IMA Conference on Mathematics of the Climate System

Date: Tuesday 13 – Thursday 15 September 2011
Location: University of Reading

This conference will be about the construction and use of mathematical and computational models of the climate system, from the conceptual to the comprehensive. The conceptual models aid our understanding of how certain climate processes interact, and enable us to assess, interpret and diagnose the comprehensive models. Also, the conceptual models provide readily understandable paradigms for dynamical climate-system behaviour, which may be tested in the comprehensive models.
The conference will focus on four related topics:

Extraction of deterministic and stochastic models from measurements and simulations of the climate system;
Reduced complexity models and their dynamics;
Confronting scientific hypotheses about the climate system with data;
Mathematically-based diagnostic studies of climate dynamics and statistics based on comprehensive models and reanalyses.

Confirmed Invited Speakers

Daan Crommelin (CWI, Amsterdam)
Title: Estimation of coarse-grained stochastic models from timeseries

Abstract:
Inference of stochastic processes from timeseries data is part of a modeling approach that is used in various places in atmosphere-ocean-climate science. It allows one to extract simple, effective models for the coarse-grained behaviour of quantities whose underlying, detailed dynamics can be highly complex. Examples range from estimating eddy diffusivities to inferring models from paleorecords.

Estimation of coarse-grained dynamical models can be a challenging task: the models are often assumed to be Markov, whereas the data will typically be non-Markov at short timescales if the observed variables form only part of a larger system. I will approach this problem by looking at spectral properties of involved operators such as the Fokker-Planck operator, and discuss how to build an estimation procedure starting from these properties. I will discuss estimation in multiscale settings, subsampling, uncertainty of sampling intervals and inference from non-equilibrium data.

Michael Ghil (Ecole Normale Supérieure, Paris and UCLA, Los Angeles)
Title: Toward a Mathematical Theory of Climate Sensitivity

Abstract:
The first attempts at estimating climate sensitivity assumed a climate system in equilibrium. More recently, the IPCC focused on estimates of climate evolution over the coming century; these estimates still differ by several degrees.

We investigate here the mathematical causes of climate sensitivity, by applying random dynamical systems (RDS) theory. This theory allows one to study the random attractors of nonlinear, stochastically perturbed systems, as well as the time-dependent invariant measures supported by these attractors.

Results are presented for several simple climate models, from the classical Lorenz (1963) model to El Nino-Southern Oscillation (ENSO) models. Their attractors support random Sinai-Ruelle-Bowen (SRB) measures with nice physical properties. The response of these SRB measures to changes in poorly known model parameters is studied and implications for climate predictability are discussed.

Chris Jones (University of Warwick)
Title: Data Assimilation and Climate Research

Abstract:
Assimilating data into computational models is a central part of numerical weather prediction and yet it is not used very much in climate science. I will lay out some of the reasons for this, and suggest ways in which it will change. I will also discuss the challenges that DA will face in dealing with climate problems.

Jonathan Rougier (University of Bristol)
Title: Statistical emulators for large climate simulators

Abstract:
“As part of the PalaeoQUMP project, we would like to emulate HadCM3 North American Mid-Holocene summer temperature (MTWA) anomalies, at the resolution of the simulator (3.75 by 2.5 degrees). This will allow us to calibrate the parameterisation of HadCM3 to palaeoclimate measurements at the gridcell level, and to do continental-scale reconstructions based on these measurements.

“In the broader field of Computer Experiments the utility of emulation is clear, and its application to simulators with scalar outputs has now become standard. However, jointly emulating a large and structured collection of simulator outputs, such as a spatial field of climate quantities, is much more challenging. The three main issues are (i) handling internal variability, (ii) performing an appropriate dimensional reduction, and (iii) managing with a small number of simulator runs. These all involve subjective choices, and diagnostic evaluation is crucial.

“Here I demonstrate our HadCM3 emulator, discussing the choices we have made, how we have critiqued them, and how we can use the resulting emulator to quantify uncertainty, and to guide the next stages of the experiment.”

Joint work with Tamsin Edwards (Bristol) and Mat Collins (Exeter). http://www.maths.bris.ac.uk/~mazjcr/

Joseph Tribbia (National Centre of Atmospheric Research (NCAR) in Boulder, Colarado)
Title: Climate Shocks: Scientific Modeling Challenges in the 21st Century

Abstract:
As is the case in many aspects of society, as a scientific endeavor modeling of the climate system is reaching a stage of development where the limits of our current frameworks are within sight and are approaching rapidly. I will discuss my perspective on the approaching ‘wall’ in three areas of climate science: computing, modeling and uncertainty quantification.

Within each area, I will present the current state of the art and the evidence suggesting maturation and near saturation. Finally, I will suggest some new directions of mathematical research applied to these problems that can be promising alternatives to the current research paths that appear to be evolving towards their end states.

Presentations

Published 13th September 2011

IMA Conference on Mathematics of the Climate System

IMA