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Abstract. Use of an ocean parameter and state estimation framework – such as the Estimating the Circulation and Climate of the Ocean (ECCO) framework – could provide an opportunity to learn about the spatial distribution of the diapycnal diffusivity parameter (κρ) that observations alone cannot due to gaps in coverage. However, we show that the inclusion of misfits to observed physical variables – such as in situ temperature, salinity, and pressure – currently accounted for in ECCO is not sufficient, as κρ from ECCO does not agree closely with any observationally derived product. These observationally derived κρ products were inferred from microstructure measurements, derived from Argo and conductivity–temperature–depth (CTD) data using a strain-based parameterization of fine-scale hydrographic structure, or calculated from climatological and seafloor data using a parameterization of tidal mixing. The κρ products are in close agreement with one another but have both measurement and structural uncertainties, whereas tracers can have relatively small measurement uncertainties. With the ultimate goal being to jointly improve the ECCO state estimate and representation of κρ in ECCO, we investigate whether adjustments in κρ due to inclusion of misfits to a tracer – dissolved oxygen concentrations from an annual climatology – would be similar to those due to inclusion of misfits to observationally derived κρ products. We do this by performing sensitivity analyses with ECCO. We compare multiple adjoint sensitivity calculations: one configuration uses misfits to observationally derived κρ, and the other uses misfits to observed dissolved oxygen concentrations. We show that adjoint sensitivities of dissolved oxygen concentration misfits to the state estimate's control space typically direct κρ to improve relative to the observationally derived values. These results suggest that the inclusion of oxygen in ECCO's misfits will improve κρ in ECCO, particularly in (sub)tropical regions. 

A description and assessment of the first release of the Arctic Subpolar gyre sTate Estimate (ASTE_R1), a data‐constrained ocean‐sea ice model‐data synthesis, is presented. ASTE_R1 has a nominal resolution of 1/3° and spans the period 2002–2017. The fit of the model to an extensive (O(10⁹)) set of satellite and in situ observations was achieved through adjoint‐based nonlinear least squares optimization. The improvement of the solution compared to an unconstrained simulation is reflected in misfit reductions of 77% for Argo, 50% for satellite sea surface height, 58% for the Fram Strait mooring, 65% for Ice Tethered Profilers, and 83% for sea ice extent. Exact dynamical and kinematic consistency is a key advantage of ASTE_R1, distinguishing the state estimate from existing ocean reanalyses. Through strict adherence to conservation laws, all sources and sinks within ASTE_R1 can be accounted for, permitting meaningful analysis of closed budgets at the grid‐scale, such as contributions of horizontal and vertical convergence to the tendencies of heat and salt. ASTE_R1 thus serves as the biggest effort undertaken to date of producing a specialized Arctic ocean‐ice estimate over the 21st century. Transports of volume, heat, and freshwater are consistent with published observation‐based estimates across important Arctic Mediterranean gateways. Interannual variability and low frequency trends of freshwater and heat content are well represented in the Barents Sea, western Arctic halocline, and east subpolar North Atlantic. Systematic biases remain in ASTE_R1, including a warm bias in the Atlantic Water layer in the Arctic and deficient freshwater inputs from rivers and Greenland discharge.