Gridding, Interpolation and Contouring

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Gridding, Interpolation and Contouring

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The term gridding refers to the process of generating a grid of data values from an existing set (generally of the form {x,y,z} triples) using two-dimensional (spatial) interpolation methods. These interpolation methods assume that the attributes being modeled, z, are continuous or piecewise continuous across the study region, i.e. that z=f(x,y) exists and is single-valued for all (x,y) except where regions are explicitly masked off (i.e. excluded from modeling).

Interpolation methods often assume data points are correct (exact), but they may assume they are subject to error (generally of known or estimated extent). The models used may be exact (go precisely through the sample data points) or inexact (approximate the values at the data points). If the data points are relatively sparse and irregular, interpolation needs to be more sophisticated (subtle) than for dense, regularly spaced data. However, regularly spaced data may be subject to bias due to intrinsic frequencies in the data (spacing and/or directional effects). An interesting example cited by Burrough and McDonnell (1998) is that of soil samples taken in a field that had previously been ploughed, with values recorded being affected by the furrow patterns. Sparse datasets are typical of many applications in which data are costly or time-consuming to collect, for example using boreholes, meteorological stations, soil sampling or radiation measures.