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Bertrand Vignal
and
Witold F. Krajewski

Abstract

The vertical variability of reflectivity is an important source of error that affects estimations of rainfall quantity by radar. This error can be reduced if the vertical profile of reflectivity (VPR) is known. Different methods are available to determine VPR based on volume-scan radar data. Two such methods were tested. The first, used in the Swiss Meteorological Service, estimates a mean VPR directly from volumetric radar data collected close to the radar. The second method takes into account the spatial variability of reflectivity and relies on solving an inverse problem in determination of the local profile. To test these methods, two years of archived level-II radar data from the Weather Surveillance Radar-1988 Doppler (WSR-88D) located in Tulsa, Oklahoma, and the corresponding rain gauge observations from the Oklahoma Mesonet were used. The results, obtained by comparing rain estimates from radar data corrected for the VPR influence with rain gauge observations, show the benefits of the methods—and also their limitations. The performance of the two methods is similar, but the inverse method consistently provides better results. However, for use in operational environments, it would require substantially more computational resources than the first method.

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Gabriele Villarini
and
Witold F. Krajewski

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 (ZR) 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.

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Mircea Grecu
and
Witold F. Krajewski

Abstract

To detect anomalous propagation echoes in radar data, an automated procedure based on a neural network classification scheme has been developed. Earlier results had indicated that algorithms used to detect anomalous propagation must be calibrated before they can be applied to new sites. Developing a calibration dataset is typically laborious as it involves a human expert. To eliminate this problem, an efficient methodology of calibrating and validating neural network–based detection is proposed. Using volume scan radar reflectivity data from two WSR-88D locations, the authors demonstrate that the procedure can be calibrated easily and applied successfully to different sites.

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Mekonnen Gebremichael
and
Witold F. Krajewski

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.

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Witold F. Krajewski
and
Bertrand Vignal

Abstract

A method of detecting anomalous propagation echo in volume scan radar reflectivity data is evaluated. The method is based on a neural network approach and is suitable for operational implementation. It performs a classification of the base scan data on a pixel-by-pixel basis into two classes: rain and no rain. The results of applying the method to a large sample of Weather Surveillance Radar-1988 Doppler (WSR-88D) level II archive data are described. The data consist of over 10 000 volume scans collected in 1994 and 1995 by the Tulsa, Oklahoma, WSR-88D. The evaluation includes analyses based on radar data only and on various comparisons of radar and rain gauge data. The rain gauge data are from the Oklahoma Mesonet. The results clearly show the effectiveness of the procedure as indicated by reduced bias in rainfall accumulation and improved behavior in other statistics.

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Mekonnen Gebremichael
and
Witold F. Krajewski

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.

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Anton Kruger
and
Witold F. Krajewski

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.

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Emad Habib
and
Witold F. Krajewski

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.

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Vladislav Nešpor
,
Witold F. Krajewski
, and
Anton Kruger

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.

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Grzegorz J. Ciach
and
Witold F. Krajewski

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.

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