Improving weather and climate predictions by training of supermodels

Recent studies demonstrate that weather and climate predictions potentially improve by dynamically combining different models into a so-called "supermodel". Here, we focus on the weighted supermodel - the supermodel's time derivative is a weighted superposition of the time derivatives of the imperfect models, referred to as weighted supermodeling. A crucial step is to train the weights of the supermodel on the basis of historical observations. Here, we apply two different training methods to a supermodel of up to four different versions of the global atmosphere-ocean-land model SPEEDO. The standard version is regarded as truth. The first training method is based on an idea called cross pollination in time (CPT), where models exchange states during the training. The second method is a synchronization-based learning rule, originally developed for parameter estimation. We demonstrate that both training methods yield climate simulations and weather predictions of superior quality as compared to the individual model versions. Supermodel predictions also outperform predictions based on the commonly used multi-model ensemble (MME) mean. Furthermore, we find evidence that negative weights can improve predictions in cases where model errors do not cancel (for instance, all models are warm with respect to the truth). In principle, the proposed training schemes are applicable to state-of-the-art models and historical observations. A prime advantage of the proposed training schemes is that in the present context relatively short training periods suffice to find good solutions. Additional work needs to be done to assess the limitations due to incomplete and noisy data, to combine models that are structurally different (different resolution and state representation, for instance) and to evaluate cases for which the truth falls outside of the model class

Supermodeling Improving Predictions with an Ensemble of Interacting Models

The modeling of weather and climate has been a success story. The skill of forecasts continues to improve and model biases continue to decrease. Combining the output of multiple models has further improved forecast skill and reduced biases. But are we exploiting the full capacity of state-of-the-art models in making forecasts and projections? Supermodeling is a recent step forward in the multimodel ensemble approach. Instead of combining model output after the simulations are completed, in a supermodel individual models exchange state information as they run, influencing each other's behavior. By learning the optimal parameters that determine how models influence each other based on past observations, model errors are reduced at an early stage before they propagate into larger scales and affect other regions and variables. The models synchronize on a common solution that through learning remains closer to the observed evolution. Effectively a new dynamical system has been created, a supermodel, that optimally combines the strengths of the constituent models. The supermodel approach has the potential to rapidly improve current state-of-the-art weather forecasts and climate predictions. In this paper we introduce supermodeling, demonstrate its potential in examples of various complexity, and discuss learning strategies. We conclude with a discussion of remaining challenges for a successful application of supermodeling in the context of state-of-the-art models. The supermodeling approach is not limited to the modeling of weather and climate, but can be applied to improve the prediction capabilities of any complex system, for which a set of different models exists