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Will the PDFs incorporate the effect of natural multi-decadal variability as well as climate change?

Yes.

In detail

The model projections include the effects of at all timescales, albeit imperfectly. Models cannot predict the effect of natural internal variability of climate for a specific year, decade or longer period in the future. However, they can estimate the uncertainty due to natural internal variability, and this is done in UKCP09 for the 30-year time periods; hence the include the contributions from this source.