Estimation of theoretical maximum speedup ratio for parallel computing of grid-based distributed hydrological models

Theoretical maximum speedup ratio (TMSR) can be used as a goal for improving parallel computing methods for distributed hydrological models. Different types of distributed hydrological models need different TMSR estimation methods because of the different computing characteristics of models. Existing TMSR estimation methods, such as those for sub-basin based distributed hydrological models, are inappropriate for grid-based distributed hydrological models. In this paper, we proposed a TMSR estimation method suitable for grid-based distributed hydrological models. With this method, TMSRs for hillslope processes and channel routing processes are calculated separately and then combined to obtain the overall TMSR. A branch-and-bound algorithm and a critical path heuristic algorithm are used to estimate TMSRs for parallel computing of hillslope processes and channel routing processes, respectively. The overall TMSR is calculated according to the proportions of computing these two types of processes. A preliminary application showed that the more the number of sub-basins, the larger the TMSRs and that the compact watersheds had larger TMSRs than the long narrow watersheds.