arXiv subjects

Guillaume Bertoli

Publications and source records attributed to Guillaume Bertoli.

3 recordsLinked to original sources

arXiv2025

Representing Subgrid-Scale Cloud Effects in a Radiation Parameterization using Machine Learning: MLe-radiation v1.0

Improvements of Machine Learning (ML)-based radiation emulators remain constrained by the underlying assumptions to represent horizontal and vertical subgrid-scale cloud distributions, which continue to introduce substantial uncertainties. In this study, we introduce a method to represent the impact of subgrid-scale clouds by applying ML to learn processes from high-resolution model output with a horizontal grid spacing of 5km. In global storm resolving models, clouds begin to be explicitly resolved. Coarse-graining these high-resolution simulations to the resolution of coarser Earth System Models yields radiative heating rates that implicitly include subgrid-scale cloud effects, without assumptions about their horizontal or vertical distributions. We define the cloud radiative impact as the difference between all-sky and clear-sky radiative fluxes, and train the ML component solely on this cloud-induced contribution to heating rates. The clear-sky tendencies remain being computed with a conventional physics-based radiation scheme. This hybrid design enhances generalization, since the machine-learned part addresses only subgrid-scale cloud effects, while the clear-sky component remains responsive to changes in greenhouse gas or aerosol concentrations. Applied to coarse-grained data offline, the ML-enhanced radiation scheme reduces errors by a factor of 4-10 compared with a conventional coarse-scale radiation scheme. This shows the potential of representing subgrid-scale cloud effects in radiation schemes with ML for the next generation of Earth System Models.

physics.ao-ph↗

arXiv2021

Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions

We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, while order reduction occurs in general if using other Runge-Kutta schemes or even the exact flow itself for the diffusion part. We prove these results when the source term only depends on the space variable, an assumption which makes the splitting scheme equivalent to the Crank-Nicolson method itself applied to the whole problem. Numerical experiments suggest that the second order convergence persists with general nonlinearities.

math.AP↗

arXiv2020

Strang splitting method for semilinear parabolic problems with inhomogeneous boundary conditions: a correction based on the flow of the nonlinearity

The Strang splitting method, formally of order two, can suffer from order reduction when applied to semilinear parabolic problems with inhomogeneous boundary conditions. The recent work [L .Einkemmer and A. Ostermann. Overcoming order reduction in diffusion-reaction splitting. Part 1. Dirichlet boundary conditions. SIAM J. Sci. Comput., 37, 2015. Part 2: Oblique boundary conditions, SIAM J. Sci. Comput., 38, 2016] introduces a modification of the method to avoid the reduction of order based on the nonlinearity. In this paper we introduce a new correction constructed directly from the flow of the nonlinearity and which requires no evaluation of the source term or its derivatives. The goal is twofold. One, this new modification requires only one evaluation of the diffusion flow and one evaluation of the source term flow at each step of the algorithm and it reduces the computational effort to construct the correction. Second, numerical experiments suggest it is well suited in the case where the nonlinearity is stiff. We provide a convergence analysis of the method for a smooth nonlinearity and perform numerical experiments to illustrate the performances of the new approach.

math.NA↗