Iterative multiscale dynamic time warping (IMs-DTW): a tool for rainfall time series comparison

In many domains, such as weather forecasting, hydrology or civil protection, it is an important issue to characterize rainfall variability and intermittency in, either or both, a given time period or area. A variety of sensors, for instance, rain gauges, weather radars and satellites, are widely used for this purpose. Techniques to establish the similarity between rainfall time series are commonly based on the comparison of some extracted characteristic parameters (cumulative rainfall height, extreme values, rain occurrence, mean rain rate, etc.). The present study focuses on the development of a tool allowing to compare directly rainfall time series at a fine temporal scale. It allows quantifying the dissimilarity between the time series and determining a nonlinear relationship between their time axes. This study presents an algorithm based on a multiscale dynamic time warping approach, and it is based on the DTW algorithm applied on an iterative multiscale framework called IMs-DTW. This proposed algorithm is well suited for rain time series allowing point-to-point pairing between pairs of rainfall time. It takes the intermittency and the non-stationarity of the precipitation process into account. An application to measurements observed by four pluviometers located in the Paris area makes it possible to interpret the obtained results and to compare the IMs-DTW with more usual statistical features.