A diagnostic study of spectral multiscaling on spatio-temporal accumulations of rainfall fields based on radar measurements over Iowa

Spectral multiscaling postulates a power-law type of scaling of spectral distribution functions of stationary processes of spatial averages or their temporal accumulations, over nested and geometrically similar sub-regions of the spatial parameter space of a given spatio-temporal random field. Presently, the validity of this property is investigated using time series of spatio-temporal accumulations of rain rate fields measured by a network of Doppler radars covering the region of Iowa. Statistical evidence of spectral multiscaling is gathered and discussed through a systematic study of appropriate regression diagnostics, using two records of data. One is a 120-month record of hourly (60-min) accumulations of spatially averaged rain rate on square pixels of side length 4 km, comprising a rectangular grid of dimension 80×160 covering almost the entire State of Iowa. The other is a 74-month record of quarterly (15-min) accumulations of spatially averaged rain rate on square pixels of side length 1 km, comprising a rectangular grid of dimension 68×106 over the Cedar River basin in eastern Iowa. The diagnostic results indicate frequency-dependent scaling relationships interpreted as evidence of spectral multiscaling across a range of spatial scales.