Simulation of 3-D tidal flat topography based on fractional Brownian motion

The intertidal zone as is one of the most dynamic areas on the earth and conducting topographic surveys is very difficult. It is particularly hard to obtain elevation information when the tidal flat is a mud flat. In this article, we selected Jiuduansha (Jiuduan Shoal) tidal flat as a test area to demonstrate a fractional Brownian motion model based tidal flat elevation estimation. The Jiuduansha is a large shoal with a large mud flat located in the Changjiang River Estuary. Two Landsat TM images and two CBERS CCD images acquired in different seasons in 2008 were processed and waterlines were extracted from images of different times according to the tidal conditions. By considering the fact that the water surface is actually a curved surface, we dissected the waterlines into waterside points and assigned an elevation value to every point through interpolation of the tidal level data taken from nearby tidal observation stations at the similar time when the satellite images were acquired. With the elevation data of the waterside points and digital sea chart depth data, a digital elevation model (DEM) was constructed using the fractional Brownian motion (fBm) model with a midpoint displacement algorithm through the Matlab toolbox. Finally, a quantitative validation of the model was completed using the 17 ground survey data positions on the tidal flat measured in November 2008. The simulation results show a good visual effect and high precision. The mean square root error is 0.155m respectively for the ground survey.