Supermodels: a novel approach to reduce model errors

F. Selten, W. Wiegerinck, G. Duane, L. Kocarev and M-L Shen

Poster presentation at 4th WGNE workshop on systematic errors in weather and climate models, Exeter, 2013

An overview is presented of the super modeling results obtained so far with low-, medium and high dimensional climate models.
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Potential of Equatorial Atlantic Variability to Enhance El Niño Prediction

N.S. Keenlyside, H.Ding and M. Latif

Climate Dynamics, 38, 1965-1972, 2012

Extraordinarily strong El Niño events, such as those of 1982/83 and 1997/98, have been poorly predicted by operational seasonal forecasts made before boreal spring, despite significant advances in understanding, improved models, and enhanced observational networks. The Equatorial Atlantic Zonal Mode - a phenomenon similar to El Niño but much weaker and peaking in boreal summer - impacts winds over the Pacific, and hence affects El Niño, and also potentially its predictability. Here we show for the first time that knowledge of Equatorial Atlantic sea surface temperature (SST) significantly improves the prediction across boreal spring of observed major El Niño events and also weaker variability. Our results suggest that the poor skill of current state of the art models in predicting equatorial Atlantic SST may help explain the Pacific spring predictability barrier, and that better prediction of major El Niño events might be achieved through model improvement in the Equatorial Atlantic.
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Synchronicity From Synchronized Chaos

G.S. Duane

Under revision

The synchronization of loosely coupled chaotic oscillators, a phenomenon investigated intensively for two decades, may realize the philosophical notion of "synchronicity". Eectively unpredictable chaotic systems, coupled through only a few variables, commonly exhibit a predictable relationship that can be highly intermittent, as with philosophical "synchronicities". Synchronicity between matter and mind is realized dynamically if mind is analogized to a computer model assimilating observed data, as in meteorology. Synchronicities are meaningful, as philosophically required, if meaningfulness is related to internal coherence. Internal synchronization indeed appears necessary for synchronization between systems, as illustrated for a pair of forced-dissipative systems and for a pair of Hamiltonian systems that exhibit coherent structures. Synchronicity-as-synchronized-chaos has implications both for neural systems (biological and artificial) and for basic physics. In the former realm, it may be useful to dynamically induce dierent computational models of the same objective process to synchronize with one another as well as with that process - as may occur also in conscious mental processing. Basic physical synchronicity is manifest in the non-local quantum connections implied by Bell's theorem. The quantum world resides on a generalized synchronization "manifold", that one can either take as primitive or as evidence of a multiply-connected spacetime.
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Supermodels: Dynamically Coupled Ensembles of Imperfect Models

W. Wiegerinck and F.M. Selten

Abstract climate informatics workshop 2012

At a dozen or so institutes around the world, comprehensive climate models are being developed and improved. Each model provides reasonable simulations of the observed climate, each with its own strengths and weaknesses. In the current multi-model ensemble approach model simulations are combined a posteriori. Recently, it has been proposed to dynamically connect the models into one supermodel and learn the connection coefficients from historical observations [1]. Here we review the approach and propose a more scalable version of supermodeling.
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Forecast improvement in Lorenz 96 system

L. Basnarkov and L. Kocarev

Nonlin. Processes Geophys., 19, 569, 2012

Contemporary numerical weather prediction schemes are based on ensemble forecasting. Ensemble members are obtained by taking different (perturbed) models started with different initial conditions. We introduce one type of improved model that represents interactive ensemble of individual models. The improved model's performance is tested with the Lorenz 96 toy model. One complex model is considered as reality, while its imperfect models are taken to be structurally simpler and with lower resolution. The improved model is defined as one with tendency that is weighted average of the tendencies of individual models. The weights are calculated from past observations by minimizing the average difference between the improved model's tendency and that of the reality. It is numerically verified that the improved model has better ability for short-term prediction than any of the individual models.
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Complete synchronization of chaotic atmospheric models by connecting only a subset of state space

P.H. Hiemstra, N. Fujiwara, F.M. Selten, and J. Kurths

Nonlin. Processes Geophys., 19, 611, 2012

Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine whether connecting only a subset of the model state space can still lead to complete synchronization (CS). In addition, we evaluated whether empirical orthogonal functions (EOF) form efficient basis functions for synchronization in order to limit the number of connections. In this paper, we show that only the intermediate spectral wavenumbers (5\u201312) need to be connected in order to achieve CS. In addition, the minimum connection timescale needed for CS is 7.3 days. Both the connection subset and the connection timescale, or strength, are consistent with the time and spatial scales of the baroclinic instabilities in the model. This is in line with the fact that the baroclinic instabilities are the largest source of divergence between the two connected models. Using the Lorenz 63 model, we show that EOFs are nearly optimal basis functions for synchronization. The QG model results show that the minimum number of EOFs that need to be connected for CS is a factor of three smaller than when connecting the original state variables.
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Synchronization

With nudging terms included in the equations of a global atmospheric model,two identical models synchronize their evolution within 60 days when initialized from different initial conditions (model one in shading, model 2 in contours). In the paper it is shown that synchronization also occurs when not all state space variables are connected.

Improved modeling by coupling imperfect models

Miroslav Mirchev, G.S. Duane, W.K.S. Tang, L. Kocarev

Commun. Nonlinear Sci. Numer. Simulat., 17, 2012

Most of the existing approaches for combining models representing a single real-world phenomenon into a multi-model ensemble combine the models a posteriori. Alternatively, in our method the models are coupled into a supermodel and continuously communicate during learning and prediction. The method learns a set of coupling coefficients from short past data in order to unite the different strengths of the models into a better representation of the observed phenomenon. The method is examined using the Lorenz oscillator, which is altered by introducing parameter and structural differences for creating imperfect models. The short past data is obtained by the standard oscillator, and different weight is assigned to each sample of the past data. The coupling coefficients are learned by using a quasi- Newton method and an evolutionary algorithm. We also introduce a way for reducing the supermodel, which is particularly useful for models of high complexity. The results reveal that the proposed supermodel gives a very good representation of the truth even for substantially imperfect models and short past data, which suggests that the super-modeling is promising in modeling real-world phenomena
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A multi-model ensemble method that combines imperfect models through learning

L.A. van den Berge, F.M. Selten, W. Wiegerinck, and G.S. Duane

Earth Syst. Dynam., 2, 161-177, 2011

In the current multi-model ensemble approach climate model simulations are combined a posteriori. In the method of this study the models in the ensemble exchange information during simulations and learn from historical observations to combine their strengths into a best representation of the observed climate. The method is developed and tested in the context of small chaotic dynamical systems, like the Lorenz 63 system. Imperfect models are created by perturbing the standard parameter values. Three imperfect models are combined into one super-model, through the introduction of connections between the model equations. The connection coefficients are learned from data from the unperturbed model, that is regarded as the truth.
The main result of this study is that after learning the super-model is a very good approximation to the truth, much better than each imperfect model separately. These illustrative examples suggest that the super-modeling approach is a promising strategy to improve weather and climate simulations.
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Lorenz super model