Oceanic quantities of interest (QoIs), e.g., ocean heat content or transports, are often inaccessible to direct observation, due to the high cost of instrument deployment and logistical challenges. Therefore, oceanographers seek proxies for undersampled or unobserved QoIs. Conventionally, proxy potential is assessed via statistical correlations, which measure covariability without establishing causality. This paper introduces an alternative method: quantifying dynamical proxy potential. Using an adjoint model, this method unambiguously identifies the physical origins of covariability. A North Atlantic case study illustrates our method within the ECCO (Estimating the Circulation and Climate of the Ocean) state estimation framework. We find that wind forcing along the eastern and northern boundaries of the Atlantic drives a basin-wide response in North Atlantic circulation and temperature. Due to these large-scale teleconnections, a single subsurface temperature observation in the Irminger Sea informs heat transport across the remote Iceland-Scotland ridge (ISR), with a dynamical proxy potential of 19%. Dynamical proxy potential allows two equivalent interpretations: Irminger Sea subsurface temperature (i) shares 19% of its adjustment physics with ISR heat transport; (ii) reduces the uncertainty in ISR heat transport by 19% (independent of the measured temperature value), if the Irminger Sea observation is added without noise to the ECCO state estimate. With its two interpretations, dynamical proxy potential is simultaneously rooted in (i) ocean dynamics and (ii) uncertainty quantification and optimal observing system design, the latter being an emerging branch in computational science. The new method may therefore foster dynamics-based, quantitative ocean observing system design in the coming years.

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 1/3o and spans the period 2002-2017. The fit of the model to an extensive (O(10^9)) 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.