Which interpolation method is useful when predicting data at locations without nearby point data?

Kriging is a sophisticated geostatistical interpolation method that is particularly effective at predicting values in areas where there are no nearby point data. It works by utilizing the spatial correlation of the sampled data points to estimate values at unsampled locations. This method takes into account the distance between the sampled points and the uncertainties associated with the predictions, providing not only estimated values but also a measure of confidence in those estimates.

In contrast to Kriging, methods like Inverse Distance Weighting (IDW) primarily rely on a weighted average of nearby points without accounting for the underlying spatial structure or distribution of the data. While IDW can provide reasonable estimates, especially in data-rich areas, it may not perform as well when there are significant gaps in sampled data.

Spline interpolation tends to provide a smooth surface and can also be used for filling in gaps, but it does not incorporate the statistical properties of the data as effectively as Kriging.

Overall, Kriging excels in scenarios where the location and spatial arrangement of the data points can inform predictions, making it particularly useful for predicting data at locations without nearby measurements.