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Abstract

Since all ecological- and human-centric systems rely on a steady water supply, scientists must learn the true-underlying processes that force hydrological behavior from a few thousand catchments with available data in order to transfer that knowledge to the infinite number of ungauged catchments. While hydrologists have historically preferred to utilize physics-based equations to gain and transfer knowledge, data-driven methods for hydrological inference may provide more promising approaches. Due to the unique properties of hydrological data, such as extreme spatiotemporal dependence, high measurement uncertainty, threshold-like nonlinear processes, highly skewed distributions, non stationary relationships, uncommon causal pathway types, and high order emergent interactions, traditional statistical methods fail to learn important yet still undiscovered hydrological processes. These failures arise in a variety of hydrological studies including cross-catchment spatial analyses, single-catchment temporal analyses, and single-catchment spatiotemporal analyses, thus for each of these study types, we demonstrate previous methodological shortcomings and invalid assumptions, while developing and applying new data-driven approaches relating to information theory, causal inference, and statistical learning.