cover component within a pixel by inversion technique, a typical solution of which is the classical least squares approximation, in matrix notation,
However, since there is a constraint to sum up the fractional cover to one by Eq. (2), then a Lagrangian formulation gives the more appropriate solution:


where the U=R^TN^-1R, a =(j^TUj)^-1, J (=jj^T) is an n x n identity matrix of n x 1 js with elements =1 consisting of and N represents the sensor noise characterized by the variance-covariance matrix. The equivalent f for the soil and vegetation cover are used as the values percentage soil cover (PSC) and PVC respectively. PVC quantifies merely the portion of exposed canopy. In hydrologic modeling as will be shown later, it becomes more important to determine the fractional abundance or sparsity of vegetation, which can be adequately described by LAI. The reflectance model of Gilabert et al. (2000) is modified obtaining:
LAI=-ln(PVC)/C

C is regarded as a weighing parameter assumed to be invariant with wavelength and assumes complete absorption. Its value rather, varies with angle of light source and plant architecture. An immediate application of LAI is to compute for the interception capacity of a particular canopy for rain expressed as a function of the LAI given by:

S_r = S_r0LAI/LAI₀

where S_r is the canopy interception capacity (m), S_r0 and LAI₀ are the maximum canopy interception capacity and leaf area index (m² m^-2) respectively specific for each vegetation type.

2.4 Runoff Modeling and Sediment Routing
The overland flow runoff routing model utilizes the DEM (digital elevation model)-based diffusion wave equation according to the procedure outlined by Wang and Hjelmfelt (1998) while the sediment yield component is taken from SHESED model of Wicks and Bathhurst (1996). Both models are ideal for small flat watersheds where the main processes affecting sediment yield are soil erosion by raindrop impact and overland flow and sediment transport by overland and bed channel flows. The results of the PVC and PSC computations may be used on the following expression:

D_R = K_rF_w(1-PSC)[(1-PVC)M_R + M_D]
where D_R is the soil detached by raindrop impact (kg m^-2 s^-1), K_r is the raindrop soil erodibility coefficient varying according to the type of soil, F_w is the water depth correction factor, while M_R and M_D are momentum squared for raindrop and leaf drip respectively. Values or the expressions to obtain K_r, F_w, M_R and M_D may be taken from Wicks and Bathhurst (1996) and is still subject to calibration. Application of unmixing results to Eqs. (5) and (6) allow attribute variability within one pixel unafforded in other routing techniques.

2.5 Data Processing and Hydrologic Modeling Steps
The spectral signatures for six full-grown vegetation and three soil types were average-sliced into three ranges equivalent to the spectral sensitivity of a colour film with a minus-blue filter. Thirteen aerial photographs were scanned, registered to a 1:25,000 topographic map at 10 m resampling, and mosaicked, with correction for vignetting effects. Radiometric calibration was performed by obtaining coefficients from fitting the RGB values of homogenous landcover types with their equivalent sliced signatures. These coefficients were then applied to the whole