Carlton W. Ulbrich

Natural Variations in the Analytical Form of the Raindrop Size Distribution

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.

Path- and Area-Integrated Rainfall Measurement by Microwave Attenuation in the 1–3 cm Band

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 = KRα 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 1.2...

Systematic variation of drop size and radar‐rainfall relations

Time histories of the characteristics of the drop size distribution of surface disdrometer measurements collected at Kapingamarangi Atoll were partitioned for several storms using rain rate R, reflectivity factor Z, and median diameter of the distribution of water content D0. This partitioning produced physically based systematic variations of the drop size distribution (DSD) and Z-R relations in accord with the precipitation types viewed simultaneously by a collocated radar wind profiler. These variations encompass the complete range of scatter around the mean Z-R relations previously reported by Tokay and Short [1996] for convective and stratiform rain and demonstrate that the scatter is not random. The systematic time or space variations are also consistent with the structure of mesoscale convective complexes with a sequence of convective, transition, and stratiform rain described by various authors. There is a distinct inverse relation between the coefficient A and the exponent of the Z-R relations which has been obscured in prior work because of the lack of proper discrimination of the rain types. Contrary to previous practice it is evident that there is also a distinct difference in the DSD and the Z-R relations between the initial convective and the trailing transition zones. The previously reported Z-R relation for convective rain is primarily representative of the transition rain that was included in the convective class. The failure of present algorithms to distinguish between the initial convective and the trailing transition rains causes an erroneous apportionment of the diabatic heating and cooling and defeats the primary intent of discriminating stratiform from convective rains.

Rainfall Microphysics and Radar Properties: Analysis Methods for Drop Size Spectra

Abstract Analyses are performed of experimental drop size spectra to explore the relationships among integral parameters for rain. The data used in this work were acquired with an airborne optical 2D precipitation probe in TOGA COARE during a 4-month period in 1992–93. It is assumed that the experimental size spectra can be described by a gamma drop size distribution (DSD) of the form N(D) = N0Dμ exp(−ΛD) involving three parameters (N0, μ, Λ), which are determined using a new method of truncated moments. The method allows for truncation of the DSD at the large-diameter end of the spectrum due in part to instrumental effects and also in part to the trajectory of the aircraft through a rain streamer that has been sorted by wind shear. An effect analogous to truncation can occur at the small-diameter end of the size spectrum due to evaporation. However, truncation of the spectrum at the small-diameter end is not considered in this work. It is found that spectra with small space and timescales display conside...

Cloud Microphysical Properties, Processes, and Rainfall Estimation Opportunities

In this work the longstanding question of the connections between raindrop-size distributions (RDSDs) and radar reflectivity-rainfall rate (Z-R) relationships is revisited, this time 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 D0. This is accomplished through a theoretical analysis, using a gamma RDSD, of D0-R and W-R relations implied by the coefficients and exponents in empirical Z-R relations. The results provide a means by which these Z-R relations can be classified. The most dramatic of these classifications involves the relation between D0 and W, which shows a remarkable ordering with the rain types.

Rainfall Measurement Error by WSR-88D Radars due to Variations in Z–R Law Parameters and the Radar Constant

Abstract An investigation is made of the extent to which variations in Z–R (reflectivity factor–rainfall rate) relations can explain the systematically large offsets of radar-measured rainfall from rain gauge measurements as observed with some National Weather Service (NWS) WSR-88D radars. It is shown that theory predicts that the use by the NWS of the current default Z–R relation (Z = 300R1.4) should underestimate rainfall by about 25% in stratiform rain and overestimate it by about 33% in thunderstorm rain. Yet it is commonly observed that some WSR-88D radars systematically underestimate rainfall by a factor of 2 or more in stratiform rain and produce estimates of rainfall with acceptable accuracy for isolated thunderstorms. It is shown that variations in Z–R law parameters alone cannot explain these discrepancies, and it is proposed that their origin lies in a radar calibration offset. A comparison is made of reflectivity factors measured by the KGSP WSR-88D at Greer, South Carolina, with those determi...

Microphysics of Raindrop Size Spectra : Tropical Continental and Maritime Storms

Abstract This work uses raindrop size spectra measured at the surface in tropical continental storms to determine the associated parameters of the best-fit gamma distributions. The physical processes responsible for those parameters and their relations to the measurable radar reflectivity Z and differential reflectivity ZDR are then explored. So too are their relations to quantitative measurements of rain. Comparison is then made with corresponding features previously reported in tropical maritime regimes. The storms observed in Brazil and Arecibo, Puerto Rico, have been divided into convective (C), transition (T), and stratiform (S) segments. The raindrop size distribution (DSD) parameters are clearly defined on a gamma parameter diagram (GPD) that shows 1) how median volume drop size D0 increases from S to T to C segments of the rain while 2) the range of the spectrum breadth parameter μ increases, and the range of the slope parameter Λ decreases in the same sequence of S to C. Drop growth occurs predom...

Partitioning tropical oceanic convective and stratiform rains by draft strength

The discrimination of convective from stratiform tropical oceanic rains by conventional radar-based textural methods is problematic because of the small size and modest horizontal reflectivity gradients of the oceanic convective cells. In this work the vertical air motion measured by an aircraft gust probe is used as a discriminator which is independent of the textural methods. A threshold draft magnitude of ≈1 m s−1 separates the two rain types. Simultaneous airborne in situ observations of drop size distributions (DSD) made during the Tropical Ocean-Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE) were used to compute Z, R, and other integral parameters. The data were quality controlled to minimize misclassifications. The convective and stratiform rains, observed just below the melting level but adjusted to surface air density, are characterized by power law Z-R relations (Z = 129R1.38 (convective) and 224R1.28 (stratiform)). However, at R < 10 mm h−1, the convective population is essentially coincident with the small-drop size, small-Z portion of the stratiform population. Tokay and Short [1996] found a similar result when their algorithm did not separate the rain types unambiguously at R < 10 mm h−1. The physical reasons for the wide variability of the drop size spectra and Z-R points in stratiform rain and their overlap with that of convective rain are proposed. The subtle distinctions in the microphysical properties and the Z-R relations by rain type could not be found by Yuter and Houze (YH) using the same airborne DSD data set as that in this work and a radar-based textural classification algorithm.

The Effects of Drop Size Distribution Truncation on Rainfall Integral Parameters and Empirical Relations

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 Dmin and Dmax 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.

An observationally based conceptual model of warm oceanic convective rain in the tropics

Abstract Distinctively different Z–R relations for initial convective and transition rain at the surface were found during the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment. Initial convective rain (of 20–30-min duration) is marked by nearly constant median volume diameter of Do ≈ 2 mm and narrow drop size spectra, while R rises to >50 mm h−1. The constant form of the drop spectra independent of rain rate indicates an equilibrium distribution that accounts for the near linearity between Z and R. The form of the distribution differs from those previously reported, however. In contrast, the airborne raindrop measurements at 3 km in climatologically similar conditions show size spectra closely resembling the equilibrium collision–coalescence–breakup spectra of Hu and Srivastava and others at R > 20 mm h−1. The center of the plateau (of near-constant size) of these spectra repeatedly occurs at a drop size of 1 ± 0.1 mm whose fall speed equals the updraft speed. This suggest...