Fractal interpolation of rain rate time series

Abstract

Meteorological radar databases exist providing rain rate maps over areas with a sampling period of 2–15 min. Such two‐dimensional, rain rate map time series would have wide application in the simulation of rain scatter and attenuation of millimeter‐wave radio networks, if the sampling period were considerably shorter, i.e., of the order of 10 s or less. However, scanning a large radar at this rate is physically infeasible. This paper investigates a stochastic numerical method to interpolate point rain rate time series to shorter sampling periods while conserving the expected first‐ and second‐order statistics. The proposed method should generally be applicable to the temporal interpolation of radar‐derived rain rate maps. The method is based on the experimentally measured simple‐scaling properties of log rain rate time series. It is tested against 9 gauge years of rapid response drop‐counting rain gauge data, with a 10 s integration time, collected in the southern UK. The data are subsampled to yield time series with a 10 s rain rate measurement every 320, 640, and 1280 s. The subsampled time series are then interpolated back to a 10 s sample interval, and the first‐ and second‐order statistics are compared with the original time series.