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Efficient kriging for real-time spatio-temporal interpolation

Atmospheric data is often recorded at scattered station locations. While the data is generally available over a long period of time it cannot be used directly for extracting coherent patterns and mechanistic correlations. The only recourse is to spatially and temporally interpolate the data both to organize the station recording to a regular grid and to query the data for predictions at a particular location or time of interest. Spatio-temporal interpolation approaches require the evaluation of weights at each point of interest. A widely used interpolation approach is kriging. However, kriging has a computational cost that scales as the cube of the number of data points N , resulting in cubic time complexity for each point of interest, which leads to a time complexity of O(N) for interpolation at O(N ) points. In this work, we formulate the kriging problem, to first reduce the computational cost to O(N). We use an iterative solver (Saad, 2003), and further accelerate the solver using fast summation algorithms like GPUML (Srinivasan and Duraiswami, 2009) or FIGTREE (Morariu et al., 2008). We illustrate the speedup on synthetic data and compare the performance with other standard kriging approaches to demonstrate substantial improvement in the performance of our approach. We then apply the developed approach on ocean color data from the Chesapeake Bay and present some quantitative analysis of the kriged results.