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Ocean observations are expensive and difficult to collect. Designing effective ocean observing systems therefore warrants deliberate, quantitative strategies. We leverage adjoint modeling and Hessian uncertainty quantification (UQ) within the ECCO (Estimating the Circulation and Climate of the Ocean) framework to explore a new design strategy for ocean climate observing systems. Within this context, an observing system is optimal if it minimizes uncertainty in a set of investigator‐defined quantities of interest (QoIs), such as oceanic transports or other key climate indices. We show that Hessian UQ unifies three design concepts. (1) An observing system reduces uncertainty in a target QoI most effectively when it is sensitive to the same dynamical controls as the QoI. The dynamical controls are exposed by the Hessian eigenvector patterns of the model‐data misfit function. (2) Orthogonality of the Hessian eigenvectors rigorously accounts for redundancy between distinct members of the observing system. (3) The Hessian eigenvalues determine the overall effectiveness of the observing system, and are controlled by the sensitivity‐to‐noise ratio of the observational assets (analogous to the statistical signal‐to‐noise ratio). We illustrate Hessian UQ and its three underlying concepts in a North Atlantic case study. Sea surface temperature observations inform mainly local air‐sea fluxes. In contrast, subsurface temperature observations reduce uncertainty over basin‐wide scales, and can therefore inform transport QoIs at great distances. This research provides insight into the design of effective observing systems that maximally inform the target QoIs, while being complementary to the existing observational database.

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.