A comparison of model validation approaches for echo state networks using climate model replicates

As global temperatures continue to rise, climate mitigation strategies such as stratospheric aerosol injections (SAI) are increasingly discussed, but the downstream effects of these strategies are not well understood. As such, there is interest in developing statistical methods to quantify the evolution of climate variable relationships during the time period surrounding an SAI. Feature importance applied to echo state network (ESN) models has been proposed as a way to understand the effects of SAI using a data-driven model. This approach depends on the ESN fitting the data well. If not, the feature importance may place importance on features that are not representative of the underlying relationships. Typically, time series prediction models such as ESNs are assessed using out-of-sample performance metrics that divide the times series into separate training and testing sets. However, this model assessment approach is geared towards forecasting applications and not scenarios such as the motivating SAI example where the objective is using a data driven model to capture variable relationships. In this paper, we demonstrate a novel use of climate model replicates to investigate the applicability of the commonly used repeated hold-out model assessment approach for the SAI application. Simulations of an SAI are generated using a simplified climate model, and different initialization conditions are used to provide independent training and testing sets containing the same SAI event. The climate model replicates enable out-of-sample measures of model performance, which are compared to the single time series hold-out validation approach. For our case study, it is found that the repeated hold-out sample performance is comparable, but conservative, to the replicate out-of-sample performance when the training set contains enough time after the aerosol injection.