| Abstract | Atmospheric data is often recorded at scattered stationlocations. While the data is generally available over a
long period of time it cannot be used directly for extract-
ing coherent patterns and mechanistic correlations. The
only recourse is to spatially and temporally interpolate
the data both to organize the station recording to a reg-
ular grid and to query the data for predictions at a par-
ticular location or time of interest. Spatio-temporal in-
terpolation approaches require the evaluation of weights
at each point of interest. A widely used interpolation ap-
proach 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(N4) for
interpolation at O(N) points. In this work, we formulate
the kriging problem, to first reduce the computational cost
to O(N3). We use an iterative solver (Saad, 2003), and
further accelerate the solver using fast summation algo-
rithms 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 ap-
proach. We then apply the developed approach on ocean
color data from the Chesapeake Bay and present some
quantitative analysis of the kriged results.
|
