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.

[1]  Lawrence W. Martz,et al.  Automated channel ordering and node indexing for Raster channel networks , 1997 .

[2]  Hongxing Zheng,et al.  A distributed hydrological model with its application to the Jinghe watershed in the Yellow River Basin , 2004 .

[3]  Keith Beven,et al.  The Institute of Hydrology distributed model , 1987 .

[4]  Luis Garrote,et al.  A distributed model for real-time flood forecasting using digital elevation models , 1995 .

[5]  Zhao Ren-jun,et al.  The Xinanjiang model applied in China , 1992 .

[6]  P. E. O'connell,et al.  An introduction to the European Hydrological System — Systeme Hydrologique Europeen, “SHE”, 2: Structure of a physically-based, distributed modelling system , 1986 .

[7]  Jun Li,et al.  Diffusive wave solutions for open channel flows with uniform and concentrated lateral inflow , 2006 .

[8]  George Xian,et al.  Dynamic modeling of Tampa Bay urban development using parallel computing , 2005, Comput. Geosci..

[9]  M. Wigmosta,et al.  A distributed hydrology-vegetation model for complex terrain , 1994 .

[10]  Yu-Shu Wu,et al.  Parallel computing simulation of fluid flow in the unsaturated zone of Yucca Mountain, Nevada. , 2003, Journal of contaminant hydrology.

[11]  Ji Chen,et al.  A modified binary tree codification of drainage networks to support complex hydrological models , 2010, Comput. Geosci..

[12]  Henry Neeman,et al.  Parallelisation of a distributed hydrologic model , 2005, Int. J. Comput. Appl. Technol..

[13]  Tiejian Li,et al.  Sediment yield computation of the sandy and gritty area based on the digital watershed model , 2006 .

[14]  M. Grübsch,et al.  How to divide a catchment to conquer its parallel processing. An efficient algorithm for the partitioning of water catchments , 2001 .

[15]  Dara Entekhabi,et al.  Basin hydrologic response relations to distributed physiographic descriptors and climate , 2001 .

[16]  Katumi Musiake,et al.  DEVELOPMENT OF A GEOMORPHOLOGY-BASED HYDROLOGICAL MODEL FOR LARGE CATCHMENTS , 1998 .

[17]  Manoj K. Jha,et al.  A DEM‐based parallel computing hydrodynamic and transport model , 2012 .

[18]  R. Maxwell,et al.  Integrated surface-groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model , 2006 .

[19]  S. Sorooshian,et al.  Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system , 2004, Journal of Hydrology.

[20]  O. Kolditz,et al.  Development of a regional hydrologic soil model and application to the Beerze--Reusel drainage basin. , 2007, Environmental pollution.

[21]  Susan M. Mniszewski,et al.  Parallelization of a Fully-Distributed Hydrologic Model using Sub-basin Partitioning , 2005 .

[22]  Jan Vanderborght,et al.  Proof of concept of regional scale hydrologic simulations at hydrologic resolution utilizing massively parallel computer resources , 2010 .

[23]  Dara Entekhabi,et al.  Preserving high-resolution surface and rainfall data in operational-scale basin hydrology: a fully-distributed physically-based approach , 2004 .

[24]  P. E. O'connell,et al.  An introduction to the European Hydrological System — Systeme Hydrologique Europeen, “SHE”, 1: History and philosophy of a physically-based, distributed modelling system , 1986 .

[25]  K. Beven,et al.  A physically based, variable contributing area model of basin hydrology , 1979 .

[26]  Guangqian Wang,et al.  Digital Yellow River Model , 2007 .

[27]  Theodore K. Apostolopoulos,et al.  Parallel computation for streamflow prediction with distributed hydrologic models , 1997 .