Master's Project (M.S.) University of Alaska Fairbanks, 2019Kriging is a geostatistical interpolation method that produces predictions and prediction intervals. Classical
kriging models use Euclidean (straight line) distance when modeling spatial autocorrelation. However, for estuaries,
inlets, and bays, shortest-in-water distance may capture the system’s proximity dependencies better than Euclidean
distance when boundary constraints are present. Shortest-in-water distance has been used to krige such regions (Little
et al., 1997; Rathbun, 1998); however, the variance-covariance matrices used in these models have not been shown to
be mathematically valid. In this project, a new kriging model is developed for irregularly shaped regions in R
2
. This
model incorporates the notion of flow connected distance into a valid variance-covariance matrix through the use of a
random walk on a lattice, process convolutions, and the non-stationary kriging equations. The model developed in this
paper is compared to existing methods of spatial prediction over irregularly shaped regions using water quality data
from Puget Sound
