Large-scale cycle-like patterns (multi-millennial) that are not completely represented in the record can have impacts on the results from the Redfit and Wavelet analyses (Borradaile, 2003; Egan et al., 2022; Hochman et al., 2019; Rösch and Schmidbauer, 2018). For this reason, we detrended the data by fitting a 3rd-order polynomial regression to each proxy (Fig. 2b). The order of the model was chosen to ensure that variability with periods longer than approximately half the length of the record is removed prior to spectral analysis. Subsequently, we used the detrended time series for the Redfit analyses, as this method operates with unevenly spaced data (Schulz and Mudelsee, 2002). In contrast, the wavelet analysis requires equidistant spaced time series (Rösch and Schmidbauer, 2018). Debret et al. (2007) used a Spline interpolation for equidistant spacing, but we experienced “overoscillation” with artificial cyclicity for spline interpolations. Consequently, we applied a linear model on each time series using the average temporal resolution of each proxy (Table 1). The detrended and equidistant spaced time series act as input data for the wavelet analysis (Fig. 2b). Further, we smoothed the raw time series data by a kernel function (Härdle and Vieu, 1992) with a 500-year span, in order to extract the major positive and negative peaks in the time series for the comparison of the timing of the cycles (Fig. 2b, red line).

A principal component analysis (PCA) reduces the dimensionality of multi-proxy datasets and is widely used in the analysis of XRF elemental data (Bertrand et al., 2024; Evans et al., 2019). In this approach, the main trends within the dataset are extracted as continuous axes (Borcard et al., 2011). These axes are calculated based on the eigenvectors of the variables and their Euclidean distances, resulting in orthogonal components that are statistically independent and uncorrelated. Two PCA analyses were conducted. The first analysis PCA_freq used the extracted spectral information from the Redfit analyses as input data. The second analysis PCA_time was based on the raw proxy data in the time domain. The results of both analyses are presented in the Supplement (Figs. S7 and S8).

The Redfit algorithm works with a Lomb-Scargle Fourier transformation (Lomb, 1976; Scargle, 1982) to overcome unequal time intervals (Li et al., 2021; Schulz and Mudelsee, 2002). The process uses the Hanning window and three 50 % overlapping segments (Bunn and Korpela, 2021; Schulz and Stattegger, 1997). The raw spectrum is smoothed, segmented, and linearly interpolated to eliminate artificial high frequencies and make it consistent (Ólafsdóttir et al., 2016). Finally, the averaging of all segments results in the periodogram. The significance of the periodogram was tested against the AR1 (first-order autoregressive) process, also called red noise. Redfit uses Monte-Carlo simulations to create a set of AR1 processes and extracts various significance levels. We used critical false alarm level, that is determined by the properties of the data and therefore may be more conservative than 90 %, 95 % or 99 % confidence (Schulz and Mudelsee, 2002; Thomson, 1990). The dplR package (v1.7.1) (Bunn and Korpela, 2021) within the R (+RStudio) environment (R Core Team, 2020) was used.

The wavelet analysis (Torrence and Compo, 1998) also creates a periodogram, but the power of the cycles is linked with the temporal evolution. In contrast to Redfit, wavelet analysis reveals possible non-stationarities of the data (Debret et al., 2007). Periodic components get combined, and cycles and amplitudes can be displayed separately (Torrence and Compo, 1998). This procedure allows the detection of periods occurring only for a part of the time series (Debret et al., 2007). Here, the resulting wavelet power spectra is also tested against the AR1 process to avoid artefacts from the persistence of the data (Rösch and Schmidbauer, 2018). During the Fourier transformation, the length of the time series is increased by adding zero values to avoid false periodic events. However, this creates boundary effects as the wavelet gets closer to the edge. We avoided interpreting data within the area with increased edge effects (cone of influence) due to low accuracy of spectral information (Cazelles et al., 2008). We use the waveletComp package (v1.1) implemented by Rösch and Schmidbauer (2018) within the R environment. The algorithm uses the Morlet mother wavelet, because it keeps its shape through frequency shifts, and therefore, provides a reasonable separation from different frequency band contributors without excessive loss in temporal resolution (Cazelles et al., 2008; Goupillaud et al., 1984). The wavelet function needs equidistant spaced data (Fig. 2b) and we used a significance level of 95 %.

So far, cross-spectral analyses are typically bivariate, i.e. performed on pairs of proxies (Mudelsee et al., 2020; Ólafsdóttir et al., 2016). In order to reduce the dimensions (number of variables), we developed a procedure to group the proxies by using the significant spectra of the periodograms of the Redfit analyses. First, we extracted the spectrum of each XRF proxy from the Redfit periodogram. In a second step, we removed the non-significant parts of the spectra (Fig. 2c). The correlation analysis was done with the significant part (the values below the critical level were removed/ set to NA – “Not Available”). Due to the precondition of zero NA values throughout all variables (proxies) for a correlation analysis, we could only focus on periodicities between 1 and 4 kyr. For power values of higher frequencies, at least one variable had NA values. However, the correlation matrix (Fig. 2d) shows the correlation coefficients after Spearman and the configuration of the proxies along the axes was done by similarities of positive or negative rho values. We additionally performed a PCA in the frequency domain (PCA_freq) to evaluate the robustness of the grouping approach. The PCA results (Fig. S7) independently confirm the proxy groups identified by the correlation matrix (Fig. 2d).

RPG 1 consists mainly of proxies related to soluble elements which are known to be sensitive to authigenic precipitation. Ca, Sr and related ratios have frequently been interpreted as indicators for a changing precipitation / evaporation ratio (Davies et al., 2015; Foerster et al., 2012; Kylander et al., 2011). Although Si has the same periodicity, the peaks run in exactly opposite directions (Fig. 5). It is a well-known phenomenon that in alkaline-rich lakes, Ca and Si abundances are opposed (Czymzik et al., 2016). Typically, this is interpreted as the dominance of internal or external processes, since Si is either formed by diatoms or is delivered as detrital input (Regattieri et al., 2016). Zielhofer et al. (2017a) argued for the Sidi Ali record that changes in the water balance might affect the carbonate content, due to an increased relative enrichment of carbonates during low lake levels. The periodic signature of RPG 1 is dominated by 2 and 1 kyr cycles. The latter is in accordance with the 1 kyr periodicity of the hydroclimatic δ18O signal from the same core (Zielhofer et al., 2019b) (Fig. 4). Increased δ18O values are in accordance with low precipitation / evaporation ratios. Specifically, multiple millennial-scale peaks in δ18O during the Early and Middle Holocene (e.g., 5.0, 6.2, 8.2, 9.3 and 10.2 ka BP) reveal short-term decreases in the precipitation / evaporation ratio (Zielhofer et al., 2019b) which can be linked to RPG 1 (Fig. 7) and North Atlantic cooling (Bond events) (Bond et al., 2001). This may indicate a Holocene teleconnection between the North Atlantic climate and Western Mediterranean winter rain. In addition, δ13C values (Fig. 5) are interpreted as a groundwater inflow-related proxy (Zielhofer et al., 2017a). This subterranean process is more dominant when less winter rain feeds the lake. We observe a strong ca. 2 kyr periodicity during the Early and Middle Holocene (until 4 ka BP) and link δ13C to RPG 1 (Fig. 8f).

The Cedrus pollen show for the Early to Middle Holocene a 1 kyr periodicity (Fig. 8a). After ca. 4 ka BP, the 1 kyr pattern disappears and an ascending (around 1.5 kyr) periodicity becomes visible. In addition, the Early Holocene 2 kyr pattern prolongs until 6 ka BP. Therefore, we associate the Cedrus pollen abundance to RPG 1, which reveal significant 2 and 1 kyr cycles. As discussed in Campbell et al. (2017), Cedrus atlantica is sensitive to prolonged summer drought. For the Early Holocene, Zielhofer et al. (2019b) discussed that Cedrus responded very sensitively to the orbitally-forced summer insolation maximum. Therefore, the absence of Cedar could act as summer drought proxy in the Early Holocene. Furthermore, there is a bi-millennial-scale coincidence of short-term Cedrus peaks at 8.2 and 10.2 ka BP and decreases in Early Holocene subtropical summer sea surface temperatures (deMenocal et al., 2000) which point to a subtropical atmospheric impact at Sidi Ali during the summer season. The TOC shows a clear ca. 2 kyr periodicity and some solitary 1 kyr patterns (Fig. 8c). This fits to RPG 1. This is also supported by a high negative correlation (-0.86) between carbonates (Ca) and TOC (Zielhofer et al., 2017a). They argue that Ca and TOC are connected via aerobic/anaerobic lake-bottom conditions (organic matter preservation) due to lake-level changes.

Also belonging to RPG 1 is the K/Ti ratio, which can be used as a proxy for Saharan dust inputs. Zielhofer et al. (2017b) were able to couple the K/Ti signal from the Sidi Ali core with remote dust from the Saharan direction using provenance analyses. A peak in the K/Ti ratio at 4.2 ka BP corresponds with a hyper arid phase in the central Sahara (van der Meeren et al., 2022). The Saharan dust signal is in accordance with periodicities that are known from North Atlantic Ocean-atmosphere pattern and from monsoonal variability (Cruz et al., 2021; Gasse and Van Campo, 1994). Specifically, the Early to Middle Holocene 2 kyr periodicity is known from the Saharan and Sahelian domain (Gasse and Van Campo, 1994; Tjallingii et al., 2008).

This periodicity of RPG 2 is dominated by distinct 3.5 and 1.5 kyr patterns (Figs. 5 and 7). However, the 3.5 kyr cycles are present throughout the Holocene, whereas the 1.5 kyr pattern occurs more explicitly during the Middle and the second half of the Late Holocene (Fig. 7). Although the 3.5 kyr cycle is somewhat less trustworthy due to the short length of the total record, the dominance and grouping in the dataset seems clear.

RPG 2 consists of proxies that are commonly interpreted as indicator of detrital influx (Fe, Ti, K, and related ratios; used and described for Sidi Ali in Zielhofer et al. (2017a) or bioproductivity (Si/Ti, S, S/Ti) processes (Davies et al., 2015; Kylander et al., 2011). Additionally, the Fe/Ti and Mn/Ti ratios show also multi-centennial (340–600 years) periodicity patterns (Figs. 5 and 7). This corresponds partly with patterns of RPG 1 and stronger with RPG 3. The general temporal pattern of the included proxies (Fig. 5) shows that this group can be differentiated in two subgroups (Fe, K, Ti vs. Fe/Ti, Mn/Ti, S, S/Ti, Si/Ti). The observed opposing behaviour may be a result of varying detrital sedimentation rates versus a biogenetic sedimentation rate. The XRF-based interpretation is supported by the magnetic susceptibility as a local erosion proxy (Zielhofer et al., 2017a). The magnetic susceptibility shows a distinct and persistent 3.5 kyr and a Middle Holocene 1.5 kyr periodicity (Fig. 8b). Furthermore, multi-centennial periodicities are less pronounced. This spectral pattern is similar to that of RPG 2. Zielhofer et al. (2017a) reported a high correlation between Fe and magnetic susceptibility due to terrestrial input. The coarse-grained local endmember derived from grain-size EMMA is interpreted to reflect local catchment erosion and short-distance sediment supply to Lake Sidi Ali (Zielhofer et al., 2017b). However, Redfit and wavelet analyses reveal no clear or persistent expression of the ∼ 1.5 and ∼ 3.5 kyr cycles in the frequency domain of this proxy (Figs. 4 and 8d), indicating that local erosion processes might not only be paced by these millennial-scale periodicities but also by human land use and disturbance in the catchment (Bourchachen et al., 2025; Campbell et al., 2017; Cheddadi et al., 2015).

RPG 3 consists only of two XRF-derived proxies, Mn and Fe/Mn. Both are known as redox sensitive (Davies et al., 2015; Davison, 1993). However, Mn is more affected by redox processes compared to Fe (Boyle, 2002). Fe corresponds with RPG 2 and seems to be mainly reflecting detrital input. The effect of redox processes is strongly dominated by lake-level variations and subsequent strengths and duration of lake stratification and circulation (mictic) properties (Davies et al., 2015). The lake level of Sidi Ali is controlled by winter-rain variations and its hydroclimatic consequences (Zielhofer et al., 2019b). Therefore, a possible interpretation for RPG 3 is that it reflects combined influences of processes related to both RPG 1 and RPG 2. The periodicity pattern of RPG 3 supports this explanation, as it shows patterns of both, RPG 1 and 2. The mix of ca. 2, 1.5, 1 kyr and several multi-centennial cycles is clearly in contrast to those of RPG 1 and 2 (Figs. 5 and 7). Fe and Mn are associated with detrital input which is also driven by catchment related processes. The subsequent redox-related alteration rather corresponds with periodicities that are associated with RPG 1. Moreover, multi-centennial periodicities occur also in redox-sensitive proxies, like the magnetic susceptibility record (Figs. 5 and 7).

The bimillennial cycle is a well-known periodicity in Holocene palaeoclimate studies (Azuara et al., 2020; Goslin et al., 2018). Generally, it is considered to be triggered by solar forcing via the Hallstatt cycle (Steinhilber et al., 2012; Usoskin et al., 2016). In the North Atlantic realm, Stewart et al. (2017) presented a Bromine record from a peat bog in Scotland that shows a distinct 2 kyr cycle pattern (Fig. 9a). This Bromine record measured by cs-XRF reflects the storminess of the adjacent Atlantic Ocean. Stewart et al. (2017) reconstruct past variations in North Atlantic storminess and atmospheric circulation, reflecting changes in the NAO. As such, it represents an important archive of North Atlantic climate variability, which is directly relevant for interpreting hydroclimatic changes at Sidi Ali due to the strong influence of NAO-like westerly variation on moisture transport into the Mediterranean region.

Regarding the Western Mediterranean, the composite speleothem record from the Chaara Cave located in the Middle Atlas covers the entire Holocene. Ait Brahim et al. (2019) presented there a δ18O value-based Western Mediterranean rainfall index. The wavelet power spectrum shows high power values for a 2 kyr cycle since the Middle Holocene (Fig. 9b). We suggest that the Western Mediterranean precipitation / evaporation ratio might be influenced by a bi-millennial periodicity. However, the same frequency analysis for the δ18O speleothem record of the nearby Grotte du Piste Cave (Wassenburg et al., 2016) did not reveal any bi-millennial periodicity (Fig. 9c). Hence, the climatic imprint of bi-millennial periodicities in Mediterranean hydroclimatic records remains still under debate. In contrast, a speleothem record located in the SW High Atlas Mountains (Wintimdouine Cave) is discussed as the airmass trajectory which is driven by the West African Monsoon system and consequently by the tropical realm (Sha et al., 2019). Wavelet analyses show a ca. 2 kyr cycle pattern (Fig. 9d) which is in accordance with the Saharan and sub-Saharan realm (Gasse, 2000; Gasse and Van Campo, 1994; van der Meeren et al., 2022).

The eddy cycle is discussed as solar forcing mechanism behind this millennial cycle pattern (Debret et al., 2007; Steinhilber et al., 2012) and seems to affect the Atlantic precipitation regime (Zielhofer et al., 2017a). Wavelet analysis of the total solar irradiance (TSI) shows a millennial cycle which is present during the last 9.5 ka BP, although its amplitude varies through time (Steinhilber et al., 2012). The 1 kyr millennial cycle is well-known in many palaeoclimatic records (Debret et al., 2009; Soon et al., 2014; Zhao et al., 2021). During the Holocene, the Scottish Shebster peat record (Stewart et al., 2017) shows a significant 1 kyr cycle of North Atlantic storminess until 4 ka BP (Fig. 9a).

In the Western Mediterranean, the 1 kyr pattern in the rainfall index from the Chaara Cave (Ait Brahim et al., 2019) seems present from the onset of the Holocene until ca. 8 ka BP and again from ca. 4 ka BP (Fig. 9b). The Grotte du Piste speleothem record (Wassenburg et al., 2016) shows only a minor, but not highly significant 1 kyr cycle from ca. 10 to ca. 5 ka BP (Fig. 9c). Regarding the potential impact of sub-Saharan and Saharan air masses, the δ18O record from Sha et al. (2019) does not show a clear 1 kyr pattern (Fig. 9d). Kuhlmann et al. (2004) argues that there is a distinct border between the tropical monsoonal impact and the North Atlantic impact between 27 and 30° N. They used the 1 kyr cycle pattern for the differentiation between the two impacts. In this context, they described that there is no 1 kyr periodicity in the African tropics in the Holocene.

The multi-centennial periodicity patterns cluster around 700 and between 600 to 340 years (Fig. 4). These patterns are also related to solar forcing, with unnamed cycles at ca. 340, 500 and 710 years (Steinhilber et al., 2012). Furthermore, Soon et al. (2014) demonstrated that the multi-centennial cycles are a result of Atlantic Ocean dynamic responses of the solar forcing. The multi-centennial periodicities are also reflected in the Moroccan speleothems from the Middle Atlas (Ait Brahim et al., 2019; Wassenburg et al., 2016; Fig. 9b and c), suggesting periodic winter-rain variability. The NAO record from Olsen et al. (2012) which is related to winter rain (over Greenland), also shows periodicities for the 700 and 340 years cycles (Fig. 9e). Surprisingly, the Atlantic storminess record from Stewart et al. (2017) includes almost no visible multi-centennial periodicities (Fig. 9a). As we find the majority of multi-centennial cycles in the hydroclimatic proxy group (RPG 1), we suggest that it is dominated by Atlantic forcing mechanisms which is in accordance with Zielhofer et al. (2019b).

The observed cycle length around 200 years is known as de Vries cycle (Steinhilber et al., 2012). The cycle has been proposed to be modulated in amplitude by the longer Hallstatt cycle, implying that its climatic imprint may vary through time rather than being continuously expressed (Komitov, 2024; Usoskin et al., 2016). Periodicities of similar lengths are found in many proxy-based studies (Ojala et al., 2015; Soon et al., 2014). Two speleothem records from North and South Morocco that cover the last 1000 years, included ca. 200 years periodicities and linked them to NAO-like variations (Ait Brahim et al., 2017, 2018). They argue that the de Vries cycle varies between dry and humid conditions. This would also affect the lake level of Sidi Ali, thus altering the redox processes at the lake floor and within the lake sediments. Accordingly, these lake-level–driven changes are reflected in the detrital proxies of RPG 2 and in the redox-sensitive proxies of RPG 3. The latter additionally exhibit a ∼ 170 years periodicity, which may tentatively be linked to the de Vries cycle, although the statistical robustness of this specific periodicity is limited and its interpretation therefore remains cautious (see Sect. 5.1).

The 1.5 kyr cycle in the Holocene, on the other hand, is subject of many studies (Debret et al., 2007; Fletcher et al., 2013; Soon et al., 2014). Nevertheless, there is an open debate about the frequency framing (distinct separation between 1.8 to 1.5 kyr often not achievable, due to dating uncertainties) and the fundamental forcing of this pattern (Dima and Lohmann, 2009; Soon et al., 2014). The derived NAO index of Olsen et al. (2012) shows, even though not highly significant, a ca. 1.5 kyr pattern (Fig. 9e). Due to the time span of the NAO record, the pattern is only visible from ca. 5 to ca. 2 ka BP. Other studies also suggest a 1.5 kyr periodicity that is stable since the Middle Holocene (Azuara et al., 2020; Smith et al., 2016). The marine record of Bond et al. (1997) shows a similar pattern. There is a transition from 1 kyr periodicity to 1.5 kyr periodicity in the Middle Holocene. However, Witt and Schumann (2005) detected a significant ca. 1.5 kyr cycle in Greenland ice core data, which is valid for the entire Holocene. Furthermore, Soon et al. (2014) identified a persistent 1.5 kyr cycle in a nitrate record in an Antarctic ice core. One can argue that the persistent Holocene-wide cycling is due to solar forcing, whereas the Middle Holocene shift from 1 to 1.5 kyr seems to be the dynamic response of the Atlantic Ocean circulations. As we see the onset of the 1.5 kyr cycle in RPG 2 in the Middle Holocene (Fig. 7), we assume an external forcing that is specifically affecting catchment processes and terrestrial supply. The clear mechanisms remain still unknown. The speleothem records in the Middle Atlas do not show a distinct 1.5 kyr pattern (Fig. 9b and 9c). The speleothem record of Sha et al. (2019) from the SW High Atlas shows a ca. 1.5 kyr pattern between ca. 7.5 and 2 ka BP, although statistically not highly significant (Fig. 8d). The Saharan-related processes, thus, seem to follow this pattern. Similar to the 1.5 kyr pattern, the 3.5 kyr periodicity is difficult to attribute to a specific forcing mechanism. It seems that catchment-related processes and local terrestrial supply differ from supra- regional North Atlantic or sub-tropical hydroclimatic forcing.