NADP Spatial Interpolation Error Analysis

1. NADP Spatial Interpolation Error Analysis

2. Site Specific Errors • Interpolation errors were calculated for each NADP NTN site, for every analyte from 1985-2010. • The analytes included were Ca2+, Cl-, K+, Mg2+, Na+, NH4+, NO3-, SO42-, and pH • The errors are the result of using a bootstrap or cross-validation technique. Each data points is removed from the interpolator one at a time, and it’s value is then predicted based on the remaining data. This allows a comparison of the measured and the predicted values at each site to be made, where the residualis simply the measured value minus the predicted value. This data can be used to gain an overall better understanding of the interpolation accuracy. The final product of this process is a spreadsheet for each analyte similar to the one shown in the example above.

3. Root Mean Square Error The root mean square error (RMSE) is represented by a single value, and indicates how closely the interpolation model predicts the measured values. A smaller RMSE is preferred, and is indicative of a better interpolation model. In addition to site specific errors, a RMSE was calculated for each analyte from 1985-2010, using all valid NADP NTN sites in the lower 48. Using the RMSE data, analyte trend plots were constructed in order to visualize annual trends in the interpolation accuracy. An example trend plot for SO42-. The year is given on the x-axis, while the overall interpolation RMSE (mg/L) is shown on the y-axis.

4. Detrended RMSE Some of the RSME plots showed temporal trends coincident with the underlying trends in concentrations. To remove the effects of the underlying trend, we divided the annual RSME by the annual spatial concentration average. The annual spatial average is simply the mean of all interpolated map grid cells.

5. File Index of http://nadp.sws.uiuc.edu/dl/interpolation/