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Topographic Modeling

Topographic Modeling

Use Topographic Modeling to create shaded relief surfaces from digital elevation data and to extract parameters such as slope, aspect, and their derivatives.

You can also run a script to perform topographic modeling using ENVITopographicModelingTask.

See the following sections:


This section provides an overview of slope, aspect, and other parameters that are used in topographic modeling. For a more detailed background, consult the references at the end of this topic.

For every point in a digital elevation model (DEM), you can compute a number of parameters that represent the change in surface relative to neighboring points. A moving window, or kernel, is used for this purpose. The kernel is used to fit a quadratic surface to the DEM and to derive the appropriate parameters. Varying the size of the kernel allows measurements at various scales.

Slope represents the change in elevation (dz) over a given distance (dx). More specifically, it measures the maximum rate of change in elevation between a given point and its surrounding points. ENVI computes slope both in degrees and percentages. Values range from 0 (a horizontal plane) to 90 degrees.

Aspect is the compass direction that a slope is facing. Values range from 0 (north) to 360 degrees, increasing in a clockwise direction. ENVI assigns a value of 180 to pixels whose slope is 0.

Curvature is the rate of the change of slope; thus, it is the first derivative of slope and the second derivative of the local surface. Positive curvature is called convexity, while negative curvature is called concavity. Two forms of convexity—profile and plan—provide vertical and horizontal orthogonal measures of curvature, respectively. Together, they are used to study how water near the surface accelerates and converges.

Profile convexity is the vertical component of curvature. It is the curvature of the surface along the steepest downhill direction, where the effects of gravity are maximized. Profile convexity affects the velocity of water flow, and it influences erosion and deposition.

Plan convexity is the horizontal component of curvature. It measures the rate of change of the aspect along a contour, orthogonal to the direction of the steepest slope, where the effects of gravity are minimized.

Longitudinal convexity measures the curvature orthogonally in the downslope. It intersects with the plane of the slope normal and the aspect direction. It can determine whether flowing water will accelerate or decelerate over a given point.

In cases where the slope normal is not vertical, other measures of curvature are used. These are cross-sectional convexity, minimum curvature, and maximum curvature, shown in the equations below. The terms a, b, and c represent the coefficients in a quadratic surface (Evans, 1980).

Cross-sectional convexity measures the curvature orthogonally across the steepest downhill direction. It intersects with the plane of the slope normal and the perpendicular aspect direction. It can determine whether flowing water will converge or diverge over a given point.

Minimum curvature is the smallest local curvature in any direction, and maximum curvature is the largest local curvature in any direction. Both measures apply to the entire surface.

Finally, shaded relief is computed as the cosine of the incidence angle, which is the angle between a vector pointed toward the sun and a vector normal to the surface. Values range from 0 to 1.

Run the Topographic Modeling Tool

  1. From the Toolbox, select Terrain > Topographic Modeling. The Topographic Modeling dialog appears.
  2. Select a digital elevation image for input. Perform optional spatial subsetting and masking, then click OK.
  3. Select the Products to create. The choices are as follows:
    • Slope: The slope in degrees
    • Aspect
    • Shaded Relief
    • Profile Convexity
    • Plan Convexity
    • Longitudinal Convexity
    • Cross Sectional Convexity
    • Minimum Curvature
    • Maximum Curvature
    • RMS: A root mean square (RMS) error image that indicates how well the quadratic surface fits the real surface
    • Slope Percent
  4. Enter the Kernel Size (in pixels) used for processing. The default value is 2 pixels, which represents a 2 x 2 moving window.
  5. Optional: Enter the Azimuth angle of the model in degrees. The value will only be used for the Shaded Relief product. The default value is 45 degrees.
  6. Optional: Enter the Elevation angle of the model in degrees. The value will only be used for the Shaded Relief product. The default value is 45 degrees.
  7. Optional: Enter the X and Y Pixel Size values for the output image, in meters.
  8. Enter a filename and location for the Output Raster.
  9. Enable the Preview check box to see a preview of the settings before you click OK to process the data. The preview is calculated only on the area in the Image window and uses the resolution level at which you are viewing the image. See Preview for details on the results.
  10. Enable the Display result check box to display the output image in the Image window when processing is complete.
  11. Click OK. ENVI adds the resulting output to the Data Manager and, if the Display Result check box was enabled, adds the layer to the Layer Manager and displays the output in the Image window.


This example uses a National Elevation Dataset (NED) digital elevation model (DEM), available from the U.S. Geological Survey. The resolution is 1/3-arc seconds with a pixel size of 0.00009259 degrees.

The Topographic Modeling tool was run using default values. The following are the resulting images that were created:

Slope (Degrees)



Shaded Relief


Profile Convexity

Plan Convexity


Cross Sectional Convexity

Minimum Curvature


Maximum Curvature

Slope Percent

RMS Error


Evans, I. "General Geomorphometry, Derivatives of Altitude, and Descriptive Statistics." In Spatial Analysis in Geomorphology. Methuen, 1972.

Evans, I. "An Integrated System of Terrain Analysis and Slope Mapping." Zeitschrift für Geomorphologie N.F., Supplement-Band 36 (1980): 274-295.

Goudie, A. Geomorphological Techniques, 2nd Edition. London and New York: Routledge, Taylor & Francis, 1990.

Wood, J. "Scale-Based Characterizations of Digital Elevation Models." In Innovations in GIS 3. Taylor & Francis, 1996.

Wood, J. The Geomorphological Characterization of Digital Elevation Models, Ph.D. Thesis, University of Leicester, Department of Geography, Leicester, UK, 1996.

See Also

Topographic Shading, Extract Topographic Features, Create Hill Shade Images, Replace Bad Values

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