  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 spatio-temporal climate data. Like other
neural networks, ESNs are non-interpretable black-box models, which poses a
hurdle for understanding variable relationships. We address this issue by
developing feature importance methods for ESNs in the context of
spatio-temporal 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 select a time period that includes the 1991 volcanic
eruption of Mount Pinatubo. This event was a significant stratospheric aerosol
injection, which we use as a proxy for an artificial stratospheric aerosol
injection. Using the proposed approach, we are able to characterize
relationships between pathway variables associated with this event.
