Global Ocean Modelling with Adaptive Unstructured Grid Methods

Lead Research Organisation: Imperial College London
Department Name: Earth Science and Engineering

Abstract

Ocean circulation is clearly important on a water-dominated planet in the throes of climate change. Ocean modelling technologies are therefore crucially important to our abilities to forecast change. However, despite significant advances over the past decade, ocean general circulation models are based on essentially the same finite difference methods and fixed structured grids employed in the earliest models developed in the 1960s. Although unstructured mesh modelling has long been a goal of many oceanographers, attempts to apply such methods the global circulation have failed due to challenges with high aspect ratio domains and in treating the Coriolis and buoyancy terms accurately and stably on unstructured meshes. Over the past few years important solutions to these problems have been developed and incorporated into the Imperial College Ocean Model (ICOM). This model has the best available parallel mesh adaptivity methods, a suite of options for spatial derivatives (such as high-resolution methods for density/tracer advection), novel robust treatments of geostrophic and hydrostatic balance, optimised bathymetry and coastline geometries, and large eddy adaptive turbulence models. In this project we will take advantage of more than a decade of development work on our new ocean model ICOM and produce, in managed stages, a global circulation model that fully incorporates 3D adaptive and unstructured mesh technology. As a result we will be able to simultaneously resolve flow at scales ranging from 10s km (boundary currents) to 100s m (downwelling currents) with minimal parametisation and maximal capture of the physics. In addition, by taking advantage of our state-of-the-art meshing tools, initial surface resolution will be focussed on areas of bathymetric change. This will impart computational efficiency since it will reduce the number of nodes and elements required to capture geometric complexity. Our approach will allow the mesh to move in response to eddies or density layers in a manner akin to hybrid coordinate approaches. The topology of the meshes and node density will also be optimised to gain maximum flexibility, power and robustness from our novel modelling approach. The quality of the adaptive model's simulation of the global ocean will be assessed by examining how, in multi-decadal integrations, it reproduces the essential dynamics of the oceans through detailed comparisons with recent in-situ observational datasets and available remote sensing datasets and also against simulations performed at the National Oceanography Centre Southampton (NOC) by current ocean models, such as NEMO and OCCAM, at a variety of grid resolutions. Simulations will be conducted on parallel computing clusters at Imperial College, NOC, and the UK's HECToR supercomputing facility where scaling properties on large numbers of processors will be determined. In addition to developing new adaptive mesh techniques on the sphere we will show how various forms of mesh movement vertically and horizontally, and mesh structural changes can each enhance solution quality. We will study the performance of a range of error measures which are based on representations of the flow dynamics. Our mesh generation package Terreno will be generalised so that static meshes are able to provide high quality simulations in isolation from mesh adaptivity. We will also demonstrate that model spin-up can be rapidly achieved with progressively increased resolution. The resulting advances in ocean modelling capabilities will cement the UK's position firmly at the forefront of unstructured and adaptive mesh ocean modelling, and is expected to be a major ocean modelling milestone for the UK. Overall this project will contribute considerably towards the production of an open source ocean model for the UK and worldwide ocean modelling communities. It will also provide an important contribution to NERC's Oceans2025 programme by delivering Work Package 9.8.

Publications


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Cotter C (2009) LBB stability of a mixed Galerkin finite element pair for fluid flow simulations in Journal of Computational Physics
Fang F (2009) A POD reduced-order 4D-Var adaptive mesh ocean modelling approach in International Journal for Numerical Methods in Fluids
Farrell P (2011) Conservative interpolation between volume meshes by local Galerkin projection in Computer Methods in Applied Mechanics and Engineering
Farrell P (2009) Conservative interpolation between unstructured meshes via supermesh construction in Computer Methods in Applied Mechanics and Engineering
 
Description This project has furthered the development of the Fluidity-ICOM modelling framework. It has pushed the application of novel finite element and control volume based discretisation methods on unstructured and adapting meshes to large scale high aspect ratio problems in 3D. In particular the following research directions have been pursued:



1. Novel finite element discretisation pairs for large scale ocean application: A new family of continuous/discontinuous finite element pairs for the representation of velocity and pressure developed within Fluidity-ICOM for the accurate representation of geophysical balances have been further tested. In particular, large scale high-aspect ratio test cases of baroclinic wind-driven gyres, baroclinically unstable jets, restratification problems and global scale tides and tsunamis have been investigated with comparisons between discretisation options and other models made.



2. Mesh adaptivity for large scale ocean application: When applying three-dimensional mesh adaptivity on the above large scale test cases numerical problems with the loss of balance have been identified and analysed. A new 'flavour' of mesh adaptivity has been developed to get around these problems. This new so-called 2+1D mesh adaptivity involves the computation of a three-dimensional error measure, but then adapts the horizontal mesh in 2D using a vertically-collapsed form of the error measure before then adapting in 1D down every column of nodes from the 2D horizontal mesh. This means that nodes are always aligned one above another which assists in the representation of balance, and it should be noted does not impose a significant restriction on the adapted meshes that are produced.



3. Representation of spherical geometries: At large simulation scales, with potentially coarse mesh elements, the mismatch between the spherical (or ellipsoidal) nature of the Earth and its numerical representation can result in spurious motion. This was identified early on in the project as a bottle neck to the successful simulation of large-scale problems. This issue is not present in other models which perform a coordinate transformation to a flat geometry before discretisation. The developed fix involves the use of super-parametric elements where the geometry of elements can be represented using higher-order elements - the order can be increased until the spurious motion is below acceptable limits. This fix was successfully demonstrated on spherical geometries in serial computations, but unfortunately due to issues on how information is shared between sub-domains in parallel simulations a major rewrite of the core of Fluidity-ICOM was required to achieve this fix in parallel. This issue is now largely addressed but did impact on the realistic global applications that were possible within the project.



4. Comparisons with other ocean models: Comparisons of large scale Fluidity-ICOM simulations were made with both NEMO and MITgcm, in particular for barotropic and baroclinic wind-driven gyre test problems. Limited use was made of NEMO in the end as MITgcm was found an easier model to work with, and for us performed faster than NEMO on our available clusters. Interesting results were found, including the facts that Fluidity-ICOM appears to scale to large numbers of processors better than these structured mesh models for a fixed problem size (although the work required per degree of freedom is higher). Compared to available analytical solutions, the models yielded similar errors for the same mesh resolution, but for baroclinic problems further work is required to understand the difference seen between all three models.



Other developments were made in terms of flexible mesh generation of the sphere, the development of post-processing tools, and in geophysical turbulence modelling. The open source model development approach was improved through the move of code hosting to servers external to Imperial and the introduction of code review procedures, and annual training workshops have continued successfully. A number of new users of the model, in particular from industry have also been attracted and engaged with.
Sectors Aerospace, Defence and Marine,Energy,Manufacturing, including Industrial Biotechology
 
Description The Met office building on the numerical methods we developed within the GungHo project. The Institute of Atmospheric Physics in China have incorporated the adaptive mesh adaptivity approach into their regional scale atmospheric model to transport pollution and chemistry and are experiencing substantial savings in CPU time (or greater resolution) that will be used operationally to achieve results that we can be more confident in. The adaptive methods (interpolation) have been incorporated into open-Foam - the most well used open source CFD code. The work on ocean modelling is also helping exploration companies determine where to look for oil and gas.
First Year Of Impact 2009
Sector Education,Energy
Impact Types Societal,Economic