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Institut für Wasser- und Umweltsystemmodellierung - IWS



"Application of FFT-based Algorithms for Large-Scale Universal Kriging Problems"

Computational power and storage capacities often pose heavy limitations to the size of the problem able to be addressed in Kriging. For estimation on regular grids and the generalized case of an uncertain and spatially varying mean, we compile a toolbox of FFT-based (spectral) methods for Kriging that is highly efficient in storage and computational complexity. The general theme is to apply, improve or extend existing FFT-based algorithms for basic operations on covariance matrices which apply when covariance matrices have Toeplitz structure. The discussed FFT-based algorithms are easily applicable for the case of regular grids. In case of irregularly scattered data, we trace the problem back to sparse but regular finer grids of measurements. We also present several fast approximations for the estimation variance of Kriged fields that are asymptotically exact for certain limiting cases. The computational efficiency and reduction of storage requirements over existing Kriging algorithms are discussed and demonstrated in test cases.