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NASA NTRS1993

Marked point process models of raindrop-size distributions

The principal process considered in this paper is the flux of raindrops through a volume of the atmosphere. This process is of fundamental importance for a wide variety of engineering and environmental problems, notably remote sensing of precipitation, infiltration of rainfall, soil erosion, atmospheric deposition of pollutants, and design of microwave communication systems. A marked point process model is developed in which the point process represents the arrival times of drops at the upper surface of a sample volume and the mark associated with a drop is its diameter. In the model, both the rate of occurrence of raindrops and the distribution of drop diameters vary randomly over time. Results that relate the drop-size distribution within the sample volume to the probability law of the drop-arrival process are presented. These results allow straightforward comparisons between temporal characterizations of drop-size distributions and spatial characterizations. Representations for derived processes such as rainfall rate and reflectivity are shown to be quite accurate using raindrop data from North Carolina.

Smith, James A.↗

NASA NTRS1982

Rain measurements from space using a modified Seasat-type radar altimeter

The incorporation in the 13.5 GHz Seasat-type radar altimeter of a mode to measure rain rate is investigated. Specifically, an algorithm is developed relating the echo power at the various range bins, to the rain rate taking into consideration Mie scattering and path attenuation. The dependence of the algorithm on rain drop size distribution and nonuniform rain structure are examined and associated uncertainties defined. A technique for obtaining drop size distribution through the measurements of power at the top of the raincell and power difference through the cell also is investigated together with an associated error analysis. A description of the minor hardware modifications to the basic Seasat design is given for implementing the rain measurements.

Goldhirsh, J.↗

NASA NTRS1992

A study of rain estimation methods from space using dual-wavelength radar measurements at near-nadir incidence over ocean

A question arising from the recent interest in spaceborne weather radar is what methods can be used to estimate precipitation parameters from space. In this paper, dual-wavelength airborne radar data obtained from flights conducted during 1988 and 1989 are used to compare rain rates derived from backscattering and attenuation methods. To help interpret the results the surface reference methods are studied by means of scatterplots of the surface cross sections at the two frequencies under rain and no-rain conditions. Approximate criteria are given on combining attenuation and backscattering methods to increase the effective dynamic range of the radar. The dual-wavelength capability of the radar is also used to examine the vertical structure of the precipitation. Another factor affecting the accuracy of the methods is the drop-size distribution. In the final section of the paper a procedure to estimate the profiled drop-size distribution is applied to the measured radar data.

Meneghini, R.↗

NASA NTRS1981

Potential of dual-measurement techniques for accurate determination of instantaneous rainfall rate from space

The incorporation in the 13.5 GHz SEASAT type radar altimeter of a mode to measure rain rate is investigated. Specifically, an algorithm is developed relating the echo power at the various range bins to the rain rate, taking into consideration Mie scattering and path attenuation. The dependence of the algorithm on rain drop size distribution, and non-uniform rain structure are examined and associated uncertainties defined. A technique for obtaining drop size distribution through the measurements of power at the top of the raincell and power difference through the cell is also investigated together with an associated error analysis. A description of the minor hardware modifications to the basic SEASAT design is given for implementing the rain measurements.

Ulbrich, C. W.↗

NASA NTRS2013

Hydrometeor Size Distribution Measurements by Imaging the Attenuation of a Laser Spot

The optical extinction of a laser due to scattering of particles is a well-known phenomenon. In a laboratory environment, this physical principle is known as the Beer-Lambert law, and is often used to measure the concentration of scattering particles in a fluid or gas. This method has been experimentally shown to be a usable means to measure the dust density from a rocket plume interaction with the lunar surface. Using the same principles and experimental arrangement, this technique can be applied to hydrometeor size distributions, and for launch-pad operations, specifically as a passive hail detection and measurement system. Calibration of a hail monitoring system is a difficult process. In the past, it has required comparison to another means of measuring hydrometeor size and density. Using a technique recently developed for estimating the density of surface dust dispersed during a rocket landing, measuring the extinction of a laser passing through hail (or dust in the rocket case) yields an estimate of the second moment of the particle cloud, and hydrometeor size distribution in the terrestrial meteorological case. With the exception of disdrometers, instruments that measure rain and hail fall make indirect measurements of the drop-size distribution. Instruments that scatter microwaves off of hydrometeors, such as the WSR-88D (Weather Surveillance Radar 88 Doppler), vertical wind profilers, and microwave disdrometers, measure the sixth moment of the drop size distribution (DSD). By projecting a laser onto a target, changes in brightness of the laser spot against the target background during rain and hail yield a measurement of the DSD's second moment by way of the Beer-Lambert law. In order to detect the laser attenuation within the 8-bit resolution of most camera image arrays, a minimum path length is required. Depending on the intensity of the hail fall rate for moderate to heavy rainfall, a laser path length of 100 m is sufficient to measure variations in optical extinction using a digital camera. For hail fall only, the laser path may be shorter because of greater scattering due to the properties of hailstones versus raindrops. A photodetector may replace the camera in automated installations. Laser-based rain and hail measurement systems are available, but they are based on measuring the interruption of a thin laser beam, thus counting individual hydrometeors. These systems are true disdrometers since they also measure size and velocity. The method reported here is a simple method, requiring far less processing, but it is not a disdrometer.

Lane, John↗

NASA NTRS2004

Spray Characteristics of a Hybrid Twin-Fluid Pressure-Swirl Atomizer

The spray performance of a fuel injection system applicable for use in main combustion chamber of an oxidizer-rich staged combustion (ORSC) cycles is presented. The experimental data reported here include mean drop size and drop size distribution, spray cone half-angle, and momentum rate (directly related to spray penetration). The maximum entropy formalism, MEF, method to predict drop size distribution is applied and compared to the experimental data. Geometric variables considered include the radius of the injector inlet orifice plate through which oxidizer flows (&) and the exposed length from the fuel inlet to the injector exit plane (L2). Operating conditions that were varied include the liquid mass flow rate and air mass flow rate. For orifices B and C there is a significant dependence of D3Z on both the air and liquid mass flow rates, as well as on L2. For the A orifice, the momentum rate of the air flow appears to exceed a threshold value above which a constant D32 is obtained. Using the MEF method, a semi-analytical process was developed to model the spray distribution using two input parameters (q = 0.4 and Dso). The momentum rate of the spray is directly related to the air and liquid mass flow rates. The cone half angle of the spray ranges from 25 to 17 degrees. The data resulting from this project will eventually be used to develop advanced rocket systems.

Durham, M. J.↗

NASA NTRS2022

Limitations of Separate Cloud and Rain Categories in Parameterizing Collision-Coalescence for Bulk Microphysics Schemes

Warm rain collision-coalescence has been persistently difficult to parameterize in bulk microphysics schemes. We use a flexible bulk microphysics scheme with bin scheme process parameterizations, called AMP, to investigate reasons for the difficulty. AMP is configured in a variety of ways to mimic bulk schemes and is compared to simulations with the bin scheme upon which AMP is built. We find that an important limitation in traditional bulk schemes is the use of separate cloud and rain categories. When the drop size distribution is instead represented by a continuous distribution, the simulation of cloud-to-rain conversion is substantially improved. We also find large sensitivity to the threshold size to distinguish cloud and rain in traditional schemes; substantial improvement is found by decreasing the threshold from 40 to 25 μm. Neither the use of an assumed functional form for the size distribution nor the choice of predicted distribution moments has a large impact on the ability of AMP to simulate rain production. When predicting four total moments of the liquid drop size distribution, either with a traditional two-category, two-moment scheme with a reduced size threshold, or a four-moment single-category scheme, errors in the evolution of mass and the cloud size distribution are similar, but the single-category scheme has a substantially better representation of the rain size distribution. Optimal moment combinations for the single-category approach are investigated and appear to be linked more to the information content they provide for constraining the size distributions than to their correlation with collision-coalescence rates.

autoconversion↗

NASA NTRS2002

Impact of MIE-Resonances on the Atmospheric Absorption of Water Clouds

Clouds strongly modulate radiative transfer processes in the Earth's atmosphere. Studies, which simulate bulk properties of clouds, such as absorption, require methods that accurately account for multiple scattering among individual cloud particles. Multiple scattering processes are well described by MIE-theory, if interacting particles have a spherical shape. This is a good assumption for water droplets. Thus, simulations for water clouds (especially for interactions with solar radiation) usually apply readily available MIE-codes. The presence of different drop-sizes, however, necessitates repetitive calculations for many sizes. The usual representation by a few sizes is likely to miss contributions from densely distributed, sharp resonances. Despite their usually narrow width, integrated over the entire size-spectrum of a cloud droplet distribution, the impact of missed resonances could add up. The consideration of these resonances tends to increase cloud extinction and cloud absorption. This mechanism for a larger (than by MIE-methods predicted) solar absorption has the potential to explain observational evidence of larger than predicted cloud absorption at solar wavelengths. The presentation will address the absorption impact of added resonances for typical properties of water clouds (e.g. drop size distributions, drop concentrations and cloud geometry). Special attention will be given to scenarios with observational evidence of law than simulated solar absorption; particularly if simultaneous measurements of cloud micro- and macrophysical properties are available.

Wiscombe, W.↗

NASA NTRS1986

Some comments on passive microwave measurement of rain

It is argued that because microwave radiation interacts much more strongly with hydrometeors than with cloud particles, microwave measurements from space offer a significant chance of making global precipitation estimates. Over oceans, passive microwave measurements are essentially attenuation measurements that can be very closely related to the rain rate independently of the details of the drop-size distribution. Over land, scattering of microwave radiation by the hydrometeors, especially in the ice phase, can be used to estimate rainfall. In scattering, the details of the drop-size distribution are very important and it is therefore more difficult to achieve a high degree of accuracy. The SSM/I (Special Sensor Microwave Imager), a passive microwave imaging sensor that will be launched soon, will have dual-polarized channels at 85.5 GHz that will be very sensitive to scattering by frozen hydrometeors. Other sensors being considered for the future space missions would extend the ability to estimate rain rates from space. The ideal spaceborne precipitation-measurement system would use the complementary strengths of passive microwave, radar, and visible/infrared measurements.

Wilheit, Thomas T.↗

NASA NTRSDate not supplied

Comparison of Bimodal Ice Shapes on Full-Chord and Hybrid CRM Midspan Models

An ice shape database has been created to document ice accretions on a full-chord length and hybrid versions of a 65 percent scale size of the mid-span section of the Common Research Model resulting from an exposure to a Super-cooled Large Drop (SLD) icing cloud with a bimodal drop size distribution. The ice shapes created were documented with photographs, laser scanned surface measurements over a section of the model span, and measurement of the ice mass over the same section of each ice accretion. Drop distribution effects were evaluated by using the same IRT icing conditions except with either monomodal or bimodal drop distributions. Ice shapes resulting from the bimodal distribution as well as from monomodal distributions of identical cloud droplet Median Volume Diameter (MVD) were obtained and compared. Results indicated that the ice shapes resulting from the monomodal and bimodal drop size distributions have similar 2D Maximum Combined Cross Section, or MCCS, ice shape around the model leading edge region and equivalent ice mass measurement per unit span to within the IRT SLD cloud calibration uncertainty, as expected with this approach, but the bimodal distributions have distinctly larger ice feathers that extended further back on the chord of the model. For most test conditions, the overall size and shape of the main ice accretions compared well between the full-chord and hybrid models.

Icing↗

NASA NTRSDate not supplied

Comparison of Bimodal Ice Shapes on Full-Chord and Hybrid CRM Midspan Models

Icing , Simulation, Validation↗

NASA NTRSDate not supplied

Comparison of Bimodal Ice Shapes on Full-Chord and Hybrid CRM Midspan Models

Icing↗

NASA NTRS2014

Laser Calibration of an Impact Disdrometer

A practical approach to developing an operational low-cost disdrometer hinges on implementing an effective in situ adaptive calibration strategy. This calibration strategy lowers the cost of the device and provides a method to guarantee continued automatic calibration. In previous work, a collocated tipping bucket rain gauge was utilized to provide a calibration signal to the disdrometer's digital signal processing software. Rainfall rate is proportional to the 11/3 moment of the drop size distribution (a 7/2 moment can also be assumed, depending on the choice of terminal velocity relationship). In the previous case, the disdrometer calibration was characterized and weighted to the 11/3 moment of the drop size distribution (DSD). Optical extinction by rainfall is proportional to the 2nd moment of the DSD. Using visible laser light as a means to focus and generate an auxiliary calibration signal, the adaptive calibration processing is significantly improved.

calibration↗

NASA NTRS1990

Microwave scattering from wind- and rain-roughened seas

Microwave scattering from wind- and rain-roughened seas is studied under the assumption that, for light wind and light rain, the processes contributing to the scatterometer signal are independent. It is argued that calibrations from exclusively rain and exclusively wind conditions are all that is needed to predict scatterometer cross section for combined conditions. It is demonstrated that scatterometer response to a rain-roughened water surface is linear, but the slope of the relationship is sensitive to drop-size distribution. It is concluded that first-order wind and rain can be regarded as independent processes. Average cross section varies linearly with rainfall rate, but the slope of the relationship is a function of drop-size distribution. For combined light rain plus light wind, sigma-c is found to be well predicted by the addition of wind and rain models.

Bliven, Larry F.↗

NASA NTRS1997

Microphysical Retrievals Over Stratiform Rain Using Measurements from an Airborne Dual-Wavelength Radar-Radiometer

The need to understand the complementarity of the radar and radiometer is important not only to the Tropical Rain Measuring Mission (TRMM) program but to a growing number of multi-instrumented airborne experiment that combine single or dual-frequency radars with multichannel radiometers. The method of analysis used in this study begins with the derivation of dual-wavelength radar equations for the estimation of a two-parameter drop size distribution (DSD). Defining a "storm model" as the set of parameters that characterize snow density, cloud water, water vapor, and features of the melting layer, then to each storm model there will usually correspond a set of range-profiled drop size distributions that are approximate solutions of the radar equations. To test these solutions, a radiative transfer model is used to compute the brightness temperatures for the radiometric frequencies of interest. A storm model or class of storm models is considered optimum if it provides the best reproduction of the radar and radiometer measurements. Tests of the method are made for stratiform rain using simulated storm models as well as measured airborne data. Preliminary results show that the best correspondence between the measured and estimated radar profiles usually can be obtained by using a moderate snow density (0.1-0.2 g/cu cm), the Maxwell-Garnett mixing formula for partially melted hydrometeors (water matrix with snow inclusions), and low to moderate values of the integrated cloud liquid water (less than 1 kg/sq m). The storm-model parameters that yield the best reproductions of the measured radar reflectivity factors also provide brightness temperatures at 10 GHz that agree well with the measurements. On the other hand, the correspondence between the measured and modeled values usually worsens in going to the higher frequency channels at 19 and 34 GHz. In searching for possible reasons for the discrepancies, It is found that changes in the DSD parameter Mu, the radar constants, or the path-integrated attenuation can affect the high frequency channels significantly. In particular, parameters that cause only modest increases in the median mass diameter of the snow, and which have a minor effect on the radar returns or the low frequency brightness temperature, can produce a strong cooling of the 34 GHz brightness temperature.

Meneghini, Robert↗

NASA NTRS2010

DSD Characteristics of a Mid-Winter Tornadic Storm Using C-Band Polarimetric Radar and Two 2D-Video Disdrometers

Drop size distributions in an evolving tornadic storm are examined using C-band polarimetric radar observations and two 2D-video disdrometers. The E-F2 storm occurred in mid-winter (21 January 2010) in northern Alabama, USA, and caused widespread damage. The evolution of the storm occurred within the C-band radar coverage and moreover, several minutes prior to touch down, the storm passed over a site where several disdrometers including two 2D video disdrometers (2DVD) had been installed. One of the 2DVDs is a low profile unit and the other is a new next generation compact unit currently undergoing performance evaluation. Analyses of the radar data indicate that the main region of precipitation should be treated as a "big-drop" regime case. Even the measured differential reflectivity values (i.e. without attenuation correction) were as high as 6-7 dB within regions of high reflectivity. Standard attenuation-correction methods using differential propagation phase have been "fine tuned" to be applicable to the "big drop" regime. The corrected reflectivity and differential reflectivity data are combined with the co-polar correlation coefficient and specific differential phase to determine the mass-weighted mean diameter, Dm, and the width of the mass spectrum, (sigma)M, as well as the intercept parameter , Nw. Significant areas of high Dm (3-4 mm) were retrieved within the main precipitation areas of the tornadic storm. The "big drop" regime assumption is substantiated by the two sets of 2DVD measurements. The Dm values calculated from 1-minute drop size distributions reached nearly 4 mm, whilst the maximum drop diameters were over 6 mm. The fall velocity measurements from the 2DVD indicate almost all hydrometeors to be fully melted at ground level. Drop shapes for this event are also being investigated from the 2DVD camera data.

Thurai, M.↗

NASA NTRS2003

On the Use of the Log-Normal Particle Size Distribution to Characterize Global Rain

Although most parameterizations of the drop size distributions (DSD) use the gamma function, there are several advantages to the log-normal form, particularly if we want to characterize the large scale space-time variability of the DSD and rain rate. The advantages of the distribution are twofold: the logarithm of any moment can be expressed as a linear combination of the individual parameters of the distribution; the parameters of the distribution are approximately normally distributed. Since all radar and rainfall-related parameters can be written approximately as a moment of the DSD, the first property allows us to express the logarithm of any radar/rainfall variable as a linear combination of the individual DSD parameters. Another consequence is that any power law relationship between rain rate, reflectivity factor, specific attenuation or water content can be expressed in terms of the covariance matrix of the DSD parameters. The joint-normal property of the DSD parameters has applications to the description of the space-time variation of rainfall in the sense that any radar-rainfall quantity can be specified by the covariance matrix associated with the DSD parameters at two arbitrary space-time points. As such, the parameterization provides a means by which we can use the spaceborne radar-derived DSD parameters to specify in part the covariance matrices globally. However, since satellite observations have coarse temporal sampling, the specification of the temporal covariance must be derived from ancillary measurements and models. Work is presently underway to determine whether the use of instantaneous rain rate data from the TRMM Precipitation Radar can provide good estimates of the spatial correlation in rain rate from data collected in 5(sup 0)x 5(sup 0) x 1 month space-time boxes. To characterize the temporal characteristics of the DSD parameters, disdrometer data are being used from the Wallops Flight Facility site where as many as 4 disdrometers have been used to acquire data over a 2 km path. These data should help quantify the temporal form of the covariance matrix at this site.

Meneghini, Robert↗

NASA NTRS1994

The meteorological parameterization of specific attenuation in rain viewed at Nadir

Polynomial expressions are presented for the parameterization of the specific attenuation in rain from 9 to 38 GHz that are applicable to a wide range of naturally occurring drop size distributions and for viewing angles close to nadir. Because the temperature T affects the specific attenuation at some frequencies, expressions for the polynomial coefficients as functions of T are also provided for -10C less than or equal to T less than or equal to 30C. The advantage of this parameterization is that even without a detailed specification of the drop size distribution, useful estimates of the specific attenuation are often possible given only two out of three parameters, namely, the rainfall rate R, the rainwater content W, or D(sub m) (the mass-weighted mean drop diameter), particularly if the temperature is also specified.

Jameson, A. R.↗