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NASA NTRS2012

Recent Advances in Improvement of Forecast Skill and Understanding Climate Processes Using AIRS Version-5 Products

AIRS/AMSU is the state of the art infrared and microwave atmospheric sounding system flying aboard EOS Aqua. These observations, covering the period September 2002 until the present, have been analyzed using the AIRS Science Team Version-5 retrieval algorithm. AIRS is a high spectral resolution infrared grating spectrometer with spect,ral coverage from 650 per centimeter extending to 2660 per centimeter, with low noise and a spectral resolving power of 2400. A brief overview of the AIRS Version-5 retrieval procedure will be presented, including the AIRS channels used in different steps in the retrieval process. Many researchers have used these products to make significant advances in both climate and weather applications. Recent significant results of these experiments will be presented, including results showing that 1) assimilation of AIRS Quality Controlled temperature profiles into a General Circulation Model (GCM) significantly improves the ability to predict storm tracks of intense precipitation events; and 2) anomaly time-series of Outgoing Longwave Radiation (OLR) computed using AIRS sounding products closely match those determined from the CERES instrument, and furthermore explain that the phenomenon that global and especially tropical mean OLR have been decreasing since September 2002 is a result of El Nino/La Nina oscillations during this period.

Susskind, Joel↗
NASA NTRS2019

First Steps in the Creation of a Joint MISR/MODIS Ocean Color Atmospheric Correction Algorithm

We are creating a new algorithm that combines observations from MISR and MODIS (both on the NASA Terra spacecraft) to improve atmospheric correction and coverage for ocean color data products. The algorithm utilizes information rich, multi-angle MISR observations for atmospheric correction, applied to MODIS. Our goal is to produce atmospherically corrected Remote Sensing Reflectance from MODIS with enhanced coverage and accuracy, for input to downstream bio-optical ocean parameter retrieval algorithms.An important aspect of this work is the utilization of multi-angle views of the reflected ocean surface sun glint. Usually, such observations are avoided, since the intensity of the glint overwhelms any contribution from the ocean body. However, MISR's multi-angle observations see varying degrees of glint, which means they can be used to better determine aerosol optical properties (Kaufman et al., 2002, Ottaviani et al., 2013), and to identify surface wind speeds that govern the glint pattern. The latter could be utilized to replace the wind speeds taken from ancillary sources that are currently used to conservatively mask potential glint contamination in MODIS observations.To assess this capability, and to identify the appropriate parameterization, we present an analysis using the Generalized Nonlinear Retrieval Analysis (GENRA, Vukicevic et al., 2009) information content assessment. This technique is also easily modified to act as a Bayesian retrieval algorithm, for which initial results are discussed. Finally, we describe the status of integrating MISR data into the processing capabilities of the Ocean Biology Processing Group (OBPG) at NASA, and show the first ocean color vicarious calibration (Franz et al., 2007) of the MISR instrument.

Knobelspiesse, Kirk↗
NASA NTRSDate not supplied

A Modeling and Simulation Study for the GeoXO Atmospheric Composition Instrument (ACX): System Level SO2 and O3 Retrieval Performance as a Function of SNR

NOAA’s Geostationary Extended Observations (GeoXO) program is planning to include a hyperspectral UV/visible atmospheric composition instrument in geostationary orbit slated for operations by the early 2030s. Trace gas retrievals provide critical information about our Earth’s system as it relates to both natural and anthropogenic activity. This work focused on the impacts of the signal-to-noise ratio (SNR) on the retrieval uncertainty of SO2 and O3. An end-to-end physics-based imaging system and scene modeling and simulation framework was developed to assess instrument performance considerations in support of the planned GeoXO atmospheric composition instrument (ACX). The framework is composed of three primary components: 1) simulated at-sensor radiance via radiative transfer models of a known atmospheric composition, 2) a noise model driven by previous and planned sensor specifications, and 3) a physical retrieval algorithm. In this analysis, the tropospheric concentrations of SO2 and O3 in the atmospheric column were varied in the boundary layer (0-3 km) and at an elevation of 5 km with a thickness of 1-2 km; the uncertainty in retrieval was studied for various SNR levels for multiple viewing geometries and solar zenith angles. This effort supports the development of the GeoXO ACX instrument by providing a simulated ACX performance assessment of the system-level retrieval performance as a function of SNR, particularly with respect to the wavelength range of interest (approximately 305 – 340 nm) for SO2 and O3 trace gas retrievals.

Monica Cook↗
NASA NTRS1984

NROSS scatterometer - An instrument for global oceanic wind observations

One of the instruments - the NROSS scatterometer or SCATT - to be launched on the Navy Remote Ocean Sensing System spacecraft in 1989 is discussed. To determine wind speed and direction that SCATT will measure the ocean normalized radar cross section (NRCS) by illuminating the ocean's surface with microwave pulses and measuring the return signal power. A wind retrieval algorithm is used to compute the wind speed and direction from the measured NRCS. Winds over at least 90 percent of the global, ice-free ocean will be observed at least once every two days. For NASA users, the system will retrieve winds with an accuracy of plus or minus 2 m/s or 10 percent whichever is greater, for wind speeds ranging from 3 to 30 m/s.

Li, F.↗
NASA NTRS2006

The Continuous Monitoring of Desert Dust using an Infrared-based Dust Detection and Retrieval Method

Airborne dust and sand are significant aerosol sources that can impact the atmospheric and surface radiation budgets. Because airborne dust affects visibility and air quality, it is desirable to monitor the location and concentrations of this aerosol for transportation and public health. Although aerosol retrievals have been derived for many years using visible and near-infrared reflectance measurements from satellites, the detection and quantification of dust from these channels is problematic over bright surfaces, or when dust concentrations are large. In addition, aerosol retrievals from polar orbiting satellites lack the ability to monitor the progression and sources of dust storms. As a complement to current aerosol dust retrieval algorithms, multi-spectral thermal infrared (8-12 micron) data from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Meteosat-8 Spinning Enhanced Visible and Infrared Imager (SEVIRI) are used in the development of a prototype dust detection method and dust property retrieval that can monitor the progress of Saharan dust fields continuously, both night and day. The dust detection method is incorporated into the processing of CERES (Clouds and the Earth s Radiant Energy System) aerosol retrievals to produce dust property retrievals. Both MODIS (from Terra and Aqua) and SEVERI data are used to develop the method.

Duda, David P.↗
NASA NTRS2008

Atmospheric Parameter Climatologies from AIRS: Monitoring Short-, and Longer-Term Climate Variabilities and 'Trends'

The AIRS instrument is currently the best space-based tool to simultaneously monitor the vertical distribution of key climatically important atmospheric parameters as well as surface properties, and has provided high quality data for more than 5 years. AIRS analysis results produced at the GODDARD/DAAC, based on Versions 4 & 5 of the AIRS retrieval algorithm, are currently available for public use. Here, first we present an assessment of interrelationships of anomalies (proxies of climate variability based on 5 full years, since Sept. 2002) of various climate parameters at different spatial scales. We also present AIRS-retrievals-based global, regional and 1x1 degree grid-scale "trend"-analyses of important atmospheric parameters for this 5-year period. Note that here "trend" simply means the linear fit to the anomaly (relative the mean seasonal cycle) time series of various parameters at the above-mentioned spatial scales, and we present these to illustrate the usefulness of continuing AIRS-based climate observations. Preliminary validation efforts, in terms of intercomparisons of interannual variabilities with other available satellite data analysis results, will also be addressed. For example, we show that the outgoing longwave radiation (OLR) interannual spatial variabilities from the available state-of-the-art CERES measurements and from the AIRS computations are in remarkably good agreement. Version 6 of the AIRS retrieval scheme (currently under development) promises to further improve bias agreements for the absolute values by implementing a more accurate radiative transfer model for the OLR computations and by improving surface emissivity retrievals.

Molnar, Gyula↗
NASA NTRS2010

Radiometric Quality of the MODIS Bands at 667 and 678nm

The MODIS instruments on Terra and Aqua were designed to allow the measurement of chlorophyll fluorescence effects over ocean. The retrieval algorithm is based on the difference between the water-leaving radiances at 667nm and 678nm. The water-leaving radiances at these wavelengths are usually very low relative to the top- of-atmosphere radiances. The high radiometric accuracy needed to retrieve the small fluorescence signal lead to a dual gain design for the 667 and 678nm bands. This paper discusses the benefits obtained from this design choice and provides justification for the use of only one set of gains for global processing of ocean color products. Noise characteristics of the two bands and their related products are compared to other products of bands from 412nm to 2130nm. The impact of polarization on the two bands is discussed. In addition, the impact of stray light on the two bands is compared to other MODIS bands.

Meister, Gerhard↗
NASA NTRS2011

Radiometric Quality of the MODIS Bands at 667 and 678nm

The MODIS instruments on Terra and Aqua were designed to allow the measurement of chlorophyll fluorescence effects over ocean. The retrieval algorithm is based on the difference between the water-leaving radiances at 667nm and 678nm. The water-leaving radiances at these wavelengths are usually very low relative to the top-of-atmosphere radiances. The high radiometric accuracy needed to retrieve the small fluorescence signal lead to a dual gain design for the 667 and 678nm bands. This paper discusses the benefits obtained from this design choice and provides justification for the use of only one set of gains for global processing of ocean color products. Noise characteristics of the two bands and their related products are compared to other products of bands from 412nm to 2130nm. The impact of polarization on the two bands is discussed. In addition, the impact of stray light on the two bands is compared to other MODIS bands.

Meister, Gerhard↗
NASA NTRS2011

Aerosol Constraints from Multi-Angle Imaging That Modelers Can Use

As we continue to develop, refine, and apply the MISR aerosol products to a range of scientific questions, the strengths and limitations of the data content regarding aerosol optical depth (AOD), aerosol type, and plume height mapping have become pretty clear. Optimizing the operational algorithms to take advantage of the multi-angle, multi-spectral radiance information content is challenging in some situations, so we have also developed a number of specialized tools that run only on individual cases. These include the MISR Research Aerosol Retrieval algorithm, the highest-quality aerosol plume heights derived from the MINX software, and MISR-MODIS aerosol transport mapping code. This presentation will focus on some of the research products we are creating, with emphasis on those that might be most useful for constraining aerosol transport models, As we have acquired more than 11 years of once-weekly global coverage from MISR, discussion with the group will consider where and when having these products would maximize our contribution to AeroCom modeling efforts, in the context of practical limitations on specialized product generation.

Kahn, Ralph↗
NASA NTRSDate not supplied

Climate Fingerprinting Sounder Product (ClimFiSP) Skin Temperature Trends Analysis

Climate fingerprinting Sounder Product (ClimFiSP) has been developed at NASA Langley Research Center which includes daily skin temperature, surface emissivity, air temperature, H2O, trace gases, and cloud properties on 0.5x0.5 grid. Those properties are derived from IR hyper-spectral radiance measured by AIRS on Aqua and CrIS on SNPP and JPSS series. Global skin temperature trends have been derived using more than 20 years of monthly mean skin temperature data from ClimFiSP. The ClimFiSP algorithm use the spectral fingerprinting methodology that allows a low latency procession of more than two decades long satellite data record. The computational cost can be reduced by more than two orders of magnitude as compared with traditional Level-Level2-Level3 retrieval algorithms. In this presentation the global skin temperature trend from ClimFiSP will be compared with skin temperature trend derived from CLIMCAPS, ERA5, GISTEMP, HadCRUT5, and IASI data products, and the results show that pattern of ClimFiSP global skin temperature trends overall matches well with other datasets. The zonally averaged skin temperature anomaly will also be validated using those datasets. It is expected that ClimFiSP surface temperature data can serve as an important complement for surface-based estimates, especially in the regions where the spatial coverage of the surface-based observations is scarce.

Liqiao Lei↗
NASA NTRSDate not supplied

Deriving a Suite of Climate Data Records from 21-years of Sounder Observations

Two retrieval algorithms, a Single Field-of-view Sounder Atmospheric Product (SiFSAP) Level 2 algorithm and a Climate Fingerprinting Sounder Product (ClimFiSP) Level 3 algorithm, have been developed at NASA Langley Research Center. In this presentation, we will demonstrate the radiance closure build into these two algorithms. This is possible due to the use of a principal-component-based radiative transfer model (PCRTM). The PCRTM enables the inclusion of all available spectral information from hyperspectral IR sounders. It also has fast and accurate capability of modeling observed cloudy radiance spectra directly. The SiFSAP, which fits sounder radiance spectra using PCRTM as forward model and an optimal estimation as inverse model, has 3-times higher spatial resolution and 9-times denser data products comparing to current NASA and NOAA operational IR sounder products. With great support from NASA sounder SIPS, the SiFSAP algorithm has been delivered to NASA GES DISC for L2 and L3 data generation and releasing. The ClimFiSP uses a spectral fingerprinting method to directly generate L3 data products from spatiotemporally averaged L1 data. The goal of ClimFiSP is to generate high-quality climate data records (CDRs) from multiple IR sounders (e.g. Aqua AIRS, SNPP CrIS, NOAA-20 and NOAA-21 CrIS) using a consistent retrieval methodology. Using CHIRP L1 data, we have generated 20-years of CDRs for atmospheric temperature, water vapor, and trace gas profiles, as well as cloud and surface properties. The algorithm will be transitioned to Sounder SIPS soon and eventually to NASA GES DISC.

Xu Liu↗
NASA NTRS2010

Use of Quality Controlled AIRS Temperature Soundings to Improve Forecast Skill

AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU-A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU-A are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. Also included are the clear column radiances used to derive these products which are representative of the radiances AIRS would have seen if there were no clouds in the field of view. All products also have error estimates. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20 percent, in cases with up to 90 percent effective cloud cover. The products are designed for data assimilation purposes for the improvement of numerical weather prediction, as well as for the study of climate and meteorological processes. With regard to data assimilation, one can use either the products themselves or the clear column radiances from which the products were derived. The AIRS Version 5 retrieval algorithm is now being used operationally at the Goddard DISC in the routine generation of geophysical parameters derived from AIRS/AMSU data. A major innovation in Version 5 is the ability to generate case-by-case level-by-level error estimates for retrieved quantities and clear column radiances, and the use of these error estimates for Quality Control. The temperature profile error estimates are used to determine a case-by-case characteristic pressure pbest, down to which the profile is considered acceptable for data assimilation purposes. The characteristic pressure p(sub best) is determined by comparing the case dependent error estimate (delta)T(p) to the threshold values (Delta)T(p). The AIRS Version 5 data set provides error estimates of T(p) at all levels, and also profile dependent values of pbest based on use of a Standard profile dependent threshold (Delta)T(p). These Standard thresholds were designed as a compromise between optimal use for data assimilation purposes, which requires highest accuracy (tighter Quality Control), and climate purposes, which requires more spatial coverage (looser Quality Control). Subsequent research using Version 5 sounding and error estimates showed that tighter Quality Control performs better for data assimilation proposes, while looser Quality Control better spatial coverage) performs better for climate purposes. We conducted a number of data assimilation experiments using the NASA GEOS-5 Data Assimilation System as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The model was run at a horizontal resolution of 0.5 degree latitude x 0.67 degree longitude with 72 vertical levels. These experiments were run during four different seasons, each using a different year. The AIRS temperature profiles were presented to the GEOS-5 analysis as rawinsonde profiles, and the profile error estimates (delta)T(p) were used as the uncertainty for each measurement in the data assimilation process.

Susskind, Joel↗
NASA NTRS2011

Hyperspectral Remote Sensing of Atmosphere and Surface Properties

Atmospheric Infrared Sounder (AIRS), Infrared Atmospheric Sounding Interferometer (IASI), and Cross-track Infrared Sounder (CrIS) are all hyper-spectral satellite sensors with thousands of spectral channels. Top of atmospheric radiance spectra measured by these sensors contain high information content on atmospheric, cloud, and surface properties. Exploring high information content contained in these high spectral resolution spectra is a challenging task due to computation e ort involved in modeling thousands of spectral channels. Usually, only very small fractions (4{10 percent) of the available channels are included in physical retrieval systems or numerical weather forecast (NWP) satellite data assimilations. We will describe a method of simultaneously retrieving atmospheric temperature, moisture, cloud, and surface properties using all available spectral channels without sacrificing computational speed. The essence of the method is to convert channel radiance spectra into super-channels by an Empirical Orthogonal Function (EOF) transformation. Because the EOFs are orthogonal to each other, about 100 super-channels are adequate to capture the information content of the radiance spectra. A Principal Component-based Radiative Transfer Model (PCRTM) developed at NASA Langley Research Center is used to calculate both the super-channel magnitudes and derivatives with respect to atmospheric profiles and other properties. There is no need to perform EOF transformations to convert super channels back to spectral space at each iteration step for a one-dimensional variational retrieval or a NWP data assimilation system. The PCRTM forward model is also capable of calculating radiative contributions due to multiple-layer clouds. The multiple scattering effects of the clouds are efficiently parameterized. A physical retrieval algorithm then performs an inversion of atmospheric, cloud, and surface properties in super channel domain directly therefore both reducing the computational need and preserving the information content of the IASI measurements. The inversion algorithm is based on a non-linear Levenberg-Marquardt method with climatology covariance matrices and a priori information as constraints. One advantage of this approach is that it uses all information content from the hyper-spectral data so that the retrieval is less sensitive to instrument noise and eliminates the need for selecting a sub-set of the channels.

Liu, Xu↗
NASA NTRS2012

Thermal Behaviour of Unusual Local-Scale Surface Features on Vesta

On Vesta, the region of the infrared spectrum beyond approximately 3.5 micrometers is dominated by the thermal emission of the asteroid's surface, which can be used to determine surface temperature by means of temperature-retrieval algorithms. The thermal behavior of areas of unusual albedo seen at the local scale can be related to physical properties that can provide information about the origin of those materials. Dawn's Visible and Infrared Mapping Spectrometer (VIR) hyperspectral cubes are used to retrieve surface temperatures, with high accuracy as long as temperatures are greater than 180 K. Data acquired in the Survey phase (23 July through 29 August 2011) show several unusual surface features: 1) high-albedo (bright) and low-albedo (dark) material deposits, 2) spectrally distinct ejecta, 3) regions suggesting finer-grained materials. Some of the unusual dark and bright features were re-observed by VIR in the subsequent High-Altitude Mapping Orbit (HAMO) and Low-Altitude Mapping Orbit (LAMO) phases at increased pixel resolution. To calculate surface temperatures, we applied a Bayesian approach to nonlinear inversion based on the Kirchhoff law and the Planck function. These results were cross-checked through application of alternative methods. Here we present temperature maps of several local-scale features that were observed by Dawn under different illumination conditions and different local solar times. Some bright terrains have an overall albedo in the visible as much as 40% brighter than surrounding areas. Data from the IR channel of VIR show that bright regions generally correspond to regions with lower thermal emission, i.e. lower temperature, while dark regions correspond to areas with higher thermal emission, i.e. higher temperature. This behavior confirms that many of the dark appearances in the VIS mainly reflect albedo variations. In particular, it is shown that during maximum daily insolation, dark features in the equatorial region may rise to temperatures greater than 270 K. However, individual features may show different thermal behaviours, as a result of differences in composition and/or structure (e.g, average grain size of the surface regolith, porosity, etc.). To complement the temperature and near-infrared emissivity derived from the infrared spectra, a separate work is devoted to calculate thermal inertia and other thermal properties using theoretical models which solve the heat equation for airless bodies, and model the distribution of temperatures due to surface roughness variations.

Tosi, F.↗
NASA NTRS2004

Comparison of TOMS, SBW & SBUV/2 Version 8 Total Column Ozone Data with Data from Groundstations

The Nimbus-7 and Earth Probe Total Ozone Mapping Spectrometer (TOMS) data as well as SBUV and SBUV/2 data have been reprocessed with a new retrieval algorithm (Version 8) and an updated calibration procedure. An overview will be presented systematically comparing ozone values to an ensemble of Brewer and Dobson spectrophotometers. The comparisons were made as a function of latitude, solar zenith angle, reflectivity and total ozone. Results show that the accuracy of the TOMS retrieval has been improved when aerosols are present in the atmosphere, when snow/ice and sea glint are present, and when ozone in the northern hemisphere is extremely low. TOMS overpass data are derived from the single TOMS best match measurement, almost always located within one degree of the ground station and usually made within an hour of local noon. The Version 8 Earth Probe TOMS ozone values have decreased by an average of about 1% due to a much better understanding of the calibration of the instrument. N-7 SBUV as well as the series of NOAA SBUV/2 column ozone values have also been processed with the Version 8 algorithm and have been compared to values from an ensemble of groundstations. Results show that the SBW column ozone values agree well with the groundstations and the datasets are useful for trend studies.

Labow, G. J.↗
NASA NTRS2011

Evaluating the Assumptions of Surface Reflectance and Aerosol Type Selection Within the MODIS Aerosol Retrieval Over Land: The Problem of Dust Type Selection

Aerosol Optical Depth (AOD) and Angstrom exponent (AE) values derived with the MODIS retrieval algorithm over land (Collection 5) are compared with ground based sun photometer measurements at eleven sites spanning the globe. Although, in general, total AOD compares well at these sites (R2 values generally over 0.8), there are cases (from 2 to 67% of the measurements depending on the site) where MODIS clearly retrieves the wrong spectral dependence, and hence, an unrealistic AE value. Some of these poor AE retrievals are due to the aerosol signal being too small (total AOD<0.3) but in other cases the AOD should have been high enough to derive accurate AE. However, in these cases, MODIS indicates AE values close to 0.6 and zero fine model weighting (FMW), i.e. dust model provides the best fitting to the MODIS observed reflectance. Yet, according to evidence from the collocated sun photometer measurements and back-trajectory analyses, there should be no dust present. This indicates that the assumptions about aerosol model and surface properties made by the MODIS algorithm may have been incorrect. Here we focus on problems related to parameterization of the land-surface optical properties in the algorithm, in particular the relationship between the surface reflectance at 660 and 2130 nm.

Mielonen, T.↗
NASA NTRS2012

Assimilation of the Microwave Limb Sounder Radiances

It has been shown that the assimilation of limb-sounder data can significantly improve the representation of ozone in NASA's GEOS Data Assimilation Systems (GEOS-DAS), particularly in the stratosphere. The studies conducted so far utilized retrieved data from the MIPAS, POAM, ILAS and EOS Microwave Limb Sounder (EOS MLS) instruments. Direct assimilation of the radiance data can be seen as the natural next step to those studies. The motivation behind working with radiances is twofold. First, retrieval algorithms use a priori data which are either climatological or are obtained from previous analyses. This introduces additional uncertainty and, in some cases, may lead to "self-contamination"- when the a priori is taken from the same assimilation system in which subsequently ingests the retrieved observations. Second, radiances can be available in near real time thus providing an opportunity for operational assimilation, which could help improve the use of infrared radiance instruments from operational satellite instruments. In this presentation we summarize our ongoing work on an implementation of the assimilation of EOS MLS radiances into the GEOS-5 DAS. This work focuses on assimilation of band 7 brightness temperatures which are sensitive to ozone. Our implementation uses the MLS Callable Forward Model developed by the MLS team at NASA JPL as the observation operator. We will describe our approach and recent results which are not yet final. In particular, we will demonstrate that this approach has a potential to improve the vertical structure of ozone in the lower tropical stratosphere as compared with the retrieved MLS product. We will discuss the computational efficiency of this implementation.

Wargan, K.↗
NASA NTRS2012

Assessment of Polarization Effect on Efficiency of Levenberg-Marquardt Algorithm in Case of Thin Atmosphere Over Black Surface

The Levenberg-Marquardt algorithm [1, 2] provides a numerical iterative solution to the problem of minimization of a function over a space of its parameters. In our work, the Levenberg-Marquardt algorithm retrieves optical parameters of a thin (single scattering) plane parallel atmosphere irradiated by collimated infinitely wide monochromatic beam of light. Black ground surface is assumed. Computational accuracy, sensitivity to the initial guess and the presence of noise in the signal, and other properties of the algorithm are investigated in scalar (using intensity only) and vector (including polarization) modes. We consider an atmosphere that contains a mixture of coarse and fine fractions. Following [3], the fractions are simulated using Henyey-Greenstein model. Though not realistic, this assumption is very convenient for tests [4, p.354]. In our case it yields analytical evaluation of Jacobian matrix. Assuming the MISR geometry of observation [5] as an example, the average scattering cosines and the ratio of coarse and fine fractions, the atmosphere optical depth, and the single scattering albedo, are the five parameters to be determined numerically. In our implementation of the algorithm, the system of five linear equations is solved using the fast Cramer s rule [6]. A simple subroutine developed by the authors, makes the algorithm independent from external libraries. All Fortran 90/95 codes discussed in the presentation will be available immediately after the meeting from sergey.v.korkin@nasa.gov by request.

Korkin, S.↗