DSD Model Research Articles

Raindrop Size Distribution Modeling from a Statistical Rain Parameter Relation and Its Application to the TRMM Precipitation Radar Rain Retrieval Algorithm

AbstractA generalized method is presented to derive a “two scale” raindrop size distribution (DSD) model over a spatial or temporal domain in which a statistical rain parameter relation exists. The two-scale model is generally defined as a model in which one DSD parameter is allowed to vary rapidly and the other is constant over a certain space or time domain. The existence of a rain parameter relation such as the radar reflectivity–rainfall rate (Z–R) relation over a spatial or temporal domain is an example of such a two-scale DSD model. A procedure is described that employs a statistical rain parameter relation with an assumption of the gamma DSD model. An example using Z–R relations obtained at Kototabang, West Sumatra, is presented. The result shows that the resulting two-scale DSD model expressed by conventional DSD parameters depends on the assumed value of parameter μ while rain parameter relations such as k–Ze relations from those models using different μ values are very close to each other, indicating the stability of the model against the variation of μ and the validity of this method. The result is applied to the DSD model for the Tropical Rainfall Measuring Mission (TRMM) precipitation radar 2A25 (versions 5 and 6) algorithm. The derivation procedure of the 2A25 DSD model is described. Through the application of this model, it has become possible to make a logically well-organized rain profiling algorithm and reasonable rain attenuation correction and rainfall estimates, as described in an earlier paper by Iguchi et al.

Feasibility of Raindrop Size Distribution Parameter Estimation with TRMM Precipitation Radar

This paper studies the feasibility of estimating raindrop size distribution (DSD) parameters from Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) measurements. A methodology is described for DSD estimation with PR, in which parameter “e” or “a” in the Z-R relation Z=aRb is used as a DSD parameter. The e parameter is an adjustment factor for α in the relation between the attenuation coefficient κ and the effective radar reflectivity factor Ze (κ = αZeβ) that makes the attenuation correction stable by using the path-integrated attenuation estimated from the surface echo as a reference. e is also recognized as a path-averaged DSD parameter. Large (small) e corresponds to small (large) a, i.e., to small (large) median volume diameters (D0s) with the assumption of the gamma DSD model. e exhibits a clear diurnal variation over land suggesting that afternoon convection causes DSDs with large D0s. In contrast, there is no significant diurnal variation over the ocean. e also exhibits a clear negative correlations with the storm-top height deduced from the PR and with the lightning flash rate, both of which again suggest that deep convections over land produce large D0s. There are several error sources that may produce bias errors in the DSD estimates: non-uniform beam filling (NUBF) within the PR antenna beam, non-liquid hydrometeors aloft (such as hail), and variation in the Normalized Radar Cross Section (NRCS) under rain as compared with no-rain conditions. Preliminary evaluations are performed on these error sources, which generally cause negative errors in e (i.e., overestimation of raindrop size). Nevertheless, comparisons of PR- and disdrometer-estimated a (in Z=aRb) generally are in agreement at various locations over both land and oceanic sites. This result suggests the feasibility of PR estimation of DSD. It is concluded that, at the present stage, PR estimates of global DSD distribution should be considered to be “qualitative.” Nevertheless, it would be useful to study the tuning of spaceborne radar algorithms and climatological studies of cloud microphysics.

Diagnosing the Intercept Parameter for Exponential Raindrop Size Distribution Based on Video Disdrometer Observations: Model Development

Abstract The exponential distribution N(D) = N0 exp(−ΛD) with a fixed intercept parameter N0 is most commonly used to represent raindrop size distribution (DSD) in rainfall estimation and in single-moment bulk microphysics parameterization schemes. Disdrometer observations show that the intercept parameter is far from constant and systematically depends on the rain type and intensity. In this study, a diagnostic relation of N0 as a function of rainwater content W is derived based on two-dimensional video disdrometer (2DVD) measurements. The data reveal a clear correlation between N0 and W in which N0 increases as W increases. To minimize the effects of sampling error, a relation between two middle moments is used to derive the N0–W relation. This diagnostic relation has the potential to improve rainfall estimation and bulk microphysics parameterizations. A parameterization scheme for warm rain processes based on the diagnostic N0 DSD model is formulated and presented. The diagnostic N0-based parameterization scheme yields less evaporation and accretion for stratiform rain than that using fixed N0.

Variability of rain drop size distribution and its effect on the Z– R relationship: A case study for intense Mediterranean rainfall

This paper presents an analysis of the variability of rain drop size distributions in intense Mediterranean rainfall and its impact on the reflectivity — rain-rate conversion. Two concurrent approaches for estimating the Z– R relationship from DSD measurements are reviewed: (1) non-linear regression techniques on the scattergraphs of the ( Z, R) pairs derived for each DSD spectra; (2) use of a DSD model fitting based on a scaling law formulation. The two approaches are implemented over a DSD dataset of 75 h of Mediterranean rain collected with a ground-based optical DSD sensor. As a result of the heterogeneity of the rain processes, the seasonal Z– R relationship coefficients obtained are very diverse and strongly dependent on the fitting methodology. A consistency test of the seasonal Z– R relationships is proposed to assess the most reliable estimation procedures in terms of rainfall estimation. Using the DSD-derived rain-rate time series as a reference, it is shown that the regression techniques are significantly better than the DSD modelling approach. The same consistency test shows that event-fitted Z– R relationships do not systematically improve the test scores, supporting the idea that the intra-event DSD variability is dominant. This finding is confirmed with an in-depth analysis of one rain event, showing evidence of rainfall organisation into several phases each one presenting very stable scale and shape DSD parameters over several hours, and abrupt transitions from one phase to the next. A rain-typing algorithm applied to the 3D reflectivity data observed concomitantly with an operational S-band radar is consistently able to recognise the two most intense phases of the rain event as convective.

Improving Parameterization of Rain Microphysics with Disdrometer and Radar Observations

Abstract Disdrometer observations indicate that the raindrop size distribution (DSD) can be represented by a constrained-gamma (CG) distribution model. The model is used to retrieve DSDs from polarization radar measurements of reflectivity and differential reflectivity and to characterize rain microphysics and physical processes such as evaporation, accretion, and precipitation. The CG model parameterization is simplified to a single parameter for application in single-moment numerical models. This simplified parameterization is applied in the Variational Doppler Radar Analysis System (VDRAS) using Kessler-type parameterizations for model initialization and forecasting. Results are compared to those for the Marshall–Palmer (MP) DSD model. It is found that the simplified CG model parameterization better preserves the stratiform rain and produces better forecasts than the MP model parameterization.

X-band Polarimetric Radar Rainfall Measurements in Keys Area Microphysics Project

Abstract The Keys Area Microphysics Project (KAMP), conducted as part of NASA’s Fourth Convective and Moisture Experiment (CAMEX-4) in the lower Keys area, deployed a number of ground radars and four arrays of rain gauge and disdrometer clusters. Among the various instruments is an X-band dual-polarization Doppler radar on wheels (XPOL), contributed by the University of Connecticut. XPOL was used to retrieve rainfall rate and raindrop size distribution (DSD) parameters to be used in support of KAMP science objectives. This paper presents the XPOL measurements in KAMP and the algorithm developed for attenuation correction and estimation of DSD model parameters. XPOL observations include the horizontal polarization reflectivity ZH, differential reflectivity ZDR, and differential phase shift ΦDP. Here, ZH and ZDR were determined to be positively biased by 3 and 0.3 dB, respectively. A technique was also applied to filter noise and correct for potential phase folding in ΦDP profiles. The XPOL attenuation correction uses parameterizations that relate the path-integrated specific (differential) attenuation along a radar ray to the filtered-ΦDP (specific attenuation) profile. Attenuation-corrected ZH and specific differential phase shift (derived from filtered ΦDP profiles) data are then used to derive two parameters of the normalized gamma DSD model, that is, intercept (Nw) and mean drop diameter (D0). The third parameter (shape parameter μ) is calculated using a constrained μ–Λ relationship derived from the measured raindrop spectra. The XPOL attenuation correction is evaluated using coincidental nonattenuated reflectivity fields from the Key West Weather Surveillance Radar-1988 Doppler (WSR-88D), while the DSD parameter retrievals are statistically assessed using DSD parameters calculated from the measured raindrop spectra. Statistics show that XPOL DSD parameter estimation is consistent with independent observations. XPOL estimates of water content and Nw are also shown to be consistent with corresponding retrievals from matched ER-2 Doppler radar (EDOP) profiling observations from the 19 September airborne campaign. Results shown in this paper strengthen the applicability of X-band dual-polarization high resolution observations in cloud modeling and precipitation remote sensing studies.

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...

High-Resolution Rainfall Estimation from X-Band Polarimetric Radar Measurements

Abstract The paper presents a rainfall estimation technique based on algorithms that couple, along a radar ray, profiles of horizontal polarization reflectivity (ZH), differential reflectivity (ZDR), and differential propagation phase shift (ΦDP) from X-band polarimetric radar measurements. Based on in situ raindrop size distribution (DSD) data and using a three-parameter “normalized” gamma DSD model, relationships are derived that correct X-band reflectivity profiles for specific and differential attenuation, while simultaneously retrieving variations of the normalized intercept DSD parameter (Nw). The algorithm employs an iterative scheme to intrinsically account for raindrop oblateness variations from equilibrium condition. The study is facilitated from a field experiment conducted in the period October–November 2001 in Iowa City, Iowa, where observations from X-band dual-polarization mobile radar (XPOL) were collected simultaneously with high-resolution in situ disdrometer and rain-gauge rainfall meas...

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...

Modelling of Drop Size Distribution of Rain from Rain Rate and Attenuation Measurements at Millimeter and Optical Wavelengths

This paper describes a technique for modelling of rain drop size distributions at Calcutta in terms of negative exponential function, from the measurements of rain rate and attenuation over a dual wavelength LOS link at millimeter and optical frequencies. The DSD model obtained is then used to determine the attenuation at 94 GHz, for comparison with experimentally obtained attenuation at 94 GHz. This is also compared with the attenuation calculated by considering other experimentally obtained DSD models. The best fit negative exponential distribution function (modified M-P model) is presented along with some other experimentally obtained and reference models.

The dsd model in heptacoordinate stereochemistry: a comparison with experiment

The diamond-square-diamond or dsd model provides a simple description for heptacoordinate interconversion. We compare it to NMR information. It appears that the model is almost always compatible with experimental facts, at least when the dsd processes do not lead to isomerization.

Rainfall Parameter Estimation from Dual-Radar Measurements Combining Reflectivity Profile and Path-integrated Attenuation

Abstract Rain rate estimation properties of multiparameter radar measurements combining radar reflectivity and microwave attenuations are studied through simulations using a two-year disdrometer dataset. In the first simulation, properties of “complete” multiparameter measurements, where error-free measurements are assumed for each radar resolution cell, are investigated. The result indicates that dual-parameter (DP) measurements provide an excellent accuracy in rain rate estimation. Most of the DP measurements possible from space are “semi-” dual-parameter (SDP) measurements, defined as DP measurements in which spatial resolution for the attenuation measurement is coarser than the resolution required for rain profiling. Considering this fact, an SDP measurement simulation is also made. The SDP measurement is an extension of the concept of the DP measurement in terms of the spatial resolution, and can provide information on raindrop size distribution (DSD) by employing a “two-scale” DSD model. It is shown...

Radiative capture of fast neutrons by 89Y and 140Ce

The γ-ray spectra from the reactions 89Y(n, γ) 90Y and 140Ce(n, γ) 141Ce have been measured in the neutron energy range of 6.2–15.6 MeV. The pulse-height spectra were recorded with NaI(Tl) spectrometers and time-of-flight techniques were used to improve signal-to-background ratio. Capture cross sections were determined for γ-ray transitions to the two 2 d 5 2 levels at 0 and 203 keV of 90Y and to the 2 f 7 2 ground state of 141Ce as well as integrated cross sections to bound states in these nuclei. The observed γ-ray spectra and partial radiative capture cross sections were compared with predictions of the direct-semidirect capture theory. The resonance behaviour with neutron energy of both the ground-state and integrated partial capture cross sections shows the validity of the semidirect model for 89Y and 140Ce in the region of neutron energy encompassing the giant-dipole resonance. The observed symmetry of the cross sections about the peak of the resonance argues strongly for the complex form of the particle-vibration coupling interaction. A detailed comparison of the predictions of the DSD model using the complex coupling interaction shows that the capture cross sections are relatively insensitive to the real part of the interaction.