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- Author or Editor: Witold F. Krajewski x
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Abstract
This paper describes the design and operation of a two-dimensional video disdrometer (2DVD) for in situ measurements of precipitation drop size distribution. The instrument records orthogonal image projections of raindrops as they cross its sensing area, and can provide a wealth of information, including velocity and shape, of individual raindrops. The 2DVD is a sensitive optical instrument that is exposed to rain, high humidity, and possibly high temperatures. These and other issues such as calibration procedures impact its performance. Under low-wind conditions, the instrument can provide accurate and detailed information on drop size, terminal velocity, and drop shape in a field setting, and the instrument's advantages far outweigh its disadvantages.
Abstract
This paper describes the design and operation of a two-dimensional video disdrometer (2DVD) for in situ measurements of precipitation drop size distribution. The instrument records orthogonal image projections of raindrops as they cross its sensing area, and can provide a wealth of information, including velocity and shape, of individual raindrops. The 2DVD is a sensitive optical instrument that is exposed to rain, high humidity, and possibly high temperatures. These and other issues such as calibration procedures impact its performance. Under low-wind conditions, the instrument can provide accurate and detailed information on drop size, terminal velocity, and drop shape in a field setting, and the instrument's advantages far outweigh its disadvantages.
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 multicomponent radar-based algorithm for real-time precipitation estimation is developed. The algorithm emphasizes the combined use of weather radar observations and in situ rain gauge rainfall measurements. The temporal and spatial scales of interest are hourly to storm-total accumulations for areas of 4 km2 to approximately 16 km2. The processing steps include beam–height-effect correction, vertical integration, convective–stratiform classification, conversion from radar observables to rainfall rate, range-effect correction, and transformation of the estimated rainfall rates from polar coordinates to a Cartesian grid. Additionally, the algorithm applies advection correction to the gridded rainfall rates to minimize the temporal sampling effect and, subsequently, aggregates the corrected rainfall rates to 1-hourly, 3-hourly, and storm-total accumulations. The system applies different parameter values for convective and stratiform regimes. The calibration of the system is formulated as a global optimization problem, which is solved using the Gauss–Newton adaptive stochastic method. The algorithm is cast in a recursive formulation with parameters adjusted in real time. Evaluation of the system is based on an extensive dataset from the Melbourne, Florida, WSR-88D radar site.
Abstract
A multicomponent radar-based algorithm for real-time precipitation estimation is developed. The algorithm emphasizes the combined use of weather radar observations and in situ rain gauge rainfall measurements. The temporal and spatial scales of interest are hourly to storm-total accumulations for areas of 4 km2 to approximately 16 km2. The processing steps include beam–height-effect correction, vertical integration, convective–stratiform classification, conversion from radar observables to rainfall rate, range-effect correction, and transformation of the estimated rainfall rates from polar coordinates to a Cartesian grid. Additionally, the algorithm applies advection correction to the gridded rainfall rates to minimize the temporal sampling effect and, subsequently, aggregates the corrected rainfall rates to 1-hourly, 3-hourly, and storm-total accumulations. The system applies different parameter values for convective and stratiform regimes. The calibration of the system is formulated as a global optimization problem, which is solved using the Gauss–Newton adaptive stochastic method. The algorithm is cast in a recursive formulation with parameters adjusted in real time. Evaluation of the system is based on an extensive dataset from the Melbourne, Florida, WSR-88D radar site.
Abstract
The performance of a real-time radar rainfall estimation algorithm is examined based on an extensive dataset of volume scan reflectivity and rain gauge rainfall measurements from the WSR-88D site in Melbourne, Florida. Radar rainfall estimates are evaluated based on the following radar–rain gauge statistics: mean difference (bias), normalized root-mean-square difference, and correlation coefficient. The spatiotemporal scales of interest are hourly accumulations over 4 km × 4 km grids. First, the authors demonstrate the convergence properties of the algorithm’s adaptive parameter estimation procedure and conduct sensitivity tests of the system with respect to changes in the parameter values. Second, the major components of the algorithm are compared with the operational WSR-88D Precipitation Processing Subsystem. The authors show reduction in the radar–rain gauge root-mean-square difference up to 40%, resulting from the new parameterization schemes and the real-time calibration procedure. When rainfall classification is included, the reduction is higher (up to 50%). The authors show that correction for rain field advection moderately improves estimation accuracy (up to 20%). Finally, the authors show that the algorithm can effectively remove range-dependent systematic errors in radar observations.
Abstract
The performance of a real-time radar rainfall estimation algorithm is examined based on an extensive dataset of volume scan reflectivity and rain gauge rainfall measurements from the WSR-88D site in Melbourne, Florida. Radar rainfall estimates are evaluated based on the following radar–rain gauge statistics: mean difference (bias), normalized root-mean-square difference, and correlation coefficient. The spatiotemporal scales of interest are hourly accumulations over 4 km × 4 km grids. First, the authors demonstrate the convergence properties of the algorithm’s adaptive parameter estimation procedure and conduct sensitivity tests of the system with respect to changes in the parameter values. Second, the major components of the algorithm are compared with the operational WSR-88D Precipitation Processing Subsystem. The authors show reduction in the radar–rain gauge root-mean-square difference up to 40%, resulting from the new parameterization schemes and the real-time calibration procedure. When rainfall classification is included, the reduction is higher (up to 50%). The authors show that correction for rain field advection moderately improves estimation accuracy (up to 20%). Finally, the authors show that the algorithm can effectively remove range-dependent systematic errors in radar observations.
Abstract
The WSR-88D Precipitation Processing Subsystem (PPS) is a multicomponent rainfall-estimation algorithm with a large number of parameters controlling its performance. Currently, the parameter values of the PPS are set based on limited experimental studies and do not account for rainfall-regime differences. This translates into potential increase of uncertainty in the system-estimated precipitation products.
The authors propose to formulate the PPS calibration as a global optimization problem. The parameter values are determined by optimizing a selected criterion at the level of gridded hourly rainfall-accumulation products. The criterion is the root-mean-square difference between the hourly radar rainfall products and rainfall accumulations from rain gauges under the radar umbrella. The main advantages of this approach are 1) it simultaneously estimates the optimal parameters providing an integral assessment of the algorithm’s performance, and 2) it allows for an assessment of the relative importance of the PPS parameters in the full context of rainfall estimation.
The optimization approach is illustrated using two months of Melbourne, Florida, WSR-88D radar-reflectivity data and the corresponding rain gauge measurements. Global optimization of the PPS parameters yields a reduction of 10% on average and up to 22% on individual days with respect to the default system. The illustration is completed by a sensitivity analysis of the PPS to identify the most significant parameters.
Abstract
The WSR-88D Precipitation Processing Subsystem (PPS) is a multicomponent rainfall-estimation algorithm with a large number of parameters controlling its performance. Currently, the parameter values of the PPS are set based on limited experimental studies and do not account for rainfall-regime differences. This translates into potential increase of uncertainty in the system-estimated precipitation products.
The authors propose to formulate the PPS calibration as a global optimization problem. The parameter values are determined by optimizing a selected criterion at the level of gridded hourly rainfall-accumulation products. The criterion is the root-mean-square difference between the hourly radar rainfall products and rainfall accumulations from rain gauges under the radar umbrella. The main advantages of this approach are 1) it simultaneously estimates the optimal parameters providing an integral assessment of the algorithm’s performance, and 2) it allows for an assessment of the relative importance of the PPS parameters in the full context of rainfall estimation.
The optimization approach is illustrated using two months of Melbourne, Florida, WSR-88D radar-reflectivity data and the corresponding rain gauge measurements. Global optimization of the PPS parameters yields a reduction of 10% on average and up to 22% on individual days with respect to the default system. The illustration is completed by a sensitivity analysis of the PPS to identify the most significant parameters.
Abstract
This study proposes a flood potential index suitable for use in streamflow forecasting at any location in a drainage network. We obtained the index by comparing the discharge magnitude derived from a hydrologic model and the expected mean annual peak flow at the spatial scale of the basin. We use the term “flood potential” to indicate that uncertainty is associated with this information. The index helps communicate flood potential alerts to communities near rivers where there are no quantitative records of historical floods to provide a reference. This method establishes a reference that we can compare to forecasted hydrographs and that facilitates communication of their relative importance. As a proof of concept, the authors present an assessment of the index as applied to the peak flows that caused severe floods in Iowa in June 2008. The Iowa Flood Center uses the proposed approach operationally as part of its real-time hydrologic forecasting system.
Abstract
This study proposes a flood potential index suitable for use in streamflow forecasting at any location in a drainage network. We obtained the index by comparing the discharge magnitude derived from a hydrologic model and the expected mean annual peak flow at the spatial scale of the basin. We use the term “flood potential” to indicate that uncertainty is associated with this information. The index helps communicate flood potential alerts to communities near rivers where there are no quantitative records of historical floods to provide a reference. This method establishes a reference that we can compare to forecasted hydrographs and that facilitates communication of their relative importance. As a proof of concept, the authors present an assessment of the index as applied to the peak flows that caused severe floods in Iowa in June 2008. The Iowa Flood Center uses the proposed approach operationally as part of its real-time hydrologic forecasting system.
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 authors investigate a disdrometer that provides information on raindrop size distribution, terminal velocity, and shape using video imaging technology. Two video cameras are enclosed in a large box and provide images of the passing drops. The box modifies the air flow, and this in turn affects the drop trajectories, causing some of the drops to miss the sensing area in the instrument’s opening. The authors investigate the distortion of the trajectories using numerical simulation methods of computational fluid dynamics. This approach enables the authors to quantify the effects of wind velocity and direction on the instrument’s measurement of drop size distribution. The results of the study lead to the conclusion that the shape of the enclosure of the instrument causes errors in the detection of the small drops. Small drops can get caught in a vortex that develops over the inlet. Some of them end up being counted more than once as they cross the sensing area while others are carried away and not counted at all. Also, the spatial distribution of the drops passing across the sensing area is distorted by the wind. The computational results are supported by observational evidence.
Abstract
The authors investigate a disdrometer that provides information on raindrop size distribution, terminal velocity, and shape using video imaging technology. Two video cameras are enclosed in a large box and provide images of the passing drops. The box modifies the air flow, and this in turn affects the drop trajectories, causing some of the drops to miss the sensing area in the instrument’s opening. The authors investigate the distortion of the trajectories using numerical simulation methods of computational fluid dynamics. This approach enables the authors to quantify the effects of wind velocity and direction on the instrument’s measurement of drop size distribution. The results of the study lead to the conclusion that the shape of the enclosure of the instrument causes errors in the detection of the small drops. Small drops can get caught in a vortex that develops over the inlet. Some of them end up being counted more than once as they cross the sensing area while others are carried away and not counted at all. Also, the spatial distribution of the drops passing across the sensing area is distorted by the wind. The computational results are supported by observational evidence.
