The radiative transfer equations are well known, but radiation parametrizations in atmospheric models are computationally expensive. A promising tool for accelerating parametrizations is the use of machine learning techniques. In this study, we develop a machine learning-based parametrization for the gaseous optical properties by training neural networks to emulate a modern radiation parametrization (RRTMGP). To minimize computa- tional costs, we reduce the range of atmospheric conditions for which the neural networks are applicable and use machine-specific optimized BLAS functions to accelerate matrix computations. To generate training data, we use a set of randomly perturbed atmospheric profiles and calculate optical properties using RRTMGP. Predicted optical properties are highly accurate and the resulting radiative fluxes have average errors within 0.5 W m −2 compared to RRTMGP. Our neural network-based gas optics parametrization is up to four times faster than RRTMGP, depending on the size of the neural networks. We further test the trade-off between speed and accuracy by training neural networks for the narrow range of atmospheric conditions of a single large-eddy simulation, so smaller and therefore faster networks can achieve a desired accuracy. We conclude that our machine learning-based parametrization can speed-up radiative transfer computations while retaining high accuracy. This article is part of the theme issue ‘Machine learning for weather and climate modelling’.

Abstract. The representation of snow processes in most large-scale hydrological and climate models is known to introduce considerable uncertainty into the predictions and projections of water availability. During the critical snowmelt period, the main challenge in snow modeling is that net radiation is spatially highly variable for a patchy snow cover, resulting in large horizontal differences in temperatures and heat fluxes. When a wind blows over such a system, these differences can drive advection of sensible and latent heat from the snow-free areas to the snow patches, potentially enhancing the melt rates at the leading edge and increasing the variability of subgrid melt rates. To get more insight into these processes, we examine the melt along the upwind and downwind edges of a 50 m long snow patch in the Finseelvi catchment, Norway, and try to explain the observed behavior with idealized simulations of heat fluxes and air movement over patchy snow. The melt of the snow patch was monitored from 11 June until 15 June 2019 by making use of height maps obtained through the photogrammetric structure-from-motion principle. A vertical melt of 23 ± 2.0 cm was observed at the upwind edge over the course of the field campaign, whereas the downwind edge melted only 3 ± 0.4 cm. When comparing this with meteorological measurements, we estimate the turbulent heat fluxes to be responsible for 60 % to 80 % of the upwind melt, of which a significant part is caused by the latent heat flux. The melt at the downwind edge approximately matches the melt occurring due to net radiation. To better understand the dominant processes, we represented this behavior in idealized direct numerical simulations, which are based on the measurements on a single snow patch by Harder et al. (2017) and resemble a flat, patchy snow cover with typical snow patch sizes of 15, 30, and 60 m. Using these simulations, we found that the reduction of the vertical temperature gradient over the snow patch was the main cause of the reductions in vertical sensible heat flux over distance from the leading edge, independent of the typical snow patch size. Moreover, we observed that the sensible heat fluxes at the leading edge and the decay over distance were independent of snow patch size as well, which resulted in a 15 % and 25 % reduction in average snowmelt for, respectively, a doubling and quadrupling of the typical snow patch size. These findings lay out pathways to include the effect of highly variable turbulent heat fluxes based on the typical snow patch size in large-scale hydrological and climate models to improve snowmelt modeling.

Abstract. Atmospheric boundary layers and other wall-bounded flows are often simulated with the large-eddy simulation (LES) technique, which relies on subgrid-scale (SGS) models to parameterize the smallest scales. These SGS models often make strong simplifying assumptions. Also, they tend to interact with the discretization errors introduced by the popular LES approach where a staggered finite-volume grid acts as an implicit filter. We therefore developed an alternative LES SGS model based on artificial neural networks (ANNs) for the computational fluid dynamics MicroHH code (v2.0). We used a turbulent channel flow (with friction Reynolds number Reτ=590) as a test case. The developed SGS model has been designed to compensate for both the unresolved physics and instantaneous spatial discretization errors introduced by the staggered finite-volume grid. We trained the ANNs based on instantaneous flow fields from a direct numerical simulation (DNS) of the selected channel flow. In general, we found excellent agreement between the ANN-predicted SGS fluxes and the SGS fluxes derived from DNS for flow fields not used during training. In addition, we demonstrate that our ANN SGS model generalizes well towards other coarse horizontal resolutions, especially when these resolutions are located within the range of the training data. This shows that ANNs have potential to construct highly accurate SGS models that compensate for spatial discretization errors. We do highlight and discuss one important challenge still remaining before this potential can be successfully leveraged in actual LES simulations: we observed an artificial buildup of turbulence kinetic energy when we directly incorporated our ANN SGS model into a LES simulation of the selected channel flow, eventually resulting in numeric instability. We hypothesize that error accumulation and aliasing errors are both important contributors to the observed instability. We finally make several suggestions for future research that may alleviate the observed instability.

Abstract. Atmospheric boundary layers and other wall-bounded flows are often simulated with the large-eddy simulation (LES) technique, which relies on subgrid-scale (SGS) models to parameterize the smallest scales. These SGS models often make strong simplifying assumptions. Also, they tend to interact with the discretization errors introduced by the popular LES approach where a staggered finite-volume grid acts as an implicit filter. We therefore developed an alternative LES SGS model based on artificial neural networks (ANNs) for the computational fluid dynamics code MicroHH (v2.0), which can be run in direct numerical simulation (DNS) and LES mode. We used a turbulent channel flow (with a friction Reynolds number Reτ = 590) as a test case. The developed SGS model has been designed to require fewer simplifying assumptions, and to compensate for the instantaneous discretization errors introduced by the staggered finite-volume grid. We trained the ANNs based on instantaneous flow fields from a direct numerical simulation (DNS) of the selected channel flow. In general, we found excellent agreement between the ANN predicted SGS fluxes and the SGS fluxes derived from DNS for flow fields not used during training (with the correlation coefficient ρ mostly varying between 0.6 and 1.0), showing the potential ANNs may have to construct highly accurate SGS models. However, we observed an artificial build-up of turbulence kinetic energy at high wave modes when we directly incorporated our ANN SGS model into a LES simulation of the selected channel flow, eventually resulting in numeric instability. We hypothesized that error accumulation and aliasing errrors, were both important contributors to the observed instability. Several obstacles therefore remain before the a priori promise of our ANN LES SGS model, can be successfully leveraged in practical applications.

The radiative transfer equations are well-known, but radiation parametrizations in atmospheric models are computationally expensive. A promising tool for accelerating parametrizations is the use of machine learning techniques. In this study, we develop a machine learning-based parametrization for the gaseous optical properties by training neural networks to emulate the Rapid Radiative Transfer model for General circulation Model applications -Parallel (RRTMGP). To minimize computational costs, we reduce the range of atmospheric conditions for which the neural networks are applicable and use machine-specific optimised BLAS functions to accelerate matrix computations. To generate training data, we use a set of randomly perturbed atmospheric profiles and calculate optical properties using RRTMGP. Predicted optical properties are highly accurate and the resulting radiative fluxes have errors within 1.2 W m −2 for longwave and 0.12 W m −2 for shortwave radiation. Our parametrization is 3 to 7 times faster than RRTMGP, depending on the size of the neural networks. We further test the trade-off between speed and accuracy by training neural networks for a single LES case, so smaller and therefore faster networks can achieve a desired accuracy, especially for shortwave radiation. We conclude that our machine learningbased parametrization can speed-up radiative transfer computations whilst retaining high accuracy.