Stochastic in Space and Time: 1. Characterizing Orographic Gradients in Mean Runoff and Daily Runoff Variability

Mountain topography alters the phase, amount, and spatial distribution of precipitation. Past efforts focused on how orographic precipitation can alter spatial patterns in mean runoff, with less emphasis on how time-varying runoff statistics may also vary with topography. Given the importance of the magnitude and frequency of runoff events to fluvial erosion, we evaluated whether orographic patterns in mean runoff and daily runoff variability can be constrained using the global WaterGAP3 water model data. Model runoff data are validated against observational data in the contiguous United States, showing agreement with mean runoff in all settings and daily runoff variability in settings where rainfall-runoff predominates. In snowmelt-influenced settings, runoff variability is overestimated by the water model data. Cognizant of these limitations, we use the water model data to develop relationships between mean runoff and daily runoff variability and how these are mediated by snowmelt fraction in mountain topography globally. A global analysis of topographic controls on hydroclimatic variables using a random forest model was ambiguous. Instead, relationships between topography and runoff parameters are better assessed at the mountain range scale. Rulesets linking topography to mean runoff and snowmelt fraction are developed for three mid-latitude mountain landscapes-British Columbia, European Alps, and Greater Caucasus. Increasing topographic elevation and relief together leads to higher mean runoff and lower runoff variability due to the increasing contribution of snowmelt. The three sets of empirical relationships developed here serve as the basis for a suite of numerical experiments in our companion manuscript (Part 2, Forte & Rossi, 2024a, ). It has long been understood that mountain ranges can have profound influences on the location and intensity of precipitation, for example, through the formation of rain shadows. Less clear is how these "orographic effects" are reflected in the details of river runoff, specifically how much runoff varies from day-to-day. Understanding this variability of runoff is important as differences in variability directly influence how rivers respond to changes in rock uplift rate. Here, we use results from a global water model integrated with topography data to explore how runoff variability is related to topography in high relief landscapes. Consistent with prior work, we find and expand on the observation that mean runoff and runoff variability are inversely correlated and that the nature of their relation fundamentally depends on how much runoff comes from snowmelt as opposed to rain. In turn, both mean runoff and the importance of snowmelt are positively correlated with aspects of topography. Our results imply that incorporating variability into models of coupled developing orographic patterns in runoff and landscape evolution is critical and we identify a simple framework within which to develop such models. Examples of these models are presented in a companion work (Part 2, Forte & Rossi, 2024a, ). WaterGAP3 water model data overestimate daily runoff variability in snowmelt-influenced watersheds Global relationships between mean runoff and daily runoff variability are strongly mediated by snowmelt fraction Topographic drivers of mean runoff, snowmelt fraction, and daily runoff variability are best assessed at the mountain range scale