Interpolation Lab

 

Interpolation is the process of determining unknown values based on their spatial relationship to existing values. Without knowing specific values for specific locations, interpolation can infer the value of that location based on its relationship to the locations with known value. Many methods of Interpolation exist, each calculating the unknown values in a unique way. The methods used in this lab are IDW (Inverse Distance Weighting), Kriging, and Spline.  IDW uses a linear-weighted combination set of sample points to determine unknown value. It uses the theory that the farther two cells are from each other the less influence they have one each other. This follows Tobler’s law of distance decay where things generally become less and less connected as distance between them increases. So points that are closer to the known values are weighted heavier than points that are farther from the known values. Kriging on the other hand “assumes that the distance or direction between sample points reflects a correlation that can be used to explain variation in the surface”,(Childs 3). Kriging predicts values of a specified radius using a sophisticated weighted average technique.  The Spline method estimates values in an attempt to minimize surface curvature. It attempts to create a smooth layer that runs through all input values filling in the unknown values in between.

For this lab we interpolated the current amount of rainfall in Los Angeles County along with traditional Normal rainfall values for Los Angeles County. First we constructed a table in excel with all the rain gauge stations in L.A. county and added their latitude and longitude coordinates, which we had to convert into decimal degree format.  Columns for current rainfall and normal rainfall were made and then the excel table was exported as a .dbf file.  In Arcmap a Los Angeles county Boundary shapefile was added and then the excel table was added. The rain gauge stations were displayed using “display X-Y values”, based on the Latitude/longitude coordinates.  Two different interpolation methods were then applied to the data points resulting in two different outputs. One was based on the IDW method.  The other was based on the Kriging method. Both these methods were applied to the Normal rainfall value and the Current rainfall values. Once the interpolations were performed difference maps were made using the raster calculator to show the difference between current rainfall value and normal rainfall values.  It appears that the eastern part of the county received more rainfall than the western portion, and the current rainfall value are less than what normal rainfall values usually are.

I think the Inverse distance weighting technique is the best interpolation method to use for this task. Because of the nature of precipitation usually there is a gradual change in values, with areas of similarity generally decreasing with distance from each other. The IDW method is a deterministic interpolation technique that creates a surface based on measured points where as kriging is a geostatistical approach which is a more advanced surface prediction technique. Kriging would not be as accurate for this data set because a directional bias in the data values is not known.