Statistical analysis of beach profiles - A spatiotemporal functional approach

Beach profile data sets provide valuable insight into the morphological evolution of sandy shorelines. However, beach monitoring schemes often show large variability in temporal and spatial intervals between beach profiles. Moreover, beach profiles are often incomplete (i.e. only a part of the profile is measured) and data gaps are unavoidable. The resulting irregular sets of beach profiles complicate statistical analysis and previous studies on the morphological evolution and the effects of external influences have often omitted incomplete beach profiles. In this perspective, a statistical model is suggested to study beach profiles and to identify the effects of external influences. To be precise, the statistical model can be used (1) to determine the temporal and spatial variability of beach profiles while accounting for autoregressive dependencies in space and time, (2) to identify effects of external influences, (3) to predict complete beach profiles at unknown locations (i.e., interpolation between beach profiles), and (4) to forecast complete beach profiles accounting for external influences, such as storm events or nourishments. To illustrate the applicability of this model to irregular beach profile data, this state-of-the-art functional, spatiotemporal model was applied to beach profiles of the island of Sylt, Germany. In a first case study on submerged beach profiles, a decreasing temporal dependency between the profiles in the offshore direction was revealed, highlighting that less frequent measurements of offshore areas would suffice. A second analysis of the emerged beach profiles revealed the general effect of storm conditions (wave heights > 5 m) on subsequently measured beach profiles, which was statistically significant, and the profiles eroded with approximately 0.2-0.7 m in height. In summary, this study proposes and explores the application of a state-of-the-art statistical model to investigate beach profile changes from increasingly diverse and large profile data in coastal engineering and management.