Determine the Stumpf 2003 Model Parameters for Multispectral Remote Sensing Shallow Water Bathymetry

The Stumpf 2003 model is a widely used model for shallow water bathymetry estimation for multi-spectral remote sensing. There are three parameters should be determined in this model. One is the parameter n in the term of a logarithmic ratio, and the other two parameters are m(0) and m(1), which are determined by a linear regression. In many researches the n is assigned as a constant directly. There is no more discussion on how to determine these parameters, especially for the value of n. In this paper, it suggest a two-step-method when using the Stumpf 2003 model for bathymetry estimation. The first step determines the value of the parameter n according to the linearity between the term of a logarithmic ratio and water depth. The second step is to obtain the other two parameters mo and m1 by a conventional linear regression. The method is tested and verified using a WorldView-2 (WV2) multi-spectral image and the corresponding in-situ water bathymetry by a sonar. 512 samples are extracted randomly as a train dataset, these data are used to train the Stumpf 2003 model; the remain 129 samples are collected as a validation dataset. The results show that using the two-step-method can improve the accuracy of bathymetry estimation. According to the train dataset, the RMSE is 3.829 using the model parameters (n=54.766) determined by this method, while the RMSE is 4.005 using the model parameters (n=1000) determined in the conventional way. Similar RMSE results also obtained for the validation dataset, they are 1.753 (n=54.766) and 1.816 (n=1000) respectively. It also shows an improvement. So this paper suggest to use the two-step-method to determine the model parameters for bathymetry estimation when using Stumpf 2003 model.