University of Maryland-College Park
Topographic Maps part of Cutting Edge:Career Development:Pursuing an Academic Career 2010:Teaching Activities
This geology lab is designed to teach students the basic skills needed to read, construct, and interpret topographic maps. The goal of this lab is to help students build direct connections between the topography and volcanic history of Mt. St. Helens.
Topographic signatures of lithologies in the Modi Khola valley of central Nepal part of Vignettes:Vignette Collection
Rock resistivity to erosion plays a vital role in the evolution of the Earth's topography. Since different rock types exhibit different levels of resistivity to erosion, the more resistant rock types tend to develop more prominent topographic formations in the landscape overtime. Comparing topographic parameters, specifically slope and curvature, of the Earth's surface for different rock types using Geographic Information Systems (GIS) can help us advance the frontier of landslide prediction and our understanding of mountain belt formation and destruction. How can you extract a topographic signature of a rock type from the landscape? GIS software enables topographic characteristics to be extracted relatively simply and quickly from digital elevation models (DEMs) of the Annapurna range of central Nepal. The Modi Khola flows across a ductile shear zone which places high-grade Greater Himalayan metasedimentary rocks on medium-grade Lesser Himalayan metasedimentary rocks near the center of the Himalayan fold-thrust belt in map view (Figure 2). The frequent occurrence of landslides, detailed geologic maps by Martin et al. (2010), and a 25 m resolution DEM created from digitized contour lines provide a unique opportunity to illustrate relationships between topography and rock type in the Modi Khola valley of central Nepal. In detail, the Greater Himalayan metasedimentary rocks contain gniess and schist and interbedded quartzite; Calc-silicate schist, calc-silicate gneiss, and marble; and Granitic augen gneiss. The Lesser Himalayan metasedimentary rocks are comprised of a variety of metamorphosed sandstone, slate, marble, quartzite, phyllite, and the Ulleri granitic gneiss. Differences in composition for each rock type could be reflected in the topography based on the resistance to erosion of each lithology. Slope and curvature of the landscape for each rock type Slope can be extracted directly from the topography in ArcGIS using the slope function within the spatial analyst toolbox. In a GIS system, the slope is defined as the rate of change of elevation in the direction of the steepest descent at each grid cell in the DEM. Curvature describes how much a surface is curved at a particular point in the landscape. Mathematically, curvature is defined as the reciprocal of the radius of a circle that is tangent to a point on a curve [Roberts, 2001]. Tightly folded terrain has large curvature values, while flat terrain has zero curvature. Roberts (2001) uses the surface skin of an apple and the mathematical plane carved from a knife to help visualize the concept of curvature. If you cut the top of an apple off, it creates a much smaller circle than if you slice an apple through the middle. The curvature of the smaller circle will be much larger because of the tighter bend of the line required to complete the circle. An infinite number of cuts can be made through the apple, allowing an infinite number of curvature values to be extracted. According to Roberts (2001), the most useful subset of curvatures is defined by planes which are orthogonal to the surface: maximum and minimum curvature. Averaging maximum and minimum curvature yields the mean curvature. The slope and mean curvature grids created from a 25 m DEM of the Modi Khola valley are shown in Figure 3. Zonal Statistic Maps Once slope and curvature grids are generated, slope and curvature values can be extracted for each lithologic unit in the study region using the zonal statistics tool in ArcGIS. Using the zonal statistics tool you can create a series of maps coloring each lithologic unit by the mean, minimum, maximum, range, and standard deviation of the slope and curvature values distributed across the topography in each rock unit. The zonal slope statistics maps illustrate significantly high slope values in the Greater Himalayan rocks that vary from 1 to 79 degrees slope. The Lesser Himalayan rocks tend to have lower slope values than Greater Himalayan rocks and vary only between 1 and 65 degrees slope. Slope values do not increase from south to north consistently, but rather fluctuate as they cross different lithologic units. Formation II, Lower foreland basin strata, undivided Gondwanas, Dhading, and the Ulleri granite all exhibit significantly higher mean slope values than other lithologies (Figure 4). Consequently, dips and peaks that occur in slope data from the north to the south are well reflected by the average curvature data. Peaks in slope data correspond to positive curvature values or convex topography, while dips in slope data relate to negative curvature values or concave topography. The zonal mean curvature maps visually delineate this fluctuation of positive to negative curvature across the range (Figure 5). Overall, the topographic fingerprints of lithologies in the Modi Khola valley exhibit only subtle differences in slope and curvature. Results and Conclusions Studies of lithology and topography in New Zealand show that regions with varying rates of precipitation and tectonic uplift express the same average slope of 39 degrees for regions comprised of the sedimentary rock greywacke [Korup et al., 2008]. However, Korup et al. (2008) emphasize that the topographic signature of the underlying bedrock may not be reflected unless hillslopes are at the limit of their mechanical strength, which would produce landsliding. The Modi Khola valley receives extreme amounts of precipitation (up to 8 m/yr in some parts) [Bookhagen and Burbank, 2006], which produces frequent landslide events. While rock type likely plays a pivotal role in landscape evolution, perhaps extreme climatic conditions of the Himalaya altered the topography and erased or concealed the topographic signature from lithologies in the Modi Khola valley. Landslide events cover the terrain with debris, resculpting the landscape, regardless of the location of different lithologic units. The frequent mass-wasting occurring in the Modi Khola valley may have covered the expected expression of different rock types in the landscape. The subtle differences in the topographic signature of lithologies in the Modi Khola valley further illuminates the importance of other mechanisms responsible for landscape evolution processes. Perhaps extreme climatic and tectonic conditions prohibit the topographic signature of rock types to express themselves in the landscape. For each environment of study, the balance between tectonics, erosion, and composition of the Earth's material drive the landscape evolution process. The weight and role of each factor in sculpting of the landscape may vary across different environments on the Earth's surface. Acknowledgements Special thanks to Aaron Martin, The University of Maryland, for making this project possible by providing a detailed geologic map of the Modi Khola valley [Martin et al., 2010]. Tank Ojha, The University of Arizona, kindly provided digitized contour lines for the Modi Khola valley which were interpolated into a DEM by Tom Fedenczuk, The University of Hawaii.
Digital Topography: Should you choose a TIN or raster interpolation of the landscape? part of Vignettes:Vignette Collection
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.