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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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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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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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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 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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Felipe Quintero, Witold F. Krajewski, and Marcela Rojas

Abstract

This study proposes a flood potential index suitable for use in streamflow forecasting at any location in a drainage network. We obtained the index by comparing the discharge magnitude derived from a hydrologic model and the expected mean annual peak flow at the spatial scale of the basin. We use the term “flood potential” to indicate that uncertainty is associated with this information. The index helps communicate flood potential alerts to communities near rivers where there are no quantitative records of historical floods to provide a reference. This method establishes a reference that we can compare to forecasted hydrographs and that facilitates communication of their relative importance. As a proof of concept, the authors present an assessment of the index as applied to the peak flows that caused severe floods in Iowa in June 2008. The Iowa Flood Center uses the proposed approach operationally as part of its real-time hydrologic forecasting system.

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Bong-Chul Seo and Witold F. Krajewski

Abstract

This study explores the scale effects of radar rainfall accumulation fields generated using the new super-resolution level II radar reflectivity data acquired by the Next Generation Weather Radar (NEXRAD) network of the Weather Surveillance Radar-1988 Doppler (WSR-88D) weather radars. Eleven months (May 2008–August 2009, exclusive of winter months) of high-density rain gauge network data are used to describe the uncertainty structure of radar rainfall and rain gauge representativeness with respect to five spatial scales (0.5, 1, 2, 4, and 8 km). While both uncertainties of gauge representativeness and radar rainfall show simple scaling behavior, the uncertainty of radar rainfall is characterized by an almost 3 times greater standard error at higher temporal and spatial resolutions (15 min and 0.5 km) than at lower resolutions (1 h and 8 km). These results may have implications for error propagation through distributed hydrologic models that require high-resolution rainfall input. Another interesting result of the study is that uncertainty obtained by averaging rainfall products produced from the super-resolution reflectivity data is slightly lower at smaller scales than the uncertainty of the corresponding resolution products produced using averaged (recombined) reflectivity data.

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James A. Smith and Witold F. Krajewski

Abstract

In this paper procedures are developed for estimating the mean field bias of radar rainfall estimates. Mean field bias is modeled as a random process that varies not only from storm to storm but also over the course of a storm. State estimates of mean field bias are based on hourly raingage data and hourly accumulations of radar rainfall estimates. The procedures are developed for the precipitation processing systems used with products of the Next Generation Weather Radar (NEXRAD) system. To implement the state estimation procedures, parameters of the bias model must be specified. Likelihood-based procedures are developed for estimating these parameters. A simulation experiment is carried out to assess performance of the parameter estimation procedure. Convergence of parameter estimators is rapid for the cases studied, with data from approximately 25 storms providing parameter estimates of acceptable accuracy. The state estimation procedures are applied to radar and raingage data from the 27 May 1987 storm, which was centered near the NSSL radar in Norman, Oklahoma. The results highlight dependence of the state estimation problem on the parameter estimation problem.

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Emmanouil N. Anagnostou and Witold F. Krajewski

Abstract

A multicomponent radar-based algorithm for real-time precipitation estimation is developed. The algorithm emphasizes the combined use of weather radar observations and in situ rain gauge rainfall measurements. The temporal and spatial scales of interest are hourly to storm-total accumulations for areas of 4 km2 to approximately 16 km2. The processing steps include beam–height-effect correction, vertical integration, convective–stratiform classification, conversion from radar observables to rainfall rate, range-effect correction, and transformation of the estimated rainfall rates from polar coordinates to a Cartesian grid. Additionally, the algorithm applies advection correction to the gridded rainfall rates to minimize the temporal sampling effect and, subsequently, aggregates the corrected rainfall rates to 1-hourly, 3-hourly, and storm-total accumulations. The system applies different parameter values for convective and stratiform regimes. The calibration of the system is formulated as a global optimization problem, which is solved using the Gauss–Newton adaptive stochastic method. The algorithm is cast in a recursive formulation with parameters adjusted in real time. Evaluation of the system is based on an extensive dataset from the Melbourne, Florida, WSR-88D radar site.

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