Unstructured mesh dynamical core for atmospheric modelling using geophysically-optimal finite elements

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


Numerical Weather Prediction (NWP) is the science of combining computer models of the atmosphere with observational data and measurements to produce a forecast of the weather. A key ingredient of any NWP model is the 'dynamical core' which is a model of how the dynamical quantities (wind speed and direction, temperature, pressure and density) evolve in the atmosphere over time. All of these quantities are stored on a grid (for example on a latitude-longitude grid with wind speed being stored at each degree of latitude and longitude), and a crucial question is how small the grid boxes need to be for accurate weather prediction. It is known that the predictive skill of an NWP model increases as the grid boxes get smaller (because the model represents small scale motion such as storms more accurately). However, making smaller boxes means that more values of the dynamical quantities need to be stored, and hence the model requires more computational power and time. In recent years, there has been increased interest in using 'adaptive grids': grids which can have different sizes of boxes in different regions of the globe. This could mean having smaller grid boxes over the British Isles so that a more accurate forecast is made for that region. It could also mean having smaller grid boxes in the region surrounding a storm in the North Atlantic; the storm is moving and hence the size of grid boxes might need to change so that the smaller grid boxes follow the storm. This approach is called adaptive mesh refinement, and allows models which require less computational power and time because small boxes are only used where they are needed. When adaptive mesh refinement is used, triangular boxes are often used instead of squares, because they tessellate more easily and so can be arranged into grids with a very complex structure. Using adaptive meshes creates new challenges, since many years of research have gone into making NWP models on latitude-longitude grids. In particular, it is important to design a dynamical core which correctly represents the propagation of waves through the atmosphere and the interaction between the pressure and the velocity (called geostrophy) that takes place due to the rotation of the Earth. This can be achieved by using a 'staggered grid' that stores velocity, density and pressure at different locations in each grid box. There has been much recent research on the best way to construct a staggered grid on triangles: this project is about a particular choice (called P1dg-P2) which has been shown to have very stable and accurate wave propagation and representation of geostrophy compared to other methods. The aim of this project is to make a thorough investigation of P1dg-P2 in a simplified model context which will allow scientists at operational forecast centres (such as the UK Met Office) to assess whether P1dg-P2 should be developed further for NWP.


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Description This project has produced a benchmark shallow-water dynamical core for numerical weather prediction, using finite element methods that are suitable for adaptive mesh refinement. It has shown that the P1dg-P2 scheme originally proposed is unsuitable but a new scheme was developed, BDFM1-P1dg, which has the correct balance of velocity and pressure degrees of freedom so as to avoid spurious modes.
Exploitation Route This project is in close collaboration with the UK Met Office and it's output is feeding into the Next Generation Weather and Climate Prediction programme.
Sectors Environment

Description This project provided mathematical analysis of numerical discretisations methods invented by me, that showed how to avoid certain problems with dispersion properties that are critical to use in operational weather forecasting. This work was sufficient to alleviate Met Office concerns about the methods and they are now being developed for use in the Met Office forecast model.
First Year Of Impact 2013
Sector Environment
Impact Types Policy & public services

Description Further funding from EPSRC
Amount £1,287,360 (GBP)
Funding ID EP/L000407/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 11/2013 
End 10/2018
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