  Max-stable random fields can be constructed according to Schlather (2002)
with a random function or a stationary process and a kind of random event
magnitude. These are applied for the modelling of natural hazards. We simply
extend these event-controlled constructions to random fields of maxima with
non-max-stable dependence structure (copula). The theory for the variant with a
stationary process is obvious; the parameter(s) of its correlation function
is/are determined by the event magnitude. The introduced variant with random
functions can only be researched numerically. The scaling of the random
function is exponentially determined by the event magnitude. The location
parameter of the Gumbel margins depends only on this exponential function in
the researched examples; the scale parameter of the margins is normalized. In
addition, we propose a method for the parameter estimation for such
constructions by using Kendall's tau. The spatial dependence in relation to the
block size is considered therein. Finally, we briefly discuss some issues like
the sampling.
