The Energy Budget of an Altimeter-Derived Baroclinic Tide Model

Over the last few years a number of groups have created maps of the baroclinic tide from satellite altimeter measurements of sea-surface height (SSH). These maps can be used as predictive models for the baroclinic tides, e.g., for removing aliased tidal signals from altimetry, but they can also be used to diagnose aspects of the tidal dynamics. This presentation uses the High Resolution Emprical Tide (HRET) model to compute the phase speed, energy, energy flux, and energy flux divergence of the first few baroclinic modes for the M2, S2, K1, and O1 tides, and compares these with independent estimates from the literature.

The phase speed of the waves in HRET are compared with the theoretically-predicted phase speeds computed from stratification. For the mode-1 M2 waves which are determined most accurately, the theoretical and observed phase speeds agree very well; however, there is a small bias, namely, the theoretical phase speed exceeds the observed phase speed by 1 to 2%. This offset could reflect either a methodological estimation bias, issues with the data used to compute the theoretical phase speed, or a limitation of the theory for the vertical modes.

The phase speed results provide some confidence in the usefulness of linear wave dynamics for interpreting the HRET SSH. Using a simplified form of the momentum equations, the area-integrated kinetic plus potential energy of the mode-1 M2 tide is found to be 43 PJ, larger than in other baroclinic tide models, and with nearly isotropic directional distribution. For mode 1, the divergence of the energy flux diagnosed from HRET agrees well with previous estimates based on the barotropic tides. For the most accurately-determined mode-1 M2 tide, the results provide new information about sources and sinks of baroclinic energy along the continental shelves, and they are used to examine the accuracy of a commonly-used approximation of the baroclinic energy flux.