Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements
SIAM Journal on Scientific Computing Society for Industrial and Applied Mathematics 40:2 (2018) A1121-A1148
Abstract:
In moving mesh methods, the underlying mesh is dynamically adapted without changing the connectivity of the mesh. We specifically consider the generation of meshes which are adapted to a scalar monitor function through equidistribution. Together with an optimal transport condition, this leads to a Monge–Ampere equation ` for a scalar mesh potential. We adapt an existing finite element scheme for the standard Monge–Ampere ` equation to this mesh generation problem; this is a mixed finite element scheme, in which an extra discrete variable is introduced to represent the Hessian matrix of second derivatives. The problem we consider has additional nonlinearities over the basic Monge–Ampere equation due to the implicit dependence of the monitor func- ` tion on the resulting mesh. We also derive an equivalent Monge–Ampere-like equa- ` tion for generating meshes on the sphere. The finite element scheme is extended to the sphere, and we provide numerical examples. All numerical experiments are performed using the open-source finite element framework Firedrake.A Simple Pedagogical Model linking Initial-Value Reliability with Trustworthiness in the Forced Climate Response.
Bulletin of the American Meteorological Society (2017)
A personal perspective on modelling the climate system
Animal Behaviour Royal Society 472:2188 (2016)
Abstract:
Given their increasing relevance for society, I suggest that the climate science community itself does not treat the development of error-free ab initio models of the climate system with sufficient urgency. With increasing levels of difficulty, I discuss a number of proposals for speeding up such development. Firstly, I believe that climate science should make better use of the pool of post-PhD talent in mathematics and physics, for developing next-generation climate models. Secondly, I believe there is more scope for the development of modelling systems which link weather and climate prediction more seamlessly. Finally, here in Europe, I call for a new European Programme on Extreme Computing and Climate to advance our ability to simulate climate extremes, and understand the drivers of such extremes. A key goal for such a programme is the development of a 1km global climate system model to run on the first exascale supercomputers in the early 2020s.On the reliability of seasonal climate forecasts.
Journal of the Royal Society, Interface 11:96 (2014) 20131162
Abstract:
Seasonal climate forecasts are being used increasingly across a range of application sectors. A recent UK governmental report asked: how good are seasonal forecasts on a scale of 1-5 (where 5 is very good), and how good can we expect them to be in 30 years time? Seasonal forecasts are made from ensembles of integrations of numerical models of climate. We argue that 'goodness' should be assessed first and foremost in terms of the probabilistic reliability of these ensemble-based forecasts; reliable inputs are essential for any forecast-based decision-making. We propose that a '5' should be reserved for systems that are not only reliable overall, but where, in particular, small ensemble spread is a reliable indicator of low ensemble forecast error. We study the reliability of regional temperature and precipitation forecasts of the current operational seasonal forecast system of the European Centre for Medium-Range Weather Forecasts, universally regarded as one of the world-leading operational institutes producing seasonal climate forecasts. A wide range of 'goodness' rankings, depending on region and variable (with summer forecasts of rainfall over Northern Europe performing exceptionally poorly) is found. Finally, we discuss the prospects of reaching '5' across all regions and variables in 30 years time.Improving weather forecast skill through reduced precision data assimilation
Monthly Weather Review American Meteorological Society 146 (2017) 49-62