Source-to-source adjoint Algorithmic Differentiation of an ice sheet model written in C

Abstract

Algorithmic Differentiation (AD) has become a powerful tool to improve our understanding of the Earth System, because it can generate adjoint code which permits efficient calculation of gradients that are essential to sensitivity studies, inverse problems, parameter estimation and data assimilation. Most source-to-source transformation tools, however, have been designed for FORTRAN and support for C remains limited. Here we use the Adjoinable Land Ice Flow model (ALIF), a C clone of the C++ Ice Sheet System Model (ISSM) and employ source-to-source AD to produce its adjoint code. We present the first running source-to-source adjoint of ALIF, and its application to basal drag inversion under Pine Island Glacier, West Antarctica. ALIF brought several challenges to AD tool development, such as the correct treatment of the context code, which does not compute the differentiable function, but controls this computation through the setup of data structures, including possible aliasing, as well as data-flow reversal in the presence of pointers and dynamic memory, which are ubiquitous in codes such as ISSM and ALIF. We present the strategies we have developed to overcome these challenges.