2. Interpolating Surfaces

3. 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

4. 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.

5. 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.

6. 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.

7. Discrete points (SST)

8. 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

9. 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.

10. IDW

11. 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

12. Kriging

13. 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

14. 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