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Mekonnen Gebremichael and Witold F. Krajewski

Abstract

On the basis of temporally sampled data obtained from satellites, spatial statistics of rainfall can be estimated. In this paper, the authors compare the estimated spatial statistics with their “true” or ensemble values calculated using 5 yr of 15-min radar-based rainfall data at a spatial domain of 512 km × 512 km in the central United States. The authors conducted a Monte Carlo sampling experiment to simulate different sampling scenarios for variable sampling intervals and rainfall averaging periods. The spatial statistics used are the moments of spatial distribution of rainfall, the spatial scaling exponents, and the spatial cross correlations between the sample and ensemble rainfall fields. The results demonstrated that the expected value of the relative error in the mean rain-rate estimate is zero for rainfall averaged over 5 days or longer, better temporal sampling produces average fields that are “less noisy” spatially, an increase in the sampling interval causes the sampled rainfall to be increasingly less correlated with the true rainfall map, and the spatial scaling exponent estimators could give a bias of 40% or less. The results of this study provide a basis for understanding the impact of temporal statistics on inferred spatial statistics.

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Mekonnen Gebremichael and Witold F. Krajewski

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The main objective of this study is to assess the ability of radar-derived rainfall products to characterize the small-scale spatial variability of rainfall. The authors use independent datasets from high-quality dense rain gauge networks employed during the Texas and Florida Underflights (TEFLUN-B) and Tropical Rainfall Measuring Mission component of the Large-Scale Biosphere–Atmosphere (TRMM-LBA) field experiments conducted by NASA in 1998 and 1999. A detailed comparison between gauge- and radar-derived spatial variability estimates is carried out by means of a correlation function, covariance, variogram, scaling characteristics, and variance reduction due to spatial averaging. Emphasis is given to the correlation function because it is involved in most of these statistics. The approach followed in the analysis addresses the problems associated with the traditional estimation methods and the recognized differences in the scales of observation. The performance of the radar-derived correlation function is evaluated in two ways: by direct comparison with gauge-derived correlation function and by quantifying its effect on one of the applications, that is, gauge sampling uncertainty estimation. Results show that, at separation distances shorter than about 5 km, radar-derived correlations are lower than those obtained from gauges. Three sources of uncertainty that may have caused the discrepancy between gauge- and radar-derived correlations are identified, and their effects are quantified to the extent possible. The error introduced in gauge sampling uncertainty estimates due to the use of radar-derived correlation function is within 30%. Discrepancies between gauge- and radar-rainfall fields are also observed in terms of the other spatial statistics.

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Dawit A. Zeweldi and Mekonnen Gebremichael

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In this study, a comparison of the spatial patterns of high-resolution precipitation products obtained from the Climate Prediction Center’s morphing technique (CMORPH), which is a satellite-only product, and gauge-adjusted Next Generation Weather Radar (NEXRAD) rainfall observations is performed using a variety of statistical techniques for the Little Washita watershed region in Oklahoma for a 3-yr period. Results show that 1) the performance statistics of CMORPH show tremendous variability from one hour to the next, suggesting that the performance statistics are dynamic in time, and therefore each satellite rainfall product should be accompanied by an error product to make it more meaningful; 2) CMORPH is positively biased in summer and negatively biased in winter, consistent with the findings of previous studies; 3) CMORPH spatial fields tend to be smoother than NEXRAD output; 4) the errors are temporally correlated, in particular within the range from 1 to 6 accumulation hours, implying that averaging CMORPH products over these time scales does not reduce the errors significantly; and 5) the errors become less correlated in time as the averaging time scale increases to the range from 6 to 24 h.

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Bin Pei, Firat Y. Testik, and Mekonnen Gebremichael

Abstract

Motivated by the field observations of fall velocity and axis ratio deviations from predicted terminal velocity and equilibrium axis ratio values, the combined effects of raindrop fall velocity and axis ratio deviations on dual-polarization radar rainfall estimations were investigated. A radar rainfall retrieval algorithm [Colorado State University–Hydrometeor Identification Rainfall Optimization (CSU-HIDRO)] served as the test bed. Subsequent investigations determined that the available field measurements, which were very limited in scope, of the fall velocity and axis ratio deviations indicated rain-rate estimation errors of approximately 20%. Based on these findings, a sensitivity study was then performed using uncorrelated fall velocity and axis ratio deviations around the predicted values. Significant rain-rate estimation errors were observed for the realistic combinations of fall velocity and axis ratio deviations. It was shown that the maximum rain-rate estimation error can reach up to approximately 200% for combinations of fall velocity and axis ratio deviations (5000 drop size distribution samples were simulated for each combination) between −10% and +10% of the predicted values for each. The maximum standard deviation of errors was as great as 75% for the same combinations of fall velocity and axis ratio deviations. The authors found that use of dual-polarization radars to accurately estimate rainfall, during natural rain events, also requires a reanalysis of the parameterizations for raindrop fall velocity and axis ratio. These parameterizations should consider both the coupling between these two parameters and factors that may introduce any possible deviations of the predicted values of these parameters.

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Feyera A. Hirpa, Mekonnen Gebremichael, and Thomas Hopson

Abstract

This study focuses on the evaluation of 3-hourly, 0.25° × 0.25°, satellite-based precipitation products: the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42RT, the NOAA/Climate Prediction Center morphing technique (CMORPH), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN). CMORPH is primarily microwave based, 3B42RT is primarily microwave based when microwave data are available and infrared based when microwave data are not available, and PERSIANN is primarily infrared based. The results show that 1) 3B42RT and CMORPH give similar rainfall fields (in terms of bias, spatial structure, elevation-dependent trend, and distribution function), which are different from PERSIANN rainfall fields; 2) PERSIANN does not show the elevation-dependent trend observed in rain gauge values, 3B42RT, and CMORPH; and 3) PERSIANN considerably underestimates rainfall in high-elevation areas.

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Jonathan Woody, Robert Lund, and Mekonnen Gebremichael

Abstract

High-resolution satellite precipitation estimates, such as the Climate Prediction Center morphing technique (CMORPH), provide alternative sources of precipitation data for hydrological applications, especially in regions where adequate ground-based instruments are unavailable. These estimates are, however, subject to large errors, especially at times of heavy precipitation. This paper presents a method to distributionally convert a set of CMORPH estimates into ground-based Next Generation Weather Radar (NEXRAD) estimates. As our concern lies with floods and extreme precipitation events, a peaks-over-threshold extreme value approach is adopted that fits a generalized Pareto distribution to the large precipitation estimates. A quantile matching transformation is then used to convert CMORPH values into NEXRAD values. The methods are applied in the analysis of 6 yr of precipitation observations from 625 pixels centered around eastern Oklahoma.

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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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Dawit A. Zeweldi, Mekonnen Gebremichael, and Charles W. Downer

Abstract

The objective is to assess the use of the Climate Prediction Center morphing method (CMORPH) (~0.073° latitude–longitude, 30 min resolution) rainfall product as input to the physics-based fully distributed Gridded Surface–Subsurface Hydrologic Analysis (GSSHA) model for streamflow simulation in the small (21.4 km2) Hortonian watershed of the Goodwin Creek experimental watershed located in northern Mississippi. Calibration is performed in two different ways: using rainfall data from a dense network of 30 gauges as input, and using CMORPH rainfall data as input. The study period covers 4 years, during which there were 24 events, each with peak flow rate higher than 0.5 m3 s−1. Streamflow simulations using CMORPH rainfall are compared against observed streamflows and streamflow simulations using rainfall from a dense rain gauge network. Results show that the CMORPH simulations captured all 24 events. The CMORPH simulations have comparable performance with gauge simulations, which is striking given the significant differences in the spatial scale between the rain gauge network and CMORPH. This study concludes that CMORPH rainfall products have potential value for streamflow simulation in such small watersheds. Overall, the performance of CMORPH-driven simulations increases when the model is calibrated with CMORPH data than when the model is calibrated with rain gauge data.

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Alemseged T. Haile, Tom Rientjes, Ambro Gieske, and Mekonnen Gebremichael

Abstract

The water resource of the Blue Nile River is of key regional importance to the northeastern African countries. However, little is known about the characteristics of the rainfall in the basin. In this paper, the authors presented the space–time variability of the rainfall in the vicinity of Lake Tana, which is the source of the Blue Nile River. The analysis was based on hourly rainfall data from a network of newly installed rain gauges, and cloud temperature indices from the Meteosat Second Generation (MSG–2) Spinning Enhanced Visible and Infrared Imager (SEVIRI) satellite sensor. The spatial and temporal patterns of rainfall were examined using not only statistical techniques such as exceedance probabilities, spatial correlation structure, harmonic analysis, and fractal analysis but also marginal statistics such as mean and standard deviation. In addition, a convective index was calculated from remote sensing images to infer the spatial and temporal patterns of rainfall. Heavy rainfall is frequent at stations that are relatively close to the lake. The correlation distances for the hourly and the daily rainfall are found at about 8 and 18 km, respectively. The rainfall shows a strong spatially varying diurnal cycle. The nocturnal rainfall was found to be higher over the southern shore of Lake Tana than over the mountainous area farther to the south. The maximum convection occurs between 1600 and 1700 local standard time (LST) over the Gilgel Abbay, Ribb, and Gumara catchments, and between 2200 and 2300 LST over Lake Tana and the Megech catchments. In addition, the hourly rainfall of the station with the highest elevation is relatively closely clustered as compared to those stations at lower elevation. The study provides relevant information for understanding rainfall variation with elevation and distance from a lake. This understanding benefits climate and hydrological studies, water resources management, and energy development in the region.

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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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