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

Spectral multi-scaling postulates a power-law type of scaling of spectral distribution functions of stationary processes of spatial averages, over nested and geometrically similar sub-regions of the spatial parameter space of a given spatio-temporal random field. Presently a new framework is formulated for down-scaling processes of spatial averages, following naturally from the postulate of spectral multi-scaling, and key ingredients required for its implementation are described. Moreover, results from an extensive diagnostic study are presented, seeking statistical evidence supportive of spectral multi-scaling. Such evidence emerges from two sources of data. One is a 13 year long historical record of radar observations of rainfall in southeastern UK (Chenies radar), with high spatial (2 km) and temporal (5 min) resolution. The other is an ensemble of rain rate fields simulated by a spatio-temporal random pulse model fitted to the historical data. The results are consistent between historical and simulated rainfall data, indicating frequency-dependent scaling relationships interpreted as evidence of spectral multi-scaling across a range of spatial scales.