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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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Alexandros A. Ntelekos, Konstantine P. Georgakakos, and Witold F. Krajewski

Abstract

Quantifying uncertainty associated with flash flood warning or forecast systems is required to enable informed decision making by those responsible for operation and management of natural hazard protection systems. The current system used by the U.S. National Weather Service (NWS) to issue flash-flood warnings and watches over the Unites States is a purely deterministic system. The authors propose a simple approach to augment the Flash Flood Guidance System (FFGS) with uncertainty propagation components. The authors briefly discuss the main components of the system, propose changes to improve it, and allow accounting for several sources of uncertainty. They illustrate their discussion with examples of uncertainty quantification procedures for several small basins of the Illinois River basin in Oklahoma. As the current FFGS is tightly coupled with two technologies, that is, threshold-runoff mapping and the Sacramento Soil Moisture Accounting Hydrologic Model, the authors discuss both as sources of uncertainty. To quantify and propagate those sources of uncertainty throughout the system, they develop a simple version of the Sacramento model and use Monte Carlo simulation to study several uncertainty scenarios. The results point out the significance of the stream characteristics such as top width and the hydraulic depth on the overall uncertainty of the Flash Flood Guidance System. They also show that the overall flash flood guidance uncertainty is higher under drier initial soil moisture conditions. The results presented herein, although limited, are a necessary first step toward the development of probabilistic operational flash flood guidance forecast-response systems.

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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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Ganesh R. Ghimire, Witold F. Krajewski, and Felipe Quintero

Abstract

Incorporating rainfall forecasts into a real-time streamflow forecasting system extends the forecast lead time. Since quantitative precipitation forecasts (QPFs) are subject to substantial uncertainties, questions arise on the trade-off between the time horizon of the QPF and the accuracy of the streamflow forecasts. This study explores the problem systematically, exploring the uncertainties associated with QPFs and their hydrologic predictability. The focus is on scale dependence of the trade-off between the QPF time horizon, basin-scale, space-time scale of the QPF, and streamflow forecasting accuracy. To address this question, the study first performs a comprehensive independent evaluation of the QPFs at 140 U.S. Geological Survey (USGS) monitored basins with a wide range of spatial scales (~10 – 40,000 km2) over the state of Iowa in the Midwestern United States. The study uses High-Resolution Rapid Refresh (HRRR) and Global Forecasting System (GFS) QPFs for short and medium-range forecasts, respectively. Using Multi-Radar Multi-Sensor (MRMS) quantitative precipitation estimate (QPE) as a reference, the results show that the rainfall-to-rainfall QPF errors are scale-dependent. The results from the hydrologic forecasting experiment show that both QPFs illustrate clear value for real-time streamflow forecasting at longer lead times in the short- to medium-range relative to the no-rain streamflow forecast. The value of QPFs for streamflow forecasting is particularly apparent for basin sizes below 1,000 km2. The space-time scale, or reference time (tr) (ratio of forecast lead time to basin travel time) ~ 1 depicts the largest streamflow forecasting skill with a systematic decrease in forecasting accuracy for tr > 1.

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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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Bong-Chul Seo, Felipe Quintero, and Witold F. Krajewski

Abstract

This study addresses the uncertainty of High-Resolution Rapid Refresh (HRRR) quantitative precipitation forecasts (QPFs), which were recently appended to the operational hydrologic forecasting framework. In this study, we examine the uncertainty features of HRRR QPFs for an Iowa flooding event that occurred in September 2016. Our evaluation of HRRR QPFs is based on the conventional approach of QPF verification and the analysis of mean areal precipitation (MAP) with respect to forecast lead time. The QPF verification results show that the precipitation forecast skill of HRRR significantly drops during short lead times and then gradually decreases for further lead times. The MAP analysis also demonstrates that the QPF error sharply increases during short lead times and starts decreasing slightly beyond 4-h lead time. We found that the variability of QPF error measured in terms of MAP decreases as basin scale and lead time become larger and longer, respectively. The effects of QPF uncertainty on hydrologic prediction are quantified through the hillslope-link model (HLM) simulations using hydrologic performance metrics (e.g., Kling–Gupta efficiency). The simulation results agree to some degree with those from the MAP analysis, finding that the performance achieved from the QPF forcing decreases during 1–3-h lead times and starts increasing with 4–6-h lead times. The best performance acquired at the 1-h lead time does not seem acceptable because of the large overestimation of the flood peak, along with an erroneous early peak that is not observed in streamflow observations. This study provides further evidence that HRRR contains a well-known weakness at short lead times, and the QPF uncertainty (e.g., bias) described as a function of forecast lead times should be corrected before its use in hydrologic prediction.

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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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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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Ganesh R. Ghimire, Witold F. Krajewski, and Felipe Quintero

Abstract

Incorporating rainfall forecasts into a real-time streamflow forecasting system extends the forecast lead time. Since quantitative precipitation forecasts (QPFs) are subject to substantial uncertainties, questions arise on the trade-off between the time horizon of the QPF and the accuracy of the streamflow forecasts. This study explores the problem systematically, exploring the uncertainties associated with QPFs and their hydrologic predictability. The focus is on scale dependence of the trade-off between the QPF time horizon, basin-scale, space–time scale of the QPF, and streamflow forecasting accuracy. To address this question, the study first performs a comprehensive independent evaluation of the QPFs at 140 U.S. Geological Survey (USGS) monitored basins with a wide range of spatial scales (~10–40 000 km2) over the state of Iowa in the midwestern United States. The study uses High-Resolution Rapid Refresh (HRRR) and Global Forecasting System (GFS) QPFs for short and medium-range forecasts, respectively. Using Multi-Radar Multi-Sensor (MRMS) quantitative precipitation estimate (QPE) as a reference, the results show that the rainfall-to-rainfall QPF errors are scale dependent. The results from the hydrologic forecasting experiment show that both QPFs illustrate clear value for real-time streamflow forecasting at longer lead times in the short- to medium-range relative to the no-rain streamflow forecast. The value of QPFs for streamflow forecasting is particularly apparent for basin sizes below 1000 km2. The space–time scale, or reference time t r (ratio of forecast lead time to basin travel time), ~1 depicts the largest streamflow forecasting skill with a systematic decrease in forecasting accuracy for t r > 1.

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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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