Quantifying Dynamical Proxy Potential Through Shared Adjustment Physics in the North Atlantic

Abstract

Oceanic quantities of interest (QoIs), for example, 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 and (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.

Bathymetric Influences on Antarctic Ice‐Shelf Melt Rates

“…High-resolution studies of ice-shelf bathymetry (for instance, through gravity analysis and seismic inversion) are possible, but are very limited in scope. As our understanding of sub-shelf bathymetry evolves, our adjoint-based method could be adapted to identify candidate locations where high-resolution observational campaigns can be most impactful -for instance, by assessing the potential information gain in important quantities of interest, as in Loose et al (2020). Additionally, patterns of spatial variability in sensitivity (such as that seen on the flank of Dotson trough) could inform requirements for airborne gravity surveys (in terms of aircraft speed and altitude) to ensure such variability is captured.…”

Leveraging Uncertainty Quantification to Design Ocean Climate Observing Systems

“…Exact definitions for the model calculations of HT ISR and   can be found in Loose et al (2020). We quantify dynamical and effective proxy potential of the five-year mean of the observations for the five-year mean of our QoI, for zero lag.…”

“…As in Loose et al (2020), the control variables are comprised of the time-mean, spatially-varying forcing fields Q net,↑ , EPR, τ x , and τ y (Table 1). These two-dimensional forcing fields, F m (i, j), m = 1, …, 4, are flattened LOOSE AND HEIMBACH 10.1029/2020MS002386 8 of 25 , equal to 4 times the number of model surface grid cells covering the global ocean (next to last column, Table 1).…”

“…These two-dimensional forcing fields, F m (i, j), m = 1, …, 4, are flattened LOOSE AND HEIMBACH 10.1029/2020MS002386 8 of 25 , equal to 4 times the number of model surface grid cells covering the global ocean (next to last column, Table 1). We assign each of the four forcing fields, F m (i, j), a spatially constant prior standard deviation, ΔF m (last column, Table 1; see also Loose et al, 2020). Moreover, prior cross-correlations are set to zero, corresponding to the assumption that the decorrelation length in the surface forcing is less than the grid scale (∼1°).…”

“…In this simple case, proxy potential can be understood as the dynamical analog of statistical correlation (squared) between observation and QoI, with the important distinction that proxy potential accounts only for covariability that has dynamical underpinnings. The goal of this study is to leverage Hessian UQ to generalize the notion of proxy potential introduced by Loose et al (2020) in three important ways (Section 2): first, by extending this concept from a single observational asset to full observing systems; second, by quantifying observational redundancy versus complementarity; and third, by accounting for observational noise.…”