Downscaling rainfields in space and time, using the String of Beads model in time series mode

摘要

The String of Beadsmodel is a space-time model of rainfields measured by weather radar. It is heredriven by two auto-regressive time series models, one atthe image scale, the other at the pixel scale, to model the temporal correlationstructure of the wet-period process. The marginaldistribution of the pixel scale intensities on a given radar-rainfall image isdescribed by a log-normal distribution. The spatial dependencestructure of each image is defined by a power spectrum approximated by a powerlaw function with a negative exponent. It is demonstratedthat this stochastic modelling approach is valid because the images sampled areeffectively stationary above a scale of 30 km, which isless than a quarter of the image width. By advecting a simulated sequence ofimages along the same cumulative advection vector as theobserved event and matching the image-scale statistics of each simulated imagewith those of the corresponding observed image, a simulatedsequence of plausible images is generated which mimics (has the same space-timestatistics as) the observed event but differs from it indetail. Aggregating the pixel scale intensities in each sequence over a numberof time and space intervals and then comparing their spatialand temporal statistics, demonstrates that the model captures the intermediatescale behaviour well, showing satisfactorily its ability todownscale rainfall in space and time. The model thus has potential as anoperational space-time model of rainfields. style="line-height: 20px;">Keywords: Space-time, rainfield modelling, weather radar, multifractals, Gaussian random fields