Geoprocessing tool reference > 3D Analyst toolbox > Raster Interpolation toolset
Hydrologically correct surfaces: Topo to Raster in 3D Analyst |
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Release 9.3
Last modified January 23, 2009 |
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The Topo to Raster function is an interpolation method specifically designed for the creation of hydrologically correct digital elevation models (DEMs). Topo to Raster is based on the ANUDEM program developed by Michael Hutchinson (1988, 1989). See Hutchinson and Dowling (1991) for an example of a substantial application of ANUDEM and for additional associated references. A brief summary of ANUDEM and some applications is given in Hutchinson (1993).
Topo to Raster interpolates elevation values for a raster, imposing constraints that ensure
- A connected drainage structure
- Correct representation of ridges and streams from input contour data
Topo to Raster is the only ArcGIS interpolator specifically designed to work intelligently with contour inputs.
The following sections provide additional information on the interpolation process and tips on getting the most out of the Topo to Raster function.
The interpolation process
The interpolation procedure has been designed to take advantage of the types of input data commonly available and the known characteristics of elevation surfaces. The method uses an iterative finite difference interpolation technique. It is optimized to have the computational efficiency of local interpolation methods, such as inverse distance weighted interpolation, without losing the surface continuity of global interpolation methods, such as kriging and spline. It is essentially a discretized thin plate spline technique (Wahba, 1990), in which the roughness penalty has been modified to allow the fitted DEM to follow abrupt changes in terrain such as streams and ridges.
Water is the primary erosive force determining the general shape of most landscapes. For this reason, most landscapes have many hilltops (local maximums) and few sinks (local minimums), resulting in a connected drainage pattern. Topo to Raster uses this knowledge about surfaces and imposes constraints on the interpolation process that result in a connected drainage structure and correct representation of ridges and streams. This imposed drainage condition produces higher accuracy surfaces with less input data. The quantity of input data can be up to an order of magnitude less than normally required to adequately describe a surface with digitized contours, further minimizing the expense of obtaining reliable DEMs. The global drainage condition also virtually eliminates any need for editing or postprocessing to remove spurious sinks in the generated surface.
The program acts conservatively in removing sinks and will not impose the drainage conditions in locations that would contradict the input elevation data. Such locations normally appear in the diagnostic file as sinks. Use this information to correct data errors, particularly when processing large datasets.
The drainage enforcement process
The purpose of the drainage enforcement process is to remove all sink points in the output DEM that have not been identified as sinks in the input sink coverage. The program assumes that all unidentified sinks are errors, since sinks are generally rare in natural landscapes (Goodchild and Mark, 1987).
The drainage enforcement algorithm attempts to clear spurious sinks by modifying the DEM, inferring drainage lines via the lowest saddle point in the drainage area surrounding each spurious sink. Since sink clearance is subject to the elevation tolerance, the program is conservative when attempting to clear spurious sinks. In other words, it does not clear spurious sinks that would contradict input elevation data by more than an input tolerance.
Drainage enforcement can also be supplemented with the incorporation of stream line data. This is useful when a more accurate placement of streams is required.
The drainage enforcement can be turned off, in which case the sink clearing process is ignored. This can be useful if you have contour data of something other than elevation—for example, temperature—for which you want to create a surface.
Use of contour data
Contours have historically been the most common method for storage and presentation of elevation information. Unfortunately, this method is also the most difficult to properly utilize with general interpolation techniques. The disadvantage lies in the undersampling of information between contours, especially in areas of low relief.
At the beginning of the interpolation process, Topo to Raster uses information inherent to the contours to build a generalized drainage model. By identifying areas of local maximum curvature in each contour, the areas of steepest slope are identified, and a network of streams and ridges is created (Hutchinson, 1988). This information is used to ensure proper hydrogeomorphic properties of the output DEM and may also be used to verify accuracy of the output DEM.
After the general morphology of the surface has been determined, contour data is also used in the interpolation of elevation values at each cell.
When the contour data is used to interpolate elevation information, all contour data is read and generalized. A maximum of 50 data points are read from these contours within each cell. At the final resolution, only one critical point is used for each cell. For this reason, having a contour density with several contours crossing output cells is redundant.
Multiresolution interpolation
This program uses a multiresolution interpolation method, starting with a coarse raster and working toward the finer, user-specified resolution. At each resolution, drainage conditions are enforced, interpolation performed, and the number of remaining sinks is recorded in the diagnostic file.
Making the most of Topo to Raster
Following are a variety of topics of interest if you want to maximize available resources to create the best possible DEMs.
Creating and mosaicking adjacent rasters
Sometimes it will be necessary to create DEMs from adjacent tiles of input data. Typically, this will result when input datasets are derived from a map sheet series or when the input data must be processed in several pieces.
The Topo to Raster interpolation process uses input data from surrounding areas to define the morphology and drainage of the surface, then interpolates output values. To make the most accurate predictions at the edges of the area of interest, the extent of the input datasets should be greater than the area of interest. The Margin option provides a method for trimming the edges of output DEMs based on a user-specified distance.
Even with the above precaution, the edges of the output DEM may not be as reliable as the rest of the dataset. Without the above precaution, the edges of the dataset would be interpolated with half as much information. Because of the unreliability of the edges in DEMs, when multiple output DEMs are to be combined into a single raster, you should set a larger extent for each of the output DEMs so that they predict into the adjacent areas, overlapping a few cells with one another. Without this overlap, when merging the output DEMs, the edges may not be smooth.
Thus, when combining multiple output DEMs from Topo to Raster, remember the following:
- The output extent for each DEM should be a few cells larger than the areas of interest so there will be some overlap between the DEMs when they are merged.
- The extent of the input datasets to each Topo to Raster interpolation should be even larger than the increased area of interest so the edges can be predicted as accurately as possible.
When the DEMs have been created, they can best be combined using the Mosaic tool in the Data Management toolbox in geoprocessing or the Mosaic function in Map Algebra. This function provides options to handle overlapping areas to smooth the transition between datasets.
Evaluating output
All created surfaces should be evaluated to ensure that the data and parameters supplied to the program resulted in realistic representations of the surface. There are many ways to evaluate the quality of an output surface depending on the type of input available to create the surface.
The most common evaluation is to create contours from the new surface and compare them to the input contour data. It is best to create these new contours at one-half the original contour interval to examine the results between contours. Drawing the original contours and the newly created contours on top of one another can help identify interpolation errors. Contours can be generated with the Contour function.
Another method of visual comparison is to compare the optional output drainage dataset with known streams and ridges. The drainage dataset contains the streams and ridges that were generated by the program during the drainage enforcement process. These streams and ridges should coincide with known streams and ridges in the area. If a stream dataset was used as input, the output streams should almost perfectly overlay the input streams, although they may be a little more generalized.
A common method for evaluating the quality of a generated surface is to withhold a percentage of the input data from the interpolation process. After generating the surface, the height of these known points can be subtracted from the generated surface to examine how closely the new surface represents the true surface. These differences can be used to calculate a measure of error for the surface, such as root mean squared error.
The diagnostic file created can be used to evaluate how effectively the tolerance settings are clearing sinks in the input data. Decreasing the values of the tolerances can make the program behave more conservatively in clearing sinks.
Contour biasing
There is a minor biasing in the interpolation algorithm that causes input contours to have a stronger effect on the output surface at the contour. This bias can result in a slight flattening of the output surface as it crosses the contour. This can contribute to misleading results when calculating the profile curvature of the output surface but is otherwise not noticeable.
Topo to Raster references
Goodchild, M. F., and D. M. Mark. 1987. The fractal nature of geographic phenomena. Annals of Association of American Geographers. 77 (2): 265–278.
Hutchinson, M. F. 1988. Calculation of hydrologically sound digital elevation models. Paper presented at Third International Symposium on Spatial Data Handling at Sydney, Australia.
Hutchinson, M. F. 1989. A new procedure for gridding elevation and stream line data with automatic removal of spurious pits. Journal of Hydrology 106: 211–232.
Hutchinson, M. F., and T. I. Dowling. 1991. A continental hydrological assessment of a new grid-based digital elevation model of Australia. Hydrological Processes 5: 45–58.
Hutchinson, M. F. 1993. Development of a continent-wide DEM with applications to terrain and climate analysis. In Environmental Modeling with GIS, ed. M. F. Goodchild et al., 392–399. New York: Oxford University Press.
Hutchinson, M. F. 1996. A locally adaptive approach to the interpolation of digital elevation models. In Proceedings, Third International Conference/Workshop on Integrating GIS and Environmental Modeling. Santa Barbara, CA: National Center for Geographic Information and Analysis. See http://www.ncgia.ucsb.edu/conf/SANTA_FE_CD-ROM/sf_papers/hutchinson_michael_dem/local.html.
Wahba, G. 1990. Spline models for Observational data. Paper presented at CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia: Soc. Ind. Appl. Maths.