A case study of geoestatistical interpolation to meteorological fields

We apply a Kriging interpolation, a geostatistic method, to meteorology and compare it with other traditional interpolations, i.e. the spline interpolation and the method whose weight is inversely proportional to the distance to a power. Two meteorological fields used in the paper are the sea-surface pressure field and the geo-potential height field on 500 hPa, respectively. An ideal field with a sharp variation is also used in our numerical investigation. The numerical results show that the Kriging is more accurate than the other two methods used if related parameters are well set and only the sampling points located in a small area around the estimated points. Even for the interpolation around the sharp area the Kriging still behaves well, while others did not. On the boundary of the interpolation field, there exist big errors for the spline while not for the Kriging. The results also indicate that the accuracy of the Kriging is not sensitive to stationary assumption. Though some preprocess may improve the field stability, it cannot always raise the accuracy of the Kriging efficiently. In addition, the default assumption of the method of the inverse distance to a power is isotropy. As the meteorological fields are usually isotropic within 3000 km, it is not surprise that the interpolation methods with weights only related to the distances to a power between the interpolating points are wildly employed in meteorology despite its simplicity.