Abstract

1. Introduction

The main purpose of this paper is to test the possibility of inverting a non-linear model of ground reflectance on AVIRIS scenes containing both forested areas and several types of agricultural fields. In this simple model, we first separate the soil fraction from the green vegetation fraction which is described by a Kubelka-Munk formula for an optically thick medium. Chlorophyll and water are taken into account by using their respective specific absorption coefficients gleaned in the literature. The temporal variability of the suspected biochemical signature is also examined as scenes were acquired on the same test sites at about two weeks interval.

2. Test Site Description

The agricultural study area is situated approximately 20 km West of the City of Freiburg in the Upper Rhine Valley and has an extension of 6 x 4 km This test site contains both forested areas (19%) and agricultural areas (50%). The agricultural part is intensively cultivated with the main crops being wheat, corn, barley, potatoes, sugar beet, and vine. The average field size of approximately 1.5 ha is representative for small scale European farming. The area is topographically flat at an altitude of 200 m above sea level. The soils are dominated by the quarternary sediments of the Rhine River and thus show a great variety of grain size distribution and high porosity. The latter accompanied by low clay contents results in high infiltration rates requiring the irrigation of the intensive cultivation areas of corn.

The Black Forest test site is located near the town of Villingen/Schwennigen at an altitude ranging from 800 to 960 m above sea level. Beside some small areas covered by Scots pine (Pinus silvestris L.) and silver fir (Abies alba Mill.), the dominant tree specie of the overall region is Norway spruce (Picea abies) with tree ages from 80 to 120 years and tree heights from 30 to 40 m. The understory is mainly composed of blueberries and of young spruce and fir trees for rejuvenation. Soils are dominated by sandy-loamy acid brown earths.

3. Modeling Leaf Spectra

We are presently working on radiative transfer models which explicitly include the leaf biochemical components. These biochemicals are introduced by considering each of their contribution in the spectral absorption coefficient of the leaf tissue. It is not the purpose of this paper to present this work which has not yet reached its conclusions. However, the studies conducted so far on laboratory spectra have shown:

• that the 1.7 mm feature cannot tee explained by water alone,
• that it-cannot be reproduced by using the specific absorption coefficient spectra available today for lignin (wood), cellulose, starch or proteins,
• that the model based on chlorophyll and water can reproduce accurately the spectrum in some spectral regions where these two components dominate the absorption (from 0.5 to 0.73 mm and from 1.5 to 1.65 mm respectively),
• that the amplitude of the 1.7 m m is dependent on the type of vegetation: thus in Figure l, one can notice that the residual is higher for the spruce needles than for the other plant leaves.

4. Processing of AVIRIS Data

As the AVIRIS scenes contained both forested areas with a high vegetation cover and agricultural fields of which some have a low cover, the analysis had to take into account the soil reflectance. This was done in the simplest way by assembling a linear mixing of soil and vegetation spectra; we therefore write:
 

Rp(l ) = as× Rs(l ) + av× Rv(l )

(l)

where R_p(l ) is the reflectance of the pixel, R_s(l ) is the soil reflectance, R_v(l ) is the vegetation reflectance, a_s and a_v are the corresponding abundances in the pixel spectrum. The soil spectrum was taken from the image as the mean spectrum of a small area known to be bare soil, and assumed to be representative of the scene. The vegetation spectrum was modeled with a Kubelka-Munk formula adapted for an optically thick homogeneous medium:
 

	(2)
	(3)

where w ₀(l ) is the single scattering albedo of the medium, k(l ) its absorption coefficient, and s its scattering coefficient. As the diffusion phenomena inside leaf tissues are mainly due to multiple reflections and refractions, s can reasonably be assumed to be wavelength independent. Allen and Richardson (1968) also described the interaction of light with a plant canopy with the Kubelka-Munk theory, one must however highlight that the scattering coefficient defined by these authors (let note s') is in fact a backscattering coefficient which differs from the scattering coefficient by a factor two: s = 2 x s'. Equation 2 depends on the definition adopted. Regarding the absorption in vegetation, we assume that it is mainly due to chlorophyll and water and write:
 

(4)

where k_chl(l ) is the specific absorption coefficient of chlorophyll a+b expressed in cm^{2× m} g^-1, k_w(l ) is the specific absorption coefficient of water expressed in cm^-1 (we used for chlorophylls the in vivo absorption coefficient of Jacquemoud and Baret (1990) and the measurements of Curcio and Petty (1951) for water), c_chl is the chlorophyll concentration expressed in mg× cm^-2, and c_w is the equivalent water thickness expressed in cm. Finally, a_chl and a_w defined as the above concentrations divided by the scattering coefficient are the independent parameters of the vegetation spectrum model.

By combining formula (1), (2), (3) and (4), one obtains a model of the pixel reflectance as a non-linear function of four parameters, a_s, a_v, a_chl, and a_w: these parameters have been determined by least mean square fitting on the AVIRIS pixel reflectance by using a Marquardt algorithm (Marquardt, 1963). Two spectral windows were used in the fitting: the region ranging from 0.5 to 0.73 mm and that from 1.5 to 1.65 mm where the chlorophyll and water absorptions are respectively dominant. Once the fitting is performed, we can compute a "Green Vegetation Fraction" of the pixel, defined by:
 

(5)

We also retrieve a measured spectrum of the green vegetation fraction R_vm(l ):
 

(6)

Assuming that the 1.7 mm feature is an absorption due to a component of vegetation, we logically evaluate its magnitude from the absorptance corresponding to the measured (A_vm) and fitted vegetation spectra (A_v). The absorptance has been defined in this study as k/s and obtained by combining equations (2) and (3):
 

(7)

The residual has then been evaluated in the 1.65 to 1.76 mm spectral interval as:
 

(8)

where the average is taken on the N AVIRIS channels in this spectral window. In addition, several vegetation indices such as the NDVI (Normalized), the MSI Moisture Stress Index), ...etc have been computed. This analysis procedure was applied to four AVIRIS scenes (the Black Forest the Freiburg test sites on two dates). The processing of one scene took about 8 hours of computing tame on a SUN SPARC 10 workstation.

5. Results

The results of the analysis performed on a part of the Freiburg test site, which contains both forested surfaces (2 large areas at the top/right part and a smaller one in the right corner of the image) and agricultural units, are gathered in Figures 4 and 5. The rectangular area in the top left corner of the image is a small lake; a small town is located in the centre of the image. The images in the left column of the figures represent processed AVIRIS data from the overflight of the 5th of July, the right column of the 22nd of July. By comparing the images from the two overflights a number of qualitative comments can already be made, but a detailed interpretation will only be possible by the confrontation with ground data, which are at the moment not available.

Over the forested regions, all the calculated indices and parameters are very stable from one overflight to the other, this was to be expected as a forest does not change significantly within a two week period. On the contrary, all the parameters calculated on the agricultural units reflect the growing and harvesting cycle of vegetation. Compared with the vegetation indices NDVI and MSI, the chlorophyll and water parameter (a_chl and a_w) demonstrate a higher sensitivity to the growing process. However, the interpretation of these two parameters is difficult as the hypothesis of the model to have an optically thick canopy probably does not hold on the fields. The image of the Green Vegetation Fraction seems to contain essentially the same information as the NDVI image although showing a better dynamics with respect to the cover type.

Major emphasis has been placed on the residual image in the spectral region of 1.7 mm because different biochemical components like lignin and cellulose have absorption features near this wavelength region. While prediction of the vegetation spectral reflectance by the model does not vary significantly in accuracy with wavelength in the other spectral domains, the residual seems to be higher around 1.7 mm specially in the case of the forest spectrum (Figure 3). This is strengthened by Figure 5 where it is obvious that this residual clearly discriminates between forest and other types of vegetation. Within the forest, the spatial variability of the residual is clearly correlated with that of the Moisture Stress Index MSI (negative correlation) and the water parameter a_w (positive correlation). The situation is more complex regarding the agricultural units within the test site. By comparing the two residual images, several fields appear brighter (higher residual) on the 22nd of July, which could ; be related to the maturation of the different crops. A definite interpretation (taking into account the very low values of the residual) will only be possible by comparing these images with the agricultural and meteorological data of the local authorities.

A comparison of the AVIRIS images of the Black Forest test site revealed no significant differences between the two overflights regarding the calculated vegetation indices and parameters. Of major interest are three well documented plots within this forest, of which two have been fertilized with ammonium sulfate of different concentrations for the last three years. According to our analysis eventual effects of the fertilization on canopy characteristics like chlorophyll concentration, water content and the biochemical components in the 1.7 mm region were not detectable.

6. Conclusion

This work has also shown the possibility of inverting non-linear models of the green vegetation spectrum on imaging spectrometer data. Although the model used is excessively simple, it contains explicitly the effect of the two main components which are chlorophyll and water, and is able to describe accurately the spectrum shape in two spectral windows. This result is encouraging to pursue this approach by using more detailed models which will make use of the entire spectrum and will provide parameters more easily interpretable in terms of the canopy characteristics.

7. References