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  • Author or Editor: Grzegorz J. Ciach x
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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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Grzegorz J. Ciach, Witold F. Krajewski, and James A. Smith

Abstract

No abstract available.

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Grzegorz J. Ciach, Mark L. Morrissey, and Witold F. Krajewski

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.

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Witold F. Krajewski, Grzegorz J. Ciach, Jeffrey R. McCollum, and Ciprian Bacotiu

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.

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Grzegorz J. Ciach, Witold F. Krajewski, Emmanouil N. Anagnostou, Mary L. Baeck, James A. Smith, Jeffrey R. McCollum, and Anton Kruger

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.

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