Xiaowen Li

Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing

In the case where a vegetation cover can be regarded as a collection of individual, discrete plant crowns, the geometric-optical effects of the shadows that the crowns cast on the background and on one another strongly condition the brightness of the vegetation cover as seen from a given viewpoint in the hemisphere. An asymmetric hotspot, in which the shape of the hotspot is related to the shape of the plant crowns in the scene, is created. At large zenith angles illumination shadows will preferentially shadow the lower portions of adjacent crowns. Further, these shadows will be preferentially obscured since adjacent crowns will also tend to obscure the lower portions of other crowns. This effect produces a bowl-shaped bidirectional reflectance distribution function (BRDF) in which the scene brightness increases at the functions edges. Formulas describing the hotspot and mutual-shadowing effects are derived, and examples that show how the shape of the BRDF is dependent on the shape of the crowns, their density, their brightness relative to the background, and the thickness of the layer throughout which the crown centers are distributed are presented. >

Geometric-Optical Modeling of a Conifer Forest Canopy

A geometric-optical forest canopy model that treats conifers as cones casting shadows on a contrasting background can explain the major portion of the variance in a remotely sensed image of a forest stand. The model is driven by interpixel variance generated from three sources: 1) the number of crowns in the pixel; 2) the size of individual crowns; and 3) overlapping of crowns and shadows. The model uses parallel-ray geometry to describe the illumination of a three-dimensional cone and the shadow it casts. Cones are assumed to be randomly placed and may overlap freely. Cone size (height) is distributed lognormally, and cone form, described by the apex angle of the cone, is-fixed in the model but allowed to vary in its application. The model can also be inverted to provide estimates of the size, shape, and spacing of the conifers as cones using remote imagery and a minimum of ground measurements. Field tests using both 10-and 80-m multispectral imagery of two test conifer stands in northeastern California produced reasonable estimates for these parameters. The model appears to be sufficiently general and robust for application to other geometric shapes and mixtures of simple shapes. Thus it has wide potential use not only in remote sensing of vegetation, but also in other remote sensing situations in which discrete objects are imaged at resolutions sufficiently coarje that they canot be resolved individually.

Geometric-Optical Bidirectional Reflectance Modeling of a Conifer Forest Canopy

A geometric-optical forest canopy model that treats conifers as cones casting shadows on a contrasting background explains the major anisotropies in bidirectional reflectance measurements of a conifer forest canopy taken from the literature. The model uses parallelray geometry to describe the illumination and viewing of conifers as three-dimensional cones. Cones are randomly placed and overlap freely. Cone size (height) is distributed lognormally, and cone form, described by the apex angle of the cone, is a negative exponential function of height. The cones are first presumed to be solid dark gray Lambertian objects, located on a lighter gray Lambertian background. To add realism, translucence is added and light is allowed to pass through cones with negative exponential attenuation. Both computer simulation and analytical closed-form expressions are implemented. The results show a good qualitative agreement with the directional reflectance measurements of the conifer stand, indicating that the three-dimensional nature of the canopy is a key factor in determining its directional reflectance.

A Hybrid Geometric Optical-Radiative Transfer Approach for Modeling Albedo and Directional Reflectance of Discontinuous Canopies

A new model for the bidirectional reflectance of a vegetation cover combines principles of geometric optics and radiative transfer. It relies on gap probabilities and path length distributions to model the penetration of irradiance from a parallel source and the single and multiple scattering of that irradiance in the direction of an observer. The model applies to vegetation covers of discrete plant crowns that are randomly centered both on the plane and within a layer of variable thickness above it. Crowns assume a spheroidal shape with arbitrary height to width ratio. Geometric optics easily models the irradiance that penetrates the vegetation cover directly, is scattered by the soil, and exits without further scattering by the vegetation. Within a plant crown, the probability of scattering is a negative exponential function of path length. Within-crown scattering provides the source for singly-scattered radiation, which exits with probabilities proportional to further path-length distributions in the direction of exitance (including the hotspot effect). Single scattering provides the source for double scattering, and then higher order pairs of scattering are solved successively by a convolution function. Early validations using data from a conifer stand near Howland, Maine, show reasonable agreement between modeled and observed reflectance.

Modeling the gap probability of a discontinuous vegetation canopy

A model is presented for the gap probability of a discontinuous vegetation canopy, such as forest, savanna, or shrubland. The case in which the distribution of individual canopy sizes and shapes is known and individual canopies are randomly distributed but do not overlap, and the case in which the canopies to intersect and/or overlap such that foliage density remains constant with the overlap area are both considered, although an exact solution is provided only for the latter. A comparison of modeled gap probabilities with observed gap probabilities for a Maryland (US) pine stand (as taken from the literature) shows good agreement for zenith angles of illumination up to about 45 degrees . Above 45 degrees , the fit worsens, presumably because the horizontal branch structure of the pine canopy is less attenuating as the illumination angle approaches the horizon. >

A conceptual model for effective directional emissivity from nonisothermal surfaces

The conventional definition of emissivity requires the source of radiation to be isothermal in order to compare its thermal emission to that of a blackbody at the same temperature. This requirement is not met for most land surfaces considered in thermal infrared remote sensing. Thus, the effective or equivalent emissivity of nonisothermal surfaces has been a poorly defined but widely used concept for years. Recently, several authors have attempted to define this concept more clearly. Unfortunately, definitions such as ensemble emissivity (e-emissivity) and emissivity derived from the surface bidirectional reflectance distribution function (r-emissivity), J. Norman et al. (1995), do not fully satisfy current needs for estimating true land surface temperature (LST). The present authors suggest the use of an additional term, the apparent emissivity increment, which considers the effects of geometric optics to explain the directional and spectral dependence in LST caused by the three-dimensional (3D) structure and subpixel temperature distribution of the surface. They define this quantity based upon the emissivity derived from the bidirectional reflectance distribution function (/spl epsi//sub BRDF/) for isothermal surfaces and present a conceptual model of thermal emission from nonisothermal land surfaces. Their study also indicates that an average LST corresponding to the hemispherical wideband /spl epsi//sub BRDF/ Will be useful in remote sensing-based LST modeling and inversion.

Improvement on the inversion of kernel-driven BRDF model

Kernel-driven model was chosen to calculate global albedo in the project of multiangular remote sensor MODIS. The best kernels were selected by the venerable “least square” method. The result of this method was very unstable when only a small amount of angular observations is available. A new criterion has been estalished, called “least variance” for the kernel’s selection. It takes into consideration the effects of model and measurement based on the information inverse theory. Several tests showed that “least variance” has many advantages. First, it is less sensitive to noises. Second, it operates well in small sample size. Third, it depends less on the sampling position.