Delineation and characterisation of hydrological watersheds based on

the Delaunay triangulation approach

Subjects

Methods

Results Conclusions

Martial Oggier, Hydrology Group, Department of Geography, University of Berne, Switzerland, martial_oggier@hotmail.com

The procedure in this work consists of the stepsshown in figure 1. The first step is to create a TINfrom DEM. On the one hand, this involves to thinout the DEM or in other words to select thesignificant points of the DEM. This is done inArcGIS by using the function “Raster to Multipoint”(esri 2016). Here, a z-value can be determined.This is the maximum allowable difference betweenthe height of the input DEM and the height of theoutput TIN. On the other hand, the selected pointsare triangulated with the R-package “Rtriangle”(Shewchuk 1996) according to the Delaunaycriterion. The triangulation conforms to theDelaunay criterion if the circumcircle of the threevertices forming a triangle contains no other vertex(figure 2).

The next step is the pre-processing of the terrainmodel. This is crucial because flat areas and pitshinder flow routing and therefore, it is not possibleto delineate the watershed properly. Flat areas areremoved by slightly modifying the heights of theflat triangle’s vertices. The method to remove sinksis to find a lower point in the neighbourhood and tolower the points in between in a descending way. Asimple example is illustrated in figure 3. Numbersin parenthesis indicate the heights of the points.

The last step is to delineate the watershed. Forthis, an outlet point must be selected. Each flowsection is defined by a from-node and a to-node,and the flow sections are connected by this nodes.So, the triangles that constitute the watershed arefound by tracking the upstream flow sectionsstarting at the outlet point.

Digital terrain models (DTMs) are used in manyscientific fields and have received an increasinginterest in the last decades. The two mostimportant forms of DTMs are the well-knownraster-based digital elevation model (DEM) and thetriangulated irregular network (TIN). In hydrology,DTMs are especially used to extract drainage

to eight directions and (4) loss of elevationinformation due to the interpolation process.Therefore, the main aim of this work is to developan algorithm for determining flow paths anddelineating watersheds on TINs. The investigationareas are the Turtmanntal, the alpine valley of riverTurtmänna and the watershed of river Broye.

networks and watersheds. Most algorithms toderive hydrologic structures are implemented forDEMs because of their simplicity and availability.However, DEMs have some distinctdisadvantages: (1) their non-continuous 2D datastructure, (2) they are tied to a constant resolution,(3) calculations of gradients are usually restricted

The red lines in figure 6 and figure 8 represent theborder of the watersheds defined by the FOEN.Only small differences can be observed comparingthese watershed areas with the ones derived fromthe TIN. These results indicate that the TIN is aneffective alternative to extract drainage networksand watersheds. As the TIN watershed is three-dimensional, the terrain is represented morerealistic and it is possible to calculate the 3D areaof the watershed (table 1). For the watershed ofthe Turtmänna the 3D area is about 19% greaterthan the 2D area, for the watershed of the Broyethere is a difference of about 2%. As aconsequence, for water balance calculationsshould be considered a 3D TIN derived watershedarea, at least in alpine regions.

Figure 2: Delaunay Triangulation (Jones et al. 1990)

Figure 1: Flow chart of the work steps

Figure 5: flow paths Turtmanntal March 2017

After pre-processing the data, the flow paths canbe determined. The flow paths are composed ofdifferent flow sections, these flow sections arerepresented in different colours in figure 4. The firstflow section (blue) starts at the centroid (blackdots) of each triangle and follows the path ofsteepest descent to the point where it intersectsthe edge of the triangle (red dots). Then theadjacent triangle is tested if it slopes downwardfrom the edge with the point of intersection or if itslopes towards that edge. In case of a downhillslope, the water flows over the face of the adjacenttriangle and the flow path continues to the point ofintersection of this triangle (flow section two,magenta). In case of an uphill slope, the waterfollows the edge because the two triangles form achannel. Flow section three (green) is defined by

DE

M to

TIN

Thin out high resolution data

Pre

-pro

cess

ing

Removal ofFlat Areas

Hyd

rolo

gy

DelaunayTriangulation

Removal ofPits

DelineateWatershed

DetermineFlow Paths

Figure 3: Removal of a pit (Silveira and van Ostrum 2007)

the point of intersection and the lower endpoint ofthe edge. Finally, there is a need to consider thesituation when the flow path meets a vertex. Here,the water can either flow across a triangle or followan edge like in the situation before. All downwardsurrounding triangles and edges are tested. If atriangle passes the test, the flow path continuesacross the face of this triangle to the point ofintersection (flow section 4, light blue). If an edgepasses the test, the flow path continues along thisedge (flow section 5, orange). All flow paths makethe entire drainage network.

Figure 4: Flow sections on a simple TIN

Figure 6: watershed Turtmänna

Literature: esri, Environmental Systems Research Institute (2016): Raster to Multipoint. http://desktop.arcgis.com/en/arcmap/10.3/tools/3d-analyst-toolbox/raster-to-multipoint.htm. Zugriff: 28.03.2017. Shewchuk JR (1996): Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In Lin MC and Manocha D (eds.), Applied Computational Geometry: Towards Geometric Engineering, volume 1148 series Lecture Notes in Computer Science, pp. 203-222. Springer-Verlag.

Turtmänna Broyeinput points/input triangles 138‘571/277’790 102‘200/205’083flow sections in total 580’385 444‘634 area (FOEN/2D/3D) 112.6/108.5/129.1 km2 415.9/421.6/429.5 km2

mean area of triangles 1181 4321altitude (min./mean/max.) 618/2442/4149 m a.s.l. 441/719/1513 m a.s.l.

Table 1: Characteristics of the TINs / watersheds

Figure 7: flow paths region of the Broye Figure 8: watershed Broye