A new approach to guaranteeing physical wave propagation on triangular meshes for numerical weather prediction

Lead Research Organisation: Imperial College London
Department Name: Dept of Aeronautics

Abstract

Numerical weather prediction (NWP) is the science of building computer models of the atmosphere and using them, in combination with measurements from around the globe, to predict the weather and climate. In an NWP forecast model, the surface of the Earth is divided up into a grid. When the grid is made finer, the forecast model can get more realistic, but requires bigger computers. To get sufficiently realistic forecasts, it is becoming necessary to use many computer processors (chips) working together in parallel. In the ideal case, as you add more processors, the model runs faster. However, for the type of grids used by most established operational forecast centre (including the UK Met Office), there becomes a point where adding more processors does not make the model run faster. This is because the grids are latitude-longitude grids (like the grid systems used in maps) which means that at the North and South pole, all of the lines of longitude converge. These lines represent too many connections between processors, which slow down the computation. To avoid this problem, many people have proposed using triangle or hexagon grids (rather than the quadrilaterals used in the latitude-longitude grid) which can cover the sphere more uniformly. The UK Met Office has resisted adopting these grids because the triangles and hexagons can support types of atmospheric waves which do not exist in the real atmosphere; the quadrilaterals do not have this problem. In this project, we will investigate a very simple solution: a triangular grid with equal coverage over the sphere can be turned into a quadrilateral grid by subdividing each triangle into three quadrilaterals. The aim of this project is to make some very preliminary investigations of the accuracy of NWP models that use this idea. If these investigations show that the method is accurate enough, this will lead to more substantial developments of the method and the potential to allow accurate weather forecasts and climate simulations on computers with enormous numbers of processors, leading to more accurate weather and climate predictions.

Publications

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Melvin T (2014) A two-dimensional mixed finite-element pair on rectangles 2D Mixed Finite-Element Pair in Quarterly Journal of the Royal Meteorological Society

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Staniforth A (2013) Analysis of a mixed finite-element pair proposed for an atmospheric dynamical core in Quarterly Journal of the Royal Meteorological Society

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Cotter C (2016) Embedded discontinuous Galerkin transport schemes with localised limiters in Journal of Computational Physics

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Cotter CJ (2016) Mixed finite elements for global tide models. in Numerische mathematik

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Cotter C (2012) Mixed finite elements for numerical weather prediction in Journal of Computational Physics

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Cotter C (2014) Variational formulations of sound-proof models Variational Sound-Proof Models in Quarterly Journal of the Royal Meteorological Society

 
Description The aim of this project is to apply mathematical analysis to the BDFM1-P1dg finite element scheme that is being proposed by the PI for massively parallel numerical weather prediction models. We have found that these types of schemes can exhibit zero group velocity modes, but that these can be prevented by an adjustment of the mass matrix.
Exploitation Route This project is in close collaboration with the UK Met Office and is feeding into the GungHo Dynamical Core project.
Sectors Environment

 
Description The findings are mathematical results which allow my numerical methods to be used with confidence. These are now being developed as part of the Met Office project to build a new dynamical core for their weather and climate model.
First Year Of Impact 2013
Sector Environment
Impact Types Policy & public services

 
Description A scalable dynamical core for Next Generation Weather and Climate Prediction - Phase 2
Amount £367,916 (GBP)
Organisation Research Councils UK (RCUK) 
Sector Public
Country United Kingdom
Start 03/2013 
End 02/2015
 
Description Ongoing colloboration with UK Met Office staff 
Organisation Meteorological Office UK
Country United Kingdom 
Sector Academic/University 
PI Contribution We have developed several collaborative interactions with UK Met Office staff
Start Year 2011
 
Title Slicemodels 
Description This is a code for benchmarking our suite of compatible finite element methods for numerical weather prediction in a vertical slice configuration. 
Type Of Technology Software 
Year Produced 2015 
Open Source License? Yes  
Impact This tool is being used to benchmark numerical schemes for the NERC/Met Office/STFC UK Dynamical Core project ("Gung Ho"). 
URL https://bitbucket.org/colinjcotter/slicemodels
 
Title dcore 
Description Software implementing a numerical model for a 3D dynamical core on the sphere using compatible finite element methods. 
Type Of Technology Software 
Year Produced 2016 
Open Source License? Yes  
Impact This software is being used to benchmark numerical algorithms being developed for the UK Met Office forecast model. 
URL https://github.com/firedrakeproject/dcore
 
Description ICMS Public talk 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Public/other audiences
Results and Impact As part of the International Centre for Mathematical Sciences workshop we organised in Edinburgh, we hosted a public talk on climate uncertainty given by David Stainforth. The idea was to engage the public with the importance of mathematics in climate research, particularly in the combination of climate/weather models and statistics in order to understand and quantify uncertainty.

We received excellent feedback about the talk through the ICMS.
Year(s) Of Engagement Activity 2015