Methods for watershed division

Fig. ​Fig.1b1b shows our watershed division method. To perform hydrography vectorization, we use the level-02 global basin definitions by HydroBASINS (https://hydrosheds.org/images/inpages/HydroBASINS_TechDoc_v1c.pdf) to roughly re-organize the data into 61 global river basins, because these are more hydrologically meaningful units for hydrography extraction, compared to the original data organized as 1150 5° × 5° tiles. In addition, organizing data into 61 basins allows for efficient computation as allowed by the computer memory. We note, however, that the HydroBASINS basin boundaries (sourced from ~500 m SRTM data) are different from those defined by the ~90 m MERIT data. Thus, the new basins need to be re-defined. After the river networks and catchments are first extracted within the rough boundaries, all the most downstream river segments (or outlet points) within each rough basin boundary are identified (globally there are 57,025 of such outlet points). They are then traced back upstream to determine the upstream drainage boundaries. These drainage polygons are dissolved (i.e., combined) if their outlets are within the same level-02 HydroBASINS boundary, which eventually re-defines the 61 global basins.

The 57,025 drainage basins upstream of the global outlet points are further split into smaller watershed units, upon which the variable D_d is applied globally. To divide the watersheds, we follow the Pfafstetter coding²⁴ as it is the most widely used methodology for coding and referencing nested hierarchical global river basins. The Pfafstetter coding uses nine-digit algebra to indicate the topological information of the river network and their locations, e.g., even for tributaries and odd for main stems; the larger the number is, the farther away it is from the basin outlets. For level-01 to level-03 Pfafstetter coding that requires grouping of continental basins where subjective decisions are needed to determine the complex continent break-out, we follow the definition of HydroBASINS²⁵ to assign the codes. Starting from level-03, the Pfafstetter codes are assigned following Verdin & Verdin²⁴. The stopping criteria for the hierarchical watershed splitting is imposed until all basin areas are under 5000 km², because imposing this criterion would eventually lead to 156,571 watersheds with a median size of 461 km² (Fig. S1), which is considered as the reasonable size to apply variable D_d following some pre-assessments explained in Section 2.4, Text S1, & Fig. S2. This level of watershed is approximately equivalent to HydroBASINS²⁵ level-08 classification (median size: 475.7 km²).