The future international Surface Water and Ocean Topography (SWOT) Mission, planned for launch in 2021, will make high-resolution 2D observations of sea-surface height using SAR radar interferometric techniques. SWOT will map the global and coastal oceans up to 77.6^∘ latitude every 21 days over a swath of 120 km (20 km nadir gap). Today’s 2D mapped altimeter data can resolve ocean scales of 150 km wavelength whereas the SWOT measurement will extend our 2D observations down to 15–30 km, depending on sea state. SWOT will offer new opportunities to observe the oceanic dynamic processes at scales that are important in the generation and dissipation of kinetic energy in the ocean, and that facilitate the exchange of energy between the ocean interior and the upper layer. The active vertical exchanges linked to these scales have impacts on the local and global budgets of heat and carbon, and on nutrients for biogeochemical cycles. This review paper highlights the issues being addressed by the SWOT science community to understand SWOT’s very precise sea surface height (SSH)/surface pressure observations, and it explores how SWOT data will be combined with other satellite and in situ data and models to better understand the upper ocean 4D circulation (x, y, z, t) over the next decade. SWOT will provide unprecedented 2D ocean SSH observations down to 15–30 km in wavelength, which encompasses the scales of “balanced” geostrophic eddy motions, high-frequency internal tides and internal waves. This presents both a challenge in reconstructing the 4D upper ocean circulation, or in the assimilation of SSH in models, but also an opportunity to have global observations of the 2D structure of these phenomena, and to learn more about their interactions. At these small scales, ocean dynamics evolve rapidly, and combining SWOT 2D SSH data with other satellite or in situ data with different space-time coverage is also a challenge. SWOT’s new technology will be a forerunner for the future altimetric observing system, and so advancing on these issues today will pave the way for our future.

The global sulphur cycle has been simulated using a general circulation model with a focus on the source and oxidation of atmospheric dimethylsulphide (DMS). The sensitivity of atmospheric DMS to the oceanic DMS climatology, the parameterisation of the sea-air transfer and to the oxidant fields have been studied. The importance of additional oxidation pathways (by O₃ in the gas- and aqueous-phases and by BrO in the gas phase) not incorporated in global models has also been evaluated. While three different climatologies of the oceanic DMS concentration produce rather similar global DMS fluxes to the atmosphere at 24-27 Tg S yr ^-1, there are large differences in the spatial and seasonal distribution. The relative contributions of OH and NO₃ radicals to DMS oxidation depends critically on which oxidant fields are prescribed in the model. Oxidation by O₃ appears to be significant at high latitudes in both hemispheres. Oxidation by BrO could be significant even for BrO concentrations at sub-pptv levels in the marine boundary layer. The impact of such refinements on the DMS chemistry onto the indirect radiative forcing by anthropogenic sulphate aerosols is also discussed.

This paper examines the ability of optical reflectance data assimilation to improve snow depth and snow water equivalent simulations from a chain of models with the SAFRAN meteorological model driving the detailed multilayer snowpack model Crocus now including a two-stream radiative transfer model for snow, TARTES. The direct use of reflectance data, allowed by TARTES, instead of higher level snow products, mitigates uncertainties due to commonly used retrieval algorithms.Data assimilation is performed with an ensemble-based method, the Sequential Importance Resampling Particle filter, to represent simulation uncertainties. In snowpack modeling, uncertainties of simulations are primarily assigned to meteorological forcings. Here, a method of stochastic perturbation based on an autoregressive model is implemented to explicitly simulate the consequences of these uncertainties on the snowpack estimates.Through twin experiments, the assimilation of synthetic spectral reflectances matching the MODerate resolution Imaging Spectroradiometer (MODIS) spectral bands is examined over five seasons at the Col du Lautaret, located in the French Alps. Overall, the assimilation of MODIS-like data reduces by 45 % the root mean square errors (RMSE) on snow depth and snow water equivalent. At this study site, the lack of MODIS data on cloudy days does not affect the assimilation performance significantly. The combined assimilation of MODIS-like reflectances and a few snow depth measurements throughout the 2010/2011 season further reduces RMSEs by roughly 70 %. This work suggests that the assimilation of optical reflectances has the potential to become an essential component of spatialized snowpack simulation and forecast systems. The assimilation of real MODIS data will be investigated in future works.

Ocean circulation is dominated by turbulent geostrophic eddy fields with typical scales ranging from 10 to 300 km. At mesoscales (>50 km), the size of eddy structures varies regionally following the Rossby radius of deformation. The variability of the scale of smaller eddies is not well known due to the limitations in existing numerical simulations and satellite capability. Nevertheless, it is well established that oceanic flows (<50 km) generally exhibit strong seasonality. In this study, we present a basin‐scale analysis of coherent structures down to 10 km in the North Atlantic Ocean using two submesoscale‐permitting ocean models, a NEMO‐based North Atlantic simulation with a horizontal resolution of 1/60 (NATL60) and an HYCOM‐based Atlantic simulation with a horizontal resolution of 1/50 (HYCOM50). We investigate the spatial and temporal variability of the scale of eddy structures with a particular focus on eddies with scales of 10 to 100 km, and examine the impact of the seasonality of submesoscale energy on the seasonality and distribution of coherent structures in the North Atlantic. Our results show an overall good agreement between the two models in terms of surface wave number spectra and seasonal variability. The key findings of the paper are that (i) the mean size of ocean eddies show strong seasonality; (ii) this seasonality is associated with an increased population of submesoscale eddies (10–50 km) in winter; and (iii) the net release of available potential energy associated with mixed layer instability is responsible for the emergence of the increased population of submesoscale eddies in wintertime.

Smoothers are increasingly used in geophysics. Several linear Gaussian algorithms exist, and the general picture may appear somewhat confusing. This paper attempts to stand back a little, in order to clarify this picture by providing a concise overview of what the different smoothers really solve, and how. The authors begin addressing this issue from a Bayesian viewpoint. The filtering problem consists in finding the probability of a system state at a given time, conditioned to some past and present observations (if the present observations are not included, it is a forecast problem). This formulation is unique: any different formulation is a smoothing problem. The two main formulations of smoothing are tackled here: the joint estimation problem (fixed lag or fixed interval), where the probability of a series of system states conditioned to observations is to be found, and the marginal estimation problem, which deals with the probability of only one system state, conditioned to past, present, and future observations. The various strategies to solve these problems in the Bayesian framework are introduced, along with their deriving linear Gaussian, Kalman filter-based algorithms. Their ensemble formulations are also presented. This results in a classification and a possible comparison of the most common smoothers used in geophysics. It should provide a good basis to help the reader find the most appropriate algorithm for his/her own smoothing problem.

A central task of physical oceanography is the prediction of ocean circulation at various time scales. Mathematical techniques are used in this domain not only for the modeling of ocean circulation but also for the enhancement of simulation through data assimilation. The ocean circulation model of concern here, namely, HYCOM, is briefly presented through its variables, equations, and specific vertical coordinate system. The main part of this paper focuses on the Kalman filter as a data assimilation method, and especially on how this mathematical technique, usually associated with a prohibitively high computing cost for operational sciences, is simplified in order to make it applicable to the simulation of realistic ocean circulation models. Some practical issues are presented, such as a brief explanation about ocean observation systems, together with examples of data assimilation results.