A Watershed Delineation Algorithm for 2D Flow Direction Grids

In this paper we propose an algorithm and associated data model for creating a watershed boundary using a 2D Flow Direction Grid. Flow Direction Grids (FDGs) are common abstractions for hydrodynamic models and are utilized for delineating physical systems (e.g. watersheds, fluvial, and non-fluvial flow paths). The proposed algorithm and associated data model provides geometric speed increases in watershed boundary retrieval while keeping storage constraints linear in comparison to existing techniques. The algorithm called Haag Shokoufandehs' March (HSM) relies on an existing data structure, the modified nested set model, originally described by Celko and applied to hydrodynamic models by Haag and Shokoufandeh in 2017. The proposed algorithm creates watershed boundaries by marching around the edges of its' corresponding region, never entering the internal area. In contrast to existing algorithms that scales in proportional to the area of the underlying region, the complexity of the HSM algorithm is proportional to the boundary length. Results for a group of tested watersheds (n = 14,718) in the approximately 36,000 km^2 Delaware River Watershed show a reduction of between 0 and 99% in computational complexity using a 30 m DEM vs. existing techniques. Larger watersheds have a consistent reduction in the number of (read) operation complexity, with the largest watershed resulting in approximately 35 million reads using traditional techniques compared to approximately 45 thousand using the HSM algorithm, respectively. Modelled estimates of the complexity for the approximately 6.1 million km^2 Amazon River basin show a reduction from 6.7 billion to 1.4 million reads.