Long-term morphodynamic evolution of estuaries: An inverse problem

A new technique for predicting long-term variations in estuary morphology is developed using a morphological evolution equation that isolates diffusive and non-diffusive processes in estuaries. The contribution from non-diffusive processes to the morphological changes of the estuary is incorporated in the governing equation by a source function. The source function is derived by solving an inverse problem using historic survey data of the Humber estuary, UK covering a period of 150 years. Source functions derived for the consecutive pairs of bathymetry surveys show a significant structure persistent throughout the entire data set. Large scale features such as tidal channels, tidal flats and linear banks in the outer estuary are persistently visible in the source function. Empirical Orthogonal Function (EOF) analysis is used to analyse the spatial and temporal variation in the source function. The first spatial eigenfunction which corresponds to the time-mean value of the source function captures over 92% of the mean square of the data. Over 65% of the data variance is captured by the first six eigenfunctions. The first temporal eigenfunction which corresponds to the mean value of the source function is almost constant as expected.