Special Issue "Radiative Transfer Modelling and Applications in Remote Sensing"

A special issue of Remote Sensing (ISSN 2072-4292).

Deadline for manuscript submissions: closed (31 July 2018).

Special Issue Editors

Dr. Yuri Knyazikhin
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Guest Editor
Boston University, 675 Commonwealth Avenue, Boston, MA 02215, USA
Interests: forward and inverse radiative transfer theory; developing satellite products; numerical radiative transfer equation; analyses of satellite data
Dr. Alexander Marshak
E-Mail Website
Guest Editor
NASA/GSFC, 8800 Greenbelt Rd, Greenbelt, MD 20771-2400
Tel. 301-614-6122
Interests: radiative transfer in clouds and vegetation canopy; active and passive remote sensing of clouds and aerosol; analysis of geophysical datasets
Dr. Matti Mõttus
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Guest Editor
VTT Technical Research Centre of Finland, PO Box 1000, Tekniikantie 1, Espoo, FIN-02044 VTT, Finland
Tel. +358 40 849 3037
Interests: forest reflectance models; imaging spectroscopy of vegetation photosynthesis; application of photon recollision probability in vegetation reflectance models; spectral measurements from leaf to canopy scales; radiation field inside vegetation canopies; hyperspectral remote sensing

Special Issue Information

Dear Colleagues,

The radiative transfer theory provides the most logical linkage between observations and physical processes that generate signals in optical remote sensing. The radiative transfer equation, therefore, is an integral part of Earth remote sensing, since it provides the most efficient tool for accurate retrievals of Earth properties from satellite data. Advances in radiative transfer modeling enhance our ability to detect and monitor changes in our planet through new methodologies and technical approaches to analyze and interpret measurements from space-borne sensors.

We invite scientists working on forward and inverse radiative transfer to contribute to this Special Issue. Topics of interest include (a) theoretical aspects of radiative transfer that can advance remote sensing techniques; (b) models for radiative transfer in the atmosphere and the Earth's surface that further our understanding of information content of multiangle, spectral and polarimetric data; (c) analyses of 3D effects in radiative transfer and associated uncertainties in interpretation of remotely sensed data; and (d) methodologies that minimize the discretizing effects in numerical solutions of the radiative transfer equation. Contributions related to development of various indices that correlate with parameters of the atmosphere and land surface are also encouraged. However, we expect that such papers will provide analyses of underlying physical mechanisms of the correlation, which is required to distinguish causality from correlations in interpretation of remote sensing data. 

Dr. Yuri Knyazikhin
Dr. Alexander Marshak
Dr. Matti Mõttus
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Remote Sensing is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • radiative transfer equation
  • inverse technique
  • multiangle, spectral and polarimetric signals
  • computational methods
  • remote sensing indices

Published Papers (12 papers)

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Research

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Open AccessArticle
Decoupling Canopy Structure and Leaf Biochemistry: Testing the Utility of Directional Area Scattering Factor (DASF)
Remote Sens. 2018, 10(12), 1911; https://doi.org/10.3390/rs10121911 - 29 Nov 2018
Abstract
Biochemical properties retrieved from remote sensing data are crucial sources of information for many applications. However, leaf and canopy scattering processes must be accounted for to reliably estimate information on canopy biochemistry, carbon-cycle processes and energy exchange. A coupled leaf-canopy model based on [...] Read more.
Biochemical properties retrieved from remote sensing data are crucial sources of information for many applications. However, leaf and canopy scattering processes must be accounted for to reliably estimate information on canopy biochemistry, carbon-cycle processes and energy exchange. A coupled leaf-canopy model based on spectral invariants theory has been proposed, that uses the so-called Directional Area Scattering Factor (DASF) to correct hyperspectral remote sensing data for canopy structural effects. In this study, the reliability of DASF to decouple canopy structure and biochemistry was empirically tested using simulated reflectance spectra modelled using a Monte Carlo Ray Tracing (MCRT) radiative transfer model. This approach allows all canopy and radiative properties to be specified a priori. Simulations were performed under idealised conditions of directional-hemispherical reflectance, isotropic Lambertian leaf reflectance and transmittance and sufficiently dense (high LAI) canopies with black soil where the impact of canopy background is negligible, and also departures from these conditions. It was shown that both DASF and total canopy scattering could be accurately extracted under idealised conditions using information from both the full 400–2500 nm spectral interval and the 710–790 nm interval alone, even given no prior knowledge of leaf optical properties. Departures from these idealised conditions: varying view geometry, bi-directional reflectance, LAI and soil effects, were tested. We demonstrate that total canopy scattering could be retrieved under conditions of varying view geometry and bi-directional reflectance, but LAI and soil effects were shown to reduce the accuracy with which the scattering can be modelled using the DASF approach. We show that canopy architecture, either homogeneous or heterogeneous 3D arrangements of canopy scattering elements, has important influences over DASF and consequently the accuracy of retrieval of total canopy scattering. Finally, although DASF and total canopy scattering could be retrieved to within 2.4% of the modelled total canopy scattering signal given no prior knowledge of leaf optical properties, spectral invariant parameters were not accurately retrieved from the simulated signal. This has important consequences since these parameters are quite widely used in canopy reflectance modelling and have the potential to help derive new, more accurate canopy biophysical information. Understanding and quantifying the limitations of the DASF approach as we have done here, is an important step in allowing the wider use of these methods for decoupling canopy structure and biochemistry. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
Application of a Three-Dimensional Radiative Transfer Model to Retrieve the Species Composition of a Mixed Forest Stand from Canopy Reflected Radiation
Remote Sens. 2018, 10(10), 1661; https://doi.org/10.3390/rs10101661 - 20 Oct 2018
Abstract
The paper introduces a three-dimensional model to derive the spatial patterns of photosynthetically active radiation (PAR) reflected and absorbed by a non-uniform forest canopy with a multi-species structure, as well as a model algorithm application to retrieve forest canopy composition from reflected PAR [...] Read more.
The paper introduces a three-dimensional model to derive the spatial patterns of photosynthetically active radiation (PAR) reflected and absorbed by a non-uniform forest canopy with a multi-species structure, as well as a model algorithm application to retrieve forest canopy composition from reflected PAR measured along some trajectory above the forest stand. This radiative transfer model is based on steady-state transport equations, initially suggested by Ross, and considers the radiative transfer as a function of the structure of individual trees and forest canopy, optical properties of photosynthesizing and non-photosynthesizing parts of the different tree species, soil reflection, and the ratio of incoming direct and diffuse solar radiation. Numerical experiments showed that reflected solar radiation of a typical mixed forest stand consisting of coniferous and deciduous tree species was strongly governed by canopy structure, soil properties and sun elevation. The suggested algorithm based on the developed model allows for retrieving the proportion of different tree species in a mixed forest stand from measured canopy reflection coefficients. The method accuracy strictly depends on the number of points for canopy reflection measurements. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
Influence of Leaf Specular Reflection on Canopy Radiative Regime Using an Improved Version of the Stochastic Radiative Transfer Model
Remote Sens. 2018, 10(10), 1632; https://doi.org/10.3390/rs10101632 - 14 Oct 2018
Abstract
Interpreting remotely-sensed data requires realistic, but simple, models of radiative transfer that occurs within a vegetation canopy. In this paper, an improved version of the stochastic radiative transfer model (SRTM) is proposed by assuming that all photons that have not been specularly reflected [...] Read more.
Interpreting remotely-sensed data requires realistic, but simple, models of radiative transfer that occurs within a vegetation canopy. In this paper, an improved version of the stochastic radiative transfer model (SRTM) is proposed by assuming that all photons that have not been specularly reflected enter the leaf interior. The contribution of leaf specular reflection is considered by modifying leaf scattering phase function using Fresnel reflectance. The canopy bidirectional reflectance factor (BRF) estimated from this model is evaluated through comparisons with field-measured maize BRF. The result shows that accounting for leaf specular reflection can provide better performance than that when leaf specular reflection is neglected over a wide range of view zenith angles. The improved version of the SRTM is further adopted to investigate the influence of leaf specular reflection on the canopy radiative regime, with emphases on vertical profiles of mean radiation flux density, canopy absorptance, BRF, and normalized difference vegetation index (NDVI). It is demonstrated that accounting for leaf specular reflection can increase leaf albedo, which consequently increases canopy mean upward/downward mean radiation flux density and canopy nadir BRF and decreases canopy absorptance and canopy nadir NDVI when leaf angles are spherically distributed. The influence is greater for downward/upward radiation flux densities and canopy nadir BRF than that for canopy absorptance and NDVI. The results provide knowledge of leaf specular reflection and canopy radiative regime, and are helpful for forward reflectance simulations and backward inversions. Moreover, polarization measurements are suggested for studies of leaf specular reflection, as leaf specular reflection is closely related to the canopy polarization. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
Implications of Whole-Disc DSCOVR EPIC Spectral Observations for Estimating Earth’s Spectral Reflectivity Based on Low-Earth-Orbiting and Geostationary Observations
Remote Sens. 2018, 10(10), 1594; https://doi.org/10.3390/rs10101594 - 05 Oct 2018
Cited by 2
Abstract
Earth’s reflectivity is among the key parameters of climate research. National Aeronautics and Space Administration (NASA)’s Earth Polychromatic Imaging Camera (EPIC) onboard National Oceanic and Atmospheric Administration (NOAA)’s Deep Space Climate Observatory (DSCOVR) spacecraft provides spectral reflectance of the entire sunlit Earth in [...] Read more.
Earth’s reflectivity is among the key parameters of climate research. National Aeronautics and Space Administration (NASA)’s Earth Polychromatic Imaging Camera (EPIC) onboard National Oceanic and Atmospheric Administration (NOAA)’s Deep Space Climate Observatory (DSCOVR) spacecraft provides spectral reflectance of the entire sunlit Earth in the near backscattering direction every 65 to 110 min. Unlike EPIC, sensors onboard the Earth Orbiting Satellites (EOS) sample reflectance over swaths at a specific local solar time (LST) or over a fixed area. Such intrinsic sampling limits result in an apparent Earth’s reflectivity. We generated spectral reflectance over sampling areas using EPIC data. The difference between the EPIC and EOS estimates is an uncertainty in Earth’s reflectivity. We developed an Earth Reflector Type Index (ERTI) to discriminate between major Earth atmosphere components: clouds, cloud-free ocean, bare and vegetated land. Temporal variations in Earth’s reflectivity are mostly determined by clouds. The sampling area of EOS sensors may not be sufficient to represent cloud variability, resulting in biased estimates. Taking EPIC reflectivity as a reference, low-earth-orbiting-measurements at the sensor-specific LST tend to overestimate EPIC values by 0.8% to 8%. Biases in geostationary orbiting approximations due to a limited sampling area are between 0.7 % and 12%. Analyses of ERTI-based Earth component reflectivity indicate that the disagreement between EPIC and EOS estimates depends on the sampling area, observation time and vary between 10 % and 23%. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
Spectral Invariant Provides a Practical Modeling Approach for Future Biophysical Variable Estimations
Remote Sens. 2018, 10(10), 1508; https://doi.org/10.3390/rs10101508 - 20 Sep 2018
Cited by 3
Abstract
This paper presents a simple radiative transfer model based on spectral invariant properties (SIP). The canopy structure parameters, including the leaf angle distribution and multi-angular clumping index, are explicitly described in the SIP model. The SIP model has been evaluated on its bidirectional [...] Read more.
This paper presents a simple radiative transfer model based on spectral invariant properties (SIP). The canopy structure parameters, including the leaf angle distribution and multi-angular clumping index, are explicitly described in the SIP model. The SIP model has been evaluated on its bidirectional reflectance factor (BRF) in the angular space at the radiation transfer model intercomparison platform, and in the spectrum space by the PROSPECT+SAIL (PROSAIL) model. The simulations of BRF by SIP agreed well with the reference values in both the angular space and spectrum space, with a root-mean-square-error (RMSE) of 0.006. When compared with the widely-used Soil-Canopy Observation of Photochemistry and Energy fluxes (SCOPE) model on fPAR, the RMSE was 0.006 and the R2 was 0.99, which shows a high accuracy. This study also suggests the newly proposed vegetation index, the near-infrared (NIR) reflectance of vegetation (NIRv), was a good linear approximation of the canopy structure parameter, the directional area scattering factor (DASF), with an R2 of 0.99. NIRv was not influenced much by the soil background contribution, but was sensitive to the leaf inclination angle. The sensitivity of NIRv to canopy structure and the robustness of NIRv to the soil background suggest NIRv is a promising index in future biophysical variable estimations with the support of the SIP model, especially for the Deep Space Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) observations near the hot spot directions. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
Simulation of Bidirectional Reflectance in Broken Clouds: From Individual Realization to Averaging over an Ensemble of Cloud Fields
Remote Sens. 2018, 10(9), 1342; https://doi.org/10.3390/rs10091342 - 22 Aug 2018
Cited by 1
Abstract
In this paper, we describe the results of simulating the bidirectional reflectance in three-dimensional (3D) cloud fields. For the calculations of reflectance, we use original statistical algorithms that ensure the effects of atmospheric sphericity and molecular absorption in the solar spectral range are [...] Read more.
In this paper, we describe the results of simulating the bidirectional reflectance in three-dimensional (3D) cloud fields. For the calculations of reflectance, we use original statistical algorithms that ensure the effects of atmospheric sphericity and molecular absorption in the solar spectral range are accounted for. Cloud fields are simulated on the basis of a Poisson model of broken clouds; clouds are approximated by truncated paraboloids of rotation. The cloud heterogeneity effect on the averaging of reflection functions over an ensemble of cloud fields is estimated using numerical averaging of the stochastic radiative transfer equation, using a randomization. The simulation is performed for a mono-directional receiver with wavelength channels 0.55 and 2.15 µm, different realizations with small and moderate cloud fractions, and a set of sun-view geometries. With the appearance of an isolated cloud in the sky, the reflection function is determined by cloud presence/absence on the line of sight (LS), shading of LS by clouds/non-obscuration directed “toward the Sun,” and illumination of LS by cloud-reflected radiation. Passage to cloud fields gives rise to such additional factors as mutual shading and multiple scattering between clouds, which are mainly determined by cloud elements located near LS and directed “toward the Sun”. Strong fluctuations of reflectance as a function of the relative azimuth angle between sun and view directions in a specific realization are smoothed out after averaging over an ensemble of cloud fields. In interpreting the results of retrieving the cloud characteristics according to measurements of reflected radiation, it should be kept in mind that for fixed illumination conditions, the mean bidirectional reflectance may differ several-fold from bidirectional reflectance in a specific 3D cloud structure. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
Accelerated RAPID Model Using Heterogeneous Porous Objects
Remote Sens. 2018, 10(8), 1264; https://doi.org/10.3390/rs10081264 - 11 Aug 2018
Cited by 1
Abstract
To enhance the capability of three-dimensional (3D) radiative transfer models at the kilometer scale (km-scale), the radiosity applicable to porous individual objects (RAPID) model has been upgraded to RAPID3. The major innovation is that the homogeneous porous object concept (HOMOBJ) used for a [...] Read more.
To enhance the capability of three-dimensional (3D) radiative transfer models at the kilometer scale (km-scale), the radiosity applicable to porous individual objects (RAPID) model has been upgraded to RAPID3. The major innovation is that the homogeneous porous object concept (HOMOBJ) used for a tree crown scale is extended to a heterogeneous porous object (HETOBJ) for a forest plot scale. Correspondingly, the radiosity-graphics-combined method has been extended from HOMOBJ to HETOBJ, including the random dynamic projection algorithm, the updated modules of view factors, the single scattering estimation, the multiple scattering solutions, and the bidirectional reflectance factor (BRF) calculations. Five cases of the third radiation transfer model intercomparison (RAMI-3) have been used to verify RAPID3 by the RAMI-3 online checker. Seven scenes with different degrees of topography (valleys and hills) at 500 m size have also been simulated. Using a personal computer (CPU 2.5 GHz, memory 4 GB), the computation time of BRF at 500 m is only approximately 13 min per scene. The mean root mean square error is 0.015. RAPID3 simulated the enhanced contrast of BRF between backward and forward directions due to topography. RAPID3 has been integrated into the free RAPID platform, which should be very useful for the remote sensing community. In addition, the HETOBJ concept may also be useful for the speedup of ray tracing models. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
Maximizing the Information Content of Ill-Posed Space-Based Measurements Using Deterministic Inverse Method
Remote Sens. 2018, 10(7), 994; https://doi.org/10.3390/rs10070994 - 22 Jun 2018
Cited by 2
Abstract
For several decades, operational retrievals from spaceborne hyperspectral infrared sounders have been dominated by stochastic approaches where many ambiguities are pervasive. One major drawback of such methods is their reliance on treating error as definitive information to the retrieval scheme. To overcome this [...] Read more.
For several decades, operational retrievals from spaceborne hyperspectral infrared sounders have been dominated by stochastic approaches where many ambiguities are pervasive. One major drawback of such methods is their reliance on treating error as definitive information to the retrieval scheme. To overcome this drawback and obtain consistently unambiguous retrievals, we applied another approach from the class of deterministic inverse methods, namely regularized total least squares (RTLS). As a case study, simultaneous simulated retrieval of ozone (O3) profile and surface temperature (ST) for two different instruments, Cross-track Infrared Sounder (CrIS) and Tropospheric Emission Spectrometer (TES), are considered. To gain further confidence in our approach for real-world situations, a set of ozonesonde profile data are also used in this study. The role of simulation-based comparative assessment of algorithms before application on remotely sensed measurements is pivotal. Under identical simulation settings, RTLS results are compared to those of stochastic optimal estimation method (OEM), a very popular method for hyperspectral retrievals despite its aforementioned fundamental drawback. Different tweaking of error covariances for improving the OEM results, used commonly in operations, are also investigated under a simulated environment. Although this work is an extension of our previous work for H2O profile retrievals, several new concepts are introduced in this study: (a) the information content analysis using sub-space analysis to understand ill-posed inversion in depth; (b) comparison of different sensors for same gas profile retrieval under identical conditions; (c) extended capability for simultaneous retrievals using two classes of variables; (d) additional stabilizer of Laplacian second derivative operator; and (e) the representation of results using a new metric called “information gain”. Our findings highlight issues with OEM, such as loss of information as compared to a priori knowledge after using measurements. On the other hand, RTLS can produce “information gain” of ~40–50% deterministically from the same set of measurements. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessFeature PaperEditor’s ChoiceArticle
Realistic Forest Stand Reconstruction from Terrestrial LiDAR for Radiative Transfer Modelling
Remote Sens. 2018, 10(6), 933; https://doi.org/10.3390/rs10060933 - 13 Jun 2018
Cited by 17
Abstract
Forest biophysical variables derived from remote sensing observations are vital for climate research. The combination of structurally and radiometrically accurate 3D “virtual” forests with radiative transfer (RT) models creates a powerful tool to facilitate the calibration and validation of remote sensing data and [...] Read more.
Forest biophysical variables derived from remote sensing observations are vital for climate research. The combination of structurally and radiometrically accurate 3D “virtual” forests with radiative transfer (RT) models creates a powerful tool to facilitate the calibration and validation of remote sensing data and derived biophysical products by helping us understand the assumptions made in data processing algorithms. We present a workflow that uses highly detailed 3D terrestrial laser scanning (TLS) data to generate virtual forests for RT model simulations. Our approach to forest stand reconstruction from a co-registered point cloud is unique as it models each tree individually. Our approach follows three steps: (1) tree segmentation; (2) tree structure modelling and (3) leaf addition. To demonstrate this approach, we present the measurement and construction of a one hectare model of the deciduous forest in Wytham Woods (Oxford, UK). The model contains 559 individual trees. We matched the TLS data with traditional census data to determine the species of each individual tree and allocate species-specific radiometric properties. Our modelling framework is generic, highly transferable and adjustable to data collected with other TLS instruments and different ecosystems. The Wytham Woods virtual forest is made publicly available through an online repository. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
A Method of Retrieving BRDF from Surface-Reflected Radiance Using Decoupling of Atmospheric Radiative Transfer and Surface Reflection
Remote Sens. 2018, 10(4), 591; https://doi.org/10.3390/rs10040591 - 11 Apr 2018
Cited by 1
Abstract
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 used in aerosol retrievals, cloud retrievals, atmospheric modeling, and other applications. Ground based measurements of reflected radiance draw increasing [...] Read more.
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 used in aerosol retrievals, cloud retrievals, atmospheric modeling, and other applications. Ground based measurements of reflected radiance draw increasing attention as a source of information about anisotropy of surface reflection. Derivation of BRDF from surface radiance requires atmospheric correction. This study develops a new method of retrieving BRDF on its whole domain, making it immediately suitable for further atmospheric RT modeling applications. The method is based on the integral equation relating surface-reflected radiance, BRDF, and solutions of two auxiliary atmosphere-only RT problems. The method requires kernel-based BRDF. The weights of the kernels are obtained with a quickly converging iterative procedure. RT modeling has to be done only one time before the start of iterative process. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Open AccessArticle
EPIC Spectral Observations of Variability in Earth’s Global Reflectance
Remote Sens. 2018, 10(2), 254; https://doi.org/10.3390/rs10020254 - 07 Feb 2018
Cited by 5
Abstract
NASA’s Earth Polychromatic Imaging Camera (EPIC) onboard NOAA’s Deep Space Climate Observatory (DSCOVR) satellite observes the entire sunlit Earth every 65 to 110 min from the Sun–Earth Lagrangian L1 point. This paper presents initial EPIC shortwave spectral observations of the sunlit Earth reflectance [...] Read more.
NASA’s Earth Polychromatic Imaging Camera (EPIC) onboard NOAA’s Deep Space Climate Observatory (DSCOVR) satellite observes the entire sunlit Earth every 65 to 110 min from the Sun–Earth Lagrangian L1 point. This paper presents initial EPIC shortwave spectral observations of the sunlit Earth reflectance and analyses of its diurnal and seasonal variations. The results show that the reflectance depends mostly on (1) the ratio between land and ocean areas exposed to the Sun and (2) cloud spatial and temporal distributions over the sunlit side of Earth. In particular, the paper shows that (a) diurnal variations of the Earth’s reflectance are determined mostly by periodic changes in the land–ocean fraction of its the sunlit side; (b) the daily reflectance displays clear seasonal variations that are significant even without including the contributions from snow and ice in the polar regions (which can enhance daily mean reflectances by up to 2 to 6% in winter and up to 1 to 4% in summer); (c) the seasonal variations of the sunlit Earth reflectance are mostly determined by the latitudinal distribution of oceanic clouds. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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Review

Jump to: Research

Open AccessReview
An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes
Remote Sens. 2018, 10(11), 1805; https://doi.org/10.3390/rs10111805 - 14 Nov 2018
Cited by 2
Abstract
Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead [...] Read more.
Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere. Full article
(This article belongs to the Special Issue Radiative Transfer Modelling and Applications in Remote Sensing)
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