The 2022 National Defense Strategy of the United States listed climate change as a serious threat to national security. Climate intervention methods, such as stratospheric aerosol injection, have been proposed as mitigation strategies, but the downstream effects of such actions on a complex climate system are not well understood. The development of algorithmic techniques for quantifying relationships between source and impact variables related to a climate event (i.e., a climate pathway) would help inform policy decisions. Data-driven deep learning models have become powerful tools for modeling highly nonlinear relationships and may provide a route to characterize climate variable relationships. In this paper, we explore the use of an echo state network (ESN) for characterizing climate pathways. ESNs are a computationally efficient neural network variation designed for temporal data, and recent work proposes ESNs as a useful tool for forecasting spatiotemporal climate data. However, ESNs are noninterpretable black-box models along with other neural networks. The lack of model transparency poses a hurdle for understanding variable relationships. We address this issue by developing feature importance methods for ESNs in the context of spatiotemporal data to quantify variable relationships captured by the model. We conduct a simulation study to assess and compare the feature importance techniques, and we demonstrate the approach on reanalysis climate data. In the climate application, we consider a time period that includes the 1991 volcanic eruption of Mount Pinatubo. This event was a significant stratospheric aerosol injection, which acts as a proxy for an anthropogenic stratospheric aerosol injection. We are able to use the proposed approach to characterize relationships between pathway variables associated with this event that agree with relationships previously identified by climate scientists.
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. Here, 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.
Deep neural networks (NNs) typically outperform traditional machine learning (ML) approaches for complicated, non-linear tasks. It is expected that deep learning (DL) should offer superior performance for the important non-proliferation task of predicting explosive device configuration based upon observed optical signature, a task which human experts struggle with. However, supervised machine learning is difficult to apply in this mission space because most recorded signatures are not associated with the corresponding device description, or “truth labels.” This is challenging for NNs, which traditionally require many samples for strong performance. Semi-supervised learning (SSL), low-shot learning (LSL), and uncertainty quantification (UQ) for NNs are emerging approaches that could bridge the mission gaps of few labels and rare samples of importance. NN explainability techniques are important in gaining insight into the inferential feature importance of such a complex model. In this work, SSL, LSL, and UQ are merged into a single framework, a significant technical hurdle not previously demonstrated. Exponential Average Adversarial Training (EAAT) and Pairwise Neural Networks (PNNs) are chosen as the SSL and LSL methods of choice. Permutation feature importance (PFI) for functional data is used to provide explainability via the Variable importance Explainable Elastic Shape Analysis (VEESA) pipeline. A variety of uncertainty quantification approaches are explored: Bayesian Neural Networks (BNNs), ensemble methods, concrete dropout, and evidential deep learning. Two final approaches, one utilizing ensemble methods and one utilizing evidential learning, are constructed and compared using a well-quantified synthetic 2D dataset along with the DIRSIG Megascene.