Drop Size Distribution Model Research Articles

SEASONAL ANALYSIS AND PREDICTION OF RAINFALL EFFECTS IN EASTERN SOUTH AFRICA AT MICROWAVE FREQUENCIES

Network fade countermeasures for link budget can be better implemented based on the knowledge of seasonal variability of rainfall attenuation in a locality. Therefore, in this study, a seasonal approach is applied to estimate the efiects of spatial rainfall attenuation in Durban (29 - 52'S, 30 - 58'E), South Africa using two- year rainfall data obtained from the RD-80 Joss-Waldvogel (J-W) distrometer. An analysis is undertaken for difierent seasons to obtain the rainfall rate exceedences at 0.001%, 0.01%, 0.1% and 1% of time. Consequently, rainfall drop-size distribution (DSD) models are developed for the control site at difierent seasons for the same period. The probability density analysis for each model indicates that the lognormal distribution best flts the summer and autumn season with percentage root-mean-square errors (RMS) of 30% and 26% respectively; gamma distribution flts winter season with RMS error of 16% and Weibull distribution flts spring season with RMS error of 26%. The results from the rainfall rate and rainfall DSD are combined to estimate the rainfall speciflc attenuation, by applying spherical droplet assumption for Mie scattering techniques, between 2GHz and 1000GHz. With this, the seasonal k and fi coe-cients for speciflc attenuation are derived from the best rainfall DSD models, using regression technique at 2.5GHz, 25GHz, 40GHz and 100GHz. At these frequencies, the results show that the predicted speciflc attenuation coe-cients for all seasonal rainfall rates at the control site are lower, when compared to those from ITU-R models. It is concluded that speciflc attenuation levels may be similar and more intense in summer and autumn seasons, while, lower and less intense in autumn and winter seasons at similar rainfall rates.

Regime analysis of rainfall drop-size distribution models for microwave terrestrial networks

In this study, parameters of statistical models for estimating the rainfall specific attenuation in Durban, South Africa are derived. The rainfall data in this work are based on 2-year measurements obtained via the Joss-Waldvogel RD-80 disdrometer between January 2009 and December 2010. Four rainfall regimes are applied: drizzle, widespread, shower and thunderstorm types. Using the third, fourth and sixth moments of the measured data, estimators for four rainfall drop-size distribution (DSD) models – 3-parameter lognormal model, negative exponential model, 3-parameter Weibull model and the modified gamma model – are computed. The specific attenuation estimates from our model are compared with the values from predicted measurements alongside the International Telecommunication Union (ITU) estimates for frequencies between 2 and 100 GHz. The results from the specific attenuation estimation are compared with the semi-empirical measurements for their respective regimes using root-mean-square and χ2 error tests. From the results, the best models for the various regimes are: Weibull model for drizzle regime, modified gamma model for widespread and shower regimes and lognormal model for the thunderstorm regime.

Truncated Gamma Drop Size Distribution Models for Rain Attenuation in Singapore

A model that is less sensitive to errors in the extreme small and large drop diameters, the gamma model with central moments (3, 4 and 6), is proposed to model the rain drop size distribution of Singapore. This is because, the rain rate estimated using measured drop size distribution shows that the contributions of lower drop diameters are small as compared to the central drop diameters. This is expected since the sensitivity of the Joss distrometer degrades for small drop diameters. The lower drop diameters are therefore removed from the drop size data and the gamma model is redesigned for its moments. The effects of the removal of a particular rain drop size diameter on the specific rain attenuation (in dB) and the slant-path rain attenuation calculations with forward scattering coefficients for vertical polarization are analyzed at Ku-band, Ka-band and Q-band frequencies. It is concluded that the sensitivity of the Joss distrometer although affects the rain rate estimation at low rain rates, does not affect the slant path rain attenuation on microwave links. Therefore, the small drop diameters can be ignored completely for slant path rain attenuation calculations in the tropical region of Singapore.

A relationship between rain radar reflectivity and height elevation variance of ringwaves due to the impact of rain on the sea surface

Raindrops impacting the rough sea modify its surface and its backscattering coefficient. This roughness change essentially depends on the rain content in very large drops, which is highly variable from one drop size distribution model to another. However, it has been observed that the radar reflectivity of raindrops has a drop size dependence very similar to that of the ringwaves induced by rain on the surface. From a numerical analysis on various drop size distributions, rain rates, and frequencies from 3 to 35 GHz, a relationship between the sea surface elevation variance of ringwaves resulting from drop impact and the rain radar reflectivity Z is established. It is found to be weakly dependent on the raindrop size distribution model. This link is expected to lead to better estimates of the surface roughness, and in turn, via electromagnetic scattering models, it could improve algorithms for near nadir rain radar retrieval.

Validation of western and eastern Pacific rainfall estimates from the TRMM PR using a radiative transfer model

Rainfall estimates from the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) facility algorithm over the eastern Pacific are lower than those from the TRMM Microwave Imager (TMI) facility algorithm and a PR‐consistent advanced microwave radiometer algorithm, while they are in good agreement over the western Pacific. We investigate the consistency between TMI‐observed brightness temperatures (TBs) for the 19 GHz channel and those simulated from the PR rainfall estimates using a radiative transfer model. Discrepancies between observed TBs and simulated TBs from the PR are larger for the eastern Pacific than for the western Pacific, indicating that PR underestimates rainfall over the eastern Pacific. It is hypothesized that drop size distributions (DSDs) in the eastern Pacific have stronger maritimity (i.e., more small to medium sized raindrops) than the initial DSD model of the PR algorithm, representative of the “data‐rich” western Pacific, leading to underestimation of rain by the PR. Differences in the adjustable parameter of the PR algorithm, implying changes in the DSD, and the vertical structure of PR‐observed reflectivity over the western and eastern Pacific support the hypothesis.

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.

Evaluation of X-Band Polarimetric-Radar Estimates of Drop-Size Distributions From Coincident S-Band Polarimetric Estimates and Measured Raindrop Spectra

Recent research has demonstrated the value of polarimetric measurements for the correction of rain-path attenuation at X-band radar frequency and the estimation of rain parameters including drop-size distributions (DSD). The issue this paper is concerned with is to what degree uncertainties in attenuation correction can affect the estimation of DSD. Since attenuation-correction uncertainty enhances with rain path, our hypothesis is that DSD retrieval uncertainty at X-band may deteriorate with range. In this paper, we evaluate the relative accuracy of X-band DSD retrieval against DSD estimates from S-band radar observations and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</i> <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">situ</i> disdrometer spectra. We present comparisons of various techniques for estimating DSD model parameters from attenuation-corrected X-band dual-polarization radar data. Coincident X-band polarimetric-radar (XPOL) and S-band polarimetric-radar dual-polarized radar measurements from the International H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O Project experiment as well as coincident XPOL (MP-X) measurements over disdrometer during a typhoon storm case in Japan are used to assess the accuracy of the different DSD retrieval algorithms applied to X-band radar measurements.

Sources of Errors in Rainfall Measurements by Polarimetric Radar: Variability of Drop Size Distributions, Observational Noise, and Variation of Relationships between R and Polarimetric Parameters

Abstract Using a set of long-term disdrometric data and of actual radar measurements from the McGill S-band operational polarimetric radar, several sources of errors in rain measurement with polarimetric radar are explored in order to investigate their relative importance and the feasibility of a polarimetric technique for estimating R in the context of the McGill S-band operational radar that performs a full volume scan of 24 plan position indicators (PPIs) every 5 min. The sources of errors considered are the variability of drop size distributions (DSDs), observational noise, and systematic variation of the relationships between R and polarimetric parameters at different climate regimes. Additional polarimetric parameters dramatically reduce the effect of the DSD variability on rain estimates by radar. The effectiveness of various multiparameter relationships is investigated. The relationships from the literature that are derived from the DSD model and measured DSDs at a different climate regime differ from those derived from the disdrometric dataset herein. An application of these relationships to the Montreal dataset results in a bias (about 10%–20%) and the significant random error resulting from the DSD variability. These errors should be eliminated by using a relationship suitable for the local climate. Assuming a measurement noise as expected from a slow scanning polarimetric radar [∼1 rotation per minute (rpm)] and a 10-min smoothing, the R − (Zh, ZDR) relationship outperforms the conventional R − Zh because of the combined effect of the DSD variability and measurement errors. In addition, the marginal measurement noise that is required to have the same accuracy of R − Zh and R − (Zh, ZDR) algorithms is obtained as a function of temporal smoothing. The quantified measurement noise of the McGill S-band fast scanning operational radar (∼6 rpm) is significantly larger than that of a slow scanning radar, implying that a temporal averaging of ZDR of 1 h is needed to achieve some gain with R − (Zh, ZDR).

On the Influence of Assumed Drop Size Distribution Form on Radar-Retrieved Thunderstorm Microphysics

Abstract Polarimetric radar measurements are used to retrieve drop size distributions (DSD) in subtropical thunderstorms. Retrievals are made with the single-moment exponential drop size model of Marshall and Palmer driven by radar reflectivity measurements and with a two-parameter constrained-gamma drop size model that utilizes reflectivity and differential reflectivity. Results are compared with disdrometer observations. Retrievals with the constrained-gamma DSD model gave better representation of total drop concentration, liquid water content, and drop median volume diameter and better described their natural variability. The Marshall–Palmer DSD model, with a fixed intercept parameter, tended to underestimate the total drop concentration in storm cores and to overestimate significantly the concentration in stratiform regions. Rainwater contents in strong convection were underestimated by a factor of 2–3, and drop median volume diameters in stratiform rain were underestimated by 0.5 mm. To determine possible DSD model impacts on numerical forecasts, evaporation and accretion rates were computed using Kessler-type parameterizations. Rates based on the Marshall–Palmer DSD model were lower by a factor of 2–3 in strong convection and were higher by about a factor of 2 in stratiform rain than those based on the constrained-gamma model. The study demonstrates the potential of polarimetric radar measurements for improving the understanding of precipitation processes and microphysics parameterization in numerical forecast models.

Combined Radar and Radiometer Analysis of Precipitation Profiles for a Parametric Retrieval Algorithm

Abstract A methodology to analyze precipitation profiles using the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and precipitation radar (PR) is proposed. Rainfall profiles are retrieved from PR measurements, defined as the best-fit solution selected from precalculated profiles by cloud-resolving models (CRMs), under explicitly defined assumptions of drop size distribution (DSD) and ice hydrometeor models. The PR path-integrated attenuation (PIA), where available, is further used to adjust DSD in a manner that is similar to the PR operational algorithm. Combined with the TMI-retrieved nonraining geophysical parameters, the three-dimensional structure of the geophysical parameters is obtained across the satellite-observed domains. Microwave brightness temperatures are then computed for a comparison with TMI observations to examine if the radar-retrieved rainfall is consistent in the radiometric measurement space. The inconsistency in microwave brightness temperatures is reduced by iterating the retrieval procedure with updated assumptions of the DSD and ice-density models. The proposed methodology is expected to refine the a priori rain profile database and error models for use by parametric passive microwave algorithms, aimed at the Global Precipitation Measurement (GPM) mission, as well as a future TRMM algorithms.

A differential attenuation based algorithm for estimating precipitation from dual-wavelength spaceborne radar

An algorithm for estimating precipitation from dual-wavelength spaceborne radar measurements is formulated and investigated. The algorithm is based on a single-wavelength attenuation-correction procedure applied within discrete ranges [r1, r2] along a radar ray, satisfying the condition r2 – r1 ≤ 750 m. The attenuation-correction procedure is based on two parameters, namely the integrated attenuation from the top of the atmosphere to r1 and the intercept parameter (N*0) of the normalized gamma drop size distribution model. The N*0 value is assumed constant within the discrete range. A cost function is defined to evaluate the discrepancy between the two-wavelength precipitation estimates obtained from the corrected reflectivity profile within the discrete range. Consequently, the path-integrated attenuation to r1 and N*0 is determined through optimization, minimizing the cost function. The algorithm is investigated using synthetic data, i.e., derived from cloud model simulations, and airborne observations from the fourth convection and moisture experiment (CAMEX-4).

First Results of DSD Measurement by Videodistrometer in the Czech Republic in 1998-1999

The first results of the almost one year drop size distribution (DSD) measurement in the Czech Republic are summarised in this study. The ESA-ESTEC 2D videodistrometer was used to measure the rain drop parameters. The average DSD is shown to be of the gamma type. One minute DSDs were evaluated to test the accuracy of analytical DSD models. Parameters of gamma distribution and exponential distribution functions were evaluated for the whole data set as well as for the various rain rate intervals. Regression technique and the method of moments were applied to estimate the parameters of DSD. It is shown that the μ parameter value strongly depends on the method of computation as well as on the rain type. Its average value is about 0.59 for the average (smooth) one minute DSD while an average value of un-smoothed DSD is 11.0 (moment method) or 5.4 (regression technique). The Joss's shape parameter and the Tokay-Short's parameter CS estimating roughly the rain type are also discussed (if CS>1, the event should be convective). The tendency of increasing numerical value of the CS parameter with the increasing rain rate was observed (the DSDs were distributed into classes respecting the rain rate value) and thus the idea of the convectivity occurrence bounded with the higher CS parameter value was supported. The study also compares the parameters of the average DSD with the averages of parameter values of all 4 183 one minute DSDs.

Drop size effects on rain-generated ring-waves with a view to remote sensing applications

This paper presents an analysis of drop size effects on ring-wave spectra and radar scatterometer returns from a water surface agitated by artificial rain. For this purpose, monodisperse and polydisperse rain events were generated in the laboratory for a wide range of rain rates and various drop sizes. The water droplets reached the surface at terminal velocity. In all cases, the radar average power is well modelled by a linear function of the power spectral density at the Bragg resonant wavelength. The drop size is found to have a strong impact on the spectral shape of the ring-waves and on their total energy. A log-Gaussian model characterizes well the ring-wave spectra and empirical expressions of the spectrum parameters are given. Ring-wave energy increases with rain rate and drop size, and is found to be proportional to the kinetic energy of a single drop, indicating that one may use a model in which all drops contribute to the ring-wave energy in proportion to their squared momentum. The results from the monodisperse rain experiments are used to construct a model for natural rain. Data from the polydisperse rain experiments show that a nonlinear model which relates dissipation to the total rainfall rate provides excellent agreement with the measurements. This analysis also shows the important impact of a few large drops on the ring-wave spectrum. The model proposed can be extended to natural rains either by using measurements of the drop size distribution or by assuming a drop size distribution model that is appropriate to the study region. It is concluded that it is important to characterize ring-wave spectra as a function of rain rate and drop size distribution to develop robust radar scattering models for rain-roughened seas.

A 3D drop-size distribution model based on the convolution of raindrops at terminal velocity

Using a matrix of drop size distributions (DSDs), measured by a microscale array of disdrometers, a method of spatial and temporal DSD interpolation is presented. The goal of this interpolation technique is to estimate the DSD above the disdrometer array as a function of three spatial coordinates, time and drop diameter. This interpolation algorithm assumes simplified drop dynamics, based on cloud advection and terminal velocity of raindrops. Once a 3D DSD has been calculated, useful quantities such as radar reflectivity Z and rainfall rate R can be computed and compared with corresponding rain gauge and weather radar data.

Kinetic energy of rain and its functional relationship with intensity

The rain kinetic energy (KE) is a widely used indicator of the potential ability of rain to detach soil. However, rain kinetic energy is not a commonly measured meteorological parameter. Therefore, empirical laws linking the rain kinetic energy to the more easily available rain intensity (I) have been proposed based on drop-size and drop-velocity measurements. The various mathematical expressions used to relate rain kinetic energy and rain intensity available from the literature are reported in this study. We focus our discussion on the two expressions of the kinetic energy used: the rain kinetic energy expended per volume of rain or volume-specific kinetic energy (KEmm, Jm−2mm−1) and the rain kinetic energy rate or time-specific kinetic energy (KEtime, Jm−2h−1). We use statistical and micro-physical considerations to demonstrate that KEtime is the most appropriate expression to establish an empirical law between rain kinetic energy and rain intensity. Finally, considering the existing drop-size distribution models from literature, we show that the most suitable mathematical function to link KE and I is a power law. The constants of the power law are related to rain type, geographical location and measurement technique.

An Areal Rainfall Estimator Using Differential Propagation Phase: Evaluation Using a C-Band Radar and a Dense Gauge Network in the Tropics

Abstract An areal rainfall estimator based on differential propagation phase is proposed and evaluated using the Bureau of Meteorology Research Centre (BMRC) C-POL radar and a dense gauge network located near Darwin, Northern Territory, Australia. Twelve storm events during the summer rainy season (December 1998–March 1999) are analyzed and radar–gauge comparisons are evaluated in terms of normalized error and normalized bias. The areal rainfall algorithm proposed herein results in normalized error of 14% and normalized bias of 5.6% for storm total accumulation over an area of around 100 km2. Both radar measurement error and gauge sampling error are minimized substantially in the areal accumulation comparisons. The high accuracy of the radar-based method appears to validate the physical assumptions about the rain model used in the algorithm, primarily a gamma form of the drop size distribution model, an axis ratio model that accounts for transverse oscillations for D ≤ 4 mm and equilibrium shapes for D > ...

Millimeter-Wave Attenuation Due to Fog and Clouds

The parameters of gamma drop size distribution model of fog and clouds are derived based on the liquid water content and optical visibility, the attenuation are calculated and discussed with this model and empirical relations of the liquid water content and the visibility or other parameters of fog and clouds. A new empirical formula to estimate fog and clouds attenuation is presented based on the Reyleigh absorption approximation, which is more accurate in general and can be used in wider frequency and temperature range than other empirical formulas.

Parameterization for narrow band shortwave optical properties of water clouds

Based on the drop size distribution models built from the observational data of microphysical properties of water clouds, the relationships between the optical properties and microphysical characteristics of water clouds have been investigated, and some different parameterization schemes of cloud optical properties have been analyzed. It is found that with the parameterization scheme, in addition to the equivalent radius, also including the mean radius of cloud droplet size distribution, the role of small cloud drops might be able to be considered more properly and better accuracies of parameterization calculation of cloud optical properties can be obtained, compared with that of using only the equivalent radius as parameter.

Reflectivity and Attenuation at Millimeter to Infrared Wavelengths for Advection Fogs at Four Locations

Recent drop size distribution data from four advection fog sites are reanalyzed for the purpose of predicting millimeter-wave and infrared to visible wavelength reflectivity and attenuation coefficients in such fogs. A gamma drop size distribution model is shown to be an adequate fit to measured distributions of typical fog drop diameters. Conclusions are drawn with respect to the relationships between the reflectivity and the attenuation to the liquid water content. A possible method is outlined for using ground-based measurement of liquid water content for the purpose of predicting arbitrary slant-path reflectivity and attenuation at the smaller wavelengths.

A Comparison of Techniques to Estimate Vertical Air Motions and Raindrop Size Distributions

Abstract Doppler velocity spectra collected at vertical incidence contain information on vertical air motions and drop-size distributions with high spatial and temporal resolution. In the past, the computational interdependence between vertical air velocities and drop-size distributions has severely limited the accuracy with which they could be estimated. A dual-wavelength technique is applied in which vertical air motion is determined independently of the drop-size distribution. The Rogers reflectivity method and an extended version of the Hauser-Amayenc method are also applied. The latter technique fits Doppler spectra in a nonlinear least-squares sense using two exponential drop-size distribution models. Results of applying each method to Oklahoma squall line data are compared and the strengths and weaknesses of the three techniques are assessed. For the methods tested, there is a trade-off between potential accuracy and potential for successful application. For example, the dual wavelength method is t...