## Empirical Relationship Based on Vegetation Indices

Vegetation indices are designed to maximize sensitivity to the vegetation characteristics while minimizing confounding factors such as soil background reflectance, directional, or atmospheric effects.

The most commonly used vegetation indices utilize the information contained in red and near-infrared (NIR) canopy reflectances or radiances. They are combined in the form of ratios: ratio vegetation index (RVI) or normalized difference vegetation index (NDVI).

RVI = Pred /Pnir NDVI = (pnir - Pred)/(Pnir + Pred) [6]

where p^D and pNIR represent spectral reflectances in the red and NIR regions.

These indices enhance the contrast between soil and vegetation but minimize the effects of illumination conditions. However, they are sensitive to optical properties of soil background. For a given amount of vegetation, darker soil substrates result in higher vegetation index (VI) values. The soil adjusted vegetation index (SAVI) is used to suppress the soil effect:

The constant C is introduced in order to minimize soil-brightness influences. It can vary from zero to infinity as a function of the canopy density. If C = 0, SAVI is equivalent to NDVI.

The enhanced vegetation index (EVI) is developed to optimize the vegetation signal with improved sensitivity in high biomass regions:

Pnir - Pred

Where pBlue is the surface reflectance at the blue band, and Cb C2 are the coefficients of the aerosol resistance term, X is the canopy background adjustment factor, and G is the gain factor.

A common procedure to estimate LAI is to establish an empirical relationship between VI and LAI by statistically fitting observed LAI values to the corresponding SVI. Among proposed LAI—VI relations are the following forms:

L = Ax3 + Bx2 + Cx + D L = A + BxC L = - 1/2A ln(l - x) L = f (x)

Where x is either VI or reflectances derived from remotely sensed data. Coefficients A, B, C, and D are empirical parameters and vary with vegetation types. The last equation is a generic function of any form. Given a set of coefficients, the equations can be applied to remotely sensed images to map the spatial LAI distributions.

Generally, the vegetation indices approach a saturation level asymptotically for LAI ranging from 2 to 6, depending on the type of VI used, the vegetation studied, and experimental conditions. The advantage of this approach is its simplicity and ease of computation. The major limitation of this VI approach is that there is no universal LAI-VI equation applicable to diverse vegetation types because the empirical coefficients depend primarily on vegetation types. To operationally use this VI approach, an LAI-VI equation must be established for each vegetation type, for example, coniferous, deciduous, mixed forests and nonforest vegetation. However, this would require substantial LAI measurements and corresponding remote-sensing data.

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