Decadal to secular time scales variability in temperature measurements over France



[1] The influence of inter-decadal and secular variability on the annual mean air surface temperature variability over France is characterized for the period 1880–2005, together with a description of their regional distribution. After a descriptive study of temperature linear trends over the century, the oscillatory components of the series are investigated through continuous and discrete wavelet transform. This study reveals the importance of inter-decadal time scales (40–60 and 60–80 years) and particularly the evolution of their phase shift in the latest epoch of the high temperatures rise over France (since 1980).

1. Introduction

[2] According to the Intergovernmental Panel on Climate Change (IPCC) [2000, 2001], European temperatures have increased by 0.8°C during the last century. Different synoptic climatologies confirm that this increase has not been continuous throughout the century, as temperatures slightly decreased from roughly 1950 to 1980 [Hansen et al., 2001; Jones and Moberg, 2003], suggesting that climate variability at inter-decadal time scales may play a role. In addition, Luterbacher et al. [2004] show that the intensity of the latest warming phase, from 1980 to present, is very likely to be unprecedented for the past 500 years. A variety of recent papers, conducted by means of simple linear trend analysis of homogenised climate series, confirm these features over France [Moisselin et al., 2002], or for the neighbouring Grand Duché of Luxembourg [Drogue et al., 2005], but standard linear trend analysis fails to capture the oscillatory components of the series.

[3] In this short note, we wish to give a different insight on the evolution of the time-series of temperatures averaged over France, by recognizing and describing the different time scales that affect the surface temperatures. The fine 1° × 1° resolution of the studied data set allows us to investigate details in the spatial patterns of the changes. After presenting the data set used and the methodology employed, the annual mean time series of temperatures from 1880 to 2005 over France is described for its general linear trend and different epochs of variability.

[4] The spectral characteristics of the time-series of temperatures averaged over France and the time-series at each gridpoint are investigated through a continuous wavelet transformation (CWT), while a discrete wavelet transform (DWT) is used to separate and quantify the different spectral bands.

2. Data and Methodology

[5] The data set used here consists of 70 long time-series of temperature available over France, most covering the period 1880–2005, constructed and homogenised by Meteo-France according to Caussinus and Mestre [2004]. These time-series are used to produce a 1880–2005 monthly grid (resolution 1° × 1°), from which monthly anomaly fields are computed against the 1961–1990 monthly means. The annual gridpoint anomalies are spatially averaged to compute the France annual time series of temperature anomalies over France.

[6] The time series analysis is conducted using several methods. A linear trend is fitted to the time-series, based on a generalized least squares linear regression with AR(1) errors. Analyses of spatial linear trends are derived from contour plots of the slopes of the linear trends fitted to the time-series at each individual gridpoint.

[7] A Continuous Wavelet Transform (CWT) [Torrence and Compo, 1998] allows us to identify the spectral bands, while a Discrete Wavelet Transform (DWT) [Craigmile and Percival, 2002] is used to filter the time series on these bands. DWT is performed using a discrete Meyer mother wavelet. For the wavelet decomposition level, we chose a six level decomposition where the inter-decadal time scales are separated within the 5th (D5: ≅ 30-to-55 year periods) and 6th level (D6: ≅ 55-to-90 years period) while the lower frequency oscillations, that is, the trend (secular time scales) are represented in the approximation A6. Higher frequencies are captured within the first four details (1-to-4); the inter-annual time scales are located in the first two levels (D1 and D2: ≅ 2-to-9 years periods), decadal time scales being given in the 3rd and 4th levels (D3 and D4: ≅ 9-to-30 years periods). In addition we also apply an Empirical Modal Decomposition (EMD) [Huang et al., 1998; Flandrin and Gonçalves, 2004].

3. Temporal Linear Trend Estimated at Each Gridpoint

[8] The time-series of the annual mean air temperature anomalies averaged over France for the period 1880–2005 is shown in Figure 1. On the whole period 1880–2005, the estimated slope is equal to 0.94°C/century. However, this increase is not monotonous. A simple visual inspection of the annual means reveals that from 1880 to roughly 1950, temperatures increased at an estimated rate of +0.10°C per decade. In contrast, from 1950 to 1980, temperatures decreased by −0.045°C per decade. The 1980–2005 epoch is characterized by an impressive raise rate of +0.54°C per decade.

Figure 1.

Time series of annual mean temperature anomalies over France smoothed by means of kernel regression (solid, Epanechnikov kernel, bandwith 9 years) and fitted by linear trend (dotted).

[9] The geographic pattern of these annual mean linear trends is also interesting. The general picture of the 1900–2005 geographic slopes (Figure 2, left), shows that the higher linear trends are located in southern France. Instead after 1980 (Figure 2, right), the greatest impact of this rise concerns North and East of France.

Figure 2.

Spatial temperature linear trends for the period (left) 1900–2005 and (right) 1980–2005, in °C per decade.

[10] Analyses of spatial linear trends of minimum and maximum temperatures (not shown here) together with 1931–2000 spatial linear trends of sunshine duration series [Moisselin and Canellas, 2005] gives a first explanation to the spatial patterns of the 1900–2005 rise. While sunshine duration has increased in the south (+0.5% per decade on average), it decreases in the north of France (up to −1% per decade). This decrease in sunshine duration has a relative cooling effect that mainly affects maximum rather than minimum temperatures. As a consequence, maximum temperature (and hence mean temperature) increase is less important in the north over most of the XXth century.

4. Variability

[11] The CWT analysis (Figure 3) of the annual mean time-series over France reveals inter-annual time scales dominated by a 5-to-8 year periodicity, which is known in Europe to be highly correlated with the NAO (North Atlantic Oscillation) [Hurrell et al., 2003]. The France temperature series also presents a period of high amplitudes at decadal scales between 1940 and 1960, as well as a period with greater amplitudes at bidecadal scales between 1880 and 1920. We can also remark that it presents high amplitudes at 40-to-60 year scales as well as at 60-to-80 year scales. Because the length of the time span is rather short, we tested the inter-decadal time scales for significance, using a red noise (AR(1)) wavelet background spectrum [Torrence and Webster, 1998]. The variability at inter-decadal time scales (40–80 years) is significant at the 0.10 level from about 1940 to the end of the period. Those multi-decadal oscillations are also found to be significant by means of Multichannel Singular Spectrum Analysis over a gridded reconstruction of annual temperatures over Europe [Shabalova and Weber, 1999] and global mean temperature records [Schlesinger and Ramankutty, 1994]. [Parker et al., 1992] of the much longer Central England Temperatures (CET) (not shown here) confirms these features – see also Benner [1999].

Figure 3.

Continuous wavelet amplitude (in °C) analysis of the annual mean temperature anomalies over France.

[12] The DWT decomposition reveals that the inter-annual (Figure 4a) and decadal (Figure 4b) timescales (D1-to-D4) summed together explain more than 60% of the annual mean 1880–2005 variance, but the sum of these first four details (not shown here) does not contribute much to the linear trend over the century (0.0048°C/dec), neither over the last 30 years (0.056°C/decade). Figure 4c shows inter-decadal timescales, while the secular component A6 exhibits a regular increasing trend that can be linked directly to climate change (Figures 4d and 5) .

Figure 4.

Multiresolution Resolution Analysis with non-decimated discrete wavelets of the annual mean temperature anomalies over France, (a) D1 (solid) and D2 (dashed) interannual details, (b) D3 (solid) and D4 (dashed) decadal details, (c) D5 (solid) and D6 (dashed) interdecadal details, and (d) secular component A6 (solid) and D5 + D6 (dashed).

Figure 5.

Time series of annual mean temperature anomalies over France (black), (A6 + D5 + D6) reconstruction (solid black), and A6 (dashed).

[13] When summed (Figure 4d), the inter-decadal time scales (D5 + D6) explain less than 15% of the total variance, but they contribute to a great part of the increase after 1980: 0.49°C per decade since 1980, compared with 0.002°C per decade since 1900. This sum (particularly D5) also contributes to the negative slope visible from 1950 to 1980 (−0.018°C/decade) in the annual time series (Figure 4d). The corresponding slope (1950–1980) of the inter-annual time scales (D1+D2) is equal to −0.03°C per decade. Note that D5 and D6 are almost in phase opposition from 1900-to-1950, explaining the lack of significant contribution of these modes to the secular linear trend over these years. Comparing the summed D5 + D6 + A6 components to the original annual mean time series (Figure 5) reveals an outstanding agreement over most of the observed period between observations and the reconstructed D5 + D6 + A6 trend. An examination of the DWT of the CET time series since 1700 confirms the above result (not shown here).

[14] Finally, the Empirical Modal Decomposition of the series (Figure 6) confirms this decomposition and the different modes obtained through DWT. This demonstrates that the result is robust to choice of decomposition method.

Figure 6.

Intrinsic Mode Functions (IMF) of the Empirical Modal Decomposition, (a) IMF1 (solid) and IMF2 (dashed) interannual details, (b) IMF3 (solid) and IMF4 (dashed) decadal details, (c) IMF5 (solid) and IMF6 (dashed) interdecadal details, and (d) secular component IMF7 (solid) and IMF5 + IMF6 (dashed).

[15] The spatial patterns of the secular and inter-decadal timescales (Figure 7) exhibit the same features as those observed in the spatial temperature linear trends (Figure 2). Regionally, the A6 component (secular trend) is more intense in the south of France, therefore explaining the secular pattern (Figure 7, left, to be compared with Figure 2, left). On the contrary, the spatial linear trends of the sum of the inter-decadal time scales (D5 + D6 in Figure 7, right, to be compared to Figure 2, right) for the most recent period (1980–2005) are higher in North and East of France, explaining why the more intense trends of temperatures are located in these regions over the recent period.

Figure 7.

(left) A6 spatial linear trends reconstructed for period 1900–2005 and (right) D5 + D6 spatial linear trends reconstructed for period 1980–2005 (in °C per decade).

5. Conclusion

[16] As a short conclusion, wavelet analysis (continuous and discrete) reveals that a significant part of the latest warming (1980–today) as well as part of the previous cooling (1950–1980) observed on France temperature time series are due to the sum of two inter-decadal components. This is confirmed by the results of an alternative EMD method. The monotonous secular trend, associated with global warming is clearly modulated by inter-decadal time scales. This interdecadal variability has contributed to additional regional warming in particular since 1980. In France, this warming was larger in the northern and north-eastern parts.


[17] We wish to thank Patrick Flandrin for his EMD software, as well as Hannah Clark for her manuscript comments and corrections.