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Global biogeochemical ocean models are invaluable tools to examine how physical, chemical, and biological processes interact in the ocean. Satellite-derived ocean color properties, on the other hand, provide observations of the surface ocean, with unprecedented coverage and resolution. Advances in our understanding of marine ecosystems and biogeochemistry are strengthened by the combined use of these resources, together with sparse in situ data. Recent modeling advances allow the simulation of the spectral properties of phytoplankton and remote sensing reflectances, bringing model outputs closer to the kind of data that ocean color satellites can provide. However, comparisons between model outputs and analogous satellite products (e.g., chlorophyll a) remain problematic. Most evaluations are based on point-by-point comparisons in space and time, where spuriously large errors can occur from small spatial and temporal mismatches, whereas global statistics provide no information on how well a model resolves processes at regional scales. Here, we employ a unique suite of methodologies, the Probability Density Functions to Evaluate Models (PDFEM), which generate a robust comparison of these resources. The probability density functions of physical and biological properties of Longhurst's provinces are compared to evaluate how well a model resolves related processes. Differences in the distributions of chlorophyll a concentration (mg m−3) provide information on matches and mismatches between models and observations. In particular, mismatches help isolate regional sources of discrepancy, which can lead to improving both simulations and satellite algorithms. Furthermore, the use of radiative transfer in the model to mimic remotely sensed products facilitates model–observation comparisons of optical properties of the ocean.

Wind work at the air-sea interface is the transfer of kinetic energy between the ocean and the atmosphere and, as such, is an important part of the ocean-atmosphere coupled system. Wind work is defined as the scalar product of ocean wind stress and surface current, with each of these two variables spanning, in this study, a broad range of spatial and temporal scales, from 10 km to more than 3000 km and hours to months. These characteristics emphasize wind work's multiscale nature. In the absence of appropriate global observations, our study makes use of a new global, coupled ocean-atmosphere simulation, with horizontal grid spacing of 2–5 km for the ocean and 7 km for the atmosphere, analyzed for 12 months. We develop a methodology, both in physical and spectral spaces, to diagnose three different components of wind work that force distinct classes of ocean motions, including high-frequency internal gravity waves, such as near-inertial oscillations, low-frequency currents such as those associated with eddies, and seasonally averaged currents, such as zonal tropical and equatorial jets. The total wind work, integrated globally, has a magnitude close to 5 TW, a value that matches recent estimates. Each of the first two components that force high-frequency and low-frequency currents, accounts for ∼ 28 % of the total wind work and the third one that forces seasonally averaged currents, ∼ 44 %. These three components, when integrated globally, weakly vary with seasons but their spatial distribution over the oceans has strong seasonal and latitudinal variations. In addition, the high-frequency component that forces internal gravity waves, is highly sensitive to the collocation in space and time (at scales of a few hours) of wind stresses and ocean currents. Furthermore, the low-frequency wind work component acts to dampen currents with a size smaller than 250 km and strengthen currents with larger sizes. This emphasizes the need to perform a full kinetic budget involving the wind work and nonlinear advection terms as small and larger-scale low-frequency currents interact through these nonlinear terms. The complex interplay of surface wind stresses and currents revealed by the numerical simulation motivates the need for winds and currents satellite missions to directly observe wind work.

This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of data constraints and control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The baseline ECCO v4 solution is a dynamically consistent ocean state estimate without unidentified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found to be physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model–data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.