Application of adjoint frequency response analysis to low-mode internal tides on the Australian North West Shelf

An adjoint model is a useful tool to calculate the sensitivity of an objective function to model input data including forcing. However, interpreting the results is not necessarily straightforward because both the sensitivity and forcing vary in space and time. This study proposes to combine adjoint modeling and the frequency response analysis to distil the results into maps of 'source function' for individual frequencies. Since the spatial integral of the source function yields the (Fourier) amplitude of the objective function, the maps provide a convenient way to identify the source regions for periodic variation of the objective function. As an example, the method is applied to semi-diurnal internal tides on the Australian North West Shelf using the adjoint of MITgcm generated by OpenAD. The objective function is vertical mode 1 internal tides at a site of mooring observation on the shelf. The results are compared with the common 'forcing function' of internal tides, which can be calculated from barotropic tidal currents, bottom slope, and vertical modes, without numerical modeling. The comparison is used to illustrate how the source function complements the forcing function: the forcing function is useful to identify generation regions that are important overall, whereas the source function is useful to identify generation regions relevant to sites of interest, such as observation sites. The comparison shows that the source function is particularly useful to identify remote generation regions, which are difficult to identify from the forcing function.