1 Introduction

During the early-to-middle Holocene period 11,000 to 5000 years before the present, known as the “Green Sahara”, the currently arid landscapes over the Sahel and Sahara were widely replaced by shrubs, grasslands, rivers, and lakes (Claussen and Gayler 1997; Demenocal et al. 2000; Kohfeld and Harrison 2000; Holmes 2008; Armitage et al. 2015; Claussen et al. 2017). For this humid and green Sahara period with significantly amplified rainfall, multiple studies based on reconstructions and climate model simulations tried to explain the reasons for the dramatic climate change. However, in nearly all climate model simulations, forcing and feedbacks from increased summer insolation, land surface and vegetation cover changes, atmosphere-ocean interaction, and dust emission reduction have failed to fully reproduce the magnitude of rainfall changes compared with proxy evidence (Kutzbach and Liu 1997; Braconnot et al. 1999; Demenocal et al. 2000; Harrison et al. 2014; Pausata et al. 2016; Claussen et al. 2017; Tierney et al. 2017; Hopcroft and Valdes 2019). A few simulations have been able to reproduce a better match with proxy data when considering the representation of dynamic vegetation, changes of land cover and soil type, and dust and aerosol emissions reduction, but generally those feedbacks in climate models are insufficient to reconcile the discrepancy (Claussen and Gayler 1997; Claussen et al. 1999; Hargreaves et al. 2013; Tierney et al. 2017). A deeper understanding of fundamental dynamical processes may help us to narrow this gap.

African Easterly Waves (AEWs) are synoptic-scale disturbances that originate from central North Africa east of 10\({^\circ E}\) and propagate westward during the boreal summer season. AEWs are characterised by synoptic-scale periodicities of 2–7 days and wavelength of 2000–5000 km, with their most prominent signature at the level of the African Easterly Jet (AEJ) at around 650–700 hPa (Carlson 1969a; Reed et al. 1977; Diedhiou et al. 1998; Thorncroft and Hodges 2001; Mekonnen et al. 2006; Parker and Diop-Kane 2017). AEWs are important in initiating organised convective systems and modulating summer rainfall over tropical West Africa and Sahel regions during their westward propagation. On the other hand, convective systems could directly drive AEWs growth and propagation as well as modulate the strength and position of the AEJ (Hall et al. 2006; Berry and Thorncroft 2012; Russell et al. 2020). AEWs also play an important role in seeding the genesis of tropical depressions that then grow into Atlantic tropical storms and hurricanes (Reed et al. 1977; Parker and Diop-Kane 2017; Dandoy et al. 2021). Although some studies have suggested that the AEW activity was weakened when the Sahara was vegetated and summer rainfall and convection were greatly enhanced (Gaetani et al. 2017), few studies have focused on the AEW regime and its effect on summer rainfall variability under the Holocene warm climate.

African easterly waves mainly initiate over central North Africa east of 10\({^\circ E}\) via the upstream triggering regime Mekonnen et al. (2006); Kiladis et al. (2006); Parker and Diop-Kane (2017). The triggering finite-amplitude perturbations that lead to the generation of AEWs are linked to localized convective heating near the entrance of the AEJ (Hall et al. 2006; Thorncroft et al. 2008). Furthermore, although small-scale perturbations could also be generated from large-scale unstable background flow via the wave-mean flow interaction, it is not very clear what the role of the large-scale dynamic instabilities is in stimulating those perturbations and promoting the AEWs genesis over the central North Africa. One of the challenges is that large-scale baroclinic and barotropic instabilities are too slow to explain the fast initiation of the wave precursors. However, after the AEWs initiated, feedback from combined baroclinic and barotropic instabilities is important for the wave development and structure evolution. The slow growth of AEWs during their westward propagation within the Western African Monsoon (WAM) system is consistent with the slow growth rate of instability feedback (Parker and Diop-Kane 2017).

Here we conduct simulations with the EC-Earth climate model to quantify the relative importance of AEWs mechanisms in affecting summer rainfall variability over the Sahel and West Africa during the mid-Holocene. Considering the difficulty of separating the roles of different factors when changing vegetation, aerosols/dust and GHG concentrations together, as well as the uncertainty in some of these factors, we use the standard simulation protocol of the Coupled Model Intercomparison Project Phase 6 (CMIP6) (Eyring et al. 2016), and the Paleoclimate Modeling Intercomparison Project Phase 4 (PMIP4) (Otto-Bliesner et al. 2017). Although this must be seen just as a first step, it makes it easier to understand the change in AEW dynamics in these mid-Holocene (MH) simulations. The EC-Earth simulations conducted in our work have no prescribed vegetation change or dust reduction, and the vegetation distribution and dust emissions are retained at their pre-industrial (PI) level (Otto-Bliesner et al. 2017). Our main goal is to understand the response of AEW activity to mid-Holocene orbital forcing, the mechanisms affecting it, and the effect of AEWs on the differences in summer rainfall variability between the MH and PI simulations.

2 Simulations and methods

2.1 EC-earth simulations

PI and MH simulations were conducted with the EC-Earth climate model (Hazeleger et al. 2010), version 3.3.1. The atmospheric component is the Integrated Forecast System model (IFS cycle 36r4) from the European Centre for Medium-range Weather Forecasts (ECMWF), with T159 spectral resolution (\({1.125^\circ }\)) and 62 vertical levels. IFS is coupled with the H-TESSEL land surface model, the Nucleus for European Modelling of the Ocean (NEMO) version 3 ocean model and the Louvain-la-Neuve Sea Ice model version 3, and the coupling process is conducted by the OASIS 3 coupler. Following the CMIP6 DECK piControl (Eyring et al. 2016) and the PMIP4 mid-Holocene protocols (Otto-Bliesner et al. 2017), the PI and MH simulations have different orbital forcing and slightly different greenhouse gas concentrations (Table 1), but they both use preindustrial aerosol concentrations and vegetation cover. We conduct a 700 years spin-up run to reach the equilibrium, and then simulate for 150 years and 200 years for the PI and MH periods respectively, and we use daily data for the last 50 years in the analysis.

Table 1 Boundary conditions in the PI and MH simulations\(^{a}\)
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2.2 Effect of instabilities and energy conversions on AEWs

Baroclinic and barotropic instability through reversed meridional potential vorticity (PV) gradients are expressed by the Charney-Stern criterion (Charney and Stern 1962). To further understand the AEWs regime evolution during the MH warm period, here we use the quasigeostrophic (QG) assumption for the conservation of PV in the Charney-Stern necessary conditions (Charney and Stern 1962; Hsieh and Cook 2007, 2008), and compare and quantify the influence of baroclinic and barotropic instabilities on AEWs evolution. The meridional gradient of the zonal mean PV (\({\overline{q}}\)) in pressure coordinates (p) is:

$$\begin{aligned} \frac{\partial {\overline{q}}}{\partial y}= \,& {} \frac{\partial }{\partial y} \overline{\left[f+ {\bigtriangledown }^2{ \psi }+ \frac{\partial }{\partial p}\left(\frac{p f_0^2 }{R S_p} \frac{\partial \psi }{\partial p}\right)\right]}\nonumber \\=\, & {} \beta - \frac{\partial ^2 {\overline{u}}}{\partial y^2}-\frac{\partial }{\partial p}\left(\frac{p f_0^2 }{R S_p} \frac{\partial {\overline{u}}}{\partial p}\right) \end{aligned}$$
(1)

The overbar in Eq. (1) represents a zonal average between 10\({^\circ E}\) and 25\({^\circ E}\). R is the gas constant, \({\varphi }\) is the latitude, p is the pressure, \({f_0}\) is the Coriolis parameter at the reference latitude and \({\beta = \frac{\partial f}{\partial y}}\) represents the meridional gradient of the Coriolis parameter, \( {\psi } \) is the geostrophic streamfunction on pressure levels, u is the zonal wind component, and \(S_p\) is the zonal mean static stability (\({-\frac{{\overline{T}} }{\overline{ \theta }} \frac{\partial \overline{ \theta }}{\partial p}}\)).

On the right hand side (RHS) of Eq. (1), the Charneys-Stern criterion represents a hybrid baroclinic-barotropic instability regime, via the vertical and horizontal wind shears in the mean flow, respectively. Specifically, the quantity \(BCL= \beta -\frac{\partial }{\partial p}(\frac{p f_0^2 }{R S_p} \frac{\partial {\overline{u}}}{\partial p})\) can be used to diagnose the baroclinic instability criterion, whereas \(BTR=\beta - \frac{\partial ^2 {\overline{u}}}{\partial y^2}\) for the barotropic regime. Once initiated, the AEW perturbations can grow via the baroclinic or barotropic instability or by a combined process. Note that the Charney-Stern criterion only provides a necessary, but not necessarily sufficient, condition for instability.

The approximate energy conversions from the zonal mean flow to the AEWs by baroclinic and barotropic processes are diagnosed as \(C_{A1}\) and \(C_{K}\) (Hsieh and Cook 2007, 2008), respectively:

$$\begin{aligned}{} & {} C_{A1}\approx - \frac{\overline{v'T'}}{\overline{\sigma } g} \frac{\partial {\overline{T}} }{\partial y} \end{aligned}$$
(2)
$$\begin{aligned}{} & {} C_{K} \approx - \frac{\overline{u'v'}}{g} \frac{\partial {\overline{u}} }{\partial y}- \frac{\overline{u'\omega '}}{g} \frac{\partial {\overline{u}} }{\partial p} \end{aligned}$$
(3)

\(\overline{ \sigma }\) is \(R{S_p}/p\), \(\omega \) is the estimated vertical motion from the horizontal winds using the continuity equation (Holton and Hakim 2012), the overbar in Eqs. (2) and (3) represents a zonal average as in (1), and primes denote deviations from the zonal mean.

2.3 Wave-mean flow interaction on AEWs

We further apply the Elliassen-Palm (E-P) flux theory for quantifying the relationship between modulated baroclinic-barotropic instability and large-scale background flow, mainly via the discussion of interactions between eddy fluxes and zonal mean flow (Eliassen 1960; Edmon Jr et al. 1980). Here we consider the QG E-P flux in the latitude-pressure (\(\varphi \), p) plane: \({\overrightarrow{F}=(F_\varphi ,F_p)}\) and its divergence \({\nabla \cdot \overrightarrow{F}}\):

$$\begin{aligned} F_ \varphi= & {} -r_0 \cos { \varphi } \overline{ u'v' } \end{aligned}$$
(4)
$$\begin{aligned} F_p=\, & {} f r_0 \cos { \varphi } \frac{\overline{ v' {\theta }' }}{\overline{ {\theta }_p }} \end{aligned}$$
(5)
$$\begin{aligned} \nabla \cdot \overrightarrow{F}= & {} {\frac{1}{r_0 \cos \varphi }} \frac{\partial }{\partial \varphi }({ F_\varphi \cos \varphi })+ \frac{\partial }{\partial p} F_p={r_0 \cos \varphi } \overline{ v' q' } \end{aligned}$$
(6)

Overbars in Eqs. (4) and (5) represent zonal mean values between \({10^ \circ E}\) and \({25^ \circ E}\), \({\varphi }\) is the latitude, \({r_0}\) is the radius of the Earth, \({\theta }\) is the potential temperature, and \({\theta _p}\) is the pressure derivative of \({\theta }\). Note that, under the QG assumptions, the E-P flux divergence equals the meridional eddy PV flux (Edmon Jr et al. 1980; Andrews 1987; Vallis 2017).

Then we transfer Eq. (1) into height coordinates (z):

$$\begin{aligned} \frac{\partial {\overline{q}}}{\partial y} =\beta - \frac{\partial ^2 {\overline{u}}}{\partial y^2}-\frac{\partial }{\partial z}\left(\frac{f_0^2}{N^2}\frac{\partial {\overline{u}}}{\partial z}\right) \end{aligned}$$
(7)

where \(N^2\) is the transformed zonal mean static stability (\({-\frac{{\overline{T}} }{\overline{ \theta }} \frac{\partial \overline{ \theta }}{\partial z}}\)).

The potential vorticity equation under unforced (e.g. adiabatic and frictionless) conditions, linearized around a zonally averaged state, becomes:

$$\begin{aligned} \frac{\partial {\overline{q}}}{\partial t} + \frac{\partial }{\partial y} {\overline{{v' q'}}}=0 \end{aligned}$$
(8)

By taking the y-derivative of Eq. (8) and using Eq. (7) we get:

$$\begin{aligned}{}\left[\frac{\partial ^2 }{\partial y^2}+\frac{\partial }{\partial z}\left(\frac{f_0^2}{N^2} \frac{\partial }{\partial z}\right)\right] \frac{\partial {\overline{u}}}{\partial t}= \frac{\partial ^2 }{\partial y^2} {\overline{{v' q'}}} \end{aligned}$$
(9)

The elliptic nature of the operator in Eq. (9) will produce a response on \(\frac{\partial {\overline{u}}}{\partial t}\) with a larger scale than the right side of equation (i.e. \(\overline{v' q'}\)). Qualitatively, comparison of the two sides of the equation suggests:

$$\begin{aligned} \Delta \frac{\partial {\overline{u}}}{\partial t} \propto \Delta {\overline{{v' q'}}} \end{aligned}$$
(10)

3 Results

3.1 Modulation of summer rainfall variability by AEWs

Fig. 1
figure 1

Seasonal changes (June–September) of mean daily precipitation between the MH and PI periods (unit: mm/day)

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The pattern of summer (June–September) rainfall change between the MH and PI periods indicates an intensification and a northward shift of the rain belt during the MH period, with a latitudinal migration extending to 16\({^\circ N}\) (Fig. 1). However, our simulation failed to reproduce the large magnitude of the summer precipitation increase in Sahara and its northward extension to 30\({^\circ N}\) (Pausata et al. 2016; Tierney et al. 2017; Claussen et al. 2017). This discrepancy with proxy data exists in almost all GCM simulations (Hargreaves et al. 2013; Pausata et al. 2016; Tierney et al. 2017), except for some in which a significant reduction of dust concentrations and a vegetated Sahara background have been prescribed (Claussen and Gayler 1997; Claussen et al. 1999; Harrison et al. 2014; Pausata et al. 2016).

Fig. 2
figure 2

a Power spectrum for summer (June–September) daily meridional wind at 700 hPa in PI (black) and MH (red) periods (Box mean in \({15^\circ W}\)-\({25^\circ E}\) and \({7^\circ N}\)-\({15^\circ N}\)) respectively. b as (a), but for the summer daily precipitation. Dashed lines in a and b denote the theoretical Markov red noise spectrum

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To investigate the relationship between summer rainfall and AEWs variability during the mid-Holocene, we conduct a power spectrum analysis for summer daily precipitation and meridional wind at 700 hPa where AEWs have the strongest signal. The power spectrum is averaged over the area (\({15^\circ W}\)-\({25^\circ E}\), \({7^\circ N}\)-\({15^\circ N}\)) where rainfall is greatly enhanced during the mid-Holocene boreal summers, and then averaged over 50 years of simulation.

The spectra of meridional wind and summer rainfall only show slightly enhanced variability on the synoptic (3–6 days) time scale during the PI period (Figure 2a and b). By comparison, the synoptic time scale (3–6 days) variability in both variables is significantly intensified during the mid-Holocene, peaking at a four-day cycle. Thus, the power spectrum results show significantly enhanced AEW activity and its modulating influence on summer rainfall variability in the mid-Holocene.

Fig. 3
figure 3

a and b Seasonal variance (June–September) of the 3-to-6 day filtered meridional wind at 700 hPa in the PI and MH periods, respectively (unit \({m^2}\).\({s^{-2}}\)). c and d as (a) and (b), but for 850 hPa. The black and blue horizontal lines in (a) and (b) represent the northern and southern AEWs track, respectively

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As AEWs activity is greatly enhanced during the mid-Holocene, we further quantify the variability of the southern and northern tracks of AEWs, to investigate changes of wave track locations and intensities compared to that of the PI period. We first conduct a 3-to-6 day filtering for the meridional wind at 700 and 850 hPa respectively, then we further calculate the variances of filtered values and average them over 50 years to derive the climatological distribution of AEWs tracks during the MH and PI boreal summers.

Figure 3a shows the location of southern AEWs tracks is nearby \({12^\circ N}\) during the PI period, and peaks over the West Africa; the northern AEW track is located at \({20^\circ N}\), and peaks over the Atlantic ocean. The locations of southern and northern tracks at 700 hPa are similar to modern climate, as shown in reanalysis and CMIP5 multimodel ensemble simulations (Skinner and Diffenbaugh 2014; Parker and Diop-Kane 2017). Specifically, the location of the southern AEW track is between \({8^\circ N}\) and \({12^\circ N}\), with the typical position at \({10^\circ N}\). The northern AEW track has the same latitudinal position at \({20^\circ N}\) in both our PI simulation and present climate, along the intertropical discontinuity (ITD, also known as the intertropical front, ITF) location. During the mid-Holocene (Fig. 3b), both the southern and the northern AEW track are enhanced, with a particularly pronounced change in the intensity of the southern track. The southern AEW track shifts northward from \({12^\circ N}\) in PI to \({15^\circ N}\) in MH.

Although previous studies show that the northern AEW track is more pronounced at 850 hPa than 700 hPa, there is no clear separation of the two tracks at this level in our simulations either in the PI or the MH period (Fig. 3c and d). This result is similar to the conclusion of CMIP5 multimodel ensemble analysis in modern climate as discussed by Skinner and Diffenbaugh (2014), which is probably caused by the coarse resolution of the models. Moreover, we find the intensity of AEWs is also greatly enhanced at 850 hPa during the mid-Holocene (Fig. 3d), together with a poleward migration of position compared to that of the PI period (Fig. 3c).

In general, the increases in summer rainfall over the Sahel and West Africa shown in Fig. 1 and its synoptic-scale variability in Fig. 2b have a close relationship with the enhanced AEWs activity during the mid-Holocene (Figs. 2a and 3). Based on the analysis of Figs. 1b and 3, we conclude that the rainfall changes are mainly caused by the greatly enhanced activity of the southern AEW track. In addition, the maximum of AEW activity at \({15^\circ N}\) at 850 hPa (Fig. 3d) is close to the location of the southern track at 700 hPa (Fig. 3b), which shows the deep and moist structure of southern AEWs and supports their importance for the variability of summer rainfall over the Sahel and West Africa during the mid-Holocene. By comparison, the AEWs in the northern track with their shallow structure and relatively drier conditions likely only make a minor contribution to the rainfall change in those regions (Parker and Diop-Kane 2017).

Fig. 4
figure 4

a Seasonal changes (June–September) of standard deviation of daily precipitation between MH and PI periods (unit: mm/day). b as (a), but for AEW’s contribution by 3-to-6 day’s filtering. The box region in (a) and (b) is about (\({15^\circ W}\)-\({25^\circ E}\), \({7^\circ N}\)-\({20^\circ N}\)), with area averaged values of 2.8 and 2.1 mm/day in (a) and (b) respectively

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To further quantify the contribution of enhanced AEWs activity to the increased summer rainfall of the mid-Holocene, we compare the daily standard deviation of rainfall between the MH and PI periods (Fig. 4). The changes in the summer rainfall (Fig. 1) and its standard deviation (Fig. 4a) are closely related, though the pattern of the latter is partly amplified and shifted slightly northward.We use the band-pass filtering of 3-to-6 day for summer rainfall to retain the AEWs contribution,and calculate the change in its standard deviation from the PI to the MH period (Fig. 4b).Then we calculate mean values over the area (\({15^\circ W}\)-\({25^\circ E}\), \({7^\circ N}\)-\({20^\circ N}\)) which covers the area of increasing summer rainfall. We find the increase in standard deviation of rainfall (and by implication, the increase in the mean rainfall) in this area is to a large extent explained by enhanced synoptic-scale AEW activity. The average increase in the 3-to-6 day standard deviation (2.1 mm/day) suggests a 75% AEW-related contribution to the total standard deviation increase of 2.8 mm/day (Fig. 4), which is consistent with the conclusion from Figs. 2 and 3 that the enhanced AEWs activity modulates summer rainfall variability significantly during the mid-Holocene.Based on the analysis in Fig. 3, we further extract the AEWs kinetic energy by using the 3-to-6 day band-pass filtered variance of the 700 and 850 hPa meridional wind, respectively, and then average them in the box region in Fig. 4 (15\({^\circ W}\)-25\({^\circ E}\), 7\({^\circ N}\)-20\({^\circ N}\)). Consistent with the analysis of Figs. 2 and 3, we find AEWs at 700 and 850 hPa are both greatly enhanced with the wave energies doubled (i.e. 3.54 \({m^{2}s^{-2}}\) at 700 hPa, and 3.06 \({m^{2}s^{-2}}\) at 850 hPa) in the mid-Holocene compared with the PI (i.e. 1.57 \({m^{2}s^{-2}}\) at 700 hPa, and 1.29 \({m^{2}s^{-2}}\) at 850 hPa).

Fig. 5
figure 5

a Summer mean changes of surface net solar radiation (color, unit: \( W {m^{-2}}\)) and 2 m temperature (contours with interval of 0.5 \( ^\circ C\)) from PI to MH periods. Dashed contours represent negative values. b Summer mean changes of latent heat flux (color, unit: \(W {m^{-2}}\)), low-level horizontal moisture flux at 925 hPa (vectors, unit: \({g {kg^{-1}}}\) \({m} {s^{-1}}\)), and \(\omega \) (red contours) at 700 hPa. Negative colored values in (b) denote upward latent heat flux anomalies. \(\omega \) anomalies in (b) have interval of 0.02 Pa \({s^{-1}}\), and dashed contours represent negative values and enhanced upward motion

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3.2 Pathways to surface cooling and enhanced thermal gradients

There is a negative net solar radiation anomaly in the mid-Holocene between 5\({^\circ N}\) and 18\({^\circ N}\) at the surface (Fig. 5a). Combined with positive solar radiation anomalies over the tropical Atlantic Ocean and north of 18\({^\circ N}\), this results in enhanced meridional thermal gradients over the Sahel and West Africa. From Fig. 6a, the orbital forcing actually increases the clear-sky net solar radiation, as the Northern Hemisphere (NH) receives more incoming radiation in the boreal summers during the MH period. However, increasing cloud cover (Fig. 6c) increases the difference between the actual and clear-sky net solar radiation (Fig. 5b), thus explaining the decrease in the former in Fig. 5a. This decrease in radiation heating, together with an increase in evaporation (discussed later), leads to a reduction of surface temperature over the Sahel.

Fig. 6
figure 6

a Seasonal changes of surface clear-sky net solar radiation (color, unit: \( W {m^{-2}}\)) between MH and PI periods. b as (a) but for seasonal changes of the surface net solar radiation minus surface clear-sky net solar radiation (unit: \( W {m^{-2}}\)). c as (a) but for seasonal changes of total cloud cover (unit: 0–1). d as (a) but for seasonal changes of evaporation fraction (color) and surface layer (0–7 cm) volumetric soil water (contour). The volumetric soil water in (d) has contour interval of 0.02 \({m^3} {m^{-3}}\), and solid contours denote positive values

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Moreover, meridional gradients of surface temperature are enhanced north of 14\({^\circ N}\) (Fig. 5a), which promotes stronger low-level westerlies, which further promotes a stronger and northward shifted WAM and larger moisture flux transport from the Atlantic Ocean to West Africa and Sahel. The moistened air layer enhances the moist static energy and convective instability in the lower troposphere, triggering large-scale rising motion at 700 hPa and moist convection and increasing summer rainfall over the Sahel and West Africa (Fig. 5b). On the other hand, the thermal gradient decreases at the southern flank of 14\({^\circ N}\) (Fig. 5a).

For the cooling of the land surface and enhanced meridional thermal gradients over the Sahel and West Africa, two pathways are relevant. The first one is mentioned above, that the decrease of surface net solar radiation caused by the increased cloudiness will force a radiative cooling effect and enlarge the meridional thermal contrast. The second pathway is about the land-atmosphere feedback. The soil moisture is enhanced during the MH period (Fig. 6d), and the moistening of the soil further modulates the land surface evaporation. We calculate the evaporative fraction (EF) as the ratio between the latent heat flux (LH) to the sum of the latent and sensible heat (SH) fluxes (Nichols and Cuenca 1993).

$$\begin{aligned} EF=\frac{LH }{SH+LH}=\frac{1 }{1+B_0} \end{aligned}$$
(11)

where \(B_0=SH/LH\) is the non-dimensional Bowen ratio that depends on moisture availability at the surface (Bowen 1926). Figure 6d indicates a strong link from increased summer mean soil moisture to increased EF and hence to larger latent heat flux (Fig. 5b). The enhanced evaporation cools the surface and leaves less energy to the sensible heat flux, which extends the cooling to the near-surface air.

In our work, we do not attempt to quantify the individual contributions of the solar radiation and latent heat flux pathways to the surface cooling and the enhanced meridional thermal gradient north of the cooling area, as these pathways occur simultaneously. In addition, it is important to note that the relationship between the changes in the WAM, surface energy balance, meridional temperature gradient and AEW activity is not unidirectional. The northward shift in the WAM is ultimately triggered by the increased Northern Hemisphere summer insolation, but the resulting chain of events that enhances the AEW activity may amplify this shift. As AEWs generate precipitation and cloudiness, and as evapotranspiration in West Africa is moisture-limited, the decreases in the Bowen ratio and surface solar radiation must partly result from the AEWs themselves. The same therefore also applies to the change in the temperature gradient that modulates the AEW activity. On the other hand, the increase in atmospheric latent heat release resulting from increased precipitation needs to be balanced by increased rising motion near 15\({^\circ N}\) (Fig. 5b). This increase in rising motion is an important component of the northward shift in the WAM circulation.

3.3 Effects of baroclinic and barotropic instability on amplified AEWs

Fig. 7
figure 7

a Summer mean distribution of combined baroclinic and barotropic instability parameter (i.e. the RHS in Eq. (1), unit: \({10^{-11}m^{-1}s^{-1}}\), shaded) and u-wind (contours, unit: 1 \({m s^{-1}}\)) in the PI period. b as (a), but for the changes between the MH and PI periods. c Change of baroclinic instability (i.e. BCL). d Change of barotropic instability (i.e. BRT). U-wind in (a) and (b), and the instability metrics in (a)–(d) are averaged between 10\({^\circ E}\) and 25\({^\circ E}\)

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As barotropic and baroclinic instability are important mechanisms for the growth and structure evolution of AEWs after they are initiated in central North Africa, we further evaluate the presence of the PV reversal required by the Charney-Stern instability criterion [i.e. Eq. (1)]. From Fig. 7a, during the PI period, the summer mean distribution of the RHS of Eq. (1)is indicative of combined barotropic and baroclinic instability (represented by negative values) between 9 and 16\({^\circ N}\) in the middle troposphere, and the AEJ core around 600 hPa is closely co-located with the unstable region with reversed PV gradients. Besides, low-level combined instability also exists at and below 850 hPa north of the AEJ.

Compared with PI, there is a northward shift of combined instabilities and AEJ in the midtroposphere and stronger low-level westerlies during the mid-Holocene (Fig. 7b). The latitude of enhanced combined instability at 17\({^\circ N}\) is located north of the surface cooling zone shown in Figs. 5 and 6, and strong surface heating occurs below the level of enhanced combined instability. This heating will promote low-level thermal advection below the AEJ core and strengthen vertical wind shear and baroclinic instabilities (Pytharoulis and Thorncroft 1999; Thorncroft and Hodges 2001; Parker and Diop-Kane 2017).

Based on the above analysis, we further quantify the contribution from barotropic and baroclinic regimes separately. The baroclinic instability contribution (i.e. BCL, Fig. 7c) is found to have a larger negative magnitude than the barotropic regime (i.e. BRT, Fig. 7d), and the core of its increase is located further north (18 vs. 16\({^\circ N}\)).

3.4 Wave-mean flow interaction on AEWs

Fig. 8
figure 8

Summer mean changes of zonally averaged u-wind, E-P flux and its divergence between the MH and PI periods. \({F_p}\) and \({F_\varphi }\) vector component anomalies (colored) are scaled by \({10^{-5} \cos { \varphi } \sqrt{\frac{p_o}{p}}}\) and \({\frac{1}{3.14 r_0}} \sqrt{\frac{p_o}{p}}\) respectively. E-P flux divergence anomalies are represented by black contours with interval of 50 \({m^{-2}s^{-2}}\) in (a), and u-wind anomalies are black contours with interval of 1 \({ms^{-1}}\) in (b). The zonal average in E-P flux and u-wind is between \({10^\circ E}\) and \({25^\circ E}\). Dashed contours represent negative values

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From Eqs. (9) and (10), when E-P flux divergence is negative (i.e. \(\overline{v' q'}<0\)), it will promote a westward acceleration (i.e. \(\frac{\partial {\overline{u}}}{\partial t}<0\)) over a broader region, and by contrast, positive E-P flux divergence will produce an eastward acceleration (Andrews 1987; Vallis 2017). During the MH period, enhanced upward E-P flux anomalies exist in middle-to-low troposphere with E-P convergence anomalies maxima located near 17 \({^\circ N}\) and 700 hPa (Fig. 8a), which induces a westward acceleration associated with enhanced easterlies in the midtroposphere (Fig. 8b). By contrast, positive E-P flux divergence anomalies exist in the lower troposphere below 850 hPa, inducing an eastward acceleration accompanied with enhanced westerlies within the WAM system. Consistent with previous studies (Dwyer and O’Gorman 2017), the strongest E-P flux anomalies are latitudinally co-located with the stronger low-level westerlies caused by the enhanced meridional thermal gradient discussed in Sect. 3.2.

The drivers of climate change during the mid-Holocene (i.e. orbital forcing, vegetation cover, dust, and so on) are very different from the currently ongoing global warming caused by significantly increased GHG concentrations. However, it is interesting to note that the upward E-P fluxes and the westerlies have been found to shift poleward both under the mid-Holocene and current warm climates (Lu et al. 2010; Schneider et al. 2010; Donohoe et al. 2014; Dwyer and O’Gorman 2017). The extent to which this similarity results from common dynamical mechanisms is an important topic for further research.

Fig. 9
figure 9

a Seasonal changes of mean flow to eddy energy conversion (\(C_{A1}\)) between the MH and PI periods. (b) as (a), but for the corresponding barotropic energy conversion (\(C_{K}\)). The contour intervals in (a) and (b) are 5\(\times \) \({10^{-6}s^{-1}}\) and 1\(\times \) \({10^{-6}s^{-1}}\) respectively, and the zonal mean is between 10\({^\circ E}\) and 25\({^\circ E}\). Dashed contours represent negative values

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Moreover, the E-P flux convergence anomalies (12 to 21\({^\circ N}\)) are located where zonally-averaged meridional PV gradients have strong negative anomalies, representing enhanced baroclinic instability (Figs. 7c and 8). This enhances the AEW generation by increasing the dominant baroclinic energy conversion \(C_{A1}\) (Fig. 9a), in association with a greatly promoted vertical wind shear (i.e., eastward acceleration of the flow in the lower troposphere and westward acceleration in the midtroposphere) shown in Fig. 7b. The barotropic instability contribution and associated energy conversion \(C_{K}\) to enhanced AEWs activity is much weaker (Figs. 7d, 9b; note the smaller contour interval in Fig. 9b than Fig. 9a), but these barotropic processes still play a non-negligible role in the growth of AEWs and further modulation of summer rainfall during the mid-Holocene. Besides, consistent with previous research (Hsieh and Cook 2008), we find baroclinic conversion \(C_{A1}\) dominates in the lower troposphere (850 hPa) below the AEJ core and north of the AEJ, peaking nearby the strongest vertical wind shear region. By contrast, barotropic conversion \(C_{K}\) locates in the midtroposphere south of the AEJ, mainly caused by enhanced horizontal wind shear (Figs. 7b, 8, and 9b).

4 Discussion

Some questions remains open due to the limitations of paleoclimate simulations conducted in this research. Synoptic-scale AEWs have a close relationship with convective systems. On one hand, AEWs are important in initiating organised convective systems and modulating summer rainfall. On the other hand, convective systems could directly affect AEWs growth and westward propagation (Hall et al. 2006; Berry and Thorncroft 2012; Russell et al. 2020). However, our GCM simulations with the T159 resolution are too coarse to resolve any convective details, which is a common challenge in most CMIP6 and PMIP4 climate models. The practical problem is the need to parameterize convection as a surrogate for explicit simulation, which would require a resolution much higher than what is possible in EC-Earth or other global models, especially as paleoclimate simulations must be run at least for hundreds of years.

One possible approach is applying a convection-permitting climate model like HCLIM38 (Belušić et al. 2020) in the paleoclimate study, using boundary conditions from GCM simulations. Such a regional-to-global coupling framework for time-slice simulations would provide the opportunity to track convective systems and AEWs evolution details across different climates states. Exploring of high-resolution modeling in paleoclimate is also necessary and important for understanding and interpreting the evidence for paleo-weather extreme events that exists in high-resolution fossil/microfossil proxies (Yan et al. 2020).

Another limitation in our work is the highly simplified experimental setting, with no change in vegetation or dust concentrations. For the real world “Green Sahara” era, abundant proxy evidences indicate a substantial increase in precipitation, significantly changed vegetation cover, and reduced dust emissions during the mid-Holocene period (Harrison et al. 2014; Pausata et al. 2016; Claussen et al. 2017; Tierney et al. 2017; Hopcroft and Valdes 2019). Without doubt, forcing factors like vegetation cover, dust, and aerosols are very important for a more complete understanding of the mid-Holocene climate state.

GCM simulations that include changes in vegetation and aerosols also have their limitations and drawbacks. First, changing multiple factors simultaneously makes it difficult to understand their individual impacts on the AEW regime during the mid-Holocene. Second, there are still major uncertainties in our understanding of the vegetation-atmosphere-aerosols/biochemistry couplings and their representation in climate models. Therefore, the simple experimental design in this study serves as a first step that allows an easier quantification of the effect of (mainly) orbital forcing on the AEW regime. Nonetheless, we believe that future simulations with vegetation cover and aerosols changes are still necessary and important. Those future simulations can help us to better understand AEW mechanisms during the mid-Holocene.

5 Conclusions

The mid-Holocene was a warm period with greatly enhanced summer rainfall and a northward shift of the WAM system. Previous studies show that AEWs are the dominant synoptic-scale phenomena that play an important role modulating moist convection and summer rainfall within the WAM system (Carlson 1969b; Kiladis et al. 2006; Parker and Diop-Kane 2017). We conduct simulations by using the fully-coupled EC-Earth model to quantify AEW’s influence on summer rainfall variability and northward migration over the Sahel and West Africa during the mid-Holocene.

Without a vegetated Sahara background, our climate simulations have failed to reproduce the magnitude of rainfall changes as compared to proxy evidence for the mid-Holocene. However, the AEW activity is greatly enhanced during the mid-Holocene in our simulations, with wave kinetic energies doubled from that in PI, and enhanced AEWs significantly modulate the summer rainfall variability over the Sahel and West Africa on the synoptic (3-to-6 days) time scale. Moreover, our simulations show that low-level westerlies are enhanced, which forces a stronger WAM and promotes a stronger low-level moisture flux from the Atlantic Ocean to inland, with middle-level rising motion significantly enhanced during the mid-Holocene.

As the increase in summer rainfall over the Sahel and West Africa has a close relationship with enhanced synoptic-scale AEW activity, we further analyze the southern and northern tracks during the mid-Holocene. The southern AEW track at 700 hPa is greatly strengthened and migrates poleward from \({12^\circ N}\) (PI) to \({15^\circ N}\) (MH), peaking over the Sahel and West Africa. By contrast, the northern AEW track at 700 hPa remains near \({20^\circ N}\) in both the PI and the MH simulations, with a smaller increase in intensity than found for the southern track. The AEW activity at 850 hPa is also greatly intensified and shifts poleward, but there is no clear separation between the southern and northern AEW tracks at this level in our simulations. In general, our simulations show the variability of summer rainfall over the Sahel and West Africa is mainly modulated by the greatly enhanced activity of southern AEW track. The northern AEW track has a minor contribution to rainfall changes in the above-mentioned regions.

Although orbital forcing during the mid-Holocene increases incoming solar radiation in the Northern Hemisphere during the boreal summer, our MH simulation results show a reduction of surface net solar radiation and a cooling over the Sahel and West Africa and enhanced meridional thermal gradients to the north of 14\({^\circ N}\). One possible pathway is the decrease in solar radiation caused by the increased cloudiness that accompanies the northward shift in the WAM. Another possible pathway is increased evaporative fraction and associated enhanced upward latent heat flux, allowed by the moistening of the soil. As a result of this, less energy is available for heating the near-surface air by the sensible heat flux. These two mechanisms together cool the surface where precipitation increases, and the enhanced meridional temperature gradient to the north of the cooling further enhances the low-level monsoonal westerly flow with more water vapor advected to Sahel and West Africa. Under favorable circulation features in middle-to-low troposphere, moist convection and associated rainfall are promoted during the mid-Holocene boreal summers. However, the relationship between the changes in the WAM, surface energy balance, meridional temperature gradient and AEW activity is not unidirectional, which means the two possible pathways explained above are not the whole picture for understanding those mechanisms.

By analysing the wave-mean flow interaction process over the central North Africa, we further quantify the influence of baroclinic and barotropic instabilities on AEW’s amplification via the Charney-Stern criterion diagnosis and the associated energy conversions. The enhanced baroclinic instability in the midtroposphere plays a larger role in promoting AEWs development than the barotropic regime during the mid-Holocene, under the influence of strong surface heating. Most importantly, enhanced AEW activity is essential for promoting moist convection and summer rainfall over the Sahel and West Africa during the mid-Holocene, resulting in a northern shift of the summer rainfall band.

At last, it is worthy to note that our results of AEW response to orbital forcing during the mid-Holocene could connect to a broader picture of AEW dynamics in different climate states (Skinner and Diffenbaugh 2014; Martin and Thorncroft 2015; Bercos-Hickey and Patricola 2021). Although the drivers of climate change during the mid-Holocene were very different from those in the current, GHG-driven global warming, there is an important qualitative similarity. The GHG-induced global warming is stronger in the more continental Northern Hemisphere, whereas in the mid-Holocene, a similar hemispheric contrast arose from increased solar radiation in the Northern Hemisphere in summer. For both the GHG-induced warming (Bercos-Hickey and Patricola 2021) and in our mid-Holocene simulations, we find increased rainfall over the Sahel and West Africa, enhanced meridional thermal gradients, and strengthened AEWs, together with the poleward migrated and weakened AEJ. For instability regimes, both increased baroclinic and barotropic energy conversions promote the AEWs growth in those two warm climates. A notable difference is that the baroclinic energy conversion produces a larger contribution to changes in AEWs in our MH simulations, while the barotropic process is more important to projected future AEWs changes (Bercos-Hickey and Patricola 2021). Furthermore, we find that a greatly enhanced southern AEW track dominates the changes in synoptic scale variability and rainfall in our mid-Holocene simulation, while there is less change in the northern track. This is consistent with projected AEW track changes in future climate with increased GHGs (Bercos-Hickey and Patricola 2021).