DOE OSTI2015
The project takes a hierarchical approach. The supermodeling scheme was first studied exhaustively with simple systems of ordinary differential equations. Results were described in detail in the previous report. The principal findings were that 1) for highly non-linear systems, such as Lorenz-63, including systems which describe phenomena on very different (atmosphere/ocean) times scales, supermodeling is far superior to any form of output-averaging; 2) negative coefficients can be used to advantage in situations where all models err in the same way, but to different degrees; 3) an interesting variant of supermodeling, “weighted supermodeling”, is the limiting case where inter-model nudging coefficients in the originally conceived “connected supermodel” become infinite, but with fixed ratios, corresponding to a direct combination of the tendencies that appear in corresponding equations for the alternative models; 4) noise is useful for avoiding local optima in training the inter-model coefficients in the supermodel. The supermodeling scheme was then investigated with simple quasigeostrophic (QG) models. As described in the previous report, it was found that QG models on a sphere can be coupled most efficaciously by working in a basis which captures the most variance, rather than the most instability, a somewhat unexpected result that still deserves scrutiny in a broader context. Further studies (since the last report) with QG channel models addressed the central question of when supermodeling is superior to output averaging in situations where nonlinearites are less extreme than with the ODEs initially studied. It was found that for realistic variations in a parameter in the QG model, output averaging is sufficient to capture all but the most subtle quantitative and qualitative behavior. Supermodeling helps when qualitative differences between the models result from unrealistically large parameter differences, or when very detailed spatial structure of the modes of variability are of interest. Therefore, the scheme may still be useful in the case of full climate models with qualitatively different parametrization schemes. A supermodel was constructed from the intermediate-complexity SPEEDO model, a primitive equation model with ocean and land. Versions defined by different parameter choices, in a realistic range, were connected and the coefficients trained. Some improvement was found as compared to output averaging. The learning algorithm used thus far gives sub-optimal, but still useful results when the CO 2 level and other parameters are varied. Spatial structure remains to be studied. The first use of supermodeling with full climate models has been with variants of the ECHAM model that use different convection schemes. As yet the models are only connected at the ocean-atmosphere interface, where weighted combinations of fluxes from the two atmospheres are passed to a common ocean, and the weights adapted during a training period. The supermodel was surprisingly successful at avoiding unrealistic features such as the double-ITCZ (Intertropical Convergence Zone), a problem that arises in both of the two models run separately. The supermodels constructed thus far have not identified dynamical regime shifts in future climate. Thus the planned connection with the work of Tsonis on the relationship between regime shifts and synchronization/de-synchronization among the major climate modes (see U. Wisconsin report) has not yet been made. However the network analysis of the climate system, in observations and models, that was done in conjunction with that study, shows that models differ strongly from one another and from observations in regard to the dynamical structure described by correlation networks [Steinhaeuser and Tsonis 2013], providing a further justification for supermodeling. Toward a general software framework for supermodeling, three versions of CAM (the Community Atmosphere Model) at NCAR were configured for inter-model nudging using the DART (Data Assimilation Research Testbed) capability to stop and re-start models in synchrony. It was clearly established that the inter-model nudging adds almost no computational burden to the runs, but there appears to be a problem with the re-initialization software that is still being debugged. Publications: Several papers were published on the basic idea of the interactive multi-model (supermodel) including demonstrations with low-order ODEs. The last of these, a semi-philosophical review paper on the relevance of synchronization generally, encountered considerable resistance but was finally published in Entropy [Duane 2015]. A paper on the ECHAM/COSMOS supermodel, containing the most promising results so far [Shen et al. 2015] is presently under review.