Interpolating Surfaces

Spatial interpolation Spatial interpolation is used to take known values and interpolate them into a surface, deriving new estimated surface values. Spatial interpolation is based on the notion that points which are close together in space tend to have similar value attributes. This is known as positive spatial autocorrelation. An interpolated surface is created, usually a raster dataset, through the input of data collected at the discrete sample points

Interpolation in QGIS Raster tool provides tools for spatial data analysis that apply statistical theory and techniques to the modeling of discrete spatially referenced data. QGIS support other geoprocessing engines for interplotation (GRASS, SAGA, GDAL, OGR etc) by ctivating the processing extension. QGIS Spatial Analyst uses Inverse Distance Weighted (IDW), Triangulated Irregular Network (TIN), Regularized Splines with Tension (RST), Kriging or Trend Surface interpolation methods to estimate depth, temperature, rainfall, contamination concentrations or other spatially continuous phenomena.

Methods of surface representation Points. X,Y,Z values define the location of a sample and the change characteristic represented by the Z value. Can be regular or irregular. Contours. Join locations of equal value, e.g a line can connect recorded temperature values. Grids. An array of cells of equal size that are arranged in rows and columns, each cell contains an attribute value that represents a change in Z value. TIN. Triangulated irregular network is a vector data structure used to store and display models as a continuaou surface.

Raster interpolation Interpolation predicts values for cells in a raster from a limited number of sample data points. The example shows a point dataset (left) and a raster interpolated from these points (right). Unknown values are “interpolated” using a mathematical formula using the values of nearby known points.

Discrete points (SST)

Interpolation methods Most interpolation methods assume a smooth or continuous gradient exists between sampled points There are two types of interpolation modules that assume continuous gradients: Inverse Distance Weighted Kriging

Inverse Distance Weighted Sample points are weighted during interpolation such that the influence of one point relative to another declines with distance from the predicted point Measured values closest to the prediction location will have more influence on the predicted value than those farther away.

IDW

Kriging Surrounding measured values are weighted to derive a predicted value for an unmeasured location. Weights are based on the distance between the measured points, the prediction locations, and the overall spatial arrangement among the measured points. Most appropriate when the spatially correlated distance or directional bias in data is known

Kriging

Comparison Surface temperature grid Both surfaces use Analysis Mask to mask the land area IDW has masked the land area Kriging did not interpolate data sparse areas

Which method to use? Spline surface passes exactly through each sample point best for surfaces that are already smooth, e.g. Elevations IDW will pass through none of the points assumes variable decreases in influence with distance from sampled location Kriging is a geostatistical method that uses statistical techniques for predicting values if you already know correlated distances or directional bias in data