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Detection of shallow water depth using remotely sensed data
A linear relationship y = ax + b was assumed between the
reflectance (x) and the depth (y). The rectangular domain D may be viewed as a
matrix of order m x n, which is comprised of reflectance matrix Dr
and depth matrix Dd . In the above relationship, a and b were
calculated using the least square approximation in the domain D as
 = 
 The depths at the 2(m+n+2) immediate neibouring pixels of the domain D were computed using the transformation equation 
-------------------- (1)This process is repeated by updating the domain until it merges with the full region of interest. A model region (study area) was selected in conjunction with the satellite imagery and this can be viewed as a 1024 x 1024 pixels. In this region, the bathymetry data was available only for a small area [91x193 pixels]. A 10 x 10 matrix with significant depth variation was selected as the basic domain D, where both reflectance and depth values were available. The Digital Numbers representing reflectance and depth matrices of D are shown in Table 1 and Table 2. Statistical analysis shows that these two matrices are correlated with a correlation coefficient of -0.99. The immediate neighbouring elements of D were computed using the transformation equation (1) and D was updated to 12 x12 matrix, including the new elements. The reflectance and depth matrices of order 12x12 corresponding to the updated domain are shown in Table 3 and Table 4 . The observed depth values of this new domain are shown in Table 5. The comparison of observed and computed depths versus reflectance is given in Fig. 2. The process was repeated with the updated domain until the whole region is covered. Results and Conclusions The Domain Rippling Scheme is a useful technique for the estimation of water depths over shallow water region. The digital satellite image with reflectance values is successfully transformed to depth image using this technique and is shown in Plate 2. A rigorous correlation analysis was done for the observed and computed depth values with various matrix sizes. The correlation analysis results are briefed in Table 6. It is found that the computed and observed depth values have good correlation, particularly in the shallow water region (Fig. 2). It can be seen that for the area under study, the intensity variation with depth is proportionate in shallow water region upto -3m depth contour. Hence it can be concluded that the present method can be restricted to shallow water depths. The analysis can be improved by assuming a nonlinear relationship between the reflectance and the water depth for deeper water region. Also it is important to consider the parameters like suspended sediment concentration and bed characteristics in the model which influence the reflectance. 
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