Sep 22, 2016 - A cellular automata API. ⢠A high performance, open source C++ library. ⢠Developed at the University of Exeter (Centre for Water. Systems).
Hexagonal cellular automata for flood modelling
September 22, 2016
L. M. de Sousa1 , M. J. Gibson2 , A. S. Chen2 , D. Savić2 and J. P. Leitão1 1 Swiss
Federal Institute of Aquatic Science and Technology; 2 University of Exeter
Outline
1. CADDIES and CAFlood 2. Why Hexagons? 3. EAT8a Test 4. Results 5. Analysis 6. Summary and future work
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CADDIES and CAFlood
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CADDIES and CAFlood
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CADDIES
A cellular automata API • A high performance, open source C++ library • Developed at the University of Exeter (Centre for Water Systems) • Classes: Grid, Box, Function, Clock, . . . • Compilation for diverse back-ends • Focus on parallel computing: • OpenMP - multi-core processors • OpenCL - multi-core graphical cards
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CADDIES and CAFlood
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CAFlood
A fast flood analysis model • Developed on the CADDIES API • Applies a numerical simplification of Manning’s equation: • weight based system for inter-cellular water transfer • high performance maintaining accuracy
• Main simulation results: • Water depths (and levels) • Water velocities Guidolin M, Chen AS, Ghimire B, Keedwell EC, Djordjević S, Savić DA. 2016. A weighted cellular automata 2D inundation model for rapid flood analysis, Environmental Modelling & Software, Volume 84, Pages 378-394
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CADDIES and CAFlood
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The CAFlood engine 2 3
0
1
4
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CADDIES and CAFlood
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The CAFlood engine water mass
2 3
0
1 time step
4
cell edge length water depth
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CADDIES and CAFlood
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The CAFlood worlds
Water levels
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North-South velocities
CADDIES and CAFlood
East-West velocities
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Why Hexagons?
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Why Hexagons?
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Anisotropic neighbourhood The border paradox with squared grids
Goolay MJE. 1969. Hexagonal parallel pattern transformations. IEEE Transactions on Computers. 18(8):733-740.
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Why Hexagons?
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Hexagonal neighbourhood Unequivocal and isotropic
Goolay MJE. 1969. Hexagonal parallel pattern transformations. IEEE Transactions on Computers. 18(8):733-740.
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Why Hexagons?
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Hexagons in the Fourier spectrum Gains in sampling and computation efficiency
Fourier transform with hexagons vs. squares: • Less 13.4% samples to capture the same signal • Less 25% computational cycles to calculate the transform • Less 25% memory usage Mersereau R. 1979. The processing of hexagonally sampled two-dimensional signals. In: Proceedings of the IEEE ; Vol. 67. p. 930-949. de Sousa et alia
Why Hexagons?
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Hexagons in the Fourier spectrum Biological sampling systems are hexagonal
Light receiving cells in mammals eyes are distributed in an hexagonal pattern
Yellot JI. 1981. Spectral consequences of photoreceptor sampling in the rhesus retina. Science. (212):382-385.
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Why Hexagons?
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Hexagons reproduce the Navier-Stokes equation
An hexagonal grid with six flow vectors linking each cell to its neighbours approaches the Navier-Stokes equilibrium in the continuum
Frisch U, Hasslacher B, Pomeu Y. 1986. Lattice-gas automata for the Navier-Stokes equation. Physical Review Letters. 56(14):1505-1508.
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Why Hexagons?
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Hexagons preserve flow directions better
de Sousa LM, Nery F, Sousa R, Matos, J. 2006. Assessing the accuracy of hexagonal versus square tiled grids in preserving DEM surface flow directions. Procs. of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences. de Sousa et alia
Why Hexagons?
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The HexASCII specification and API
41 2
21 31 42
11 22 32 12
43 23 33
2.2
13
O
3.1
15º
ncols 4 nrows 3 xll 3.1 yll 2.2 side 2 no_data 9999 angle 15 11 21 31 41 12 22 32 42 13 23 33 43
de Sousa LM, Leitão JP. 2016. HexASCII: a file format for cartographical hexagonal grids International Journal of Geographical Information Science. In review. https://github.com/ldesousa/HexAsciiBNF
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Why Hexagons?
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The hexagonal CAFlood worlds
Water levels
North-South velocities
Northwest-Southeast velocities
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Why Hexagons?
Southwest-Northeast velocities
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EAT8a Test
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EAT8a Test
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The EAT8a test
Rain and water inflow events • Real topography • 966 x 406 meters area • 4 m2 cells • Total simulation time: 18 000 seconds • Rain event: 400 mm/hr in the [60, 240] seconds interval • Water inflow event: • • • •
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inflow area of 1x1 m at the north east corner active in the [1 200; 3 300] seconds interval gradual volume increase and decrease volume inflow peak of 2 m3 /s at 2 300 seconds
EAT8a Test
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Digital elevation models
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EAT8a Test
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Results
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Results
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Execution times
Single processor run • Squares : 18m 25s • Hexagons : 24m 30s • 33% increase in run time • There is one extra velocities world!
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Results
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Flooded areas Areas over 100 m2 with more than 0.15 m of water depth
0
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Results
Flood areas (hexagons) Flood areas (squares) 125
250 m
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Peak Water Depth
Water depth (m) ]0; 0.15] ]0.15; 0.3] ]0.3; 0.45] ]0.45; 0.6] ]0.6; 1]
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Results
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Peak Water Velocity
Velocity (m/s) >1.5 ]1.2; 1.5] ]0.8; 1.2] ]0.4; 0.8] ]0; 0.4]
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Results
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Analysis
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Analysis
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Peak Water Depth Peak Water Depth
Peak Water Depth shape
0.20
Hexagons Squares
60
0.15
density
Water depth (m)
40
0.10
20 0.05
0
0.00 0.00
0.02
0.04
0.06
Water depth (m)
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Hexagons
Squares
Cell shape
Analysis
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Peak Water Velocity Peak Water Velocity
Peak Water Velocity 1.25
shape Hexagons Squares 6 1.00
Velocity (m/s)
0.75
density
4
0.50
2
0.25
0
0.00 0.00
0.25
0.50
0.75
1.00
Velocity (m/s)
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Hexagons
Squares
Cell shape
Analysis
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Water Velocity at 600 seconds Water Velocity at 600 seconds
Water Velocity at 600 seconds 1.25
shape Hexagons Squares 6 1.00
Velocity (m/s)
0.75
density
4
0.50
2
0.25
0
0.00 0.00
0.25
0.50
0.75
1.00
Velocity (m/s)
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Hexagons
Squares
Cell shape
Analysis
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Water Velocity at 2 400 seconds Water Velocity at 2 400 seconds
Water Velocity at 2 400 seconds 1.25
shape Hexagons Squares 6 1.00
Velocity (m/s)
0.75
density
4
0.50
2
0.25
0
0.00 0.00
0.25
0.50
0.75
1.00
Velocity (m/s)
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Hexagons
Squares
Cell shape
Analysis
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Flood Hazard Maximum water depth and velocity at 600 and 2 400 seconds
600 sec. Squares 600 sec. Hexagons 2 400 sec. Squares 2 400 sec. Hexagons
Defra/Environment Agency Flood and Coastal Defence. Flood Risks to People Phase 1. R&D Technical Report FD2317. de Sousa et alia
Analysis
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Summary and future work
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Summary and future work
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Summary
Conclusions so far
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Summary and future work
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Summary
Conclusions so far • Hexagons are slower: one extra velocities world
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Summary and future work
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Summary
Conclusions so far • Hexagons are slower: one extra velocities world • Flooded areas are similar, terrain aspect is the main flow driver
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Summary and future work
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Summary
Conclusions so far • Hexagons are slower: one extra velocities world • Flooded areas are similar, terrain aspect is the main flow driver • Higher number of cells with low water depth with hexagons
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Summary and future work
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Summary
Conclusions so far • Hexagons are slower: one extra velocities world • Flooded areas are similar, terrain aspect is the main flow driver • Higher number of cells with low water depth with hexagons • Relevant differences in water velocity
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Summary and future work
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Summary
Conclusions so far • Hexagons are slower: one extra velocities world • Flooded areas are similar, terrain aspect is the main flow driver • Higher number of cells with low water depth with hexagons • Relevant differences in water velocity • Are squared automata underestimating risk?
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Summary and future work
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Future Work
Further developments
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Summary and future work
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Future Work
Further developments • Confirm flood risk assessment with hexagons
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Summary and future work
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Future Work
Further developments • Confirm flood risk assessment with hexagons • Lower resolution grids: any advantages of hexagonal automata vs. squared automata?
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Summary and future work
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Future Work
Further developments • Confirm flood risk assessment with hexagons • Lower resolution grids: any advantages of hexagonal automata vs. squared automata? • Parallelisation - can it improve hexagonal automata performance?
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Summary and future work
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Thank you! http://www.eawag.ch/en/department/sww/projects/caddies/ https://git.exeter.ac.uk/groups/caddies
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Summary and future work
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Grid Geometry Cell and neighbourhood dimensions for 1 m2 cells
0.62
1
1.18 1
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1.42
Summary and future work
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