A stochastic framework for downscaling processes of spatial averages based on the property of spectral multiscaling and its statistical diagnosis on spatio-temporal rainfall fields

► We introduce a new framework for down-scaling processes of spatial averages, shaped by the postulate of spectral multiscaling. ► We develop methodology for statistical diagnosis of spectral multi-scaling. ► We apply the diagnostic methodology on observed and simulated rain fields. ► Spectral multi-scaling furnishes a genuine spatio-temporal diagnostic tool for evaluating models of dynamic phenomena with spatio-temporal variability.