  Contour maps are widely used to display estimates of spatial fields. Instead
of showing the estimated field, a contour map only shows a fixed number of
contour lines for different levels. However, despite the ubiquitous use of
these maps, the uncertainty associated with them has been given a surprisingly
small amount of attention. We derive measures of the statistical uncertainty,
or quality, of contour maps, and use these to decide an appropriate number of
contour lines, that relates to the uncertainty in the estimated spatial field.
For practical use in geostatistics and medical imaging, computational methods
are constructed, that can be applied to Gaussian Markov random fields, and in
particular be used in combination with integrated nested Laplace approximations
for latent Gaussian models. The methods are demonstrated on simulated data and
an application to temperature estimation is presented.
