ALBERT

Description: Most data assimilation algorithms require the inverse of the covariance matrix of the observation errors. In practical applications, the cost of computing this inverse matrix with spatially correlated observation errors is prohibitive. Common practices are therefore to subsample or combine the observations so that the errors of the assimilated observations can be considered uncorrelated. As a consequence, a large fraction of the available observational information is not used in practical applications. In this study, a method is developed to account for the correlations of the errors that will be present in the wide-swath sea surface height measurements, for example, the Surface Water and Ocean Topography (SWOT) mission. It basically consists of the transformation of the observation vector so that the inverse of the corresponding covariance matrix can be replaced by a diagonal matrix, thus allowing to genuinely take into account errors that are spatially correlated in physical space. Numerical experiments of ensemble Kalman filter analysis of SWOT-like observations are conducted with three different observation error covariance matrices. Results suggest that the proposed method provides an effective way to account for error correlations in the assimilation of the future SWOT data. The transformation of the observation vector proposed herein yields both a significant reduction of the root-mean-square errors and a good consistency between the filter analysis error statistics and the true error statistics.

Description: Conventional altimetry measures a one-dimensional profile of sea surface height (SSH) along the satellite track. Two-dimensional SSH can be reconstructed using mapping techniques; however, the spatial resolution is quite coarse even when data from several altimeters are analyzed. A new satellite mission based on radar interferometry is scheduled to be launched in 2020. This mission, called Surface Water and Ocean Topography (SWOT), will measure SSH at high resolution along a wide swath, thus providing two-dimensional images of the ocean surface topography. This new capability will provide a large amount of data even though they are contaminated with instrument noise and geophysical errors. This paper presents a tool that simulates synthetic observations of SSH from the future SWOT mission using SSH from any ocean general circulation model (OGCM). SWOT-like data have been generated from a high-resolution model and analyzed to investigate the sampling and accuracy characteristics of the future SWOT data. This tool will help explore new ideas and methods for optimizing the retrieval of information from future SWOT missions.

Description: Simulated along-track ocean altimetry data were used to implement the use of a nonlinear dynamic propagator to perform three-dimensional (time and 2D space) interpolation of mesoscale sea surface height (SSH). The method is an inverse approach to processing altimetry data unevenly sampled in time and space into high-level gridded altimetry maps. The inverse approach, similar to the standard objective mapping, contains some correction terms to the innovation vectors to account for nonlinear dynamics. Another key improvement is to solve for the covariance functions through a Green’s function approach. From the Observing System Simulation Experiments carried out to simulate a three-satellite constellation over the Gulf Stream region, the new method can significantly reduce mapping errors and improve the resolving capabilities compared to the standard linear objective analysis such as that used by the AVISO gridding.

Description: Utilizing the framework of effective surface quasigeostrophic (eSQG) theory, this study explores the potential of reconstructing the 3D upper-ocean circulation structures, including the balanced vertical velocity w field, from high-resolution sea surface height (SSH) data of the planned Surface Water and Ocean Topography (SWOT) satellite mission. Specifically, the authors utilize the 1/30°, submesoscale-resolving, OFES model output and subject it to the SWOT simulator that generates the along-swath SSH data with expected measurement errors. Focusing on the Kuroshio Extension region in the North Pacific where regional Rossby numbers range from 0.22 to 0.32, this study finds that the eSQG dynamics constitute an effective framework for reconstructing the 3D upper-ocean circulation field. Using the modeled SSH data as input, the eSQG-reconstructed relative vorticity ζ and w fields are found to reach a correlation of 0.7–0.9 and 0.6–0.7, respectively, in the 1000-m upper ocean when compared to the original model output. Degradation due to the SWOT sampling and measurement errors in the input SSH data for the ζ and w reconstructions is found to be moderate, 5%–25% for the 3D ζ field and 15%–35% for the 3D w field. There exists a tendency for this degradation ratio to decrease in regions where the regional eddy variability (or Rossby number) increases.

Description: The future Surface Water Ocean Topography (SWOT) mission aims to observe water bodies and short-scale ocean surface topography with unprecedented spatial resolution and accuracy. However, the topography estimates will be contaminated by errors of various signals (geophysical and instrumental) featuring, in large part, strong dependencies on the radar range direction (cross track). This study shows that a cross-spectral analysis performed along track for all cross-track combinations can detect most of these errors and can provide estimates of their power spectral densities. From a series of outputs of the SWOT science team simulator, a cross-spectral method was developed to simulate the estimation of the error budget compared to the actual error budget in the simulator. The study determined that the error spectra of the dominant terms can be estimated at very high accuracy. Beyond the obvious applications for the future SWOT data calibration and validation, the spectral estimates of the error budget will have applications for state estimate problems using SWOT data.

Description: The dynamic optimal interpolation (DOI) method merges altimetric sea surface height (SSH) data into maps that are continuous in time and space. Unlike the traditional linear optimal interpolation (LOI) method, DOI has the advantage of considering a nonlinear temporal propagation of the SSH field. DOI has been successfully applied to along-track pseudo-observations in observing system simulation experiments (OSSEs), demonstrating a reduction in interpolation error in highly turbulent regions compared to LOI mapping. In the present study, we further extend the validation of the DOI method by an observing system experiment (OSE). We applied and validated the DOI approach with real nadir-altimetric observations in four regional configurations. Overall, the qualitative and quantitative assessments of these realistic SSH maps confirm the higher level of performance of the DOI approach in turbulent regions. It is more of a challenge to outperform the conventional LOI mapping in coastal and low-energy regions. Validations against LOI maps distributed by the Copernicus Marine Environment Monitoring Service indicate a 10%–15% increase in average performance and an improved resolution limit toward shorter wavelengths. The DOI method also shows improved mesoscale mapping of intense jets and fronts and reveals new eddies with smoother trajectories.

Description: Measurement of sea surface height (SSH) over a finite swath along satellite tracks has been planned for future space missions. The effect of water vapor in the troposphere on the delay of radar signal must be corrected for in the SSH measurement. The efficacy of a nadir-looking radiometer that has been the approach for conventional altimetry is examined in the study. The focus is placed on the cross-track variability of water vapor that is not measured by the nadir-looking radiometer. Simulations of the 2D field of water vapor were performed by spectral analysis of existing radiometer data. The residual error from the application of the correction made by a nadir-looking radiometer was computed over the global ocean and compared to the SSH signal estimated from satellite altimeter data. Global maps of the signal-to-error ratio (the square root of spectral variance at wavelengths shorter than 500 km) were created, showing values of 20–50 in the regions of high SSH variability of the boundary currents and the Antarctic Circumpolar Current, and 3–5 in the regions of low SSH variability in the tropics. Improvement in the correction by using a two-beam radiometer looking off nadir for measuring the slope of the cross-track variability was also explored, leading to a reduction of the error to below 1 cm at wavelengths of 10–500 km.

Description: Conventional radar altimeter makes measurement of sea surface height (SSH) in one-dimensional profiles along the ground tracks of a satellite. Such profiles are combined via various mapping techniques to construct two-dimensional SSH maps, providing a valuable data record over the past two decades for studying the global ocean circulation and sea level change. However, the spatial resolution of the SSH is limited by both coarse sampling across the satellite tracks and the instrument error in the profile measurements. A new satellite mission based on radar interferometry offers the capability of making high-resolution wide-swath measurement of SSH. This mission is called Surface Water and Ocean Topography (SWOT), which will demonstrate the application of swath altimeter to both oceanography and land hydrology. This paper presents a brief introduction to the design of SWOT, its performance specification for SSH, and the anticipated spatial resolution and coverage, demonstrating the promise of SWOT for fundamental advancement in observing SSH. A main objective of the paper is to address issues in the anticipated transition of conventional profile altimetry to swath altimetry in the future—in particular, the need for consistency of the new observing system with the old for extending the existing data record into the future. A viable approach is to carry a profile altimeter in the SWOT payload to provide calibration and validation of the new measurement against the old at large scales. This is the baseline design of SWOT. The unique advantages of the approach are discussed in the context of a new standard for observing the global SSH in the future.

Description: Many issues may challenge standard interpolation techniques to produce high-resolution gridded maps of sea surface height in the context of future missions like Surface Water and Ocean Topography (SWOT). The present study proposes a new method to address these challenges. Based on the conservation of potential vorticity, the method provides a simple dynamic approach to interpolation through temporal gaps between high spatial resolution observations. For gaps shorter than 20 days, the dynamic interpolation is extremely efficient and allows for the reconstruction of the time evolution of small mesoscale eddies (below 100 km) that would be smoothed out by conventional methods based on optimal mapping. Such a simple approach offers some perspectives for developing high-level products from high-resolution altimetry data in the future.

Description: In the Kalman filter standard algorithm, the computational complexity of the observational update is proportional to the cube of the number y of observations (leading behavior for large y). In realistic atmospheric or oceanic applications, involving an increasing quantity of available observations, this often leads to a prohibitive cost and to the necessity of simplifying the problem by aggregating or dropping observations. If the filter error covariance matrices are in square root form, as in square root or ensemble Kalman filters, the standard algorithm can be transformed to be linear in y, providing that the observation error covariance matrix is diagonal. This is a significant drawback of this transformed algorithm and often leads to an assumption of uncorrelated observation errors for the sake of numerical efficiency. In this paper, it is shown that the linearity of the transformed algorithm in y can be preserved for other forms of the observation error covariance matrix. In particular, quite general correlation structures (with analytic asymptotic expressions) can be simulated simply by augmenting the observation vector with differences of the original observations, such as their discrete gradients. Errors in ocean altimetric observations are spatially correlated, as for instance orbit or atmospheric errors along the satellite track. Adequately parameterizing these correlations can directly improve the quality of observational updates and the accuracy of the associated error estimates. In this paper, the example of the North Brazil Current circulation is used to demonstrate the importance of this effect, which is especially significant in that region of moderate ratio between signal amplitude and observation noise, and to show that the efficient parameterization that is proposed for the observation error correlations is appropriate to take it into account. Adding explicit gradient observations also receives a physical justification. This parameterization is thus proved to be useful to ocean data assimilation systems that are based on square root or ensemble Kalman filters, as soon as the number of observations becomes penalizing, and if a sophisticated parameterization of the observation error correlations is required.