As climate modellers prepare their code for kilometre-scale global simulations, the computationally demanding radiative transfer parameterization is a prime candidate for machine learning (ML) emulation. Because of the computational demands, many weather centres use a reduced spatial grid and reduced temporal frequency for radiative transfer calculations in their forecast models. This strategy is known to affect forecast quality, which further motivates the use of ML-based radiative transfer parameterizations. This paper contributes to the discussion on how to incorporate physical constraints into an ML-based radiative parameterization, and how different neural network (NN) designs and output normalisation affect prediction performance. A random forest (RF) is used as a baseline method, with the European Centre for Medium-Range Weather Forecasts (ECMWF) model ecRad, the operational radiation scheme in the Icosahedral Nonhydrostatic Weather and Climate Model (ICON), used for training. Surprisingly, the RF is not affected by the top-of-atmosphere (TOA) bias found in all NNs tested (e.g., MLP, CNN, UNet, RNN) in this and previously published studies. At lower atmospheric levels, the RF is able to compete with all NNs tested, but its memory requirements quickly become prohibitive. For a fixed memory size, most NNs outperform the RF except at TOA. For the best emulator, we use a recurrent neural network architecture which closely imitates the physical process it emulates. We additionally normalize the shortwave and longwave fluxes to reduce their dependence from the solar angle and surface temperature respectively. Finally, we train the model with an additional heating rates penalty in the loss function.

This paper continues the exploration of Machine Learning (ML) parameterization for radiative transfer for the ICOsahedral Nonhydrostatic weather and climate model (ICON). Three ML models, developed in Part I of this study, are coupled to ICON. More specifically, a UNet model and a bidirectional recurrent neural network (RNN) with long short-term memory (LSTM) are compared against a random forest. The ML parameterizations are coupled to the ICON code that includes OpenACC compiler directives to enable GPUs support. The coupling is done through Infero, developed by ECMWF, and PyTorch-Fortran. The most accurate model is the bidirectional RNN with physics-informed normalization strategy and heating rate penalty, but the fluxes above 15 km height are computed with a simplified formula for numerical stability reasons. The presented setup enables stable aquaplanet simulations with ICON for several weeks at a resolution of about 80 km and compare well with the physics-based radiative transfer solver ecRad. However, the achieved speed up when using the emulators and the minimum required memory usage relative to the GPU-enabled ecRad depend strongly on the Neural Network (NN) architecture. Future studies may explore physics-constraint emulators that predict heating rates inside the atmospheric model and fluxes at the top.

As climate modellers prepare their code for kilometre-scale global simulations, the computationally demanding radiative transfer parameterization is a prime candidate for machine learning (ML) emulation. Because of the computational demands, many weather centres use a reduced spatial grid and reduced temporal frequency for radiative transfer calculations in their forecast models. This strategy is known to affect forecast quality, which further motivates the use of ML-based radiative transfer parameterizations. This paper contributes to the discussion on how to incorporate physical constraints into an ML-based radiative parameterization, and how different neural network (NN) designs and output normalisation affect prediction performance. A random forest (RF) is used as a baseline method, with the European Centre for Medium-Range Weather Forecasts (ECMWF) model ecRad, the operational radiation scheme in the Icosahedral Nonhydrostatic Weather and Climate Model (ICON), used for training. Surprisingly, the RF is not affected by the top-of-atmosphere (TOA) bias found in all NNs tested (e.g., MLP, CNN, UNet, RNN) in this and previously published studies. At lower atmospheric levels, the RF can compete with all NNs tested, but its memory requirements quickly become prohibitive. For a fixed memory size, most NNs outperform the RF except at TOA. The most accurate emulator is a recurrent neural network architecture that closely imitates the physical process it emulates. The shortwave and longwave fluxes are normalized to reduce their dependence on the solar angle and surface temperature respectively. The model are, furthermore, trained with an additional heating rates penalty in the loss function.