Working with Digital Elevation Data


Interpolating and analyzing surface features on DEM data in a raster GIS environment.

ESRI ArcView GIS v3.2, SunOS
Spatial Analyst Extension

Data Inputs
Region of Interest City of Kanata, Ontario, Canada
Projection UTM, zone 18, NAD 83, units meters
Coverage Data kan_spothts Elevation data
  kan_roads2 Roads / transportation
  dem_aoi Area of interest

Analysis Properties
Extent dem_aoi
Cell Size 10m (600x600)

Table 1 shows a summary of elevation values for kan_spothts.
Sum 742738.7
Count 7790
Mean 95.3
Maximum 132.6
Minimum 63.1
Range 69.5
Variance 149.0
Standard Deviation 12.2

Surface Functions and Generators: Principles

Often called gridding, interpolation creates images by estimating values for pixel centres (nodes) on a regular network of rows and columns from regularly or irregularly scattered data points.

These functions output cell values by interpolating from a set of nearest input points. The most appropriate method is dependent on the distribution of input points and the type of surface generated.

The general trend is as input sample points increase, local anomalies are subdued, as shown in Figure 1.

[Interpolation Trend]


Various interpolation and surface analysis were performed on the study area. Command logs from Spatial Analyst are shown below to carry out the specified procedures.


IDW_10 = IDW(kan_spothts.shp,Zval,#,2,SAMPLE,12,#,10,348000, 5018000, 354000, 5024000)

hlshd1 = HILLSHADE(/gcpdbc/tkralidi/0dem/idw_10,315,45,#,#)

slope1 = SLOPE(/gcpdbc/tkralidi/0dem/idw_10)

ctour1.shp = CONTOUR(/gcpdbc/tkralidi/0dem/idw_10,INTERVAL,5,60)
[Resulting IDW Map]


grid1 = SPLINE(/gcpdbc/tkralidi/0dem/kan_spothts.shp,Zval,REGULARIZED,0.1,12,10,348000, 5018000, 354000, 5024000)

hlshd1 = HILLSHADE(/gcpdbc/tkralidi/0dem/spl_10,315,45,#,#)

slope1 = SLOPE(/gcpdbc/tkralidi/0dem/spl_10)

ctour2.shp = CONTOUR(/gcpdbc/tkralidi/0dem/spl_10,INTERVAL,5,60)
[Resulting Spline Map]

Analytical Hillshading

Hillshading determines the hypothetical illumination of a surface. This can be done for analysis or graphical reasons. For analysis it can be used to determine the length of time and intensity of the sun at a given location. Graphically it can visually enhance the surface.

IDW vs. Spline Interpolation: Differences
Inverse Distance Weighting Interpolation Explained

Inverse distance weighted (IDW) interpolation determines cell values using a linearly weighted combination of a set of sample points. The weight is a function of inverse distance, i.e.

value = 1 / d^e

The surface being interpolated should be that of a locationally dependent variable.

The power parameter in IDW controls the significance of the surrounding points upon the interpolated value. A higher power results in less influence from distant points.

A larger power will result in less influence from surrounding points, i.e. nearby data will have the most influence and the surface will have more detail (less smooth). 2 is a common value.

The influence of an input point on an interpolated value is isotropic (uniform). Input points can be passed by number or fixed radius.

The output value of a cell using IDW is limited to the range of the inputs used to interpolate, because IDW is a weighted average. For example, you cannot create ridges or valleys if these extremes have not already been sampled.

The best results from IDW are obtained when sampling is moderately dense with regard to local variation. If the sampling is sparse or uneven, the results may not sufficiently represent the desired surface.

Spline Interpolation Explained

Spline interpolation differs from IDW in that it minimizes the total curvature of the surface. This method is best for subtle variations in surface values such as elevation, water table heights, or pollution concentrations.

If there are large changes in the surface within a short horizontal distance, the spline algorithm can overshoot estimated values.

As a result, there were more potential for errors during the spline implementation.

The difference between the two types of interpolation is displayed in the output grid produced. As the spline did not make concrete connectivity, a continuous surface was produced. Figure 2 shows the difference between spline and IDW outputs.

Figure 2: IDW and Spline Interpolation Results from Identical Input Data Samples
[IDW Results]

[Spline Results]

In the study area, some surface areas remained constant in the IDW method, but showing some oscillation in the spline implementation, a result of the potential error that can occur when there are gaps in the data, such as over/undershoots.

IDW Contouring vs. Spline Contouring

The IDW contours produced a discrete data model. An uncertainty found in the interpolation is how to deal with 'edge effects', where one point is very close to the edge of the data limits, or how to deal with irregularly spaced points, thereby skewing the data values when creating a TIN, or contour features.

When applying spline contours, a smooth surface was produced due to the spline algorithm, which produces a continuous surface with minimum curvature. However, some values derived had very high variance (possible errors) as a result. Table 2 shows a statistical result of the contour tables from both spline and IDW inputs:

Table 2: Spline vs. IDW Contour Statistics
  Spline IDW
Sum 48340 49320
Count 494 504
Mean 98 98
Maximum 130 130
Minimum 65 65
Range 65 65
Variance 193 167
Standard Deviation 14 13

As a result, more variation occurs within the spline derived contouring, as shown in the fields 'variance' and 'Standard Deviation'. The smoothness of the spline algorithm is shown when comparing the Value count between methods i.e. the smoother surface of the spline is shown in the less number of points, as compared to slightly more data points in the IDW scenario.

IDW Sloping vs. Spline Sloping

Slope identifies the maximum rate of change in value from each cell to its neighbours. An output slope rid can be calculated as percent or degree of slope.

Again, the range or variance occurred more with the spline slope than the IDW slope. The highest degree of slope in the IDW was 21.145, whereas the highest for the spline was 36.144.

IDW Variations

Using IDW interpolation, output grid results were analyzed using various input parameters.

The following trends were found when performing various interpolations with IDW.

Table 3: Trends Found Using Various IDW Input Parameters
Parameter Effect
No of Neighbours More points = more averaging, subdue local anomaly
Less points = less averaging, enhance local anomaly
Power Larger value = less influence from surrounding points, nearby data will have most influence, surface has more detail (less smooth)
Lesser value = less detail, smoother effect
Barriers If line coverage used for barrier, used as a break that limits the search for input sample points (cliff, ridge, or other interruption)

Tom Kralidis
November 2000