**Scope**

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

**Software**

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) |

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.

**Method**

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**

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)

**Spline**

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)

**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.

**Analysis
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**

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