  In applications of climate information, coarse-resolution climate projections
commonly need to be downscaled to a finer grid. One challenge of this
requirement is the modeling of sub-grid variability and the spatial and
temporal dependence at the finer scale. Here, a post-processing procedure is
proposed for temperature projections that addresses this challenge. The
procedure employs statistical bias correction and stochastic downscaling in two
steps. In a first step, errors that are related to spatial and temporal
features of the first two moments of the temperature distribution at model
scale are identified and corrected. Secondly, residual space-time dependence at
the finer scale is analyzed using a statistical model, from which realizations
are generated and then combined with appropriate climate change signal to form
the downscaled projection fields. Using a high-resolution observational gridded
data product, the proposed approach is applied in a case study where
projections of two regional climate models from the EURO-CORDEX ensemble are
bias-corrected and downscaled to a 1x1 km grid in the Trondelag area of Norway.
A cross-validation study shows that the proposed procedure generates results
that better reflect the marginal distributional properties of the data product
and have better consistency in space and time than empirical quantile mapping.
