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Mekonnen Gebremichael
,
Witold F. Krajewski
,
Mark L. Morrissey
,
George J. Huffman
, and
Robert F. Adler

Abstract

This study provides an intensive evaluation of the Global Precipitation Climatology Project (GPCP) 1° daily (1DD) rainfall products over the Mississippi River basin, which covers 435 1° latitude × 1° longitude grids for the period of January 1997–December 2000 using radar-based precipitation estimates. The authors’ evaluation criteria include unconditional continuous, conditional (quasi) continuous, and categorical statistics, and their analyses cover annual and seasonal time periods. The authors present spatial maps that reflect the results for the 1° grids and a summary of the results for three selected regions. They also develop a statistical framework that partitions the GPCP–radar difference statistics into GPCP error and radar error statistics. They further partition the GPCP error statistics into sampling error and retrieval error statistics and estimate the sampling error statistics using a data-based resampling experiment. Highlights of the results include the following: 1) the GPCP 1DD product captures the spatial and temporal variability of rainfall to a high degree, with more than 80% of the variance explained, 2) the GPCP 1DD product proficiently detects rainy days at a large range of rainfall thresholds, and 3) in comparison with radar-based estimates the GPCP 1DD product overestimates rainfall.

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Emmanouil N. Anagnostou
,
Marios N. Anagnostou
,
Witold F. Krajewski
,
Anton Kruger
, and
Benjamin J. Miriovsky

Abstract

The paper presents a rainfall estimation technique based on algorithms that couple, along a radar ray, profiles of horizontal polarization reflectivity (Z H ), differential reflectivity (Z DR), and differential propagation phase shift (ΦDP) from X-band polarimetric radar measurements. Based on in situ raindrop size distribution (DSD) data and using a three-parameter “normalized” gamma DSD model, relationships are derived that correct X-band reflectivity profiles for specific and differential attenuation, while simultaneously retrieving variations of the normalized intercept DSD parameter (N w ). The algorithm employs an iterative scheme to intrinsically account for raindrop oblateness variations from equilibrium condition. The study is facilitated from a field experiment conducted in the period October–November 2001 in Iowa City, Iowa, where observations from X-band dual-polarization mobile radar (XPOL) were collected simultaneously with high-resolution in situ disdrometer and rain-gauge rainfall measurements. The observed rainfall events ranged in intensity from moderate stratiform precipitation to high-intensity (>50 mm h−1) convective rain cells. The XPOL measurements were tested for calibration, noise, and physical consistency using corresponding radar parameters derived from coincidentally measured raindrop spectra. Retrievals of N w from the attenuation correction scheme are shown to be unbiased and consistent with N w values calculated from independent raindrop spectra. The attenuation correction based only on profiles of reflectivity measurements is shown to diverge significantly from the corresponding polarimetric-based corrections. Several rain retrieval algorithms were investigated using matched pairs of instantaneous high-resolution XPOL observations with rain rates from 3-min-averaged raindrop spectra at close range (∼5 km) and rain-gauge measurements from further ranges (∼10 km). It is shown that combining along-a-ray (corrected ZH , Z DR, and specific differential phase shift) values gets the best performance in rainfall estimation with about 40% (53%) relative standard deviation in the radar–disdrometer (radar–gauge) differences. The case-tuned reflectivity–rainfall rate (ZR) relationship gives about 65% (73%) relative standard deviation for the same differences. The systematic error is shown to be low (∼3% overestimation) and nearly independent of rainfall intensity for the multiparameter algorithm, while for the standard ZR it varied from 10% underestimation to 3% overestimation.

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Hatim O. Sharif
,
Fred L. Ogden
,
Witold F. Krajewski
, and
Ming Xue

Abstract

The prediction uncertainty of a hydrologic model is closely related to model formulation and the uncertainties in model parameters and inputs. Currently, the foremost challenges concern not only whether hydrologic model outputs match observations, but also whether or not model predictions are meaningful and useful in the contexts of land use and climate change. The latter is difficult to determine given that model inputs, such as rainfall, have errors and uncertainties that cannot be entirely eliminated. In this paper the physically based simulation methodology developed by Sharif et al. is used to expand this investigation of the propagation of radar rainfall estimation errors in hydrologic simulations. The methodology includes a physics-based mesoscale atmospheric model, a three-dimensional radar simulator, and a two-dimensional infiltration-excess hydrologic model. A time series of simulated three-dimensional precipitation fields over a large domain and a small study watershed are used, which allows development of a large set of rainfall events with different rainfall volumes and vertical reflectivity profiles. Simulation results reveal dominant range-dependent error sources, and frequent amplification of radar rainfall estimation errors in terms of predicted hydrograph characteristics. It is found that in the case of Hortonian runoff predictions, the variance of hydrograph prediction error due to radar rainfall errors decreases for all radar ranges as the event magnitude increases. However, errors in Hortonian runoff predictions increase significantly with range, particularly beyond about 80 km, where the reflectivity signal is increasingly dominated by three-dimensional rainfall heterogeneity with increasing range under otherwise ideal observing conditions.

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Efrat Morin
,
Witold F. Krajewski
,
David C. Goodrich
,
Xiaogang Gao
, and
Soroosh Sorooshian

Abstract

Meteorological radar is a remote sensing system that provides rainfall estimations at high spatial and temporal resolutions. The radar-based rainfall intensities (R) are calculated from the observed radar reflectivities (Z). Often, rain gauge rainfall observations are used in combination with the radar data to find the optimal parameters in the ZR transformation equation. The scale dependency of the power-law ZR parameters when estimated from radar reflectivity and rain gauge intensity data is explored herein. The multiplicative (a) and exponent (b) parameters are said to be “scale dependent” if applying the observed and calculated rainfall intensities to objective function at different scale results in different “optimal” parameters. Radar and gauge data were analyzed from convective storms over a midsize, semiarid, and well-equipped watershed. Using the root-mean-square difference (rmsd) objective function, a significant scale dependency was observed. Increased time- and space scales resulted in a considerable increase of the a parameter and decrease of the b parameter. Two sources of uncertainties related to scale dependency were examined: 1) observational uncertainties, which were studied both experimentally and with simplified models that allow representation of observation errors; and 2) model uncertainties. It was found that observational errors are mainly (but not only) associated with positive bias of the b parameter that is reduced with integration, at least for small scales. Model errors also result in scale dependency, but the trend is less systematic, as in the case of observational errors. It is concluded that identification of optimal scale for ZR relationship determination requires further knowledge of reflectivity and rain-intensity error structure.

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Witold F. Krajewski
,
Mark L. Morrissey
,
James A. Smith
, and
David T. Rexroth

Abstract

A Monte Carlo simulation study is conducted to investigate the performance of the area-threshold method of estimating mean areas rainfall. The study uses a stochastic space-time model of rainfall as the true rainfall-field generator. Simple schemes of simulating radar observations of the simulated rainfall fields are employed. The schemes address both random and systematic components of the radar rainfall-estimation process. The results of the area-threshold method are compared to the results based on conventional averaging of radar-estimated point rainfall observations. The results demonstrate that when the exponent parameter in the ZR relationship has small uncertainty (about ±10%), the conventional method works better than the area-threshold method. When the errors are higher (±20%), the area-threshold method with optimum threshold in the 5–10 mm h−1 range performs best. For even higher errors in the ZR relationship, the area-threshold method with a low threshold provides the best performance.

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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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Jeffrey R. McCollum
,
Witold F. Krajewski
,
Ralph R. Ferraro
, and
Mamoudou B. Ba

Abstract

A bias-adjusted radar rainfall product is created and used for evaluation of two satellite rainfall estimation algorithms. Three years of collocated rainfall estimates from radar, rain gauges, a microwave satellite algorithm, and a multispectral (visible through near-infrared) algorithm were collected over the continental United States from July 1998 through July 2001. The radar and gauge data are compared to determine the locations and times at which the rainfall occurrences estimated by these two sensors are in sufficient agreement for the data to be used for validation. This procedure serves as quality control for both sensors and determines the locations at which the radar has difficulty detecting rainfall and should not be used in a validation dataset. For the data remaining after quality control, the gauge data are used for multiplicative adjustment of the radar estimates to remove the radar bias with respect to the gauges. These bias-adjusted estimates are compared with the satellite rainfall estimates to observe the evolution of the satellite biases over the 3-yr period. The multispectral algorithm was under development throughout the 3-yr period, and improvement is evident. The microwave algorithm overestimates rainfall in the summer months, underestimates in the winter months, and has an east-to-west bias gradient, all of which are consistent with physical explanations and previous findings. The multispectral algorithm bias depends highly on diurnal sampling; there is much greater overestimation for the daytime overpasses. These results are applicable primarily to the eastern half of the United States, because few data in the western half remain after quality control.

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Mekonnen Gebremichael
,
Witold F. Krajewski
,
Mark Morrissey
,
Darin Langerud
,
George J. Huffman
, and
Robert Adler

Abstract

This paper focuses on estimating the error uncertainty of the monthly 2.5° × 2.5° rainfall products of the Global Precipitation Climatology Project (GPCP) using rain gauge observations. Two kinds of GPCP products are evaluated: the satellite-only (MS) product, and the satellite–gauge (SG) merged product. The error variance separation (EVS) method has been proposed previously as a means of estimating the error uncertainty of the GPCP products. In this paper, the accuracy of the EVS results is examined for a variety of gauge densities. Three validation sites—two in North Dakota and one in Thailand—all with a large number of rain gauges, were selected. The very high density of the selected sites justifies the assumption that the errors are negligible if all gauges are used. Monte Carlo simulation studies were performed to evaluate sampling uncertainty for selected rain gauge network densities. Results are presented in terms of EVS error uncertainty normalized by the true error uncertainty. These results show that the accuracy of the EVS error uncertainty estimates for the SG product differs from that of the MS product. The key factors that affect the errors of the EVS results, such as the gauge density, the gauge network, and the sample size, have been identified and their influence has been quantified. One major finding of this study is that 8–10 gauges, at the 2.5° scale, are required as a minimum to get good error uncertainty estimates for the SG products from the EVS method. For eight or more gauges, the normalized error uncertainty is about 0.86 ± 0.10 (North Dakota: Box 1) and 0.95 ± 0.10 (North Dakota: Box 2). Results show that, despite its error, the EVS method performs better than the root-mean-square error (rmse) approach that ignores the rain gauge sampling error. For the MS products, both the EVS method and the rmse approach give negligible bias. As expected, results show that the SG products give better rainfall estimates than the MS products, according to most of the criteria used.

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Merhala Thurai
,
Kumar Vijay Mishra
,
V. N. Bringi
, and
Witold F. Krajewski

Abstract

Data analyses for the mobile Iowa X-band polarimetric (XPOL) radar from a long-duration rain event that occurred during the NASA Iowa Flood Studies (IFloodS) field campaign are presented. A network of six 2D video disdrometers (2DVDs) is used to derive four rain-rate estimators for the XPOL-5 radar. The rain accumulation validations with a collocated network of twin and triple tipping-bucket rain gauges have highlighted the need for combined algorithms because no single estimator was found to be sufficient for all cases considered. A combined version of weighted and composite algorithms is introduced, including a new R(A h, Z dr) rainfall estimator for X band, where A h is the specific attenuation for horizontal polarization and Z dr is the differential reflectivity. Based on measurement and algorithm errors, the weights are derived to be as piecewise constant functions over reflectivity values. The weights are later turned into continuous functions using smoothing splines. A methodology to derive the weights in near–real time is proposed for the composite-weighted algorithm. Comparisons of 2-h accumulations and 8-h event totals obtained from the XPOL-5 with 12 rain gauges have shown 10%–40% improvement in normalized bias over individual rainfall estimators. The analyses have enabled the development of rain-rate estimators for the Iowa XPOL.

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C. Bryan Young
,
A. Allen Bradley
,
Witold F. Krajewski
,
Anton Kruger
, and
Mark L. Morrissey

Abstract

Next-Generation Weather Radar (NEXRAD) multisensor precipitation estimates will be used for a host of applications that include operational streamflow forecasting at the National Weather Service River Forecast Centers (RFCs) and nonoperational purposes such as studies of weather, climate, and hydrology. Given these expanding applications, it is important to understand the quality and error characteristics of NEXRAD multisensor products. In this paper, the issues involved in evaluating these products are examined through an assessment of a 5.5-yr record of multisensor estimates from the Arkansas–Red Basin RFC. The objectives were to examine how known radar biases manifest themselves in the multisensor product and to quantify precipitation estimation errors. Analyses included comparisons of multisensor estimates based on different processing algorithms, comparisons with gauge observations from the Oklahoma Mesonet and the Agricultural Research Service Micronet, and the application of a validation framework to quantify error characteristics. This study reveals several complications to such an analysis, including a paucity of independent gauge data. These obstacles are discussed and recommendations are made to help to facilitate routine verification of NEXRAD products.

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