There is growing evidence that large-scale climate oscillations have direct influence on a region's water resources. Khaliq et al. (2006) summarized a number of studies where associations between climate patterns and basin-scale hydrological processes have been developed. Most of the research concerning the Mediterranean basin and particularly North African climate is related to the analysis of rainfall and temperature variability.
A leading pattern of weather and climate variability over the Northern Hemisphere is the North Atlantic Oscillation (NAO). NAO refers to a redistribution of atmospheric mass between the Arctic and the subtropical Atlantic, and swings from one phase to another producing large changes in surface air temperature, winds, storminess and precipitation over the Atlantic as well as the adjacent continents (Hurrell and Deser, 2009). A number of studies have shown that NAO strongly influences the Mediterranean basin (Adjez, 2000; Jacobeit et al., 2001; Dünkeloh and Jacobeit, 2003). According to Marshall et al. (2001), drier than normal conditions occur during high NAO index winters over much of central and southern Europe, the northern Mediterranean countries and western North Africa. Using principal component analysis, Luterbacher et al. (2005) found NAO to be well correlated with Mediterranean rainfalls comparatively to other large-scale climate patterns. Correlation analysis carried out by Sâadaoui and Sakka (2007) put in evidence statistically significant positive correlations of about 0.3 between northern African precipitation and NAO while western European precipitation is found to be negatively correlated with NAO. The research of Xoplaki et al. (2004) covering the Mediterranean basin leads to the conclusion that interdecadal changes in the first canonical correlation mode of wet season precipitation are related to variations in the NAO and are responsible for comparable time-scale variations of the Mediterranean precipitation throughout the 20th Century.
On the other hand, Ropelewski and Halpert (1987) found evidence for El Niño Southern Oscillation (ENSO)-related precipitation variability in northern Africa and southern Europe. However, they noticed that ‘implied ENSO relationships in these regions are difficult to understand or attribute to any of the known ENSO-related atmospheric circulation changes’. They also remarked that this ENSO relationship is unstable in time. The sign of ENSO-related precipitation anomalies for the 1932–1953 period was opposite to that observed for both the earlier and the later period. Mariotti et al. (2002a) distinguished two different periods: the period 1925–1940 with lack of significant correlation between Euro-Mediterranean seasonal rainfall and ENSO and the second half of the 20th Century characterized by no correlation. Mariotti et al. (2002b) also found that in spring and autumn, ENSO-like global sea-surface temperatures (SST) anomalies are significantly correlated with western Mediterranean rainfall anomalies. However, they admit that ‘… the mechanisms of how these SST anomalies exert their influence in the far away Euro-Mediterranean region are poorly known’. On the other hand, Brönnimann et al. (2007) established that ENSO has a considerable influence on temperature and precipitation for Europe and North Africa. According to Zanchettin et al. (2008), El Niño/La Niña impacts on European wintertime rainfalls are found to be modulated by decadal phases of the Pacific Decadal Oscillation (PDO). In fact, ENSO is linked to the North African Asian (NAA) jet stream which is an upper-tropospheric jet that extends from the subtropical Atlantic across North Africa, the eastern Mediterranean, the Middle East, central Asia, and Japan to the North Pacific (Shaman and Tziperman, 2007). Unlike temperature and precipitation data, the linkage between streamflows and climate indices variability in the Mediterranean region is not yet adequately investigated. The results found by Eltahir (1996) suggest that the influence of ENSO on streamflows in Africa is modest. Kalayci and Kahya (2006) used principal component analysis and found that Turkish streamflows are sensitive to the variations of NAO while the fifth principal component of Turkish streamflows was shown to be significantly correlated with ENSO.
Statistical tools such as correlation analysis, empirical orthogonal functions or principal component analysis are widely used for the study of teleconnections. During the last decade, wavelet analysis has proven its power for the study of non-stationary and nonlinear relationships. In this context, wavelet analysis was used in several regions to study precipitation teleconnection to climate anomalies (e.g. Gan et al., 2007) and the links between the occurrence of annual maximum streamflows and climate patterns (e.g. Zhang et al., 2007). For instance, Coulibaly and Burn (2004) identified statistical links between annual Canadian streamflows and dominant modes of climate variability using scale-averaged wavelet power spectra, and recommended cross-wavelet analyses for exploring climate–streamflow relationships.
The present paper focuses on the study of statistical teleconnections between mid-latitude climate patterns (e.g. NAO), tropical climate patterns (e.g. ENSO) and the upper Medjerda River Basin hydro-climatology. Wavelet analysis is adopted to enhance such teleconnections. The paper is organized as follows: a description of the hydro-climatic data and selected climate indices is presented in Section 2. The methodology is presented in Section 3. The results of the study are discussed in Section 4 beginning with the identification of dry and wet seasons followed by variability of precipitations. The influence of teleconnection patterns on precipitations and streamflows results are presented next. The paper ends with a summary and a list of conclusions in Section 5.
2.1. Hydro-climatic data
The region under study is the upper part of the Medjerda River Basin, a trans-boundary river, located in northern Tunisia and which accounts for the Mediterranean water budget in the Blue Plan (Margat, 2004). The water resources and agricultural potential of this region is crucial for the Tunisian economy. Therefore, the optimal management of these resources is of primary importance. In this region, floods are generated by rainfall. Hydro-climatic data is provided by the National Water Resources Division of Tunisia and are related to six rainfall stations (Figure 1). These rainfall stations were chosen for their long-term records (generally exceeding 50 years) and for their good data quality. Monthly precipitation datasets are available. Table I presents the description of precipitation stations, along with the statistical characteristics of annual precipitations. Additionally, streamflow observations at annual time scale are considered. Figure 1 illustrates the location of the three streamflow stations used in this study (Ghardimaou, Jendouba and Bou Salem) as well as each precipitation and streamflow time series. A regional Standardized Precipitation Index (SPI) was considered to identify wet from dry years. The SPI was originally proposed by McKee et al. (1993) to measure the occurrence of drought conditions. Then, a regional precipitation time series is constructed from the average of the six monthly rainfall time series.
Table I. Rainfall stations characteristics
Maximum registered monthly rainfall (mm) (year)
Mean annual rainfall (mm)
Standard Deviation (mm)
Coefficient of Variation
2.2. Choice of climate indices data
The commonsense climate index (Hansen et al., 1998) is a simple measure of the degree (if any) to which practical climate change is occurring. It is expected to have positive values when warming occurs and negative values for cooling. Some of the selected indices are related to the Northern Hemisphere, while others are related to the Mediterranean region and the tropical region. One of the well known climate patterns is NAO, which is defined as the normalized average SLP difference between Ponta Delgada (Azores Lisbon) in Portugal and Stykkisholmur/Reykjavik in Iceland. Renewed interest in NAO has been observed since the 1990s due to a sustained positive phase which has significant implications for the entire North Atlantic region. During a positive NAO phase, southern Europe, the Mediterranean, northern Africa and Greenland have cooler and drier conditions. When NAO is in a negative phase the opposite weather patterns occur. We followed Lòpez-Moreno et al. (2007) to define a strong NAO-positive phase, when the NAO index exceeds the threshold of one standard deviation and one mean.
Numerous indices are used to measure the strength of ENSO. In this study, indices driven from observational SST data over different regions of the Pacific (e.g. NINO3, NINO3.4 and NINO4) are used in addition to SLP anomalies between Tahiti and Darwin in Australia (namely the Southern Oscillation Index, SOI). Another ENSO indicator is the Multivariate ENSO Index (MEI) based on the first un-rotated principal component of six main physical variables observed over the Tropical Pacific which are SLP, zonal and meridional components of the surface wind, sea surface and air temperature, and cloudiness fraction of the sky. Positive values of the MEI indicate warm ENSO phases and negative values indicate cold phases. Strong and extreme ENSO years are defined following Brönnimann et al. (2007) characterising ‘strong’ and ‘extreme’ as years outside ± 1 or ± 2 standard deviations in each ENSO index. Moreover, ENSO index exhibits more frequent and irregular oscillations around 5–7 years and is mainly related to SSTs at tropical latitudes over the Pacific Ocean.
The Pacific Decadal Oscillation (PDO) index which is defined as the leading principal component of the North Pacific monthly SST variability (poleward of 20°N) is also adopted in this study because of its well known long persistence with periodicities ranging from 15 to 20 and 50 to 70 years. It is mainly associated with SSTs in the North Pacific Ocean. The use of ENSO and PDO indices, therefore, allows enhancing the short-run and long-run interpretation of the behaviour of climate and hydro-climatologic variables in the region.
Among regional oscillation indices, we choose to explore the Mediterranean Oscillation index (MOAC) and the Western Mediterranean Oscillation index (WeMOI). MOAC (Conte et al., 1989) is defined as the normalized pressure difference between Algiers (36.4°N, 3.1°E) and Cairo (30.1°N, 31.4°E). WeMOI (Martin-Vide and Lopez-Bustins, 2006) consists in the difference between the standardized surface pressure values recorded at Padua (45.40°N, 11.48°E) in northern Italy, an area with a relatively high barometric variability due to the influence of the central European anticyclone, and San Fernando (Cádiz) (36.28°N, 6.12°W) in southwestern Spain, an area often influenced by the Azores anticyclone.
Table II reports strong El Niño and La Niña years as well as strong positive and negative NAO years and their corresponding wet and dry years based on total annual rainfall. We may notice that the 1950s generally represents a wet period marked by La Niña years. Particularly, three La Niña years followed by wet periods may be identified. The 1950 La Niña year is followed by a succession of wet years (1952 and 1953). Similarly the 1956 La Niña is followed by the 1957–1959 wet period. Finally, La Niña year 1971 is followed by the wet year 1973. On the other hand, we may outline that some El Niño phases are followed by dry years: The 1958 El Niño is linked to the 1960 and 1961 dry periods, the extreme El Niño year of 1983 could be linked to the 1985 dry year, and, respectively, 1987 with 1989, 1992 with the extreme dry period 1993–1994 and the extreme El Niño 1998 with 2000. Conversely, the NAO–precipitation relationship is not stable and we may point out that the 1969 negative NAO phase was followed by the 1970 dry year and that the 1979 negative NAO phase was followed by 1981 dry year. Similarly, we notice that in 1967, NAO was in its positive phase while 1969 was wet. However, the early 1990s was dominated by positive NAO while this period was marked by the extreme dry spell of 1993–1994.
Table II. El Niño and La Niña years, positive and negative NAO years and wet and dry calendar years based on a regional SPI from the total annual rainfall observed from 1950 to 2003 at the six precipitation stations (‘Extreme’ events are marked by asterisk and ‘Severe’ events are underlined)
In order to study precipitations and streamflows on a seasonal basis, the first step must be devoted to identifying the seasonal behaviour of these variables. For streamflow data, radial plots of the dates of occurrence of maximum peak flows are used to define flood seasons (Cunderlik et al., 2004a, 2004b; Ouarda et al., 2006). For each calendar month from September to August, the number of annual maximum peak flows occurring during the month converted to percentages to develop a frequency distribution in the form of histograms. This frequency distribution is used to differentiate the flood season, during which most floods occur, from the dry season as well as the month with the maximum number of floods.
3.2. Analysis of the statistical significance of teleconnection changes
Correlations between climate indices and both rainfall and streamflows are investigated. In order to assess the robustness of these correlations, the method of Van Oldenborgh and Burgers (2005) described by Sterl et al. (2007) is adopted. A Monte Carlo analysis is used to test whether ‘the strength of the teleconnection is a chance result’. A moving window of time series is therefore constructed adopting sub-periods of length N years and then used to run regressions. The idea is to consider the rainfall (respectively streamflow) variable (denoted by P(t)) as being composed of two parts, one directly related to a given climate index I(t) and the other one uncorrelated denoted by η(t)
Where c = cov(I(t), P(t))/(σI.σP) is the correlation and r = cov(I(t), P(t))/σI2 = cσP/σI is the regression between P(t) and I(t). σI and σP are, respectively, the standard deviation of the climate index and the rainfall (respectively streamflow) variable. The error η(t) has zero mean, unit standard deviation and is assumed uncorrelated with I(t).
Now if we use the time series restricted to sub-periods (referred by using the symbol ∼), the regression can be written as follows:
Where . As stated by Sterl et al. (2007) r̃(t) will vary even for a purely stochastic η(t). The statement ‘the strength of the teleconnection does not change significantly in time’ implies that these variations are small. Using the Monte Carlo analysis, we replace η(t) in Equation (1) by a standardized Gaussian process (zero mean, unit standard deviation) and simulate the probability density function (PDF) of r̃(t) by using a large number (1.000) of stochastic series of η(t). If the observed values of r̃(t) lie within the PDF they are ‘small’, and the strength of the teleconnections does not change in time. The observed variations in r̃(t) can be explained as the result of a stochastic process brought about by the combined action of all other, represented by η(t). Conversely, if the observed values of r̃(t) lie outside the Probability Density Function (PDF) we may conclude that the teleconnections themselves have changed. To compare the two PDFs, we adopt a robust test statistic described by Wilks (2006). The level of the test is defined as the probability of falsely rejecting the null hypothesis, given that it is true. Type I error, and its probability (the level of the test) is denoted α. Type I errors are defined in contrast to Type II errors, which occur if the null hypothesis H0 is not rejected when it is in fact false. The Type II error is denoted β. α and β vary conversely. Usually the rejection region is defined by the value of α. The value α = 95% is generally adopted.
3.3. Wavelet analysis
Wavelets are families of basis functions with interesting mathematical properties, such as localisation in space or time and in frequency. By decomposing a non-stationary time series in time-frequency space, one can determine the dominant modes of variability of a given variable and how these modes change in time. As stated by Torrence (1997), wavelet analysis provides an unbiased method of examining the variations in variance of a time series compared to the biased method of the windowed Fourier transform (Kaiser, 1994). According to Loboda et al. (2006), wavelets have brought a revolution in both theory and practice for the identification of non-stationary signals and the study of co-variability of various time series in frequency and time domains. We apply the statistical tests developed by Torrence and Compo (1998). The reader is referred to Torrence and Compo (1998). Here we summarize only the main concepts of the method. The continuous wavelet transform of a discrete sequence of observations xn is defined as the convolution of xn with a scaled and translated wavelet ψ(ξ) that depends on a non-dimensional time parameter ξ,
Where n is the localized time index, s the wavelet scale, δt is the sampling period, N is the number of points in the time series, and asterisk (*) indicates the complex conjugate. The wavelet function selected for this study is the Morlet wavelet. According to Labat (2005) the Morlet wavelet function provides a good balance between time and frequency localisations and describes well the shape of the hydrological signals. By varying the wavelet scale s and shifting along the localized time index n, a graphical illustration may show the amplitude as a function of scale and how it varies in time. The description of the fluctuation of the variance at different scales (i.e. wavelet periods) may be illustrated by the wavelet power spectrum which, when normalized with σ−2 (where σ2 is the variance), gives a measure of the power relative to white noise. While the global wavelet spectrum can be defined by averaging in time the power spectrum. By averaging variance in scale at multiple locations for a given variable, one can assess the spatial and temporal variability of a field of data and then construct the power Hovmöller diagram. The 95% confidence level is computed using the corresponding lag − 1 autocorrelation at each location.
To see the repartition of the covariance between two signals x and y in the time-scale space, one may adopt the cross-wavelet power spectrum as
where is described earlier and is the complex conjugate of . The cross-wavelet analysis finds regions where both time series show high common power. Confidence levels can be derived from the square root of the product of two chi-squared distributions.
To find regions where the two time series co-vary, even if they do not have high power, wavelet coherence is calculated. The phase relationship in time-frequency space is described by the phase angle difference. A significance test, based on a Monte Carlo analysis through a red noise model based on the autocorrelation functions of the two time series, described by Grinsted et al. (2004), is used here.
4. Results and discussion
4.1. Identification of dry and wet seasons
Generally, two groups of precipitation mechanism can be distinguished in north Tunisia; first, precipitations issued from air masses formed on the Atlantic and circulating in northern Africa (group I) and second, precipitations formed as a consequence of the convection (group II). Accordingly, the seasons in Tunisia could spread principally from November to March on the one side and from May to September on the other, separated by two intermediate months, April and October. In the two intermediate months, the two characters conjugate to favour precipitations. This description is very useful to separate rainfall seasons.
In order to identify runoff seasons, we adopt daily streamflow records. Ghardimou gauging station (which is a boundary station between Tunisia and Algeria) is considered as reference station. The 50-year daily streamflow observations are explored to extract the annual maximum values and the month of flood occurrence for each year. The resulting histogram is presented in Figure 2. It illustrates that all observed annual peak flow occurred during the September–May period. The percent of annual peak flows observed during the 5 months from December to April is 82% and varies between 14 and 22% with a maximum of 22% for December. On the basis of these results, two seasons are adopted: one from December to April (S1) and the second from May to November (S2). The first flood season coincides with the rainy season that spreads over the same December–April period. Figure 3 supports the results of the relative frequencies of annual peak flow occurrences. It can be seen from annual peak flow locations in the compass graph, that flood occurrences are concentrated between December and April. Figure 3 also illustrates the location of the mean day of Ghardimou annual peak flow denoted and the annual peak flow variability measure denoted v̄ in polar location-variance coordinates. The value of is about 28.45° indicating that the mean day of annual peak flow is January 29. The value 0.6 of the resultant vector v̄ indicates a low variability in the date of occurrence of annual peak flow.
4.2. Spatial and temporal variability of seasonal precipitation
The wavelet power spectra and global power spectra for each rainfall station are reported in Figure 4 for wet season precipitation (S1) and in Figure 5 for dry season precipitation (S2). From these diagrams, we can distinguish the bands associated with significant activities. Black contour lines in the wavelet spectra enclose peaks (energy) significant at 95% confidence level for a red-noise process while the blue contour lines enclose peaks significant at 90% confidence level. It may be concluded that, for the wet season, most of the activity was in the 2–8-year band. All stations reveal that the activity which is organized in the 2–8-year band is observed after 1940. Only one precipitation series (Beni Mtir2, Figure 4(c)) exhibits most of the activity after 1970. For dry seasonal precipitation, wavelet power spectra exhibit, in general, dominant modes of variability organized in both the 2–8 and more that 16-year bands. For 2 out of 6 precipitation stations, the dominant pattern is localized in the 5–8-year band. Scattered activity is observed for the 2–3-year band. Compared to wet season, summer to autumn seasonal precipitation variability is continuous in time. Global wavelet power spectra reveal generally three modulations; first in the 2–3-year period, second in the 5–8 and finally in the large periods centred on 24 years. The strongest modulation was centred on 6 years. Overall, seasonal precipitation appears to be organized in preferred bounds of periods and dominated by activities in the 2–3 and 5–8-year bands.
A spatio-temporal variability analysis of seasonal precipitation for each of the period bounds distinguished above (2–3 and 5–8-year bounds) was then performed. The scale-averaged wavelet powers for the set of 12 seasonal precipitation time series from 6 rainfall stations and 2 seasons (S1 and S2) are presented using the power Hovmöller time-longitude diagram in Figure 6(a) to (d). The plots on the left correspond to power Hovmöller diagram for S1 precipitation while those on the right correspond to precipitation for S2. Plots in the upper and lower rows correspond to scale-averaged wavelet power computed over the 2–3 and 5–8-year bands, respectively. The dashed black contours in ‘panel A’ in each figure enclose periods found statistically significant at 5% level. The ‘panel B’ in each figure represents mean power over space (or over all longitudes), and hence the temporal fluctuation of seasonal precipitation over the entire area of study. The ‘panel C’ corresponds to time-averaged power at each longitude.
The 2–3-year scale (Figure 6(a)) accounts for up to 80% of the variance for S1 precipitation in 1950s at Zaouem and Beja Inrat station and more than 90% of the variance in the beginning of 2000s for Ghardimaou and Beni Mtir2. However, for S2 the 2–3-year band accounts for more than 80% of the variance in the 1950s at Jendouba and Zaouem, while in the beginning of 2000s it explains only 60% of the variance. For S1, there appears to be some spatial coherence in the early part of the record, with activities around 1950s occurring near the eastern part of the studied area (Figure 6(a)–A). This is generally followed by a period of little activity during 1960s to late 1980s. Most significant activity is observed for the western stations located at 8.3–8.7 longitudes, while those in the eastern part show little activity. When considering the space-averaged power, the proportion of variance explained by 2–3-year band ranges from a low of 2% in the beginning of 1980s to about 77% in 2000s (Figure 6(a)–B) for the season S1. Also, Figure 6(a)–B illustrates peaks in the space-averaged power for 1970s and 1980s but no activity in 1960s. Significant precipitation activities tend to be well organized in both space and time. Hence significant precipitation activities in the 2–3-year scale band have short lifespans and seem to be irregular. However, the space-averaged variance explained by 2–3-year band for the dry seasonal precipitation (S2) ranges from 6% in 1980 to 66% in 2000s. A moderate activity can also be distinguished for the 1960s. Overall, the 2–3-year scale explains the best wet as well as dry season rainfall variability.
The wet seasonal precipitation variability for the 5–8-year scale (Figure 6(c)) accounts for up to only 30% of the variance in 1960s for the entire region of study with the exception of central part. Another activity which explains more than 20% of the variance is visible for the period starting from 1990s to the beginning of 2000s. This scale exhibits the only significant precipitation activity for the 1960s at Ghardimou. For dry seasonal precipitation, a significant activity is perceptible for the Ghardimou station in the 1970s and it explains about 20% of the variance. The analysis of spatio-temporal variability, presented above, using Hovmöller power spectrum reveals a clear difference between periods of most intense activity and intensity of the variability for wet and dry seasonal precipitation.
The distinct patterns of variability, noted for the two seasonal precipitations and their possible links to climate patterns, are investigated in the following sections using cross-wavelet and wavelet coherence analyses after a correlation analysis.
4.3. Influence of climate patterns on precipitation at the annual time scale
Linear correlation analysis for three lag times (i.e. 0, − 1 and − 2 years) between precipitation and climate indices is firstly achieved. Mean annual values of NAO, PDO, SOI, NINO3, NINO3.4, NINO4, MEI, MOAC and WeMOI indices are used. The results of this analysis are summarized in Table III for a common historical period. The Student t-test of significance is performed for correlations. Strong correlations between precipitation and ENSO indices are found at a time delay of − 2 years. For this lag time we particularly notice that NINO3.4, NINO4 and MEI exhibit correlations up to − 0.49. Such a result is relevant with the findings of Knippertz el al. (2003) who evaluate that most precipitations stations south of 45°N, especially along the western Mediterranean coast and in northern Africa, reveal negative, often significant correlations with ENSO down to r = − 0.4. Furthermore, such delay of 24 months seems to be in agreement with Rodó et al. (1997) findings using multi-taper method (MTM) spectral analysis. They noticed that ‘… the delay between ENSO onset, in winter (DJF) and the moment when its impact is seen on rainfall in Mediterranean basin ranges between 3 and 21 months’. Delays are in accordance with previous studies for global teleconnections associated with extremes of the Southern Oscillation (Horel and Wallace, 1981; Ropelewski and Halpert, 1987).
Table III. Values of linear lag correlation coefficients of total annual precipitations and indices of climate patterns (significant values at the 5 % level are shown in bold)
While at − 1 year lag the highest correlation is found between precipitation observed at Jendouba and annual NAO. However, at lag 0 WeMOI is significantly correlated but to only two precipitation stations. Moreover, MOAC and PDO did not reveal any clear relationship for the annual precipitation.
To test ‘if the strength of the teleconnection is a chance result’, we run the statistical significance test proposed by Sterl et al. (2007). Figure 7(a) illustrates the kernel density function of the coefficient of regression of SOI and precipitation (at Jendouba, 104 year length) at lag time − 2 years and the kernel of regressions between SOI and a purely Gaussian process (generated by using a Monte Carlo analysis). In comparison to the kernel of SOI-precipitation which is centred on 0.26, the SOI-Gaussian process kernel density is centred on − 0.2. Figure 7(b) shows the cumulative distribution functions of the simulated and observed regression coefficients. The test conducted at the 5% level reveals that the test statistic is falling to the right side of a critical value (Figure 7(b)) which corresponds to 0.14, for the fixed test level. This implies rejecting the null hypothesis that the correlations at lag time − 2 years are a chance result and that the strength of ENSO teleconnections does not change in time. Since the area under the probability density function of the null distribution to the right of the critical value is 0.05 (5%), we verify that β is below 0.1 (10%), an exact value of 7.5% to conclude the significance of correlations. Hence, results suggest that correlations of − 2 year lag time delay between ENSO climate indices and precipitation at the different stations are significant at the 5% level and results are not a chance result.
It is recommended examining the wavelet coherence and the phase arrows to extract connections between precipitation and climate patterns. Figures 8, 9 and 10 presents the wavelet coherence between NAO, ENSO and MO climate indices and annual precipitation at the rainfall stations where the coherence was obvious. The tick contours enclose periods of statistically significant coherence and phase difference is presented by vectors.
4.3.1. NAO-related precipitation
At the annual time scale, NAO reveals the most significant coherence in the 2–5-year band with an opposite phase difference (Figure 8(a) and (c)). In the 2-year band, the coherence is scattered. Before 1940, there is no coherence with winter NAO (Figure 8(b) and (d)) in the 2–5-year period, while annual NAO displays stronger coherence in the first half of the century. However, at the interdecadal scales, the most significant coherence between winter NAO and annual precipitation occurred mainly in the first half of the century. The 1920s and 1930s, in addition to the period beginning with 1970, is characterized by the strongest coherence where the two signals were out of phase.
4.3.2. ENSO-related precipitation
Strong correlation patterns between ENSO indices and precipitation are found. For the period from 1967 to 2003, there is a shift in the period of maximum coherence with ENSO SSTs (e.g. NINO3.4 (Figure 9(a) and NINO4 (Figure 9(b)); changing from around 3 years down to around 8 years. For example, from the end of 1960s to the middle of 1980s, there is a high coherence peak for the 3–6-year period, which corresponds to the sequence of El Niño/La Niña events coupled with weak/strong rainfalls. These results suggest that even during times of weak ENSO-precipitation relationship, the two phenomena still show occasionally strong interactions. Most of the time, the wavelet coherence between ENSO indices and annual precipitation is between 0.5 and 0.8 in the 3–8-year band. On the other hand, there is low coherence outside the 2–8-year-period band, suggesting that independent processes (e.g. noise) operate at both smaller and larger scales. Only with SOI (Figure 9(c), the coherence appears in the larger scales (i.e. 20–28-year band).
4.3.3. MO-related precipitation
Most of the coherence between winter WeMOI (Figure 10(a)) and annual precipitation is observed in the 3–10-year band. The strongest coherence is some times being of over 0.9. At the beginning of the century (i.e. 1910s), Precipitation was in phase with WeMOI (Figure 10(b)) with a coherency in the period 3–7 years. However, in the second half of the century (i.e. 1960s to mid 1970s), there is a shift in the period of significant coherence to the 6–10-year band with a relationship changing to the out of phase. Moreover, the 1980s is marked by another changing phase. Cross-wavelet analysis doesn't demonstrate strong power of MOAC (Figure 10(c)) on precipitation while coherence exhibits very strong coherence for the 2–6-year scale from 1960s to the end of the 1970s. It was a changing phase difference within this period of coherency in 1967. Generally, the usefulness of the wavelet coherence is especially apparent for time periods where both wavelet power spectra show minimal power, yet there is still high coherence.
4.4. ENSO teleconnections with seasonal precipitation
Seasonal precipitation time series are considered in this section. For wet season S1 corresponding to the aggregated precipitations from December to April, three monthly (September, October and November (SON)) mean ENSO climate indices are used. Similarly, mean ENSO climate indices from February to April (FMA)) are crossed to dry season precipitations aggregated from May to November, also called S2. The main results for wet seasonal precipitations at Jendouba and ENSO indices cross-wavelet analysis are presented in Figure 11 while results related to dry seasonal precipitations are presented in Figure 12.
ENSO-Wet: Cross-wavelet spectra of ENSO SSTs in addition to MEI with wet seasonal precipitation indicate powers in the 2–8-year band but with different levels of control. NINO3.4 (Figure 11) was the best in illustrating its strength on wet seasonal precipitation. The significant pattern in the 2–8-year band begins in 1967 for NINO3.4 wavelet spectra and influences mainly the wet seasonal precipitation in the beginning of the 1970s. Besides, the strongest pattern in the cross-wavelet spectra is observed in the large band from 1985 to 2003 in the 3–7-year band. The SOI exhibits two different periods of activity. The first oscillation of large amplitude is in the 3–7-year band and an interdecadal oscillation is mainly from 1970 to 1990. Cross-wavelet spectrum between SOI and wet seasonal precipitation at Jendouba demonstrates a significant control of SOI in the same periods as ENSO SSTs. Moreover, an insignificant control of SOI is detected before 1969. Moreover, the wet periods of 1950s, 1980s and 1990s are well influenced by strong La Niña events.
ENSO-dry: Cross-wavelet spectra for ENSO indices (Figure 12) illustrate a dominant pattern in the 4–6 year band after 1984. Another activity is shown during the second half of the 1950s. This time period is characterized by relatively moderate seasonal precipitations, i.e. the time period is characterized with drought-ridden years.
The cross-wavelet spectra clearly demonstrate the advantage of using three monthly mean climate indices for investigating temporal variability of S2 precipitation. Thus, the seasonal partitioning of precipitations proved helpful to better understand local linkages between climate indices and seasonal precipitation patterns. These results are investigated in details in the next paragraph using correlation analysis at different wavelet bands between climate patterns and seasonal precipitation.
4.4.1. Correlation of activities at different wavelet bands
Most of the cross-wavelet spectra between climate indices and precipitation conducted above reveal that the connection is organized in preferred bands of 2–3 and 5–8 years. Thus, the following analysis aims to examine possible time delay between precipitation and climate patterns. Correlations between each scale year band of the climate index and seasonal precipitation are presented in Table IV and V, respectively, for S1 and S2. From Table IV, it can be noticed that at interannual scales, moderate correlations are generally observed. This is mainly with ENSO indices (e.g. MEI). At one season lead time, NAO seems to be the most correlated with wet seasonal precipitation. Besides PDO-precipitation connection in some stations (e.g. Beja INRAT) can also be considered good. At the interdecadal time scales, generally good correlations are obtained with the exception of PDO where an insignificant correlation is noted with all rainfall stations. It can also be seen that ENSO and Mediterranean Oscillation indices as well as NAO are well correlated in the large scales. A noticeable strong positive correlation is observed between seasonal precipitations at Beni Mtir2 and NAO with one seasonal lag time in the 5–8-year band. Results confirm those of Xoplaki et al. (2004) who led to the conclusion that interdecadal changes in the first canonical correlation mode of wet season precipitation are related to variations in the NAO index and are responsible for comparable time scale variations of the Mediterranean precipitation throughout the 20th Century.
Table IV. Correlation coefficients between scale-averaged wavelet power spectra of wet seasonal precipitation and mean September–October–November (SON) seasonal indices of climate patterns. (In the left correlation at one season lead time, in the right, the highest correlation at one season to − 5 years, and between brackets the corresponding lead time. Number in bold represents the strongest correlation value for a station in a fixed year band.* Implies not significant correlation, at the seasonal time delay, at the 5% level. A grey cell indicates no significant correlation at the 5 % level)
Table V. Correlation coefficients between scale-averaged wavelet power spectra of dry seasonal precipitation and mean February–March–April (FMA) mean seasonal indices of climate patterns. Remaining notational convention is the same as in Table IV
Teleconnections between dry seasonal precipitations and mean FMA climate patterns at different scales presented in Table V reveal significant correlations at the different period bands. Generally, the interannual variability of precipitation is interlinked to MOAC, PDO and NINO4. With ENSO (e.g. NINO4), strong correlation is extracted with a seasonal time delay and a maximum of − 2 years. As in the correlation analysis using annual precipitation time series, a − 2 year time delay is found. Mariotti et al. (2002b) found that in spring and autumn ENSO-like global SST anomalies are significantly correlated with western Mediterranean rainfall anomalies. However, they established that the second half of the 20th Century is characterized by no correlation between Euro-Mediterranean seasonal rainfall and ENSO, while in this study the summer–autumn precipitations in the Medjerda basin are found to be strongly correlated to ENSO at the interannual time scale.
Hence, the advantage of using the seasonal time scale can be deduced. PDO displays also strong positive links to precipitation with the same time delay. Climate indices in the 5–8-year band demonstrate similar results according to the different time periods. It is noteworthy that precipitation correlations to MOAC, PDO and NINO3.4 are strong. At the interdecadal scales, strong negative correlations are obtained with ENSO. NINO4 and Mediterranean indices are the most influencing seasonal dry precipitation. One of the most prominent features from the correlation between the different scale-averaged wavelet powers is the influence of more than one climate index on seasonal precipitation. Furthermore, the division of precipitation on two seasons explains better the influence of a climate pattern on dry or wet seasonal precipitation. It allows finding a shorter time delay of strong significant correlations.
4.5. Rainfall–streamflow relationship
A wavelet analysis of precipitation links to streamflow at the Ghardimaou station is necessary to explore before undertaking the analysis of climate–streamflow teleconnections. The wavelet coherence and wavelet cross-spectrum between rainfall and streamflow are exposed in Figure 13. It reveals that until 1976 the two signals were coherent in the 3–6-year period and the phase difference was null, while from 1976 to 1986, no significant coherence can be captured in this period. A noticeable feature is the change in the period of significant coherence (5–8-year period) accompanied with an opposite phase state. We suggest relating the change around 1976 in the coherence and phase to some previous works conclusion that documented change in the Mediterranean precipitation. The year 1976 was documented by Kingumbi et al. (2005) as the beginning of dry period in central Tunisia rainfalls. In addition, Crisciani et al. (1994) analysed air pressure and sea-level pressures (SLP) at Trieste (Italy) in relation with ENSO phases. They demonstrated that the period 1976–1986 was dominated by low pressures and high SLP at Trieste (Italy), while the previous and the following periods were characterized by inverse phenomena. This period (mid-1970s to mid-1980s) corresponds mainly to El Niño situations; and it contains the extreme El Niño phase of 1983. Sterl et al. (2007) stated that since the mid-1970s there have been more and stronger El Niños than in the previous 1950–1975 period. They argued that during the same period one can find twice El Niños than La Niñas. Moreover, as discussed by Mariotti et al. (2002a), the increase in Mediterranean water deficit from the 1970s to the 1990s corresponds to a switch from a low to high NAO. In addition, precipitation appears to be mostly responsible for this water deficit's increase. As NAO index increases from 1970 to roughly 1993, winter precipitation decreases. However, for our data, it is important to notice that the streamflow discharges observed since 1986 may not only be influenced by the natural El Niño situations but they could also be influenced by the anthropogenic effects. In effect, the Ain Dalia Dam began functioning since 1986, upstream of Ghardimaou, on the Algerian side.
4.6. Influence of climate patterns on streamflows
Given these results of precipitation–climate teleconnections, we propose to extend the analysis to the study of streamflows teleconnections to large-scale climate oscillations. Strong correlations between streamflow records and ENSO indices of up to − 0.52 are found with MEI in addition to PDO (−0.4) and WeMOI (0.31). The use of wavelet analysis helps to enhance the description of multiannual associations between the evaluated indices that would be otherwise hidden or underrepresented by a simple point-to-point cross-correlation analysis. Figure 14 illustrates the results of the wavelet analyses for the total annual streamflows at Jendouba station with mean annual climate indices. The variability in annual streamflows is clearly dominated by peaks with periods between 2 and 7 years.
ENSO indices (e.g. Figure 14 for NINO3.4) demonstrate considerable influence for explaining the variability in annual streamflows. Three intense activities can be noted from the cross-wavelet spectra: 1950s, the beginning of the 1970s and the middle of the 1980s. The first activity is concentrated in the 5–8-year band and the two other in the 3–5-year band. Thus, the same strong activities are observed for most of ENSO indices (see wavelet power spectra). The results of the Mediterranean Oscillation index (i.e. MOAC) are similar to those of ENSO, with the exception of 1950s activity which is due to unavailability of data for 1950s. MOAC database is available since 1959. The WeMOI seems to have less influence on the annual streamflows.
Comparatively, results obtained through cross-wavelet analysis climate indices and annual streamflows at downstream stations Jendouba and Bou Salem demonstrate the same features as Ghardimaou that can be summarized in the power of ENSO in modulating the streamflows. Cross-wavelet power spectra for the climate indices and annual Jendouba streamflows reveal that there is no significant covariability with PDO and ENSO in the 1950s. Prior to 1950, cross-wavelet spectrum exhibits strong teleconnection between SOI and Jendouba streamflows.
5. Summary and conclusions
It has been shown that different climate patterns influence Mediterranean climate; however there is only limited published information on the influence of climate patterns on Tunisian hydro-climatology. The objective of this work was to investigate temporal variability of precipitations and their links to large-scale climate phenomena for the upper trans-boundary Medjerda River Basin, located in northern Tunisia, in order to provide guidelines for better management of water and agricultural resources ENSO, NAO, PDO and Mediterranean teleconnection patterns (i.e. MOAC and WeMOI) are selected to develop such analysis. To investigate linkages between various climate patterns and precipitation patterns, correlation analysis and wavelet analysis approaches were undertaken. The wavelet analysis included wavelet, cross-wavelet and coherence spectra in addition to correlation analysis between scale-averaged power spectra.
ENSO indices are found to be well correlated with precipitations at a time delay of − 2 years. Particularly, NINO3.4, NINO4 and MEI exhibit the strongest coefficient of correlation. Wavelet spectra of seasonal precipitation display a dominant pattern localized in the 2–3 and 5–8-year bands. Hovmöller power spectrum of seasonal precipitations shows a clear difference between periods of the most intense activity of precipitation from wet to dry seasons. The cross-wavelet power spectra, scale-averaged powers and wavelet coherence spectra demonstrate how dominated precipitation by various climate patterns is. The results of this study demonstrate that precipitation variability can be simultaneously modulated by different climate patterns, suggesting that a combination between climate patterns could be explored for better understanding of the co-variability of climate–precipitation phenomenon. Furthermore, separation of annual precipitation regime into two (i.e. wet and dry) seasonal precipitation regimes proved useful to better put into evidence the influence of climate patterns. This division is found helpful in finding a shorter time delay which exhibits stronger correlation especially between NAO and wet seasonal precipitation compared to annual time scale. Moreover, the influence of climate patterns is found to be changing from time to time and from one period to the other. Precipitation fluctuations seem to be better explained by global-scale ENSO processes. This relationship suggests the possible role of La Niña phase for generating severe rainfall events and that of El Niño phase for drought occurrences. Strong coherence is extracted from precipitation–streamflow relationship.
In the light of these results, climate–streamflows teleconnections have been investigated. Temporal variability of streamflows is seen to be linked, through precipitation, to large-scale climate oscillations. It is suggested that NAO, ENSO (i.e. either SOI or NINO4), MOAC and WeMO patterns could be useful to explain annual streamflows. Results of ENSO–streamflow linkages support ENSO–precipitation findings; La Niña phase in generating severe floods, and that of El Niño phase for generating moderate floods. This observation indirectly confirms the relationship of El Niño phase with drought occurrences. Therefore, the findings of this study would provide a set of climate predictors that would be useful to characterize hydrological regimes. Overall results encourage studying potential of ENSO, PDO and MO indices for long-term forecasting of seasonal precipitation in the Medjerda River Basin.