Recent technological developments have resulted in two techniques for estimating surface velocity with higher resolution than can be achieved from presently available nadir altimeter data: (1) Geostrophically computed estimates from high-resolution sea surface height (SSH) measured interferometrically by the wide-swath altimeter on the Surface Water and Ocean Topography (SWOT) Mission with a planned launch in 2021; and (2) Measurements of ocean surface velocity from a Doppler scatterometer mission that is in the early planning stages, referred to here as a Winds and Currents Mission (WaCM). In this study, we conduct an analysis of the effects of uncorrelated measurement errors and sampling errors on the errors of the measured and derived variables of interest (SSH and geostrophically computed velocity and vorticity for SWOT, and surface velocity and vorticity for WaCM). Our analysis includes derivations of analytical expressions for the variances and wavenumber spectra of the errors of the derived variables, which will be useful to other studies based on simulated SWOT and WaCM estimates of velocity and vorticity. We also discuss limitations of the geostrophic approximation that must be used for SWOT estimates of velocity.
The errors of SWOT and WaCM estimates of velocity and vorticity at the full resolutions of the measured variables are too large for the unsmoothed estimates to be scientifically useful. It will be necessary to smooth the data to reduce the noise variance. We assess the resolution capabilities of smoothed estimates of velocity and vorticity from simulated noisy SWOT and WaCM data based on a high-resolution model of the California Current System (CCS). By our suggested minimum threshold signal-to-noise (S/N) variance ratio of 10 (a standard deviation ratio of 3.16), we conclude that the wavelength resolution capabilities of maps of velocity and vorticity constructed from WaCM data with a swath width of 1200 km are, respectively, about 60 km and 90 km in 4-day averages. For context, the radii of resolvable features are about four times smaller than these mesoscale wavelength resolutions. If the swath width can be increased to 1800 km, the wavelength resolution capabilities of 4-day average maps of surface velocity and vorticity would improve to about 45 km and 70 km, respectively. Reducing the standard deviation of the uncorrelated measurement errors from the baseline value of
m s?1 to a value of 0.25 m s?1 would further improve these resolution capabilities to about 20 km and 45 km.
SWOT data will allow mapping of the SSH field with far greater accuracy and space–time resolution than are presently achieved by merging the data from multiple nadir altimeter missions. However, because of its much narrower 120-km measurement swath compared with WaCM and the nature of the space–time evolution of the sampling pattern during each 21-day repeat of the SWOT orbit, maps of geostrophically computed velocity and vorticity averaged over the 14-day period that is required for SWOT to observe the full CCS model domain are contaminated by sampling errors that are too large for the estimates to be useful for any amount of smoothing considered here. Reducing the SSH measurement errors would do little to improve SWOT maps of velocity and vorticity. SWOT estimates of these variables are likely to be useful only within individual measurement swaths or with the help of dynamic interpolation from a data assimilation model. By our criterion, in-swath SWOT estimates of velocity and vorticity have wavelength resolution capabilities of about 30 km and 55 km, respectively.
In comparison, in-swath estimates of velocity and vorticity from WaCM data with
m s?1 have a wavelength resolution capability of about 130 km for both variables. Reducing the WaCM measurement errors to
m s?1 would improve the resolution capabilities to about 50 km and 75 km for velocity and vorticity, respectively. These resolutions are somewhat coarser than the in-swath estimates from SWOT data, but the swath width is more than an order of magnitude wider for WaCM. Instantaneous maps of velocity and vorticity constructed in-swath from WaCM data will therefore be much less prone to edge effect problems in the spatially smoothed fields.
Depending on the precise value of the threshold adopted for the minimum S/N ratio and on the details of the filter used to smooth the SWOT and WaCM data, the resolution capabilities summarized above may be somewhat pessimistic. On the other hand, aspects of measurement errors and sampling errors that have not been accounted for in this study will worsen the resolution capabilities presented here. Another caveat to keep in mind is that the resolution capabilities deduced here from simulations of the CCS region during summertime may differ somewhat at other times of year and in other geographical regions where the signal variances and wavenumber spectra of the variables of interest differ from the CCS model used in this study. Our analysis nonetheless provides useful guidelines for the resolutions that can be expected from SWOT and WaCM.