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NASA NTRS1977

Analyses of atmospheric extinction data obtained by astronomers. I - A time-trend analysis of data with internal accidental errors obtained at four observatories

Long-term time-trend analysis was performed on astronomical atmospheric extinction data in wideband UBV and various narrow-band systems recorded at Cerro Tololo, Kitt Peak, Lick, and McDonald observatories. All of the data had to be transformed into uniform monochromatic extinction data before trend analysis could be performed. The paper describes the various reduction techniques employed. The time-trend analysis was then carried out by the method of least squares. A special technique, called 'histogram shaping', was employed to adjust for the fact that the errors of the reduced monochromatic extinction data were not essentially Gaussian. On the assumption that there are no compensatory background and local extinction changes, the best values obtained for extinction trends due to background aerosol changes during the years 1960 to 1972 are 0.006 + or - 0.013 (rms) and 0.009 + or - 0.009 (rms) stellar magnitudes per air mass per decade in the blue and yellow wavelength regions, respectively.

Taylor, B. J.↗

NASA NTRS1979

First results from the large probe infrared radiometer experiment

During the descent to the surface of Venus, the large probe infrared radiometer measured the net thermal radiative flux in several spectral bandpasses. Preliminary analysis has permitted us to estimate (1) the infrared extinction coefficient profile attributable to aerosols, with respect to their visible profile, in the upper atmosphere of Venus and (2) the water vapor mixing ratio below the clouds. An indication of the composition of a multicomponent cloud is seen in the data from the spectral bandpass from 6 to 7 micrometers.

Boese, R. W.↗

NASA NTRS1992

Coherent CO2 lidar: A superior system for observing clouds?

Lidars have long been used to study various parameters of clouds. NOAA's Wave Propagation Laboratory has operated a coherent CO2 lidar for over a decade, using Doppler to study wind fields and turbulence, atmospheric absorption for Differential Absorption Lidar (DIAL) applications, backscatter to investigate aerosol distributions, and backscatter and extinction measurements on clouds. A system under development for our laboratory promises to overcome the older system's problems of large size, frequency instability, and need for continual operator attention. We are also thoroughly evaluating the capabilities of CO2 lidar for observing clouds, including development of some new techniques. CO2 lidar provides a view of clouds different in many ways from that of lidars at other extinction measurements from clouds. This discussion argues in support of the proposition: coherent CO2 lidar can be a superior lidar system for measuring most cloud properties.

Eberhard, Wynn L.↗

NASA NTRS2000

Global Monitoring of Clouds and Aerosols Using a Network of Micro-Pulse Lidar Systems

Long-term global radiation programs, such as AERONET and BSRN, have shown success in monitoring column averaged cloud and aerosol optical properties. Little attention has been focused on global measurements of vertically resolved optical properties. Lidar systems are the preferred instrument for such measurements. However, global usage of lidar systems has not been achieved because of limits imposed by older systems that were large, expensive, and logistically difficult to use in the field. Small, eye-safe, and autonomous lidar systems are now currently available and overcome problems associated with older systems. The first such lidar to be developed is the Micro-pulse lidar System (MPL). The MPL has proven to be useful in the field because it can be automated, runs continuously (day and night), is eye-safe, can easily be transported and set up, and has a small field-of-view which removes multiple scattering concerns. We have developed successful protocols to operate and calibrate MPL systems. We have also developed a data analysis algorithm that produces data products such as cloud and aerosol layer heights, optical depths, extinction profiles, and the extinction-backscatter ratio. The algorithm minimizes the use of a priori assumptions and also produces error bars for all data products. Here we present an overview of our MPL protocols and data analysis techniques. We also discuss the ongoing construction of a global MPL network in conjunction with the AERONET program. Finally, we present some early results from the MPL network.

Welton, Ellsworth J.↗

NASA NTRS2001

A Chronology of Annual-Mean Effective Radii of Stratospheric Aerosols from Volcanic Eruptions During the Twentieth Century as Derived From Ground-based Spectral Extinction Measurements

Stratospheric extinction can be derived from ground-based spectral photometric observations of the Sun and other stars (as well as from satellite and aircraft measurements, available since 1979), and is found to increase after large volcanic eruptions. This increased extinction shows a characteristic wavelength dependence that gives information about the chemical composition and the effective (or area weighted mean) radius of the particles responsible for it. Known to be tiny aerosols constituted of sulfuric acid in a water solution, the stratospheric particles at midlatitudes exhibit a remarkable uniformity of their column-averaged effective radii r(sub eff) in the first few months after the eruption. Considering the seven largest eruptions of the twentieth century, r(sub eff) at this phase of peak aerosol abundance is approx. 0.3 micrometers in all cases. A year later, r(sub eff) either has remained about the same size (almost certainly in the case of the Katmai eruption of 1912) or has increased to approx. 0.5 micrometers (definitely so for the Pinatubo eruption of 1991). The reasons for this divergence in aerosol growth are unknown.

Strothers, Richard B.↗

NASA NTRS2016

Forecasting the Northern African Dust Outbreak Towards Europe in April 2011: A Model Intercomparison

In the framework of the World Meteorological Organisation's Sand and Dust Storm Warning Advisory and Assessment System, we evaluated the predictions of five state-of-the-art dust forecast models during an intense Saharan dust outbreak affecting western and northern Europe in April 2011. We assessed the capacity of the models to predict the evolution of the dust cloud with lead times of up to 72 hours using observations of aerosol optical depth (AOD) from the AErosol RObotic NETwork (AERONET) and the Moderate Resolution Imaging Spectroradiometer (MODIS) and dust surface concentrations from a ground-based measurement network. In addition, the predicted vertical dust distribution was evaluated with vertical extinction profiles from the Cloud and Aerosol Lidar with Orthogonal Polarization (CALIOP). To assess the diversity in forecast capability among the models, the analysis was extended to wind field (both surface and profile), synoptic conditions, emissions and deposition fluxes. Models predict the onset and evolution of the AOD for all analysed lead times. On average, differences among the models are larger than differences among lead times for each individual model. In spite of large differences in emission and deposition, the models present comparable skill for AOD. In general, models are better in predicting AOD than near-surface dust concentration over the Iberian Peninsula. Models tend to underestimate the long-range transport towards northern Europe. Our analysis suggests that this is partly due to difficulties in simulating the vertical distribution dust and horizontal wind. Differences in the size distribution and wet scavenging efficiency may also account for model diversity in long-range transport.

dust storms↗

NASA NTRS1994

Effects of the Mount Pinatubo eruption on the radiative and chemical processes in the troposphere and stratosphere

The Lawrence Livermore National Laboratory two-dimensional zonally-averaged chemical-radiative-transport model of the global atmosphere was used to study the effects of the 15 June 1991 eruption of the Mt. Pinatubo volcano on stratospheric processes. SAGE 2 time-dependent aerosol surface area density and optical extinction data were used as input into the model. By 22 December 1991, a maximum equatorial change of -1.8 percent in column ozone was derived from heterogeneous chemical processes that convert NO(x) into HNO3 on sulfuric acid aerosols. Radiative feedbacks from increased aerosol optical thickness independently changes column ozone by approximately -3.5 percent for the same period. This occurs from increasing the net heating of the lower stratosphere, which indirectly increases chemical reaction rates via their temperature dependence and from changes in actinic fluxes, which directly modify photodissociation rates. Including both heterogeneous and radiative effects changes column ozone by -5.5 percent. The model-derived change overestimates the decrease in column ozone relative to the TOMS instrument on the Nimbus 7 satellite. Maximum local ozone decreases of 12 percent were derived in the equatorial region, at 25 km. Model-derived column NO2 peaked (-14 percent) at 30 deg S in October 1991. The timing of the NO2 peak is consistent with observation, but the model underestimates the magnitude of the decrease. Local concentrations of NO(x) (NO + NO2), ClO(x) (Cl + ClO), and HO(x) (OH + HO2), in the lower stratosphere between 30 deg S and 30 deg N, were calculated to have changed by -40 percent, +100 to +160 percent, and +120 to +140 percent respectively.

Kinnison, Douglas E.↗

NASA NTRS1974

Multi-spectral extinction measurements to deduce the complex refractive index and the size distribution of aerosol particles

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Kuriyan, J. G.↗

NASA NTRS2005

Effects of Aerosol on Atmospheric Dynamics and Hydrologic Processes during Boreal Spring and Summer

Global and regional climate impacts of present-day aerosol loading during boreal spring are investigated using the NASA finite volume General Circulation Model (fvGCM). Three-dimensional distributions of loadings of five species of tropospheric aerosols, i.e., sulfate, black carbon, organic carbon, soil dust, and sea salt are prescribed from outputs of the Goddard Ozone Chemistry Aerosol Radiation and Transport model (GOCART). The aerosol loadings are used to calculate the extinction coefficient, single scattering albedo, and asymmetric factor at eleven spectral wavelengths in the radiative transfer code. We find that aerosol-radiative forcing during boreal spring excites a wavetrain-like pattern in tropospheric temperature and geopotential height that emanates from Northern Africa, through Eurasia, to northeastern Pacific. Associated with the teleconnection is strong surface cooling over regions with large aerosol loading, i.e., China, India, and Africa. Low-to-mid tropospheric heating due to shortwave absorption is found in regions with large loading of dust (Northern Africa, and central East Asia), and black carbon (South and East Asia). In addition pronounced surface cooling is found over the Caspian Sea and warming over Eurasian and northeastern Asia, where aerosol loadings are relatively low. These warming and cooling are components of teleconnection pattern produced primarily by atmospheric heating from absorbing aerosols, i.e., dust from North Africa and.black carbon from South and East Asia. Effects of aerosols on atmospheric hydrologic cycle in the Asian monsoon region are also investigated. Results show that absorbing aerosols, i.e., black carbon and dust, induce large-scale upper-level heating anomaly over the Tibetan Plateau in April and May, ushering in an early onset of the Indian summer monsoon. Absorbing aerosols also enhance lower-level heating and anomalous ascent over northern India, intensifying the Indian monsoon. Overall, the aerosol-induced large-scale surface temperature cooling leads to a reduction of monsoon rainfall over the East Asia continent, and adjacent oceanic regions.

Lau, William K. M.↗

NASA NTRS2005

Effects of Aerosol on Atmospheric Dynamics and Hydrologic Processes During Boreal Spring and Summer

Global and regional climate impacts of present-day aerosol loading during boreal spring are investigated using the NASA finite volume General Circulation Model (fvGCM). Three-dimensional distributions of loadings of five species of tropospheric aerosols, i.e., sulfate, black carbon, organic carbon, soil dust, and sea salt are prescribed from outputs of the Goddard Ozone Chemistry Aerosol Radiation and Transport model (GOCART). The aerosol loadings are used to calculate the extinction coefficient, single scattering albedo, and asymmetric factor at eleven spectral wavelengths in the radiative transfer code. We find that aerosol-radiative forcing during boreal spring excites a wavetrain-like pattern in tropospheric temperature and geopotential height that emanates from Northern Africa, through Eurasia, to northeastern Pacific. Associated with the teleconnection is strong surface cooling over regions with large aerosol loading, i.e., China, India, and Africa. Low-to-mid tropospheric heating due to shortwave absorption is found in regions with large loading of dust (Northern Africa, and central East Asia), and black carbon (South and East Asia). In addition pronounced surface cooling is found over the Caspian Sea and warming over Eurasian and northeastern Asia, where aerosol loadings are relatively low. These warming and cooling are components of teleconnection pattern produced primarily by atmospheric heating from absorbing aerosols, i.e., dust from North Africa and black carbon from South and East Asia. Effects of aerosols on atmospheric hydrologic cycle in the Asian monsoon region are also investigated. Results show that absorbing aerosols, i.e., black carbon and dust, induce large-scale upper-level heating anomaly over the Tibetan Plateau in April and May, ushering in an early onset of the Indian summer monsoon. Absorbing aerosols also enhance lower-level heating and anomalous ascent over northern India, intensifying the Indian monsoon. Overall, the aerosol-induced large-scale surface tempera- cooling leads to a reduction of monsoon rainfall over the East Asia continent, and adjacent oceanic regions.

Lau, William K. M.↗

NASA NTRS2009

Studies of a Space Lidar Instrument for the ASCENDS Mission

Abshire, J. B.↗

NASA NTRS2009

Pulsed Airborne Lidar Measurements of Atmospheric CO2 Column Absorption and Line Shapes from 3-13 km Altitudes

We have developed a lidar technique for measuring the tropospheric C02 concentrations as a candidate for NASA's planned ASCENDS mission. Our technique uses two pulsed laser transmitters allowing simultaneous measurement of a C02 absorption line in the 1570 nm band, 02 extinction in the Oxygen A-band and surface height and backscatter. The lidar measures the energy and time of flight of the laser echoes reflected from the atmosphere and surface. The lasers are stepped in wavelength across the C02 line and an 02 line region during the measurement. The receiver uses a telescope and photon counting detectors, and measures the background light and energies of the laser echoes from the surface along with scattering from any aerosols in the path. The gas extinction and column densities for the C02 and 02 gases are estimated from the ratio of the on- and off- line signals via the DIAL technique. Time gating is used to isolate the laser echo signals from the surface, and to reject laser photons scattered in the atmosphere. We have developed an airborne lidar to demonstrate the C02 measurement from the NASA Glenn Lear 25 aircraft. The airborne lidar steps the pulsed laser's wavelength across a selected C02 line with 20 steps per scan. The line scan rate is 450 Hz and laser pulse widths are I usec. The time resolved laser backscatter is collected by a 20 cm telescope, detected by a photomultiplier and is recorded by a photon counting system. We made initial airborne measurements on flights during October and December 2008. Laser backscatter and absorption measurements were made over a variety of land and water surfaces and through thin and broken clouds. Atmospheric C02 column measurements using the 1571.4, 1572.02 and 1572.33 nm C02 lines. Two flights were made above the DOE SGP ARM site at altitudes from 3-8 km. These nights were coordinated with DOE investigators who Hew an in-situ C02 sensor on a Cessna aircraft under the path. The increasing C02 line absorptions with altitudes were evident and comparison with in-situ measurements showed agreements to 6 ppm. This spring we improved the aircraft's nadir window. During July and August 2009 we made 9 additional 2 hour long flights and measured the atmospheric C02 absorption and line shapes using the 1572.33 nm C02 line. Measurements were made at stepped altitudes from 3-13 km over a variety of surface types in Nebraska, Illinois, the SGP ARM site, and near and over the Chesapeake Bay in North Carolina and Virginia. Strong laser signals and clear line shapes were observed at all altitudes, and some measurements were made through thin clouds. The flights over the ARM site were underflown with in-situ measurements made from the DOE Cessna. The Oklahoma and east coast t1ights were coordinated with a LaRC/ITT C02 lidar on the LaRC UC-12 aircraft, a LaRC in~situ C02 sensor, and the Oklahoma flights also included a JPL C02 lidar on a Twin Otter aircraft. Ed Browell and Gary Spiers led the LaRC and JPL teams. More details of the t1ights, measurements and analysis will be described in the presentation.

Abshire, J. B.↗

NASA NTRS2002

Overview of ACE-Asia Spring 2001 Investigations On Aerosol-Radiation Interactions

ACE-Asia's extensive measurements from land, ocean, air and space quantified aerosol-radiation interactions. Results from each platform type, plus satellite-suborbital combinations, include: 1. Time series of multiwavelength aerosol optical depth (ADD), Angstrom exponent (alpha), single-scattering albedo (SSA), and size distribution from AERONET radiometry at 13 stations. In China and Korea AOD and alpha were strongly anticorrelated (reflecting transient dust events); dust volume-size modes peaked near 8 microns diameter; and SSA(dust) greater than SSA(pollution). 2. Calculations and measurements of photosynthetically active radiation and aerosols in China yield 24-h average downward surface radiative forcing per AOD(500 nm) of -27 W/sq m (400-700 nm). 3. The Hawaii-Japan cruise sampled a gradient with AOD(500 nm) extremes of 0.1 and 1.1. Shipboard measurements showed that adding dust to pollution increased SSA(550 nm, 55% RH), typically from -0.91 to approx. 0.97. Downwelling 8-12 micron radiances showed aerosol effects, especially in the major April dust event, with longwave forcing estimated at -5 to 15 W/sq m. 4. Extinction profiles from airborne sunphotometry and total-direct-diffuse radiometry show wavelength dependence often varying strongly with height, reflecting layering of dust-dominated over pollution-dominated aerosols. Comparing sunphotometric extinction profiles to those from in situ measurements (number and composition vs size, or scattering and absorption) shows layer heights agree, but extinction sometimes differs. 5. Airborne solar spectral flux radiometry yields absorption spectra for layers. Combining with AOD spectra yields best-fit aerosol single scattering albedo spectra. 6. Visible, NIR and total solar fluxes combined with AOD give radiative forcing efficiencies at surface and aloft.

Russell, P. B.↗

NASA NTRS2010

Pulsed Airborne Lidar Measurements of Atmospheric CO2 Column Absorption and Line Shapes from 3-13 km Altitudes

We have developed a pulsed lidar technique for measuring the tropospheric CO2 concentrations as a candidate for NASA's planned ASCENDS space mission. Our technique uses two pulsed laser transmitters allowing simultaneous measurement of a CO2 absorption line in the 1570 nm band, O2 extinction in the Oxygen A-band and surface height and backscatter. The lidar measures the energy and time of flight of the laser echoes reflected from the atmosphere and surface. The lasers are rapidly and precisely stepped in wavelength across the CO2 line and an O2 line region during the measurement. The direct detection receiver uses a telescope and photon counting detectors, and measures the background light and energies of the laser echoes from the surface along with scattering from any aerosols in the path. The gas extinction and column densities for the CO2 and O2 gases are estimated from the ratio of the on- and off- line signals via the DIAL technique. Time gating is used to isolate the laser echo signals from the surface, and to reject laser photons scattered in the atmosphere. The time of flight of the laser pulses are also used to estimate the height of the scattering surface and to identify cases of mixed cloud and ground scattering. We have developed an airborne lidar to demonstrate the CO2 measurement from the NASA Glenn Lear-25 aircraft. The airborne lidar steps the pulsed laser's wavelength across the selected CO2 line with 20 steps per scan. The line scan rate is 450 Hz, the laser pulse widths are 1 usec, and laser pulse energy is 24 uJ. The time resolved laser backscatter is collected by a 20 cm telescope, detected by a photomultiplier and is recorded by a photon counting system. We made initial airborne measurements on flights during fall 2008. Laser backscatter and absorption measurements were made over a variety of land and water surfaces and through thin clouds. The atmospheric CO2 column measurements using the 1572.33 nm CO2 lines. Two flights were made above the US Department of Energy's (DOE) SGP ARM site at altitudes from 3-8 km. These flights were coordinated with DOE investigators who flew an in-situ CO2 sensor on a Cessna aircraft under the path. The increasing CO2 line absorptions with altitudes were evident and comparison with in-situ measurements showed agreements to 6 ppm. In spring 2009 we improved the aircraft's nadir window and during July and August we made 9 additional 2 hour long flights and measured the atmospheric CO2 absorption and line shapes using the 1572.33 nm CO2 line. Measurements were made at stepped altitudes from 3-13 km over a variety of surface types in Nebraska, Illinois, the SGP ARM site, and near and over the Chesapeake Bay in North Carolina and eastern Virginia. Strong laser signals and clear CO2 line shapes were observed at all altitudes, and some measurements were made through thin clouds. The flights over the ARM site were underflown with in-situ measurements made from the DOE Cessna. Analysis shows that the average signal levels follow predicted values, the altimetry measurements had an uncertainty of about 4 m, and that the average optical line depths follow the number density calculated from in-situ sensor readings. The Oklahoma and east coast flights were coordinated with a LaRC/ITT CO2 lidar on the LaRC UC-12 aircraft, a LaRC in-situ CO2 sensor, and the Oklahoma flights also included a JPL CO2 lidar on a Twin Otter aircraft. More details of the flights, measurements, analysis and scaling to space will be described in the presentation.

Abshire, James↗

NASA NTRS2001

Airborne Sunphotometer Studies of Aerosol Properties and Effects, Including Closure Among Satellite, Suborbital Remote, and In situ Measurements

Airborne sunphotometry has been used to measure aerosols from North America, Europe, and Africa in coordination with satellite and in situ measurements in TARFOX (1996), ACE-2 (1997), PRIDE (2000), and SAFARI 2000. Similar coordinated measurements of Asian aerosols are being conducted this spring in ACE-Asia and are planned for North American aerosols this summer in CLAMS. This paper summarizes the approaches used, key results, and implications for aerosol properties and effects, such as single scattering albedo and regional radiative forcing. The approaches exploit the three-dimensional mobility of airborne sunphotometry to access satellite scenes over diverse surfaces (including open ocean with and without sunglint) and to match exactly the atmospheric layers sampled by airborne in situ measurements and other radiometers. These measurements permit tests of the consistency, or closure, among such diverse measurements as aerosol size-resolved chemical composition; number or mass concentration; light extinction, absorption, and scattering (total, hemispheric back and 180 deg.); and radiative fluxes. In this way the airborne sunphotometer measurements provide a key link between satellite and in situ measurements that helps to understand any discrepancies that are found. These comparisons have led to several characteristic results. Typically these include: (1) Better agreement among different types of remote measurements than between remote and in situ measurements. (2) More extinction derived from transmission measurements than from in situ measurements. (3) Larger aerosol absorption inferred from flux radiometry than from in situ measurements. Aerosol intensive properties derived from these closure studies have been combined with satellite-retrieved fields of optical depth to produce fields of regional radiative forcing. We show results for the North Atlantic derived from AVHRR optical depths and aerosol intensive properties from TARFOX and ACE-2. Companion papers show analogous, preliminary results for Asian-Pacific aerosols and results of SAFARI-2000 closure studies on African aerosols.

Russlee, Philip B.↗

NASA NTRS1983

The formation of polar stratospheric clouds

Measurements of the stratospheric aerosol by SAM II during the northern and southern winters of 1979 showed a pronounced increase in extinction on occasions when the temperature fell to a low value (below 200 K). The correlation between extinction and temperature is evaluated on the basis of thermodynamic considerations. As the temperature falls, the hygroscopic aerosols absorb water vapor from the atmosphere, growing as they do so. The effect of the temperature on the size distribution and composition of the aerosol is determined, and the optical extinction at 1 micron wavelength is calculated using Mie scattering theory. The theoretical predictions of the change in extinction with temperature and humidity are compared with the SAM II results at 100 mb, and the water vapor mixing ratio and aerosol number density are inferred from these results. A best fit of the theoretical curves to the SAM II data gives a water vapor content of 5-6 ppmv, and a total particle number density of 6-7 particles/cu cm.

Steele, H. M.↗

NASA NTRSDate not supplied

Lidar Simulations of Backscatter and Extinction Uncertainty Estimates for ACCP Assessments

As part of the NASA Aerosols and Clouds, Convection, and Precipitation (ACCP) pre-formulation study, several lidar instruments are being assessed for their capabilities in advancing the science objectives enumerated in the most recent Earth Sciences Decadal Survey. These assessments are conducted using the NASA Langley Research Center(LaRC) lidar simulator, which produces profiles of backscatter and extinction uncertainty estimates for a given set of input parameters. Specifically, attention is focused onevaluating the science benefits and improvements of a candidate two-wavelength space-based High Spectral Resolution Lidar (HSRL) compared to an elastic backscatter lidar with similar capabilities to the Cloud-Aerosol Lidar with Orthogonal Polarization(CALIOP), flying aboard the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite. In this talk, simulations of satellite-based HSRL and those of a CALIOP-like system are compared for different atmospheric scenes that capture varying total aerosol loadings, aerosol vertical distributions, and aerosol types.The results of these analyses are presented as functions of averaging resolution(horizontal/vertical), lighting conditions (daytime/nighttime), surface type (land/ocean),and wavelength (532 nm/1064 nm). Also, simulations of multiple aerosol layers and of aerosols beneath transparent cirrus clouds are shown to demonstrate the consequent impacts on underlying backscatter and extinction uncertainties, and to better differentiate the performance of HSRL compared to that of CALIOP for real-world atmospheric scenarios.

Travis D. Toth↗

NASA NTRS1980

Investigation of multiple scattering effects in aerosols

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Deepak, A.↗