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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Improved evaluation of optical depth components from Langley plot data

A simple, iterative procedure to determine the optical depth components of the extinction optical depth measured by a solar radiometer is presented. Simulated data show that the iterative procedure improves the determination of the exponent of a Junge law particle size distribution. The determination of the optical depth due to aerosol scattering is improved as compared to a method which uses only two points from the extinction data. The iterative method was used to determine spectral optical depth components for June 11-13, 1988 during the MAC III experiment.

Biggar, S. F.↗
NASA NTRS1992

Wind Profiles Derived from Volume Imaging Lidar Data: Enhancements to the Algorithm and Comparisons with Insitu Observations

This paper presents wind measurements made with the University of Wisconsin Volume Imaging Lidar (VIL) during Aug. 1989 as part of the First ISLSCP (International Satellite Land Surface Climatology Project) Field Experiment (FIFE). Enhancements to the algorithm are described. Comparisons of these results to aircraft, balloon, and surface based wind measurements are presented. Observations of the spatial variance of aerosol backscatter are also compared to measurements of the convective boundary layer depth. Measurements are based on two-dimensional cross correlations between horizontal image planes showing the spatial distribution of aerosol scattering observed by the lidar at intervals of approximately 3 minutes. Each image plane covers an area of 500-1000 sq km and the winds calculated represent area averages.

Piironen, A. K.↗
NASA NTRS1991

Ozone and aerosol distributions measured by airborne lidar during the 1988 Arctic Boundary Layer Experiment

Consideration is given to O3 and aerosol distributions measured from an aircraft using a DIAL system in order to study the sources and sinks of gases and aerosols over the tundra regions of Alaska during summer 1988. The tropospheric O3 budget over the Arctic was found to be strongly influenced by stratospheric intrusions. Regions of low aerosol scattering and enhanced O3 mixing ratios were usually correlated with descending air from the upper troposphere or lower stratosphere.

Browell, Edward V.↗
NASA NTRS1991

Visible and near IR lidar backscatter observations on the GLOBE Pacific Survey missions

Measurement techniques and initial results of the Global Backscatter Experiment (GLOBE) performed in November 1989 and May-June 1990 to provide data on prevailing values of atmospheric backscatter cross section are presented. The upper troposphere aerosol scattering cross section was low in the Southern Hemisphere for the May-June flights and low in the Northern Hemisphere for the November flights. The initial results indicate that the instrumentation and calibration techniques applied for the near IR lidar measurements were successful.

Spinhirne, James D.↗
NASA NTRS1992

Large-scale variability of ozone and aerosols in the summertime Arctic and sub-Arctic troposphere

The results of mesoscale and large-scale studies of the distribution of aerosols and O3 using primarily an airborne DIAL system are reported. The tropospheric composition at high latitudes is found to be strongly influenced by stratospheric intrusions. Regions of low-aerosol scattering and enhanced O3 mixing ratios are correlated with descending air from the lower stratosphere. Over 37 percent of the troposphere along the flight track at latitudes higher than 57 deg N had significantly enhanced O3 levels due to stratospheric intrusions, and in the 4-6 km latitude range the tropospheric extent of the enhanced O3 exceeded 56 percent. Ozone mixing ratios of 80 ppbv at 6 km are common, with vertical O3 gradients of over 11 ppbv/km observed across the base of strong intrusions. In the mixed layer over the tundra, O3 was in the 25-35 ppbv range with a gradient of 5.5 ppbv/km, while in the continental polar air masses, the average gradient in the lower troposphere is 7.4 ppbv/km, indicating more downward transport of O3 at higher latitudes.

Browell, E. V.↗
NASA NTRS1994

Ozone and aerosol distributions in the summertime troposphere over Canada

Measurements of ozone (O3) and aerosol distributions were made with an airborne lidar system in the lowland and boreal forest regions of eastern Canada during July - August 1990 as part of the NASA Global Tropospheric Experiment/Arctic Boundary Layer Expedition (ABLE) 3B. Aerosol and O3 profiles were measured simultaneously above and below the Electra aircraft from near the surface to above the tropopause on long-range flights over these important ecosystems. A broad range of atmospheric conditions were encountered during repeated flights over intensive study sites in the Hudson Bay lowlands near Moosonee, Ontario, and over the boreal forest near Schefferville, Quebec. The tropospheric composition in this high-latitude region was found to be strongly influenced by stratospheric intrusions. Regions of low aerosol scattering and enhanced O3 mixing ratios were correlated with descending air from the lower stratosphere. Over 33% of the troposphere (0-12 km) along our flight track at latitudes from about 45 deg to 55 deg N had significantly enhanced O3 due to stratospheric intrusions, and in the middle to upper troposphere the extent of the enhanced O3 gnerally exceeded 40%. Ozone mixing ratios of 80 parts per billion by volume (ppbv) near 6 km were common in strong intrusions. In the boundary layer over the lowlands, O3 was in the 20-30 ppbv range with a vertical O3 gradient of 6.7 ppbv/km to about 45 ppbv at 3 km. Above 6 km the background tropospheric O3 profile was nearly constant with an average value of 53 ppbv. Due to forest fires in Canada and Alaska, plumes from biomass-burning sources were observed on many flights. Biomass-burning plumes influenced about 25% of the free troposphere below 4 km, and in some of the plumes, O3 was enhanced by 10-20 ppbv over ambient levels of 30-45 ppbv. Several air masses transported from the tropical Pacific were observed over Canada in the middle to upper troposphere with O3 levels 10-20 ppbv below background values of 50-55 ppbv.

Browell, E. V.↗
NASA NTRS1998

Double-Edge Molecular Technique for Doppler Lidar Wind Measurement

The double-edge lidar technique for measuring the wind using molecular backscatter is described. Two high spectral resolution edge filters are located in the wings of the Rayleigh-Brillouin profile. This doubles the signal change per unit Doppler shift, the sensitivity, and gives nearly a factor of two improvement in measurement accuracy. The use of a crossover region is described where the sensitivity of a molecular and aerosol-based measurement are equal. This desensitizes the molecular measurement to the effects of aerosol scattering over a frequency range of +/- 100 m/s. We give methods for correcting for short-term frequency jitter and drift using a laser reference frequency measurement and methods for long-term frequency correction using a servo control system. The effects of Rayleigh-Brillouin scattering on the measurement are shown to be significant and are included in the analysis. Simulations for a conical scanning satellite-based lidar at 355 nm show an accuracy of 2-3 m/s for altitudes of 2 to 15 km for a 1 km vertical resolution, a satellite altitude of 400 km and a 200 km x 200 km spatial resolution. Results of ground based wind measurements are presented.

Flesia, Cristina↗
NASA NTRS1999

Raman LIDAR Detection of Cloud Base

Advantages introduced by Raman lidar systems for cloud base determination during precipitating periods are explored using two case studies of light rain and virga conditions. A combination of the Raman lidar derived profiles of water vapor mixing ratio and aerosol scattering ratio, together with the Raman scattered signals from liquid drops, can minimize or even eliminate some of the problems associated with cloud boundary detection using elastic backscatter lidars.

Demoz, Belay↗
NASA NTRS2001

Sensing, Spectra and Scaling: What's in Store for Land Observations

Bill Pecora's 1960's vision of the future, using spacecraft-based sensors for mapping the environment and exploring for resources, is being implemented today. New technology has produced better sensors in space such as the Landsat Thematic Mapper (TM) and SPOT, and creative researchers are continuing to find new applications. However, with existing sensors, and those intended for launch in this century, the potential for extracting information from the land surface is far from being exploited. The most recent technology development is imaging spectrometry, the acquisition of images in hundreds of contiguous spectral bands, such that for any pixel a complete reflectance spectrum can be acquired. Experience with Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) has shown that, with proper attention paid to absolute calibration, it is possible to acquire apparent surface reflectance to 5% accuracy without any ground-based measurement. The data reduction incorporates in educated guess of the aerosol scattering, development of a precipitable water vapor map from the data and mapping of cirrus clouds in the 1.38 micrometer band. This is not possible with TM. The pixel size in images of the earth plays and important role in the type and quality of information that can be derived. Less understood is the coupling between spatial and spectral resolution in a sensor. Recent work has shown that in processing the data to derive the relative abundance of materials in a pixel, also known is unmixing, the pixel size is an important parameter. A variance in the relative abundance of materials among the pixels is necessary to be able to derive the endmembers or pure material constituent spectra. In most cases, the 1 km pixel size for the Earth Observing System Moderate Resolution Imaging Spectroradiometer (MODIS) instrument is too large to meet the variance criterion. A pointable high spatial and spectral resolution imaging spectrometer in orbit will be necessary to make the major next step in our understanding of the solid earth surface and its changing face.

Goetz, Alexander F. H.↗
NASA NTRS2002

Dynamical Studies of the Middle Atmosphere Using High Resolution Doppler Imager Observations

This report summarizes the activities of NASA grant NAG5-11068, "Dynamicai Studies of the Middle Atmosphere Using High Resolution Doppler Imager Observations." The High Resolution Doppler Imager (HRDI) on the Upper Atmosphere Research Satellite (UARS) has been providing direct measurements of the Earth's horizontal wind field in the stratosphere, mesosphere and lower thermosphere. Mesospheric temperatures, ozone, and O((sup 1) D) densities, and stratospheric aerosol extinctions coefficients, are also retrieved. The goal of HRDI is to measure the vector winds in the stratosphere (10-40 km), mesosphere, and lower thermosphere (approximately 50-120 km) during the day, and the lower thermosphere at night (approximately 95 km) to an accuracy of 5 m/s. The horizontal wind vector is measured by observing the Doppler shift of rotational lines of molecular oxygen along two lines of sight. In addition to winds, temperatures and volume emission rates are determined in the mesosphere and lower thermosphere, from which ozone and O((sup 1) D) concentrations can be derived, and aerosol scattering coefficients are determined in the stratosphere. UARS was launched on September 12, 1991, into a 585-km circular orbit inclined 57 degrees to the equator HRDI was activated September 28, 1991 and following a period of checkout and adjustment of the instrument parameters, scientific observations began November 2, 199 1. HRDI operated nearly continuously from launch until April 1995. At that time the UARS solar array drive failed, forcing the instruments to time-share the available power. From July 1995 to July 1996 HRDI operated approximately 50% of the time. At that point, one of the three spacecraft batteries failed and from then until September 1998 the duty cycle was less than 20% per month, At that time it was determined that HRDI could operate during each daytime pass, which increased the daytime duty cycle to close to l00%, while nighttime operations were limited to about a week per month. In the fall of 1999, the second tape recorder failed requiring a real time contact with a TRDSS satellite to retrieve that data. This resulted in about 60% data collection efficiency. Finally, in the summer of 2000, the second star sensor failed requiring the spacecraft attitude to be controlled by a three axis magnetometer and sun sensor. This resulted in a loss of attitude knowledge but operations continue with the anticipation of correcting the attitude. A new method for determining the tide and mean structure from satellite data in conjunction with a new tidal model has been devised. For brevity, it shall be referred to as the TMAT or Tide-Mean Assimilation Technique. Most previous methods of tidal analysis are based on various ways of slicing the data set.

Skinner, Wilbert↗
NASA NTRS2004

Laser Sounder for Global Measurement of CO2 Concentrations in the Troposphere from Space: Progress

We describe progress toward developing a laser-based technique for the remote measurement of the tropospheric CO2 concentrations from orbit. Our goal is to demonstrate a lidar technique and instrument technology that will permit measurements of the CO2 column abundance in the lower troposphere from aircraft at the few ppm level, with a capability of scaling to permit global CO2 measurements from orbit. Accurate measurements of the tropospheric CO2 mixing ratio from space are challenging due to the many potential error sources. These include possible interference from other trace gas species, the effects of temperature, clouds, aerosols & turbulence in the path, changes in surface reflectivity, and variability in dry air density caused by changes in atmospheric pressure, water vapor and topographic height. Some potential instrumental errors include frequency drifts in the transmitter, small transmission and sensitivity drifts in the instrument. High signal-to-noise ratios and measurement stability are needed for mixing ratio estimates at the few ppm level. We have been developing a laser sounder approach as a candidate for a future space mission. It utilizes multiple different laser transmitters to permit simultaneous measurement of CO2 and O2 extinction, and aerosol backscatter in the same measurement path. It directs the narrow co-aligned laser beams from the instrument's fiber lasers toward nadir, and measures the energy of the strong laser echoes reflected from the Earth's land and water surfaces. During the measurement its narrow linewidth lasers are rapidly tuned on- and off- selected CO2 line near 1572 nm and an O2 absorption line near 770 nm. The receiver measures the energies of the laser echoes from the surface and any clouds and aerosols in the path with photon counting detectors. Ratioing the on- to off-line echo pulse energies for each gas permits the column extinction and column densities of CO2 and O2 to be estimated simultaneously via the differential absorption lidar technique. For the on-line wavelengths, the side of the selected absorption lines are used, which due to pressure broadening, weights the measurements to the lower troposphere, where CO2 variations caused by surface sources and sinks are largest. Simultaneous measurements of O2 column abundance are made using an identical approach using an O2 line. The laser backscatter profiles from clouds and aerosols are measured with other lidar channels, which permits identifying measurements influenced by clouds and/or aerosol scattering in the path. For space use, our lidar would continuously measure at nadir in near polar circular orbit. Using dawn and dusk measurements made over the same region will make it possible to sample the diurnal variations in CO2 mixing ratios. A 1-m diameter telescope is used for the receiver for all wavelengths. When averaging over 50 seconds, our calculations show a SNR of approximately 1500 is achievable for each gas at each on- and off-line measurement. Measurements from such a mission can be used to generate monthly global maps of the lower tropospheric CO2 column abundance. Our calculations show global coverage with an accuracy of a few ppm with a spatial resolution of approximately 50,000 sq. km are achievable each month. We have demonstrated some key elements of the laser, detector and receiver approaches in the laboratory and with measurements over a 206 m horizontal path. These include stable measurements of CO2 line shapes in an absorption cell using a fiber laser amplifier seeded by a tunable diode laser, measurement of small amplitude changes at low optical signal levels with the PMT receiver, and comparison of the horizontal path measurements of CO2 against those from an in-situ instrument.

Abshire, J. B.↗
NASA NTRS2011

Submillimeter Remote Sensing of Planetary and Cometary Atmospheres and LRO/LCROSS Observations of the Moon

Submillimeter remote sensing of planetary and cometary atmospheres have been proposed for Venus and Mars while MIRO on Rosetta will observe the coma of Comet 67P/Churyumov - Cierasimenko in December 2015, UARS and AURA MLS have observed millimeter and submillimeter molecule emissions in the Earth's stratosphere for many decades, Observations of submillimeter wave molecular emissions provide a wealth of information not obtainable by alternative techniques. Submillimeter line emissions exhibit linear temperature dependence, insensitivity to aerosol scattering, extinction, and have separated transitions with well determined line-shapes. These observations have high sensitivities to trace chemical species and can; 1) Fully resolve the line profiles of molecules with high resolution, 2) Provide deterministic retrievals of species abundance, temperature, and pressure, and 3) Measure Doppler shifts of detected molecules for wind velocities.

Chin, Gordon↗
NASA NTRS2011

NASA Tech Briefs, July 2011

Topics covered include: 1) Collaborative Clustering for Sensor Networks; 2) Teleoperated Marsupial Mobile Sensor Platform Pair for Telepresence Insertion Into Challenging Structures; 3) Automated Verification of Spatial Resolution in Remotely Sensed Imagery; 4) Electrical Connector Mechanical Seating Sensor; 5) In Situ Aerosol Detector; 6) Multi-Parameter Aerosol Scattering Sensor; 7) MOSFET Switching Circuit Protects Shape Memory Alloy Actuators; 8) Optimized FPGA Implementation of Multi-Rate FIR Filters Through Thread Decomposition; 9) Circuit for Communication Over Power Lines; 10) High-Efficiency Ka-Band Waveguide Two-Way Asymmetric Power Combiner; 11) 10-100 Gbps Offload NIC for WAN, NLR, and Grid Computing; 12) Pulsed Laser System to Simulate Effects of Cosmic Rays in Semiconductor Devices; 13) Flight Planning in the Cloud; 14) MPS Editor; 15) Object-Oriented Multi Disciplinary Design, Analysis, and Optimization Tool; 16) Cryogenic-Compatible Winchester Connector Mount and Retaining System for Composite Tubes; 17) Development of Position-Sensitive Magnetic Calorimeters for X-Ray Astronomy; 18) Planar Rotary Piezoelectric Motor Using Ultrasonic Horns; 19) Self-Rupturing Hermetic Valve; 20) Explosive Bolt Dual-Initiated from One Side; 21) Dampers for Stationary Labyrinth Seals; 22) Two-Arm Flexible Thermal Strap; 23) Carbon Dioxide Removal via Passive Thermal Approaches; 24) Polymer Electrolyte-Based Ambient Temperature Oxygen Microsensors for Environmental Monitoring; 25) Pressure Shell Approach to Integrated Environmental Protection; 26) Image Quality Indicator for Infrared Inspections; 27) Micro-Slit Collimators for X-Ray/Gamma-Ray Imaging; 28) Scatterometer-Calibrated Stability Verification Method; 29) Test Port for Fiber-Optic-Coupled Laser Altimeter; 30) Phase Retrieval System for Assessing Diamond Turning and Optical Surface Defects; 31) Laser Oscillator Incorporating a Wedged Polarization Rotator and a Porro Prism as Cavity Mirror; 32) Generic, Extensible, Configurable Push-Pull Framework for Large-Scale Science Missions; 33) Dynamic Loads Generation for Multi-Point Vibration Excitation Problems; 34) Optimal Control via Self-Generated Stochasticity; 35) Space-Time Localization of Plasma Turbulence Using Multiple Spacecraft Radio Links; 36) Surface Contact Model for Comets and Asteroids; 37) Dust Mitigation Vehicle; 38) Optical Coating Performance for Heat Reflectors of the JWST-ISIM Electronic Component; 39) SpaceCube Demonstration Platform; 40) Aperture Mask for Unambiguous Parity Determination in Long Wavelength Imagers; 41) Spaceflight Ka-Band High-Rate Radiation-Hard Modulator; 42) Enabling Disabled Persons to Gain Access to Digital Media; 43) Cytometer on a Chip; 44) Principles, Techniques, and Applications of Tissue Microfluidics; and 45) Two-Stage Winch for Kites and Tethered Balloons or Blimps.

Source record↗
NASA NTRS2018

Portable, Low-Cost, Column Carbon Dioxide and Methane Measurements for Validating Satellite Observations in Remote Locations

We present a low-cost (~$10K per instrument), portable solution to ground-based validation of satellite observations for difficult to reach locations with precisions of 1 ppm XCO2 and 10 ppb XCH4 for hourly data products. While Total Carbon Column Observing Network (TCCON) is the gold-standard for ground validation, there are locations where a ground column validation data point would be useful but conditions are not conducive to a permanent station. Examples include wetlands, thawing permafrost, the tropics, the Amazon, sub-Saharan Africa, as well as locations without a power grid or with geopolitical conflict. In addition, the low-cost and portability mean a geographical region can be studied in depth with multiple instruments. This passive, sun-pointing instrument is a miniaturized, laser heterodyne radiometer (mini-LHR) that has been under development by our team since 2009. It can be operated either in tandem with AERONET (a global network of 500 instruments that measure aerosol optical depth), or as a stand-alone instrument with a low-cost (~$3K), light-weight sun tracker. One of the main benefits of the mini-LHR is that it can quickly reach remote locations and provide a validation measurement even if there is limited or no infrastructure at the site. The instrument weighs ~10 lbs, fits into a backpack, and is powered by two folding solar panels and a battery pack. In clear conditions, the instrument can be set-up in under an hour. Portability means that mini-LHRs can be easily moved for side-by-side comparisons with other mini-LHRs and with TCCON which simplifies assessing instrument bias as well as accuracy. Like TCCON, the mini-LHR points directly at the sun with a narrow field-of-view and is its insensitivity to cloud and aerosol scattering that is common to nadir-pointing passive satellite approaches. Here we present a collection of sample data sets to demonstrate performance from locations that vary in climate, altitude, solar zenith angle, hours of sun per day, etc., as well as data from side-by-side TCCON comparisons. Retrievals of CO2 and CH4 were completed using the NASA/Goddard's Planetary Spectrum Generator (PSG) that incorporates meteorological inputs from Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2) data set.

Wilson, Emily W.↗
NASA NTRS2019

Matrix Exponential in C/C++ Version of Vector Radiative Transfer Code IPOL

We use only left eigenvectors to evaluate the matrix exponential in the method of discrete ordinates for the vector radiative transfer equation, which neglects circular polarization, in a plane-parallel atmosphere. This is contrary to a common practice of using the right eigenvectors to evaluate the matrix exponential combined with the left eigenvectors to avoid the inversion of the matrix of the right ones. Two numerical tests for Rayleigh and Aerosol scattering confirm our idea. For better explanation of our approach and for independent crosscheck of our results, we distribute an example in C/C++.

Sergey Korkin↗
NASA NTRS2019

Impacts of the Mount Pinatubo eruption on ENSO in the GEOS seasonal-to-subseasonal forecasting system

The eruption of Mount Pinatubo in June 1991 introduced a perturbation of the Earth's global energy budget by increasing the stratospheric aerosol loading by an order of magnitude, with effects on the global climate. In this presentation we analyze the effects of the Mt. Pinatubo eruption on the seasonal forecast performed with Goddard Earth Observing System Seasonal-to Subseasonal (GEOS-S2S) system, an Earth System Model that includes an interactive ocean and a bulk aerosol model coupled to radiation. We performed 10-member ensembles for the year after the eruption (June 1991-May 1992) at ~0.5 horizontal resolution, with and without the inclusion of the Mt. Pinatubo eruption. In GEOS-S2S, the eruption leads to ta strengthening of El Nino peaking in January 1992. The strengthening is mainly due to the weakening of the trade winds, which is caused by a attening of the temperature gradient across the Pacic due to a differential response to the volcanic forcing between the central and eastern Pacic (ocean-dynamical thermostat). This response largely depends on the assumed size for the volcanic aerosols. Indeed, we performed simulations assuming a volcanic aerosol effective radius of 0.35 m (similar to tropospheric aerosol, and the default in GEOS) and 0.6 m (closer to observations of volcanic aerosol from Pinatubo-sized eruptions). We nd that in the latter case the tropical radiative forcing is lower, since smaller aerosols scatter shortwave radiation more eciently than larger ones. Accordingly, the impact on ENSO is not statistically signicant when a larger and more realistic particle radius is assumed.

Aquila, Valentina↗
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.↗
NASA NTRS1973

Comparison of Lidar and In-Situ Measurements of Stratospheric Aerosols

This paper will present the results of a comparative study conducted in Laramie, Wyoming, during the summer and fall of 1972, as part of the Department of Transportation's Climatic Impact Assessment Program (ClAP). The study included independent, and nearly simultaneous, measurements of stratospheric aerosols using a LIDAR system and a balloon-borne in-situ particle counter. The LIDAR provides a remote measurement of volume backscatter (aerosols and molecules) in a narrow wavelength region centered at the ruby wavelength (6943R); whereas the balloon-borne in-situ counter measures aerosol concentration by counting aerosols greater than approx. 0.30 microns in diameter as they are pumped through a chamber and scatter white light forward into photo-detectors. The comparison of measurements that will be discussed using the two techniques involves formulating the LIDAR data so that it is compatible with the counter data. The formulation includes separation of the scattering due to aerosols from the total and displaying this in terms of aerosol scattering function. Aerosol scattering function is proportional to aerosol concentration if the aerosol parameters, such as size distribution and composition, are constant with altitude. In separating the aerosol scattering from the total, the need for real atmospheric number density over the Standard Atmosphere is also discussed.

Melfi, S. H.↗