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Michael G. Schlax and Dudley B. Chelton

Abstract

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°.

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Dudley B. Chelton and Michael G. Schlax

Abstract

A formalism is presented for determining the wavenumber-frequency transfer function associated with an irregularly sampled multidimensional dataset. This transfer function reveals the filtering characteristics and aliasing patterns inherent in the sample design. In combination with information about the spectral characteristics of the signal, the transfer function can be used to quantify the spatial and temporal resolution capability of the dataset. Application of the method to idealized Geosat altimeter data (i.e., neglecting measurement errors and data dropouts) concludes that the Geosat orbit configuration is capable of resolving scales of about 3° in latitude and longitude by about 30 days.

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Michael G. Schlax and Dudley B. Chelton

Abstract

The frequency-domain characteristics of the successive corrections method in one dimension are investigated through the calculation of smoother weights and filter transfer functions. The successive corrections algorithm acts as a low-pass filter that behaves similarly to noniterative smoothers. The spectral content of fixed-span successive corrections estimates depends upon the number of iterations, the selected weighting function and the grid to which the dataset is interpolated. For a given weighting function and grid, increasing the number of iterations for the fixed-span case results in filter transfer functions with increased cutoff frequency and rolloff. Within data gaps, the use of more than one iteration leads to estimates that are more likely to be contaminated by high-frequency variability in the data. It is shown that variable-span successive corrections estimates are nearly independent of the choice of weights for the initial iterations and are almost equivalent to estimates obtained using a single iteration. The greater computational requirements of multiple-iteration successive corrections is a disadvantage for general applications.

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Dudley B. Chelton and Michael G. Schlax

Abstract

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 JasonENVISAT 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.

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Michael G. Schlax, Dudley B. Chelton, and Michael H. Freilich

Abstract

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 datasets.

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Diana J. M. Greenslade, Dudley B. Chelton, and Michael G. Schlax

Abstract

A formalism recently developed for determining the effects of sampling errors on objectively smoothed fields constructed from an irregularly sampled dataset is applied to investigate the relative merits of single and multiple satellite altimeter missions. For small smoothing parameters, the expected squared error of smoothed fields of sea surface height (SSH) varies geographically at any particular time and temporally at any particular location. The philosophy proposed here for determining the resolution capability of SSH fields constructed from altimeter data is to identify smoothing parameters that are sufficiently large to satisfy two criteria: 1) the expected squared errors of the estimates of smoothed SSH over the space–time estimation grid must be either spatially and temporally homogeneous to within some a priori specified degree of tolerance or smaller than some a priori specified threshold, and 2) the space–time estimation grid on which smoothed SSH estimates are constructed must satisfy the Nyquist criteria for the wavenumbers and frequencies included in the smoothed fields.

The method is illustrated here by adopting a specified tolerance of 10% variability and a nominal expected squared error threshold of 1 cm2 to determine the resolution capabilities of SSH fields constructed from 10 single and multiple combinations of altimeter measurements by TOPEX/Poseidon, the ERS Earth Resource Satellites, and Geosat. Because of the lack of coordination of the orbit configurations of these satellites (different repeat periods and different orbit inclinations), the mapping resolution capabilities of the combined datasets are not significantly better than those of fields constructed from TOPEX/Poseidon data alone. The benefits of coordinated multiple missions are demonstrated by consideration of several multiple combinations of 10-, 17-, and 35-day orbit configurations.

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Dudley B. Chelton, Michael G. Schlax, and Roger M. Samelson

Abstract

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.

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Dudley B. Chelton, Roland A. deSzoeke, Michael G. Schlax, Karim El Naggar, and Nicolas Siwertz

Abstract

Global 1° × 1° climatologies of the first baroclinic gravity-wave phase speed c 1 and the Rossby radius of deformation λ 1 are computed from climatological average temperature and salinity profiles. These new atlases are compared with previously published 5° × 5° coarse resolution maps of λ 1 for the Northern Hemisphere and the South Atlantic and with a 1° × 1° fine-resolution map of c 1 for the tropical Pacific. It is concluded that the methods used in these earlier estimates yield values that are biased systematically low by 5%–15% owing to seemingly minor computational errors. Geographical variations in the new high-resolution maps of c 1 and λ 1 are discussed in terms of a WKB approximation that elucidates the effects of earth rotation, stratification, and water depth on these quantities. It is shown that the effects of temporal variations of the stratification can be neglected in the estimation of c 1 and λ 1 at any particular location in the World Ocean. This is rationalized from consideration of the WKB approximation.

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Peter Gaube, Dudley B. Chelton, Roger M. Samelson, Michael G. Schlax, and Larry W. O’Neill

Abstract

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.

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Richard W. Reynolds, Thomas M. Smith, Chunying Liu, Dudley B. Chelton, Kenneth S. Casey, and Michael G. Schlax

Abstract

Two new high-resolution sea surface temperature (SST) analysis products have been developed using optimum interpolation (OI). The analyses have a spatial grid resolution of 0.25° and a temporal resolution of 1 day. One product uses the Advanced Very High Resolution Radiometer (AVHRR) infrared satellite SST data. The other uses AVHRR and Advanced Microwave Scanning Radiometer (AMSR) on the NASA Earth Observing System satellite SST data. Both products also use in situ data from ships and buoys and include a large-scale adjustment of satellite biases with respect to the in situ data. Because of AMSR’s near-all-weather coverage, there is an increase in OI signal variance when AMSR is added to AVHRR. Thus, two products are needed to avoid an analysis variance jump when AMSR became available in June 2002. For both products, the results show improved spatial and temporal resolution compared to previous weekly 1° OI analyses.

The AVHRR-only product uses Pathfinder AVHRR data (currently available from January 1985 to December 2005) and operational AVHRR data for 2006 onward. Pathfinder AVHRR was chosen over operational AVHRR, when available, because Pathfinder agrees better with the in situ data. The AMSR–AVHRR product begins with the start of AMSR data in June 2002. In this product, the primary AVHRR contribution is in regions near land where AMSR is not available. However, in cloud-free regions, use of both infrared and microwave instruments can reduce systematic biases because their error characteristics are independent.

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