The primary objective for terrestrial remote sensing is to provide qualitative and quantitative information about the state and behavior of continental surfaces. This depends on the resolution of an inverse problem to retrieve several parameters that characterize surface radiances measured by satellite sensors. Such an inversion is made up of two basic elements, namely a model of the radiance field and a numerical algorithm that determines models parameters by an optimal fitting between observed and predicted radiance fields.
The objectives of the project discussed here were to understand the radiation transport within plant canopies and within the atmosphere (aerosol layers, water and ice clouds), to develop a physical modeling of relevant processes, and to extract information of interest about land surface characteristics through an inversion procedure.
A number of canopy bidirectional reflectance models have been developed in recent decades, generally falling into three categories. (1) Computer simulation models (including Monte-Carlo and radiosity) require an explicit description of the medium and of all interaction processes taking place between light and the targets, principally according to the laws of geometrical optics. The resolution of the problem is made on a photon-by-photon basis. These models are very realistic, generally very time consuming, and use too many parameters to allow for their inversion. (2) On the other extreme, empirical or semi-empirical models only describe the shape of the Bidirectional Reflectance Factor (BDRF) by using more or less simple mathematical functions. The parameters used generally have no intrinsic physical meaning. (3) Conversely, physical models, such as those described below, can be inverted, use measurable quantities as variables, and are based on the analytical or numerical resolution of a transport equation with appropriate boundary conditions. Hybrid models have also been developed with some of the advantages and disadvantages of the three types.
In the classical radiation transport equation in a plane-parallel medium the extinction coefficient is modified to take into account the hot-spot effect. Very simple boundary conditions are selected: at the ground there is a Lambertian surface, and a clear-sky at mosphere overlays the canopy. The leaf scattering phase function is computed using the bi-Lambertian model of Ross and Nilson. In this model a fraction rL of the intercepted energy is re-radiated as a cosine distribution around the leaf normal, another part tLis transmitted on the other side in the same manner, and the residual fraction is absorbed.
When observing the radiation exiting a vegetation canopy near the retro-solar direction (where no shadows occur) we can observe a specific signature called the hot-spot effect, corresponding to an increase of reflectance. This feature is related to the finite size of the leaves and to the holes between these leaves. An important element of the model discussed here is a parameterization which compensates for this hot-spot effect.
With these specifications and parameterizations, it is possible to solve the radiation transport problem and derive a physical BDRF model. Some analytical solutions can be obtained for uncollided and first-collided radiations including the hot-spot effect. The computation of multiple scattering contribution is made by means of the Discrete Ordinates Method. Finally, a model emerges using a limited number of parameters for describing the architecture of the canopy, the Leaf Area Index, a hot-spot parameter, parameters for the leaf angle distribution, specified leaf optical properties, and soil albedo. An example of what the model can produce is seen in Figure 5.1, a polar plot of the BDRF of an erectophile canopy as a function of the viewing angle.
Typical values were used for the canopy parameters, and the hot-spot parameter was 2rL=0.20
For some applications (for instance as the bottom condition in atmospheric problems or for inversion purposes) it is necessary to have fast, but still realistic models. Therefore a simplified version of the model was developed to accelerate BDRF calculations. In this model the multiple scattering contribution was approximated considering an isotropic scattering phase function and non-dependence on the viewing angle. Advantages of this model include the fact that it is about 30 times faster than the exact resolution version, with discrepancies of less than 1% in the visible range. The principle drawback is that the simplified model shows about 5% average difference with respect to the exact resolution in the near infra-red (because multiple scattering was considered as independent of the viewing angle the difference is important at nadir and for large viewing zenith angles). Accordingly, this simplified model presents a good compromise between accuracy and computational time.
These two models were compared with a Monte-Carlo ray-tracing code developed by Yves Govaerts at the JRC in Ispra, Italy. In this model the hot-spot is not parameterized but appears naturally because of the finite size of the leaves and their spatial arrangement while it was simply included in the previous models by means of a geometrical modification of the extinction coefficient. Figure 5.2a compares the results of the three models for a planophile canopy over a dark soil in the visible region; Figure 5.2b compares model results for an erectophile canopy and a bright soil in the near infra-red.
As can be seen in the figures, the agreement between the three models is excellent in the visible, especially in the hot-spot region. In the near infra-red the exact model is still in very good agreement with the Monte-Carlo, and as expected, the simplified model diverges slightly. These comparisons validate the parameterization used for the hot-spot effect.
The Inversion Problem
In the inverse problem the data are BDRFs and the unknowns are the model canopy characteristics. For solving this problem we minimize a non-linear merit function using an iterative numerical algorithm to find the set of model parameters that best fit the data. The minimization process starts with an initial guess for each of the parameters, which are also subject to fixed upper and lower bounds (chosen according to physical constraints). Results of a sensitivity study reveal that in this inversion, retrievals of the Leaf Area Index (LAI) are easier in the visible over bright soils and in the near infra-red over dark soils ( i. e. in the regions where there is the maximum contrast between soil and canopy). The computational time increases non-linearly with the number of inverted parameters and there are difficulties in simultaneously inverting more than seven parameters. There is also a need for sampling in the hot-spot direction to improve the retrieval of all parameters. Leaf reflectance and transmittance were shown to be little influenced by errors made on the retrieval of other parameters and are always accurately retrieved. Finally, the soil albedo is found to be very difficult to estimate.
This model was then applied to the FIFE 1989 data set, for measurements made by Don Deering with the PARABOLA instrument for three wavelengths. The data set includes measured BiDirectional Reflectance Factors for several solar zenith angles ranging from 33.5° to 74.1°. Canopy characteristics were also measured (site 916, 4439-PAR) or determined through an averaging scheme taking account of the species abundances. Inversions were made separately in each channel and for each solar zenith angle. In a first step, perfect clear-sky conditions were assumed. Simultaneously inverting all of the parameters yielded the following results: the estimation of leaf optical properties is very accurate; the LAI was better estimated than expected from the previous sensitivity study; and the retrieved average leaf inclination angle indicates erectophile leaves. Good agreement was found between retrieved and measured canopy characteristics, with the near infra-red channel delivering the best results for canopy architecture.
The diffuse part of incident radiation was found to be about 5%, 10% and 15% respectively in channels 1, 2 and 3. Then another series of inversions was conducted consider ing direct plus diffuse sky light. The results were not very different from the previous ones, except for the Leaf Angle Distribution which was found slightly more erectophile with an Average Leaf Inclination Angle about 64° in all channels while the measured ALA was 65°. These results show that it is possible to accurately retrieve all canopy characteristics from actual reflectance measurements by means of an inversion procedure.
IWACS Models
There is a need to couple the vegetation canopy with the atmosphere, making corrections that account for the effects of aerosol layers, water clouds and ice clouds above the surface. Coupled models are also required because the assumption that downward radiation at the top-of-the-canopy is the sum of direct plus isotropic diffuse components is inadequate. In addition, it is wrong for atmospheric problems to approximate vegetated surfaces as Lambertian reflectors. With all of this in mind, an Ice-Water-Aerosols -Canopy-Soil (IWACS) model was developed.
Figure 5.3 shows the concept behind a coupled atmosphere-canopy model. The first step is specifying the properties of the atmosphere. Atmospheric layers are considered as turbid media with a random orientation of the scattering elements in 3-dimensional space, so their scattering phase function is rotationally invariant. For aerosols, it is calculated using Henyey-Greenstein function, for spherical water droplets the Mie theory was used, and for ice crystals, computations were made with a Monte-Carlo ray-tracing code. The ice crystals modeled were bullet-rosettes with four branches because cirrus clouds are known to be composed of this type of particle. The scattering matrix for ice crystals and water droplets was determined and the transport problem could then be solved.
The upward radiation at the top of the atmosphere in the visible range is plotted when a typical vegetation canopy is surmounted by an aerosol layer, a cirrus cloud, or a water cloud, for several small optical depths (see Figure 5.4).
When the optical depth increases, the hot-spot peak disappears and the reflectance increases at large viewing angles. For water clouds and ice clouds, this peak was cut because it extended beyond the graphs. In both cases the shape of the curves are very different from the previous case and we can recognize on both sides of the hot-spot peak typical features characteristic of ice clouds and water droplets (rainbows). In the near infra-red region, the behavior is very similar, but the net atmospheric effect is to decrease reflectance instead of increasing it.
When there are thin water or ice clouds above the vegetation canopy they are easy to detect, but thin aerosols layers are difficult to detect and may have a significant impact on the retrieval of canopy characteristics by means of inversion techniques or by using vegetation indices. These results emphasize the importance of atmospheric corrections for both satellite- and ground-based measurements.