Edward A. Brandes

Radar Measurement of Rainfall—A Summary

Abstract Radar can produce detailed precipitation information for large areas from a single location in real time. Although radar has been used experimentally for nearly 30 years to measure rainfall, operational implementation has been slow. Today we find that data are 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. Areal and point rainfall estimates are often in error by a factor of two or more. Error sources reside in measurement of radar reflectivity factor, evaporation and advection of precipitation before reaching the ground, and variations in the drop-size distribution and vertical air motions. Nevertheless, radar can be of lifesaving usefulness by alerting forecasters to the potential for flash flooding. The most successful technique for improving the radar rainfall estimates has been to “calibrate” the radar with rain g...

Experiments in Rainfall Estimation with a Polarimetric Radar in a Subtropical Environment

Abstract A unique dataset consisting of high-resolution polarimetric radar measurements and dense rain gauge and disdrometer observations collected in east-central Florida during the summer of 1998 was examined. Comparison of the radar measurements and radar parameters computed from the disdrometer observations supported previous studies, which indicate that oscillating drops in the free atmosphere have more spherical apparent shapes in the mean than equilibrium shapes. Radar–disdrometer comparisons improved markedly when using an empirical axis ratio relation developed from observational studies and representing more spherical drop shapes. Fixed-form power-law rainfall estimators for radar reflectivity (ZH), specific differential phase (KDP), specific differential phase–differential reflectivity (KDP, ZDR), and radar reflectivity–differential reflectivity (ZH, ZDR) were then determined using the disdrometer observations. Relations were produced for both equilibrium shapes and the empirical axis ratios. P...

A method for estimating rain rate and drop size distribution from polarimetric radar measurements

Polarimetric radar measurements are sensitive to the size, shape and orientation of raindrops and provide information about drop size distribution (DSD), canting angle distribution and rain rate. The authors propose and demonstrate a method for retrieving DSD parameters for calculating rain rate and the characteristic particle size. The DSD is assumed to be a gamma distribution and the governing parameters are retrieved from radar measurements: reflectivity (Z/sub HH/), differential reflectivity (ZDR), and a constrained relation between the shape (CL) and slope (/spl Lambda/) parameters derived from video disdrometer observations. The estimated rain rate is compared with that obtained from more traditional methods and the calculated characteristic size is compared with the measured values. The calculated K/sub DP/ based on the retrieved Gamma DSD is also compared with measurements. The proposed method shows improvement over the existing models and techniques because it can retrieve all three parameters of the gamma distribution. For maintaining the continuity of earlier published results, raindrop shape is assumed to be equilibrium.

Optimizing Rainfall Estimates with the Aid of Radar

Abstract Estimates of precipitation are improved when raingage observations are used to calibrate quantitative radar data as well as to estimate precipitation in areas without radar data. Estimated areal precipitation depth errors for nine rainfalls over a 3000 km2 watershed averaged 13 and 14% (1.5 and 1.8 mm) when the radar was calibrated by networks of raingages having densities of one gage per 900 and 1600 km2. Areal precipitation estimates derived from rainfalls observed at the gages alone produced errors of 21 and 24% (2.5 and 3.0 mm). Adjusting the radar data by a single calibration factor (the simple average ratio of gage-observed and radar-inferred rainfall at all input gages without regard to the spatial variation among ratios) resulted in error reduction to 18% (2.1 mm). Radar data added to gage observations also increased the explained variance in point rainfall estimates above that from gages alone, from 53 to 77% and 46 to 72% for the above gage densities.

A Statistical and Physical Description of Hydrometeor Distributions in Colorado Snowstorms Using a Video Disdrometer

Abstract Winter-storm hydrometeor distributions along the Front Range in eastern Colorado are studied with a ground-based two-dimensional video disdrometer. The instrument provides shape, size, and terminal velocity information for particles that are larger than about 0.4 mm. The dataset is used to determine the form of particle size distributions (PSDs) and to search for useful interrelationships among the governing parameters of assumed distribution forms and environmental factors. Snowfalls are dominated by almost spherical aggregates having near-exponential or superexponential size distributions. Raindrop size distributions are more peaked than those for snow. A relation between bulk snow density and particle median volume diameter is derived. The data suggest that some adjustment may be needed in relationships found previously between temperature and the concentration and slope parameters of assumed exponential PSDs. A potentially useful relationship is found between the slope and shape terms of the ...

Analysis of Video Disdrometer and Polarimetric Radar Data to Characterize Rain Microphysics in Oklahoma

Abstract In this paper, data from three 2-dimensional video disdrometers (2DVDs) and an S-band polarimetric radar are used to characterize rain microphysics in Oklahoma. Sampling errors from the 2DVD measurements are quantified through side-by-side comparisons. In an attempt to minimize the sampling errors, a method of sorting and averaging based on two parameters (SATP) is proposed. The shape–slope (μ–Λ) relation of a constrained gamma (C-G) model is then refined for the retrieval of drop size distributions (DSDs) from polarimetric radar measurements. An adjustable term that is based on observed radar reflectivity and differential reflectivity is introduced to make the C-G DSD model more applicable. Radar retrievals using this improved DSD model are shown to provide good agreement with disdrometer observations and to give reasonable results, including in locations near the leading edge of convection where poorly sampled large drops are often observed.

Drop Size Distribution Retrieval with Polarimetric Radar: Model and Application

Polarimetric radar measurements are used to retrieve properties of raindrop distributions. The procedure assumes that drops are represented by a gamma distribution and retrieves the governing parameters from an empirical relation between the distribution shape and slope parameters and measurements of radar reflectivity and differential reflectivity. Retrieved physical characteristics of the drop size distribution (DSD) were generally well matched with disdrometer observations. The method is applied to select storms to demonstrate utility. Broad DSDs were determined for the core (high reflectivity) regions of thunderstorms. Largest drop median volume diameters were at the leading edge of the storm core and were displaced slightly downwind from updrafts. Rainy downdrafts exhibited what are believed to be equilibrium DSDs in which breakup and accretion are roughly in balance. DSDs for stratiform precipitation were dominated by relatively large drops. Median volume diameters at the ground were closely related to the intensity of an overlying bright band. The radar measurements suggest that, although DSDs in stratiform rain were also broad and nearly constant in the rain layer, they were not at equilibrium but were merely steady. DSD invariance is attributed to small total drop numbers, which result in few collisions.

The Shape–Slope Relation in Observed Gamma Raindrop Size Distributions: Statistical Error or Useful Information?

Abstract The three-parameter gamma distribution n(D) = N0Dµ exp(–ΛD) is often used to characterize a raindrop size distribution (DSD). The parameters µ and Λ correspond to the shape and slope of the DSD. If µ and Λ are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified, which facilitates retrieval of rain parameters from remote measurements. It is important to determine whether the µ–Λ relation arises from errors in estimated DSD moments, or from natural rain processes, or from a combination of both statistical error and rain physics. In this paper, the error propagation from moment estimators to rain DSD parameter estimators is studied. The standard errors and correlation coefficient are derived through systematic error analysis. Using numerical simulations, errors in estimated DSD parameters are quantified. The analysis shows that errors in moment estimators do cause correlations among the estimated DSD parameters and cause a linear relation between est...

IMPROVING QPE AND VERY SHORT TERM QPF An Initiative for a Community-Wide Integrated Approach

Accurate quantitative precipitation estimates (QPE) and very short term quantitative precipitation forecasts (VSTQPF) are critical to accurate monitoring and prediction of water-related hazards and water resources. While tremendous progress has been made in the last quarter-century in many areas of QPE and VSTQPF, significant gaps continue to exist in both knowledge and capabilities that are necessary to produce accurate high-resolution precipitation estimates at the national scale for a wide spectrum of users. Toward this goal, a national next-generation QPE and VSTQPF (Q2) workshop was held in Norman, Oklahoma, on 28–30 June 2005. Scientists, operational forecasters, water managers, and stakeholders from public and private sectors, including academia, presented and discussed a broad range of precipitation and forecasting topics and issues, and developed a list of science focus areas. To meet the nations needs for the precipitation information effectively, the authors herein propose a community-wide int...

Polarimetric Radar Estimators Based on a Constrained Gamma Drop Size Distribution Model

Abstract Raindrop size distribution (DSD) retrieval from remote radar measurements or from in situ disdrometer measurements is an important area of research. If the shape (μ) and slope (Λ) of a three-parameter gamma distribution n(D) = N0Dμ exp(−ΛD) are related to one another, as recent disdrometer measurements suggest, the gamma DSD model is simplified to a two-parameter DSD, that is, a constrained gamma DSD. An empirical relation between the μ and Λ was derived using moments estimated from video-disdrometer measurements. Here, the effects of DSD truncation on a μ and Λ relation were analyzed. It was shown that characteristic size and variance of size of a constrained gamma DSD depend only on the shape parameter μ. Assuming that a constrained gamma DSD is valid, S-band polarimetric radar–based estimators for rain rate, median volume diameter, specific propagation phase, attenuation, and differential attenuation were derived. The radar-based estimators were used to obtain the spatial distribution of DSD p...