The Accuracies of Crossover and Parallel-Track Estimates of Geostrophic Velocity from TOPEX/Poseidon and Jason Altimeter Data

Mean-squared errors of surface geostrophic velocity estimates from the crossover and parallel-track methods are calculated for altimeters in the Ocean Topography Experiment (TOPEX)/Poseidon and Jason orbits. As part of the crossover method analysis, the filtering properties and errors of cross-track speed estimates are examined. Velocity estimates from both the crossover and parallel-track methods have substantial mean-squared errors that exceed 20% of the signal standard deviation, differ systematically between the zonal and meridional components, and vary with latitude. The measurement errors on the zonal and meridional velocity component estimates from both methods increase at low latitudes owing to the inverse dependence of geostrophic velocity on the Coriolis parameter. Additional latitudinal variations result for the parallel-track method because of the poleward convergence of the satellite ground tracks and the presence of orbit error, and for the crossover method because of the changing angle between the ascending and descending ground tracks. At high latitudes, parallel-track estimates, have elevated measurement errors in both components, while only the zonal component is so affected for the crossover method. Along-track smoothing is efficient for mitigating measurement errors for crossover estimates, and the filtering properties of the smoothed estimates are simply related to the spectrum of cross-track speeds. Such smoothing is less effective for parallel-track estimates, and the filtering properties are more difficult to characterize because of the sampling geometry and the convergence of the parallel ground tracks at high latitudes. If suitable along-track smoothing is applied in the crossover method, root-mean-squared errors (rmse's) of about 30% or less of the signal standard deviation can be obtained for each orthogonal velocity component over the latitude range 5°–60°. With 2-cm orbit errors, the parallel-track method yields estimates of the meridional velocity component with errors that exceed 40% at all latitudes. If orbit errors can be reduced to 1-cm standard deviation, the parallel-track method yields an rmse smaller than 30% in both orthogonal components for the latitude range 5°–55°

The Accuracies of Smoothed Sea Surface Height Fields Constructed from Tandem Satellite Altimeter Datasets

A technique previously developed for assessing the effects of sampling errors on sea surface height (SSH) fields constructed from satellite altimeter data is extended to include measurement errors, thus providing estimates of the total mean-squared error of the SSH fields. The measurement error contribution becomes an important consideration with the greater sampling density of a coordinated tandem satellite mission. Mean-squared errors are calculated for a variety of tandem altimeter sampling patterns. The resolution capability of each sampling pattern is assessed from a subjectively chosen but consistent set of criteria for the mean value and the spatial and temporal inhomogeneity of the root-mean-squared errors computed over a representative large collection of estimation times and locations. For a mean mapping error threshold tolerance criterion of 25% of the signal standard deviation, the filter cutoff wavelength and period defining the resolution capability of SSH fields constructed from a tandem TOPEX/Poseidon (T/P) and Jason satellite sampling pattern with evenly spaced ground tracks are about 2.2° by 20 days. This can be compared with the resolution capability of about 6° by 20 days that can be obtained from a single altimeter in the T/P orbit. A tandem T/P–Jason mission with 0.75° spacing between simultaneously sampled parallel tracks that has been suggested for estimating geostrophic velocity yields an SSH mapping resolution capability of about 3.7° by 20 days. For the anticipated factor-of-2 larger orbit errors for ENVISAT compared with Jason, the resolution capability of a tandem Jason–ENVISAT scenario is about 3° by 20 days. For mapping the SSH field, the tandem T/P–Jason sampling patterns with evenly spaced, interleaved ground tracks and either a 5-day or a 0-day offset is far better than the other tandem altimeter mission scenarios considered here. For the highest-resolution mapping, the 5-day offset is preferable to the 0-day offset. The scientific benefits of such a tandem mission are discussed in the context of two specific examples: Rossby wave dispersion and investigation of eddy–mean flow interaction

Detecting aliased tidal errors in altimeter height measurements

A simple statistic is derived for quantifying the potential for the aliasing of tidal errors in a given linear estimate of sea surface height constructed from altimeter data. The existence of M2 tidal constituent errors in Geosat data processed in the traditional way (i.e., with orbit errors removed using least squares fits to 1 cycle per revolution sinusoids) which are of sufficient magnitude to alias into apparently westward propagating ocean features is demonstrated by artificially inducing aliasing. The aliasing statistic presented here responds clearly to the induced aliasing and to actual aliasing caused by real data dropouts in the Geosat data. The potential for aliasing M2 tidal errors is shown to vary with latitude depending on the time interval between ascending and descending ground tracks near the location of interest. The methods developed here are applied to Geosat data from the northeast Atlantic to demonstrate the presence of M2 tidal error aliasing in those data

Aliased tidal errors in TOPEX/POSEIDON sea surface height data

Alias periods and wavelengths for the M2, S2, N2, K1, O1, and P1 tidal constituents are calculated for TOPEX/POSEIDON. Alias wavelengths calculated in previous studies are shown to be in error, and a correct method is presented. With the exception of the K1 constituent, all of these tidal aliases for TOPEX/POSEIDON have periods shorter than 90 days and are unlikely to be confounded with long-period sea surface height signals associated with real ocean processes. In particular, the correspondence between the periods and wavelengths of the M: alias and annual baroclinic Rossby waves that plagued Geosat sea surface height data is avoided. The potential for aliasing residual tidal errors in smoothed estimates of sea surface height is calculated for the six tidal constituents. The potential for aliasing the lunar tidal constituents M2, N2, and O1 fluctuates with latitude and is different for estimates made at the crossovers of ascending and descending ground tracks than for estimates at points midway between crossovers. The potential for aliasing the solar tidal constituents S2, K1, and P1 varies smoothly with latitude. S2 is strongly aliased for latitudes within 50 degrees of the equator, while K1 and P1 are only weakly aliased in that range. A weighted least squares method for estimating and removing residual tidal errors from TOPEX/POSEIDON sea surface height data is presented. A clear understanding of the nature of aliased tidal error in TOPEX/POSEIDON data aids the unambiguous identification of real propagating sea surface height signals. Unequivocal evidence of annual period, westward propagating waves in the North Atlantic is presented

Spectral charactersitics of time-dependent orbit errors in altimeter height measurements

A mean reference surface and time-dependent orbit errors are estimated simultaneously for each exact-repeat ground track from the first two years of Geosat sea level estimates based on the Goddard Earth model (GEM)-T2 orbits. Motivated by orbit theory and empirical analysis of Geosat data, the time-dependent orbit errors are modeled as 1 cycle per revolution (cpr) sinusoids with slowly varying amplitude and phase. The method recovers the known "bow tie effect" introduced by the existence of force model errors within the precision orbit determination (POD) procedure used to generate the GEM-T2 orbits. The bow tie pattern of 1-cpr orbit errors is characterized by small amplitudes near the middle and larger amplitudes (up to 160 cm in the 2 years of data considered here) near the ends of each 5- to 6-day orbit arc over which the POD force model is integrated. A detailed examination of these bow tie patterns reveals the existence of daily modulations of the amplitudes of the 1-cpr sinusoid orbit errors with typical and maximum peak-to-peak ranges of about 14 cm and 30 cm, respectively. The method also identifies a daily variation in the mean orbit error with typical and maximum peak-to-peak ranges of about 6 cm and 30 cm, respectively, that is unrelated to the predominant 1-cpr orbit error. It is suggested that the two daily signals arise from daily adjustments of the drag coefficient in the GEM-T2 POD procedure. Application of the simultaneous solution method to the much less accurate Geosat height estimates based on the Naval Astronautics Group orbits concludes that the accuracy of POD is not important for collinear altimetric studies of time-dependent mesoscale variability (wavelengths shorter than 1000 km), as long as the time-dependent orbit errors are dominated by 1-cpr variability and a long-arc (several orbital periods) orbit error estimation scheme such as that presented here is used. The accuracy of POD becomes more important for studies of larger-scale variability

The influence of mesoscale eddies on the detection of quasi-zonal jets in the ocean

Westward propagating Gaussian eddies with statistical characteristics estimated from altimeter observations but with purely random starting locations and times produce striated features in time-averaged maps of zonal velocity. The striations in these simulations have magnitudes and meridional scales comparable to those reported from time-averaged altimeter observations and model output in the central North Pacific and the California Current System. Time averages over the data records presently available are therefore not suitable for unambiguous detection of quasi-zonal jets. The presence of mapping error and background isotropic eddy kinetic energy also bias the regionally-averaged anisotropy of time averaged velocity fields, thus compromising the interpretation of anisotropy statistics

Satellite observations of mesoscale eddy-induced Ekman pumping

Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 45 (2015): 104–132, doi:10.1175/JPO-D-14-0032.1.Three mechanisms for self-induced Ekman pumping in the interiors of mesoscale ocean eddies are investigated. The first arises from the surface stress that occurs because of differences between surface wind and ocean velocities, resulting in Ekman upwelling and downwelling in the cores of anticyclones and cyclones, respectively. The second mechanism arises from the interaction of the surface stress with the surface current vorticity gradient, resulting in dipoles of Ekman upwelling and downwelling. The third mechanism arises from eddy-induced spatial variability of sea surface temperature (SST), which generates a curl of the stress and therefore Ekman pumping in regions of crosswind SST gradients. The spatial structures and relative magnitudes of the three contributions to eddy-induced Ekman pumping are investigated by collocating satellite-based measurements of SST, geostrophic velocity, and surface winds to the interiors of eddies identified from their sea surface height signatures. On average, eddy-induced Ekman pumping velocities approach O(10) cm day−1. SST-induced Ekman pumping is usually secondary to the two current-induced mechanisms for Ekman pumping. Notable exceptions are the midlatitude extensions of western boundary currents and the Antarctic Circumpolar Current, where SST gradients are strong and all three mechanisms for eddy-induced Ekman pumping are comparable in magnitude. Because the polarity of current-induced curl of the surface stress opposes that of the eddy, the associated Ekman pumping attenuates the eddies. The decay time scale of this attenuation is proportional to the vertical scale of the eddy and inversely proportional to the wind speed. For typical values of these parameters, the decay time scale is about 1.3 yr.This work was funded by NASA Grants NNX08AI80G, NNX08AR37G, NNX13AD78G, NNX10AE91G, NNX13AE47G, and NNX10AO98G.2015-07-0

Sampling Errors in Wind Fields Constructed from Single and Tandem Scatterometer Datasets

Sampling patterns and sampling errors from various scatterometer datasets are examined. Four single and two tandem scatterometer mission scenarios are considered. The single scatterometer missions are ERS (with a single, narrow swath), NSCAT and ASCAT (dual swaths), and QuikSCAT (a single, broad swath obtained from the SeaWinds instrument). The two tandem scenarios are combinations of the broad-swath SeaWinds scatterometer with ASCAT and QuikSCAT. The dense, nearly uniform distribution of measurements within swaths, combined with the relatively sparse, nonuniform placement of the swaths themselves create complicated space–time sampling patterns. The temporal sampling of all of the missions is characterized by bursts of closely spaced samples separated by longer gaps and is highly variable in both latitude and longitude. Sampling errors are quantified by the expected squared bias of particular linear estimates of component winds. Modifications to a previous method that allow more efficient expected squared bias calculations are presented and applied. Sampling errors depend strongly on both the details of the temporal sampling of each mission and the assumed temporal scales of variability in the wind field but are relatively insensitive to different spatial scales of variability. With the exception of ERS, all of the scatterometer scenarios can be used to make low-resolution (3° and 12 days) wind component maps with errors at or below the 1 m s⁻¹ level. Only datasets from the broad-swath and tandem mission scenarios can be used for higher-resolution maps with similar levels of error, emphasizing the importance of the improved spatial and temporal coverage of those missions. A brief discussion of measurement errors concludes that sampling error is generally the dominant term in the overall error budget for maps constructed from scatterometer dataset

Summertime Coupling between Sea Surface Temperature and Wind Stress in the California Current System

Satellite observations of wind stress and sea surface temperature (SST) are analyzed to investigate ocean–atmosphere interaction in the California Current System (CCS). As in regions of strong SST fronts elsewhere in the World Ocean, SST in the CCS region is positively correlated with surface wind stress when SST fronts are strong, which occurs during the summertime in the CCS region. This ocean influence on the atmosphere is apparently due to SST modification of stability and mixing in the atmospheric boundary layer and is most clearly manifest in the derivative wind stress fields: wind stress curl and divergence are linearly related to, respectively, the crosswind and downwind components of the local SST gradient. The dynamic range of the Ekman upwelling velocities associated with the summertime SST-induced perturbations of the wind stress curl is larger than that of the upwelling velocities associated with the mean summertime wind stress curl. This suggests significant feedback effects on the ocean, which likely modify the SST distribution that perturbed the wind stress curl field. The atmosphere and ocean off the west coast of North America must therefore be considered a fully coupled system. It is shown that the observed summertime ocean–atmosphere interaction is poorly represented in the NOAA North American Mesoscale Model (formerly called the Eta Model). This is due, at least in part, to the poor resolution and accuracy of the SST boundary condition used in the model. The sparse distribution of meteorological observations available over the CCS for data assimilation may also contribute to the poor model performance