How can we be confident in the Weather Generator output if we aren't sure the statistics of the climate will stay the same?

This a recognised assumption of the UKCP09 Weather Generator and hence why the Weather Generator should only be seen as a tool that can be used to integrate the 25 km probabilistic information to produce statistics of daily climate for the future. The uncertainties and limitations of using the Weather Generator should be fully understood before it is used.

In detail

The UKCP09 Weather Generator is based on the assumption that the baseline climate can be described in terms of statistical relationships, which can then be perturbed in order to simulate realisations of future daily climate that are consistent with the UKCP09 probabilistic climate projections.