Comment on gmd-2021-221

doi:10.5194/gmd-2021-221-rc1

Abstract

In alternative to using the standard multi-model ensemble (MME) approach to combine the output of different models to improve prediction skill, models can also be combined dynamically to form a so-called supermodel. The supermodel approach allows for a quicker correction of the model errors. In this study we focus on weighted supermodels, in which the supermodel state is a weighted superposition of different imperfect model states. The estimation, “the training”, of the optimal weights of this combination is a critical aspect in the construction of a supermodel. In our previous works two algorithms were developed: (i) cross pollination in time (CPT-based technique), and, (ii) a synchronization based learning rule (synch rule). Those algorithms have been so far applied under the assumption of complete and noise-free observations. Here we go beyond and consider the more realistic case of noisy data that do not cover the full system's state and are not taken at each model's computational time step. We revise the training methods to cope with this observational scenario, while still being able to estimate accurate weights. In the synch rule an additional term is introduced to maintain physical balances, while in CPT nudging terms are added to let the models stay closer to the observations during training. Furthermore, we propose a novel formulation of the CPT method allowing for the weights to be negative. This makes it possible for CPT to deal with cases in which the individual model biases have the same sign, a situation that hampers constructing a skilful weighted supermodel based on positive weights. With these developments, both CPT and the synch rule have been made suitable to train a supermodel consisting of state-of-the-art weather or climate models.

Highlights

In alternative to using the standard multi-model ensemble (MME) approach to combine the output of different models to improve prediction skill, models can be combined dynamically to form a so-called supermodel
The models are weighted in a MME, as is the case for, e.g. the Coupled Model Intercomparison Project (CMIP) runs in the Intergovernmental Panel on Climate Change (IPCC) re30 ports
The synch rule is initialized with certain values for q and during training the weights are updated according to the rule, such that the supermodel synchronizes with the observations

Summary

Introduction

Climate models are continuously improving over time. This is made evident by the succession of the Coupled Model Intercomparison Project (CMIP), which is currently at its sixth stage (Eyring et al, 2016). By combining the models dynamically into a supermodel, model errors can be reduced at an earlier stage, potentially mitigating error propagation This is helpful since the climate system is not linear, which causes initial errors to spread over different variables and regions. The supermodel improves the statistics of simulated climate, as in the MME, it can give an improved model trajectory if the models are well enough synchronized. The CPT trajectory tends to explore a larger area of the phase space 55 than the individual models, enhancing the chance to pass in the vicinity of an observation Another efficient training method, referred to as the “synch rule”, was introduced by Selten et al (2017). The method, originally developed by Duane et al (2007) for parameter estimation, is based on the synchronization theory of different systems

Methods

Results

Conclusion