Digital Topography: Should you choose a TIN or raster interpolation of the landscape?

Lisa Walsh
The University of Maryland, Geology Department
Author Profile

Shortcut URL: https://serc.carleton.edu/48146

Location

Continent: Asia
Country: Nepal
State/Province:Annapurna Range
City/Town: Pokhara
UTM coordinates and datum: none

Setting

Climate Setting: Humid
Tectonic setting: Continental Collision Margin
Type: Process, Computation

Figure 1: SRTM voids in the central Nepalese Himalaya Details


Figure 2: A) Photo of Modi Khola valley in Annapurna Range of central Nepal with Macchapucchare summitt (looking toward Northeast), B) Photo of Macchapucchare summitt, C) TIN interpolation of Macchapucchare summitt, D) Multiquadric radial basis function interpolation of Macchapucchare summitt. Details


Figure 3: The TIN interpolation created a continuous digital topographic surface by connecting a triangulated network of lines between known points of elevation along contour lines while a raster interpolation creates a continuous digital topographic surface by placing a grid of regularly spaced points over contour lines. Details


Figure 4: A) 3-D view of contour lines of Macchapucchare summit looking due North, B) TIN triangulation network, C)Interpolated TIN surface, D) Slope map of Macchapucchare summitvshowing irregular flat terraces created from TIN interpolation, E) Slope map of Macchapucchare summit showing ellimination of irregular flat terraces using the multiquadric radial basis function. Details


Description

The recent explosion of Geographic Information System (GIS) tools enable geoscientists to visualize the Earth's surface in three dimensions using digital topography. Digital topography can be represented in either vector or raster format. Vector format uses a series of irregularly spaced elevation points connected by lines into a triangulated irregular network (TIN). Raster format divides the topographic surface into equally spaced intervals or a gridded array and then displays the elevation value for each grid cell (called a digital elevation model or DEM). Choosing to represent digital topography in either vector or raster (TIN or DEM) format depends on the type of GIS analysis a user wants to perform.

The DEM type decision depends on the analysis of interest

Digital vector topography can clearly define boundaries, such as valley floors or ridge lines. Often, digital data acquired from satellites are collected in a gridded fashion. Examples of satellite derived gridded data are precipitation data, landcover, or vegetation type. More qualitative cultural data, such as population, employment, election results, etc are usually collected by state or county agencies and are visualized in vector format. The collection methods for the data researchers want to compare to digital topography and the importance of boundaries plays a significant role in the decision to represent topography as a TIN or DEM.

A case study from the Annapurna Range of Central Nepal

In 2000, the shuttle radar topography mission (SRTM) collected rasterized elevation data across 80% of the globe, generating a DEM covering the Earth's surface from 60°N to 60°S latitude [JPL, 2000]. The SRTM project yielded publically available, high resolution DEMs at 1 arc-second (~30 m) resolution in the United States and 3 arc-second (~90 m) worldwide. Unfortunately, glaciated and extremely steep topography reflected radar beams away from the shuttle receiver during the data collection process, creating data voids in some mountainous terrains [Luedeling et al., 2007]. For example, SRTM data surrounding the mountain peaks in the central Nepalese Himalaya contain approximately 4,200,000 km2 of data voids (Figure 1). This absence of SRTM data makes models of mountain summits in the Himalaya difficult to visualize.

One way to resolve this data void problem is to digitize contour lines from topographic maps and use the elevation data from the contour lines to create a TIN or DEM. Digital topography can be created by extracting elevation points from digitized contour lines to interpolate the shape of the surface between the elevation points. Macchapucchare, or the "fish tail" summit, is a mountain peak in the Annapurna Range of central Nepal. The distinctive "fish tail" or double peak topography of Macchapucchare's summit make it an ideal location to study the differences between the TIN and DEM interpolation methods (Figure 2). The Ghandruk topographic map is the topographic map that contains the Macchapucchare summit. SRTM data for the Ghandruk topographic map region contain 9,713 km2 of data void area (Figure 1).

TIN Interpolation

Interpolation is a method used to create new elevation points using information from a discrete set of known elevation points. The new elevation points are combined with known elevation points to create a continuous plane representing the Earth's surface. Before creating the interpolation, digitized contour lines must be converted to points. The known elevation points are concentrated along the trace of the contour lines, leaving large gaps of unknown elevation points between contour lines. If the elevation points were spaced in a regular gridded fashion, the elevation values could automatically be converted into a raster DEM. Typically the TIN interpolation method works best for creating digital topography from irregularly spaced known elevation points, like points extracted from contour lines. The TIN interpolation produces a triangulated network that builds connections between each known elevation points (Figure 3). The elevation can be calculated at any location on the TIN using the geometry of the triangle faces. However, the TIN interpolation sometimes creates irregular flat terraces on ridge lines and in valleys resulting from the connection of the different triangle faces [Ware, 1998; Barbalic and Omerbegovic, 1999]. The slope map in figure 4d illuminates these unrealistic irregular flat terraces not seen in the actual topography of Macchapucchare.

Raster Interpolation

There are several different types of raster interpolations, depending on how you want to fit a gridded surface to your contour lines or other elevation source. The multiquadric radial basis function is a raster interpolation that reduces the appearance of irregular flat terraces seen in the topography in a the TIN interpolation (Figure 4e). The multiquadric radial basis function uses a model to fit a surface to the known, irregularly spaced elevation points [Hardy, 1990; Buhmann, 2003]. The function searches around each known elevation point in a radial manner and locates the next closest known elevation point. Closer elevation points are weighted with more importance in the calculation of the unknown elevation points located between the two known elevation points. Therefore, the proximity of known elevation points controls the computation of the interpolated surface. Alternatively, valley bottom (from river location) and ridge lines can be digitized and incorporated into the TIN interpolation method to minimize irregular flat terraces and smoothing of ridge lines.

TIN vs. Raster interpolation of Macchapucchare (The "fish tail" peak)

Both the TIN interpolation and multiquadric radial basis function interpolations of points from digitized contour lines generate topography to fill data voids in the SRTM data. The TIN interpolation more accurately defines the "fish tail" peak of Macchapucchare, but also produces flat irregular terraces in the digital topography. The multiquadric radial basis function essentially eliminates flat irregular terraces from the digital topography, but also generates some smoothing of Macchapucchare's distinctive double peak (Figure 2). The choice between a vector (TIN interpolation) or raster (multiquadric radial basis function) representation of the Earth's surface depends on which topographic characteristics you want to explore in the landscape. The TIN interpolation produces a more realistic visual representation, while the multiquadric radial basis function generates more accurate representation and measurement of slope.

Acknowledgments

Special thanks to Aaron Martin, The University of Maryland, for making this project possible by providing detailed field maps and photography of the Modi Khola valley [Martin et al., 2010]. Tank Ojha of the University of Arizona, kindly provided digitized contour lines for the Modi Khola valley which were interpolated into a DEM by Tom Fedenczuk at the University of Hawaii.

Associated References

  • Barbalic, D., and V. Omerbegovic (1999), Correction of horizontal areas in TIN terrain modeling – algorithm, ESRI International User Conference, http://proceedings.esri.com/library/userconf/proc99/proceed/papers/pap924/p924.htm.
  • Buhmann, M.D. (2003), Radial Basis Functions: Theory and Implementations, Published by Cambridge University Press, Cambridge, United Kingdom, ISBN 0521633389, 9780521633383. 259 pages.
  • Ferranti, Johnathan. Digital Elevation Data of Asia. http://www.viewfinderpanoramas.org/dem3.html
  • Hardy, R.L. (1990), Theory and applications of the multiquadric biharmonic method, Computers and mathematics with applications, 19, 163-208.
  • Ware, J.M. (1998), A procedure for automatically correcting invalid flat triangles occurring in triangulated contour data, Computers & Geosciences, 24(2), 141-150.
  • Jet Propulsion Laboratory (JPL), NASA, California Institute of Technology, 2000, Shuttle Radar Topography Mission: The mission to map the world. http://www2.jpl.nasa.gov/srtm/
  • Luedeling et al., 2007, Filling the voids in the SRTM elevation model – A TIN-based delta surface approach, ISPRS, Journal of Photogrammertry & Remote Sensing, v. 62, p. 283-294.
  • Martin, A.J., J. Ganguly, and P.G. DeCelles (2010), Metamorphism of Greater and Lesser Himalayan rocks exposed in the Modi Khola valley, central Nepal, Contributions to Mineralogy and Petrology, v. 159, p. 203-223, doi:10.1007/x00410-009-0424-3.
  • NASA JPL - Shuttle Radar Topography Mission. http://www2.jpl.nasa.gov/srtm/index.html
  • Walsh, L.S., 2009, Topographic signatures in the Himalaya: A geospatial survey of the interaction between tectonics and erosion in the Modi Khola valley, central Nepal [M.S. Thesis]: University of Maryland, 218 pages.