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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.

 

Regional ocean general circulation models are generally forced at the boundaries by mesoscale ocean dynamics and barotropic tides. In this work we provide evidence that remotely forced internal waves can be a significant source of energy for the dynamics. We compare global and regional model solutions within the California Current System. Both models have similar inputs, forcings, and identical grids and numerics. The global model has a steric height power spectrum consistent with mooring observations at superinertial frequencies, while the regional model spectrum is weaker. The regional model also has less sea surface height variance at high wavenumber than the global model. The vertical velocity variance is significantly larger in the global model, except in the sheltered Southern California Bight. While the regional model has roughly equal high‐pass baroclinic and barotropic kinetic energy levels, the global model high‐pass baroclinic kinetic energy is 28% (0.39 PJ) greater than the barotropic energy. An internal wave energy flux analysis reveals that the regional model domain boundaries act as a sink of 183 MW, while in the global model the analysis domain boundaries act as a source of 539 MW. This 722 MW difference can account for the relative increase of 0.39 PJ high‐pass baroclinic energy in the global model, assuming a baroclinic kinetic energy dissipation time in the domain of approximately 6.3 days. The results here imply that most regional ocean models will need to account for internal wave boundary fluxes in order to reproduce the observed internal wave continuum spectrum.

 

Abstract. We present a new capability of the ice sheet model SICOPOLIS that enables flexible adjoint code generation via source transformation using the open-source algorithmic differentiation (AD) tool OpenAD.The adjoint code enables efficient calculation of the sensitivities of a scalar-valued objective function or quantity of interest (QoI) to a range of important, often spatially varying and uncertain model input variables, including initial and boundary conditions, as well as model parameters.Compared to earlier work on the adjoint code generation of SICOPOLIS, our work makes several important advances:(i) it is embedded within the up-to-date trunk of the SICOPOLIS repository – accounting for 1.5 decades of code development and improvements – and is readily available to the wider community;(ii) the AD tool used, OpenAD, is an open-source tool;(iii) the adjoint code developed is applicable to both Greenland and Antarctica, including grounded ice as well as floating ice shelves, with an extended choice of thermodynamical representations.A number of code refactorization steps were required. They are discussed in detail in an Appendix as they hold lessons for the application of AD to legacy codes at large.As an example application, we examine the sensitivity of the total Antarctic Ice Sheet volume to changes in initial ice thickness, austral summer precipitation, and basal and surface temperatures across the ice sheet.Simulations of Antarctica with floating ice shelves show that over 100 years of simulation the sensitivity of total ice sheet volume to the initial ice thickness and precipitation is almost uniformly positive, while the sensitivities to surface and basal temperature are almost uniformly negative. Sensitivity to austral summer precipitation is largest on floating ice shelves from Queen Maud to Queen Mary Land. The largest sensitivity to initial ice thickness is at outlet glaciers around Antarctica. Comparison between total ice sheet volume sensitivities to surface and basal temperature shows that surface temperature sensitivities are higher broadly across the floating ice shelves, while basal temperature sensitivities are highest at the grounding lines of floating ice shelves and outlet glaciers. A uniformly perturbed region of East Antarctica reveals that, among the four control variables tested here, total ice sheet volume is the most sensitive to variations in austral summer precipitation as formulated in SICOPOLIS.Comparison between adjoint- and finite-difference-derived sensitivities shows good agreement, lending confidence that the AD tool is producing correct adjoint code.The new modeling infrastructure is freely available at http://www.sicopolis.net (last access: 2 April 2020) under the development trunk. 

We present a new capability of the ice sheet model SICOPOLIS that enables flexible adjoint code generation via source transformation using the open-source algorithmic differentiation (AD) tool OpenAD. The adjoint code enables efficient calculation of sensitivities of a scalar-valued objective function or quantity of interest (QoI) to a range of important, often spatially varying model input variables, including initial and boundary conditions, as well as model parameters. Compared to earlier work on adjoint code generation of SICOPOLIS, our work is based on several important advances: (i) it is embedded within the up-to-date trunk of the SICOPOLIS repository – accounting for one and a half decades of code development and improvements – and is readily available to the wider community; (ii) the AD tool used, OpenAD, is an open-source tool; (iii) the adjoint code developed is applicable to both Greenland and Antarctica, including grounded ice as well as floating ice shelves, and with an extended choice of thermodynamical representations. A number of code refactorization steps were required. They are discussed in detail in an Appendix as they hold lessons for application of AD to legacy codes at large. As an example application, we examine the sensitivity of the total Antarctic Ice Sheet volume to changes in initial ice thickness, summer precipitation, and basal and surface temperatures across the ice sheet. Simulations of Antarctica with floating ice shelves show that over 100 years of simulation the sensitivity of total ice sheet volume to the initial ice thickness and precipitation is almost uniformly positive, while the sensitivities to surface and basal temperature are almost uniformly negative. Sensitivity to summer precipitation is largest on floating ice shelves from Queen Maud to Queen Mary Land. The largest sensitivity to initial ice thickness is at outlet glaciers around Antarctica. Comparison between total ice sheet volume sensitivities to surface and basal temperature shows that surface temperature sensitivities are higher broadly across the floating ice shelves, while basal temperature sensitivities are highest at the grounding lines of floating ice shelves and outlet glaciers. A uniformly perturbed region of East Antarctica reveals that, among the four control variables tested here, total ice sheet volume is most sensitive to variations in summer precipitation as formulated in SICOPOLIS. Comparison between adjoint- and finite-difference-derived sensitivities shows good agreement, lending confidence that the AD tool is producing correct adjoint code. The new modeling infrastructure is freely available at www.sicopolis.net under the development trunk. 

SICOPOLIS-AD is a version of the ice sheet model SICOPOLIS (originally [1]: www.sicopolis.net) used to produce adjoint sensitivities of chosen control variables. It can be used to assess the sensitivity of some quantity of interest to perturbations in variables that may affect that quantity of interest. For example, it can be used to comprehensively and quantitatively assess exactly how the volume of the Greenland Ice Sheet is sensitive to changes in surface temperature at each point on the ice sheet. This document provides basic startup and troubleshooting methods, as well as some best practices for making changes in the code for the purposes of adjoint production.