Maximum speedup ratio curve (MSC) in parallel computing of the binary-tree-based drainage network

Restricted computational capacity has become a key factor in limiting the development of a majority of distributed basin models. Parallel computing is one of the most effective methods for solving this problem. Although many parallel-computing methods have been employed in basin models, few studies have carried out theoretical research on parallel characteristics of river basins. In this paper, the drainage network of river basins is treated as a binary-tree structure. Using the binary-tree theory, we find that there exists a maximum speedup curve (MSC) for an arbitrary drainage network. The x-coordinate of the MSC represents the number of processors used during the computing, while the y-coordinate corresponds to the maximum speedup ratio (MSR) that can be obtained. Under several essential assumptions, the theoretical function of MSC is established. The function indicates that the MSC consists of an ascending section and a horizontal section. A parallel algorithm capable of acquiring the MSC is proposed as well. Using this algorithm, the MSC is tested at two different-resolution drainage networks of the Lhasa River Basin. A 2-year rainfall-runoff process is simulated. The results prove the existence of MSC. However, primarily influenced by the load imbalance of subbasins, the simulation values of MSR are usually smaller than the theoretical ones.