An Approach to Empirical Mapping of Incoherent Internal Tides for SWOT

Separating balanced motions from internal waves is one of the major challenges facing the SWOT mission. In many areas tides are an important internal wave component, which being quasi-regular, might be estimated and removed. Maps of coherent internal tides (IT) are already available as corrections for SWOT data, but in many areas the incoherent component is at least as large, and this remains problematic. Here we describe initial tests of a new scheme for direct estimation of this incoherent component, using the sparse sampling that will be available from SWOT, plus perhaps a few nadir altimeters. Our scheme is based on fitting all sea surface heights (SSH) data in a short (e.g., 2 week) time window within a small area (e.g., 7 x 7 degrees) using a set of spatio-temporal basis functions defined by tidal frequency and spatial structure derived from the HYCOM model run with tides. More specifically, we derive spatial basis functions from Principal Component Analysis (PCA) of the series of complex harmonic constants estimated for two week overlapping time windows extracted from the steric component of a one year run of hourly HYCOM SSH outputs. As an initial "proof of concept" test we focus on an area off the Amazon Shelf, where temporally incoherent internal tides are known to be significant. Synthetic SWOT data are generated by sampling the same one year HYCOM run used for PCA, using the NASA swotsimulator with SWOT-like noise added. A stationary IT component, defined by harmonic analysis of the yearlong HYCOM run, as well as long-wave signals, estimated by smoothing along track, was subtracted from the synthetic data prior to estimating temporally varying basis function coefficients for each time window with least squares. Results were compared to harmonically analyzed HYCOM SSH fields in every time window, to define percent of signal fit. In areas where variable M2 IT is strongest, the stationary IT component accounts for under ~40% of total M2 IT signal; fitting residuals with the derived basis functions explains a further ~40% of the IT variance, making the fraction of M2 IT signal fit by the combined (stationary + time variable) ~80% on average.