Factors affecting multiscaling analysis of rainfall time series

Abstract. Simulations based on random multiplicative cascade models are used to investigate the uncertainty in estimates of parameters characterizing the multiscaling nature of rainfall time series. The principal parameters used and discussed are the spectral exponent, β, and the K(q) function which characterizes the scaling of the moments. By simulating a large number of series, the sampling variability of parameter estimates in relation to the length of the time series is assessed and found to be in excess of 10%-20% for fields less than ~10⁴ points in length. The issue of long time series which may consist of physically distinct processes with different statistics is addressed and it is shown that highly variable data mixed with an equal amount of less variable data of similar strength is dominated entirely by the statistics of the highly variable data. The effects on the estimates of β and K(q) with the addition of white noise or the tipping bucket effect (quantization) can also be significant, particularly following gradient transformations. Some high resolution rainfall data are also analyzed to illustrate how a single instrumental glitch can strongly bias results and how mixing physically different processes together can lead to incorrect conclusions.