Abstract
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.
Highlights
An important ingredient to characterizing and quantifying our uncertainty in expected climate change outcomes is our understanding of ice sheet dynamics
We present the sensitivity of the volume of the Antarctic Ice Sheet with respect to several control variables as a proof of concept, rather than extending the work in the direction of optimization, which will be the subject of future studies
The adjoint-derived sensitivities are compared to finite-difference perturbations, either at single points or over a patch of the domain that has been uniformly perturbed, to demonstrate that the adjoint model is sufficiently consistent with sensitivities derived via finite differences
Summary
An important ingredient to characterizing and quantifying our uncertainty in expected climate change outcomes is our understanding of ice sheet dynamics. Ice flow critically depends on quantities that we either cannot measure (such as the friction or thermal forcing between ice and the bedrock below it), that parameterize subgrid-scale processes or empirical constitutive laws (such as the routing of meltwater or fracture propagation), or that we may never be able to measure in the present day (such as the rate of snowfall in the past) These unknown or uncertain variables can be construed as sets of parameters that we must infer or calibrate if we are to make projections with ice sheet models, and these parameters must both satisfy, by some measure, the assumed model physics and the sparsely made observations across such large bodies. In the language of optimal estimation and control theory, these parameters are referred to as control variables (Gelb, 1974)
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