Predicting Morphodynamics for Beach Intertidal Systems in the North Sea: A Space-Time Stochastic Approach

The ability to accurately predict beach morphodynamics is of primary interest for coastal scientists and managers. With this goal in mind, a stochastic model of a sandy macrotidal barred beach is developed that is based on cross-shore elevation profiles. Intertidal elevation was monitored from monthly to annually for 19 years through Real Time Kinematics-GPS (RTK-GPS) and LiDAR surveys, and monthly during two years with an RTK-GPS. In addition, during two campaigns of about two weeks, intensive surveys on a daily basis were performed with an RTK-GPS on a different set of profiles. Based on the measurements, space and time variograms are constructed in order to assess the spatial and temporal dependencies of these elevations. A separable space-time covariance model is then built from them in order to generate a large number of plausible future profiles at arbitrary time instants t + τ, starting from observed profiles at time instants t. For each simulation, the total displaced sand volume is computed and a distribution is obtained. The mean of this distribution is in good agreement with the total displaced sand volume measured on the profiles, provided that they are lower than 45 m³/m. The time variogram also shows that 90% of maximum variability is reached for a time interval τ of three years. These results demonstrate how the temporal evolution of an integrated property, like the total displaced sand volume, can be estimated over time. This suggests that a similar stochastic approach could be useful for estimating other properties as long as one is able to capture the stochastic space-time variability of the underlying processes.