Improving weather and climate predictions by training of supermodels

Abstract

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.

Training a supermodel with noisy and sparse observations: a case study with CPT and the synch rule on SPEEDO - v.1

“…The imperfect models and the observations might be in different phases, resulting in a converse sign of the synchronization error e. Interestingly, it is still possible to obtain converged weights in this case, only that the weights differ substantially from those obtained with more nudging towards the observations. In the first experiment of Schevenhoven et al (2019) the weights for temperature, vorticity and divergence all turned out to be around 0.3 for imperfect model 1 and 0.7 for imperfect model 2. We apply the same amount of nudging to the same imperfect models, except that the observations are available every second time step, instead of every time step.…”

“…The obtained weights will not be perfect and possibly not as optimal as weights obtained with a cost function minimization approach. On the other hand, the results in Schevenhoven et al (2019) show that the models are on short term linear enough to let the CPT approach work well. Moreover, CPT is a very fast method, and only few iterations are necessary as compared to the common approach of minimization of a cost function.…”

“…This section recalls the general structure of a weighted supermodel as defined in Schevenhoven et al (2019), and summarizes the supermodel structure used with the coupled atmosphere-ocean-land model SPEEDO (Severijns and Hazeleger, 2010); full details can be found in Schevenhoven et al (2019). We shall then describe how the supermodel formulations are modified to handle time-sparse noisy data.…”

“…In Schevenhoven et al (2019) the weighted supermodel was defined by combining the tendencies of the individual models.…”

“…We have extended the use of the synch rule to the training of supermodels (Selten et al, 2017;Schevenhoven et al, 2019).…”