Bivariate fractal interpolation for estimating rough channel bedform

The rough bedform is estimated using the self-similar characteristics of bedforms together with the bivariate fractal interpolation method that is based upon the iterative function system. The interpolation fields A_k are determined using the Kriging interpolation method with a spherical variogram for Kriging. The vertical scaling factors s_m,n are obtained through the use of the multi-variate statistical analysis of interpolated data. The results show that the similarity between the estimated bedforms and the initial bedforms can be improved with increasing the number of data items interpolation i_c. In particular, when i_c approaches to a very low value of the threshold (0.0625), a high level similarity in bedforms is reached. The estimated fractal dimension will be also close to its theoretical value. The bivariate fractal interpolation method can be used as an effective means of estimating irregular bedforms in rough channels with a high level similarity, where observed data are insufficient.