Building a physics-constrained, fast and stable machine learning-based radiation emulator
Authors: Bertoli Guillaume , Schemm Sebastian , Ozdemir Firat , Szekely Eniko , Perez Cruz Fernando 
Published: June 2022

&lt;p&gt;Atmospheric radiative transfer, which describes the evolution of radiation emitted by the Sun, the Earth's surface, clouds, and greenhouse gases, is an essential component of climate and weather modeling. In climate models, the transfer of radiation is approximated by parameterizations. Theoretically, however, with sufficient computing power, the electromagnetic radiation equations could be solved, but in practice this is out of reach.&amp;#160; The current operational radiative transfer solver in the Icosahedral Nonhydrostatic Weather and Climate Model (ICON) is ecRad, which, developed at ECMWF, is one of the most advanced available radiative transfer parameterizations.&amp;#160; It considers surface optics, gas optics, aerosol optics and cloud optics [1]. It is an accurate radiation parametrization but remains computationally expensive. Therefore, the radiation solver is usually not invoked at every time step and only runs on a reduced spatial grid, which can affect prediction accuracy, or only in a 1D setting without 3D transfer.&lt;/p&gt;&lt;p&gt;In this project, we are trying to develop an ecRad solver improved by machine learning to speed up the computation without loss of accuracy. Machine learning-based parametrizations would in general allow to fully replace existing sub-grid scale parameterizations, once trained from data. However, such parametrizations do not necessarily preserve essential physical quantities, which can lead to instabilities, model drifts or unphysical behavior as observed in [2] and [3].&lt;/p&gt;&lt;p&gt;We present here an emulation strategy, composed of three steps. First, we continue to call ecRad on a significantly coarser grid to predict the clear-sky radiation. We thereby use ecRad as a regularizer while reducing computation costs. Then, we interpolate the data on the full spatial grid using Gaussian processes. Finally, we predict the effect of the clouds on the radiation with random forests. The underlying idea is to avoid unphysical climate drifts and to support the generalization capabilities of the ML method.&lt;/p&gt;&lt;p&gt;Our first numerical experiments on an aqua planet simulation are promising. We hope to obtain a valuable outcome when considering more complex datasets with seasonality and realistic topography. Our final goal is to run a full ICON simulation with a machine learning enhanced ecRad parametrization, though the online performance remains open. There the clear-sky low resolution radiation field, computed with ecRad in the first part of our strategy, is expected to play a central role in model stability.&lt;/p&gt;&lt;p&gt;[1] &lt;em&gt;Hogan, R. J., &amp; Bozzo, A. (2018). A flexible and efficient radiation scheme for the ECMWF model. Journal of Advances in Modeling Earth Systems, 10, 1990-2008. &lt;/em&gt;&lt;/p&gt;&lt;p&gt;[2] &lt;em&gt;Brenowitz, N. D., &amp; Bretherton, C. S. (2018). Prognostic validation of a neural network unified physics parametrization. Geophysical Research Letters, 17, 6289&amp;#8211;6298&lt;/em&gt;&lt;/p&gt;&lt;p&gt;[3] &lt;em&gt;Brenowitz, N. D., and Bretherton, C. S. (2019). Spatially Extended Tests of a Neural Network Parametrization Trained by Coarse&amp;#8208;Graining, J. Adv. Model. Earth Syst., 11, 2728&amp;#8211;2744&lt;/em&gt;&lt;/p&gt;