Interpolation and Trend Surface Analysis in Advanced Spatial Analysis and Modeling

Introduction

'In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. Surface interpolation functions make predictions from sample measurements for all locations in a raster dataset whether or not a measurement has been taken at the location. There is a variety of ways to derive a prediction for each location; each method is referred to as a model. With each model, there are different assumptions made of the data, and certain models are more applicable for specific data. The Interpolation tools are
generally divided into deterministic and geostatistical methods' (ArcGis 2004). In this study IDW is used as the deterministic interpolator and Global Polynomial interpolation as geostatistical interpolator.

'Trend surface analysis is a method used for the analysis of change over space which attempts to decompose each observation on a spatially distributed variable into acomponent associated with any regional trends present in the data and a component associated with purely local effects. This separation into two components is accomplished by fitting a best-fit surface of a previously specified type using standard regression techniques' (Unwin, 1975). In this study, our main objective is to interpolate the average income for the City of Calgary using ArcGis and calculate a First and Second Order Trend Surface using S-Plus.

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Point Pattern Analysis in Advanced Spatial Analysis and Modeling

Introduction

The analysis of point data in space, in order to obtain patterns in the points that inform something about the underlying process that generated the points, is often termed as point pattern analysis (Fotheringham et al. 2000). The objective in learning more about spatial patterns is to assess spatial dependence so that we may ultimately correct our statistical analyses based upon dependent spatial data and to learn whether geographic phenomena cluster in space. The need of the quantitative measures of spatial pattern is because it is simply not sufficient to rely on one’s visual interpretation of a map (Rogerson 2006, 224). Point pattern analysis is particularly popular in the fields of biology (Diggle, 1983 in Fotheringham et al., 2000), epidemiology (Diggle et al. in Fotheringham et al., 2000) and the analysis of crime patterns (Bailey and Gatrell, 1995 in Fotheringham et al., 2000). This study focuses on the spatial pattern of the Park centers in the residential areas of Calgary.

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