EPPES web site

EPPES - ensemble prediction and parameter estimation system

This page is accompanying the following two articles:

Järvinen H, Laine M, Solonen A, Haario H. 2011. Ensemble prediction and parameter estimation system: the concept, Quarterly Journal of the Royal Meteorological Society, early view. (doi:10.1002/qj.923)
Laine M, Solonen A, Haario H, Järvinen H. 2011. Ensemble prediction and parameter estimation system: the method, Quarterly Journal of the Royal Meteorological Society, early view. (doi:10.1002/qj.922)

In these research articles, a concept is introduced and an algorithmic method described to include model parameter estimation in an ensemble prediction systems (EPS) used for probabilistic uncertainty assessment in operational numerical weather prediction (NWP). Such an EPS system is used at the ECMWF, for example. Here the target is to estimate so-called closure parameters that represent sub-grid scale physical processes, such as boundary layer turbulence or cloud microphysics. The physical parametrization schemes are used to express unresolved variables by predefined parameters rather than by explicit modelling.

The method for ensemble prediction and parameter estimation system (EPPES) is based on adding parameter perturbations to the ensemble members in addition to initial value and stochastic physics perturbations. Importance sampling algorithm is used to weight the proposed parameters in accordance to a suitable forecast skill score metric and an hierarchical statistical model is used to sequentially aggregate the information about the parameter uncertainty in the ensembles.

In the paper, the EPPES method is demonstrated using a stochastic version of the Lorenz 95 model. In addition to that example, a simple linear model is used here to demonstrate the convergence of the method.

The examples are coded in Matlab and the example web pages are produced directly from the Matlab code using the publish command. The source code for the examples can be downloaded here: eppes_examples.zip. If you wan to run the examples yourself, you will need some statistical utility functions that are part of the MCMC toolbox for Matlab (direct link to the toolbox code: mcmcstat.zip).

Linear model example

Fig. 1 Linear model example for EPPES
Click the plot to enlarge.

In this example (see the Matlab file eppes_example_linear.m) the correctness of the EPPES algorithm is demonstrated in the sense that when the observation came from a hierarchical Gaussian model, the estimates will converge to their true values. At each iteration time window, the observations are generated from y~N(θ,Σ_obs) where the mean θ will be random, i.e. the value of theta is drawn from a hyper distribution θ~N(μ,Σ). The parameters μ and Σ are then estimated sequentially.

Stochastic Lorenz 95 example

Fig. 2 Lorenz 95 example for EPPES
Click the plot to enlarge.

In this example (Matlab file eppes_example_l95.m) a modified Lorenz 95 [Wilks, 2005] system is used with 2 dimensional parameter that parameterize the effect of fast state variables used in generating the observations but not in the forecast model.

See the EPPES method article for details and further references to the stochastic Lorenz 95 model. The model code used here is based on ECMWF training course material by Martin Leutbecher and it is used with kind permission.

EPPES - ensemble prediction and parameter estimation system

Linear model example

Stochastic Lorenz 95 example

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