B. D. Ganapol

LEAFMOD: A New Within-Leaf Radiative Transfer Model

Abstract We describe the construction and verification of a within-leaf radiative transfer model called LEAFMOD (Leaf Experimental Absorptivity Feasibility MODel). In the model, the one-dimensional radiative transfer equation in a slab of leaf material with homogeneous optical properties is solved. When run in the forward mode, LEAFMOD generates an estimate of leaf reflectance and transmittance given the leaf thickness and optical characteristics of the leaf material (i.e., the absorption and scattering coefficients). In the inverse mode, LEAFMOD computes the total within-leaf absorption and scattering coefficient profiles from measured reflectance, transmittance, and leaf thickness. Inversions with simulated data demonstrate that the model appropriately decouples scattering and absorption within the leaf, producing fresh leaf absorption profiles with peaks at locations corresponding to the major absorption features for water and chlorophyll. Experiments with empirical input data demonstrate that the amplitude of the fresh leaf absorption coefficient profile in the visible wavebands is correlated with pigment concentrations as determined by wet chemical analyses, and that absorption features in the near-infrared wavebands related to various other biochemical constituents can be identified in a dry-leaf absorption profile.

LCM2: A coupled leaf/canopy radiative transfer model

Abstract Two radiative transfer models have been coupled to generate vegetation canopy reflectance as a function of leaf chemistry, leaf morphology (as represented by leaf scattering properties), leaf thickness, soil reflectance, and canopy architecture. A model of radiative transfer within a leaf, called LEAFMOD, treats the radiative transfer equation for a slab of optically uniform leaf material, providing an estimate of leaf hemispherical reflectance and transmittance as well as the radiance exiting the leaf surfaces. The canopy model then simulates radiative transfer within a mixture of leaves, with each having uniform optical properties as determined by LEAFMOD, assuming a bi-Lambertian leaf scattering phase function. The utility of the model, called LCM2 (Leaf/Canopy Model version 2), is demonstrated through predictions of radiometric measurements of canopy reflectance and sensitivity to leaf chlorophyll and moisture content.

Remote sensing of vegetation canopy photosynthetic and stomatal conductance efficiencies

Abstract 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 semiempirical 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 (E p ), and stomatal efficiencies (E s ) are calculated for various geometrical, optical, and illumination conditions. A base case is defined to investigate the dynamics of E p and E s with respect to ground cover, clump leaf area index, soil reflectance, and atmospheric conditions. The contribution of various radiative fluxes to estimates of E p is evaluated and the magnitude of errors in bulk canopy formulation of problem parameters are quantifieid. The nature and sensitivity of the relationship between E p and E s to NDVI is investigated and an algorithim is proposed for use in operational remote sensing.

Analysis of vegetation isolines in red-NIR reflectance space

Abstract The characteristic behavior of red–near-infrared (NIR) reflectance-based vegetation isolines were analyzed by focusing on its three features: the slope, NIR-intercept, and the intersection between the vegetation isoline and the soil line. These properties are the key factors in understanding variations of vegetation index values with changes of canopy background brightness, known as background noise. The analysis was conducted based on a vegetation isoline equation derived by using the representation of canopy reflectance by the adding method. The isoline parameters, slopes, and NIR-intercepts of vegetation isolines were numerically obtained by the SAIL canopy model. Some of the known behaviors of the vegetation isoline were simulated and analyzed in detail.

A highly accurate technique for the solution of the non-linear point kinetics equations

The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step gives results that are comparable to those obtained using other popular and more complicated methods. The algorithm developed using a Taylor series expansion is simple, completely transparent, and highly accurate. The procedure is tested using a variety of initial conditions and input data, including step reactivity, ramp reactivity, sinusoidal, and zigzag reactivity. These results are compared to those obtained using other methods.

The Fn method for the one-angle radiative transfer equation applied to plant canopies☆

Abstract 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. Although the most widely used transport models such as the moments formulations collapse the photon directional information into a limited number of directions (usually two or four), the more sophisticated methods such as discrete ordinates can, in principle, employ an unlimited number of discrete directions. These discrete methods, however, also contain spatial discretization error and lack testing against more accurate Numerical formulations for specific vegetation canopy scattering kernels. In this article, we consider a semianalytical approach to the solution of the one-angle radiative transfer equation in slab geometry called the F n method. This method has a its basis two integral equations specifying the intensities exiting the vegetation canopy boundaries. The solution is then obtained through an expansion in a set of basis functions with expansion coefficients to be determined. These coefficients are obtained from a collocation procedure resulting in a set of algebraic equations solved by matrix inversion. The advantage of this method is that only discretization in the angular variable is required, thus avoiding spatial truncation error entirely. The paper begins by considering a canopy where all the leaves are oriented at the same angle. Lambertian scattering will be assumed with unequal leaf reflectance and transmittance. This simple model contains all the difficulties of the more complex model incorporating a general leaf angle distribution which is to be considered in the latter part of the presentation. A sensitivity analysis is performed including variation of the numerical and model parameters. In addition, discrete ordinates calculations as well as field measurements are compared to the F n results.

A closed-form solution to HZE propagation

An analytic solution for high-energy heavy ion transport assuming straight-ahead and velocity-conserving interactions with constant nuclear cross-reactions is given in terms of a Greens function. The series solution for the Greens function is rapidly convergent for most practical applications. The Greens 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.

The Generation of Time-Dependent Neutron Transport Solutions in Infinite Media

The multiple collision technique as applied to the monoenergetic time-dependent neutron transport equation for pulsed plane source emission in an infinite medium is used to obtain the flux due to a pulsed point source in the same medium. This result is then integrated to determine the flux due to the corresponding pulsed line source problem. The semi-infinite albedo problem is also shown to be solvable using the multiple collision approach. A generalization to include delayed neutrons follows directly from the multiple collision treatment, as does an equivalence between a monoenergetic time-dependent problem and a particular stationary slowing down problem in infinite geometry. Results are tabulated and comparisons are made to provide benchmark solutions to the fundamental time-dependent transport problems considered and thus bridge the gap between theory and practice.

The non-equilibrium Marshak wave problem: A transport theory solution

Abstract An analytic solution to a particular Marshak problem is given. The radiative transfer model used is the one-group grey transport description coupled with the material energy balance. This solution provides a benchmark for validating time-dependent radiative transfer algorithms and constitutes a transport solution to the same problem previously solved using diffusion and low-order P - N approximations. Typical numerical results are given for surface and integral quantities and comparisons are made with the previously reported diffusion solution, as well as with a Monte Carlo result.

A consistent theory of neutral particle transport in an infinite medium

Abstract The solution to the age-old infinite medium Greens function is revisited using the hindsight of the past coupled with the wisdom of the present. A new solution is found based on a blend of the theories developed by F. Vanmassenhove and C. Grosjean, E. Inonu, K. Case and J. Mika. The solution is obtained from well-known recurrence relations and is shown to reduce to the singular eigenfunction representation of Case. Closure is shown to be a consequence of the infinite medium Greens function.