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.tation of the physical processes the model is intended to describe. Nevertheless, with the best possible models in hand, more accurate predictions can be obtained by making good use of all of them, thus exploiting multi-model information.In order to reduce the impact of model errors on predictions, it is common practice to combine the predictions of a collection of different models in a statistical fashion. This is referred to as the multi-model ensemble (MME) approach: the MME mean prediction is often more skillful as model errors tend to average out (Weigel et al., 2008), whereas the spread between the model predictions is naturally interpreted as a Published by Copernicus Publications on behalf of the European Geosciences Union.
Abstract.Weather and climate models have improved steadily over time as witnessed by objective skill scores, although significant model errors remain. Given these imperfect models, predictions might be improved by combining them dynamically into a so-called "supermodel". In this paper a new training scheme to construct such a supermodel is explored using a technique called cross pollination in time (CPT). In the CPT approach the models exchange states during the prediction. The number of possible predictions grows quickly with time, and a strategy to retain only a small number of predictions, called pruning, needs to be developed. The method is explored using low-order dynamical systems and applied to a global atmospheric model. The results indicate that the CPT training is efficient and leads to a supermodel with improved forecast quality as compared to the individual models. Due to its computational efficiency, the technique is suited for application to state-of-the art high-dimensional weather and climate models.
The SPEEDO global climate model (an atmosphere model coupled to a land and an ocean/sea-ice model with about 250.000 degrees of freedom) is used to investigate the merits of a new multi-model ensemble approach to the climate prediction problem in a perfect model setting. Two imperfect models are generated by perturbing parameters. Connection terms are introduced that synchronize the two models on a common solution, referred to as the supermodel solution. A synchronization-based learning algorithm is applied to the supermodel through the introduction of an update rule for the connection coefficients. Connection coefficients cease updating when synchronization errors between the supermodel and solutions of the "true" equations vanish. These final connection coefficients define the supermodel. Different supermodel solutions, but with equivalent performance, are found depending on the initial values of the connection coefficients during learning. The supermodels have a climatology and a climate response to a CO increase in the atmosphere that is closer to the truth as compared to the imperfect models and the standard multi-model ensemble average, showing the potential of the supermodel approach to improve climate predictions.
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