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Mark L. Morrissey, Witold F. Krajewski, and Michael J. McPhaden

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.

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Emmanouil N. Anagnostou, Witold F. Krajewski, and James Smith

Abstract

The most common rainfall measuring sensor for validation of radar-rainfall products is the rain gauge. However, the difference between area-rainfall and rain gauge point-rainfall estimates imposes additional noise in the radar–rain gauge difference statistics, which should not be interpreted as radar error. A methodology is proposed to quantify the radar-rainfall error variance by separating the variance of the rain gauge area-point rainfall difference from the variance of radar–rain gauge ratio. The error in this research is defined as the ratio of the “true” rainfall to the estimated mean-areal rainfall by radar and rain gauge. Both radar and rain gauge multiplicative errors are assumed to be stochastic variables, lognormally distributed, with zero covariance. The rain gauge area-point difference variance is quantified based on the areal-rainfall variance reduction factor evaluated in the logarithmic domain. The statistical method described here has two distinct characteristics: first, it proposes a range-dependent formulation for the error variance, and second, the error variance estimates are relative to the mean rainfall at the radar product grids. Two months of radar and rain gauge data from the Melbourne, Florida, WSR-88D are used to illustrate the proposed method. The study concentrates on hourly rainfall accumulations at 2- and 4-km grid resolutions. Results show that the area-point difference in rain gauge rainfall contributes up to 60% of the variance observed in radar–rain gauge differences, depending on the radar grid size, the location of the sampling point in the grid, and the distance from the radar.

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Grzegorz J. Ciach, Witold F. Krajewski, and James A. Smith

Abstract

No abstract available.

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Mark N. French, Hervé Andrieu, and Witold F. Krajewski

Abstract

Radar reflectivity is used to estimate meteorological quantities such as rainfall rate, liquid water content, and the related quantity, vertically integrated liquid (VIL) water content. The estimation of any of these quantities depends on several assumptions related to the characteristics of the physical processes controlling the occurrence and character of water in the atmosphere. Additionally, there are many sources of error associated with radar observations, such as those due to brightband, hail, and drop size distribution approximations. This work addresses one error of interest, the radar reflectivity observation error; other error sources are assumed to be corrected or negligible. The result is a relationship between the uncertainty in VIL water content and radar reflectivity measurement error. An example application illustrates the estimation of VIL uncertainty from typical radar reflectivity observations and indicates that the coefficient of variation in VIL is much larger than the coefficient of variation in radar reflectivity.

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Marco Borga, Emmanouil N. Anagnostou, and Witold F. Krajewski

Abstract

Brightband effects are one of the more important causes of vertical variability of reflectivity and severely affect the accuracy of rainfall estimates from ground-based radar. Monte Carlo simulation experiments are performed to investigate the efficiency of a procedure for the correction of errors related to the vertical variability of reflectivity. The simulation model generates three-dimensional radar reflectivity fields. Brightband effects are simulated through a physically based model of melting-layer reflectivity observations. Sensitivity of the correction procedure for a number of different precipitation scenarios and radar systems is analyzed. Overall, the identification method is found to be a robust procedure for correction of brightband effects. Results indicate a dependence of the effectiveness of the correction procedure on mean altitude and spatial variability of the melting layer.

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Paul A. Kucera, Witold F. Krajewski, and C. Bryan Young

Abstract

Geographic information systems (GISs) combined with digital elevation models (DEMs) provide opportunities to evaluate weather radar beam blockage and other ground clutter phenomena. The authors explore this potential using topographic information and a simple beam propagation model for the complex terrain of Guam. To evaluate the effect of different DEM resolutions, they compare the simulated patterns of complete and partial beam blockage with probability of detection maps derived from a large database of level II radar reflectivity for the U.S. Air Force Weather Surveillance Radar-1988 Doppler (WSR-88D) on Guam. The main conclusion of the study is that the GIS approach provides useful insight into the actual pattern of blocked areas. The DEM resolution plays a role in resolving the blocked patterns. In general, higher DEM resolution provides better results although widely available lower-resolution DEMs can provide valuable information about beam-blocking effects.

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RADAR-Rainfall Uncertainties

Where are We after Thirty Years of Effort?

Witold F. Krajewski, Gabriele Villarini, and James A. Smith

Thirty years ago, Wilson and Brandes determined that radar data was “underutilized and both confusion and misunderstanding exist about the inherent ability of radar to measure rainfall, about factors that contribute to errors, and about the importance of careful calibration and signal processing.” In their seminal work, they addressed these issues by delineating the strengths and weaknesses of radar data and offering a detailed discussion of the different sources of uncertainties associated with radar-based estimates of rainfall. After three decades, we want to underscore the importance of Wilson and Brandes' paper by using it as a reference for discussing subsequent improvements in operational radar-rainfall technology in the United States. We replicated their analysis as closely as we could and present the results in this paper. Our results, which are based on an analysis of Weather Surveillance Radar-1988 Doppler (WSR-88D) data, indicate fairly substantial improvement in terms of the statistical measures used by Wilson and Brandes.

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Emad Habib, Witold F. Krajewski, and Grzegorz J. Ciach

Abstract

This study discusses questions of estimating correlation coefficient of point rainfall as observed at two measuring stations. The focus is on issues such as sensitivity to sample size, extreme rain events, and distribution of rainfall. The authors perform extensive analysis based on a two-point data-driven rainfall model that simulates the intermittence and extreme variability of rainfall using a bivariate mixed-lognormal distribution. The study examines the commonly used product–moment estimator along with an alternative transformation-based estimator. The results show a high level of bias and variance of the traditional correlation estimator, which are caused mostly by significant skewness levels that characterize rainfall observations. Application using data from a high-density cluster indicated the advantages of using the alternative estimator. The overall aim of the study is to draw the attention of researchers working with rainfall to some commonly disregarded issues when they seek accurate and reliable correlation information.

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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, Ganesh R. Ghimire, and Felipe Quintero

ABSTRACT

The authors explore persistence in streamflow forecasting based on the real-time streamflow observations. They use 15-min streamflow observations from the years 2002 to 2018 at 140 U.S. Geological Survey (USGS) streamflow gauges monitoring the streams and rivers throughout Iowa. The spatial scale of the basins ranges from about 7 to 37 000 km2. Motivated by the need for evaluating the skill of real-time streamflow forecasting systems, the authors perform quantitative skill assessment of persistence schemes across spatial scales and lead times. They show that skill in temporal persistence forecasting has a strong dependence on basin size, and a weaker dependence on geometric properties of the river networks. Building on results from this temporal persistence, they extend the streamflow persistence forecasting to space through flow-connected river networks. The approach simply assumes that streamflow at a station in space will persist to another station which is flow connected; these are referred to as pure spatial persistence forecasts (PSPF). The authors show that skill of PSPF of streamflow is strongly dependent on the monitored versus predicted basin area ratio and lead times, and weakly related to the downstream flow distance between stations. River network topology shows some effect on the hydrograph timing and timing of the peaks, depending on the stream gauge configuration. The study shows that the skill depicted in terms of Kling–Gupta efficiency (KGE) > 0.5 can be achieved for basin area ratio > 0.6 and lead time up to 3 days. The authors discuss the implications of their findings for assessment and improvements of rainfall–runoff models, data assimilation schemes, and stream gauging network design.

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