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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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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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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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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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Ali Tokay, Anton Kruger, and Witold F. Krajewski

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.

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Witold F. Krajewski, R. Raghavan, and V. Chandrasekar

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.

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Witold F. Krajewski and James A. Smith

Abstract

A statistical framework for climatological ZR 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 ZR parameters can be estimated by maximum likelihood, a procedure with optimal large sample properties. A general nonparametric framework for climatological ZR 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 ZR 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 ZR model parameter estimates. These results are particular useful for error analysis of precipitation products that are derived using climatological ZR relations. One example is the large-area rainfall estimates derived using the height-area rainfall threshold (HART) technique.

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Jeffrey R. McCollum and Witold F. Krajewski

Abstract

The relationship between monthly mean area-averaged rainfall and monthly mean fractional rainfall occurrence is used to develop a new method of open ocean rainfall estimation. This method uses acoustic sensors attached to drifting buoys to sample rainfall occurrence in space and time. The fractional rainfall occurrences measured by the sensors are used in a linear relationship to estimate monthly rainfall averaged over large (i.e., 2.5° × 2.5°) areas. This estimation method is tested for different scenarios using a stochastic model. Results support the feasibility of this new rainfall estimation scheme. Simulations show that the existing density of drifting buoys is inadequate, but densities around 10 times the existing density will give correlation coefficients between estimated and true rainfall around 0.55. Estimates obtained with this method may be used to calibrate and/or validate the satellite-based methods of open ocean rainfall.

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