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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, Witold F. Krajewski, and James A. Smith

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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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Bong-Chul Seo, Witold F. Krajewski, and Alexander Ryzhkov

Abstract

This study demonstrates an implementation of the prototype quantitative precipitation R estimation algorithm using specific attenuation A for S-band polarimetric radar. The performance of R(A) algorithm is assessed, compared to the conventional algorithm using radar reflectivity Z, at multiple temporal scales. Because the factor α, defined as the net ratio of A to specific differential phase, is a key parameter of the algorithm characterized by drop size distributions (e.g., differential reflectivity Z dr dependence on Z), the estimation equations of α and a proper number of Z drZ samples required for a reliable α estimation are examined. Based on the dynamic estimation of α, the event-based evaluation using hourly rain gauge observations reveals that the performance of R(A) is superior to that of R(Z), with better agreement and lower variability. Despite its superiority, the study finds that R(A) leads to quite consistent overestimations of about 10%–30%. It is demonstrated that the application of uniform α over the entire radar domain yields the observed uncertainty because of the heterogeneity of precipitation in the domain. A climatological range-dependent feature of R(A) and R(Z) is inspected in the multiyear evaluation at yearly scale using rain totals for April–October. While R(Z) exposes a systematic shift and overestimation, each of which arise from the radar miscalibration and bright band effects, R(A) combining with multiple R(Z) values for solid/mixed precipitation shows relatively robust performance without those effects. The immunity of R(A) to partial beam blockage (PBB) based on both qualitative and quantitative analyses is also verified. However, the capability of R(A) regarding PBB is limited by the presence of the melting layer and its application requirement for the total span of differential phase (e.g., 3°), which is another challenge for light rain.

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Mekonnen Gebremichael, Thomas M. Over, and Witold F. Krajewski

Abstract

In view of the importance of tropical rainfall and the ubiquitous need for its estimates in climate modeling, the authors assess the ability of the Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) to characterize the scaling characteristics of rainfall by comparing the derived results with those obtained from the ground-based radar (GR) data. The analysis is based on 59 months of PR and GR rain rates at three TRMM ground validation (GV) sites: Houston, Texas; Melbourne, Florida; and Kwajalein Atoll, Republic of the Marshall Islands. The authors consider spatial scales ranging from about 4 to 64 km at a fixed temporal scale corresponding to the sensor “instantaneous” snapshots (∼15 min). The focus is on the scaling of the marginal moments, which allows estimation of the scaling parameters from a single scene of data. The standard rainfall products of the PR and the GR are compared in terms of distributions of the scaling parameter estimates, the connection between the scaling parameters and the large-scale spatial average rain rate, and deviations from scale invariance. The five main results are as follows: 1) the PR yields values of the rain intermittence scaling parameter within 20% of the GR estimate; 2) both the PR and GR data show a one-to-one relationship between the intermittence scaling parameter and the large-scale spatial average rain rate that can be fit with the same functional form; 3) the PR underestimates the curvature of the scaling function from 20% to 50%, implying that high rain-rate extremes would be missed in a downscaling procedure; 4) the majority of the scenes (>85%) from both the PR and GR are scale invariant at the moment orders q = 0 and 2; and 5) the scale-invariance property tends to break down more likely over ocean than over land; the rainfall regimes that are not scale invariant are dominated by light storms covering large areas. Our results further show that for a sampling size of one year of data, the TRMM temporal sampling does not significantly affect the derived scaling characteristics. The authors conclude that the TRMM PR has the ability to characterize the basic scaling properties of rainfall, though the resulting parameters are subject to some degree of uncertainty.

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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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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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Stanislaw Moszkowicz, Grzegorz J. Ciach, and Witold F. Krajewski

Abstract

The problem of anomalous propagation (AP) echoes in weather radar observations has become especially important now that rainfall data from fully automatic radar systems are sometimes applied in operational hydrology. Reliable automatic detection and suppression of AP echoes is one of the crucial problems in this area.

This study presents characteristics of AP patterns and the initial results of applying a statistical pattern classification method for recognition and rejection of such echoes. A classical radar (MRL-5) station operates in central Poland performing volume scanning every 10 min. Two months of hourly data (June and September of 1991) were chosen to create learning and verification samples for the AP detection algorithm. Each observation was thoroughly analyzed by an experienced radar meteorologist. The features taken into account were visually estimated local texture and overall morphology of echo pattern, vertical echo structure, time evolution (using animation), and the general synoptic information. For each 4 km × 4 km pixel of 933 observations the human classification was recorded resulting in a sample of 631 166 points with recognized echo type, 14.6% of them being AP echoes. The unsuppressed AP echo impact on monthly accumulated precipitation was 59% of the actual sum for the month of June and as much as 97% for September.

Three Bayesian discrimination functions were investigated. They differ in selection of the feature vector. This vector consisted of various local radar echo parameters: for example, maximum reflectivity, echo top, and horizontal gradients. The coefficients of the functions were calibrated using the June sample. The AP echo recognition error was about 6% for the best-performing function, when applied to an independent (September) sample, which would make the method acceptable for operational use.

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Grzegorz J. Ciach, Witold F. Krajewski, and Gabriele Villarini

Abstract

Although it is broadly acknowledged that the radar-rainfall (RR) estimates based on the U.S. national network of Weather Surveillance Radar-1988 Doppler (WSR-88D) stations contain a high degree of uncertainty, no methods currently exist to inform users about its quantitative characteristics. The most comprehensive characterization of this uncertainty can be achieved by delivering the products in a probabilistic rather than the traditional deterministic form. The authors are developing a methodology for probabilistic quantitative precipitation estimation (PQPE) based on weather radar data. In this study, they present the central element of this methodology: an empirically based error structure model for the RR products.

The authors apply a product-error-driven (PED) approach to obtain a realistic uncertainty model. It is based on the analyses of six years of data from the Oklahoma City, Oklahoma, WSR-88D radar (KTLX) processed with the Precipitation Processing System algorithm of the NEXRAD system. The modeled functional-statistical relationship between RR estimates and corresponding true rainfall consists of two components: a systematic distortion function and a stochastic factor quantifying remaining random errors. The two components are identified using a nonparametric functional estimation apparatus. The true rainfall is approximated with rain gauge data from the Oklahoma Mesonet and the U.S. Department of Agriculture (USDA) Agricultural Research Service Micronet networks. The RR uncertainty model presented here accounts for different time scales, synoptic regimes, and distances from the radar. In addition, this study marks the first time in which results on RR error correlation in space and time are presented.

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Alexandros A. Ntelekos, James A. Smith, and Witold F. Krajewski

Abstract

The climatology of thunderstorms and flash floods in the Baltimore, Maryland, metropolitan region is examined through analyses of cloud-to-ground (CG) lightning observations from the National Lightning Detection Network (NLDN) and discharge observations from 11 U.S. Geological Survey (USGS) stream gauging stations. A point process framework is used for analyses of CG lightning strikes and the occurrences of flash floods. Analyses of lightning strikes as a space–time point process focus on the mean intensity function, from which the seasonal, diurnal, and spatial variation in mean lightning frequency are examined. Important elements of the spatial variation of mean lightning frequency are 1) initiation of thunderstorms along the Blue Ridge, 2) large variability of lightning frequency around the urban cores of Baltimore and Washington D.C., and 3) decreased lightning frequency over the Chesapeake Bay and Atlantic Ocean. Lightning frequency has a sharp seasonal maximum around mid-July, and the diurnal cycle of lightning frequency peaks between 2100 and 2200 UTC with a frequency that is more than an order of magnitude larger than the minimum frequency at 1200 UTC. The seasonal and diurnal variation of flash flood occurrence in urban streams of Baltimore mimics the seasonal and diurnal variation of lightning. The peak of the diurnal frequency of flash floods in Moores Run, a 9.1-km2 urban watershed in Baltimore City, occurs at 2200 UTC. Analyses of the lightning and flood peak data also show a close link between the occurrence of major thunderstorms systems and flash flooding on a regional scale.

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