The Application of Mathematical Analysis to Examine the Beach Erosion along the Upper Texas Coast

Abstract

The upper Texas coast has been severely damaged by repeated beach erosion without any landfall of tropical storm. Since the average wave height was lower than 1.5 m and the mean tide range was smaller than 0.5 m there, they were not enough to explain the extreme erosion along the coast. Many studies had been conducted to find the causes of continuous erosion and then overwash was suspected by morphological analysis. The past studies, through the analysis of the observation data, concluded that the impact of remote storm might be a major cause of coastal erosion. The Texas Land Office has developed a master plan for coastal resilience and they switched to recovery from investigation. However, beach erosion is still a complicated process and continuous erosion has not been studied until now. For that reason, we here propose an alternative way for the further examination. A mathematical approach called as Empirical Orthogonal Function (EOF) is chosen to analyze spatiotemporal variations. We here applied the EOF method to the observed beach profile data to examine the spatiotemporal characteristics of waves related to the erosion problem. During the observation, the landfall of hurricane was made in the study area and it would be an interesting analysis of affected or unaffected beach change by storm. The short and long-term variations by landfall of storm or impact of remote storm were also studied by EOF method respectively. The dominance of cross-shore process such as overwash was also analyzed in this study.