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A semiempirical method for analysis of the reflectance spectra of binary mineral mixtures

A simple semiempirical method is presented for determination of the spectral reflectance of a powdered binary mineral mixture. This technique uses a two-stream radiative transfer model (a modified Kubelka-Munk model) on a particulate medium of isotroic scatterers The particles are assumed to be much larger than the wavelength of light under consideration. This same method can be used to determine the relative proportion of components in a mixture for which the spectral reflectance is known. Binary mixtures of olivine, two pyroxenes, and magnetite are used to test this model. The theoretical and empirical results agree approximately within experimental errors.

Johnson, P. E.↗

Simple radiative transfer model for relationships between canopy biomass and reflectance

A modified Kubelka-Munk model has been utilized to derive useful equations for the analysis of apparent canopy reflectance. Based on the solution to the model simple working equations were formulated by employing reflectance characteristic parameters. The relationships derived show the asymptotic nature of reflectance data that is typically observed in remote sensing studies of plant biomass. They also establish the range of expected apparent canopy reflectance values for specific plant canopy types. The usefulness of the simplified equations was demonstrated by the exceptionally close fit of the theoretical curves to two separately acquired data sets for alfalfa and shortgrass prairie canopies.

Park, J. K.↗

Plant, soil, and shadow reflectance components of row crops

Data from the first Earth Resource Technology Satellite (LANDSAT-1) multispectral scanner (MSS) were used to develop three plant canopy models (Kubelka-Munk (K-M), regression, and combined K-M and regression models) for extracting plant, soil, and shadow reflectance components of cropped fields. The combined model gave the best correlation between MSS data and ground truth, by accounting for essentially all of the reflectance of plants, soil, and shadow between crop rows. The principles presented can be used to better forecast crop yield and to estimate acreage.

Richardson, A. J.↗

Prospect redux

The remote estimation of leaf biochemical content from spaceborne platforms has been the subject of many studies aimed at better understanding of terrestrial ecosystem functioning. The major ecological processes involved in exchange of matter and energy, like photosynthesis, primary production, evaportranspiration, respiration, and decomposition can be related to plant properties e.g., chlorophyll, water, protein, cellulose and lignin contents. As leaves represent the most important plant surfaces interacting with solar energy, a top priority has been to relate optical properties to biochemical constituents. Two different approaches have been considered: first, statistical correlations between the leaf reflectance (or transmittance) and biochemical content, and second, physically based models of leaf scattering and absorption developed using the laws of optics. Recently reviewed by Verdebout et al., the development of models of leaf optical properties has resulted in better understanding of the interaction of light with plant leaves. Present radiative transfer models mainly use chlorophyll and/or water contents as input parameters to calculate leaf reflectance. Inversion of these models allows to retrieve these constituents from spectrophotometric measurements. Conel et al. recently proposed a two-stream Kubelka-Munk model to analyze the influence of protein, cellulose, lignin, and starch on leaf reflectance, but in fact, the estimation of leaf biochemistry from remote sensing is still an open question. In order to clarify it, a laboratory experiment associating visible/infrared spectra of plan leaves both with physical measurements and biochemical analyses was conducted at the Joint Research Center during the summer of 1993. This unique data set has been used to upgrade the PROSPECT model, by including leaf biochemistry.

Jacquemoud, S.↗

Reflectance of vegetation, soil, and water

The author has identified the following significant results. The Kubelka-Munk model, a regression model, and a combination of these models were used to extract plant, soil, and shadow reflectance components of vegetated surfaces. The combination model was superior to the others; it explained 86% of the variation in band 5 reflectance of corn and sorghum, and 90% of the variation in band 6 reflectance of cotton. A fractional shadow term substantially increased the proportion of the digital count sum of squares explained when plant parameters alone explained 85% or less of the variation. Overall recognition of 94 agricultural fields using simultaneously acquired aircraft and spacecraft MSS data was 61.8 and 62.8%, respectively; recognition of vegetable fields larger than 10 acres and taller than 25 cm, rose to 88.9 and 100% for aircraft and spacecraft, respectively. Agriculture and rangeland, were well discriminated for the entire county but level 2 categories of vegetables, citrus, and idle cropland, except for citrus, were not.

Wiegand, C. L.↗

A mathematical model for crop spectral-temporal trajectories based on a plant growth model

The Kubelka-Munk radiative transfer model is combined with an approximation of Kauth-Thomas greeness and brightness transforms to derive approximate closed form expressions for crop greeness and brightness surrogates in terms of canopy biomass. The greeness relation derived resembles an existing empirical relation between leaf area index and greeness. A simple growth model based on interception and utilization of photosynthetically active radiation is developed and used to describe the time evolution of greeness and brightness. The model developed does not yet yield definitive profile calculations but suggests a conceptual framework which may be found useful for further profile analysis.

Woolford, T. L.↗

Relation of the diffuse reflectance remission function to the fundamental optical parameters.

The Kubelka-Munk equations describing the diffuse reflectance of a powdered sample were compared to equations obtained using a uniformly-sized rough-surfaced spherical particle model. The comparison resulted in equations relating the remission function and the Kubelka-Munk constants to the index of refraction, the absorption coefficient, and the average particle diameter of a powdered sample. Published experimental results were used to test the equation relating to the remission function to the fundamental optical parameters.

Simmons, E. L.↗

Application of a two-stream radiative transfer model for leaf lignin and cellulose concentrations from spectral reflectance measurements, part 2

We used the Kubelka-Munk theory of diffuse spectral reflectance in layers to analyze influences of multiple chemical components in leaves. As opposed to empirical approaches to estimation of plant chemistry, the full spectral resolution of laboratory reflectance data was retained in an attempt to estimate lignin or other constituent concentrations from spectral band positions. A leaf water reflectance spectrum was derived from theoretical mixing rules, reflectance observations, and calculations from theory of intrinsic k- and s-functions. Residual reflectance bands were then isolated from spectra of fresh green leaves. These proved hard to interpret for composition in terms of simple two component mixtures such as lignin and cellulose. We next investigated spectral and dilution influences of other possible components (starch, protein). These components, among others, added to cellulose in hypothetical mixtures, produce band displacements similar to lignin, but will disguise by dilution the actual abundance of lignin present in a multicomponent system. This renders interpretation of band positions problematical. Knowledge of end-members and their spectra, and a more elaborate mixture analysis procedure may be called for. Good observational atmospheric and instrumental conditions and knowledge thereof are required for retrieval of expected subtle reflectance variations present in spectra of green vegetation.

Conel, James E.↗

Unsteady temperature distribution in volume reflectors

The development of unsteady temperature distributions in semitransparent scattering materials under the influence of arbitrary incident radiative flux with other than specified temperature boundary conditions is considered. Specifically, such a problem is considered for an approximate radiative transfer model which allows analytic solutions. The model represents the unsteady, one-dimensional, radiative heating of a weakly absorbing, semitransparent medium with specified conductive heat flux at one boundary. The radiation field is modeled using an approximation to the radiative heat flux obtained by solution of the Kubelka-Munk differential equations.

Weston, K. C.↗

Near-Infrared (0.67-4.7 microns) Optical Constants Estimated for Montmorillonite

Various models of the reflectance from particulate surfaces are used for interpretation of remote sensing data of solar system objects. These models rely upon the real (n) and imaginary (k) refractive indices of the materials. Such values are limited for commonly encountered silicates at visual and near-infrared wavelengths (lambda, 0.4-5 microns). Availability of optical constants for candidate materials allows more thorough modeling of the observations obtained by Earth-based telescopes and spacecraft. Two approaches for determining the absorption coefficient (alpha=2pik/lambda) from reflectance measurements of particulates have been described; one relies upon Kubelka-Munk theory and the other Hapke theory. Both have been applied to estimate alpha and k for various materials. Neither enables determination of the wavelength dependence of n, n=f(lambda). Thus, a mechanism providing this ability is desirable. Using Hapke-theory to estimate k from reflectance measurements requires two additional quantities be known or assumed: 1) n=f(lambda) and 2) d, the sample particle diameter. Typically n is assumed constant (c) or modestly varying with lambda; referred to here as n(sub 0). Assuming n(sub 0), at each lambda an estimate of k is used to calculate the reflectance and is iteratively adjusted until the difference between the model and measured reflectance is minimized. The estimated k's (k(sub 1)) are the final results, and this concludes the typical analysis.

Roush, T. L.↗

Near-infrared (0.67-4.7 micron) Optical Constants Estimated for Montmorillonite

Various models of the reflectance from particulate surfaces are used for interpretation of remote sensing data of solar system objects. These models rely upon the real (n) and imaginary (k) refractive indices of the materials. Such values are limited for commonly encountered silicates at visual and near-infrared wavelengths (lambda, 0.4-5 micron). Availability of optical constants for candidate materials allows more thorough modeling of the observations obtained by Earth-based telescopes and spacecraft. Two approaches for determining the absorption coefficient (alpha=2 pi k/lambda) from reflectance measurements of particulates have been described; one relies upon Kubelka-Munk theory and the other Hapke theory. Both have been applied to estimate alpha and k for various materials. Neither enables determination of the wavelength dependence of n, n=f(lambda). Thus, a mechanism providing this ability is desirable. Using Hapke-theory to estimate k from reflectance measurements requires two additional quantities be known or assumed: 1) n=f(lambda) and 2) d, the sample particle diameter. Typically n is assumed constant (c) or modestly varying with lambda; referred to here as n(sub 0). Assuming n(sub 0), at each lambda an estimate of k is used to calculate the reflectance and is iteratively adjusted until the difference between the model and measured reflectance is minimized. The estimated k's (k(sub l)) are the final results, and this concludes the typical analysis. Additional information is included in the original extended abstract.

Roush, T. L.↗