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).

中文翻译：

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空间和时间的随机性：1. 描述平均径流和日径流变化中的地形梯度

山地地形改变降水的相位、量和空间分布。过去的研究重点是地形降水如何改变平均径流的空间模式，而较少关注时变径流统计数据如何随地形变化。鉴于径流事件的幅度和频率对河流侵蚀的重要性，我们评估了是否可以使用全球 WaterGAP3 水模型数据来限制平均径流和日径流变化的地形模式。模型径流数据根据美国本土的观测数据进行了验证，显示与所有环境中的平均径流以及降雨径流占主导地位的环境中的日径流变化一致。在受融雪影响的环境中，水模型数据高估了径流变化。认识到这些局限性，我们使用水模型数据来开发平均径流和日径流变化之间的关系，以及全球山区地形中的融雪分数如何调节这些关系。使用随机森林模型对地形对水文气候变量的控制进行的全球分析是不明确的。相反，在山脉尺度上可以更好地评估地形和径流参数之间的关系。针对三个中纬度山区景观（不列颠哥伦比亚省、欧洲阿尔卑斯山和大高加索地区）制定了将地形与平均径流和融雪分数联系起来的规则集。由于融雪贡献的增加，地形海拔和地势的增加共同导致平均径流更高和径流变异性更低。这里开发的三组经验关系作为我们的配套手稿中一系列数值实验的基础（第 2 部分，Forte & Rossi，2024a，https://doi.org.10.1002/2023JF007327）。