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Analyses using a suite of observational datasets (Aquarius and Argo) and model simulations are carried out to examine the seasonal variability of salinity in the northern Indian Ocean (NIO). The model simulations include Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2), the European Centre for Medium-Range Weather Forecasts–Ocean Reanalysis System 4 (ECMWF–ORAS4), Simple Ocean Data Assimilation (SODA) reanalysis, and the Hybrid Coordinate Ocean Model (HYCOM). The analyses of salinity at the surface and at depths up to 200 m, surface salt transport in the top 5-m layer, and depth-integrated salt transports revealed different salinity processes in the NIO that are dominantly related to the semiannual monsoons. Aquarius proves a useful tool for observing this dynamic region and reveals some aspects of sea surface salinity (SSS) variability that Argo cannot resolve. The study revealed large disagreement between surface salt transports derived from observed- and analysis-derived salinity fields. Although differences in SSS between the observations and the model solutions are small, model simulations provide much greater spatial variability of surface salt transports due to finer detailed current structure. Meridional depth-integrated salt transports along 6°N revealed dominant advective processes from the surface toward near-bottom depths. In the Arabian Sea (Bay of Bengal), the net monthly mean maximum northward (southward) salt transport of ~50 × 106 kg s −1 occurs in July, and annual-mean salt transports across this section are about −2.5 × 106 kg s −1 (3 × 106 kg s −1).

We analyze high-resolution (1 km) simulations of the western Pacific, Gulf of Mexico, and Arabian Sea to understand submesoscale eddy dynamics. A mask based on the Okubo–Weiss parameter isolates small-scale eddies, and we further classify those with |ζ/f| ≥ 1 as being submesoscale eddies. Cyclonic submesoscale eddies exhibit a vertical depth structure in which temperature anomalies from the large-scale background are negative. Peak density anomalies associated with cyclonic submesoscale eddies are found at a depth approximately twice the mixed layer depth (MLD). Within anticyclonic submesoscale eddies, temperature anomalies are positive and have peak density anomalies at the MLD. The depth–depth covariance structure for the cyclonic and anticyclonic submesoscale eddies have maxima over a shallow region near the surface and weak off diagonal elements. The observed vertical structure suggests that submesoscale eddies have a shallower depth profile and smaller vertical correlation scales when compared to the mesoscale phenomenon. We test a two-dimensional submesoscale eddy dynamical balance. Compared to a geostrophic dynamical balance using only pressure gradient and Coriolis force, including velocity tendency and advection produces lower errors by about 20%. In regions with strong tides and associated internal waves (western Pacific and Arabian Sea), using the mixed layer integrated small-scale steric height within the dynamical equations produces the lowest magnitude errors. In areas with weak tides (Gulf of Mexico), using small-scale sea surface height (SSH) produces the lowest magnitude errors. Recovering a submesoscale eddy with the correct magnitude and rotation requires integration of small-scale specific volume anomalies well below the mixed layer.

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High-resolution (swath) altimeter missions scheduled to monitor the ocean surface in the near future have observation-error covariances (OECs) with slowly decaying off-diagonal elements. This property presents a challenge for the majority of the data assimilation algorithms which were designed under the assumption of the diagonal OECs being easily inverted. In this note, we present a method of approximating the inverse of a dense OEC by a sparse matrix represented by the polynomial of spatially inhomogeneous differential operators, whose coefficients are optimized to fit the target OEC by minimizing a quadratic cost function. Explicit expressions for the cost function gradient and the Hessian are derived. The method is tested with an OEC model generated by the SWOT simulator.