Jothiram Vivekanandan

Cloud Microphysics Retrieval Using S-Band Dual-Polarization Radar Measurements

Recent studies have shown the utility of polarimetric radar observables and derived fields for discrimination of hydrometeor particle types. Because the values of the radar observables that delineate different particle types overlap and are not sharply defined, the problem is well suited for a fuzzy logic approach. In this preliminary study the authors have developed and implemented a fuzzy logic algorithm for hydrometeor particle identification that is simple and efficient enough to run in real time for operational use. Although there are no in situ measurements available for this particle-type verification, the initial results are encouraging. Plans for further verification and optimization of the algorithm are described.

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.

Boundary Layer Clear-Air Radar Echoes: Origin of Echoes and Accuracy of Derived Winds

Abstract Boundary layer clear-air echoes are routinely observed with sensitive, microwave, Doppler radars similar to the WSR-88D. Operational and research meteorologists are using these Doppler velocities to derive winds. The accuracy of the winds derived from clear-air Doppler velocities depends on the nature of the scatterers. This paper uses dual-wavelength and dual-polarization radars to examine the cause of these echoes and the use of Doppler velocities from the clear-air return to estimate winds. The origin of these echoes has been an ongoing controversy in radar meteorology. These echoes have been attributed to refractive-index gradient (Bragg scattering) and insects and birds (particulate scattering). These echoes are most commonly observed over land from spring through autumn. Seldom do they occur over large bodies of water. Widespread clear-air echoes have also been observed in winter when temperatures are above 10°C. Radar reflectivity comparisons of clear-air echoes in Florida and Colorado wer...

Testing a procedure for automatic classification of hydrometeor types

Abstract Examples of automatic interpretation of polarimetric measurements made with an algorithm that classifies precipitation, from an Oklahoma squall line and a Florida airmass storm are presented. Developed in this paper are sensitivity tests of this algorithm to various polarimetric variables. The tests are done subjectively by comparing the fields of hydrometeors obtained using the full set of available polarimetric variables with a diminished set whereby some variables have been left out. An objective way to test the sensitivity of the algorithm to variables and rank their utility is also devised. The test involves definition of a measure, which is the number of data points classified into a category using subsets of available variables. Ratios of various measures (similar to probabilities) define the percentage of occurrence of a class. By comparing these percentages for cases in which some variables are excluded to those whereby all are included, a relative merit can be assigned to the variables....

Propagation delays induced in GPS signals by dry air, water vapor, hydrometeors, and other particulates

Dry air, water vapor, hydrometeors, and other particulates (sand, dust, aerosols, and volcanic ash) in the atmosphere introduce microwave propagation delays. These delays must be properly characterized to achieve the highest accuracy in surveying and atmospheric sensing using Global Positioning System (GPS) signals. In this paper we review the theory of microwave propagation delays induced by the above atmospheric constituents and estimate their maximum delays. Because the structure of atmospheric refractivity can be highly complex and difficult to model, and because measurement tools are unavailable for characterizing most of the refractive components, we use simplified examples to illustrate its effects. Our results show that propagation delays due to water vapor, cloud liquid, rain, and sandstorms can be significant in high-accuracy GPS applications. For instance, propagation through 1 km of heavy rain can induce 15-mm delays in L1, and because delays due to scattering are dispersive and alias as ionospheric delays in L3 processing, L3 range errors are magnified to 20 mm. Depending upon the distribution of precipitation relative to the configuration of GPS satellites, such unmodeled delays can induce horizontal and vertical errors of several centimeters.

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...

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...

An Evaluation of a Drop Distribution-Based Polarimetric Radar Rainfall Estimator

A method for estimating the governing parameters of gamma drop size distributions (DSDs) and associated rainfall rates from polarimetric radar measurements at the S band is examined. The technique uses radar reflectivity at horizontal polarization, differential reflectivity, and an empirical constraining relationship between the DSD shape factor and slope parameter. Retrieved DSD parameters show good agreement with disdrometer observations. Retrieved rainfall estimates are insensitive to drop climatological regime. Comparison with fixed-form powerlaw estimators reveals that the constrained-gamma method outperforms reflectivity estimators and is roughly equivalent to radar reflectivity‐differential reflectivity estimators optimized for local DSDs.