Drainage

Drainage

Paths

derived from TIN-based Digital Elevation Models

Graduate student:Henrique Rennó de Azeredo FreitasAdvisors:Sergio RosimJoão Ricardo de Freitas OliveiraCorina da Costa Freitas

National Institute for Space ResearchImage Processing DivisionSão José dos Campos - Brazil2013

INPE - Graduate Program in Applied Computing

Drainage

Paths

derived from TIN-based Digital Elevation Models

Summary

Introduction

Related Work and MotivationDigital Elevation ModelsTriangulated Irregular Network (TIN)Delaunay and Constrained Delaunay TriangulationFlat AreasDrainage PathsResultsConclusions and Future WorkReferences

Introduction

Terrain

modeling

and analysis raise challenges in several areasMany important and useful results are applied in HydrologyTechniques may change improving quality of results and time efficiency

Drainage Paths derived from TIN-based Digital Elevation Models

Related

Work

and

Motivation

Some techniques developed to calculate drainage paths from TINs:Plane gradient of triangles gives flow direction (Jones et al., 1990)Different conditions between TIN facets (Silfer et al., 1987)Trickle path traces sequence of edges and vertices from terrain features (Tsirogiannis, 2011)Geographic Information Systems (GIS) usually offer hydrology-specific functionalitiesMost Hydrology applications in GIS are limited to regular grids (raster) terrain models as they are much common and simple structures

Drainage Paths derived from TIN-based Digital Elevation Models

Digital

Elevation

Models

Digital Elevation Models are representations of terrain surfacesDrainage patterns from DEMs are very important in HydrologySome DEM representations include: Regular Grids Triangulated Irregular Networks (TIN) Contour Lines

Regular

Grid

Contour

Lines

TIN

Drainage

Paths derived from TIN-based Digital Elevation Models

Triangulated

Irregular Networks

TINs

are

calculated from surface-specific points with (x, y, z) coordinatesThey are good approximations representing main features of the terrainDelaunay Triangulation is commonly used (de Berg et al., 2008)

TIN

and Contour Lines

Drainage Paths derived from TIN-based Digital Elevation Models

Delaunay

Triangulation

Circumcircle

criteria maximizes minimum angle, avoiding skinny trianglesIncremental algorithm defines a hierarchy tree structure for storage of triangles and its time complexity is O(n log n) Points are inserted one at a time locally modifying the triangulation Future C++ implementation with the Terralib library (Câmara et al., 2000)

Delaunay

Criteria

Incremental algorithm tree structure

Drainage Paths derived from TIN-based Digital Elevation Models

Constrained

Delaunay

Triangulation

Edges of the original Delaunay Triangulation could intersect contour lines segments resulting in wrong terrain featuresContour lines segments are considered as restriction lines defining a Constrained Delaunay Triangulation Intersections are removed by edge rotations

Triangulations before and after removing intersections

Drainage

Paths derived from TIN-based Digital Elevation Models

Flat

Areas

Triangles

containing all vertices with same elevation valuesIt is not possible to determine flow directions, creating discontinuities Solution: new critical points are inserted into the triangulation with interpolated elevation valuesCritical points are located on 2 types of edges

Flat triangles and critical edges

Drainage

Paths derived from TIN-based Digital Elevation Models

Flat

Areas

Paths

of

flat triangles define the critical points to be linearly interpolatedElevations of neighboring contour lines help indicate upward/downward interpolationBranches found are also processed using previously interpolated values

Paths for interpolation of critical points

Drainage

Paths derived from TIN-based Digital Elevation Models

Drainage

Paths

Each

triangle defines a plane surface through its 3 verticesDrainage paths are calculated from a starting point in a triangle following the path of steepest descent given by the gradient of each plane

Plane equation coefficients and plane gradient

Paths

of

steepest descent in a TIN

Drainage Paths derived from TIN-based Digital Elevation Models

Drainage

Paths

Gradient

vectors indicate how flow continues from a vertex or another point on the edgeFlow can continue either through an adjacent triangle or along an edge

Gradient vectors define drainage paths

Drainage Paths derived from TIN-based Digital Elevation Models

Drainage

Paths

In

this

work, drainage paths are calculated starting at each triangle centroid as they approximately represent their elevationsEvery starting point elevation is considered as a priority value and starting points are arranged from highest to lowest elevationsDrainage paths being traced are connected to paths already definedAll drainage paths form a graph structure where every intersection defines a graph node and gradient vectors segments are its edges connecting the nodes

Drainage Paths derived from TIN-based Digital Elevation Models

Drainage

Paths

Nodes

and

edges of drainage paths graph

Drainage Paths derived from TIN-based Digital Elevation Models

Results

Results

were

obtained by processing contour lines and elevation points of São José dos Campos - SPInput data from a database named “Cidade Viva” made publicly available since 2003 by the Geoprocessing Service of the Urban Planning DepartmentApproximately 200000 points with xy resolution of nearly 20 m and elevation differences between contour lines of 5 mThe database contains a drainage network that is considered as a reference drainage

Drainage Paths derived from TIN-based Digital Elevation Models

Results

Drainage

network

from

the “Cidade Viva” databaseover a RapidEye image

Drainage Paths derived from TIN-based Digital Elevation Models

Results

Drainage

paths converge to

the

reference drainage network

Drainage

Paths derived from TIN-based Digital Elevation Models

Results

Drainage

paths over a TIN

Drainage

Paths

derived

from TIN-based Digital Elevation Models

Results

Drainage

networks

Drainage

Paths

derived

from TIN-based Digital Elevation Models

Results

Drainage

networks:

reference

drainage (left) and tin-based drainage (right)

Drainage Paths derived from TIN-based Digital Elevation Models

Results

Drainage

paths converge to

the

reference drainage network thus forming drainage patterns very close to the real hydrologic processes governed by the terrain surfaceThe primary and most significant concern to be considered is the quality of the results altough computational times are also important

Number of pointsNumber of trianglesNumber of graph nodesTotal execution time (s)500001488573061061.951000002650695373053.331500003966587993284.9220000051243710331096.26

Executed on a PC with Intel Core i7 2.93 GHz CPU and 8 GB of RAM memory

Drainage Paths derived from TIN-based Digital Elevation Models

Conclusions

Triangulated

irregular

terrain

models are structures that can efficiently represent terrain surfacesDrainage paths defined by plane gradients are good approximations to drainage patterns of real-world hydrologic processesProcedures and algorithms developed for processing TINs have low computational time complexitiesThe methods proposed in this work for removing flat areas, interpolating critical points elevations and delineating drainage paths are efficient and consistent with real-world water flow distribution

Drainage Paths derived from TIN-based Digital Elevation Models

Future Work

Pit

removal

in order to avoid flow discontinuitiesDefinitions of procedures for delineating watershed from the upstream nodes of the drainage networkProposal of a method for comparison of drainage networks obtained from regular grids and TINsDetailed analysis and further optimizations in the algorithms to improve computational timesIntegration of the triangulation structure and the proposed methods into the TerraHidro platform with the Terralib library

Drainage Paths derived from TIN-based Digital Elevation Models

References

Barbalić

, D.,

Omerbegović

, V. (1999). “Correction of horizontal areas in TIN terrain modeling–algorithm”, http://proceedings.esri.com/library/userconf/proc99/proceed/papers/pap924/p924.htmCâmara, G., Souza, R. C. M., Pedrosa, B. M., Vinhas, L., Monteiro, A. M. V., Paiva, J. A., Carvalho, M. T., Gattass, M. (2000). TerraLib: technology in support of GIS innovation. In II Brazilian Symposium on Geoinformatics, GeoInfo2000, pages 1–8. De Berg, M., Cheong, O., Van Kreveld, M. and Overmars, M. (2008). Computational Geometry – Algorithms and Applications, Springer, 3rd edition.

Drainage Paths derived from TIN-based Digital Elevation Models

References

Jones, N. L., Wright, S. G.,

Maidment

, D. R. (1990). Watershed delineation with triangle-based terrain models. In

Journal of Hydraulic Engineering, pages 1232–1251.Prefeitura Municipal de São José dos Campos. (2003). Base de Dados “Cidade Viva”. Departamento de Planejamento Urbano, Serviço de Geoprocessamento (in Portuguese).Tsirogiannis, C. P. (2011). Analysis of flow and visibility on triangulated terrains. PhD Thesis. Eindhoven University of Technology. Zhu, Y. and Yan, L. (2010). An improved algorithm of constrained Delaunay triangulation based on the diagonal exchange. In 2nd International Conference on Future Computer and Communication, pages 827–830.

Drainage Paths derived from TIN-based Digital Elevation Models

Thank

you very much!

Drainage

Paths derived from TIN-based Digital Elevation Models