Physics-informed machine learning: case studies for weather and climate modelling

Abstract

Machine learning (ML) provides novel and powerful ways of accurately and efficiently recognizing complex patterns, emulating nonlinear dynamics, and predicting the spatio-temporal evolution of weather and climate processes. Off-the-shelf ML models, however, do not necessarily obey the fundamental governing laws of physical systems, nor do they generalize well to scenarios on which they have not been trained. We survey systematic approaches to incorporating physics and domain knowledge into ML models and distill these approaches into broad categories. Through 10 case studies, we show how these approaches have been used successfully for emulating, downscaling, and forecasting weather and climate processes. The accomplishments of these studies include greater physical consistency, reduced training time, improved data efficiency, and better generalization. Finally, we synthesize the lessons learned and identify scientific, diagnostic, computational, and resource challenges for developing truly robust and reliable physics-informed ML models for weather and climate processes. This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

Parameterising cloud base updraft velocity of marine stratocumuli

“…Our work shows that the dependency of updraft velocity on boundary layer state can be predicted with a reasonable accuracy and machine learning methods are able to capture also the effect of variables that are important only in a limited subset of all possible conditions, like is the case with aerosol number concentrations. Our results also show that machine learning is effective when it is supported with an underlying physical dependency, which is in line with previous studies (Lipponen et al, 2013(Lipponen et al, , 2018Silva et al, 2021;Kashinath et al, 2021). The parameterisations introduced are valid only for marine stratocumulus, but extension of the training set to cover the effects of surface heat fluxes and wind shear would improve the physical foundation of updraft parameterisations, and increase the applicability of the method to continental stratiform boundary layer clouds also (e.g., Matheou and Teixeira, 2019).…”

“…For example, it has been suggested that updraft depends on the cloud top radiative cooling in case of stratocumulus (Zheng et al, 2016) or cloud base height for cumulus clouds (Zheng and Rosenfeld, 2015). Recently, machine learning approaches have gained attention, because they can be used as parameterisations with higher accuracy than traditional parameterisations and with much smaller computational costs compared to explicit simulations (e.g., Rasp et al, 2018;Silva et al, 2021;Kashinath et al, 2021).…”

Forecasting Hurricane-forced Significant Wave Heights using the Long Short-Term Memory Network in the Caribbean Sea

“…These methods have been successfully applied to the solving of differential equations in engineering (Niaki et al, 2021;Zobeiry, and Humfeld, 2021), analyzing blood flow (Arzani et al, 2021), and chaotic systems (Khodkar and Hassanzadeh, 2021). Relevant for the current discussion, these methods are also finding use in weather and climate modelling (Kashinath et al, 2021). Considering the large physical complexities in wave evolution under TC forcing (Tamizi et al, 2021), and the many nonlinearities that govern crucial processes (Yim et al, 2017;Constantin, 2018;Sharifineyestani and Tahvildari, 2021), incorporating physics-informed, or knowledge-guided machine learning should, respectively, improve and lengthen forecast efficacy and horizons.…”

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

“…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.…”