Sea Surface Height Products Research Articles

Deep Learning Improves Global Satellite Observations of Ocean Eddy Dynamics

AbstractOcean eddies affect large‐scale circulation and induce a kinetic energy cascade through their non‐linear interactions. However, since global observations of eddy dynamics come from satellite altimetry maps that smooth eddies and distort their geometry, the strength of this cascade is underestimated. Here, we use deep learning to improve observational estimates of global surface geostrophic currents and explore the implications for the cascade. By synthesizing multi‐modal satellite observations of sea surface height (SSH) and temperature, we achieve up to a 30% improvement in spatial resolution over the community‐standard SSH product. This reveals numerous strongly interacting eddies that were previously obscured by smoothing. In many regions, these newly resolved eddies lead to nearly an order‐of‐magnitude increase in the upscale kinetic energy cascade that peaks in spring and is strong enough to drive the seasonality of large mesoscale eddies. Our study suggests that deep learning can be a powerful paradigm for satellite oceanography.

Synthesizing Sea Surface Temperature and Satellite Altimetry Observations Using Deep Learning Improves the Accuracy and Resolution of Gridded Sea Surface Height Anomalies

AbstractGridded sea surface height (SSH) maps estimated from satellite altimetry are widely used for estimating surface ocean geostrophic currents. Satellite altimeters observe SSH along one‐dimensional tracks widely spaced in space and time, making accurately reconstructing the two‐dimensional (2D) SSH field challenging. Traditionally, SSH is mapped using optimal interpolation (OI). However, OI artificially smooths the SSH field leading to high mapping errors in regions with rapidly‐evolving mesoscale features such as western boundary currents. Motivated by the dynamical relation between SSH and sea surface temperature (SST) and the notion that even the chaotic evolution of mesoscale ocean turbulence may contain repeating patterns, we outline a deep learning (DL) approach where a neural network is trained to reconstruct 2D SSH by synthesizing altimetry and SST observations. In the Gulf Stream Extension region, dominated by mesoscale variability, our DL method substantially improves the SSH reconstruction compared to existing methods. Our SSH map has 17% lower root‐mean‐square error and resolves spatial scales 30% smaller than OI compared against independent altimeter observations. Surface geostrophic currents calculated from our map are closer to surface drifter observations and appear qualitatively more realistic, with stronger currents, a clearer separation between the Gulf Stream and neighboring eddies, and the appearance of smaller coherent eddies missed by other methods. Our map yields significant re‐estimations of important dynamical quantities such as eddy kinetic energy, vorticity, and strain rate. Applying our DL method to produce a global SSH product may provide a more accurate and higher resolution product for studying mesoscale ocean turbulence.

The Effects of Uncorrelated Measurement Noise on SWOT Estimates of Sea Surface Height, Velocity, and Vorticity

Abstract The Ka-band Radar Interferometer (KaRIn) on the Surface Water and Ocean Topography (SWOT) satellite will revolutionize satellite altimetry by measuring sea surface height (SSH) with unprecedented accuracy and resolution across two 50-km swaths separated by a 20-km gap. The original plan to provide an SSH product with a footprint diameter of 1 km has changed to providing two SSH data products with footprint diameters of 0.5 and 2 km. The swath-averaged standard deviations and wavenumber spectra of the uncorrelated measurement errors for these footprints are derived from the SWOT science requirements that are expressed in terms of the wavenumber spectrum of SSH after smoothing with a filter cutoff wavelength of 15 km. The availability of two-dimensional fields of SSH within the measurement swaths will provide the first spaceborne estimates of instantaneous surface velocity and vorticity through the geostrophic equations. The swath-averaged standard deviations of the noise in estimates of velocity and vorticity derived by propagation of the uncorrelated SSH measurement noise through the finite difference approximations of the derivatives are shown to be too large for the SWOT data products to be used directly in most applications, even for the coarsest footprint diameter of 2 km. It is shown from wavenumber spectra and maps constructed from simulated SWOT data that additional smoothing will be required for most applications of SWOT estimates of velocity and vorticity. Equations are presented for the swath-averaged standard deviations and wavenumber spectra of residual noise in SSH and geostrophically computed velocity and vorticity after isotropic two-dimensional smoothing for any user-defined smoother and filter cutoff wavelength of the smoothing.

An Information Flow-Based Sea Surface Height Reconstruction Through Machine Learning

The advent of satellite altimetry datasets of sea surface height (SSH) is a major advance in oceanography and other Earth system sciences. However, while the along-track data coverage is dense, the relatively poor resolution between tracks poses a challenge to the reconstruction of those processes such as mesoscale and submesoscale eddies. This study proposes a machine learning algorithm based on a causal inference tool, i.e., the Liang–Kleeman information flow (L-K IF) analysis, to address the challenge. For a region in the South China Sea where eddies frequently appear but unobserved, it is shown that the algorithm can reconstruct the desired mesoscale eddies in a remarkably successful way in geometry, orientation, strength, etc., while with the objective analysis interpolation or the traditional neural network technique, the results are not satisfactory. This study provides prospects for developing the next generation of SSH products with the available altimetry data.

Sea Surface Height Variability in the 30–120 km Wavelength Band From Altimetry Along‐Track Observations

AbstractReprocessed altimetry along‐track sea surface height (SSH) observations from multiple missions are analyzed for the SSH variability in the 30–120 km wavelength band. This band of variability is missing in the widely used global multi‐mission mapped SSH data set, known as the Archiving, Validation and Interpretation of Satellite Oceanographic Data SSH product. The SSH variability is derived from along‐track SSH variance spectra after subtracting noise floors, and its global spatial patterns are consistent among the missions and the output of a high‐resolution ocean general circulation model simulation. High SSH variability in the 30–120 km wavelength band is found in the intratropics of all ocean basins (25°S–25°N), the western boundary current outflow regions, and in five regions along the Antarctic Circumpolar Current: Agulhas Retroflection zone, Kerguelen Plateau, Macquarie Ridge, Pacific Antarctic Ridge, and Drake Passage. The average slope of the along‐track SSH spectra in the 30–120 km wavelength band in the intratropics falls between −2.14 and −1.56, consistent with the Garrett‐Munk spectral slope. The spatial patterns of the SSH variability could be used as a metric to evaluate high‐resolution numerical models and to shed light on what to expect from future high‐resolution altimetry missions.

An Adaptive Optimal Interpolation Based on Analog Forecasting: Application to SSH in the Gulf of Mexico

AbstractBecause of the irregular sampling pattern of raw altimeter data, many oceanographic applications rely on information from sea surface height (SSH) products gridded on regular grids where gaps have been filled with interpolation. Today, the operational SSH products are created using the simple, but robust, optimal interpolation (OI) method. If well tuned, the OI becomes computationally cheap and provides accurate results at low resolution. However, OI is not adapted to produce high-resolution and high-frequency maps of SSH. To improve the interpolation of SSH satellite observations, a data-driven approach (i.e., constructing a dynamical forecast model from the data) was recently proposed: analog data assimilation (AnDA). AnDA adaptively chooses analog situations from a catalog of SSH scenes—originating from numerical simulations or a large database of observations—which allow the temporal propagation of physical features at different scales, while each observation is assimilated. In this article, we review the AnDA and OI algorithms and compare their skills in numerical experiments. The experiments are observing system simulation experiments (OSSE) on the Lorenz-63 system and on an SSH reconstruction problem in the Gulf of Mexico. The results show that AnDA, with no necessary tuning, produces comparable reconstructions as does OI with tuned parameters. Moreover, AnDA manages to reconstruct the signals at higher frequencies than OI. Finally, an important additional feature for any interpolation method is to be able to assess the quality of its reconstruction. This study shows that the standard deviation estimated by AnDA is flow dependent, hence more informative on the reconstruction quality, than the one estimated by OI.

Development and evaluation of a new merged sea surface height product from multi-satellite altimeters

Satellite altimetry data has been a backbone of global oceanography research since the early 1990s. Because a satellite altimeter measures sea surface height (SSH) at the nadir point, it produces a one-dimensional profile of SSH. Along the track, an altimeter provides SSH sampling at an interval of about 7 km. However, the distance between adjacent tracks is larger than 100 km, and satellites have repeat times of 10–30 d. These characteristics limit the usefulness of altimetry data from a single satellite for scientific analysis of the space-time structure of ocean circulation. During the past two decades, there have usually been three to four altimeters in orbit at any one time. Mapping along-track measurements from multiple altimeters onto a uniform grid has been a major research theme. A popular merged data product, known as AVISO, has been developed and extensively applied to a wide variety of ocean research. One of key properties of a merged data product is its effective resolution. The effective resolution represents the minimum spatial size of an eddy or other mesoscale circulation that the data product can resolve. The AVISO data product has an effective resolution of 300 km in equatorial regions to 100 km in high latitudes. Nowadays, there are more than five satellite altimeters in orbit, including the Chinese HY-2A that was launched in 2011, and thus the density of the tracks has been much improved. However, the effective resolution of the AVISO data product has not increased accordingly. Effective resolution of mapped data is closely related to the background error correlation coefficient scale in the mapping scheme. The effective resolution is no more than twice the correlation coefficient scale even when the amount of satellite altimeter is more than 5. As the background fields contains the correct large scale information, the meso-scale or small-scale information in the background error will play a dominant role and the background error correlation coefficient scale becomes even smaller. Therefore, The option of background determines the effective resolution of mapped data. The above theory is the basement of our new proposed mapping scheme, which effectively improved the effective resolution. Another key technique is how to deal with the observation errors: to reduce time-smoothing by introducing evolution errors in observation errors and effectively mapping multi-mission satellite altimeters from different times. In this study, a new mapping system has been developed, aiming to maximize the effective resolution of the mapped data product. The formulation is based on a variational method and optimal estimation theory. The system has been applied to the South China Sea region. The product uses a regular grid with spacing of 0.08°, in comparison to 0.25° for AVISO. The product merged data from five satellites, Sentinel-3A, Jason-3, Cryosat-2, Saral/AltiKa and HY-2A. Systematic evaluations show that this new product has an effective resolution of 125 km, whereas the AVISO data product an effective resolution of 240 km for the same region. The accuracy is also significantly improved. The new proposed mapping scheme is important in the application of satellite altimeters on the study of meso-scale ocean eddies. In addition, the option of background fields and the processing method of observation error are strictly general and can be used in other schemes of high-resolution data mapping.

Characterization of a high chlorophyll plume in the northeastern Gulf of Mexico

In the northern Gulf of Mexico (NGMx), plumes of high chlorophyll shelf waters have been observed to extend across the shelf-break to the central basin. Prior research has shown an association between this cross-shelf flow of water and materials and the adjacent rotation of cyclonic and anticyclonic eddies. Satellite remote sensing data were used here to identify such an eddy-driven plume and to detect and characterize both the mechanisms driving the plume and its biogeochemical impacts. Satellite imagery included chlorophyll (CHL), fluorescence line height (FLH) and chromophoric dissolved organic matter (CDOM) measurements from SeaWiFS and MODIS-Aqua, sea surface temperatures from MODIS-Terra, QuikSCAT wind fields and a merged multi-platform sea surface height product (SSHa). In early June 2007 images, a prominent high-CHL plume (HCP) was seen extending from the continental shelf of the NGMx. A comparison of the CHL and SSHa fields revealed that the HCP was coincident with a cyclone–anticyclone pair, thus linked to an apparent cross-shelf transport. Nearest to the shelf, the CHL values associated with the transport fell within the usual CHL temporal and magnitude range for the summer CHL maximum. Further offshore, the HCP-associated CHL increase was temporally offset, occurring several weeks earlier than expected seasonal CHL peaks. Within the HCP, the relationship of CHL:CDOM:FLH notably diverged from the climatological status, supporting the hypothesis that the HCP composition includes modified shelf waters. Estimates of primary productivity across the study region revealed significant increases in productivity within the HCP's boundaries.

Characterizing implications of two-dimensional space–time orientations for principal component analysis of geographic time series

This article introduces four new modes of principal component analysis (PCA) to investigate space–time variability in an image time series. Using the concept of tensors, an image time series can be understood as a space–time cube and can be analysed using six different orientations by grouping the basic elements (voxels) of the cube across different dimensions. Voxels grouped across columns or rows of the cube to produce vectors result in profiles. Voxels grouped across different planes to produce matrices result in slices. The traditional S-mode and T-mode PCA are thus the profile modes and slice modes across time and across space, respectively. This research introduces two profile-mode orientations across longitude and latitude and two slice-mode orientations across longitude–time and latitude–time. The research shows that a more complete understanding of the spatio-temporal variability in the data set can be achieved by investigating these different orientation modes, as individual modes have the capability of capturing variability in a particular dimension of a spatio-temporal data set. A case study was carried out using weekly anomalies of the AVISO (Archiving, Validation and Interpretation of Satellite Oceanographic data) sea surface height product filtered for tropical instability waves (TIWs) for a three-year time period from 1997 to 1999 in the tropical Pacific region. The results show that PCA with longitude as the dimension of variability and latitude–time as the dimension of variability were able to capture the TIW and barotropic Rossby wave propagation across the equatorial Pacific. The other two orientation modes were able to detect dominant latitudinal locations for TIW.

Variations of the North Pacific Subtropical Mode Water from Direct Observations

Abstract Mooring measurements from the Kuroshio Extension System Study (June 2004–June 2006) and from the ongoing Kuroshio Extension Observatory (June 2004–present) are combined with float measurements of the Argo network to study the variability of the North Pacific Subtropical Mode Water (STMW) across the entire gyre, on time scales from days, to seasons, to a decade. The top of the STMW follows a seasonal cycle, although observations reveal that it primarily varies in discrete steps associated with episodic wind events. The variations of the STMW bottom depth are tightly related to the sea surface height (SSH), reflecting mesoscale eddies and large-scale variations of the Kuroshio Extension and recirculation gyre systems. Using the observed relationship between SSH and STMW, gridded SSH products and in situ estimates from floats are used to construct weekly maps of STMW thickness, providing nonbiased estimates of STMW total volume, annual formation and erosion volumes, and seasonal and interannual variability for the past decade. Year-to-year variations are detected, particularly a significant decrease of STMW volume in 2007–10 primarily attributable to a smaller volume formed. Variability of the heat content in the mode water region is dominated by the seasonal cycle and mesoscale eddies; there is only a weak link to STMW on interannual time scales, and no long-term trends in heat content and STMW thickness between 2002 and 2011 are detected. Weak lagged correlations among air–sea fluxes, oceanic heat content, and STMW thickness are found when averaged over the northwestern Pacific recirculation gyre region.

The Low-Frequency Variability of the Southern Ocean Circulation

Abstract Long time series of sea surface height (SSH), sea surface temperature, and wind stress curl are used to determine the main modes of low-frequency variability of the Southern Ocean (SO) circulation. The dominant mode is a trend of increasing SSH at an average rate of 3.3 mm yr−1. Similar trends have been reported in previous studies and the analysis indicates that the tendency of sea level increase over the SO has become more spatially homogeneous during the last decade, with changes in the increasing rate in 2000 and 2006. The other modes consist of stationary, basin-type modes, and an eastward-propagating wave. The stationary modes are particularly dominant in the Indian and Atlantic Ocean basins, where their spatial structure appears to be shaped by the basin geometry and the bottom topography. The wavelike patterns travel eastward with a period of approximately 10 years. Two waves were identified in the analysis: a complete cycle between 1997 and 2007 and a second cycle starting in 2000. Such waves have rarely been mentioned or identified in studies using recent satellite-derived SSH products.

Effects of stencil width on surface ocean geostrophic velocity and vorticity estimation from gridded satellite altimeter data

This paper examines the effect of “stencil width” on surface ocean geostrophic velocity and vorticity estimated from differentiating gridded satellite altimeter sea surface height products. In oceanographic applications, the value of the first derivative at a central grid point is generally obtained by differencing the sea surface heights at adjacent grid points. This is called a “three‐point stencil centered difference”. Here the stencil width is increased from three to five, seven, and nine points, using well‐known formulae from the numerical analysis literature. The discrepancies between velocities computed with successive stencils decreases with increasing stencil width, suggesting that wide stencil results are more reliable. Significant speed‐dependent biases (up to 10–20%) are found between results computed from three‐point stencils versus those computed from wider stencils. The geostrophic velocity, and the variance of geostrophic velocity, are underestimated with thin stencils. Similar results are seen in geostrophic velocities computed from high‐resolution model output. In contrast to the case when three‐point stencils are used, wider stencils yield estimates of the anisotropy of velocity variance that are insensitive to the differences in grid spacing between two widely used altimeter products. Three‐point stencils yield incorrect anisotropies on the 1/4° anisotropic AVISO grid; we recommend the use of 7‐point stencils. Despite the demonstrated inadequacies of the three‐point stencils, the conclusions of earlier studies based on them, that the zonally averaged midlatitude eddy kinetic energy field is nearly isotropic, are found to pertain also with wider stencils. Finally, the paper also examines the strengths and limitations of applying noise‐suppressing differentiators, versus classic centered differences, to altimeter data.

One-Centimeter Orbits in Near-Real Time: The GPS Experience on OSTM/Jason-2

The advances in Precise Orbit Determination (POD) over the past three decades have been driven in large measure by the increasing demands of satellite altimetry missions. Since the launch of Seasat in 1978, both tracking-system technologies and orbit modeling capabilities have evolved considerably. The latest in a series of precise (TOPEX-class) altimeter missions is the Ocean Surface Topography Mission (OSTM, also Jason-2). GPS-based orbit solutions for this mission are accurate to 1-cm (radial RMS) within three to five hours of real time. These GPS-based orbit products provide the basis for a near-real time sea-surface height product that supports increasingly diverse applications of operational oceanography and climate forecasting.

Decadal temperature changes in the Tasman Sea

Ocean temperature changes between 1991 and 2005 in the eastern Tasman Sea were analysed. This area was chosen because of a combination of data availability, low mesoscale variability and because of its importance in determining the climate of the downwind New Zealand landmass. A large warming extending to the full depth of the water column (c. 800 m) was found to have occurred between 1996 and 2002. This warming was seen in measurements by expendable bathythermographs and also in satellite sea surface temperature and sea surface height products, and has a clear impact on New Zealand's terrestrial temperature. The nature of the warming is discussed, together with likely forcing mechanisms. No local forcing mechanisms are consistent with the observed warming, leading to the conclusion that the signal seen in the Tasman Sea is part of a larger South Pacific‐wide phenomenon.

Gravity Anomaly Map over The Black Sea Using Corrected Sea Surface Heights from ERS1, ERS2 and Topex/Poseidon Satellite Altimetry Missions

Approximately nine-year data from ERS1, ERS2 and TOPEX/POSEIDON (T/P) satellite altimetry missions have been used for the recovery of gravity anomalies over the Black Sea. The Corrected Sea Surface Height product of Aviso/Altimetry has been proven to be homogeneous after a cross-over adjustment. The Least Squares Collocation method was applied in a so-called “remove-restore” procedure. The residual geoid heights, obtained by subtracting EGM96 geoid heights from cross-over adjusted sea surface heights, were inverted to recover residual gravity anomalies in a grid structure over the Black Sea. Finally, EGM96 free air gravity anomalies were added to the predicted residual gravity anomalies to obtain the free air gravity anomalies. In order to check the consistency with respect to an external source, these computed free air gravity anomalies were compared to ship gravity observations, and to alternative satellite altimetry derived gravity anomalies. Comparisons with the observed gravity data yielded that external consistency of the gravity anomalies computed in this study is about 3 mGal for individual ship tracks. Overall external consistency in the test area is 4.8 mGal. Comparison with other satellite altimetry derived gravity anomalies presented a good agreement.