Hello, I'm currently working on a project involving interpolation of water quality values (taken at monitoring stations) within a river polygon. The monitoring stations are fairly widely spaced, requiring me to have a large bandwidth value to ensure that the interpolation reaches each station. This value typically needs to be around 25km in order to produce an output that leaves no null gaps along the interpolated section of the river. Unfortunately this has left me with interpolated values that are very different from the known point values that the interpolation is based on.
In the first pic you can see that the point has a value of 0.005, while the cells of the output raster around the point have a much higher value, 0.126. In the second pic you can see a cluster of points with values of around 0.4, but the resulting raster has a value of only 0.134. The values seem to correctly become higher and lower as they approach/leave higher or lower value points, but the actual cell values are drastically different than the known points.
Is there a way to have the interpolation maintain the known values at the monitoring station points while still producing a raster that encompasses the entire study area?
Kernel Interpolation with Barriers is not an exact interpolator, so the surface won't pass through the input points perfectly.
At its core, kernel interpolation is performing local first-order ordinary least squares predictions. What is probably happening is that your bandwidth is so large that it is smoothing over points. Imagine you have three points along a stretch of the river; the first has a large value, the second has a small value, and the third has a large value. If you use a bandwidth large enough the these points are given nearly equal weights, your predictions will be medium, medium, medium (since that is the best linear fit to these three points).
I'm not really sure what to suggest you should do. You might want to partition your data and fit different models in different locations. The more data you have, the smaller your bandwidth should be. You could also try to simulate some new data in order to get the linear model to stabilize.