Mountain topography alters the phase, amount, and spatial distribution of precipitation. Past efforts focused on how orographic precipitation alters runoff spatial distribution, but with less emphasis on how stochastic runoff generation is also patterned on topography. Given the importance of the magnitude and frequency of stochastic runoff events to fluvial erosion, we evaluate whether orographic patterns in mean runoff and daily runoff variability can be constrained using the global WaterGAP3 water model data. Model runoff data is 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. Attempts to explain topographic controls on hydro-climatic variables using a Random Forest Regression model were less clear. Instead, relationships between topography and runoff parameters are better assessed at 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 lead 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 to this one (Part 2).