Confidence regions for the level curves of spatial data

Contour plots are often used by environmental scientists to display the distribution of a variable over a two‐dimensional region of interest, but the uncertainty associated with the estimated level curves seldom receives attention. Few methods are available for identifying the true level curve with quantifiable confidence, and typically, these methods only deal with the uncertainty at individual locations. Methodology is introduced for constructing a confidence region for the entire level curve of a Gaussian random field at a specified level. The methodology utilizes common geostatistical methods to produce confidence regions containing the entire level curve with high confidence. The validity of this approach is investigated using simulation studies involving several covariance functions, dependence levels, and response quantiles. This methodology is then applied in constructing a confidence region for a level curve of the total monthly precipitation for the state of Colorado in May 1997. Simulation results indicate that this approach works well for the level curves of Gaussian random fields under a variety of conditions. Additionally, this methodology does not depend on the location of estimated level curves, so confidence regions may appear in areas where an estimated level curve is not present. Copyright © 2014 John Wiley & Sons, Ltd.