Analysis of the drainage density of experimental and modelled tidal networks

Abstract. Based on controlled laboratory experiments, we numerically simulate the initiation and long-term evolution of back-barrier tidal networks in micro-tidal and meso-tidal conditions. The simulated pattern formation is comparable to the morphological growth observed in the laboratory, which is characterised by relatively rapid initiation and slower adjustment towards an equilibrium state. The simulated velocity field is in agreement with natural reference systems such as the micro-tidal Venice Lagoon and the meso-tidal Wadden Sea. Special attention is given to the concept of drainage density, which is measured on the basis of the exceedance probability distribution of the unchannelled flow lengths. Model results indicate that the exceedance probability distribution is characterised by an approximately exponential trend, similar to the results of laboratory experiments and observations in natural systems. The drainage density increases greatly during the initial phase of tidal network development, while it slows down when the system approaches equilibrium. Due to the larger tidal prism, the tidal basin has a larger drainage density for the meso-tidal condition (after the same amount of time) than the micro-tidal case. In both micro-tidal and meso-tidal simulations, it is found that there is an initial rapid increase of the tidal prism which soon reaches a relatively steady value (after approximately 40 yr), while the drainage density adjusts more slowly. In agreement with the laboratory experiments, the initial bottom perturbations play an important role in determining the morphological development and hence the exceedance probability distribution of the unchannelled flow lengths. Overall, our study indicates an agreement of the geometric characteristics between the numerical and experimental tidal networks.