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NASA NTRS2016

The Pilatus Unmanned Aircraft System for Lower Atmospheric Research

This paper presents details of the University of Colorado (CU) "Pilatus" unmanned research aircraft, assembled to provide measurements of aerosols, radiation and thermodynamics in the lower troposphere. This aircraft has a wingspan of 3.2 m and a maximum take-off weight of 25 kg, and it is powered by an electric motor to reduce engine exhaust and concerns about carburetor icing. It carries instrumentation to make measurements of broadband up- and downwelling shortwave and longwave radiation, aerosol particle size distribution, atmospheric temperature, relative humidity and pressure and to collect video of flights for subsequent analysis of atmospheric conditions during flight. In order to make the shortwave radiation measurements, care was taken to carefully position a high-quality compact inertial measurement unit (IMU) and characterize the attitude of the aircraft and its orientation to the upward-looking radiation sensor. Using measurements from both of these sensors, a correction is applied to the raw radiometer measurements to correct for aircraft attitude and sensor tilt relative to the sun. The data acquisition system was designed from scratch based on a set of key driving requirements to accommodate the variety of sensors deployed. Initial test flights completed in Colorado provide promising results with measurements from the radiation sensors agreeing with those from a nearby surface site. Additionally, estimates of surface albedo from onboard sensors were consistent with local surface conditions, including melting snow and bright runway surface. Aerosol size distributions collected are internally consistent and have previously been shown to agree well with larger, surface-based instrumentation. Finally the atmospheric state measurements evolve as expected, with the near-surface atmosphere warming over time as the day goes on, and the atmospheric relative humidity decreasing with increased temperature. No directional bias on measured temperature, as might be expected due to uneven heating of the sensor housing over the course of a racetrack pattern, was detected. The results from these flights indicate that the CU Pilatus platform is capable of performing research-grade lower tropospheric measurement missions.

de Boer, Gijs↗
NASA NTRS2017

Seasonal Clear-Sky Flux and Cloud Radiative Effect Anomalies in the Arctic Atmospheric Column Associated with the Arctic Oscillation and Arctic Dipole

The impact of the Arctic Oscillation (AO) and Arctic Dipole (AD) on the radiative flux into the Arctic mean atmospheric column is quantified. 3-month-averaged AO and AD indices are regressed with corresponding surface and top-of-atmosphere (TOA) fluxes from the CERES-SFC and CERES-TOA EBAF datasets over the period 2000-2014. An increase in clear-sky fluxes into the Arctic mean atmospheric column during fall is the largest net flux anomaly associated with AO, primarily driven by a positive net longwave flux anomaly (i.e. increase of net flux into the atmospheric column) at the surface. A decrease in the Arctic mean atmospheric column cloud radiative effect during winter and spring is the largest flux anomaly associated with AD, primarily driven by a change in the longwave cloud radiative effect at the surface. These prominent responses to AO and AD are widely distributed across the ice-covered Arctic, suggesting that the physical process or processes that bring about the flux change associated with AO and AD are distributed throughout the Arctic.

Hegyi, Bradley M.↗
NASA NTRS2016

Impact of MODIS SWIR Band Calibration Improvements on Level-3 Atmospheric Products

The spectral reflectance measured by the MODIS reflective solar bands (RSB) is used for retrieving many atmospheric science products. The accuracy of these products depends on the accuracy of the calibration of the RSB. To this end, the RSB of the MODIS instruments are primarily calibrated on-orbit using regular solar diffuser (SD) observations. For lambda < 0.94 microns the SDs on-orbit bi-directional reflectance factor (BRF) change is tracked using solar diffuser stability monitor (SDSM) observations. For lambda > 0.94 microns, the MODIS Characterization Support Team (MCST) developed, in MODIS Collection 6 (C6), a time-dependent correction using observations from pseudo-invariant earth-scene targets. This correction has been implemented in C6 for the Terra MODIS 1.24 micron band over the entire mission, and for the 1.375 micron band in the forward processing. As the instruments continue to operate beyond their design lifetime of six years, a similar correction is planned for other short-wave infrared (SWIR) bands as well. MODIS SWIR bands are used in deriving atmosphere products, including aerosol optical thickness, atmospheric total column water vapor, cloud fraction and cloud optical depth. The SD degradation correction in Terra bands 5 and 26 impact the spectral radiance and therefore the retrieval of these atmosphere products. Here, we describe the corrections to Bands 5 (1.24 microns) and 26 (1.375 microns), and produce three sets (B5, B26 correction on/on, on/off, and off/off) of Terra-MODIS Level 1B (calibrated radiance product) data. By comparing products derived from these corrected and uncorrected Terra MODIS Level 1B (L1B) calibrations, dozens of L3 atmosphere products are surveyed for changes caused by the corrections, and representative results are presented. Aerosol and water vapor products show only small local changes, while some cloud products can change locally by > 10%, which is a large change.

Calibration↗
NASA NTRS2016

Prebiotic Chemistry and Atmospheric Warming of Early Earth by an Active Young Sun

Nitrogen is a critical ingredient of complex biological molecules. Molecular nitrogen, however, which was outgassed Into the Earth's early atmosphere, is relatively chemically inert and nitrogen fixation into more chemically reactive compounds requires high temperatures. Possible mechanisms of nitrogen fixation include lightning, atmospheric shock heating by meteorites, and solar ultraviolet radiation. Here we show that nitrogen fixation in the early terrestrial atmosphere can be explained by frequent and powerful coronal mass ejection events from the young Sun -- so-called superflares. Using magnetohydrodynamic simulations constrained by Kepler Space Telescope observations, we find that successive superflare ejections produce shocks that accelerate energetic particles, which would have compressed the early Earth's magnetosphere. The resulting extended polar cap openings provide pathways for energetic particles to penetrate into the atmosphere and, according to our atmospheric chemistry simulations, initiate reactions converting molecular nitrogen, carbon dioxide and methane to the potent greenhouse gas nitrous oxide as well as hydrogen cyanide, an essential compound for life. Furthermore, the destruction of N2, C02 and CH, suggests that these greenhouse gases cannot explain the stability of liquid water on the early Earth. Instead, we propose that the efficient formation of nitrous oxide could explain a warm early Earth.

Airapetian, V. S.↗
NASA NTRS2017

Advection of Potential Temperature in the Atmosphere of Irradiated Exoplanets: A Robust Mechanism to Explain Radius Inflation

The anomalously large radii of strongly irradiated exoplanets have remained a major puzzle in astronomy. Based on a two-dimensional steady-state atmospheric circulation model, the validity of which is assessed by comparison to three-dimensional calculations, we reveal a new mechanism, namely the advection of the potential temperature due to mass and longitudinal momentum conservation, a process occurring in the Earth's atmosphere or oceans. In the deep atmosphere, the vanishing heating flux forces the atmospheric structure to converge to a hotter adiabat than the one obtained with 1D calculations, implying a larger radius for the planet. Not only do the calculations reproduce the observed radius of HD 209458b, but also reproduce the observed correlation between radius inflation and irradiation for transiting planets. Vertical advection of potential temperature induced by non-uniform atmospheric heating thus provides a robust mechanism to explain the inflated radii of irradiated hot Jupiters.

tmospheric effects; methods: numerical; planets an↗
NASA NTRS2017

Observations and Modeling of Thermal Structure in the Lower Atmosphere and the Upward Propagation of Tides into the Thermosphere

Thermal tides are the atmospheric response to diurnally varying thermal forcing resulting from radiative and convective heat transfer from the surface and from aerosol and gaseous heating within the atmosphere. Tides include sun-synchronous (migrating) waves driven in response to solar heating and additional non-migrating waves resulting from longitudinal variations in the distributions of topography, dust aerosol and water ice clouds. The systematic spatial mapping of temperature over 5 Mars years by the Mars Climate Sounder (MCS) has yielded a well-defined climatology of seasonally-varying temperature structures in the lower atmosphere, from 5 to ~80 km. Tide theory and Mars global circulation model (MGCM) simulations are a fruitful framework for relating temperature observations to thermal forcing by aerosol fields [1]. The analysis of density and temperature fields derived from MAVEN IUVS and NGIMS observations have revealed the presence of predominantly zonal wave 2 and 3 features at altitudes of 100-170 km that are almost certainly non-migrating tides propagating upward from the lower atmosphere [2,3]. In this presentation we will use the MCS climatology and MGCM simulations to relate the density variations seen by MAVEN with the seasonally varying tide activity in the lower atmosphere. Large amplitude perturbations in density are most sensitive to the tide components with the longest vertical wavelengths in temperature, which are well resolved in MCS observations.

Mars Climate Sounder (MCS)↗
NASA NTRS2017

NIR-Driven Moist Upper Atmospheres of Synchronously Rotating Temperate Terrestrial Exoplanets

H2O is a key molecule in characterizing atmospheres of temperate terrestrial planets, and observations of transmission spectra are expected to play a primary role in detecting its signatures in the near future. The detectability of H2O absorption features in transmission spectra depends on the abundance of water vapor in the upper part of the atmosphere. We study the three-dimensional distribution of atmospheric H2O for synchronously rotating Earth-sized aquaplanets using the general circulation model (GCM) ROCKE-3D, and examine the effects of total incident flux and stellar spectral type. We observe a more gentle increase of the water vapor mixing ratio in response to increased incident flux than one-dimensional models suggest, in qualitative agreement with the climate-stabilizing effect of clouds around the substellar point previously observed in GCMs applied to synchronously rotating planets. However, the water vapor mixing ratio in the upper atmosphere starts to increase while the surface temperature is still moderate. This is explained by the circulation in the upper atmosphere being driven by the radiative heating due to absorption by water vapor and cloud particles, causing efficient vertical transport of water vapor. Consistently, the water vapor mixing ratio is found to be well-correlated with the near-infrared portion of the incident flux. We also simulate transmission spectra based on the GCM outputs, and show that for the more highly irradiated planets, the H2O signatures may be strengthened by a factor of a few, loosening the observational demands for a H2O detection.

Fujii, Yuka↗
NASA NTRS2018

The Atmosphere-Ocean Interface Layer of NASA's Goddard Earth Observing System Model and Data Assimilation System Volume 51

The Goddard Earth Observing System (GEOS) general circulation model (GCM) includes modules for sea surface temperature (SST) diurnal warming and cool-skin layers. To support the application of a coupled atmosphere-ocean data assimilation capability, the GCM needs to be flexible enough to support both coupled atmosphere ocean general circulation model (AOGCM) and atmosphere-only (AGCM) configurations, with only minor configuration changes at the user interface. This document presents a formulation of an atmosphere-ocean interface layer (AOIL) that serves this purpose. Previous work by Akella et al. (2017) described a version of a model for near-surface temperature variations, including both both diurnal warming and cool-skin effects, that has been used since 2017 in the near-real-time GEOS FP (forward processing) weather analysis and forecasting system. The diurnal cycle of SST in that version of the GEOS atmospheric data assimilation system (ADAS) undergoes a sharp decay in the late afternoon (local time). The updated AOIL presented here includes a modification of the similarity function used in the diurnal warming model. Results from offline model runs illustrate an improvement in the near-surface (less than 0:5m depth) diurnal cycle compared to the original formulation. The new formulation requires minimal parameter tuning, and the improvements are robust across long (several month) simulation periods. This new model formulation, however, retains some deficiences from the previous module, such as a small warm bias in calm wind conditions for water depths below 1m. Our future work would include surface salinification and sea-ice into the AOIL.

Koster, Randal D.↗
NASA NTRS2013

Human and Natural Influences on the Changing Thermal Structure of the Atmosphere

Since the late 1970s, satellite-based instruments have monitored global changes in atmospheric temperature. These measurements reveal multidecadal tropospheric warming and stratospheric cooling, punctuated by short-term volcanic signals of reverse sign. Similar long- and short-term temperature signals occur in model simulations driven by human-caused changes in atmospheric composition and natural variations in volcanic aerosols. Most previous comparisons of modeled and observed atmospheric temperature changes have used results from individual models and individual observational records. In contrast, we rely on a large multimodel archive and multiple observational datasets. We show that a human-caused latitude/altitude pattern of atmospheric temperature change can be identified with high statistical confidence in satellite data. Results are robust to current uncertainties in models and observations. Virtually all previous research in this area has attempted to discriminate an anthropogenic signal from internal variability. Here, we present evidence that a human-caused signal can also be identified relative to the larger "total" natural variability arising from sources internal to the climate system, solar irradiance changes, and volcanic forcing. Consistent signal identification occurs because both internal and total natural variability (as simulated by state-of-the-art models) cannot produce sustained global-scale tropospheric warming and stratospheric cooling. Our results provide clear evidence for a discernible human influence on the thermal structure of the atmosphere.

Santer, Benjamin D.↗
NASA NTRS2018

Improving NASA GEOS Atmospheric CO2 Simulations by Calibrating CASA Surface Fluxes with an Empirical Sink

With the adoption of the Paris climate accord, efforts to monitor and understand both anthropogenic and natural carbon sources and sinks are increasing across the world. Given their low latency and global coverage, satellite observations of atmospheric carbon dioxide (CO2) are poised to make important contributions to this field. The combination of satellite data and high resolution global models can be used to monitor changes in carbon fluxes and to evaluate the consistency of nationally reported emissions estimates in support of multiple stakeholder communities. However, a consistent challenge to such work has been the high latency of surface carbon flux estimates, which are often not available for a year or more. This presentation describes the construction of surface carbon flux estimates meant to improve the near real time simulation of atmospheric CO2 with NASA's Goddard Earth Observing System (GEOS) general circulation model. The surface flux estimates begin with a collection of bottom-up fluxes which incorporate satellite measurements in their construction, e.g. vegetation indices in the Carnegie-Ames-Stanford Approach (CASA) and nighttime lights in the Open-source Data Inventory for Anthropogenic CO2 (ODIAC). From there, we take the additional step of using an empirical sink to calibrate terrestrial net biospheric exchange (NBE) to estimated values from atmospheric inversion systems. This approach removes a known, systematic bias in predicted atmospheric mixing ratios. Using these fluxes in a free running simulation, the model is able to reproduce in situ measurements with the same skill as when it uses gridded fluxes from a flux inversion system. Using these fluxes as a prior in an assimilation system, e.g. one incorporating retrievals of column CO2 from the Orbiting Carbon Observatory 2 (OCO-2), allows the analysis to capture variability in CO2 on scales that would be missed otherwise. This approach supports NASA's capability to forecast atmospheric CO2 up to two weeks in advance by leveraging a GEOS system used to produce quasi-operational weather analyses and forecasts, providing a valuable new tool to the carbon monitoring research and applications communities.

Weir, B.↗
NASA NTRS2018

Air-Sea Interactions in a High-Resolution Ocean-Atmosphere Simulation

During the past few years the Goddard Earth Observing System (GEOS) and Massachusetts Institute of Technology (MIT) modeling groups have produced, respectively, global atmosphere-only and ocean-only simulations with km-scale grid spacing. These simulations have proved invaluable for process studies and for the development of satellite and in-situ sampling strategies. Nevertheless, a key limitation of these "nature" simulations is the lack of interaction between the ocean and the atmosphere, which limits their usefulness for studying air-sea interactions and for designing observing missions to study these interactions. We present here results from a coupled GEOS-MIT "nature run" simulation, wherein we have coupled a cubed-sphere-720 (~ 1/8) configuration of the GEOS atmosphere to a lat-lon-cap-1080 (~ 1/12) configuration of the MIT ocean. We compare near-surface diagnostics of this fully coupled ocean-atmosphere simulation to equivalent atmosphere-only and ocean-only simulations. A particular focus of the comparisons is the coupled versus uncoupled differences in interactions between Sea Surface Temperature (SST) and ocean surface wind. We discuss, in particular, a several-day mode of temporal variability in the SST-wind cycle and how it is represented in the different model simulations and in observationally-based products. A mechanism for the cycle, which is driven by SST-wind feedback, is proposed.

Strobach, Ehud↗
NASA NTRS2019

Assimilation of Satellite Soil Moisture for Improved Atmospheric Reanalyses

A newly developed, weakly coupled land and atmosphere data assimilation system for NASA’s Global Earth Observing System model is presented, and used to demonstrate the benefit of assimilating satellite soil moisture into an atmospheric reanalysis. Specifically, Advanced Scatterometer and Soil Moisture Ocean Salinity soil moisture retrievals are assimilated into a system that uses the same model, atmospheric assimilation system, and atmospheric observations as the Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA-2). The atmosphere is sensitive to soil moisture only under certain conditions. Hence, while the globally averaged model improvements were small, regionally, the soil moisture assimilation induced some substantial improvements. For example, in a large region spanning from western Europe across southern Russia, the soil moisture assimilation decreased the RMSE against independent station observations of daily maximum 2-m temperature (T(sup 2m, sub max)) by up to 0.4 K, and of 2-m specific humidity (q(exp 2m)) by up to 0.5 g/kg. Over all available stations, the mean T(sup 2m, sub max) RMSE was reduced from 2.82 to 2.79 K, while the mean q(exp 2m) RMSE was reduced from 1.25 to 1.20 g/kg. The soil moisture assimilation also reduced the mean RMSE across 29 flux tower sites from 34.2 to 32.6 Wm(exp −2) for latent heating, and from 37.7 to 36.5 Wm(exp −2) for sensible heating. For all variables evaluated, the soil moisture assimilation improved the model at monthly to seasonal, rather than daily, time scales. Based on the above experiments, it is recommended that satellite soil moisture be assimilated into future reanalyses, including the follow-on to MERRA-2.

Clara Draper↗
NASA NTRS2019

A Scroll Filter System for In-Situ Resource Utilization CO2 Acquisition of the Martian Atmosphere

The Martian atmosphere, consisting mainly of gaseous CO2, is regarded as one of the main planetary resources capable of providing a significant portion of the oxygen that will be needed for human missions to the planet's surface. NASA's In-Situ Re-source Utilization (ISRU) project supports the development of oxygen generation technologies that can convert the Martian atmosphere into usable oxygen. The thin CO2 based Martian atmosphere, however, carries certain levels of dust stirred up by the Martian winds that must be filtered out at the front end of any CO2 acquisition system. Thus, the ISRU project is developing particulate filters as part of a Mars CO2 acquisition sys-tem. A prototype filter system, known as the Scroll Filter, is being tested under simulated Martian atmospheric conditions in the Mar Atmospheric Flow Loop at the NASA GRC. The measurement techniques as well as the preliminary results from a series of performance tests will be discussed.

Agui, Juan H.↗
NASA NTRS2019

Average Path Profile of Atmospheric Temperature and Humidity Structure Parameters from a Microwave Profiling Radiometer

The values of the key atmospheric turbulence parameters (structure constants) for temperature and water vapor, that is, C(exp 2)(sub T), and C(exp 2)(sub Q), are highly dependent upon the vertical height within the atmosphere thus making it necessary to specify profiles of these values along the atmospheric propagation path. The remote sensing method suggested and described in this work makes use of a rapidly integrating microwave profiling radiometer to capture profiles of temperature and humidity through the atmosphere. The integration times of currently available profiling radiometers are such that they are approaching the temporal intervals over which one can possibly make meaningful assessments of these key atmospheric parameters. These integration times, coupled with the boundary effects of the Earth’s surface are, however, unconventional for turbulence characterization; the classical Kolmogorov turbulence theory and related 2/3 law for structure functions prevalent in the inertial subrange are no longer appropriate. An alternative to this classical approach is derived from first principles to account for the nuances of turbulent mechanics met with using radiometer sensing, that is, the large-scale turbulence driven by the various possible boundary conditions within the buoyancy subrange. Analytical expressions connecting the measured structure functions to the corresponding structure parameters are obtained. The theory is then applied to an experimental scenario involving radiometric profile measurements of temperature and shows very good results.

Manning, Robert M.↗
NASA NTRS2019

Seasonal Variations in Atmospheric Composition as Measured in Gale Crater, Mars

The Sample Analysis at Mars (SAM) instrument onboard the Mars Science Laboratory Curiosity rover measures the chemical composition of major atmospheric species (CO2, N2, 40Ar,O2, and CO) through a dedicated atmospheric inlet. We report here measurements of volume mixing ratios in Gale Crater using the SAM quadrupole mass spectrometer, obtained over a period of nearly 5 years (3 Mars years) from landing. The observation period spans the northern summer of MY31 and solar longitude (L(sub S)) of 175° through spring of MY 34, L(sub S) = 12°. This work expands upon prior reports of the mixing ratios measured by SAM QMS in the first 105 sols of the mission. The SAM QMS atmospheric measurements were taken periodically, with a cumulative coverage of four or five experiments per season on Mars. Major observations include the seasonal cycle of CO2, N2, and Ar, which lags approximately 20–40° of L(sub S) behind the pressure cycle driven by CO2 condensation and sublimation from the winter poles. This seasonal cycle indicates that transport occurs on faster timescales than mixing. The mixing ratio of O2 shows significant seasonal and interannual variability, suggesting an unknown atmospheric or surface process at work. The O2 measurements are compared to several parameters, including dust optical depth and trace CH4 measurements by Curiosity. We derive annual mean volume mixing ratios for the atmosphere in Gale Crater: CO2 = 0.951 (±0.003), N2 = 0.0259 (±0.0006), 40Ar = 0.0194 (±0.0004), O2 = 1.61 (±0.09) x 10(exp ‐3), and CO = 5.8 (±0.8) x 10(exp ‐4).

Gale Crater↗
NASA NTRS2019

Laboratory for Atmospheres Instrument Systems Report

Studies of the atmospheres of our solar system's planets including our own require a comprehensive set of observations, relying on instruments on spacecraft, aircraft, balloons, and on the surface. These instrument systems perform one or both of the following: 1) provide information leading to a basic understanding of the relationship between atmospheric systems and processes, and 2) serve as calibration references for satellite instrument validation. Laboratory personnel define requirements, conceive concepts, and develop instrument systems for spaceflight missions, and for balloon, aircraft, and ground-based observations. Balloon and airborne platforms facilitate regional measurements of precipitation, cloud systems, and ozone from high-altitude vantage points, but still within the atmosphere. Such platforms serve as stepping-stones in the development of space instruments. Satellites provide nearly global coverage of the Earth with spatial resolutions and repetition rates that vary from system to system. The products of atmospheric remote sensing are invaluable for research associated with water vapor, ozone, trace gases, aerosol particles, clouds, precipitation, and the radiative and dynamic processes that affect the climate of the Earth. These parameters also provide the basic information needed to develop models of global atmospheric processes and weather and climate prediction. Laboratory scientists also participate in the design of data processing algorithms, calibration techniques, and the data processing systems.

Platnick, Steven E.↗
NASA NTRS2020

GISS Model E2.2: A Climate Model Optimized for the Middle Atmosphere. Part 1: Model Structure, Climatology, Variability and Climate Sensitivity

We introduce a new climate model (GISS E2.2) that has been specially optimized for the Middle Atmosphere, and whose output is being contributed to the CMIP6 archive. The top of the model is at a geopotential altitude of 89 km, and parameterizations of moist convection and various forms of gravity wave drag based on tropospheric processes are chosen specifically for this optimization. We first evaluate the model in its configuration as a coupled atmosphere-chemistry model with respect to its simulation of the mean state of the Middle Atmosphere, from the mesosphere down through the Upper Troposphere/Lower Stratosphere. Then we assess its use as a coupled atmosphere-ocean climate model by exploring its mean ocean climatology. To evaluate its variability, we report on its simulation of the primary modes in the troposphere, stratosphere and ocean. Two climate change simulations are presented, the responses to instantaneous increases of 2xCO2 and 4xCO2, run with two different ocean models. Sensitivity studies are performed to illustrate the effect of parameterizations on the model results. We compare these results to the lower vertical resolution/top GISS Model E2.1, whose output has also been submitted to CMIP6. The different choices made for these models are explored. It is shown that important improvements in the circulation above and below the tropopause can be obtained when attention is paid to representation of Middle Atmosphere processes in climate model development.

D. Rind↗
NASA NTRS2019

An Approach to Retrieve BRDF from Satellite and Airborne Measurements of Surface-Reflected Radiance Based on Decoupling of Atmospheric Radiative Transfer and Surface Reflection

Bi-directional Reflection Distribution Function (BRDF) defines anisotropy of the surface reflection. It is required to specify the boundary condition for radiative transfer (RT) modeling. Measurements of reflected radiance by satellite- and air-borne sensors provide information about anisotropy of surface reflection. Atmospheric correction needs to be performed to derive BRDF from the reflected radiance. Common approach for BRDF retrievals consists of the use of kernel-based BRDF and RT modeling that needs to be done anew at every step of the iterative process. The kernels’ weights are obtained by minimization of the difference between measured and modeled radiance. This study develops a new method of retrieving kernel-based BRDF that requires RT calculations to be done only once. The method employs the exact analytical expression of radiance at any atmospheric level through the solutions of two auxiliary atmosphere-only RT problems and the surface-reflected radiance at the surface level. The latter is related to BRDF and solutions of the auxiliary RT problems by a Fredholm integral equation of the second kind. The approach requires to perform RT calculations one time before the iterations. It can use observations taken at different atmospheric conditions assuming that surface conditions remain unchanged during the time span of observations. The algorithm accurately catches zero weights of the kernels that may be a concern if the number of kernels is greater than 3 in current mainstream approaches. The study presents numerical tests of the BRDF retrieval algorithm for various surface and atmospheric conditions.

Radkevich, Alexander↗