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.

Deep-sea δ18O records show a pronounced difference in Milankovitch periodicity between the Early and Late Pleistocene. δ18O is interpreted as a proxy for ice sheet volume and temperature, which led to the conclusion that glacial-interglacial cycles considerably changed their rhythm during the mid-Pleistocene. This transition is referred to as the mid-Pleistocene Transition (MPT). Specifically, the precessional component of the Milankovitch cycles is absent in Early Pleistocene δ18O records, despite its continuous presence in solar insolation forcing to the ice sheets. Climate feedbacks involving (sea) ice, geological processes and carbon and nutrient cycling have been proposed as causes of this marked change. We however show that the absence of an Early Pleistocene precession signal in deep-sea δ18O records could be the result of destructive interference of the precessional cycle in the interior ocean. Such cancellation is caused by the anti-phasing of the precessional cycle between the North Atlantic and Southern Ocean deep-water sources (see Figure). We explore the potential for cancellation in the transient setup of the Total Matrix Intercomparison model for a wide range of source signal strengths. Our results show that cancellation can cause the absence of the precessional signal due to cancellation in the interior South-Atlantic, Indian and Pacific basins. Cancellation is especially widespread for a relative end-member contribution typical for the Early Pleistocene. We therefore conclude that the precessional component is likely incompletely archived in Early Pleistocene δ18O records, and appears as an actual change in Milankovitch periodicity across the MPT. Proxies not susceptible to cancellation of precession (such as those currently retrieved across the MPT from Antarctica) would be able to verify to what extent deep-sea δ18O correctly represents Pleistocene climate.