Spatial Interpolation

Spatial interpolation is a powerful tool for extending spatial data. Since it is not physically or financially possible to measure every single point in a given area, sample points must be selected. The data from these sample points is then used to predict data in the rest of the area. In the case of precipitation, a county may want to know which cities are experiencing drought, but may not have the time or money to place a gauge station in every city. Spatial interpolation allows the county to make a good estimate on precipitation levels based on a relatively small set of points.

The interpolation maps of Los Angeles County precipitation reveal that most of the county has received the same amount or less rain than usual. The Kriging maps show that the most rain fell in the eastern side of the county, which follows the normal seasonal trend. This amount, however, was less than the normal amount of rainfall. The difference map reveals a large concentration of land that received less rainfall than usual. The Spline map shows a different, more gradual pattern. While it also reveals the most rainfall to the east, it also reveals greater-than-average rain in Santa Monica Bay. The concentration of land with less-than-average rainfall is not as pronounced in the Spline map and an overall deficiency in rainfall is better revealed throughout the county.

The best interpolation technique to display precipitation is the Spline technique. Since it reduces surface curvature from large variations, this technique produces smoother surfaces that are best suited to gradually varying trends, such as precipitation. The Inverse Distance Weight (IDW) technique would not be ideal in this situation since it requires dense sets of points. The LA Country gauge station map lacks many points in the northern rural portion of the county. Interpolation in this region would not be as accurate. Kriging is a good alternative. However, despite its mathematical complexity, it does not produce a smooth surface. Rainfall varies gradually across space. Therefore, the smoother surfaces of the Spline technique are best.