Multiresolution analysis (MRA) classification of plurennial to multi-decadal climate drivers to streamflow in France using Wavelet Transform and Geostatistical Euclidean Distance Clustering

Abstract. It is interesting to try and classify the spatial data to infer the spatial scales associated with certain characteristics within a group of time series. It is indeed very important for operational practices such as flood management and/or climate change adaptation to not only know the severity of a potential impact but also predict the spatial extent of the impact, since similar stations should suffer similar consequences. Classifications on streamflow have already been studied (Hannah etal., 2000; Renard et al., 2006; Wilson et al., 2013) and climate to rainfall or streamflow classification has also been realized by Boé and Terray (2008), Martinez et al. (2008), Martinez and Garavaglia et al. (2010) Garavaglia. Most of those studies establish classification based on annual hydrological regimes. This is in deep contrast with the study that focuses on low frequency time series. There are two axes that the present study aims at improving on. First most of the previous works were carried on raw signals while it is known that different scales of variability (TSV) characterize variabilities of geophysical signals. For instance, atmospheric pressure, precipitation, annual cycle, aquifer contribution or even tidal cycle variability may all be contributing to streamflow variabilities (Labat et al., 2000; Massei and Fournier, 2012). Several studies have highlighted the correlation between some time scales of variability in streamflow or rainfall and the corresponding scales in climatic fields (Massei et al., 2007; Massei et al., 2010; Feliks and Ghil, 2010; Fritier et al., 2012; Pinault, 2012). More specifically on streamflow, Boé and Habets (2013) have shown that multi-decadal variability in streamflow in France was impacted by large multi-decadal climate oscillation especially the Atlantic Multi-decadal Variability. Dieppois et al. (2013) Dieppois highlighted the importance of considering the different TSV in assessing the link between climate fields and local temperature and rainfall variability. Relation of hydroclimate time scales to spatial scales has also been recently also in vestigated by Laepple and Huybers (2014). Those studies highlight the importance of considering each time scale separately. Thus prior to doing a clustering analysis, the input signals must be decomposed into nearly independent components (as Palus (2014) and Jajcay et al. (2016) Jajcay pointed out, pure independence is rarely seen). The second axis is the classification method itself. Classifying fields is always difficult because the extension in two dimensions brings the notion of "general similarity" which is different from "local similarity" i.e. two fields may have differences pointwise but an otherwise similar global shape. To deal with it, fields are either represented as index (Boé and Habets, 2013; Lopez and Frances, 2013) which necessarily lose a lot of spatial information or a mean of taking into account the global shape has to be found like, for example, the Teweles-Wobus score. However the performance of such score is very variable dependent (it works well on pressure fields but less on other field variables) (Teweles and Wobus, 1954). This study presents a method called Geostatistical Euclidean Distance Clustering (GeoEDC) whose performance, by considering the field as an image, is less variable-dependent.