Modelling Typhoon Rainfall with Universal Multifractal
Authors: Chou Ching-Chun , Gires Auguste , Wang Li-Pen 
Published: February 2023

Universal Multifractal (UM) has been a useful tool to model rainfall processes across a wide range of spatialtemporal scales. Double Trace Moment (DTM) is a technique that helps estimate parameters for the UM model. Based upon the estimated UM parameters, a discrete random cascade process can be used to generate samples with realistic rainfall properties. UM parameters are of physical meanings, representing the levels of mean intermittence (C1) and the changing rate of the mean intermittency deviating from the average field (&#945;, know as the multifractality index), respectively. Therefore, these parameters are also widely used to characterise rainfall features across scales. UM has been tested in many countries under various weather conditions. However, its applications to extreme storm events, such as typhoons, are limited. In light of this, this study intends to analyse UM&#8217;s capacity of capturing and modelling extreme storm events recorded by a rainfall monitoring network in the South of Taipei City. On the roof of the Civil Engineering Research Building at National Taiwan University, an innovative extreme rainfall monitoring campaign has been set up and collecting high-quality rainfall measurements at fine timescales over the past two years. Rainfall data from several extreme rainfall events, including four typhoons and 10+ thunderstorms, has been collected. In this work, high-resolution rainfall time series from the laser disdrometer for typhoon Nalgae is used for analysis. Rainfall measurements are first aggregated from the native 10-second resolution to 80-second and coarser resolution and then downscaled back to 10-second to verify the downscaling results. The UM analysis is conducted in three different ways. The first way is to apply UM analysis to the entire time series. The resulting parameters are &#945; = 1.32 and C1 = 0.108. Then, the time series is equally divided into 16 sections such that the temporal variations in rainfall features can be observed. Similarly to the first way, the second way applies the &#8217;standard&#8217; UM analysis but to each section. This leads to &#945; ranging from 1.1 to 1.9 and C1 from 0.05 to 0.18. Finally, the third way applies &#8217;ensemble&#8217; UM analysis that concatenates divided sections into a single matrix. This results in &#945; = 1.55 and C1 = 0.125. The derived parameters are then used to sample 10-second rainfall estimates with a discrete cascade process. The performance is quantified based upon the capacity of preserving observed extreme features. We first analyse the ranges of &#945; and C1 resulting from the samples downscaled from the first and the third ways. We can see that the resulting &#945; ranging from 1.2 to 1.8 and C1 from 0.06 to 0.16, which fails resembling the aforementioned variability of the UM parameters (i.e. 1.1&#8722;1.9 and 0.05&#8722;0.18). In fact, only the second way leads to satisfactory result. This preliminary study suggests that typhoon rainfall experiences drastic behaviour changes within a short period, which requires a more &#8217;dynamic&#8217; way to model these changes well. Similar analyses will be conducted over other collected typhoons and thunderstorm events to see if the findings can be generalised.