Next generation implicit numerics for atmosphere models
Project Description
The classical numerical approaches to building atmosphere models rely on complicated splitting methods that deal with different parts of the model: waves, transport, moisture processes (clouds, evaporation, rain, ice etc), radiation, boundary layers, convection, etc. These splitting methods lead to highly complicated codes, time schemes that are difficult to analyse for stability/accuracy, and occasionally numerical artifacts the coupling of fluid dynamics and other physics. In this project we are pursuing an alternative goal: to translate as much of the system as possible into a single monolithic PDE coupling all the variables, and solve it with an implicit Runge-Kutta method. This is made possible by recent advances in massively parallel iterative methods for solving the implicit systems that come from this equation: we shift the complications from the timestepping scheme into the iterative solver.
As a first step, we will build an atmosphere model consisting of the fluid dynamics component plus moisture processes, in this framework. Moisture processes involve switches (e.g., when maximum humidity is reached, any surplus water vapour is converted into cloud); we will deal with this using advanced “Variational Inequality” Newton solvers facilitated using PETSc [1]. The spatial discretisation will be build from compatible finite element methods closely related to those being implemented in the next generation LFRic modelling system at the Met Office. The software will be developed using Firedrake [2], which is a system for solving complicated PDEs using advanced finite element methods based on domain specific languages and code generation.
The resulting modelling system will be automatically differentiable using the py-adjoint system (https://github.com/dolfin-adjoint/pyadjoint), making it suitable for blending with machine learning tools, towards our goal of hybrid physics-based/data-driven modelling approaches.
[1] S. Balay, S. Abhyankar, M. Adams, S. Benson, J. Brown, P. Brune, K. Buschelman, E. Constantinescu, L. Dalcin, A. Dener, V. Eijkhout, J. Faibussowitsch, W. Gropp, V. Hapla, T. Isaac, P. Jolivet, D. Karpeyev, D. Kaushik, M. Knepley, F. Kong, S. Kruger, D. May, L. Curfman McInnes, R. Mills, L. Mitchell, T. Munson, J. Roman, K. Rupp, P. Sanan, J Sarich, B. Smith, H. Suh, S. Zampini, H. Zhang, and H. Zhang, J. Zhang, PETSc/TAO Users Manual, ANL-21/39 - Revision 3.22, 2024. https://doi.org/10.2172/2205494, https://petsc.org/release/docs/manual/manual.pdf
[2] David A. Ham, Paul H. J. Kelly, Lawrence Mitchell, Colin J. Cotter, Robert C. Kirby, Koki Sagiyama, Nacime Bouziani, Sophia Vorderwuelbecke, Thomas J. Gregory, Jack Betteridge, Daniel R. Shapero, Reuben W. Nixon-Hill, Connor J. Ward, Patrick E. Farrell, Pablo D. Brubeck, India Marsden, Thomas H. Gibson, Miklós Homolya, Tianjiao Sun, Andrew T. T. McRae, Fabio Luporini, Alastair Gregory, Michael Lange, Simon W. Funke, Florian Rathgeber, Gheorghe-Teodor Bercea, and Graham R. Markall. Firedrake User Manual. Imperial College London and University of Oxford and Baylor University and University of Washington, first edition edition, 5 2023. doi:10.25561/104839.
Existing background work
We have a body of ten years of research in methods and software for atmosphere models, which is summarised in [3] and [4].
[3] Cotter, Colin J. “Compatible finite element methods for geophysical fluid dynamics.” Acta Numerica 32 (2023): 291-393.
[4] Gibson, Thomas H., Andrew TT McRae, Colin J. Cotter, Lawrence Mitchell, and David A. Ham. Compatible Finite Element Methods for Geophysical Flows: Automation and Implementation Using Firedrake. Springer Nature, 2019.
Main objectives of the project
This project is available to researchers with a wide variety of interests, who might focus on one or more of: * designing scalable iterative methods allowing the use of highly parallel supercomputers, * developing interative solvers that seamlessly incorporate moisture processes, * developing stabilisation schemes that allow the model to incorporate the effects of unresolved turbulent scales, * time-parallel algorithms using ParaDiag methods [5], * benchmarking the quality of the simulation in challenging testcases such as fronts and storms, * exploration of computationally optimal configurations using e.g. high order discretisations and emergent Firedrake capability on GPUs.
[5] Hope-Collins, J., Hamdan, A., Bauer, W., Mitchell, L. and Cotter, C., 2024. asQ: parallel-in-time finite element simulations using ParaDiag for geoscientific models and beyond. arXiv preprint arXiv:2409.18792.
Details of Software/Data Deliverables
- The research will contribute to open source software developed in Python (with automatically generated high performance C code)
