for this study is not able to measure the momentum of waterdrops, its accuracy for measuring their KE is excellent. It was found that the processing of the piezoelectric signal might determine which physical quantity is measured by different impactometers. It was also found that the distance between the waterdrop impact position and the impactometer center has a significant effect on the sensor output. A scheme to account for this effect is developed in this study, and the calibration curve for field applications of the impactometer is derived. In addition, an example comparison of the concurrent field measurements of KE flux using the impactometer and rainfall rates using a weighing rain gauge is given.
Abstract
The goal of this study is to improve understanding of the optimization criteria for radar rainfall (RR) products. Conditional bias (CB) is formally defined and discussed. The CB is defined as the difference between a given rain rate and the conditional average of its estimates. A simple analytical model is used to study the behavior of CB and its effect on the relationship between the estimates and the truth. This study shows the measurement errors of near-surface radar reflectivity and the natural reflectivity–rainfall rate variability can affect CB. This RR estimation error component is also compared with the commonly used mean-square error (MSE). A dilemma between the minimization of these two errors is demonstrated. Removing CB from the estimates significantly increases MSE, but minimizing MSE results in a large CB that manifests itself in underestimation of strong rainfalls.
Abstract
The goal of this study is to improve understanding of the optimization criteria for radar rainfall (RR) products. Conditional bias (CB) is formally defined and discussed. The CB is defined as the difference between a given rain rate and the conditional average of its estimates. A simple analytical model is used to study the behavior of CB and its effect on the relationship between the estimates and the truth. This study shows the measurement errors of near-surface radar reflectivity and the natural reflectivity–rainfall rate variability can affect CB. This RR estimation error component is also compared with the commonly used mean-square error (MSE). A dilemma between the minimization of these two errors is demonstrated. Removing CB from the estimates significantly increases MSE, but minimizing MSE results in a large CB that manifests itself in underestimation of strong rainfalls.
Abstract
This study discusses questions of estimating correlation coefficient of point rainfall as observed at two measuring stations. The focus is on issues such as sensitivity to sample size, extreme rain events, and distribution of rainfall. The authors perform extensive analysis based on a two-point data-driven rainfall model that simulates the intermittence and extreme variability of rainfall using a bivariate mixed-lognormal distribution. The study examines the commonly used product–moment estimator along with an alternative transformation-based estimator. The results show a high level of bias and variance of the traditional correlation estimator, which are caused mostly by significant skewness levels that characterize rainfall observations. Application using data from a high-density cluster indicated the advantages of using the alternative estimator. The overall aim of the study is to draw the attention of researchers working with rainfall to some commonly disregarded issues when they seek accurate and reliable correlation information.
Abstract
This study discusses questions of estimating correlation coefficient of point rainfall as observed at two measuring stations. The focus is on issues such as sensitivity to sample size, extreme rain events, and distribution of rainfall. The authors perform extensive analysis based on a two-point data-driven rainfall model that simulates the intermittence and extreme variability of rainfall using a bivariate mixed-lognormal distribution. The study examines the commonly used product–moment estimator along with an alternative transformation-based estimator. The results show a high level of bias and variance of the traditional correlation estimator, which are caused mostly by significant skewness levels that characterize rainfall observations. Application using data from a high-density cluster indicated the advantages of using the alternative estimator. The overall aim of the study is to draw the attention of researchers working with rainfall to some commonly disregarded issues when they seek accurate and reliable correlation information.
Abstract
Although it is broadly acknowledged that the radar-rainfall (RR) estimates based on the U.S. national network of Weather Surveillance Radar-1988 Doppler (WSR-88D) stations contain a high degree of uncertainty, no methods currently exist to inform users about its quantitative characteristics. The most comprehensive characterization of this uncertainty can be achieved by delivering the products in a probabilistic rather than the traditional deterministic form. The authors are developing a methodology for probabilistic quantitative precipitation estimation (PQPE) based on weather radar data. In this study, they present the central element of this methodology: an empirically based error structure model for the RR products.
The authors apply a product-error-driven (PED) approach to obtain a realistic uncertainty model. It is based on the analyses of six years of data from the Oklahoma City, Oklahoma, WSR-88D radar (KTLX) processed with the Precipitation Processing System algorithm of the NEXRAD system. The modeled functional-statistical relationship between RR estimates and corresponding true rainfall consists of two components: a systematic distortion function and a stochastic factor quantifying remaining random errors. The two components are identified using a nonparametric functional estimation apparatus. The true rainfall is approximated with rain gauge data from the Oklahoma Mesonet and the U.S. Department of Agriculture (USDA) Agricultural Research Service Micronet networks. The RR uncertainty model presented here accounts for different time scales, synoptic regimes, and distances from the radar. In addition, this study marks the first time in which results on RR error correlation in space and time are presented.
Abstract
Although it is broadly acknowledged that the radar-rainfall (RR) estimates based on the U.S. national network of Weather Surveillance Radar-1988 Doppler (WSR-88D) stations contain a high degree of uncertainty, no methods currently exist to inform users about its quantitative characteristics. The most comprehensive characterization of this uncertainty can be achieved by delivering the products in a probabilistic rather than the traditional deterministic form. The authors are developing a methodology for probabilistic quantitative precipitation estimation (PQPE) based on weather radar data. In this study, they present the central element of this methodology: an empirically based error structure model for the RR products.
The authors apply a product-error-driven (PED) approach to obtain a realistic uncertainty model. It is based on the analyses of six years of data from the Oklahoma City, Oklahoma, WSR-88D radar (KTLX) processed with the Precipitation Processing System algorithm of the NEXRAD system. The modeled functional-statistical relationship between RR estimates and corresponding true rainfall consists of two components: a systematic distortion function and a stochastic factor quantifying remaining random errors. The two components are identified using a nonparametric functional estimation apparatus. The true rainfall is approximated with rain gauge data from the Oklahoma Mesonet and the U.S. Department of Agriculture (USDA) Agricultural Research Service Micronet networks. The RR uncertainty model presented here accounts for different time scales, synoptic regimes, and distances from the radar. In addition, this study marks the first time in which results on RR error correlation in space and time are presented.
Abstract
The Global Precipitation Climatology Project (GPCP) established a multiyear global dataset of satellite-based estimates of monthly rainfall accumulations averaged over a grid of 2.5° × 2.5° geographical boxes. This paper describes an attempt to quantify the error variance of these estimates at selected reference sites. Fourteen reference sites were selected over the United States at the GPCP grid locations where high-density rain gauge network and high-quality data are available. A rigorous methodology for estimation of the error statistics of the reference sites was applied. A method of separating the reference error variance from the observed mean square difference between the reference and the GPCP products was proposed and discussed. As a result, estimates of the error variance of the GPCP products were obtained. Two kinds of GPCP products were evaluated: 1) satellite-only products, and 2) merged products that incorporate some rain gauge data that were available to the project. The error analysis results show that the merged product is characterized by smaller errors, both in terms of bias as well as the random component. The bias is, on average, 0.88 for the merged product and 0.70 for the satellite-only product. The average random component is 21% for the merged product and 79% for the satellite-only product. The random error is worse in the winter than in the summer. The error estimates agree well with their counterparts produced by the GPCP.
Abstract
The Global Precipitation Climatology Project (GPCP) established a multiyear global dataset of satellite-based estimates of monthly rainfall accumulations averaged over a grid of 2.5° × 2.5° geographical boxes. This paper describes an attempt to quantify the error variance of these estimates at selected reference sites. Fourteen reference sites were selected over the United States at the GPCP grid locations where high-density rain gauge network and high-quality data are available. A rigorous methodology for estimation of the error statistics of the reference sites was applied. A method of separating the reference error variance from the observed mean square difference between the reference and the GPCP products was proposed and discussed. As a result, estimates of the error variance of the GPCP products were obtained. Two kinds of GPCP products were evaluated: 1) satellite-only products, and 2) merged products that incorporate some rain gauge data that were available to the project. The error analysis results show that the merged product is characterized by smaller errors, both in terms of bias as well as the random component. The bias is, on average, 0.88 for the merged product and 0.70 for the satellite-only product. The average random component is 21% for the merged product and 79% for the satellite-only product. The random error is worse in the winter than in the summer. The error estimates agree well with their counterparts produced by the GPCP.
Abstract
This study presents a multicomponent rainfall estimation algorithm, based on weather radar and rain gauge network, that can be used as a ground-based reference in the satellite Tropical Rainfall Measuring Mission (TRMM). The essential steps are constructing a radar observable, its nonlinear transformation to rainfall, interpolation to rectangular grid, constructing several timescale accumulations, bias adjustment, and merging of the radar rainfall estimates and rain gauge data. Observations from a C-band radar in Darwin, Australia, and a local network of 54 rain gauges were used to calibrate and test the algorithm. A period of 25 days was selected, and the rain gauges were split into two subsamples to apply cross-validation techniques.
A Z–R relationship with continuous range dependence and a temporal interpolation scheme that accounts for the advection effects is applied. An innovative methodology was used to estimate the algorithm controlling parameters. The model was globally optimized by using an objective function on the level of the final products. This is equivalent to comparing hundreds of Z–R relationships using a uniform and representative performance criterion. The algorithm performance is fairly insensitive to the parameter variations around the optimum. This suggests that the accuracy limit of the radar rainfall estimation based on power-law Z–R relationships has been reached. No improvement was achieved by using rain regime classification prior to estimation.
Abstract
This study presents a multicomponent rainfall estimation algorithm, based on weather radar and rain gauge network, that can be used as a ground-based reference in the satellite Tropical Rainfall Measuring Mission (TRMM). The essential steps are constructing a radar observable, its nonlinear transformation to rainfall, interpolation to rectangular grid, constructing several timescale accumulations, bias adjustment, and merging of the radar rainfall estimates and rain gauge data. Observations from a C-band radar in Darwin, Australia, and a local network of 54 rain gauges were used to calibrate and test the algorithm. A period of 25 days was selected, and the rain gauges were split into two subsamples to apply cross-validation techniques.
A Z–R relationship with continuous range dependence and a temporal interpolation scheme that accounts for the advection effects is applied. An innovative methodology was used to estimate the algorithm controlling parameters. The model was globally optimized by using an objective function on the level of the final products. This is equivalent to comparing hundreds of Z–R relationships using a uniform and representative performance criterion. The algorithm performance is fairly insensitive to the parameter variations around the optimum. This suggests that the accuracy limit of the radar rainfall estimation based on power-law Z–R relationships has been reached. No improvement was achieved by using rain regime classification prior to estimation.
