Search Results
You are looking at 1 - 10 of 20 items for :
- Author or Editor: Witold F. Krajewski x
- Journal of Applied Meteorology and Climatology x
- Refine by Access: Content accessible to me x
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
The main objective of this study is to assess the ability of radar-derived rainfall products to characterize the small-scale spatial variability of rainfall. The authors use independent datasets from high-quality dense rain gauge networks employed during the Texas and Florida Underflights (TEFLUN-B) and Tropical Rainfall Measuring Mission component of the Large-Scale Biosphere–Atmosphere (TRMM-LBA) field experiments conducted by NASA in 1998 and 1999. A detailed comparison between gauge- and radar-derived spatial variability estimates is carried out by means of a correlation function, covariance, variogram, scaling characteristics, and variance reduction due to spatial averaging. Emphasis is given to the correlation function because it is involved in most of these statistics. The approach followed in the analysis addresses the problems associated with the traditional estimation methods and the recognized differences in the scales of observation. The performance of the radar-derived correlation function is evaluated in two ways: by direct comparison with gauge-derived correlation function and by quantifying its effect on one of the applications, that is, gauge sampling uncertainty estimation. Results show that, at separation distances shorter than about 5 km, radar-derived correlations are lower than those obtained from gauges. Three sources of uncertainty that may have caused the discrepancy between gauge- and radar-derived correlations are identified, and their effects are quantified to the extent possible. The error introduced in gauge sampling uncertainty estimates due to the use of radar-derived correlation function is within 30%. Discrepancies between gauge- and radar-rainfall fields are also observed in terms of the other spatial statistics.
Abstract
The main objective of this study is to assess the ability of radar-derived rainfall products to characterize the small-scale spatial variability of rainfall. The authors use independent datasets from high-quality dense rain gauge networks employed during the Texas and Florida Underflights (TEFLUN-B) and Tropical Rainfall Measuring Mission component of the Large-Scale Biosphere–Atmosphere (TRMM-LBA) field experiments conducted by NASA in 1998 and 1999. A detailed comparison between gauge- and radar-derived spatial variability estimates is carried out by means of a correlation function, covariance, variogram, scaling characteristics, and variance reduction due to spatial averaging. Emphasis is given to the correlation function because it is involved in most of these statistics. The approach followed in the analysis addresses the problems associated with the traditional estimation methods and the recognized differences in the scales of observation. The performance of the radar-derived correlation function is evaluated in two ways: by direct comparison with gauge-derived correlation function and by quantifying its effect on one of the applications, that is, gauge sampling uncertainty estimation. Results show that, at separation distances shorter than about 5 km, radar-derived correlations are lower than those obtained from gauges. Three sources of uncertainty that may have caused the discrepancy between gauge- and radar-derived correlations are identified, and their effects are quantified to the extent possible. The error introduced in gauge sampling uncertainty estimates due to the use of radar-derived correlation function is within 30%. Discrepancies between gauge- and radar-rainfall fields are also observed in terms of the other spatial statistics.
Abstract
On the basis of temporally sampled data obtained from satellites, spatial statistics of rainfall can be estimated. In this paper, the authors compare the estimated spatial statistics with their “true” or ensemble values calculated using 5 yr of 15-min radar-based rainfall data at a spatial domain of 512 km × 512 km in the central United States. The authors conducted a Monte Carlo sampling experiment to simulate different sampling scenarios for variable sampling intervals and rainfall averaging periods. The spatial statistics used are the moments of spatial distribution of rainfall, the spatial scaling exponents, and the spatial cross correlations between the sample and ensemble rainfall fields. The results demonstrated that the expected value of the relative error in the mean rain-rate estimate is zero for rainfall averaged over 5 days or longer, better temporal sampling produces average fields that are “less noisy” spatially, an increase in the sampling interval causes the sampled rainfall to be increasingly less correlated with the true rainfall map, and the spatial scaling exponent estimators could give a bias of 40% or less. The results of this study provide a basis for understanding the impact of temporal statistics on inferred spatial statistics.
Abstract
On the basis of temporally sampled data obtained from satellites, spatial statistics of rainfall can be estimated. In this paper, the authors compare the estimated spatial statistics with their “true” or ensemble values calculated using 5 yr of 15-min radar-based rainfall data at a spatial domain of 512 km × 512 km in the central United States. The authors conducted a Monte Carlo sampling experiment to simulate different sampling scenarios for variable sampling intervals and rainfall averaging periods. The spatial statistics used are the moments of spatial distribution of rainfall, the spatial scaling exponents, and the spatial cross correlations between the sample and ensemble rainfall fields. The results demonstrated that the expected value of the relative error in the mean rain-rate estimate is zero for rainfall averaged over 5 days or longer, better temporal sampling produces average fields that are “less noisy” spatially, an increase in the sampling interval causes the sampled rainfall to be increasingly less correlated with the true rainfall map, and the spatial scaling exponent estimators could give a bias of 40% or less. The results of this study provide a basis for understanding the impact of temporal statistics on inferred spatial statistics.
Abstract
A scheme for simulating radar-estimated rainfall fields is described. The scheme uses a two-dimensional stochastic space–time model of rainfall events and a parameterization of drop-size distribution. Based on the statistically generated drop-size distribution, radar observables, namely, radar reflectivity and differential reflectivity, are calculated. The simulated measurable variables are corrupted with random measurement error to account for radar measurement process. Subsequently, radar observables are used in rainfall estimation. Generated fields of the simulated rainfall and the corresponding radar observables are presented. Rainfall estimates from radar simulations are also presented. Use of the described radar-data simulator is envisioned in those applications where the effects of radar rainfall errors are of interest.
Abstract
A scheme for simulating radar-estimated rainfall fields is described. The scheme uses a two-dimensional stochastic space–time model of rainfall events and a parameterization of drop-size distribution. Based on the statistically generated drop-size distribution, radar observables, namely, radar reflectivity and differential reflectivity, are calculated. The simulated measurable variables are corrupted with random measurement error to account for radar measurement process. Subsequently, radar observables are used in rainfall estimation. Generated fields of the simulated rainfall and the corresponding radar observables are presented. Rainfall estimates from radar simulations are also presented. Use of the described radar-data simulator is envisioned in those applications where the effects of radar rainfall errors are of interest.
Abstract
Simultaneous observations made with optical- and impact-type disdrometers were analyzed to broaden knowledge of these instruments. These observations were designed to test how accurately they measure drop size distributions (DSDs). The instruments' use in determining radar rainfall relations such as that between reflectivity and rainfall rate also was analyzed. A unique set of instruments, including two video and one Joss–Waldvogel disdrometer along with eight tipping-bucket rain gauges, was operated within a small area of about 100 × 50 m2 during a 2-month-long field campaign in central Florida. The disdrometers were evaluated by comparing their rain totals with the rain gauges. Both disdrometers underestimated the rain totals, but the video disdrometers had higher readings, resulting in a better agreement with the gauges. The disdrometers underreported small- to medium-size drops, which most likely caused the underestimation of rain totals. However, more medium-size drops were measured by the video disdrometer, thus producing higher rain rates for that instrument. The comparison of DSDs, averaged at different timescales, showed good agreement between the two types of disdrometers. A continuous increase in the number of drops toward smaller sizes was only evident in the video disdrometers at rain rates above 20 mm h−1. Otherwise, the concentration of small drops remained the same or decreased to the smallest measurable size. The Joss–Waldvogel disdrometer severely underestimated only at very small drop size (diameter ≤ 0.5 mm). Beyond the Joss–Waldvogel disdrometer measurement limit were very large drops that fell during heavy and extreme rain intensities. The derived parameters of exponential and gamma distributions reflect the good agreement between the disdrometers' DSD measurements. The parameters of fitted distributions were close to each other, especially when all the coincident measurements were averaged. The low concentrations of very large drops observed by the video disdrometers did not have a significant impact on reflectivity measurements in terms of the relationships between reflectivity and other integral parameters (rain rate, liquid water content, and attenuation). There was almost no instrument dependency. Rather, the relations depend on the method of regression and the choice of independent variable. Also, relationships derived for S-band radars and Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) differ from each other primarily because of the higher reflectivities at the shorter PR wavelength at high rain-rate regime.
Abstract
Simultaneous observations made with optical- and impact-type disdrometers were analyzed to broaden knowledge of these instruments. These observations were designed to test how accurately they measure drop size distributions (DSDs). The instruments' use in determining radar rainfall relations such as that between reflectivity and rainfall rate also was analyzed. A unique set of instruments, including two video and one Joss–Waldvogel disdrometer along with eight tipping-bucket rain gauges, was operated within a small area of about 100 × 50 m2 during a 2-month-long field campaign in central Florida. The disdrometers were evaluated by comparing their rain totals with the rain gauges. Both disdrometers underestimated the rain totals, but the video disdrometers had higher readings, resulting in a better agreement with the gauges. The disdrometers underreported small- to medium-size drops, which most likely caused the underestimation of rain totals. However, more medium-size drops were measured by the video disdrometer, thus producing higher rain rates for that instrument. The comparison of DSDs, averaged at different timescales, showed good agreement between the two types of disdrometers. A continuous increase in the number of drops toward smaller sizes was only evident in the video disdrometers at rain rates above 20 mm h−1. Otherwise, the concentration of small drops remained the same or decreased to the smallest measurable size. The Joss–Waldvogel disdrometer severely underestimated only at very small drop size (diameter ≤ 0.5 mm). Beyond the Joss–Waldvogel disdrometer measurement limit were very large drops that fell during heavy and extreme rain intensities. The derived parameters of exponential and gamma distributions reflect the good agreement between the disdrometers' DSD measurements. The parameters of fitted distributions were close to each other, especially when all the coincident measurements were averaged. The low concentrations of very large drops observed by the video disdrometers did not have a significant impact on reflectivity measurements in terms of the relationships between reflectivity and other integral parameters (rain rate, liquid water content, and attenuation). There was almost no instrument dependency. Rather, the relations depend on the method of regression and the choice of independent variable. Also, relationships derived for S-band radars and Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) differ from each other primarily because of the higher reflectivities at the shorter PR wavelength at high rain-rate regime.
Abstract
The relationship between the fractional time raining and tropical rainfall amount is investigated using raingage data and a point process model of tropical rainfall. Both the strength and the nature of the relationship are dependent upon the resolution of the data used to estimate the fractional time raining. It is found that highly accurate estimates of rainfall amounts over periods of one month or greater can be obtained from the fractional time raining so long as high-time-resolution data are used. It is demonstrated that the relationship between the fractional time raining and monthly atoll rainfall is quasi-homogeneous within the monsoon trough region of the equatorial western Pacific.
Abstract
The relationship between the fractional time raining and tropical rainfall amount is investigated using raingage data and a point process model of tropical rainfall. Both the strength and the nature of the relationship are dependent upon the resolution of the data used to estimate the fractional time raining. It is found that highly accurate estimates of rainfall amounts over periods of one month or greater can be obtained from the fractional time raining so long as high-time-resolution data are used. It is demonstrated that the relationship between the fractional time raining and monthly atoll rainfall is quasi-homogeneous within the monsoon trough region of the equatorial western Pacific.
