Sea-Rise Flooding on Massive Dynamic Terrains

Authors Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, Jungwoo Yang

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Author Details

Lars Arge
  • MADALGO, Aarhus University, Denmark
Mathias Rav
  • SCALGO, Aarhus, Denmark
Morten Revsbæk
  • SCALGO, Aarhus, Denmark
Yujin Shin
  • MADALGO, Aarhus University, Denmark
Jungwoo Yang
  • SCALGO, Aarhus, Denmark

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Lars Arge, Mathias Rav, Morten Revsbæk, Yujin Shin, and Jungwoo Yang. Sea-Rise Flooding on Massive Dynamic Terrains. In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Predicting floods caused by storm surges is a crucial task. Since the rise of ocean water can create floods that extend far onto land, the flood damage can be severe. By developing efficient flood prediction algorithms that use very detailed terrain models and accurate sea-level forecasts, users can plan mitigations such as flood walls and gates to minimize the damage from storm surge flooding. In this paper we present a data structure for predicting floods from dynamic sea-level forecast data on dynamic massive terrains. The forecast data is dynamic in the sense that new forecasts are released several times per day; the terrain is dynamic in the sense that the terrain model may be updated to plan flood mitigations. Since accurate flood risk computations require using very detailed terrain models, and such terrain models can easily exceed the size of the main memory in a regular computer, our data structure is I/O-efficient, that is, it minimizes the number of I/Os (i.e. block transfers) between main memory and disk. For a terrain represented as a raster of N cells, it can be constructed using O(N/B log_M/B N/B) I/Os, it can compute the flood risk in a given small region using O(log_B N) I/Os, and it can handle updating the terrain elevation in a given small region using O(log²_B N) I/Os, where B is the block size and M is the capacity of main memory.

Subject Classification

ACM Subject Classification
  • Information systems → Geographic information systems
  • Computational geometry
  • I/O-algorithms
  • merge tree
  • dynamic terrain


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  1. Pankaj K. Agarwal, Lars Arge, Gerth Stølting Brodal, and Jeffrey S. Vitter. I/O-efficient Dynamic Point Location in Monotone Planar Subdivisions. In Proc. 10th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 11-20, 1999. Google Scholar
  2. Pankaj K Agarwal, Lars Arge, and Ke Yi. I/O-efficient batched union-find and its applications to terrain analysis. ACM Trans. Algorithms, 7(1):11, 2010. Google Scholar
  3. Pankaj K. Agarwal, Thomas Mølhave, Morten Revsbæk, Issam Safa, Yusu Wang, and Jungwoo Yang. Maintaining Contour Trees of Dynamic Terrains. In 31st International Symposium on Computational Geometry, volume 34, pages 796-811, 2015. Google Scholar
  4. Alok Aggarwal and Jeffrey Vitter. The Input/output Complexity of Sorting and Related Problems. Communications of the ACM, 31(9):1116-1127, 1988. Google Scholar
  5. Cici Alexander, Lars Arge, Peder Klith Bøcher, Morten Revsbæk, Brody Sandel, Jens-Christian Svenning, Constantinos Tsirogiannis, and Jungwoo Yang. Computing River Floods Using Massive Terrain Data. In Geographic Information Science, pages 3-17. Springer International Publishing, 2016. Google Scholar
  6. Lars Arge. External memory data structures. In Handbook of massive data sets, pages 313-357. 2002. Google Scholar
  7. Lars Arge, Jeffrey S Chase, Patrick Halpin, Laura Toma, Jeffrey S Vitter, Dean Urban, and Rajiv Wickremesinghe. Efficient Flow Computation on Massive Grid Terrain Datasets. GeoInformatica, 7(4):283-313, 2003. Google Scholar
  8. Lars Arge, Mathias Rav, Sarfraz Raza, and Morten Revsbæk. I/O-Efficient Event Based Depression Flood Risk. In Proc. 9th Workshop on Algorithm Engineering and Experiments, pages 259-269. SIAM, 2017. Google Scholar
  9. Lars Arge and Morten Revsbæk. I/O-efficient contour tree simplification. In International Symposium on Algorithms and Computation, pages 1155-1165. Springer, 2009. Google Scholar
  10. Lars Arge, Morten Revsbæk, and Norbert Zeh. I/O-efficient computation of water flow across a terrain. In Proceedings of the 26th annual Symposium on Computational Geometry, pages 403-412. ACM, 2010. Google Scholar
  11. Lars Arge, Yujin Shin, and Constantinos Tsirogiannis. Computing Floods Caused by Non-Uniform Sea-Level Rise. In Proc. 20th Workshop on Algorithm Engineering and Experiments, pages 97-108. SIAM, 2018. Google Scholar
  12. Lars Arge, Laura Toma, and Jeffrey Scott Vitter. I/O-efficient Algorithms for Problems on Grid-based Terrains. Journal of Experimental Algorithmics, 6:1, 2001. Google Scholar
  13. Danish Geodata Agency. Elevation Model of Denmark:Terræn (0.4 meter grid)., 2015. Google Scholar
  14. Andrew Danner. I/O Efficient Algorithms and Applications in Geographic Information Systems. PhD thesis, Department of Computer Science, Duke University, 2006. Google Scholar
  15. Andrew Danner, Thomas Mølhave, Ke Yi, Pankaj K Agarwal, Lars Arge, and Helena Mitásová. TerraStream: from Elevation Data to Watershed Hierarchies. In Proc. 15th Annual ACM International Symposium on Advances in Geographic Information Systems, page 28. ACM, 2007. Google Scholar
  16. Herbert Edelsbrunner, John Harer, and Afra Zomorodian. Hierarchical morse-smale complexes for piecewise linear 2-manifolds. Discrete and computational Geometry, 30(1):87-107, 2003. Google Scholar
  17. Herman J. Haverkort and Jeffrey Janssen. Simple I/O-efficient Flow Accumulation on Grid Terrains. CoRR, abs/1211.1857, 2012. URL:
  18. Robert E Tarjan and Uzi Vishkin. An efficient parallel biconnectivity algorithm. SIAM Journal on Computing, 14(4):862-874, 1985. Google Scholar
  19. Robert Endre Tarjan and Uzi Vishkin. Finding biconnected componemts and computing tree functions in logarithmic parallel time. In 25th Annual Symposium on Foundations of Computer Science, pages 12-20. IEEE, 1984. Google Scholar
  20. Jeffrey Scott Vitter. Algorithms and data structures for external memory. Foundations and Trendsregistered in Theoretical Computer Science, 2(4):305-474, 2008. Google Scholar
  21. Jungwoo Yang. Efficient Algorithms for Handling Massive Terrains. PhD thesis, Department of Computer Science, University of Aarhus, 2015. Google Scholar