# The Resolution Capabilities of Geostrophic Velocity, Relative Vorticity and Ekman Pumping Fields Estimated from Noisy SWOT Observations of Sea Surface Height

**CoAuthors**

**Event: **2015 Ocean Surface Topography Science Team Meeting

**Session: **Science II: Mesoscale and sub-mesoscale ocean processes: current understanding and preparation for SWOT

**Presentation type: **Type Oral

A goal of the Surface Water and Ocean Topography (SWOT) altimetry mission is to measure sea surface height (SSH) with sufficient accuracy to achieve a signal-to-noise variance ratio greater than 1 for wavelengths of 15–1000 km over 68% of the world ocean. To achieve this goal, the SWOT Science Requirements Document specifies that the wavenumber power spectral density of the white-noise component of the total SSH measurement errors must be no larger than 2 cm2/cpkm (cycles per km) for wavenumbers between 1/1000 cpkm and 1/15 cpkm. It can be shown that this corresponds to uncorrelated measurement errors with an RMS value of 2.74 cm after filtering with a half-power filter cutoff wavelength of 2 km.

The objective of this presentation is to quantify the effects of this SSH measurement noise on the resolutions of geostrophic velocity, relative vorticity and wind-driven Ekman pumping fields estimated from SWOT measurements of SSH. Derivation of these higher-order quantities from SSH requires single differentiation for geostrophic velocity, double differentiation for relative vorticity and triple differentiation for the dominant contribution to Ekman pumping. These differentiations amplify the noise in the SSH measurements, thus reducing the effective resolutions compared with that achieved for SSH itself.

The resolution capabilities will be assessed based on the SSH fields from a high-resolution model of the California Current System, with and without the addition of uncorrelated noise with the aforementioned RMS of 2.74 cm. The resolutions will be quantified from alongshore wavenumber spectral analysis and from the ratio of the variances of the signal and noise fields computed over the model domain as a function of the half-power filter cutoff of 2-dimensional smoothing with wavelengths ranging from 10 km to 100 km.

The objective of this presentation is to quantify the effects of this SSH measurement noise on the resolutions of geostrophic velocity, relative vorticity and wind-driven Ekman pumping fields estimated from SWOT measurements of SSH. Derivation of these higher-order quantities from SSH requires single differentiation for geostrophic velocity, double differentiation for relative vorticity and triple differentiation for the dominant contribution to Ekman pumping. These differentiations amplify the noise in the SSH measurements, thus reducing the effective resolutions compared with that achieved for SSH itself.

The resolution capabilities will be assessed based on the SSH fields from a high-resolution model of the California Current System, with and without the addition of uncorrelated noise with the aforementioned RMS of 2.74 cm. The resolutions will be quantified from alongshore wavenumber spectral analysis and from the ratio of the variances of the signal and noise fields computed over the model domain as a function of the half-power filter cutoff of 2-dimensional smoothing with wavelengths ranging from 10 km to 100 km.