On the interpolation of hydrologic variables: Formal equivalence of multiquadratic surface fitting and kriging

The paper focuses on the ties of kriging with a deterministic interpolation procedure, known as multiquadratic surface fitting. The two methods are compared, first from a theoretical point of view, then using a practical example. It is shown that kriging equations with a linear variogram model are identical in form to equations of multiquadratic surface fitting with cone surfaces. The issue of the accuracy of both estimators is discussed through a case study where hourly rainfall maps of real storm events collected by radar provided the reference rainfall. Random point sampling of the accumulation pattern simulated gauge returns. Eight sampling densities were used and for each density rainfall spatial distributions were estimated for a large number of realisations. It is shown that kriging performs better at lower gauge density, while at higher gauge density the accuracy of both estimators is similar.