An efficient and comprehensive method for drainage network extraction from DEM with billions of pixels using a size-balanced binary search tree

Abstract With the increasing resolution of digital elevation models (DEMs), computational efficiency problems have been encountered when extracting the drainage network of a large river basin at billion-pixel scales. The efficiency of the most time-consuming depression-filling pretreatment has been improved by using the O ( N log N ) complexity least-cost path search method, but the complete extraction steps following this method have not been proposed and tested. In this paper, an improved O ( N log N ) algorithm was proposed by introducing a size-balanced binary search tree (BST) to improve the efficiency of the depression-filling pretreatment further. The following extraction steps, including the flow direction determination and the upslope area accumulation, were also redesigned to benefit from this improvement. Therefore, an efficient and comprehensive method was developed. The method was tested to extract drainage networks of 31 river basins with areas greater than 500,000 km 2 from the 30-m-resolution ASTER GDEM and two sub-basins with areas of approximately 1000 km 2 from the 1-m-resolution airborne LiDAR DEM. Complete drainage networks with both vector features and topographic parameters were obtained with time consumptions in O ( N log N ) complexity. The results indicate that the developed method can be used to extract entire drainage networks from DEMs with billions of pixels with high efficiency.

[1]  L. Martz,et al.  Automated extraction of drainage network and watershed data from digital elevation models , 1993 .

[2]  Richard Barnes,et al.  An efficient assignment of drainage direction over flat surfaces in raster digital elevation models , 2015, Comput. Geosci..

[3]  Andrea Tribe,et al.  Automated recognition of valley lines and drainage networks from grid digital elevation models: a review and a new method , 1992 .

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

[5]  L. Martz,et al.  The assignment of drainage direction over flat surfaces in raster digital elevation models , 1997 .

[6]  Alberto Montanari,et al.  Inferring the flood frequency distribution for an ungauged basin using a spatially distributed rainfall-runoff model , 2008 .

[7]  Gregory J. McCabe,et al.  Comparison of Single and Multiple Flow Direction Algorithms for Computing Topographic Parameters in TOPMODEL , 1995 .

[8]  Long Wang,et al.  [Review of urban nonpoint source pollution models]. , 2010, Huan jing ke xue= Huanjing kexue.

[9]  L. Band.  Topographic Partition of Watersheds with Digital Elevation Models , 1986 .

[10]  S. K. Jenson,et al.  Extracting topographic structure from digital elevation data for geographic information-system analysis , 1988 .

[11]  Hao Wang,et al.  Dynamic parallelization of hydrological model simulations , 2011, Environ. Model. Softw..

[12]  L. Martz,et al.  Network and Subwatershed Parameters Extracted From Digital Elevation Models , 1993 .

[13]  Guangqian Wang,et al.  Modeling the Process of Hillslope Soil Erosion in the Loess Plateau , 2009 .

[14]  L. Martz,et al.  CATCH: a FORTRAN program for measuring catchment area from digital elevation models , 1988 .

[15]  R. Horton.  EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY , 1945 .

[16]  Roberto Rudari,et al.  A procedure for drainage network identification from geomorphology and its application to the prediction of the hydrologic response , 2005 .

[17]  Anders Wörman,et al.  Stage-dependent hydraulic and hydromorphologic properties in stream networks translated into response functions of compartmental models , 2012 .

[18]  Richard R. Jones,et al.  Algorithms for using a DEM for mapping catchment areas of stream sediment samples , 2002 .

[19]  D. Montgomery,et al.  Analysis of Erosion Thresholds, Channel Networks, and Landscape Morphology Using a Digital Terrain Model , 1993, The Journal of Geology.

[20]  John F. O'Callaghan,et al.  The extraction of drainage networks from digital elevation data , 1984, Comput. Vis. Graph. Image Process..

[21]  Serge Massicotte,et al.  Determination of the drainage structure of a watershed using a digital elevation model and a digital river and lake network , 2001 .

[22]  Pierre Soille,et al.  An Efficient Algorithm for Drainage Network Extraction on DEMs , 1994, J. Vis. Commun. Image Represent..

[23]  G. Hancock,et al.  Channel head location and characteristics using digital elevation models , 2006 .

[24]  Donald E. Knuth,et al.  Sorting and Searching , 1973 .

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

[26]  M. Cristina Rulli,et al.  A physically based watershed partitioning method , 2010 .

[27]  Hao Wang,et al.  Multi-tree Coding Method (MCM) for drainage networks supporting high-efficient search , 2013, Comput. Geosci..

[28]  Yosoon Choi,et al.  A new algorithm to calculate weighted flow-accumulation from a DEM by considering surface and underground stormwater infrastructure , 2012, Environ. Model. Softw..

[29]  I. Moore,et al.  Digital terrain modelling: A review of hydrological, geomorphological, and biological applications , 1991 .

[30]  Qing Zhu,et al.  An efficient depression processing algorithm for hydrologic analysis , 2006, Comput. Geosci..

[31]  Tiejian Li,et al.  Soil erosion and sediment transport in the gullied Loess Plateau: Scale effects and their mechanisms , 2009 .

[32]  P. Holmgren.  Multiple flow direction algorithms for runoff modelling in grid based elevation models: An empirical evaluation , 1994 .

[33]  Richard Gloaguen,et al.  TecDEM: A MATLAB based toolbox for tectonic geomorphology, Part 1: Drainage network preprocessing and stream profile analysis , 2011, Comput. Geosci..

[34]  R. Bras,et al.  A physically-based method for removing pits in digital elevation models , 2007 .

[35]  Gao Jie.  Multi-tree Coupling Method of High Resolution Drainage Network Extraction on Large-scale Basin , 2009 .

[36]  P. Cui,et al.  A new treatment of depression for drainage network extraction based on DEM , 2009 .

[37]  Sébastien Limet,et al.  Parallel Computing Flow Accumulation in Large Digital Elevation Models , 2011, ICCS.

[38]  Andrew N. Sharpley,et al.  Critical source area controls on water quality in an agricultural watershed located in the Chesapeake basin. , 2000 .

[39]  Enrique R. Vivoni,et al.  Real-world hydrologic assessment of a fully-distributed hydrological model in a parallel computing environment , 2011 .

[40]  Qi Li,et al.  Performance‐improving techniques in web‐based GIS , 2005, Int. J. Geogr. Inf. Sci..

[41]  Lawrence W. Martz,et al.  Numerical definition of drainage network and subcatchment areas from digital elevation models , 1992 .

[42]  P Yoeli.  Computer-assisted determination of the valley and ridge lines of digital terrain models , 1984 .

[43]  D. Montgomery,et al.  Channel Initiation and the Problem of Landscape Scale , 1992, Science.

[44]  Helena Mitasova,et al.  Efficient extraction of drainage networks from massive, radar-based elevation models with least cost path search , 2011 .

[45]  C. Rennó,et al.  Height Above the Nearest Drainage – a hydrologically relevant new terrain model , 2011 .

[46]  Guy Vézina,et al.  Visualizing soil surfaces and crop residues , 1993, IEEE Computer Graphics and Applications.

[47]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[48]  L. Martz,et al.  The treatment of flat areas and depressions in automated drainage analysis of raster digital elevation models , 1998 .

[49]  Jianya Gong,et al.  Extraction of drainage networks from large terrain datasets using high throughput computing , 2009, Comput. Geosci..

[50]  Zachary M. Easton,et al.  A phosphorus index that combines critical source areas and transport pathways using a travel time approach , 2012 .

[51]  María José Polo,et al.  Scale effects on the estimation of erosion thresholds through a distributed and physically-based hydrological model , 2012 .

[52]  D. Tarboton.  A new method for the determination of flow directions and upslope areas in grid digital elevation models , 1997 .

[53]  L. Wang,et al.  An efficient method for identifying and filling surface depressions in digital elevation models for hydrologic analysis and modelling , 2006, Int. J. Geogr. Inf. Sci..

[54]  Frédéric Darboux,et al.  A fast, simple and versatile algorithm to fill the depressions of digital elevation models , 2002 .

[55]  L. Martz,et al.  An outlet breaching algorithm for the treatment of closed depressions in a raster DEM , 1999 .

[56]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[57]  Chengzhi Qin,et al.  Parallelizing flow-accumulation calculations on graphics processing units - From iterative DEM preprocessing algorithm to recursive multiple-flow-direction algorithm , 2012, Comput. Geosci..

[58]  K. Beven,et al.  THE PREDICTION OF HILLSLOPE FLOW PATHS FOR DISTRIBUTED HYDROLOGICAL MODELLING USING DIGITAL TERRAIN MODELS , 1991 .

[59]  Guillermo Sapiro,et al.  A geometric framework for channel network extraction from lidar: Nonlinear diffusion and geodesic paths , 2010 .

[60]  Chun-Po Hung,et al.  REPLY to “On width function-based unit hydrographs deduced from separately random self-similar river networks and rainfall variability” , 2007 .

[61]  T. G. Freeman,et al.  Calculating catchment area with divergent flow based on a regular grid , 1991 .

[62]  J. Dozier,et al.  Automated basin delineation from digital elevation data , 1984 .

[63]  John P. Wilson,et al.  Digital terrain modeling , 2012 .

[64]  A. N. Strahler.  Quantitative analysis of watershed geomorphology , 1957 .

[65]  Masamu Aniya,et al.  Automated segmentation of hillslope profiles across ridges and valleys using a digital elevation model , 2012 .

[66]  Jon D. Pelletier,et al.  A robust, two‐parameter method for the extraction of drainage networks from high‐resolution digital elevation models (DEMs): Evaluation using synthetic and real‐world DEMs , 2013 .

[67]  Rina Dechter,et al.  The optimality of A , 1988 .