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

• Main Authors: Patrick Bogaert, Anne-Lise Montreuil, Margaret Chen
• Format: Article
• Language: English
• Published: MDPI AG 2020-11-01
• Series: Journal of Marine Science and Engineering
• Subjects: time and space variograms; intertidal barred beach morphology; stochastic modeling; space-time covariance model; data-based modeling
• Online Access: https://www.mdpi.com/2077-1312/8/11/901

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 <inline-formula><math display="inline"><semantics><mrow><mi>t</mi><mo>+</mo><mi>τ</mi></mrow></semantics></math></inline-formula>, starting from observed profiles at time instants <i>t</i>. 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 m<inline-formula><math display="inline"><semantics><msup><mrow></mrow><mn>3</mn></msup></semantics></math></inline-formula>/m. The time variogram also shows that 90% of maximum variability is reached for a time interval <inline-formula><math display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> 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.