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.↗
Engineering topics
Ganapol, B. D.
Publications and source records attributed to Ganapol, B. D..
Radiative transfer in a semiinfinite medium with a specularly reflecting boundary
A consistent solution of the radiative transfer equation characterizing photon transport in a semi-infinite medium of refractive index greater than or equal to one is obtained following the method of Sobolev. Fresnel specular reflection, Snell's law and isotropic scattering are assumed. An algorithm is developed and its accuracy is demonstrated. A numerical Laplace transform inversion leads to an efficient evaluation for the interior flux and source function distributions.
Ganapol, B. D.↗
The reflection for dense plant canopies from the one-angle radiative transfer equation
An essential component of remote sensing of vegetation canopies from satellites is fundamental understanding. Since passive remote is driven by photons, the modeling of photon interactions with vegetation is a basic building block in that understanding. Several such photon transport models have been developed during the past two decades and continue to be developed. Different approaches have been followed including monte carlo, radiosity methods, geometric shadowing, and radiative transfer. In general, each approach has application for canopies with specific attributes. This presentation concerns the application of radiative transfer to dense vegetation canopies in which the soil does not participate. The approach taken here is novel in that a consistent theory for photon transport for non-rotationally invariant leaf scattering is developed in a canopy with a general leaf angle distribution (LAD). The theory is limited to the one-angle approximation (azimuthally averaged radiance) and is based on Chandrasekhar's analytical theory. While such a model is admittedly only approximate, it does fulfill a unique function in our search for understanding. In particular, the model is simple in its construct yet contains the essential features of canopy architecture that are mainly responsible for observed responses. Thus, this model will not only be a predictive tool but also an educational one. The mathematical setting is the radiative transfer equation in a dense (semiinfinite) canopy. The leaf scattering phase function is assumed to be Lambertian with different reflectance and transmittance. In addition, abaxial and adaxial differentiation is allowed which effectively destroys optical reciprocity. The analytical solution for the canopy BRDF is obtained by manipulation of the integral transport equation (a la Chandrasekhar) for a general LAD. With discretization of the. leaf angle, the resulting set of integral equations are solved iteratively including an acceleration procedure when the single scatter albedo is near one (in the NIR). Results will be compared to the LARS soybean canopy radiances as well as to broadleaf results from a recent Ames experiment.
Ganapol, B. D.↗
Remote sensing of vegetation canopy photosynthetic and stomatal conductance efficiencies
The problem of remote sensing the canopy photosynthetic and stomatal conductance efficiencies is investigated with the aid of one- and three-dimensional radiative transfer methods coupled to a semi-empirical mechanistic model of leaf photosynthesis and stomatal conductance. Desertlike vegetation is modeled as clumps of leaves randomly distributed on a bright dry soil with partial ground cover. Normalized difference vegetation index (NDVI), canopy photosynthetic (Ep), and stomatal efficiencies (Es) are calculated for various geometrical, optical, and illumination conditions. The contribution of various radiative fluxes to estimates of Ep is evaluated and the magnitude of errors in bulk canopy formulation of problem parameters are quantified. The nature and sensitivity of the relationship between Ep and Es to NDVI is investigated, and an algorithm is proposed for use in operational remote sensing.
Myneni, R. B.↗
The application of the principles of invariance to the radiative transfer equation in plant canopies
Solutions of the radiative transfer equation describing photon interactions with vegetation canopies are important in remote sensing since they provide the canopy reflectance distribution required in the interpretation of satellite acquired information. The general one-dimensional two-angle transport problem for a finite copy of arbitrary leaf angle distribution is considered. Analytical solutions are obtained in terms of generalized Chandrasekhar's X- and Y-functions by invoking the principles of invariance. A critical step in the formulation involves the decomposition of the integral of the scattering phase function into a product of known functions of the incident and scattered photon directions. Several simplified cases previously considered in the literature are derived from the generalized solution. Various symmetries obeyed by the scattering operator and reciprocity relations are formally proved.
Ganapol, B. D.↗
The F(N) method for the one-angle radiative transfer equation applied to plant canopies
The paper presents a semianalytical solution method, called the F(N) method, for the one-angle radiative transfer equation in slab geometry. The F(N) method is based on two integral equations specifying the intensities exiting the boundaries of the vegetation canopy; the solution is obtained through an expansion in a set of basis functions with expansion coefficients to be determined. The advantage of this method is that it avoids spatial truncation error entirely because it requires discretization only in the angular variable.
Ganapol, B. D.↗
Biophysical information in asymmetric and symmetric diurnal bidirectional canopy reflectance
The authors present a theory for partitioning the information content in diurnal bidirectional reflectance measurements in order to detect differences potentially related to biophysical variables. The theory, which divides the canopy reflectance into asymmetric and symmetric functions of solar azimuth angle, attributes asymmetric variation to diurnal changes in the canopy biphysical properties. The symmetric function is attributed to the effects of sunlight interacting with a hypothetical average canopy which would display the average diurnal properties of the actual canopy. The authors analyzed radiometer data collected diurnally in the Thematic Mapper wavelength bands from two walnut canopies that received differing irrigation treatments. The reflectance of the canopies varied with sun and view angles and across seven bands in the visible, near-infrared, and middle infrared wavelength regions. Although one of the canopies was permanently water stressed and the other was stressed in mid-afternoon each day, no water stress signature was unambiguously evident in the reflectance data.
Vanderbilt, Vern C.↗
A closed-form solution to HZE propagation
An analytic solution for high energy heavy ion transport assuming straightahead and velocity conserving interactions with constant nuclear cross reactions is given in terms of a Green's function. The series solution for the Green's function is rapidly convergent for most practical applications. The green's function technique can be applied with equal success to laboratory beams as well as to galactic cosmic rays allowing laboratory validation of the resultant space shielding code.
Wilson, John W.↗
A closed form solution to HZE propagation
An analytic solution for high energy heavy ion transport assuming straightahead and velocity conserving interactions with constant nuclear cross reactions is given in terms of a Green's function. The series solution for the Green's function is rapidly convergent for most practical applications. The Green's function technique can be applied with equal success to laboratory beams as well as to galactic cosmic rays allowing laboratory validation of the resultant space shielding code.
Wilson, John W.↗