Intelligent data assimilation and uncertainty analysis

We will incorporate in our framework for model development and tuning the Ensemble Kalman Filter (EnKF) approach to data assimilation, a suite of alternative direct optimization routines, and newly developed Bayesian statistical methods that provide an alternative to optimization, and can be used to address problems of uncertainty, calibration and estimating the probability of future events.

Aiding traceability: For each of our resolutions, the model will be tuned to data and/or full complexity GCM output, using either the EnKF or alternative optimization routines.

Model calibration: The problem of finding sets of model parameters that are plausible given the available observational data will be tackled using assimilation methods, such as the EnKF, and new techniques to identify the spread of plausible models given the data rather than the 'optimal' model.

Ensembles: Taking advantage of the models' computational efficiency and of Grid technology, we will work extensively with perturbed physics ensembles in order to explore possible system behavior and derive objective probabilistic forecasts. Some methods for this have already been demonstrated and other alternatives will be explored and developed.

Bayesian approach: Unlike optimization methods, Bayesian methods do not attempt to find a 'best fit' model. Rather the emphasis is on finding a set of plausible models and assigning a probability to each. The basis of the approach is the sampling method: we treat code output as a random variable and consider code runs to be observations from the distribution of interest. We then use the resulting samples to make inferences. Since we need these samples to be large, in principle we need to run the model a very large number of times. However, a direct approach would require a prohibitive number of runs.

Emulator: The solution is the emulator - a statistical approximation to the complete model that is "trained" on a set of existing code outputs. The training set is typically a carefully designed experiment in which the dynamical model is run at parameter values that span parameter space, sometimes supplemented with additional points where the uncertainty on the emulator is large. Our emulator not only gives an approximation to the model, but also includes a measure of its own uncertainty. The emulator can then be used to run the Monte Carlo simulations needed to produce the PDFs for the model outputs. In experiments with GENIE (C-GOLDSTEIN), our emulator (written as part of the Tyndall CIAM project) runs five orders of magnitude faster than the original model. Using emulators we can estimate the uncertainty distribution of the model outputs given prior distributions on the inputs.

Dynamic emulator: The modularity of GENIE causes problems for uncertainty analysis. In order to avoid going through the entire process of building an emulator every time we substitute a module, separate dynamic emulators for each module will be built. Unlike the dynamical models the time step is not set by the accuracy of the solution of the differential equations, but can be much longer.

Traceability

GENIAL