A Within-Leaf Radiative Transfer Model with Anisotropic Scattering
The development of a within-leaf radiative transfer model for application to satellite remote sensing of terrestrial vegetation is described.
Ganapol, B. D.↗
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Radiative transfer modelling of discontinuous tree canopies at microwave frequencies
Development of a first-order radiative transfer model for predicting backscatter from tree canopies has been underway at the University of Michigan Radiation Laboratory for some time. This model is known as the Michigan Microwave Canopy Scattering (MIMICS) model. This article presents the second-generation MIMICS model (MIMICS II) which accounts for canopies with discontinuous (open) crown layer geometries. MIMICS II models open crown layers by treating the location, size, and shape of the individual tree crowns as random variables. The backscattering coefficients for the canopy are then determined by introducing statistics derived from these parameters into the radiative transfer solution. Application of the radiative transfer equations to the discontinuous canopy geometry is presented. The resulting model is a robust fully polarimetric solution that is applicable over a wide variety of canopy architectures. Model simulations are compared to results generated with the continuous canopy model. The effect of the open crown geometry is found to be most significant at shallow incidence angles and at high frequencies for trees with well-developed crowns. Under these conditions, the gaps in the crown layer give rise to a notable increase in crown layer transmissivity which allows the radar to see through to the lower layers of the canopy more easily, thereby directly affecting the backscatter contribution of the trunks and ground.
Mcdonald, K. C.↗
SNAP-8 boiler performance degradation and two-phase flow heat and momentum transfer models
SNAP-8 boiler performance degradation and two phase flow heat and momentum transfer models
Poppendiek, H. F.↗
On the assumption of vanishing temperature fluctuations at the wall for heat transfer modeling
Boundary conditions for fluctuating wall temperature are required for near-wall heat transfer modeling. However, their correct specifications for arbitrary thermal boundary conditions are not clear. The conventional approach is to assume zero fluctuating wall temperature or zero gradient for the temperature variance at the wall. These are idealized specifications and the latter condition could lead to an ill posed problem for fully-developed pipe and channel flows. In this paper, the validity and extent of the zero fluctuating wall temperature condition for heat transfer calculations is examined. The approach taken is to assume a Taylor expansion in the wall normal coordinate for the fluctuating temperature that is general enough to account for both zero and non-zero value at the wall. Turbulent conductivity is calculated from the temperature variance and its dissipation rate. Heat transfer calculations assuming both zero and non-zero fluctuating wall temperature reveal that the zero fluctuating wall temperature assumption is in general valid. The effects of non-zero fluctuating wall temperature are limited only to a very small region near the wall.
Sommer, T. P.↗
Discrete anisotropic radiative transfer modelling of solar-induced chlorophyll fluorescence: Structural impacts in geometrically explicit vegetation canopies
Solar-induced fluorescence (SIF) is a subtle but informative optical signal of vegetation photosynthesis. Remotely sensed SIF integrates environmental, physiological and structural changes that alter photosynthesis at leaf, plant and canopy scales. Radiative transfer models are ideally suited to investigate the complex sources of variability in the SIF signal to guide the interpretation of SIF retrievals from airborne and space-borne platforms. Here, we coupled the Fluspect-Cx model of leaf optical properties and chlorophyll-a fluorescence with the Discrete Anisotropic Radiative Transfer (DART) model to upscale SIF from individual leaves to three-dimensional (3D) structurally explicit canopies. For one-dimensional homogeneous (turbid-like) canopies, DART-SIF was nearly identical to SIF simulated in two existing models, SCOPE and mSCOPE (RMSE <0.221 W./sq.m.μm.sr). DART simulations in geometrically explicit 3D canopies offered four important insights regarding the influence of vegetation structure on the multi-angular top-of-canopy SIF signal. First, changes in the 3D canopy architecture of maize crops, represented by leaf density (leaf area index), and plant clumping (canopy closure) had a larger impact on SIF than the modelled photosynthetic efficiency distinction between sun-adapted and shade-adapted foliage. Second, clumping of leaves at the crop and stand levels was identified as one of the key driving factors of multi-angular anisotropy of red and far-red SIF (686 and 740 nm) for both maize and eucalyptus canopies. Third, non-photosynthetic woody material had a significant impact on top-of-canopy SIF in modelled 3D forest stands. Wood shadowing decreased the photosynthetically active radiation absorbed by green leaves, and consequently the SIF emissions, by 10% in sparse and 17% in dense eucalyptus stands. The wood obstruction (blocking) effect, quantified as a relative difference of SIF escape probabilities from canopies with and without wood in the nadir viewing direction, decreased far-red SIF by 4–6% but it had a smaller and sometimes positive influence (by less than 2%) on red SIF. Fourth, DART 3D radiative budget profiles revealed that the majority of the SIF signal from a dense eucalyptus stand originated from the top 25% of the simulated canopy. Interestingly, the introduction of bark-covered woody elements did not alter the simulated balance and omnidirectional escape factor of red SIF in this upper canopy part but did raise significantly both of them in case of far-red SIF. These results demonstrate the importance of 3D radiative transfer and radiative budget simulations for investigating SIF interactions in structurally complex plant canopies and for a better understanding of spatiotemporal and multi-angular remote sensing SIF observations.
Zbyněk Malenovský↗
Improvement and Application of Atmospheric Radiative Transfer Models for Prediction of the Climatic Effects of Aerosol
This paper presents a radiative transfer model that has been developed to accurately predict the atmospheric radiant flux in both the infrared and the solar spectrum with a minimum of computational effort. The model is designed to be included in numerical climate models. To assess the accuracy of the model, the results are compared to other more detailed models for several standard cases in the solar and thermal spectrum. As the thermal spectrum has been treated in other publications, we focus here on the solar part of the spectrum. We perform several example calculations focussing on the question of absorption of solar radiation by gases and aerosols.
Bergstrom, Robert W.↗
Improvement and Application of Atmospheric Radiative Transfer Models for Prediction of the Climatic Effects of Aerosol
This paper presents a radiative transfer model that has been developed to accurately predict the atmospheric radiant flux in both the infrared and the solar spectrum with a minimum of computational effort. The model is designed to be included in numerical climate models. To assess the accuracy of the model, the results are compared to other more detailed models for several standard cases in the solar and thermal spectrum. As the thermal spectrum has been treated in other publications we focus here on the solar part of the spectrum. We perform several example calculations focussing on the question of absorption of solar radiation by gases and aerosols.
Bergstrom, Robert W.↗
Extending radiative transfer models by use of Bayes rule
This paper presents a procedure that extends some existing radiative transfer modeling techniques to problems in atmospheric science where curvature and layering of the medium and dynamic range and angular resolution of the signal are important. Example problems include twilight and limb scan simulations. Techniques that are extended include successive orders of scattering, matrix operator, doubling, Gauss-Seidel iteration, discrete ordinates and spherical harmonics. The procedure for extending them is based on Bayes' rule from probability theory.
Whitney, C.↗
Uncertainty Quantification of GEOS-5 L-band Radiative Transfer Model Parameters Using Bayesian Inference and SMOS Observations
Uncertainties in L-band (1.4 GHz) radiative transfer modeling (RTM) affect the simulation of brightness temperatures (Tb) over land and the inversion of satellite-observed Tb into soil moisture retrievals. In particular, accurate estimates of the microwave soil roughness, vegetation opacity and scattering albedo for large-scale applications are difficult to obtain from field studies and often lack an uncertainty estimate. Here, a Markov Chain Monte Carlo (MCMC) simulation method is used to determine satellite-scale estimates of RTM parameters and their posterior uncertainty by minimizing the misfit between long-term averages and standard deviations of simulated and observed Tb at a range of incidence angles, at horizontal and vertical polarization, and for morning and evening overpasses. Tb simulations are generated with the Goddard Earth Observing System (GEOS-5) and confronted with Tb observations from the Soil Moisture Ocean Salinity (SMOS) mission. The MCMC algorithm suggests that the relative uncertainty of the RTM parameter estimates is typically less than 25 of the maximum a posteriori density (MAP) parameter value. Furthermore, the actual root-mean-square-differences in long-term Tb averages and standard deviations are found consistent with the respective estimated total simulation and observation error standard deviations of m3.1K and s2.4K. It is also shown that the MAP parameter values estimated through MCMC simulation are in close agreement with those obtained with Particle Swarm Optimization (PSO).
MCMC↗
Modeling Sea Ice Albedo and Transmittance Measurements With A Fully-Coupled Radiative Transfer Model
A rigorous treatment of the sea ice medium has been incorporated in the advanced Coupled Ocean-Atmosphere Radiative Transfer (COART) model. The inherent optical properties (IOPs) of brine pockets and air bubbles over the 0.25-4.0 μm spectral region are parameterized as a function of the vertical profile of the sea ice physical properties (temperature, salinity and density). We test the model performance using available albedo and transmittance measurements collected during the Impacts of Climate on the Ecosystems and Chemistry of the Arctic Pacific Environment (ICESCAPE) and the Surface Heat Budget of the Arctic Ocean (SHEBA) field campaigns. The observations are adequately simulated when at least three layers are used to represent bare (first-year and multi-year) ice, including a thin top layer characterized by low density and high scattering. Two layers can be sufficient to model isolated cases of multi-year ice, and apply well to ponded ice except for shallow ponds over thick ice. The albedo and transmittance of ponded ice in the visible are mainly determined by the optical properties of the ice underlying the water layer used to model the pond. Sensitivity results indicate that the air volume or ice density has the largest impact on the simulated fluxes. Possible contamination from light-absorbing impurities, such as black carbon or ice algae, is also implemented in the model and is able to effectively reduce the albedo and transmittance in the visible spectrum to further improve the model-observation agreement. The agreement between the observed and modeled spectra validates the parameterization of the sea ice IOPs, and endorses COART as an accurate tool for radiation studies in the cryosphere.
Coupled Ocean-9 Atmosphere Radiative Transfer (COA↗
Radiative transfer modeling applied to sea water constituent determination
Optical radiation from the sea is influenced by pigments dissolved in the water and contained in discrete organisms suspended in the sea, and by pigmented and unpigmented inorganic and organic particles. The problem of extracting the information concerning these pigments and particulates from the optical properties of the sea is addressed and the properties which determine characteristics of the radiation that a remote sensor will detect and measure are considered. The results of the application of the volume scattering function model to the data collected in the Gulf of Mexico and its environs indicate that the size distribution of the concentrations of particles found in the sea can be predicted from measurements of the volume scattering function. Furthermore, with the volume scattering function model and knowledge of the absorption spectra of dissolved pigments, the radiative transfer model can compute a distribution of particle sizes and indices of refraction and concentration of dissolved pigments that give an upwelling light spectrum that closely matches measurements of that spectrum at sea.
Faller, K. H.↗
Applications of an Energy Transfer Model to Three Problems in Planetary Regoliths: The Solid-State Greenhouse, Thermal Beaming, and Emittance Spectra
Several problems of interest in planetary infrared remote sensing are investigated using a new radiative-conductive model of energy transfer in regoliths: the solid-state greenhouse effect, thermal beaming, and reststrahlen spectra. The results of the analysis are as follows: (1) The solid-state greenhouse effect is self-limiting to a rise of a few tens of degrees in bodies of the outer solar system. (2) Non-Lambertian directional emissivity can account for only about 20% of the observed thermal beaming factor. The remainder must have another cause, presumably surface roughness effects. (3) The maximum in a reststrahlen emissivity spectrum does not occur exactly at the Christiansen wavelength where, by definition, the real part of the refractive index equals one, but rather at the first transition minimum in reflectance associated with the transition from particle scattering being dominated by volume scattering to that dominated by strong surface scattering. The transparency feature is at the second transition minimum and does not require the presence of a second band at longer wavelength for its occurance. Subsurface temperature gradients have only a small effect on emissivity bands.
Hapke, Bruce↗
Evaluation of Aqua MODIS Thermal Emissive Bands Stability through Radiative Transfer Modeling
Moderate Resolution Imaging Spectroradiometer (MODIS) on Aqua has been inoperation providing continuous global observations for science research and applications since2002. The long-term stability of thermal emissive bands (TEBs) of Aqua MODIS was monitoredthrough inter-comparisons with measurements by hyperspectral or multi-spectral infraredsensors or through vicarious monitoring over cold targets such as Dome-C and deep convectiveclouds. The radiative transfer modeling (RTM)-based simulation models are developed to per-form the long-term monitoring of the stability of Aqua MODIS TEBs. Long-term EuropeanCentre for Medium-Range Weather Forecasts global atmospheric reanalysis data are used asinputs to the RTM simulation. By confining ocean in low to middle latitudes as the area ofinterest, the long-term stabilities of Aqua MODIS TEBs are monitored through observationminus background (O-B) brightness temperature (BT) bias between MODIS measurements andsimulations from the RTM. In general, the RTM-based O-B analysis shows that the long-termstability of Aqua MODIS TEBs are maintained well. It is shown that Aqua MODIS surfacebands are all radiometrically stable with yearly BT bias drifts <0.005 K∕yearfor B20, B22,and B23 and∼0.01 K∕yearfor B31 and B32. The carbon dioxide (CO2) absorption channelsof Aqua MODIS, e.g., B33 to B36, are stable with a BT bias drift <0.005 K∕year. It is also foundthat after accounting for the long-term growth of greenhouse gasN2O, the O-B bias trends forB24 and B25 are quite stable with yearly BT bias drifts around 0.0002 and0.0055 K∕year,respectively. The stabilities of the moisture-sensitive channels B27 to B29 and the ozone channelB30 of Aqua MODIS are also evaluated and the remnant small variations in the O-B bias trend-ing of these channels are further discussed. The RTM-based inter-comparison of MODIS TEBmeasurements with global atmospheric and climate re-analysis data provides validation of thelong-term radiometric stability of Aqua MODIS TEBs. The analysis in this paper also demon-strates that the comparison of well-calibrated MODIS TEB measurements with RTM simulationhelps quantify the long-term impacts of global greenhouse gas concentration growth on the BTdecreases in the MODIS greenhouse gas-sensitive channels.
MODIS↗
Measurements of the Downward Longwave Radiation Spectrum over the Antarctic Plateau and Comparisons with a Line-by-Line Radiative Transfer Model for Clear Skies
A 1-year field program was conducted at South Pole Station in 1992 to measure the downward infrared radiance spectrum at a resolution of 1/ cm over the spectral range 550-1667 cm-'. The atmosphere over the Antarctic Plateau is the coldest and driest on Earth, where in winter, surface temperatures average about -60 C, the total column water vapor is as low as 300 pm of precipitable water, and the clear-sky downward longwave flux is usually less than 80 W/sq m. Three clear-sky test cases are selected, one each for summer, winter, and spring, for which high- quality radiance data are available.as well as ancillary data to construct model atmospheres from radiosondes, ozonesondes, and other measurements. The model atmospheres are used in conjunction with the line-by-line radiative transfer model (LBLRTM) to compare model calculations with the spectral radiance measurements. The high-resolution calculations of LBLRTM (approx. = 0.001/ cm) are matched to the lower-resolution measurements (1/ cm) by adjusting their spectral resolution and by applying a correction for the finite field of view of the interferometer. In summer the uncertainties in temperature and water vapor profiles dominate the radiance error in the LBLRTM calculations. In winter the uncertainty in viewing zenith angle becomes important as well as the choice of atmospheric levels in the strong near-surface temperature inversion. The spectral radiance calculated for each of the three test cases generally agrees with that measured, to within twice the total estimated radiance error, thus validating LBLRTM to this level of accuracy for Antarctic conditions. However, the discrepancy exceeds twice the estimated error in the gaps between spectral lines in the region 1250-1500/ cm, where emission is dominated by the foreign-broadened water vapor continuum.
Walden, Von P.↗
Radiance and Jacobian Intercomparison of Radiative Transfer Models Applied to HIRS and AMSU Channels
The goals of this study are the evaluation of current fast radiative transfer models (RTMs) and line-by-line (LBL) models. The intercomparison focuses on the modeling of 11 representative sounding channels routinely used at numerical weather prediction centers: 7 HIRS (High-resolution Infrared Sounder) and 4 AMSU (Advanced Microwave Sounding Unit) channels. Interest in this topic was evidenced by the participation of 24 scientists from 16 institutions. An ensemble of 42 diverse atmospheres was used and results compiled for 19 infrared models and 10 microwave models, including several LBL RTMs. For the first time, not only radiances, but also Jacobians (of temperature, water vapor and ozone) were compared to various LBL models for many channels. In the infrared, LBL models typically agree to within 0.05-0.15 K (standard deviation) in terms of top-of-the-atmosphere brightness temperature (BT). Individual differences up to 0.5 K still exist, systematic in some channels, and linked to the type of atmosphere in others. The best fast models emulate LBL BTs to within 0.25 K, but no model achieves this desirable level of success for all channels. The ozone modeling is particularly challenging, In the microwave, fast models generally do quite well against the LBL model to which they were tuned. However significant differences were noted among LBL models, Extending the intercomparison to the Jacobians proved very useful in detecting subtle and more obvious modeling errors. In addition, total and single gas optical depths were calculated, which provided additional insight on the nature of differences. Recommendations for future intercomparisons are suggested.
Garand, L.↗
Radiance and Jacobian Intercomparison of Radiative Transfer Models Applied to HIRS and AMSU Channels
The goals of this study are the evaluation of current fast radiative transfer models (RTMs) and line-by-line (LBL) models. The intercomparison focuses on the modeling of 11 representative sounding channels routinely used at numerical weather prediction centers: seven HIRS (High-resolution Infrared Sounder) and four AMSU (Advanced Microwave Sounding Unit) channels. Interest in this topic was evidenced by the participation of 24 scientists from 16 institutions. An ensemble of 42 diverse atmospheres was used and results compiled for 19 infrared models and 10 microwave models, including several LBL RTMs. For the first time, not only radiances, but also Jacobians (of temperature, water vapor, and ozone) were compared to various LBL models for many channels. In the infrared, LBL models typically agree to within 0.05-0.15 K (standard deviation) in terms of top-of-the-atmosphere brightness temperature (BT). Individual differences up to 0.5 K still exist, systematic in some channels, and linked to the type of atmosphere in others. The best fast models emulate LBL BTs to within 0.25 K, but no model achieves this desirable level of success for all channels. The ozone modeling is particularly challenging. In the microwave, fast models generally do quite well against the LBL model to which they were tuned. However significant differences were noted among LBL models. Extending the intercomparison to the Jacobians proved very useful in detecting subtle and more obvious modeling errors. In addition, total and single gas optical depths were calculated, which provided additional insight on the nature of differences. Recommendations for future intercomparisons are suggested.
Garand, L.↗
A radiative transfer model for remote sensing of laser induced fluorescence of phytoplankton in non-homogeneous turbid water
A radiative transfer computer model was developed to characterize the total flux of chlorophyll a fluoresced or backscattered photons when laser radiation is incident on turbid water that contains a non-homogeneous suspension of inorganic sediments and phytoplankton. The radiative transfer model is based on the Monte Carlo technique and assumes that: (1) the aquatic medium can be represented by a stratified concentration profile; and (2) that appropriate optical parameters can be defined for each layer. The model was designed to minimize the required computer resources and run time. Results are presented for an anacystis marinus culture.
Venable, D. D.↗
Developments in convective heat transfer models featuring seamless and selected detail surfaces, employing electroless plating
Several model/instrument concepts employing electroless metallic skin were considered for improvement of surface condition, accuracy, and cost of contoured-geometry convective heat transfer models. A plated semi-infinite slab approach was chosen for development and evaluation in a hypersonic wind tunnel. The plated slab model consists of an epoxy casting containing fine constantan wires accurately placed at specified surface locations. An electroless alloy was deposited on the plastic surface that provides a hard, uniformly thick, seamless skin. The chosen alloy forms a high-output thermocouple junction with each exposed constantan wire, providing means of determining heat transfer during tunnel testing of the model. A selective electroless plating procedure was used to deposit scaled heatshield tiles on the lower surface of a 0.0175-scale shuttle orbiter model. Twenty-five percent of the tiles were randomly selected and plated to a height of 0.001-inch. The purpose was to assess the heating effects of surface roughness simulating misalignment of tiles that may occur during manufacture of the spacecraft.
Stalmach, C. J., Jr.↗