  The climate change dispute is about changes over time of environmental
characteristics (such as rainfall). Some people say that a possible change is
not so much in the mean but rather in the extreme phenomena (that is, the
average rainfall may not change much but heavy storms may become more or less
frequent). The paper studies changes over time in the probability that some
high threshold is exceeded. The model is such that the threshold does not need
to be specified, the results hold for any high threshold. For simplicity a
certain linear trend is studied depending on one real parameter. Estimation and
testing procedures (is there a trend?) are developed. Simulation results are
presented. The method is applied to trends in heavy rainfall at 18 gauging
stations across Germany and The Netherlands. A tentative conclusion is that the
trend seems to depend on whether or not a station is close to the sea.
