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NASA NTRS1999

Cloud Thickness from Diffusion of Lidar Pulses in Clouds

Measurements of the distribution of reflected light from a laser beam incident on an aqueous suspension of particles or "cloud" with known thickness and particle size distribution are reported. The distribution is referred to as the "cloud radiative Green's function", G. In the diffusion domain, G is sensitive to cloud thickness, allowing that important quantity to be retrieved. The goal of the laboratory simulation is to provide preliminary estimates of sensitivity of G to cloud thickness,for use in the optimal design of an offbeam Lidar instrument for remote sensing of cloud thickness (THOR, Thickness from Offbeam Returns). These clouds of polystyrene microspheres suspended in water are analogous to real clouds of water droplets suspended in air. The microsphere size distribution is roughly lognormal, from 0.5 microns to 25 microns, similar to real clouds. Density of suspended spheres is adjusted so mean-free-path of visible photons is about 10 cm, approximately 1000 times smaller than in real clouds. The light source is a ND:YAG laser at 530 nm. Detectors are flux and photon-counting Photomultiplier Tube (PMTS), with a glass probe for precise positioning. A Labview 5 VI controls positioning, and data acquisition, via an NI Motion Control board connected to a stepper motor driving an Edmund linear slider, and a 16-channel 16-bit NI-DAQ board. The stepper motor is accurate to 10 microns, and step size is selectable from the VI software. Far from the incident beam, the rate of exponential increase as the direction of the incident beam is approached scales as expected from diffusion theory, linearly with the cloud thickness, and inversely as the square root of the reduced optical thickness, and is independent of particle size. Near the beam the signal begins to increase faster than exponential, due to single and low-order scattering near the backward direction, and here the distribution depends on particle size. Results are being used to verify 3D Monte Carlo radiative transfer simulations, used to estimate signal-to-noise ratios for remotely sensed off beam returns, for both homogeneous and inhomogeneous clouds. Signal-to-noise estimates show that unfiltered observations are straight forward at night, while narrow band pass filters are being studied for day.

Cahalan, Robert F.↗
NASA NTRS1989

Photoelectric return-stroke velocity and peak current estimates in natural and triggered lightning

Two-dimensional photoelectric return stroke velocities from 130 strokes are presented, including 86 negative natural, 41 negative triggered, one positive triggered, and two positive natural return strokes. For strokes starting near the ground and exceeding 500 m in length, the average velocity is 1.3 + or - 0.3 X 10 to the 8th m/s for natural return strokes and 1.2 + or - 0.3 X 10 to the 8th m/s for triggered return strokes. For strokes with lengths less than 500 m, the average velocities are slightly higher. Using the transmission line model (TLM), the shortest segment one-dimensional return stroke velocity, and either the maximum or plateau electric field, it is shown that natural strokes have a peak current distribution that is lognormal with a median value of 16 kA (maximum E) or 12 kA (plateau E). Triggered lightning has a medium peak current value of 21 kA (maximum E) or 15 kA (plateau E). Correlations are found between TLM peak currents and velocities for triggered and natural subsequent return strokes, but not between TLM peak currents and natural first return stroke velocities.

Mach, Douglas M.↗
NASA NTRS1991

Grain growth kinetics in liquid-phase-sintered zinc oxide-barium oxide ceramics

Grain growth of ZnO in the presence of a liquid phase of the ZnO-BaO system has been studied for temperatures from 1300 to 1400 C. The specimens were treated in boiling water and the grains were separated by dissolving the matrix phase in an ultrasonic bath. As a consequence 3D grain size measurements were possible. Microstructural examination shows some grain coalescence with a wide range of neck size ratios and corresponding dihedral angles, however, most grains are isolated. Lognormal grain size distributions show similar shapes, indicating that the growth mechanism is invariant over this time and temperature. All regressions between G exp n and time for n = 2 and 3 proved statistically significant. The rate constants calculated with the growth exponent set to n = 3 are on the same order of magnitude as in metallic systems. The apparent activation energy for growth is estimated between 355 and 458 kJ/mol.

Yang, Sung-Chul↗
NASA NTRS1992

An application of synthetic seismicity in earthquake statistics - The Middle America Trench

The way in which seismicity calculations which are based on the concept of fault segmentation incorporate the physics of faulting through static dislocation theory can improve earthquake recurrence statistics and hone the probabilities of hazard is shown. For the Middle America Trench, the spread parameters of the best-fitting lognormal or Weibull distributions (about 0.75) are much larger than the 0.21 intrinsic spread proposed in the Nishenko Buland (1987) hypothesis. Stress interaction between fault segments disrupts time or slip predictability and causes earthquake recurrence to be far more aperiodic than has been suggested.

Ward, Steven N.↗
NASA NTRS1995

A Bayesian approach to microwave precipitation profile retrieval

A multichannel passive microwave precipitation retrieval algorithm is developed. Bayes theorem is used to combine statistical information from numerical cloud models with forward radiative transfer modeling. A multivariate lognormal prior probability distribution contains the covariance information about hydrometeor distribution that resolves the nonuniqueness inherent in the inversion process. Hydrometeor profiles are retrieved by maximizing the posterior probability density for each vector of observations. The hydrometeor profile retrieval method is tested with data from the Advanced Microwave Precipitation Radiometer (10, 19, 37, and 85 GHz) of convection over ocean and land in Florida. The CP-2 multiparameter radar data are used to verify the retrieved profiles. The results show that the method can retrieve approximate hydrometeor profiles, with larger errors over land than water. There is considerably greater accuracy in the retrieval of integrated hydrometeor contents than of profiles. Many of the retrieval errors are traced to problems with the cloud model microphysical information, and future improvements to the algorithm are suggested.

Evans, K. Franklin↗
NASA NTRS1994

Vertical velocity in oceanic convection off tropical Australia

Time series of 1-Hz vertical velocity data collected during aircraft penetrations of oceanic cumulonimbus clouds over the western Pacific warm pool as part of the Equatorial Mesoscale Experiment (EMEX) are analyzed for updraft and downdraft events called cores. An updraft core is defined as occurring whenever the vertical velocity exceeds 1 m/sec for at least 500 m. A downdraft core is defined analogously. Over 19,000 km of straight and level flight legs are used in the analysis. Five hundred eleven updraft cores and 253 downdraft cores are included in the dataset. Core properties are summarized as distributions of average and maximum vertical velocity, diameter, and mass flux in four altitude intervals between 0.2 and 5.8 km. Distributions are approximately lognormal at all levels. Examination of the variation of the statistics with height suggests a maximum in vertical velocity between 2 and 3 km; slightly lower or equal vertical velocity is indicated at 5 km. Near the freezing level, virtual temperature deviations are found to be slightly positive for both updraft and downdraft cores. The excess in updraft cores is much smaller than that predicted by parcel theory. Comparisons with other studies that use the same analysis technique reveal that EMEX cores have approximately the same strength as cores of other oceanic areas, despite warmer sea surface temperatures. Diameter and mass flux are greater than those in the Global Atmospheric Research Program (GATE) but smaller than those in hurricane rainbands. Oceanic cores are much weaker and appear to be slightly smaller than those observed over land during the Thunderstorm Project. The markedly weaker oceanic vertical velocities below 5.8 km (compared to the continental cores) cannot be attributed to smaller total convective available potential energy or to very high water loading. Rather, it is suggested that water loading, although less than adiabatic, is more effective in reducing buoyancy of oceanic cores because of the smaller potential buoyancy below 5.8 km. Entrainment appears to be more effective in reducing buoyancy to well below adiabatic values in oceanic cores, a result consistent with the smaller oceanic core diameters in the lower cloud layer. It is speculated further that core diameters are related to boundary layer depth, which is clearly smaller over the oceans.

Lucas, Christopher↗
NASA NTRS2001

Dependence of Aerosol Light Absorption and Single-Scattering Albedo On Ambient Relative Humidity for Sulfate Aerosols with Black Carbon Cores

Atmospheric aerosols frequently contain hygroscopic sulfate species and black carbon (soot) inclusions. In this paper we report results of a modeling study to determine the change in aerosol absorption due to increases in ambient relative humidity (RH), for three common sulfate species, assuming that the soot mass fraction is present as a single concentric core within each particle. Because of the lack of detailed knowledge about various input parameters to models describing internally mixed aerosol particle optics, we focus on results that were aimed at determining the maximum effect that particle humidification may have on aerosol light absorption. In the wavelength range from 450 to 750 nm, maximum absorption humidification factors (ratio of wet to 'dry=30% RH' absorption) for single aerosol particles are found to be as large as 1.75 when the RH changes from 30 to 99.5%. Upon lesser humidification from 30 to 80% RH, absorption humidification for single particles is only as much as 1.2, even for the most favorable combination of initial ('dry') soot mass fraction and particle size. Integrated over monomodal lognormal particle size distributions, maximum absorption humidification factors range between 1.07 and 1.15 for humidification from 30 to 80% and between 1.1 and 1.35 for humidification from 30 to 95% RH for all species considered. The largest humidification factors at a wavelength of 450 nm are obtained for 'dry' particle size distributions that peak at a radius of 0.05 microns, while the absorption humidification factors at 700 nm are largest for 'dry' size distributions that are dominated by particles in the radius range of 0.06 to 0.08 microns. Single-scattering albedo estimates at ambient conditions are often based on absorption measurements at low RH (approx. 30%) and the assumption that aerosol absorption does not change upon humidification (i.e., absorption humidification equal to unity). Our modeling study suggests that this assumption alone can introduce absolute errors in estimates of the midvisible single-scattering albedo of up to 0.05 for realistic dry particle size distributions. Our study also indicates that this error increases with increasing wavelength. The potential errors in aerosol single-scattering albedo derived here are comparable in magnitude and in addition to uncertainties in single-scattering albedo estimates that are based on measurements of aerosol light absorption and scattering.

Redemann, Jens↗
NASA NTRS2010

Sectors and Large-Scale Magnetic Field Strength Fluctuations in the Heliosheath Near 110 AU: Voyager 1,2009

This paper describes observations of daily averages of the magnetic field strength B and the magnetic polarity measured by Voyager 1 (V1) in the heliosheath during 2009 between 108.5 and 112.1 AU and at heliographic latitude 34. . 4. A negative magnetic polarity sector was observed during 2009 DOY 43.255. A positive polarity sector was observed during 2009 DOY 256.365. We offer the hypothesis that the existence of the two sectors is the result of the displacement of the wavy heliospheric current sheet to the position of V1 as a result of northward flow in the heliosheath. The large size of the sectors is caused by the slow radial motion of the flow observed by V1 in the heliosheath. The distribution of B during 2009 was lognormal, in contrast to the Gaussian distributions observed by V1 in the heliosheath prior to 2009. The large-scale fluctuations of B, described by the distribution of increments of daily averages of B, have a Tsallis distribution with q = 1.6. The large-scale fluctuations of B observed by V1 during 2009 have a multifractal spectrum with the same parameters that V1 observed during 2005 close to the termination shock at 94 AU. These results suggest that the large-scale magnetic fluctuations of B are in a metastable equilibrium state in the heliosheath between 94 AU and 112.1 AU.

Burlaga, L. F.↗
NASA NTRS2018

The Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 Aerosol Extinction Retrieval Algorithm: Theoretical Basis

The theoretical basis of the Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 aerosol extinction retrieval algorithm is presented. The algorithm uses an assumed bimodal lognormal aerosol size distribution to retrieve aerosol extinction profiles at 675 nm from OMPS LP radiance measurements. A first-guess aerosol extinction profile is updated by iteration using the Chahine nonlinear relaxation method, based on comparisons between the measured radiance profile at 675 nm and the radiance profile calculated by the Gauss Seidel limb-scattering (GSLS) radiative transfer model for a spherical-shell atmosphere. This algorithm is discussed in the context of previous limb-scattering aerosol extinction retrieval algorithms, and the most significant error sources are enumerated. The retrieval algorithm is limited primarily by uncertainty about the aerosol phase function. Horizontal variations in aerosol extinction, which violate the spherical-shell atmosphere assumed in the version 1 algorithm, may also limit the quality of the retrieved aerosol extinction profiles significantly.

Loughman, Robert↗
NASA NTRS1974

Aerodynamic size distribution of suspended particulate matter in the ambient air in the city of Cleveland, Ohio

The City of Cleveland Division of Air Pollution Control and NASA jointly investigated the chemical and physical characteristics of the suspended particulate matter in Cleveland, and as part of the program, measurements of the particle size distribution of ambient air samples at five urban locations during August and September 1972 were made using high-volume cascade impactions. The distributions were evaluated for lognormality, and the mass median diameters were compared between locations and as a function of resultant wind direction. Junge-type distributions were consistent with dirty continental aerosols. About two-thirds of the suspended particulate matter observed in Cleveland is less than 7 microns in diameter.

Leibecki, H. F.↗
NASA NTRS2010

Observations of the Magnetic Field and Plasma in the Heliosheath by Voyager 2 from 2007.7 to 2009.4

The density and temperature profiles of the plasma measured by Voyager 2 (V2) behind the termination shock changed abruptly near 2008.6 from relatively large average values and large fluctuations during 2007.7 to 2008.6 (interval A) to relatively low average values and very small-amplitude fluctuations during 2008.6 to 2009.4 (interval B). This paper shows that the change in the magnetic field strength B(t) was less abrupt than the plasma changes, and the fluctuations of the magnetic field strength in interval B were of moderate amplitude, with indications of a quasiperiodic structure in part of the interval. The magnetic field was directed away from the sun (positive polarity) approx. 78% +/- 5% of the time in both interval A and interval B, changing in an irregular way from positive to negative polarities throughout the interval. The polarity distribution indicates that the minimum latitudinal extent of the heliospheric current sheet (HCS) was near V2 throughout the interval, consistent with the extrapolated minimum latitudes of the HCS computed from solar magnetic field observations. Thus, V2 was observing magnetic fields from the southern polar coronal hole most of the time. The distribution of B was lognormal in interval A and Gaussian interval B.

Burlaga, L. F.↗
NASA NTRS2015

RACORO Continental Boundary Layer Cloud Investigations: 1. Case Study Development and Ensemble Large-Scale Forcings

Observation-based modeling case studies of continental boundary layer clouds have been developed to study cloudy boundary layers, aerosol influences upon them, and their representation in cloud- and global-scale models. Three 60 h case study periods span the temporal evolution of cumulus, stratiform, and drizzling boundary layer cloud systems, representing mixed and transitional states rather than idealized or canonical cases. Based on in situ measurements from the Routine AAF (Atmospheric Radiation Measurement (ARM) Aerial Facility) CLOWD (Clouds with Low Optical Water Depth) Optical Radiative Observations (RACORO) field campaign and remote sensing observations, the cases are designed with a modular configuration to simplify use in large-eddy simulations (LES) and single-column models. Aircraft measurements of aerosol number size distribution are fit to lognormal functions for concise representation in models. Values of the aerosol hygroscopicity parameter, kappa, are derived from observations to be approximately 0.10, which are lower than the 0.3 typical over continents and suggestive of a large aerosol organic fraction. Ensemble large-scale forcing data sets are derived from the ARM variational analysis, European Centre for Medium-Range Weather Forecasts, and a multiscale data assimilation system. The forcings are assessed through comparison of measured bulk atmospheric and cloud properties to those computed in "trial" large-eddy simulations, where more efficient run times are enabled through modest reductions in grid resolution and domain size compared to the full-sized LES grid. Simulations capture many of the general features observed, but the state-of-the-art forcings were limited at representing details of cloud onset, and tight gradients and high-resolution transients of importance. Methods for improving the initial conditions and forcings are discussed. The cases developed are available to the general modeling community for studying continental boundary clouds.

Boundary layers↗
NASA NTRS2023

Thermal Infrared Dust Optical Depth and Coarse-Mode Effective Diameter Over Oceans Retrieved From Collocated MODIS and CALIOP Observations

In this study, we developed a novel algorithm based on the collocated Moderate Resolution Imaging Spectroradiometer (MODIS) thermal infrared (TIR) observations and dust vertical profiles from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) to simultaneously retrieve dust aerosol optical depth at 10 µm (DAOD10μm) and the coarse-mode dust effective diameter (Deff) over global oceans. The accuracy of the Deff retrieval is assessed by comparing the dust lognormal volume particle size distribution (PSD) corresponding to retrieved Deff with the in-situ measured dust PSDs from the AER-D, SAMUM-2 and SALTRACE field campaigns through case studies. The new DAOD10μm retrievals were evaluated first through comparisons with the collocated DAOD10.6μm retrieved from the combined Imaging Infrared Radiometer (IIR) and CALIOP observations from our previous study (Zheng et al. 2022). The pixel-to-pixel comparison of the two DAOD retrievals indicates a good agreement (R~0.7) and a significant reduction of (~50%) retrieval uncertainties largely thanks to the better constraint on dust size. In a climatological comparison, the seasonal and regional (5°×2°) mean DAOD10um retrievals based on our combined MODIS and CALIOP method are in good agreement with the two independent Infrared Atmospheric Sounding Interferometer (IASI) products over three dust transport regions (i.e., North Atlantic (NA; R = 0.9), Indian Ocean (IO; R = 0.8) and North Pacific (NP; R = 0.7)). Using the new retrievals from 2013 to 2017, we performed a climatological analysis of coarse mode dust Deff over global oceans. We found that dust Deff over IO and NP are up to 20% smaller than that over NA. Over NA in summer, we found a ~50% reduction of the number of retrievals with Deff > 5 μm from 15°W to 35°W and a stable trend of Deff average at 4.4 μm from 35°W throughout the Caribbean Sea (90°W). Over NP in spring, only ~5% of retrieved pixels with Deff > 5 μm are found from 150°E to 180°, while the mean Deff remains stable at 4.0 μm throughout eastern NP. To our best knowledge, this study is the first to retrieve both DAOD and coarse-mode dust particle size over global oceans for multiple years. This retrieval dataset provides insightful information for evaluating dust long-wave radiative effects and coarse mode dust particle size in models.

dust optical depth↗
DOE OSTI2026

Poisson Log-Normal Process for Count Data Prediction

Modeling count data is important in physics and other scientific disciplines, where measurements often involve discrete, non-negative quantities such as photon or neutrino detection events. Traditional parametric approaches can be trained to generate integer-count predictions but may struggle with capturing complex, non-linear dependencies often observed in the data. Gaussian process (GP) regression provides a robust non-parametric alternative to modeling continuous data; however, it cannot generate integer outputs. We propose the Poisson Log-Normal (PoLoN) process, a framework that employs GP to model Poisson log-rates. As in GP regression, our approach relies on the correlations between data points captured via GP kernel structure rather than explicit functional parameterizations. We demonstrate that the PoLoN predictive distribution is Poisson-LogNormal and provide an algorithm for optimizing kernel hyperparameters. Furthermore, we adapt the PoLoN approach to the problem of detecting weak localized signals superimposed on a smoothly varying background - a task of considerable interest in many areas of science and engineering. Our framework allows us to predict the strength, location and width of the detected signals. We evaluate PoLoN's performance using both synthetic and real-world datasets, including the open dataset from CERN which was used to detect the Higgs boson at the Large Hadron Collider. Our results indicate that the PoLoN process can be used as a non-parametric alternative for analyzing, predicting, and extracting signals from integer-valued data.

Saha, Anushka [Rutgers U., Piscataway]↗
NASA NTRS2020

Discovery of the Optical Afterglow and Host Galaxy of Short GRB 181123B at z = 1.754: Implications for Delay Time Distributions

We present the discovery of the optical afterglow and host galaxy of the Swift short-duration gamma-ray burst (SGRB) GRB 181123B. Observations with Gemini-North starting ≈9.1 hr after the burst reveal a faint optical afterglow with i ≈ 25.1 mag at an angular offset of 0 59 ± 0." 16 from its host galaxy. Using grizYJHK observations, we measure a photometric redshift of the host galaxy of z = 1.77+0.30-0.17. From a combination of Gemini and Keck spectroscopy of the host galaxy spanning 4500–18000 Å, we detect a single emission line at 13390 Å, inferred as Hβ at z = 1.754 ± 0.001 and corroborating the photometric redshift. The host galaxy properties of GRB 181123B are typical of those of other SGRB hosts, with an inferred stellar mass of ≈9.1 × 109Msun, a mass-weighted age of ≈0.9 Gyr, and an optical luminosity of ≈0.9L*. At z = 1.754, GRB 181123B is the most distant secure SGRB with an optical afterglow detection and one of only three at z > 1.5. Motivated by a growing number of high-z SGRBs, we explore the effects of a missing z > 1.5 SGRB population among the current Swift sample on delay time distribution (DTD) models. We find that lognormal models with mean delay times of ≈4–6 Gyr are consistent with the observed distribution but can be ruled out to 95% confidence, with an additional ≈one to five Swift SGRBs recovered at z > 1.5. In contrast, power-law models with ∝t−1 are consistent with the redshift distribution and can accommodate up to ≈30 SGRBs at these redshifts. Under this model, we predict that ≈1/3 of the current Swift population of SGRBs is at z > 1. The future discovery or recovery of existing high-z SGRBs will provide significant discriminating power on their DTDs and thus their formation channels.

K Paterson↗
NASA NTRS1997

Evolution of Structure in the Intergalactic Medium and the Nature of the LY-Alpha Forest

We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with OMEGA = 1, h = 0.5, and GAMMA = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with OMEGA = 0.4, OMEGA(sub LAMBDA) = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high-z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3; typical clouds with measured neutral hydrogen column densities N(sub H I) = 10(exp 13.3), 10(exp 13.5), and 10(exp 11.5) /sq cm correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than or equal to the mean density still appear as "clouds" because in our model more than 70% of the volume of the IGM at z = 3 is filled with gas at densities below the mean value.

Bi, Hongguang↗
NASA NTRS2021

Retrieval of Stratospheric Aerosol Size Distribution Parameters Using Satellite Solar Occultation Measurements at Three Wavelengths

In this work, a novel approach for the determination of the particle size distribution (PSD) parameters of stratospheric sulfate aerosols is presented. For this, ratios of extinction coefficients obtained from SAGE III/ISS (Stratospheric Aerosol and Gas Experiment III on the International Space Station) solar occultation measurements at 449, 756 and 1544 nm were used to retrieve the mode width and median radius of a size distribution assumed to be monomodal lognormal. The estimated errors at the peak of the stratospheric aerosol layer, on average, lie between 20% and 25% for the median radius and 5% and 7% for the mode width. The results are consistent in magnitude with other retrieval results from the literature, but a robust comparison is difficult, mainly because of differences in temporal and spatial coverage. Other quantities like number density and effective radius were also calculated. A major advantage of the described method over other retrieval techniques is that both the median radius and the mode width can be retrieved simultaneously, without having to assume one of them. This is possible due to the broad wavelength spectrum covered by the SAGE III/ISS measurements. Also, the presented method – being based on the analysis of three wavelengths – allows unique solutions for the retrieval of PSD parameters for almost all of the observed extinction spectra, which is not the case when using only two spectral channels. In addition, the extinction coefficients from SAGE III/ISS solar occultation measurements, on which the retrieval is based, are calculated without a priori assumptions about the PSD. For those reasons, the data produced with the presented retrieval technique may be a valuable contribution for a better understanding of the variability of stratospheric aerosol size distributions, e.g. after volcanic eruptions. While this study focuses on describing the retrieval method, and a future study will discuss the PSD parameter data set produced in depth, some exemplary results for background conditions in June 2017 are shown.

Felix Wrana↗
NASA NTRS1993

An approach to estimate the areal rain-rate distribution from spaceborne radar by the use of multiple thresholds

Estimates of rain rate derived from a spaceborne weather radar will be most reliable over an intermediate range of values. In forming an area average of the rain rate, an alternative to the averaging of the high-resolution estimates, irrespective of their individual accuracies, is a multiple threshold approach. The method is based on the fact that the fractional area above a particular rain-rate threshold R(j) is related to the cumulative distribution of rain rates evaluated at R(j). Varying the threshold over the effective dynamic range of the radar yields the cumulative distribution function over this range. To obtain the distribution at all rain rates, a lognormal or gamma test function is selected such that the mean-square error between the test function and the measured values is minimized. Once the unknown parameters are determined, the first-order statistics of the areawide rain-rate distribution can be found. Tests of the method with data from the SPANDAR radar provide comparisons between it and the single threshold and the direct averaging approaches.

Meneghini, R.↗