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- Author or Editor: Witold F. Krajewski x
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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
Brightband effects are one of the more important causes of vertical variability of reflectivity and severely affect the accuracy of rainfall estimates from ground-based radar. Monte Carlo simulation experiments are performed to investigate the efficiency of a procedure for the correction of errors related to the vertical variability of reflectivity. The simulation model generates three-dimensional radar reflectivity fields. Brightband effects are simulated through a physically based model of melting-layer reflectivity observations. Sensitivity of the correction procedure for a number of different precipitation scenarios and radar systems is analyzed. Overall, the identification method is found to be a robust procedure for correction of brightband effects. Results indicate a dependence of the effectiveness of the correction procedure on mean altitude and spatial variability of the melting layer.
Abstract
Brightband effects are one of the more important causes of vertical variability of reflectivity and severely affect the accuracy of rainfall estimates from ground-based radar. Monte Carlo simulation experiments are performed to investigate the efficiency of a procedure for the correction of errors related to the vertical variability of reflectivity. The simulation model generates three-dimensional radar reflectivity fields. Brightband effects are simulated through a physically based model of melting-layer reflectivity observations. Sensitivity of the correction procedure for a number of different precipitation scenarios and radar systems is analyzed. Overall, the identification method is found to be a robust procedure for correction of brightband effects. Results indicate a dependence of the effectiveness of the correction procedure on mean altitude and spatial variability of the melting layer.
Abstract
No abstract available.
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No abstract available.
Abstract
This study provides an intensive evaluation of the Global Precipitation Climatology Project (GPCP) 1° daily (1DD) rainfall products over the Mississippi River basin, which covers 435 1° latitude × 1° longitude grids for the period of January 1997–December 2000 using radar-based precipitation estimates. The authors’ evaluation criteria include unconditional continuous, conditional (quasi) continuous, and categorical statistics, and their analyses cover annual and seasonal time periods. The authors present spatial maps that reflect the results for the 1° grids and a summary of the results for three selected regions. They also develop a statistical framework that partitions the GPCP–radar difference statistics into GPCP error and radar error statistics. They further partition the GPCP error statistics into sampling error and retrieval error statistics and estimate the sampling error statistics using a data-based resampling experiment. Highlights of the results include the following: 1) the GPCP 1DD product captures the spatial and temporal variability of rainfall to a high degree, with more than 80% of the variance explained, 2) the GPCP 1DD product proficiently detects rainy days at a large range of rainfall thresholds, and 3) in comparison with radar-based estimates the GPCP 1DD product overestimates rainfall.
Abstract
This study provides an intensive evaluation of the Global Precipitation Climatology Project (GPCP) 1° daily (1DD) rainfall products over the Mississippi River basin, which covers 435 1° latitude × 1° longitude grids for the period of January 1997–December 2000 using radar-based precipitation estimates. The authors’ evaluation criteria include unconditional continuous, conditional (quasi) continuous, and categorical statistics, and their analyses cover annual and seasonal time periods. The authors present spatial maps that reflect the results for the 1° grids and a summary of the results for three selected regions. They also develop a statistical framework that partitions the GPCP–radar difference statistics into GPCP error and radar error statistics. They further partition the GPCP error statistics into sampling error and retrieval error statistics and estimate the sampling error statistics using a data-based resampling experiment. Highlights of the results include the following: 1) the GPCP 1DD product captures the spatial and temporal variability of rainfall to a high degree, with more than 80% of the variance explained, 2) the GPCP 1DD product proficiently detects rainy days at a large range of rainfall thresholds, and 3) in comparison with radar-based estimates the GPCP 1DD product overestimates rainfall.
Abstract
A Monte Carlo simulation study is conducted to investigate the performance of the area-threshold method of estimating mean areas rainfall. The study uses a stochastic space-time model of rainfall as the true rainfall-field generator. Simple schemes of simulating radar observations of the simulated rainfall fields are employed. The schemes address both random and systematic components of the radar rainfall-estimation process. The results of the area-threshold method are compared to the results based on conventional averaging of radar-estimated point rainfall observations. The results demonstrate that when the exponent parameter in the Z–R relationship has small uncertainty (about ±10%), the conventional method works better than the area-threshold method. When the errors are higher (±20%), the area-threshold method with optimum threshold in the 5–10 mm h−1 range performs best. For even higher errors in the Z–R relationship, the area-threshold method with a low threshold provides the best performance.
Abstract
A Monte Carlo simulation study is conducted to investigate the performance of the area-threshold method of estimating mean areas rainfall. The study uses a stochastic space-time model of rainfall as the true rainfall-field generator. Simple schemes of simulating radar observations of the simulated rainfall fields are employed. The schemes address both random and systematic components of the radar rainfall-estimation process. The results of the area-threshold method are compared to the results based on conventional averaging of radar-estimated point rainfall observations. The results demonstrate that when the exponent parameter in the Z–R relationship has small uncertainty (about ±10%), the conventional method works better than the area-threshold method. When the errors are higher (±20%), the area-threshold method with optimum threshold in the 5–10 mm h−1 range performs best. For even higher errors in the Z–R relationship, the area-threshold method with a low threshold provides the best performance.
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
A bias-adjusted radar rainfall product is created and used for evaluation of two satellite rainfall estimation algorithms. Three years of collocated rainfall estimates from radar, rain gauges, a microwave satellite algorithm, and a multispectral (visible through near-infrared) algorithm were collected over the continental United States from July 1998 through July 2001. The radar and gauge data are compared to determine the locations and times at which the rainfall occurrences estimated by these two sensors are in sufficient agreement for the data to be used for validation. This procedure serves as quality control for both sensors and determines the locations at which the radar has difficulty detecting rainfall and should not be used in a validation dataset. For the data remaining after quality control, the gauge data are used for multiplicative adjustment of the radar estimates to remove the radar bias with respect to the gauges. These bias-adjusted estimates are compared with the satellite rainfall estimates to observe the evolution of the satellite biases over the 3-yr period. The multispectral algorithm was under development throughout the 3-yr period, and improvement is evident. The microwave algorithm overestimates rainfall in the summer months, underestimates in the winter months, and has an east-to-west bias gradient, all of which are consistent with physical explanations and previous findings. The multispectral algorithm bias depends highly on diurnal sampling; there is much greater overestimation for the daytime overpasses. These results are applicable primarily to the eastern half of the United States, because few data in the western half remain after quality control.
Abstract
A bias-adjusted radar rainfall product is created and used for evaluation of two satellite rainfall estimation algorithms. Three years of collocated rainfall estimates from radar, rain gauges, a microwave satellite algorithm, and a multispectral (visible through near-infrared) algorithm were collected over the continental United States from July 1998 through July 2001. The radar and gauge data are compared to determine the locations and times at which the rainfall occurrences estimated by these two sensors are in sufficient agreement for the data to be used for validation. This procedure serves as quality control for both sensors and determines the locations at which the radar has difficulty detecting rainfall and should not be used in a validation dataset. For the data remaining after quality control, the gauge data are used for multiplicative adjustment of the radar estimates to remove the radar bias with respect to the gauges. These bias-adjusted estimates are compared with the satellite rainfall estimates to observe the evolution of the satellite biases over the 3-yr period. The multispectral algorithm was under development throughout the 3-yr period, and improvement is evident. The microwave algorithm overestimates rainfall in the summer months, underestimates in the winter months, and has an east-to-west bias gradient, all of which are consistent with physical explanations and previous findings. The multispectral algorithm bias depends highly on diurnal sampling; there is much greater overestimation for the daytime overpasses. These results are applicable primarily to the eastern half of the United States, because few data in the western half remain after quality control.
Abstract
This paper focuses on estimating the error uncertainty of the monthly 2.5° × 2.5° rainfall products of the Global Precipitation Climatology Project (GPCP) using rain gauge observations. Two kinds of GPCP products are evaluated: the satellite-only (MS) product, and the satellite–gauge (SG) merged product. The error variance separation (EVS) method has been proposed previously as a means of estimating the error uncertainty of the GPCP products. In this paper, the accuracy of the EVS results is examined for a variety of gauge densities. Three validation sites—two in North Dakota and one in Thailand—all with a large number of rain gauges, were selected. The very high density of the selected sites justifies the assumption that the errors are negligible if all gauges are used. Monte Carlo simulation studies were performed to evaluate sampling uncertainty for selected rain gauge network densities. Results are presented in terms of EVS error uncertainty normalized by the true error uncertainty. These results show that the accuracy of the EVS error uncertainty estimates for the SG product differs from that of the MS product. The key factors that affect the errors of the EVS results, such as the gauge density, the gauge network, and the sample size, have been identified and their influence has been quantified. One major finding of this study is that 8–10 gauges, at the 2.5° scale, are required as a minimum to get good error uncertainty estimates for the SG products from the EVS method. For eight or more gauges, the normalized error uncertainty is about 0.86 ± 0.10 (North Dakota: Box 1) and 0.95 ± 0.10 (North Dakota: Box 2). Results show that, despite its error, the EVS method performs better than the root-mean-square error (rmse) approach that ignores the rain gauge sampling error. For the MS products, both the EVS method and the rmse approach give negligible bias. As expected, results show that the SG products give better rainfall estimates than the MS products, according to most of the criteria used.
Abstract
This paper focuses on estimating the error uncertainty of the monthly 2.5° × 2.5° rainfall products of the Global Precipitation Climatology Project (GPCP) using rain gauge observations. Two kinds of GPCP products are evaluated: the satellite-only (MS) product, and the satellite–gauge (SG) merged product. The error variance separation (EVS) method has been proposed previously as a means of estimating the error uncertainty of the GPCP products. In this paper, the accuracy of the EVS results is examined for a variety of gauge densities. Three validation sites—two in North Dakota and one in Thailand—all with a large number of rain gauges, were selected. The very high density of the selected sites justifies the assumption that the errors are negligible if all gauges are used. Monte Carlo simulation studies were performed to evaluate sampling uncertainty for selected rain gauge network densities. Results are presented in terms of EVS error uncertainty normalized by the true error uncertainty. These results show that the accuracy of the EVS error uncertainty estimates for the SG product differs from that of the MS product. The key factors that affect the errors of the EVS results, such as the gauge density, the gauge network, and the sample size, have been identified and their influence has been quantified. One major finding of this study is that 8–10 gauges, at the 2.5° scale, are required as a minimum to get good error uncertainty estimates for the SG products from the EVS method. For eight or more gauges, the normalized error uncertainty is about 0.86 ± 0.10 (North Dakota: Box 1) and 0.95 ± 0.10 (North Dakota: Box 2). Results show that, despite its error, the EVS method performs better than the root-mean-square error (rmse) approach that ignores the rain gauge sampling error. For the MS products, both the EVS method and the rmse approach give negligible bias. As expected, results show that the SG products give better rainfall estimates than the MS products, according to most of the criteria used.
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.
Abstract
Analysis of data collected by four disdrometers deployed in a 1-km2 area is presented with the intent of quantifying the spatial variability of radar reflectivity at small spatial scales. Spatial variability of radar reflectivity within the radar beam is a key source of error in radar-rainfall estimation because of the assumption that drops are uniformly distributed within the radar-sensing volume. Common experience tells one that, in fact, drops are not uniformly distributed, and, although some work has been done to examine the small-scale spatial variability of rain rates, little experimental work has been done to explore the variability of radar reflectivity. The four disdrometers used for this study include a two-dimensional video disdrometer, an X-band radar-based disdrometer, an impact-type disdrometer, and an optical spectropluviometer. Although instrumental differences were expected, the magnitude of these differences clouds the natural variability of interest. An algorithm is applied to mitigate these instrumental effects, and the variability remains high, even as the observations are integrated in time. Although one cannot explicitly quantify the spatial variability from this experiment, the results clearly show that the spatial variability of reflectivity is very large.
Abstract
Analysis of data collected by four disdrometers deployed in a 1-km2 area is presented with the intent of quantifying the spatial variability of radar reflectivity at small spatial scales. Spatial variability of radar reflectivity within the radar beam is a key source of error in radar-rainfall estimation because of the assumption that drops are uniformly distributed within the radar-sensing volume. Common experience tells one that, in fact, drops are not uniformly distributed, and, although some work has been done to examine the small-scale spatial variability of rain rates, little experimental work has been done to explore the variability of radar reflectivity. The four disdrometers used for this study include a two-dimensional video disdrometer, an X-band radar-based disdrometer, an impact-type disdrometer, and an optical spectropluviometer. Although instrumental differences were expected, the magnitude of these differences clouds the natural variability of interest. An algorithm is applied to mitigate these instrumental effects, and the variability remains high, even as the observations are integrated in time. Although one cannot explicitly quantify the spatial variability from this experiment, the results clearly show that the spatial variability of reflectivity is very large.
