Learning earth system models from observations: machine learning or data assimilation?

Abstract

Recent progress in machine learning (ML) inspires the idea of improving (or learning) earth system models directly from the observations. Earth sciences already use data assimilation (DA), which underpins decades of progress in weather forecasting. DA and ML have many similarities: they are both inverse methods that can be united under a Bayesian (probabilistic) framework. ML could benefit from approaches used in DA, which has evolved to deal with real observations—these are uncertain, sparsely sampled, and only indirectly sensitive to the processes of interest. DA could also become more like ML and start learning improved models of the earth system, using parameter estimation, or by directly incorporating machine-learnable models. DA follows the Bayesian approach more exactly in terms of representing uncertainty, and in retaining existing physical knowledge, which helps to better constrain the learnt aspects of models. This article makes equivalences between DA and ML in the unifying framework of Bayesian networks. These help illustrate the equivalences between four-dimensional variational (4D-Var) DA and a recurrent neural network (RNN), for example. More broadly, Bayesian networks are graphical representations of the knowledge and processes embodied in earth system models, giving a framework for organising modelling components and knowledge, whether coming from physical equations or learnt from observations. Their full Bayesian solution is not computationally feasible but these networks can be solved with approximate methods already used in DA and ML, so they could provide a practical framework for the unification of the two. Development of all these approaches could address the grand challenge of making better use of observations to improve physical models of earth system processes. This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

Physical characteristics of frozen hydrometeors inferred with parameter estimation

“…of Gaussian errors (see e.g. Geer, 2021). The best fit to observations, known as the analysis, is obtained where the cost function has a minimum.…”

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

“…While these preliminary results indicate the basic viability of the approach, they do not cover many key aspects that need to be addressed to scale this predictor‐corrector nudging idea into more realistic situations. It is also interesting to note that the similarities and equivalence between ML and the formulation of statistical data assimilation as used widely in physical and biological sciences have been postulated [1,119].…”

“…Given the abundance of data and data‐driven tools, the development of ROMs is gaining increasing popularity nowadays. As highlighted in our introduction, there are a great number of review articles available concerning various aspects of model order reduction and its applications [23,29,37,38,44,45,52, 54‐56,67,71,95,105,106,118,165,169,183,202,204,210,220,224,225,245,262,278,287,317‐319,328,344,351,356,358,364], and more relevant to our discussion, the enabling role of model order reduction approaches in developing next generation DT systems has been also discussed [136,277]. Of particular interest, MPC [113,139,218] originated in the late seventies and has since then evolved considerably.…”

“…In this perspective letter, we aim to provide an overview of HAM strategies relevant to scientific and engineering applications. The topic spans a wide spectrum, and there are a great number of review articles on relevant discussions, methodologies, and applications [23,29,37,38,44,45,52,54‐56,67,71,95,105,106,118,165,169,183,202,204,210,220,224,225,245,262,278,287,317‐319,328,344, 351,356,358,364]. Therefore, it is not our intention to give a complete biography, but rather somehow present our subjective perspectives with an emphasis on the emerging methodologies and enabling technologies from modeling perspectives.…”

Towards hybrid modeling of the global hydrological cycle

“…In contrast to data assimilation the goal here is to develop a generalizable model, which can be applied beyond the specific forecasting task in data assimilation. Nevertheless, non-parametric machine learning approaches can also be included into data assimilation as discussed in Geer (2021).…”