30 Sep 2022
30 Sep 2022

Differentiable Programming for Earth System Modeling

Maximilian Gelbrecht1,2, Alistair White1,2, Sebastian Bathiany1,2, and Niklas Boers1,2,3 Maximilian Gelbrecht et al.
  • 1Earth System Modelling, School of Engineering & Design, Technical University Munich, Munich, Germany
  • 2Potsdam Institute for Climate Impact Research, Potsdam, Germany
  • 3Department of Mathematics and Global Systems Institute, University of Exeter, Exeter, UK

Abstract. Earth System Models (ESMs) are the primary tools for investigating future Earth system states at time scales from decades to centuries, especially in response to anthropogenic greenhouse gas release. State-of-the-art ESMs can reproduce the observational global mean temperature anomalies of the last 150 years. Nevertheless, ESMs need further improvements, most importantly regarding (i) the large spread in their estimates of climate sensitivity, i.e., the temperature response to increases in atmospheric greenhouse gases, (ii) the modeled spatial patterns of key variables such as temperature and precipitation, (iii) their representation of extreme weather events, and (iv) their representation of multistable Earth system components and their ability to predict associated abrupt transitions. Here, we argue that making ESMs automatically differentiable has huge potential to advance ESMs, especially with respect to these key shortcomings. First, automatic differentiability would allow objective calibration of ESMs, i.e., the selection of optimal values with respect to a cost function for a large number of free parameters, which are currently tuned mostly manually. Second, recent advances in Machine Learning (ML) and in the amount, accuracy, and resolution of observational data promise to be helpful with at least some of the above aspects because ML may be used to incorporate additional information from observations into ESMs. Automatic differentiability is an essential ingredient in the construction of such hybrid models, combining process-based ESMs with ML components. We document recent work showcasing the potential of automatic differentiation for a new generation of substantially improved, data-informed ESMs.

Maximilian Gelbrecht et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2022-875', Samuel Hatfield, 26 Oct 2022
  • RC2: 'Comment on egusphere-2022-875', Anonymous Referee #2, 04 Nov 2022
  • AC1: 'Response to the Comments RC1 and RC2', Maximilian Gelbrecht, 25 Nov 2022

Maximilian Gelbrecht et al.

Maximilian Gelbrecht et al.


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Short summary
Differential programming is a technique that enables the automatic computation of derivatives of the output of models with respect to model parameters. Applying these techniques to Earth System Modeling leverages the increasing availability of high-quality data to improve the models themselves. This can be done either by calibration techniques that use gradient-based optimization or by incorporating machine learning methods that can learn previously unresolved influences directly from data.