James Annan's Home Page

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Research in probabilistic climate prediction

Working Group 1 of the IPCC TAR identified the following as one of its "high priority areas for action":
"Improve methods to quantify uncertainties of climate projections and scenarios, including long-term ensemble simulations using complex models".

Efficient probabilistic parameter estimation is a key component of this, since it is model parameters that largely determine the long-term climate of a model (and so the uncertainty in parameter values also determines the uncertainty in model climate predictions). The climateprediction.net website has a lot of useful background information on this subject. However, I think they are too pessimistic about the possibility of using computationally efficient approaches to the problem.

Method

We have developed an efficient probabilistic multivariate parameter estimation scheme based on the ensemble Kalman filter (EnKF) and I think this can form the basis of a solution to the above problem. The basic idea is only a minor extension of a standard technique: augmenting the model state with parameter values means that the parameters are automatically included in the EnKF analysis scheme. The multivariate perturbations so generated are (linearly) balanced, and so the method thus avoids the wasteful integration of vast numbers of very poor models that generally occurs when parameter perturbations are selected using naive direct sampling methods. Although the Kalman filter equations are only provably optimal for linear systems, the EnKF has a good track record of providing effective solutions to nonlinear problems. Geir Evensen's page is a good place to look for more information on these.

Our implementation is based on an iterative scheme which improves accuracy in nonlinear situations with a wide prior. We have succesfully applied the technique to a range of models including the famous Lorenz model, a new computationally fast coupled atmosphere-ocean Earth system model (C-GOLDSTEIN), a simplified spectral primitive equation AGCM and most recently the state-of-the-art CCSR/NIES/FRCGC AGCM MIROC3.2 AGCM at T21L20 resolution coupled to a slab ocean.

Due to the balanced nature of the parameter perturbations generated, the method may be particularly valuable for coupled atmosphere-ocean models. The C-GOLDSTEIN model is probably too simple to be a meaningful test of this - it only has a diffusive 2D atmosphere - but we have also appplied the method successfully to the IGCM-GOLDSTEIN model (efficient spectral T21 AGCM coupled to GOLDSTEIN ocean), which resulted in an ensemble of models which ran without the need for flux adjustments. However, this model is still somewhat developmental and the overall results were not that great, so are not published. This sort of aproach should enable us to perform transient ensemble hindcast simulations tuned to historical data which I believe could significantly improve the quality and credibility of probabilistic climate forecasts.

The fly in the ointment

We think we have found a good solution to the practical and theoretical problems of multivariate parameter estimation in the perfect model world (unless the nonlinearity is truly extreme, in which case no efficient solution exists - but we have found no evidence for this). However, real applications are trickier, due to the problem of imperfectly characterised model error (the residual difference between model and data that cannot be eliminated, however carefully the model is tuned). One way of thinking about it is to ask, how do we assign numerical values to the relative likelihoods of different samples from the prior distribution? How much "better" is one model than another at predicting the future, when both are clearly imperfect?

Towards a solution?

Betting on Climate Change

I'm also interested in the use of prediction markets and ideas futures. Here's a page I wrote, based on a poster presentation I gave at the EGU in 2005. I've also had an article published on realclimate.org on the same topic. It's not clear yet where, if anywhere, it is going, but it's been interesting and instructive so far.

Publications (including a handful of non-peer-reviewed manuscripts)

2010

2009

2008

2007

2006

2005

2004

J. C. Hargreaves, J. D. Annan, N. R. Edwards and R. Marsh. Climate forecasting using an intermediate complexity Earth System Model and the Ensemble Kalman Filter.  Climate Dynamics Vol 23 Nos 7-8, pp 745-760, DOI: 10.1007/s00382-004-0471-4.

J. D. Annan. On the orthogonality of Bred Vectors. Monthly Weather Review, Vol 132, No 3, pp 843-849.