The climate in the area studied is of the oceanic type (Champeaux and Tamburini, 1995). The winter monthly average range of precipitation data is relatively homogeneous, corresponding to a winter average ranging between 184.3 mm (Chartres) and 264.1 mm (Chatillon-sur-Seine), and with a standard deviation ranging between 57.4 mm (Bretigny-sur-Orge) and 90.6 mm (Chatillon-sur-Seine).

Nine precipitation time series on the Seine watershed are used in this study (Fig. 1). Data were obtained from the database compiled for the European Climate Assessment (ECA) as presented in Klein Tank et al. (2002), who demonstrated in this paper the quality of the ECA data sets. The maximum variability of NAO occurs in winter (Hurrell et al., 2003), which is why we used cumulated winter-months (DJFM) precipitation data to evaluate the covariation between NAOI and NW European rainfall. The NAOI data used in this study were defined by Li and Wang (2003) for the 1873 to 2004 period.

As a first step, in order to identify the trend in the short-term 1951 to 2004 precipitation time series, a LOESS local polynomial regression was used, as proposed by Cleveland (1979) and developed by Cleveland and Devlin (1988). LOESS combines much of the simplicity of linear least squares regression with the flexibility of non-linear regression. At each point in the data set, a low-order polynomial is fit to a subset of the data, with explanatory variable values taken near the point whose response is being estimated. The polynomial is fit using weighted least squares, giving more weight to points near the point whose response is being estimated and less weight to points further away. The value of the regression function for the point is then obtained by evaluating the local polynomial using the explanatory variable values for that data point. A user-specified input to the procedure called the “smoothing parameter” determines how much of the data is used to fit each local polynomial. In this study, the smoothing parameter was set to 100%, which allows the lowest frequencies in the data to be detected.

In addition, segmentation was also undertaken to identify change points in terms of mean and/or variance that may be present in the data. In short-term series, classical binary segmentation is applied to the characterization of potential changes in the mean from 1951 to 2004, and compared to the variations that can be shown by LOESS smoothing. As for the long-term series, segmentation was undertaken as well to detect change points in the mean and variance, to be compared to the analysis by CWT. Here, the Pruned Exact Linear Time (PELT) method developed by Killick et al. (2011) based on the algorithm of Jackson et al. (2005) was used to detect the changes in the mean and variance through time.

CWT analysis is designed to identify the spectral structure of transient signals. It is particularly appropriate for assessing the dominant modes of variability, potentially changing through time, that characterize natural geophysical signals. Detailed explanations of the CWT methodology and its application to hydrometeorological or climatic time series are now widely documented in the literature (Anctil and Coulibaly, 2004; Labat et al., 2005; Torrence and Compo, 1998). The analysis of NAO and precipitation time series by CWT was used to compute the wavelet coherence (WCO) and phase, to highlight the relationships between the two signals using the Sowas R package by Maraun and Kurths (2004). Component extraction and reconstruction were also performed in R by wavelet multi-resolution analysis using order 18 Daubechies wavelets (Labat et al., 2000, 2002).

In the first part of this section, nine weather stations in the Seine watershed are briefly analysed in order to assess the influence of large-scale climate oscillations on the inter-annual variability of precipitation and to ensure that no local effects alter this variability.

3.1 Characteristic time scales of the North Atlantic Oscillation index/precipitation relationship

The study of short-term precipitation data highlighted two main periods that can be distinguished by a significant change in the mean with a change point located in the mid-1970s. Indeed, binary segmentation identified one change point in most precipitation series, emphasizing the existence of a period of higher winter precipitation after the mid-1970s (Fig. 2). On the other hand, LOESS smoothing also identified the existence of such a change point, but instead indicated that this corresponded to a longer-term trend involving a decrease in precipitation until the end of the study period (2004). Both segmentation and LOESS also revealed a different pattern for one weather station (Fig. 2d), emphasizing a change point in the late 1980s instead of the mid-1970s, which might be due to local effects. However, this last change point was also found in the daily precipitation data of the study area (Massei et al., 2007) as well as in the Seine flow series (Massei et al., 2009). In these studies, it was suggested that both the mid-1970s and late 1980s change points were related to changes in the time/scale variability of the NAO pattern: ∼18-year and ∼ 6-year inter-annual to pluri-decennial scales of variability were found to characterize periods covering the mid-1970s to early 2000s and late 1980s to early 2000s, respectively. It then seems useful to compare the evolution of the NAOI and changes in precipitation through wavelet coherence analysis in an attempt to better identify their degree of correlation.

The correlations between NAOI and precipitation by wavelet coherence analysis (Fig. 3) point out that most stations were characterized by three time periods of inter-annual variability, i.e. before the mid-1970s, from 1970 to 1990 and after 1990. These periods can be distinguished by the presence or absence of significant correlations on the ∼6-year variability scale. For most stations, the periods before the mid-1970s and after 1990 are characterized by a statistically significant correlation between NAOI and winter precipitation for the ∼6-year variability scale. However, no such correlation is observed at this scale for the period between the mid-1970s and 1990. These observations are similar to the results obtained by CWT and reinforce the presence of a NAOI/precipitation relationship for these scales of variability. We also note the presence, for all these periods, of a statistically significant correlation between NAOI and winter precipitation for the ∼18-year variability scale for most stations. For the time period considered, however, this low-frequency scale of variability must be interpreted with caution, more specifically in terms of variance estimation, and it falls into the cone of influence of the continuous wavelet spectrum. Nevertheless, results from the long-term analysis provided hereafter still validate at least the existence of this ∼18-year component. The phase diagram of the wavelet coherence analysis gives more information on the NAOI/precipitation relationship (Fig. 4). It appears that the two signals are out of phase over the ∼18-year variability scale. For the ∼6-year variability scale, we show a quadrature phase before the mid-1970s and since 1990. These dissimilar phase lags suggest that the NAOI/precipitation relation is more complex than a simple and stationary correlation at these scales.

3.2 Relationships between precipitation, Azores high and Icelandic low

The Icelandic low, represented by the Reykjavik SLP/Precipitation relationship, can be essentially characterized by the ∼18-year variability scale (Fig. 5A). The phase diagram of Icelandic low/precipitation wavelet coherence points out that the two signals are in phase (Fig. 5C). This result shows the presence of a good relationship (the two signals are in phase) between precipitation and the Icelandic low for the ∼18-year variability scale, and a weaker relationship (quadrature phase) between these signals for the ∼6-year and ∼11-year scales.

In order to explore the long-term evolution of precipitation variability and compare it to that of NAO, we used one long-term precipitation station (Paris) for the 1873 to 2004 period. In view of previous results, which indicate the same evolution for all the precipitation stations studied at inter-annual scales, these results are expandable to the entire Seine River watershed.

The long-term NAOI analysis by the PELT segmentation method (Fig. 6A) shows three major change points during the 1910s, the late 1930s and from the early 1960s, separating periods with a significantly different mean and variance. The main result emphasized by the PELT segmentation is that the period starting in the early 1960s is characterized by high variability of the NAOI signal. Well-known abnormally positive NAO phases during the 1990s are recovered. On the other hand, the PELT segmentation of long-term precipitation (Fig. 6B) shows two major change points (around the late 1910s and in the late 1970s). Although precipitation after 1980 is generally higher than the mean precipitation over the entire 1873 to 2004 period (significantly during the 1980s), it is not clear whether a relation can be established between NAO phases and precipitation anomalies (taking the 1873–2004 mean as a reference). The 1930s change point was only detected in the long-term NAOI and has also been reported in the SLP-SST Atlantic data (Tourré et al., 1999).

The long-term NAOI analysis by CWT (Fig. 7A) shows enhanced amplitudes for most inter-annual scales since 1960 (∼4- to 5-year, ∼8-year, ∼20-year, ∼40-year and ∼ 84-year). The NAOI spectrum also emphasizes a clear lack of energy before 1910. These results seem consistent with those obtained by the PELT segmentation. Only the ∼8-year peak, spanning the 1970 to 2000 period, appeared statistically significant between ∼1975 and 1985, although the spectrum highlights the presence of energy peaks between the ∼4- to 5-year scale and slightly higher than the 8-year scale; however, the high intermittence of energy within this scale range results in the presence on the global wavelet spectrum of a peak at ∼8 years, which is barely distinguished from the rest of the spectrum in the ∼4- to 5-year scale range. The long-term precipitation analysis by CWT (Fig. 7 B) highlights two time periods, before and after 1910, characterized by different scales of variability. The period after 1910 is clearly associated with an increase in the energy at most scales. Peaks around ∼4- to 7-year and ∼11-year are the highest in energy and statistically significant and are very localized in time, although energy is also present between the ∼21-year, ∼35-year and ∼62-year scales. In sum, continuous wavelet analysis of NAOI and precipitation for both signals highlighted a general increase in amplitude of most of their characteristic time scales, but delineating any obvious common oscillations between the two signals is not straightforward.

Wavelet coherence analysis between long-term NAOI and precipitation series was then undertaken in order to investigate the time evolution of their relationship more accurately. The coherence spectrum between NAOI and Paris precipitation (Fig. 8) displays coherent structures with peaks around ∼4.5, ∼12, ∼21 and ∼55 years, as summarized by the global wavelet coherence spectrum. A clear lack of coherence shows up for scales higher than 8 years, emphasizing the intermittence of the NAOI/precipitation relationship at these scales. For the smallest scales less than 8 years, coherence appears much more sporadic, displaying coherent structures before ∼1895, between ∼1935 and ∼1955, and after 1990. Obviously, the same time evolution as for the 1950 to 2004 period (Fig. 4) is recovered, and the ∼18-year scale of variability that previously fell into the cone of influence in short-term series is now interpretable, corresponding to the ∼21-year peak in the coherence spectrum. Our results join those of Labat et al. (2005), who reported the same scales of variability in the long-term oscillation of river discharge at the pan-European scale over the last century. Hence, our results confirm the consistency of a large-scale climatic control on hydrology. According to our analysis, the NAOI/precipitation relationship seems to have undergone a weakening between ∼1910 and ∼1950, especially on the 21-year scale, while during this period a strengthening of the 4.5-year oscillation was observed.

Precipitation components coherent with NAO can then be extracted and reconstructed from the long-term precipitation time series based on NAOI/precipitation wavelet coherence analysis (Fig. 9), which provides a time-domain visualization of the different modes of precipitation variations. Here, wavelet multi-resolution analysis was used to separate the signal into constitutive components according to the wavelet scales. Details from the multi-resolution analysis can be compared to the energy bands (from CWT) and coherent scales of variability (from WCO) detected previously. Six scale levels of decomposition were obtained using a maximum level chosen so as to consider wavelet interior coefficients only (i.e. those coefficients not subject to circular filter operations for boundary treatment). Among those six details, D1, D2 and D3 + D4 corresponded to ∼4.5-year, ∼12-year and ∼21-year scales, respectively, defined previously based on continuous wavelet analysis. On the other hand, D5 and D6 correspond to the ∼55-year scale of variability. From the wavelet reconstruction, it seems that the amplitudes of components D2–D5 increased across the period of study, more particularly since ∼1910 to 1920, which would be in accordance with the change in mean and variance detected using the PELT segmentation. Also, some periods seemed more particularly affected by an increasing variance (e.g. ∼1915–1955 and ∼1980–2004 for D2). The ∼55-year (D5 + D6) component also closely corresponds to the trend that was detected using LOESS smoothing in 1951 to 2004 (Paris station, Fig. 2 F and Fig. 10), hence showing that the trend for this period actually corresponds to this low-frequency oscillation characterizing both precipitation and NAOI. Finally, it is worth noting here that the extracted components are not necessarily associated with a significant coherence with NAO, which questions the capability of NAO to capture the climate oscillations that are actually related to precipitation fluctuations. In other words, although the NAO seems to remain a good reference for investigating links between climate oscillations and winter precipitation fluctuations in the region of interest, it is not the best climate predictor characterizing hydrological winter precipitation variations.

In this study, we investigated the inter-annual to multi-decadal variability of winter-months precipitation in the Seine River watershed (north-western France) and its potential relationships with the North Atlantic climate variability using the NAOI. We first demonstrated the presence of two change points around the mid-1970s and 1990 in the precipitation on the Seine River watershed. The first change point corresponded to a trend in the 1951 to 2004 period that separated below-average (negative anomalies) and above-average (positive anomalies) precipitation amounts compared to the 1951 to 2004 mean. For all the precipitation time series among the nine series selected in the watershed, wavelet coherence emphasized the correlation between precipitation and NAOI for variability scales of about ∼18-year as well as an inter-annual scale of ∼6-year over most of the 1951 to 2004 period, demonstrating a large-scale origin of regional and local climate variability. It is worth noting here that the same change points and/or scales of variability were also identified by many authors in other climatic or hydrological processes on a global scale (a quasi-decadal in the NAO since 1980 (Hurrell and Van Loon, 1997): global scale inter-decadal (12-year) and 6- to 7-year period fluctuations of SST and SLP in the North Atlantic and the Intertropical Convergence Zone (Grötzner et al., 1998; Tourré et al., 1999; Venegas et al., 1997) and in the Northern Oscillation Index (Schwing et al., 2002); a noticeable increase in annual minimum and median daily stream flow around 1970 (Mc Cabe and Wolock, 2002); a pronounced winter and spring warming over northern continents since about 1970 (Serreze et al., 2000), which have often been related to the observation of global environmental changes (a ∼40% reduction in plankton biomass during 1977 to 1988 relative to 1970 to 1976 in the central Gulf of Alaska (Alexander et al., 2008); a rather warm period from 1970 to 1985 was characterized by sardine dominance (Alheit and Niquen, 2004); and a rise in fish productivity after 1970 (Daskalov, 2003). According to our observations, the ∼18-year scale appeared to be related only to the variability of the Icelandic low, whereas the ∼6-year decadal fluctuation seemed mostly related to the Azores high.

A long-term analysis was made based on the availability of a 1873 to 2004 time series of both precipitation in Paris and NAOI winter (DJFM). Change points were identified during the 1910s for both signals, denoting changes in the mean and variance. The relationships between NAOI and precipitation over the long-term seemed to evolve with time, although present throughout almost the entire period, according to the scale of the internal fluctuations decomposed by multi-resolution analysis. However, the coherence decreased significantly between 1900 and 1930. The general trend in precipitation as detected by LOESS smoothing for the 1950 to 2004 period, which looked like an increasing trend, could actually be related to a longer-term ∼55-year fluctuation recorded in the longer precipitation and NAOI series, hence denoting an oscillating, pseudo-periodic feature. However, in both the NAOI and precipitation signals, a general increase in variability was determined for all characteristic time scales across the last century, which would deserve to be considered in the present context of climate change. Finally, the lack of coherence during some periods suggests that although the NAO is a good reference for characterizing the evolution of the North Atlantic climate, it is too rough to be the best predictor for local or regional hydrological variations.