  Nonparametric resampling methods such as Direct Sampling are powerful tools
to simulate new datasets preserving important data features such as spatial
patterns from observed datasets while using only minimal assumptions. However,
such methods cannot generate extreme events beyond the observed range of data
values. We here propose using tools from extreme value theory for stochastic
processes to extrapolate observed data towards yet unobserved high quantiles.
Original data are first enriched with new values in the tail region, and then
classical resampling algorithms are applied to enriched data. In a first
approach to enrichment that we label "naive resampling", we generate an
independent sample of the marginal distribution while keeping the rank order of
the observed data. We point out inaccuracies of this approach around the most
extreme values, and therefore develop a second approach that works for datasets
with many replicates. It is based on the asymptotic representation of extreme
events through two stochastically independent components: a magnitude variable,
and a profile field describing spatial variation. To generate enriched data, we
fix a target range of return levels of the magnitude variable, and we resample
magnitudes constrained to this range. We then use the second approach to
generate heatwave scenarios of yet unobserved magnitude over France, based on
daily temperature reanalysis training data for the years 2010 to 2016.
