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

Abstract

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, https://doi.org.10.1002/2023JF007327).

Stochastic in Space and Time: 2. Effects of Simulating Orographic Gradients in Daily Runoff Variability on Bedrock River Incision

“…Land surface properties like vegetation (Deal et al, 2018), soil thickness (Rossi et al, 2020), among others, may plausibly coevolve with topography in ways that can partition the landscape into domains with distinctively different rainfall runoff statistics. Furthermore, we showed in our companion paper (Forte & Rossi, 2024b) that the spatial extent of snowmelt dominated runoff events tends to dominate the far right tail of runoff distributions, especially at higher intensity thresholds. While our treatment only provides a crude representation of the endmember cases of linked versus unlinked scenarios, it provides a useful baseline for the range of outcomes for a given hydroclimatic ruleset.…”

“…Promising work characterizing potentially significant spatial variability in precipitation patterns in high relief landscapes exist (e.g., Anders et al, 2006Anders et al, , 2007Barros et al, 2000;Campbell & Steenburgh, 2014;Frei & Schär, 1998;Minder et al, 2008), but generalizing these into how this spatial stochasticity is, or is not, reflected in runoff at a similar scale remains unclear. Similarly, the analysis of WaterGAP3 data by Forte and Rossi (2024b) suggested a fundamental relationship between runoff event size and the contribution from snowmelt. Events with larger spatial footprints appear to be dominated by snowmelt events, further highlighting the interconnectedness of many of the parameters we consider.…”

“…Because the shape (c R ) and scale (R 0 ) parameters shown in Figure 2 were determined by fitting the right tail of runoff distributions above a 1% threshold, these fit parameters are no longer related to the mean of the distribution in a simple way (Forte & Rossi, 2024b). The scale parameter from the fits of daily data (R 0 ) is linearly related to the scale estimated from the mean runoff (R 0 * ) using the general equation for a Weibull distribution:…”

“…In order to uniquely prescribe the distribution of flows (e.g., Equation 19) within a part of a river profile, we need to know both R and SF so that we can modify R 0 * and c R . As described in Forte and Rossi (2024b), identifying singular, global relationships between either R or SF and topographic metrics is challenging. As such, we use the three regional relationships between mean local relief and R and maximum elevation and SF in the Greater Caucasus, European Alps, and northern British Columbia (Figures 2c and 2d).…”

“…Second, both mean runoff and daily runoff variability are dictated by their relationship to topography, specifically in response to local relief and elevation. Third, these topography-hydrology relationships are based on relationships observed in modern mountain ranges, which are described in our companion manuscript to this one (Forte & Rossi, 2024b), thus explicitly considering the role of snowmelt in modulating runoff variability. Fourth, the temporal stochasticity of each bin can either be linked or unlinked spatially.…”