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Parameterizing the Raindrop Size Distribution

This paper addresses the problem of finding a parametric form for the raindrop size distribution (DSD) that(1) is an appropriate model for tropical rainfall, and (2) involves statistically independent parameters. Such a parameterization is derived in this paper. One of the resulting three "canonical" parameters turns out to vary relatively little, thus making the parameterization particularly useful for remote sensing applications. In fact, a new set of r drop-size-distribution-based Z-R and k-R relations is obtained. Only slightly more complex than power laws, they are very good approximations to the exact radar relations one would obtain using Mie scattering. The coefficients of the new relations are directly related to the shape parameters of the particular DSD that one starts with. Perhaps most important, since the coefficients are independent of the rain rate itself, the relations are ideally suited for rain retrieval algorithms.

Haddad, Ziad S.↗

Retrieval of Raindrop Size Distribution, Vertical Air Velocity and Water Vapor Attenuation Using Dual-Wavelength Doppler Radar Observations

Two techniques for retrieving the slope and intercept parameters of an assumed exponential raindrop size distribution (RSD), vertical air velocity, and attenuation by precipitation and water vapor in light stratiform rain using observations by airborne, nadir looking dual-wavelength (X-band, 3.2 cm and W-band, 3.2 mm) radars are presented. In both techniques, the slope parameter of the RSD and the vertical air velocity are retrieved using only the mean Doppler velocities at the two wavelengths. In the first method, the intercept of the RSD is estimated from the observed reflectivity at the longer wavelength assuming no attenuation at that wavelength. The attenuation of the shorter wavelength radiation by precipitation and water vapor are retrieved using the observed reflectivity at the shorter wavelength. In the second technique, it is assumed that the longer wavelength suffers attenuation only in the melting band. Then, assuming a distribution of water vapor, the melting band attenuation at both wavelengths and the rain attenuation at the shorter wavelength are retrieved. Results of the retrievals are discussed and several physically meaningful results are presented.

Heymsfield, Gerald M.↗

On the equivalence of the dual-wavelength and polarimetric equations for estimation of the raindrop size distribution

In writing the integral equations for the median mass diameter and particle concentration, or comparable parameters of the raindrop size distribution, it is apparent that when attenuation effects are included, the forms of the equations for polarimetric and dual wavelength radars are identical. In both sets of equations, differences in the backscattering and extinction cross sections appear: in the polarimetric equations, the differences are taken with respect polarization at a fixed frequency while for the dual wavelength equations, the differences are taken with respect to wavelength at a fixed polarization. Because the forms of the equations are the same, the ways in which they can be solved are similar as well. To avoid instabilities in the forward recursion procedure, the equations can be expressed in the form of a final-value. Solving the equations in this way traditionally has required estimates of the path attenuations to the final gate: either the attenuations at horizontal and vertical polarizations at the same frequency or attenuations at two frequencies with the same polarization. This has been done for dual-frequency (air/spaceborne case) and polarimetric radars by the respective use of the surface reference technique and the differential phase shift. An alternative to solving the constrained version of the equations is an iterative procedure recently proposed in which independent estimates of path attenuation are not required. Although the procedure has limitations, it appears to be quite useful. Simulations of the retrievals help clarify the relationship between the constrained and unconstrained approaches and their application to the polarimetric and dual-wavelength equations.

Meneghini, Robert↗

An Experimental Study of Small-Scale Variability of Raindrop Size Distribution

An experimental study of small-scale variability of raindrop size distributions (DSDs) has been carried out at Wallops Island, Virginia. Three Joss-Waldvogel disdrometers were operated at a distance of 0.65, 1.05, and 1.70 km in a nearly straight line. The main purpose of the study was to examine the variability of DSDs and its integral parameters of liquid water content, rainfall, and reflectivity within a 2-km array: a typical size of Cartesian radar pixel. The composite DSD of rain events showed very good agreement among the disdrometers except where there were noticeable differences in midsize and large drops in a few events. For consideration of partial beam filling where the radar pixel was not completely covered by rain, a single disdrometer reported just over 10% more rainy minutes than the rainy minutes when all three disdrometers reported rainfall. Similarly two out of three disdrometers reported5%more rainy minutes than when all three were reporting rainfall. These percentages were based on a 1-min average, and were less for longer averaging periods. Considering only the minutes when all three disdrometers were reporting rainfall, just over one quarter of the observations showed an increase in the difference in rainfall with distance. This finding was based on a 15-min average and was even less for shorter averaging periods. The probability and cumulative distributions of a gamma-fitted DSD and integral rain parameters between the three disdrometers had a very good agreement and no major variability. This was mainly due to the high percentage of light stratiform rain and to the number of storms that traveled along the track of the disdrometers. At a fixed time step, however, both DSDs and integral rain parameters showed substantial variability. The standard deviation (SD) of rain rate was near 3 mm/h, while the SD of reflectivity exceeded 3 dBZ at the longest separation distance. These standard deviations were at 6-min average and were higher at shorter averaging periods. The correlations decreased with increasing separation distance. For rain rate, the correlations were higher than previous gauge-based studies. This was attributed to the differences in data processing and the difference in rainfall characteristics in different climate regions. It was also considered that the gauge sampling errors could be a factor. In this regard, gauge measurements were simulated employing existing disdrometer dataset. While a difference was noticed in cumulative distribution of rain occurrence between the simulated gauge and disdrometer observations, the correlations in simulated gauge measurements did not differ from the disdrometer measurements.

Tokay, Ali↗

Comparison of Raindrop Size Distribution between NASA’s S-Band Polarimetric Radar and Two-Dimensional Video Disdrometers

The ground-based-radar-derived raindrop size distribution (DSD) parameters—mass-weighted drop diameter Dmass and normalized intercept parameter NW—are the sole resource for direct validation of the National Aeronautics and Space Administration (NASA) Global Precipitation Measurement (GPM) mission Core Observatory satellite-based retrieved DSD. Both Dmass and NW are obtained from radar-measured reflectivity ZH and differential reflectivity ZDR through empirical relationships. This study uses existing relationships that were determined for the GPM ground validation (GV) program and directly compares the NASA S-band polarimetric radar (NPOL) observables of ZH and ZDR and derivedDmass and NW with those calculated by two-dimensional video disdrometer (2DVD). The joint NPOL and 2DVD datasets were acquired during three GPM GV field campaigns conducted in eastern Iowa, southern Appalachia, and western Washington State. The comparative study quantifies the level of agreement for ZH, ZDR, Dmass, and log(NW) at an optimum distance (15–40 km) from the radar as well as at distances greater than 60 km from radar and over mountainous terrain. Interestingly, roughly 10%–15% of the NPOL ZH–ZDR pairs were well outside the envelope of 2DVD-estimated ZH–ZDR pairs. The exclusion of these pairs improved the comparisons noticeably.

Ali Tokay↗

Development and Evaluation of the Raindrop Size Distribution Parameters for the NASA Global Precipitation Measurement Mission Ground Validation Program

The National Aeronautics and Space Administration Global Precipitation Measurement (GPM) mission ground validation program uses dual-polarization radar moments to estimate raindrop size distribution (DSD) parameters, the mass-weighted mean drop diameter Dmass, and normalized intercept parameter NW, to validate the GPM Core Observatory–derived DSD parameters. The disdrometer-based Dmass and NW are derived through empirical relationships between Dmass and differential reflectivity ZDR, and between NW, reflectivity ZH, and Dmass. This study employs large datasets collected from two-dimensional video disdrometers (2DVD) during six different field studies to derive the requisite empirical relationships. The uncertainty of the derived Dmass(ZDR) relationship is evaluated through comparisons of 2DVD-calculated and ZDR-estimated Dmass, where ZDR is calculated directly from 2DVD observations. Similarly, the uncertainty of the NW(ZH, Dmass) relationship is evaluated through 2DVD-calculated and Dmass and ZH-estimated NW, where Dmass and ZH are directly calculated from 2DVD observations. This study also presents the sensitivity of Dmass(ZDR) relationships to climate regime and to disdrometer type after developing three additional Dmass(ZDR) relationships from second-generation Particle Size Velocity (PARSIVEL2) disdrometer (P2) observations collected in the Pacific Northwest, in Iowa, and at Kwajalein Atoll in the tropical Pacific Ocean. The application of P2-derived Dmass(ZDR) relationship based on precipitation in the northwestern United States to P2 observations collected over the tropical ocean resulted in the highest error among comparisons of the three datasets.

Ali Tokay↗

Comparison of Raindrop Size Distribution between NASA's S-Band Polarimetric Radar and Two-Dimensional Video Disdrometers

The ground-based-radar-derived raindrop size distribution (DSD) parameters—mass-weighted drop diameter D mass and normalized intercept parameter NW—are the sole resource for direct validation of the National Aeronautics and Space Administration (NASA) Global Precipitation Measurement (GPM ) mission Core Observatory satellite-based retrieved DSD. Both D mass and NW are obtained from radar-measured reflectivity Z Hand differential reflectivity ZDR through empirical relationships. This study uses existing relationships that were determined for the GPM ground validation (GV) program and directly compares the NASA S-band polarimetric radar (NPOL) observables of Z Hand Z DR and derived D mass and NW with those calculated by two-dimensional video disdrometer (2DVD). The joint NPOL and 2DVD datasets were acquired during three GPM GV field campaigns conducted in eastern Iowa, southern Appalachia, and western Washington State. The comparative study quantifies the level of agreement for ZH, ZDR, D mass, and log (NW) at an optimum distance (15–40 km) from the radar as well as at distances greater than 60 km from radar and over mountainous terrain. Interestingly, roughly 10%–15% of the NPOLZH–Z DR pairs were well outside the envelope of 2DVD-estimatedZH–Z DR pairs. The exclusion of these pairs improved the comparisons noticeably.

Ali Tokay↗

Comparison of two different raindrop disdrometers

Different types of impact sensors, used for the measurement of drop size distribution, are described and compared. All of them generate an electrical output which is to a first order a function of the velocity and mass of impacting drops within the size range of 0.25 to 5.0 mm. The disdrometers discussed include an active styrofoam disdrometer, a passive plexiglass sensor, and a cast epoxy disdrometer sensor. The sensors are calibrated by dropping water drops of known size on the sensor, and using an oscilloscope to measure peak amplitude. Similar response characteristics are observed for the active styrofoam disdrometer and the passive plexiglass and brass sensors. The cast epoxy impact sensor is noted to have a faster response and to be more sturdy than the styrofoam or plexiglass sensors.

Rowland, J. R.↗

A wind tunnel investigation of the shape of uncharged raindrops in the presence of an external, electric field

Results of a wind tunnel experiment in which electrically uncharged water drops of 500 to 3000 microns equivalent radius are freely suspended in the vertical air stream of the UCLA cloud tunnel are presented. During this suspension the drops were exposed to external vertical electric fields of 500 to 8,000 volts/cm. The change in drop shape with drop size and electric field strength was noted and is discussed in the light of theoretical work cited in the literature which unfortunately does not take into account the effects of air flow past the drop. The wind tunnel study is documented by stills from a 16 mm film record that demonstrates the shape of water drops in response to both hydrodynamic and electric forces.

Pruppacher, H. R.↗

Estimating the Concentration of Large Raindrops from Polarimetric Radar and Disdrometer Observations

Estimation of rainfall integral parameters, including radar observables, and empirical relations between them are sensitive to the truncation of the drop size distribution (DSD), particularly at the large drop end. The sensitivity of rainfall integral parameters to the maximum drop diameter (D(sub max)) is exacerbated at C‐band since resonance effects are pronounced for large drops in excess of 5 mm diameter (D). Due to sampling limitations, it is often difficult to reliably estimate D(sub max) with disdrometers. The resulting uncertainties in D(sub max0 potentially increase errors in radar retrieval methods, particularly at C‐band, that rely on disdrometer observations for DSD input to radar models. In fact, D(sub max) is typically an assumed DSD parameter in the development of radar retrieval methods. Because of these very uncertainties, it is difficult to independently confirm disdrometer estimates of D(sub max) with polarimetric radar observations. A couple of approaches can be taken to reduce uncertainty in large drop measurement. Longer integration times can be used for the collection of larger disdrometer samples. However, integration periods must be consistent with a radar resolution volume (RRV) and the temporal and spatial scales of the physical processes affecting the DSD therein. Multiple co‐located disdrometers can be combined into a network to increase the sample size within a RRV. However, over a reasonable integration period, a single disdrometer sample volume is many orders of magnitudes less than a RRV so it is not practical to devise a network of disdrometers that has an equivalent volume to a typical RRV. Since knowledge of DSD heterogeneity and large drop occurrence in time and space is lacking, the specific accuracy or even general representativeness of disdrometer based D(sub max) and large drop concentration estimates within a RRV are currently unknown. To address this complex issue, we begin with a simpler question. Is the frequency of occurrence of large rain drops (D > 5 mm) in disdrometer observations, either stand alone or networked, generally representative and consistent with polarimetric radar observations? We first show from simulations that the concentration of large (D > 5 mm) rain drops (N(sub T5)) can be estimated from polarimetric observations of specific differential phase (K(sub dp)) and differential reflectivity (Z(sub dr)), N(sub T5)=F(K(sub dp),Z(sub dr)), or horizontal reflectivity (Z(sub h)) and Z(sub dr), N(sub T5)=(Z(sub h),Z(sub dr)). We assess the error associated with polarimetric retrieval of N(sub T5), including sensitivity to D(sub max) parameterization assumptions and measurement error in the radar simulations. Polarimetric measurements at S‐band and C‐band will then be used to retrieve estimates of N(sub T5) and compared to disdrometer estimates of N(sub T5). After careful consideration of retrieval error, we will check consistency between disdrometer and polarimetric radar estimates of N(sub T5) and the frequency of occurrence of large rain drops in a variety of precipitating regimes using data from NASA's Global Precipitation Measurement (GPM) Ground Validation (GV) program, including field campaigns such as MC3E (Oklahoma) and IFloodS (Iowa) and extended measurements over Huntsville, Alabama and NASA Wallops Flight Facility in coastal Virginia.

Carey, Lawrence D.↗

Hail Monitor Sensor

An inexpensive and simple hail monitor design has been developed that has a single piezoelectric ceramic disc and uses a metal plate as a sounding board. The structure is durable and able to withstand the launch environment. This design has several advantages over a multi-ceramic sensor, including reduced cost and complexity, increased durability, and improvement in impact response uniformity over the active surface. However, the most important characteristic of this design is the potential to use frequency discrimination between the spectrum created from raindrop impact and a hailstone impact. The sound of hail hitting a metal plate is distinctly different from the sound of rain hitting the same plate. This fortuitous behavior of the pyramid sensor may lead to a signal processing strategy, which is inherently more reliable than one depending on amplitude processing only. The initial concept has been im proved by forming a shallow pyramid structure so that hail is encouraged to bounce away from the sensor so as not to be counted more than once. The sloped surface also discourages water from collecting. Additionally, the final prototype version includes a mounting box for the piezo-ceramic, which is offset from the pyramid apex, thus helping to reduce non-uniform response (see Figure 2). The frequency spectra from a single raindrop impact and a single ice ball impact have been compared. The most notable feature of the frequency resonant peaks is the ratio of the 5.2 kHz to 3.1 kHz components. In the case of a raindrop, this ratio is very small. But in the case of an ice ball, the ratio is roughly one third. This frequency signature of ice balls should provide a robust method for discriminating raindrops from hailstones. Considering that hail size distributions (HSDs) and fall rates are roughly 1 percent that of rainfall, hailstone sizes range from a few tenths of a centimeter to several centimeters. There may be considerable size overlap between large rain and small hail. As hail occurs infrequently at KSC, the ideal HSD measurement sensor needs to have a collection area roughly 100 times greater than a raindrop-size distribution sensor or disdrometer. The sensitivity should be such that it can detect and count very small hail in the midst of intense rainfall consisting of large raindrop sizes. The dynamic range and durability should allow measurement of the largest hail sizes, and the operation and calibration strategy should consider the infrequent occurrence of hail fall over the KSC area.

Younquist, Robert↗

Cloud Microphysics Budget in the Tropical Deep Convective Regime

Cloud microphysics budgets in the tropical deep convective regime are analyzed based on a 2-D cloud resolving simulation. The model is forced by the large-scale vertical velocity and zonal wind and large-scale horizontal advections derived from TOGA COARE for a 20-day period. The role of cloud microphysics is first examined by analyzing mass-weighted mean heat budget and column-integrated moisture budget. Hourly budgets show that local changes of mass-weighted mean temperature and column-integrated moisture are mainly determined by the residuals between vertical thermal advection and latent heat of condensation and between vertical moisture advection and condensation respectively. Thus, atmospheric thermodynamics depends on how cloud microphysical processes are parameterized. Cloud microphysics budgets are then analyzed for raining conditions. For cloud-vapor exchange between cloud system and its embedded environment, rainfall and evaporation of raindrop are compensated by the condensation and deposition of supersaturated vapor. Inside the cloud system, the condensation of supersaturated vapor balances conversion from cloud water to raindrop, snow, and graupel through collection and accretion processes. The deposition of supersaturated vapor balances conversion from cloud ice to snow through conversion and riming processes. The conversion and riming of cloud ice and the accretion of cloud water balance conversion from snow to graupel through accretion process. Finally, the collection of cloud water and the melting of graupel increase raindrop to compensate the loss of raindrop due to rainfall and the evaporation of raindrop.

Li, Xiao-Fan↗