Can Non‐Euclidean Distances Improve Spatial Interpolation of Precipitation in Mountainous Regions?

ABSTRACT Mountainous regions have complex terrain that affects precipitation distribution. However, conventional Euclidean distances account only for horizontal separation and neglect vertical variations in such terrain. The non‐Euclidean distance metrics, presented herein, aim to better represent the geographic separation between two locations, considering topographic obstructions and other terrain features. Thus, they can be useful for precipitation interpolation in mountainous regions. Three non‐Euclidean distance metrics are evaluated. They are used, instead of the Euclidean distance, in an interpolation method based on a precipitation‐elevation linear profile and residual interpolation. This evaluation covers most of the Peruvian Andes (~290,000 km 2 ), divided into 12 regions in three geographic domains: the Western Slope, the Eastern Slope and the Lake Titicaca basin. Monthly precipitation data of 311 stations from the 1995 to 2019 period are used. The cross‐validation evaluation results show that using the first non‐Euclidean distance metric (NED1) instead of the Euclidean distance significantly improves the precipitation estimation in almost half of the regions (5 out of 12), while only in 1 region the estimation is worsened. In addition, the use of NED1 integrated into the presented interpolation method also outperforms Kriging with External Drift (KED), a commonly used technique for precipitation interpolation, in most regions. Thus, the use of non‐Euclidean distance metrics, and especially NED1, can improve precipitation interpolation performance when used instead of the Euclidean distance. In particular, the interpolation method coupled with NED1 would be more suitable for regions with steep topography, such as the Western Slope of the Peruvian Andes. Other mountainous regions can also benefit by using non‐Euclidean distances with this interpolation method and other interpolation methods can also expect a better performance when using non‐Euclidean distances.