53 research outputs found

    ESTIMATING LAND SURFACE ALBEDO FROM SATELLITE DATA

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    Land surface albedo, defined as the ratio of the surface reflected incoming and outgoing solar radiation, is one of the key geophysical variables controlling the surface radiation budget. Surface shortwave albedo is widely used to drive climate and hydrological models. During the last several decades, remotely sensed surface albedo products have been generated through satellite-acquired data. However, some problems exist in those products due to instrument measurement inaccuracies and the failure of current retrieving procedures, which have limited their applications. More significantly, it has been reported that some albedo products from different satellite sensors do not agree with each other and some even show the opposite long term trend regionally and globally. The emergence of some advanced sensors newly launched or planned in the near future will provide better capabilities for estimating land surface albedo with fine resolution spatially and/or temporally. Traditional methods for estimating the surface shortwave albedo from satellite data include three steps: first, the satellite observations are converted to surface directional reflectance using the atmospheric correction algorithms; second, the surface bidirectional reflectance distribution function (BRDF) models are inverted through the fitting of the surface reflectance composites; finally, the shortwave albedo is calculated from the BRDF through the angular and spectral integration. However, some problems exist in these algorithms, including: 1) "dark-object" based atmospheric correction methods which make it difficult to estimate albedo accurately over non-vegetated or sparsely vegetated area; 2) the long-time composite albedo products cannot satisfy the needs of weather forecasting or land surface modeling when rapid changes such as snow fall/melt, forest fire/clear-cut and crop harvesting occur; 3) the diurnal albedo signature cannot be estimated in the current algorithms due to the Lambertian approximation in some of the atmospheric correction algorithms; 4) prior knowledge has not been effectively incorporated in the current algorithms; and 5) current observation accumulation methods make it difficult to obtain sufficient observations when persistent clouds exist within the accumulation window. To address those issues and to improve the satellite surface albedo estimations, a method using an atmospheric radiative transfer procedure with surface bidirectional reflectance modeling will be applied to simultaneously retrieve land surface albedo and instantaneous aerosol optical depth (AOD). This study consists of three major components. The first focuses on the atmospheric radiative transfer procedure with surface reflectance modeling. Instead of executing atmospheric correction first and then fitting surface reflectance in the previous satellite albedo retrieving procedure, the atmospheric properties (e.g., AOD) and surface properties (e.g., BRDF) are estimated simultaneously to reduce the uncertainties produced in separating the entire radiative transfer process. Data from the Moderate Resolution Imaging Spectroradiometer (MODIS) onboard Terra and Aqua are used to evaluate the performance of this albedo estimation algorithm. Good agreement is reached between the albedo estimates from the proposed algorithm and other validation datasets. The second part is to assess the effectiveness of the proposed algorithm, analyze the error sources, and further apply the algorithm on geostationary satellite - the Spinning Enhanced Visible and InfraRed Imager (SEVIRI) onboard Meteosat Second Generation (MSG). Extensive validations on surface albedo estimations from MSG/SEVIRI observations are conducted based on the comparison with ground measurements and other satellite products. Diurnal changes and day-to-day changes in surface albedo are accurately captured by the proposed algorithm. The third part of this study is to develop a spatially and temporally complete, continuous, and consistent albedo maps through a data fusion method. Since the prior information (or climatology) of albedo/BRDF plays a vital role in controlling the retrieving accuracy in the optimization method, currently available multiple land surface albedo products will be integrated using the Multi-resolution Tree (MRT) models to mitigate problems such as data gaps, systematic bias or low information-noise ratio due to instrument failure, persistent clouds from the viewing direction and algorithm limitations. The major original contributions of this study are as follows: 1) this is the first algorithm for the simultaneous estimations of surface albedo/reflectance and instantaneous AOD by using the atmospheric radiative transfer with surface BRDF modeling for both polar-orbiting and geostationary satellite data; 2) a radiative transfer with surface BRDF models is used to derive surface albedo and directional reflectance from MODIS and SEVIRI observations respectively; 3) extensive validations are made on the comparison between the albedo and AOD retrievals, and the satellite products from other sensors; 4) the slightly modified algorithm has been adopted to be the operational algorithm of Advanced Baseline Imager (ABI) in the future Geostationary Operational Environmental Satellite-R Series (GOES-R) program for estimating land surface albedo; 5) a framework of using MRT is designed to integrate multiple satellite albedo products at different spatial scales to build the spatially and temporally complete, continuous, and consistent albedo maps as the prior knowledge in the retrieving procedure

    An Approach for the Long-Term 30-m Land Surface Snow-Free Albedo Retrieval from Historic Landsat Surface Reflectance and MODIS-based A Priori Anisotropy Knowledge

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    Land surface albedo has been recognized by the Global Terrestrial Observing System (GTOS) as an essential climate variable crucial for accurate modeling and monitoring of the Earth's radiative budget. While global climate studies can leverage albedo datasets from MODIS, VIIRS, and other coarse-resolution sensors, many applications in heterogeneous environments can benefit from higher-resolution albedo products derived from Landsat. We previously developed a "MODIS-concurrent" approach for the 30-meter albedo estimation which relied on combining post-2000 Landsat data with MODIS Bidirectional Reflectance Distribution Function (BRDF) information. Here we present a "pre-MODIS era" approach to extend 30-m surface albedo generation in time back to the 1980s, through an a priori anisotropy Look-Up Table (LUT) built up from the high quality MCD43A BRDF estimates over representative homogenous regions. Each entry in the LUT reflects a unique combination of land cover, seasonality, terrain information, disturbance age and type, and Landsat optical spectral bands. An initial conceptual LUT was created for the Pacific Northwest (PNW) of the United States and provides BRDF shapes estimated from MODIS observations for undisturbed and disturbed surface types (including recovery trajectories of burned areas and non-fire disturbances). By accepting the assumption of a generally invariant BRDF shape for similar land surface structures as a priori information, spectral white-sky and black-sky albedos are derived through albedo-to-nadir reflectance ratios as a bridge between the Landsat and MODIS scale. A further narrow-to-broadband conversion based on radiative transfer simulations is adopted to produce broadband albedos at visible, near infrared, and shortwave regimes.We evaluate the accuracy of resultant Landsat albedo using available field measurements at forested AmeriFlux stations in the PNW region, and examine the consistency of the surface albedo generated by this approach respectively with that from the "concurrent" approach and the coincident MODIS operational surface albedo products. Using the tower measurements as reference, the derived Landsat 30-m snow-free shortwave broadband albedo yields an absolute accuracy of 0.02 with a root mean square error less than 0.016 and a bias of no more than 0.007. A further cross-comparison over individual scenes shows that the retrieved white sky shortwave albedo from the "pre-MODIS era" LUT approach is highly consistent (R(exp 2) = 0.988, the scene-averaged low RMSE = 0.009 and bias = 0.005) with that generated by the earlier "concurrent" approach. The Landsat albedo also exhibits more detailed landscape texture and a wider dynamic range of albedo values than the coincident 500-m MODIS operational products (MCD43A3), especially in the heterogeneous regions. Collectively, the "pre-MODIS" LUT and "concurrent" approaches provide a practical way to retrieve long-term Landsat albedo from the historic Landsat archives as far back as the 1980s, as well as the current Landsat-8 mission, and thus support investigations into the evolution of the albedo of terrestrial biomes at fine resolution

    Parameterizing anisotropic reflectance of snow surfaces from airborne digital camera observations in Antarctica

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    The surface reflection of solar radiation comprises an important boundary condition for solar radiative transfer simulations. In polar regions above snow surfaces, the surface reflection is particularly anisotropic due to low Sun elevations and the highly anisotropic scattering phase function of the snow crystals. The characterization of this surface reflection anisotropy is essential for satellite remote sensing over both the Arctic and Antarctica. To quantify the angular snow reflection properties, the hemispherical-directional reflectance factor (HDRF) of snow surfaces was derived from airborne measurements in Antarctica during austral summer in 2013/14. For this purpose, a digital 180∘ fish-eye camera (green channel, 490–585 nm wavelength band) was used. The HDRF was measured for different surface roughness conditions, optical-equivalent snow grain sizes, and solar zenith angles. The airborne observations covered an area of around 1000 km × 1000 km in the vicinity of Kohnen Station (75∘0â€Č S, 0∘4â€Č E) at the outer part of the East Antarctic Plateau. The observations include regions with higher (coastal areas) and lower (inner Antarctica) precipitation amounts and frequencies. The digital camera provided upward, angular-dependent radiance measurements from the lower hemisphere. The comparison of the measured HDRF derived for smooth and rough snow surfaces (sastrugi) showed significant differences, which are superimposed on the diurnal cycle. By inverting a semi-empirical kernel-driven bidirectional reflectance distribution function (BRDF) model, the measured HDRF of snow surfaces was parameterized as a function of solar zenith angle, surface roughness, and optical-equivalent snow grain size. This allows a direct comparison of the HDRF measurements with the BRDF derived from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite product MCD43. For the analyzed cases, MODIS observations (545–565 nm wavelength band) generally underestimated the anisotropy of the surface reflection. The largest deviations were found for the volumetric model weight fvol (average underestimation by a factor of 10). These deviations are likely linked to short-term changes in snow properties

    Variability in Surface BRDF at Different Spatial Scales (30 m-500 m) Over a Mixed Agricultural Landscape as Retrieved from Airborne and Satellite Spectral Measurements

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    Over the past decade, the role of multiangle remote sensing has been central to the development of algorithms for the retrieval of global land surface properties including models of the bidirectional reflectance distribution function (BRDF), albedo, land cover/dynamics, burned area extent, as well as other key surface biophysical quantities represented by the anisotropic reflectance characteristics of vegetation. In this study, a new retrieval strategy for fine-to-moderate resolution multiangle observations was developed, based on the operational sequence used to retrieve the Moderate Resolution Imaging Spectroradiometer (MODIS) Collection 5 reflectance and BRDF/albedo products. The algorithm makes use of a semiempirical kernel-driven bidirectional reflectance model to provide estimates of intrinsic albedo (i.e., directional-hemispherical reflectance and bihemispherical reflectance), model parameters describing the BRDF, and extensive quality assurance information. The new retrieval strategy was applied to NASA's Cloud Absorption Radiometer (CAR) data acquired during the 2007 Cloud and Land Surface Interaction Campaign (CLASIC) over the well-instrumented Atmospheric Radiation Measurement Program (ARM) Southern Great Plains (SGP) Cloud and Radiation Testbed (CART) site in Oklahoma, USA. For the case analyzed, we obtained approx.1.6 million individual surface bidirectional reflectance factor (BRF) retrievals, from nadir to 75 off-nadir, and at spatial resolutions ranging from 3 m - 500 m. This unique dataset was used to examine the interaction of the spatial and angular characteristics of a mixed agricultural landscape; and provided the basis for detailed assessments of: (1) the use of a priori knowledge in kernel-driven BRDF model inversions; (2) the interaction between surface reflectance anisotropy and instrument spatial resolution; and (3) the uncertain ties that arise when sub-pixel differences in the BRDF are aggregated to a moderate resolution satellite pixel. Results offer empirical evidence concerning the influence of scale and spatial heterogeneity in kernel-driven BRDF models; providing potential new insights into the behavior and characteristics of different surface radiative properties related to land/use cover change and vegetation structure

    Global retrieval of bidirectional reflectance and albedo over land from EOS MODIS and MISR data: Theory and algorithm

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    This paper describes the theory and the algorithm to be used in producing a global bidirectional reflectance distribution function (BRDF) and albedo product from data to be acquired by the moderate resolution imaging spectroradiometer (MODIS) and the multiangle imaging spectroradiometer (MISR), both to be launched in 1998 on the AM-I satellite platform as part of NASA's Earth Observing System (EOS). The product will be derived using the kernel-driven semiempirical Ambrals BRDF model, utilizing five variants of kernel functions characterizing isotropic, volume and surface scattering. The BRDF and the albedo of each pixel of the land surface will be modeled at a spatial resolution of I km and once every 16 days in seven spectral bands spanning the visible and the near infrared. The BRDF parameters retrieved and recorded in the MODIS BRDF/albedo product will be intrinsic surface properties decoupled from the prevailing atmospheric state and hence suited for a wide range of applications requiring characterization of the directional anisotropy of Earth surface reflectance. A set of quality control flags accompanies the product. An initial validation of the Ambrals model is demonstrated using a variety of field-measured data sets for several different land cover types

    Assessing change in the Earth's land surface albedo with moderate resolution satellite imagery

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    Land surface albedo describes the proportion of incident solar radiant flux that is reflected from the Earth's surface and therefore is a crucial parameter in modeling and monitoring attempts to capture the current climate, hydrological, and biogeochemical cycles and predict future scenarios. Due to the temporal variability and spatial heterogeneity of land surface albedo, remote sensing offers the only realistic method of monitoring albedo on a global scale. While the distribution of bright, highly reflective surfaces (clouds, snow, deserts) govern the vast majority of the fluctuation, variations in the intrinsic surface albedo due to natural and human disturbances such as urban development, fire, pests, harvesting, grazing, flooding, and erosion, as well as the natural seasonal rhythm of vegetation phenology, play a significant role as well. The development of times series of global snow-free and cloud-free albedo from remotely sensed observations over the past decade and a half offers a unique opportunity to monitor and assess the impact of these alterations to the Earth's land surface. By utilizing multiple satellite records from the MODerate-resolution Imaging Spectroradiometer (MODIS), the Multi-angle Imaging Spectroradiometer (MISR) and the Visible Infrared Imaging Radiometer Suite (VIIRS) instruments, and developing innovative spectral conversion coefficients and temporal gap-filling strategies, it has been possible to utilize the strengths of the various sensors to improve the spatial and temporal coverage of global land surface albedo retrievals. The availability of these products is particularly important in tropical regions where cloud cover obscures the forest for significant periods. In the Amazon, field ecologists have noted that some areas of the forest ecosystem respond rapidly with foliage growth at the beginning of the dry season, when sunlight can finally penetrate fully to the surface and have suggested this phenomenon can continue until reductions in water availability (particularly in times of drought) impact the growth cycle. While it has been difficult to capture this variability from individual optical satellite sensors, the temporally gap-filled albedo products developed during this research are used in a case study to monitor the Amazon during the dry season and identify the extent of these regions of foliage growth

    Suivi des flux d'énergie, d'eau et de carbone à la surface : apport de la télédétection et de la modélisation du rayonnement solaire absorbé par la végétation

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    It is known that a global 4% increase of land surface albedo (also called reflectivity) may result approximately in a decrease of 0.7°C in the Earth’s equilibrium temperature. Nowadays the surface properties (including albedo) are changing under climatic and human pressure. At the same time, there is a debate that divides the scientific community about the potential trends (increase or decrease) affecting the surface incoming solar radiation since mid-1980 (resulting of a decrease or increase of aerosol concentration in the atmosphere, respectively). The Earth is a complex system driven at the surface level by three cycles (energy, water, and carbon). These cycles are not insensitive to changes of surface reflectivity, incoming radiation, or aerosol properties. For example, some argue that the increase of diffuse radiation during the last decades would have led to an exceed of carbon uptake by the Earth’s vegetation of 9.3%. The main issue raised here is to assess the added value of the knowledge in absorbed solar radiation by the surface (combination of incoming solar radiation with surface albedo) and, especially, by the vegetation for the monitoring of energy, water and carbon fluxes.In this work, I have used satellite observations and modeled the radiative transfer theory in order to make dynamic mapping of solar radiation absorbed by the surface and through the vertical dimension of the vegetation. First, I quantified each uncertainty source affecting incoming solar radiation, surface albedo and the way radiation is split between horizontal and vertical heterogeneity. In a second step, I measured the added value of using this absorbed radiation mapping of the surface by satellite to estimate the energy and water fluxes at the surface. The resulting improved scores of weather forecast models in the short-range time scale suggested potential feedbacks at the climatic time scale over sensible areas such as the Sahel region. Another significant outcome is that the developments proposed to better characterize the vertical heterogeneity within the canopy led to an improvement of 15% of annual global terrestrial gross primary production (GPP). Moreover, this study has led to measure the impact of the lack of knowledge of spatial and temporal variability of aerosol properties (concentration and type). I have shown that the tracking of temporal changes of directional properties of reflectance allows me to retrieve to the amount of aerosols in the atmosphere as precisely as other widely used methods but with a higher frequency (5 times more) by using data from geostationary satellite. Finally, this study addresses some possibilities to better track temporal changes of properties of reflectivity of surface and aerosol of atmosphere, and to access to a better monitoring of biogeochemical cycles of the terrestrial biosphere.Au niveau global, il a Ă©tĂ© estimĂ© qu’une augmentation de 4% de l’albĂ©do (ou rĂ©flectivitĂ©) de la surface provoquerait une diminution de 0,7° de la tempĂ©rature d’équilibre de la Terre. Or les propriĂ©tĂ©s des surfaces (dont l’albĂ©do) changent sous la pression climatique et l’action de l’homme. ParallĂšlement Ă  ce changement des propriĂ©tĂ©s de surface un dĂ©bat divise la communautĂ© scientifique sur une Ă©ventuelle diminution ou augmentation du rayonnement incident Ă  la surface depuis le milieu des annĂ©es 1980 (consĂ©quence d’une augmentation ou diminution de la concentration d’aĂ©rosols dans l’atmosphĂšre). La Terre est un systĂšme complexe pilotĂ© en sa surface par 3 cycles (Ă©nergie, eau et carbone). Ces cycles ne sont pas insensibles Ă  ces changements de propriĂ©tĂ© de rĂ©flectivitĂ© de surface, de rayonnement solaire incident ou de concentration en aĂ©rosols. Certains avancent ainsi qu’une augmentation du rayonnement diffus durant les derniĂšres dĂ©cennies aurait dĂ©jĂ  entraĂźnĂ© un excĂ©dent de captation de carbone par la vĂ©gĂ©tation de 9.3%. La problĂ©matique ici soulevĂ©e est d’évaluer l’apport de la connaissance du flux solaire absorbĂ© par la surface (combinaison du rayonnement solaire et de l’albĂ©do de surface) et plus particuliĂšrement par sa partie vĂ©gĂ©tative pour le suivi des flux d’énergie, d’eau et de carbone. Dans ce travail, j’ai fait appel Ă  l’observation satellitaire et Ă  la modĂ©lisation du transfert radiatif pour cartographier la dynamique du rayonnement solaire absorbĂ© par la surface et sur la verticale de la vĂ©gĂ©tation. Dans un premier temps, chacune des sources d’incertitudes sur le rayonnement incident, sur l’albĂ©do de surface mais aussi sur la rĂ©partition du rayonnement entre les hĂ©tĂ©rogĂ©nĂ©itĂ©s horizontales et verticales Ă  la surface furent quantifiĂ©es. Puis tout en discutant l’effet de ces incertitudes, j’ai mesurĂ© l’apport de l’utilisation de cette cartographie par satellite du rayonnement solaire absorbĂ© pour estimer les flux d’énergie et d’eau en surface ; ce qui amĂ©liora les scores de prĂ©vision du temps Ă  court terme et permis Ă©galement de suggĂ©rer des rĂ©troactions Ă  l’échelle climatique sur des zones sensibles tel le Sahel. Aussi une correction de biais de 15% sur l’estimation de la production primaire brute de carbone Ă  l’échelle planĂ©taire dĂ©montra l’importance des dĂ©veloppements rĂ©alisĂ©s afin de caractĂ©riser les hĂ©tĂ©rogĂ©nĂ©itĂ©s verticales dans le couvert. Finalement, ce travail m’a conduit Ă  chiffrer l’impact de la mĂ©connaissance des variabilitĂ©s spatiales et temporelles des propriĂ©tĂ©s des aĂ©rosols (concentration et type). J’ai montrĂ© que le suivi au cours du temps des propriĂ©tĂ©s de directionalitĂ© de la rĂ©flectivitĂ© de surface (tel abordĂ© dans la premiĂšre partie de mon Ă©tude) pouvait aussi permettre de remonter Ă  la quantitĂ© d’aĂ©rosol dans l’atmosphĂšre. L’utilisation d’observations issues de satellite gĂ©ostationnaire permet d’estimer la concentration en aĂ©rosol avec la mĂȘme qualitĂ© mais avec une frĂ©quence de dĂ©tection plus Ă©levĂ©e (x5 environ) que les mĂ©thodes classiques. Enfin, ce travail dresse des pistes pour amĂ©liorer la dĂ©tection des changements des propriĂ©tĂ©s de rĂ©flectivitĂ© de surface et d’aĂ©rosols de l’atmosphĂšre, et atteindre un suivi encore meilleur des cycles biogĂ©ochimiques de la biosphĂšre terrestre

    A model to estimate daily albedo from remote sensing data : accuracy assessment of MODIS MCD43 product

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    L’albedo superficial Ă©s un parĂ metre fĂ­sic que afecta al clima de la Terra i, a mĂ©s, suposa una de les majors incerteses radiatives en l’actual modelitzaciĂł climĂ tica. Aquest parĂ metre Ă©s molt variable tant a nivell espacial com temporal degut als canvis en les propietats de les superfĂ­cies i als canvis en les condicions d’il‱luminaciĂł. En conseqĂŒĂšncia, es requereix una resoluciĂł temporal diĂ ria de l’albedo per a realitzar estudis climĂ tics. L’augment de la resoluciĂł espacial dels models climĂ tics fa necessari l’estudi de les seues caracterĂ­stiques espacials a nivell global. La teledetecciĂł proporciona l’Ășnica opciĂł prĂ ctica de proporcionar dades d’albedo a nivell global amb alta qualitat i alta resoluciĂł tant espacial com temporal. El sensor MODerate Resolution Imaging Spectroradiometer (MODIS) a bord dels satĂšl‱lits Terra i Aqua presenta unes caracterĂ­stiques adequades per a l’estimaciĂł d’aquest parĂ metre. En el present treball realitzem diversos estudis buscant les possibles fonts d’incertesa del producte oficial d’albedo de MODIS (MCD43). A mĂ©s, presentem un model que millora la resoluciĂł temporal d’aquest parĂ metre.Surface albedo is a critical land physical parameter affecting the earth’s climate and is among the main radiative uncertainties in current climate modelling. This parameter is highly variable in space and time, both as a result of changes in surface properties and as a function of changes in the illumination conditions. Consequently, an albedo daily temporal resolution is required for climate studies. The increasing spatial resolution of modern climate models makes it necessary to examine its spatial features. Satellite remote sensing provides the only practical way of producing high-quality global albedo data sets with high spatial and temporal resolutions. The MODerate Resolution Imaging Spectroradiometer (MODIS) sensor on board the Terra and Aqua satellites presents the required sampling characteristics in order to derive the this parameter. In this PhD we develop several studies looking for the improvement of the official MODIS albedo product (MCD43) accuracy. Moreover, we present a model that improves the temporal resolution of this parameter

    An improved BRDF hotspot model and its use in VLIDORT for studying the impact of atmospheric scattering on hotspot directional signatures in the atmosphere

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    The term “hotspot” refers to the sharp increase in the reflectance occurring when incident (solar) and reflected (viewing) directions almost coincide in the backscatter direction. The accurate simulation of hotspot directional signatures is important for many remote sensing applications. The RossThick–LiSparse–Reciprocal (RTLSR) bidirectional reflectance distribution function (BRDF) model is widely used in radiative transfer simulations, and the hotspot model mostly used is from Maignan–BrĂ©on, but it typically requires large values of numerical quadrature and Fourier expansion terms in order to represent the hotspot accurately for its use coupled with atmospheric radiative transfer modeling (RTM). In this paper, we have developed a modified version based on the Maignan–BrĂ©on's hotspot BRDF model that converges much faster numerically, making it more practical for use in the RTMs that require Fourier expansion of BRDF to simulate the top-of-atmosphere (TOA) hotspot signatures, such as in the RTM models using the Doubling–Adding or discrete ordinate method. Using the vector linearized discrete ordinate radiative transfer model (VLIDORT), we found that reasonable TOA–hotspot accuracy can be obtained with just 23 Fourier terms for clear atmosphere and 63 Fourier terms for atmosphere with aerosol scattering. In order to study the impact of molecular and aerosol scattering on hotspot signatures, we carried out a number of hotspot signature simulations with VLIDORT. We confirmed that (1) atmospheric molecule scattering and the existence of aerosol tend to smooth out the hotspot signature at the TOA and that (2) the hotspot signature at the TOA in the near-infrared is larger than in the visible, and its impact by surface reflectance is more significant. As the hotspot amplitude at the TOA with aerosol scattering included is smaller than that with molecular scattering only, the amplitude of hotspot signature at the surface is likely underestimated in the previous analysis based on the POLDER measurements, where the atmospheric correction was based on a single-scatter Rayleigh-only calculation. This modified model can calculate the amplitude of the hotspot accurately, and, as it agrees very well with the original RossThick model away from the hotspot region, this model can be simply used in conditions with and without hotspots. However, there are some differences in this modified model compared to the original Maignan–BrĂ©on model for the scattering angles close to the hotspot point; thus, it may not be appropriate for those who need an exact representation of the hotspot angular signature.</p

    Improved estimation of surface biophysical parameters through inversion of linear BRDF models

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