On Utilizing Spatial Gradients to Discover Functional Relationships in Hydrology

Abstract The search for functional relationships is at the heart of any science, but has proven notoriously difficult in hydrology. Here, we define functional relationships as relationships between two or more variables that characterize the functions of hydrological systems. Such relationships emerge when hydrological systems are observed along environmental or anthropogenic gradients that are dominant for the respective functional behavior at the chosen scale. Since many variables within hydrological systems are rather static (e.g., geology), and given that we mostly rely on naturally occurring gradients due to the limited possibility of controlled experiments, we often make use of spatial gradients by looking across different systems in space. With the proliferation of data sets containing in situ data, spatial data products, and domain knowledge (i.e., perceptual models), we can now discover new and test existing relationships at scales and across samples of unprecedented size. In light of this development, we review some functional relationships described in the literature, selected to represent a variety of hydrological functions and spatial gradients. We then discuss their value for hydrology, focusing on three interrelated aspects: first, relationships and their process explanations as a central building block of hydrological theory; second, relationships and their associated gradients as a guide for improving observational data sets; and third, relationships as a tool for hydrological applications, especially computational models. Fueled by existing domain knowledge and emerging data‐driven methods, a renewed focus on functional relationships and their associated gradients has the potential to advance hydrology by means of integrating theory, data, and models.