Search Results

You are looking at 1 - 10 of 22 items for

  • Author or Editor: Carlton W. Ulbrich x
  • Refine by Access: All Content x
Clear All Modify Search
Carlton W. Ulbrich

Abstract

Empirical analyses are shown to imply variation in the shape or analytical form of the raindrop size distribution consistent with that observed experimentally and predicted theoretically. These natural variations in distribution shape are demonstrated by deriving relationships between pairs of integral rainfall parameters using a three parameter gamma drop size distribution and comparing the expressions with empirical. There comparisons produce values for the size distribution parameters which display a systematic dependence of one of the parameters on another between different rainfall types as well as from moment to moment within a given rainfall type. The implications of this finding are explored in terms of the use of a three-parameter gamma distribution in dual-measurement techniques to determine rainfall rate.

Full access
Carlton W. Ulbrich

Abstract

A theoretical and empirical assessment is made of a technique proposed recently for measuring rainfall rate by radar. The technique involves tuning a variable wavelength radar across the millimeter wavelength band to the wavelength where the reflectivity is a maximum. It is shown that the rainfall rate found from the latter wavelength is subject to potentially large errors due to drop size distribution variations and to uncertainty in the measurement of the reflectivity. Other sources of possible large error which are considered include Variations in the size of the pulse volume as the wavelength changes and attenuation due to clouds, gases and precipitation of the short wavelengths involved in the proposed technique.

Full access
Carlton W. Ulbrich

Abstract

A description is given of a method of estimating the effects of truncating the raindrop size distribution (DSD) at lower and upper drop diameters D min and D max which assumes that the DSD can be approximated by a gamma distribution (including the exponential distribution). The method is used to investigate the effects of DSD truncation on rainfall integral parameters (e.g., reflectivity factor, liquid water content etc.) and on empirical relations between pairs of these integral parameters. Tests of the theoretical predictions are performed using a set of drop size data collected with a Joss disdrometer. A brief description is also given of the use of the method to determine DSD truncation effects on precipitation parameters deduced from dual-measurement techniques.

Full access
Carlton W. Ulbrich

Abstract

A derivation is given of the relationships of the equivalent reflectivity factor to the vertical fluxes of mass and kinetic energy of hail. It is assumed that the hail is distributed with respect to size according to a truncated exponential distribution and that the hailstones possess backscattering cross sections appropriate to homogeneous ice spheres that are either dry or are coated with a thin layer of liquid water. It is shown that at certain radar wavelengths and water thicknesses the relationships found in this work have potential for accurately determining hail mass flux and kinetic energy flux from conventional radar reflectivity factor measurements. The optimum radar wavelengths are approximately 3 cm for the mass flux and 5 cm for the kinetic energy flux.

Full access
Carlton W. Ulbrich

Abstract

Relationships are derived which can be used in the analysis of Doppler radar spectra of hail at vertical incidence to find storm updrafts and hailstone size distribution parameters. It is assumed that the hail is spherical and homogeneous, that it is either dry or coated with a film of liquid water, and that it is distributed with respect to size according to a truncated exponential spectrum. The relations found in this work are applied to the Doppler spectra of several workers and are found to produce results which are in good agreement with observation. It is also shown how these relations can be used in the analysis of conventional, single-wavelength radar data to accurately determine hail mass and kinetic energy fluxes.

Full access
Carlton W. Ulbrich

Abstract

An investigation is made of the effects of truncating the raindrop-size distribution at minimum and maximum diameters on the results of computer simulations of dual-measurement radar methods. The dual-measurement methods investigated include those that involve the pairs of measurables (Z, A), (A, Σ), (Z DR, ZH ), and (vZ , Z), where Z, A, Σ, Z DR, Z H , and v z are the Rayleigh reflectivity factor, microwave attenuation, optical extinction, differential reflectivity, Mie reflectivity factor at horizontal polarization, and mean Doppler fall speed, respectively. It is found that the systematic offsets of calculated versus actual values of rainfall parameters observed in previous work using experimental disdrometer drop-size spectra can be attributed almost entirely to truncation effects. Any remaining offset after truncation effects have been removed can be attributed to deviations of the drop-size distribution from exponentiality. The effects of truncation on empirical relations deduced from experimental drop-size spectra are also discussed.

Full access
Carlton W. Ulbrich

Abstract

Algorithms are presented that can be used to deduce rainfall integral parameters from mean Doppler velocity and reflectivity factor at vertical incidence. Simulations are performed using experimental drop-size spectra to test the accuracy of the algorithms, as well as their sensitivity to variations in the form of the drop-size distribution. It is found from these simulations that the method produces results that are very similar to those found using other dual-measurement algorithms, such as those involving the combinations (Z, A), (Z, Σ), and (ZDR , Z) where Z, A, Σ, and ZDR are the reflectivity factor, microwave attenuation, optical extinction, and differential reflectivity, respectively. However, to realize the maximum potential accuracy of the method, a reliable means of estimating the vertical winds must he available, or the measurements must be made close to the earth's surface where such effect arc minimal. An analysis is performed of the errors in integral parameters due to the presence of vertical winds.

Full access
Daniel Rosenfeld
and
Carlton W. Ulbrich

Abstract

The question of the connections between raindrop-size distributions (RDSDS) and radar reflectivity–rainfall rate ZR relationships is explored from the combined approach of rain-forming physical processes that shape the RDSD, and a formulation of the RDSD into the simplest free parameters of the rain intensity R, rainwater content W, and median volume drop diameter D 0. This is accomplished through examination of integral parameters deduced from the RDSD associated with the host of ZR relations found in the literature. These latter integral parameters are deduced from the coefficient and exponent of empirical ZR relations using a gamma RDSD. A physically based classification of the RDSDs shows remarkable ordering of the D 0W relations, which provides insight into the fundamental causes of the systematic differences in ZR relations.

The major processes forming the RDSD are examined with respect to a mature equilibrium RDSD, which is taken as the eventual distribution. Emphasis is placed on cloud microstructure (with the two end members being “continental” and “maritime”) and cloud dynamics (with end members “convective” and “stratiform”). The influence of orography is also considered. The ZR classification scheme can explain large systematic variations in ZR relations, where R for a given Z is greater by a factor of more than 3 for rainfall from maritime compared to extremely continental clouds, a factor of 1.5–2 greater R for stratiform compared to maritime convective clouds, and up to a factor of 10 greater R for the same Z in orographic precipitation. The scheme reveals the potential for significant improvements in radar rainfall estimates by application of a dynamic ZR relation, based on the microphysical, dynamical, and topographical context of the rain clouds.

Full access
Carlton W. Ulbrich
and
David Atlas

Abstract

Diagrams are presented which display the relationships between hailstone size distribution parameters and integral quantities defined in terms of these parameters. It is assumed that the hailstones are spherical and homogeneous, are distributed with respect to size according to a truncated exponential distribution, and that they fall in still air without rain. Some of the diagrams are shown to have application for size distributions other than exponential provided that the moments of the distribution are known. Hailfall-related integral quantities depicted are the total number of hailstones per unit volume, liquid water content, kinetic energy content, fluxes of mass and kinetic energy, median volume diameter, average diameter, mass-weighted average diameter, variance of the size distribution, and number of hailstones greater than a specified minimum diameter.

Radar measurables are calculated using backscattering cross sections for spherical hailstones that are dry or coated with a thin film of liquid water of thickness t. The results are displayed on overlays for the hail parameter diagram for radar wavelengths of 3.21 cm and 10.0 cm for dry (t = 0.0) and wet (t = 0.01 cm) hail. Radar quantities shown on these overlays include the equivalent radar reflectivity factor, the mean Doppler fallspeed, the variance of the Doppler spectrum, and the ratio of the reflectivity factors for the above two radar wavelengths.

Applications of the diagram are presented, one of which uses experimental hail parameters of several investigators. Another involves analysis of 1976 National Hail Research Experiment hailpad data and the results are plotted on the diagram. Empirical results deduced from these analyses are used to construct a second form of hail parameter diagram which is convenient for analyzing possible effects due to natural or artificial modification of the hail size distribution. Experimental hail parameters are also plotted on this diagram and empirical equations are derived from these data to illustrate the relationships implied by such empirical analyses between all pairs of hail parameters. These results also are used to assess the error introduced by neglect of the contribution to remote measurables due to rain.

Full access
David Atlas
and
Carlton W. Ulbrich

Abstract

The reasons for the linear relationship between microwave attenuation A and rainfall rate R near 1 cm wavelength are explained. This linearity also implies independence of the A-R relationship from the drop size distribution (DSD), thus making attenuation measurements near this wavelength attractive for path-averaged rainfall. Regression equations of the form A = KR α are calculated for four radar wavelengths from 0.86 to 3.2 cm from drop size spectra. As predicted, α increases from about 1.04 to 1.16 and average errors of estimate of R from the regression equations increase from about 9 to 21% from 0.86 to 3.2 cm, respectively. The larger errors at 3.2 cm reflect the increased dependence on the form of DSD. Even at 3.2 cm, the errors are typically less than half those incurred from the use of reflectivity factor Z and a priori Z-R relations.

Various methods of measuring path- and area-averaged R are studied. Radar methods using standard targets fail over 30 km paths at wavelengths of 0.86 and 1.25 cm at R greater than about 9 and 20 mm h−1, respectively, because of excessive attenuation but are operative to larger mean rates at 1.78 and 3.2 cm. One-way methods between transmitter and receiver are the most suitable in terms of maximum measurable R . A wavelength between 1.5 and 2 cm provides a reasonable compromise between maximum measurable R and minimum errors. Proper measurements require the use of both vertical and horizontal polarization. Prior experiments are reviewed and explanations offered for both the large scatter in the results of some experiments and the occasional excess attenuation over theoretical prediction.

Full access