Feasibility of estimating large-scale sea surface height from surface current velocity streamfunction fields

We assess the feasibility of using measurements of ocean surface currents to infer variability in sea surface height (SSH). Motivation for this analysis comes from the availability of surface current observations afforded by Doppler scatterometry, such as the airborne DopplerScatt and a future spaceborne Winds and Current Mission (WaCM). Surface current velocities are decomposed into irrotational and non-divergent components by means of a Helmholtz decomposition, which yields the streamfunction and velocity potential. The streamfunction is hypothesized to be related to the SSH under the assumption of geostrophically balanced flow. The specific goals of this study are to (1) quantify the correspondence between the streamfunction and SSH, including assessing the range of spatial and temporal scales on which this technique is most applicable; and (2) test various numerical techniques for estimating the streamfunction and velocity potential, including the effects of expected observational noise, sampling errors, unbalanced flow components, and specification of boundary conditions in limited domains (e.g., satellite measurement swaths).

For this analysis, the surface streamfunction and velocity potential fields were computed using surface currents from high-resolution ocean model simulations, including a ROMS simulation over the California Current System and a MITgcm simulation in the entire Pacific basin. Both simulations provide instantaneous solutions for SSH and surface currents, which were used to quantify the relationship between the surface streamfunction and SSH. Cross-spectral statistics between the model SSH fields and streamfunction fields estimated from the model velocity fields indicate squared coherence values greater than 0.9 for wavelengths longer than about 100km. On these spatial scales, the transfer function is nearly unity and the phase spectra are nearly zero, consistent with our hypothesis that the surface streamfunction is related directly to the large-scale SSH field. These results suggest that instantaneous snapshots of the mesoscale SSH field can be estimated from the streamfunction field with higher resolution than the 200km by about one month resolution of SSH fields constructed from multi-mission nadir altimeter data.