Quantifying Dynamical Proxy Potential through Shared Adjustment Physics
in the North Atlantic
Abstract
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.