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Flow Computation on Massive Grid Terrains

Flow Computation on Massive Grid Terrains. Lars Arge Laura Toma Dept. of Computer Science Duke University , USA. Helena Mitasova Dept. of Marine, Earth & Atmospheric Sciences , NCSU , USA. http://www.cs.duke.edu/geo*/terraflow. Flow direction The direction water flows at a cell

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Flow Computation on Massive Grid Terrains

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  1. Flow Computation onMassive Grid Terrains Lars Arge Laura Toma Dept. of Computer Science Duke University, USA Helena Mitasova Dept. of Marine, Earth & Atmospheric Sciences, NCSU, USA http://www.cs.duke.edu/geo*/terraflow

  2. Flow direction The direction water flows at a cell Flow Routing Compute flow direction for allcells in the terrain, including flat areas Flow accumulation value Total amount of water which flows through a cellper unit width of contour Flow is distributed according to the flow directions Flow Accumulation Compute flow accumulation values for allcells in the terrain Modeling Flow on Grids

  3. Modeling Flow Sierra-Nevada DEM Flow Direction Flow Accumulation

  4. Automatic estimation of various terrain parameters watershed basins stream network topographic indices Surface saturation Soil water content Erosion Deposition Forest structure Sediment transport Solar radiation Applications

  5. Massive Data • Remote sensing data available • NASA-SRTM (whole Earth 5TB at 30m resolution) • USGS (entire US at 10m resolution) • LIDAR (1m resolution) • Ex: Appalachian Mountains dataset • 100m resolution (500MB) • 30m resolution (5.5GB) • 10m resolution (50GB) • 1m resolution (5TB)

  6. Process Massive Data? • GRASS • r.watershed, ... • Killed afterrunning for17 days on a 6700 x 4300 grid (approx 50 MB dataset) • TARDEM • flood, d8, aread8 • Killed after running for 20 days on a 12000 x 10000 grid (appox 240MB dataset) • CPU utilization5%, 3GB swap file • ArcInfo • flowdirection, flowaccumulation • Can handle the 130MB dataset • Doesn’t work for datasets bigger than 2GB

  7. TerraFlow • Terraflow is Our suite of programs for flow routing and flow accumulation on massive grids[ATV`00,AC&al`02] • Flow routing and flow accumulation modeled as graph problems and solved in optimal I/O bounds • Efficient • 2-1000 times faster on very large grids than existing software • Scalable • 1 billion elements!! (>2GB data) • Flexible • Allows for both D8 and D-inf flow modeling http://www.cs.duke.edu/geo*/terraflow

  8. r.terraflow • Port of Terraflow into GRASS • Preliminary results on • Augment with additional features • Output plateaus, depressions, tci, water outlet queries, watershed basins • Comparison with GRASS flow routines • r.watershed, r.flow, r.topidx, ... • Performance results

  9. Outline • Scalability to large data • Why standard programs are not in general scalable • One approach to improve scalability • I/O-efficient algorithms • r.terraflow • Algorithm outline • Related work and programs • Preliminary comparison and performance results • Output illustration

  10. Scalabilityto Massive Data Why? • Most GIS programss assume data fits in memory and minimize only CPU computation • But..Massive data does not fit in main memory! OS places data on disk and moves data in and out of memory • Data is moved in blocks • Accessing the disk is 1000 times slower than accessing main memory when processing massive data disk I/O is the bottleneck, rather than CPU time!

  11. Algorithm 1: Loads 10 blocks Algorithm 2: Loads 5 blocks N blocks >> N/B blocks Scalabilityto Massive Data How? • Local data accesses vs. scattered data accesses • Example: reading an array from disk • Array size N = 10 elements • Disk block size = 2 elements • Memory size = 4 elements (2 blocks) 1 5 2 6 3 8 9 4 7 10 1 2 10 9 5 6 3 4 8 7

  12. Example • r.watershed • r.watershed –m el=elev_grid dir=dir_grid ac=accu_grid • Running on a 500MHz PIII, 1GB RAM, FreeBSD • On Hawaii dataset we let it run for 17 days in which it completed 65% However good the OS, it cannot change the data access pattern of the program!!

  13. TerraFlow Approach Redesign the algorithm to be I/O-Efficient • Block size is large! at least 8KB (32KB, 64KB) • Compute on whole block while it is in memory • Avoid loading a block each time • Improved locality • Speedup = block size I/O efficient algorithms • measure of complexity: number of blocks transfered between main memory and disk http://www.cs.duke.edu/geo*/terraflow

  14. r.terraflow outline Step 1: Flow routing Water flows downhill: SFD, MFD • Compute SFD/MFD flow directions by inspecting 8 neighbor points • Identify flat areas: plateaus and sinks http://www.cs.duke.edu/geo*/terraflow

  15. Flow Routing on Flat Areas …no obvious flow direction • Plateaus • Assign flow directions such that each cell flows towards the nearest spill point of the plateau • Sinks • Either catch the water inside the sink • Assign flow directions towards the center of the sink • Or route the water outside the sink using uphill flow directions • Simulate flooding the terrain: sinks  plateaus • Assign uphill flow directions on the original terrain by assigning downhill flow directions on the flooded terrain

  16. r.terraflow outline Step 2: Compute flow accumulation • Water flows following the flow directions • Goal: Compute the total amount of water through each grid cell • Initially one unit of water in each grid cell • Every cell distributes water to the neighbors pointed to by its flow direction(s) All these steps can be solved I/O-efficiently • Flow routing: modeled as graph problems (breadth-first search, connected components, graph contraction) • Flow accumulation: sweeping using an I/O-efficient priority queue

  17. Related Work • TerraFlow’s emphasis • Computational aspects, not modeling • Flow modeling • [O’Callaghan and Mark 1984] • D8 method for flow accumulation • [Jenson and Domingue 1988] • General technique of flooding • Software • GRASS, ArcInfo,Tardem, Topaz, Tapes-G, RiverTools

  18. GRASS Raster Flow Functions • r.watershed • Most commonly used. Uses A* algorithm to determine flow of water. Ehlschlaeger, USACERL. • Input: elevation, [..] • Output: flow direction, flow accumulation, [waterhseds, stream segments, slope length, slope steepness] • Flow direction grid equivalent to running r.drain for every cell on the grid • Watershed grid equivalent to running r.water.outletfor multiple outlets • r.drain • Traces the least-cost (steepest-downslope) flow path from a given cell. Stops in pits. • Input: elevation, point coordinates • Output: least-cost path • r.water.outlet • Generates a watershed basin from a flow direction map. Ehlschlaeger, USACERL. • Input: flow direction (from r.watershed), basin coordinates • Output: watershed basin map

  19. GRASS Raster Flow Functions • r.basin.fill • Generates a raster map of watershed subbasins. Larry Band. • Input: stream network (from r.watershed), thinned ridge network (by hand!) • Output: watersheds subbasins • r.topmodel, r.topidx • Simulates TOPMODEL, Keith Beven. • Input: elevation, basin, TOPMODEL parameters file • Output: flow direction, filled elevation, tci, watersheds, [..] • r.flow, r.flowmd • Constructs flowlines, flowpath lengths and flowline densities. Flowlines stop in pits. Mitas, Mitasova, Hofierka, Zlocha. • Input: elevation, [..] • Output: flowline density, flowlines (vector), lengths • More complex models • r.water.fea - Finite element analysis program for hydrologic simulations • r.hydro.CASC2D - Fully integrated distributed cascaded 2D hydrologic modeling. • r.wrat- Water Resource Assessment Tool

  20. r.terraflow features • Input • elevation grid • Output • flow direction grid • SFD (D8) single flow directions • MFD (Dinf) multiple flow directions • flow accumulation grid • Option to switch to SFD when flow value exceeds an user-defined threshold • topographic convergence index (tci) grid • plateau and depressions grid

  21. GRASS:>r.terraflow help Description: Flow computation for massive grids. Usage: r.terraflow [-sq] elev=name filled=name direction=name watershed=name accumulation=name tci=name [d8cut=value] [memory=value] [STREAM_DIR=name] [stats=name] Flags: -s SFD (D8) flow (default is MFD) -q Quiet Parameters: elev Input elevation grid filled Output (filled) elevation grid direction Output direction grid watershed Output watershed grid accumulation Output accumulation grid tci Output tci grid d8cut If flow accumulation is larger than this value it is routed using SFD (D8) direction (meaningfull only for MFD flow only). default: infinity memory Main memory size (in MB) default: 300 STREAM_DIR Location of intermediate STREAMs default: /var/tmp stats Stats file default: stats.outv http://www.cs.duke.edu/geo*/terraflow

  22. Preliminary Experimental Results PIII dual 1GHz processor, 1GB RAM

  23. Panama DEM

  24. Panama r.terraflow MFD

  25. r.terraflow MFDzoom,3D

  26. r.terraflow SFDzoom,3D

  27. r.terraflow MFDzoom,2D

  28. r.terraflow SFDzoom,2D

  29. r.terraflow MFD TCIzoom,2D

  30. r.terraflow SFD TCIzoom,2D

  31. Flat DEM

  32. r.terraflow MFD

  33. r.terraflow SFD

  34. r.watershed

  35. Conclusions/Future Work • Work in progress • More features • Water outlet queries • Watershed delineation • Experimental analysis • Other features? • Modeling? • Other (intensive computing, I/O-bound) applications? http://www.cs.duke.edu/geo*/terraflow http://www.cs.duke.edu/geo*/terraflow http://www.cs.duke.edu/geo*/terraflow

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