Chapter 8 – Geographic Information Analysis O’Sullivan and Unwin “ Describing and Analyzing Fields” By: Scott Clobes

 Field View Attributes that are continuously variable and measurable across space, such as the surface of the Earth 1. Scalar Field – A quantity characterized only by its magnitude or amount independent of any coordinate system in which it is measured. Example: Temperature 2. Vector Field – Mapped quantities that have both magnitude and direction that are not independentof locational coordinates. Examples: Slope and Aspect Scalar fields have an equivalent vector field and vice versa.

 Modeling and Storing Field Data 1. Sampling – Measurements of the real surface. 2. Interpolation – Techniques used to predict the value of a scalar field at unknown locations from the values and locations of known points, control points. Interpolation is a continuous surface representation.

 Important Considerations for Field Data 1. The data used represents samples. It is usually impossible or impractical to measure each and every location. 2. Many fields are constantly undergoing change, so the values recorded represent a particular time and place. 3. We usually have no control over where the sample data was collected, unless we collect the measurements ourselves.

 Methods for Storing Fields 1. Digitized Contours 2. Mathematical Operations 3. Point Systems a. Surface Random b. Surface Specific c. Grid Sampling 4. TIN (Triangular Irregular Network) 5. DEM (Digital Elevation Model)

 Methods for Storing Fields

 Spatial Interpolation - Prediction of exact values of attributes at unsampled locations from measurements made at control points within the same area. - Interpolation is a type of spatial prediction. - Is dependent on spatial autocorrelation.

 Methods of Spatial Interpolation 1. Proximity Polygons - Uses the nearest location - Creates a discontinuous field - Works best with nominal data

 Methods of Spatial Interpolation 2. Local Spatial Average - Calculates the local spatial means of the sample data points. - Uses points within a specified fixed distance - All sample points are weighted equally - Continued interpolation can cause surfaces to look entirely flat, like that of a horizontal plane.

 Methods of Spatial Interpolation 2. Local Spatial Average Mean of Control Points Nearest Neighbor

 Methods of Spatial Interpolation 3. IDW (Inverse Distance Weighting) - Nearby points have more prominence / influence in the calculation - Relationship of 1 / d 2 - Tobler’s law that nearby things are more related than distant things

 Methods of Spatial Interpolation 3. IDW (Inverse Distance Weighting) The following factors can influence the results produced using IDW. a. Resolution of the sampling grid b. Alter the choice of control points used through radius or nearest neighbor c. Alter the distance weighting d. Change the form of the distance weighting function used

 Methods of Spatial Interpolation 4. Other Options a. Bicubic Spline Fitting b. Multiquadric Analysis c. TIN All of these 4 methods assume that the data at the control points are exact and they use a mathematical calculation. Once the data, method, and parameters are set, only one set of results is possible.

 Analysis Methods for Fields 1. Relative Relief – Lowest to highest values in a specified area. 2. Area / Height Relationship 3. Slope and Gradient 4. Surface Specific Points - peaks, pits, saddles, ridges, valleys, and flat plains 5. Catchments and Drainage Networks 6. Viewsheds – Line of sight 7. Surface Smoothing

 Conclusions - Most important natural phenomenon are interval or ratio scaled data and form continuous single value scalar fields. - Due to time and cost constraints, we cannot measure each and every location in a study area, so samples and interpolation must be used. - It’s important to understand how and where the sample data points (control points) are taken. - Interpolation must be approached with caution since different interpolation methods can produce different results.

 Questions 1. Name and describe the 2 different types of fields and give examples of each type. 2. Name and describe 5 different methods for storing fields. 3. What are the 3 most commonly used methods of spatial interpolation? 4. Name and describe 3 different types (there are 7 different types) of analysis methods for fields.