Question

Why is spatial interpolation often necessary with environmental data? describe at least two different interpolation methods, and include a brief description of each method and its logic.

Answer 1

Why is spatial interpolation often necessary with environmental data ?

Spatial interpolation is the process of using points with known values to estimate values at other unknown points. For example, to make a precipitation (rainfall) map for your country, you will not find enough evenly spread weather stations to cover the entire region. Spatial interpolation can estimate the temperatures at locations without recorded data by using known temperature readings at nearby weather stations. This type of interpolated surface is often called a statistical surface. Elevation data, precipitation, snow accumulation, water table and population density are other types of data that can be computed using interpolation.

In this figure you can see Temperature map interpolated from South African Weather Stations.

Describe at least two different interpolation methods, and include a brief description of each method and its logic.

There are many interpolation methods. In this introduction we will present two widely used interpolation methods called Inverse Distance Weighting (IDW) and Triangulated Irregular Networks (TIN).

Inverse Distance Weighting (IDW) :

In the IDW interpolation method, the sample points are weighted during interpolation such that the influence of one point relative to another declines with distance from the unknown point you want to create.Weighting is assigned to sample points through the use of a weighting coefficient that controls how the weighting influence will drop off as the distance from new point increases. The greater the weighting coefficient, the less the effect points will have if they are far from the unknown point during the interpolation process. As the coefficient increases, the value of the unknown point approaches the value of the nearest observational point.

In this figure Inverse Distance Weighted interpolation based on weighted sample point distance (left). Interpolated IDW surface from elevation vector points (right).

t is important to notice that the IDW interpolation method also has some disadvantages: the quality of the interpolation result can decrease, if the distribution of sample data points is uneven. Furthermore, maximum and minimum values in the interpolated surface can only occur at sample data points. This often results in small peaks and pits around the sample data points. In GIS, interpolation results are usually shown as a 2 dimensional raster layer. In figure you can see a typical IDW interpolation result, based on elevation sample points collected in the field with a GPS device.

In this figure it is the result of IDW interpolation result from irregularly collected elevation sample points (shown as black crosses).

Triangulated Irregular Network (TIN)

TIN interpolation is another popular tool in GIS. A common TIN algorithm is called Delaunay triangulation. It tries to create a surface formed by triangles of nearest neighbour points. To do this, circumcircles around selected sample points are created and their intersections are connected to a network of non overlapping and as compact as possible triangles.

In this figure Delaunay triangulation with circumcircles around the red sample data. The resulting interpolated TIN surface created from elevation vector points is shown on the right.

The main disadvantage of the TIN interpolation is that the surfaces are not smooth and may give a jagged appearance. This is caused by discontinuous slopes at the triangle edges and sample data points. In addition, triangulation is generally not suitable for extrapolation beyond the area with collected sample data points.

In this figure Delaunay TIN interpolation result from irregularly collected rainfall sample points (blue circles)