CLIMBER-2 incorporates a 2.5-dimensional statistical–dynamical atmosphere model of coarse horizontal resolution of about 10∘ latitude and 51∘ longitude and a parameterised vertical structure assuming universal profiles of temperature, humidity and meridional circulation . The atmosphere component is coupled to a zonally averaged and multi-basin dynamic ocean model based on that of , with meridional resolution of 2.5∘ latitude and 20 vertical levels. Connected to these components the model also includes a one-layer thermodynamic sea ice model with horizontal ice transport , the three-dimensional polythermal ice sheet model SICOPOLIS , the dynamic global vegetation model VECODE , a dynamic global carbon cycle model with land and ocean biogeochemistry , and modules for aeolian dust effects .

The model representation of the atmosphere–vegetation coupling is particularly important for this study. In CLIMBER-2 the interaction between these components occurs every year. Annual growing degree days and precipitation are used to compute equilibrium vegetation cover based on the approach by . In turn, the vegetation-related variables modify surface albedo, aerodynamic roughness length and evapotranspiration, which affect energy and moisture fluxes between land and atmosphere components, similarly to . Vegetation cover is computed as fractional amounts of two plant functional types: trees and grasses. Non-vegetated areas can include fractions of desert or glacier cover types. Details about atmosphere–vegetation coupling in CLIMBER-2 and parameter values are given in .

The model has a low computational cost that enables simulations over long timescales, when multiple components of the climate system can interact. Despite its coarse spatial resolution and simplifications, the model captures well past climate changes , as well as the aggregated large-scale features of modern climate . Its response to changes in boundary conditions and climate forcings is comparable to that of more comprehensive models , and it successfully simulates glacial–interglacial cycles . In fact, CLIMBER-2 is currently the only geographically explicit model which can be used for an ensemble of simulations of glacial–interglacial cycles. For the specific case of North Africa CLIMBER-2 has already been used to study its climate on multi-millennia timescales with a favourable performance e.g..

We simulate the coupled atmosphere, ocean, sea ice, land surface and vegetation dynamics for the past 190 kyr. The polythermal ice sheets model and global carbon cycle model components are not employed since we prescribe ice sheet extent and atmospheric GHG levels using available data. Simulations start from an equilibrium state attained after a 5 kyr simulation that maintained parameters set at 190 ka values. We perform 15 transient simulations prescribing possible combinations of climate forcing factors: GHG levels, ice sheet extent and orbital parameters. Forcings are prescribed either with a transient series from past evidence or with a single reference value as shown in Fig. . Reference values are taken from the transient series close to the Eemian interglacial state at about 125 ka and close to the Last Glacial Maximum (LGM) at about 21 ka. The GHG radiative forcing change from preindustrial (PI) conditions in Fig. a comes from , and it considers variations in gases, CO2, CH4 and N2O, that are in line with Antarctic ice cores . Ice sheet data are model output from a simulation also in which agrees with sea level changes in and the reconstructions of . Ice sheets are represented by a spatially distributed transient series varying mostly in the Northern Hemisphere, even though we show only the global cumulative ice volume (Fig. b). The Earth's orbital parameters (precession, obliquity and eccentricity) vary according to . We show their secular variations using the monsoon forcing index defined by , which measures an insolation gradient in the tropics relevant to monsoon systems and AHPs (Fig. c). In the text and in Fig.  we label peaks in the monsoon forcing index using MIS names to ease location of time slices when AHPs usually occur. Details about forcings, computation of the monsoon forcing index and MIS nomenclature are given in Appendix .

Experiments of past AHPs and their forcing setup combinations follow the factor separation method of for three factors: (1) GHG radiative forcing changes from the PI era, (2) ice sheet extent and (3) orbital parameters. Using this method it is possible to estimate individual (also called “pure”) and synergistic contributions of the forcing factors to a simulation outcome (or predicted climatic field). The method assumes all contributions are additive and can be separated subtracting fields of a set of sensitivity simulations. To implement the method, a specific simulation target must be chosen in order to calculate deviations from a baseline or control state (i.e. the factor separation depends on the target or point of view). We are interested in knowing how much the forcings contribute to the simulation of AHPs. We choose two simulation targets with opposing global climates and AHP situations: the Eemian interglacial at around 125 ka (i.e. warm global climate) with a strong AHP and the LGM at around 21 ka (i.e. cold global climate) with no AHP. Experiments and forcing combinations are shown in Table . Only in the control experiment E0 do all forcings vary realistically as in the transient series obtained from past data (see Fig. ). For the rest of the experiments we have two sets of simulations using the interglacial or glacial reference values shown in Table , with all possible “fixed-or-transient” combinations in each set. For instance, simulation EI4 has both GHG forcing change and ice sheets fixed at the interglacial reference values for the entire 190 kyr run (i.e. they are kept constant at interglacial levels). Likewise for EG4 but instead the fixed values are the glacial levels. Experiments EI7 and EG7 have the three forcings fixed at their respective reference points. Details and equations of the separation analyses are given in Appendix .

The low computational cost of the model and information available about future changes in the forcings enable us to also look into potential future climate change in North Africa. We are also interested in knowing how much our findings from the past can inform the future. Additional simulations start from present-day conditions in the control experiment E0 and cover the next 100 millennia after present (kyrAP). Projections of GHG radiative forcing changes from the PI era are based on the CO2 emissions scenarios of , which estimate possible cumulative amounts of carbon to be released to the atmosphere in units of gigatonnes of carbon (GtC). The emission estimates take into account both data from the reports of the Intergovernmental Panel on Climate Change (IPCC) and the size of available coal deposits to designate “moderate” or “large” amounts. Six experiments include a scenario of null emissions since preindustrial conditions (0 GtC); a moderate emissions scenario with a release of 1000 GtC; a large emissions scenario with a release of 5000 GtC; and the intermediate cases of 2000, 3000 and 4000 GtC. In these scenarios 90 % of the emissions are assumed to occur within the first few centuries of simulation, meaning there is an early peak of atmospheric concentration of CO2 that subsequently decays to an equilibrium value (higher than preindustrial). These experiments are also shown in Table . For these simulations we ignore the radiative forcing effect of other GHGs. The orbital forcing is considered to continue changing following . We keep the ice sheets fixed at the preindustrial setting, neglecting the effects of a potential complete deglaciation or a new glacial inception. The latter is justified since a large ice sheet should not emerge within the next 100 kyr, even for the moderate emissions scenario .

Results of the control simulation E0 are shown in Fig. , alongside proxy data from sediment cores SL71 and SL99 from the eastern Mediterranean Sea . The proxies in Fig. a show pulses in the ratios of fine-grained minerals (kaolinite and chlorite), always found following a sapropel layer in the sediments. The sapropel doublet during MIS 5c for core SL71 corresponds to a single event in spite of the interruption in the sediments, which could be explained by postdepositional redox reactions . The sapropel layers indicate past instances of AHPs, when enhanced riverine discharge suppressed seabed oxygenation in the Mediterranean Sea, while the amplitudes of the dust pulses reveal the strength of the hydrological cycle during their preceding AHPs since the mineral production depends on rainfall intensity (weathering). In Fig. a the dust pulses lag the sapropel layers because aeolian dust transport from waterbodies across (most likely) North Africa can only occur once arid conditions are re-established after an AHP. The comparison between the proxy data and our simulations can only be qualitative in nature since we do not model either dust transport into the Mediterranean Sea or sapropel formation. It is remarkable, however, that the control simulation E0 (Fig. b–d) shows large peaks close in time with the sapropel layers in the proxies. Also in both simulation E0 and the proxies the strongest signals happen during MIS 5e. The simulation E0 is in closer agreement with the data from core SL71, where the pulses after MIS 5c and 5a have similar magnitude. Comparison with other proxy data from marine cores off the coasts of West Africa and East Africa likewise reveals agreement in timing and in magnitude of the E0 simulation with the proxies (not shown).

In Fig.  simulation E0 shows that peak values of precipitation, the vegetation cover fraction and temperature in the Sahara region coincide with peaks in the monsoon forcing index during the past 190 kyr. The peak values are summarised in Table . In the case of precipitation (Fig. b) and temperature (Fig. d) this is most conspicuous in the summer seasonal means, with large peaks similar to those evident in the vegetation cover fraction (Fig. c). The strongest peak values occur during the last two interglacial periods at MIS 5e and 1, as well as during MIS 6e, 5c and 5a. Only these five MIS periods have a vegetation cover fraction above 70 %. The vegetation peaks happen during warmer periods when annual mean daily precipitation is greater than 0.7 mmd-1. This could accumulate to more than 250 mmyr-1, well above the minimum limit estimated to support perennial grasslands and savanna biome types in North Africa . Although this precipitation value is low compared to estimates from proxy data , any amount over 200 mmyr-1 is still distinctly greater than present-day values across the region and is within the variability range of more sophisticated climate models for the last AHP during the Holocene e.g.. Therefore we consider these peak times to be simulated past AHPs with CLIMBER-2. The oldest one at MIS 6e was also found by , and those at MIS 5c, 5a and 1 agree with the results of . Measuring from the moment the modelled vegetation starts growing until the moment it vanishes (Fig. c), the AHPs last on average 10.8 kyr, with the one at MIS 5e being the longest (12 kyr) and the one at MIS 1 the shortest (9 kyr).

A first approximation to study the effects of the forcings on the modelled AHP response follows a simple linear regression analysis. With the values from Table  we plot paired combinations of forcings and response variables in phase diagrams and fit regression lines with the ordinary least-squares method and use the statistic R2 and the p value of the F statistic as goodness-of-fit estimates. The forcings are included in the regression analysis (besides the modelled response) because even though we know that GHG levels and ice sheets are not independent from the orbital forcing, we do not know exactly how they relate to each other during AHPs. We also recognise that GHGs and ice sheets are global features, while the monsoon forcing index is a regional insolation gradient. We find there is a strong correlation (R2=0.75, p value=0.006) between the average ice sheet volume and the monsoon forcing index peaks, with the highest monsoon forcing index values having the least ice volume. In contrast, we see a weak correlation (R2=0.27, p value=0.19) between the GHG radiative forcing and the monsoon forcing index peaks.

The modelled response correlates strongly with the monsoon forcing index during its peak times, as shown in Fig. . For precipitation (Fig. a) we observe a positive linear relationship for summer seasonal (R2=0.93, p value=0.0001) and annual (R2=0.92, p value=0.0001) means; therefore higher monsoon forcing index values yield higher precipitation in the Sahara grid box. Winter precipitation being almost a flat line shows this modelled variable in the Sahara does not depend on the monsoon forcing index. In the case of vegetation (Fig. b) we see non-linear behaviour with an abrupt large jump from low (about 10 %) to high (about 70 %) vegetation coverage within a small range of variation in the monsoon forcing index from around 15 to 20 Wm-2. In fact, for vegetation cover the change-point analysis of finds a change point (i.e. a significant jump in the linear regression) between values of the monsoon forcing index of 15 and 20 Wm-2. When applied to the correlation of precipitation with the monsoon forcing index, the change-point analysis does not find a jump in the linear regression at the same level of significance as for vegetation cover. Vegetation cover values occurring past the threshold range have a strong correlation (R2=0.91, p value=0.012) with the monsoon forcing index.

We also include in Fig. b the vegetation response of sensitivity simulation EI1 (with interglacial GHG forcing) because it shows that the insolation threshold might be sensitive to the GHG forcing. With interglacial GHG radiative forcing (experiment EI1) the threshold decreases below 15 Wm-2, and the correlation past this threshold between vegetation cover and the monsoon forcing index is still strong (R2=0.93, p value=0.0005). Looking also at the GHG radiative forcing values in Table  for MIS 6b and 4 (the points close to 15 Wm-2 in Fig. ), we find that there is an average increase of about 2 Wm-2 in the GHG forcing in simulation EI1 relative to the control simulation E0. Hence we tentatively suggest that an increase in GHG forcing of some 2 Wm-2 is associated with a decrease in the threshold of the monsoon forcing index by some 5 Wm-2. This implies a sensitivity of the threshold in monsoon forcing index to a change in GHG forcing of around -2.5.

Existence of such threshold behaviour suggests that changes in the model should happen at a fast rate. Already in Fig. c we see that vegetation growth and decline phases occur rapidly. To look into the rates of change more carefully we plot in Fig.  the temporal derivatives of the forcings and the simulated vegetation fraction in the Sahara in the control experiment E0. This figure shows how the non-linear dynamics of the vegetation response does not follow smoothly the speeds of change in any of the forcings. However, vegetation growth and decline phases are coherent with times of increasing and decreasing rates, respectively, of the monsoon forcing index. In fact, we also find a strong correlation (R2=0.96, p value<0.0001) between peak speeds of change in the monsoon forcing index and peak growth and decline rates of the vegetation response. The fastest vegetation growth rate occurs during MIS 5e (59.2 %kyr-1), when a peak in the increasing rate of the monsoon forcing index coincides with a relatively strong increase in the speed of change in the GHG radiative forcing and the strongest decline rate in the ice sheet volume. Figure d shows that the vegetation growth phases, during AHP onset, usually occur at faster rates than the decline phases during AHP terminations, which is most conspicuous during MIS 6e (onset at 50.1 %kyr-1 versus termination at -31.6 %kyr-1). Only during MIS 5a is this not the case (onset at 33.7 %kyr-1 versus termination at -39.7 %kyr-1), when ice sheets do not wane at a strong pace. On average, during AHPs the vegetation growth phase lasts about 5.2 kyr and the vegetation decline about 6.2 kyr.

We suspect that differences in intensity amongst AHPs should be mainly determined by differences in the state of GHGs, ice sheets and orbital configuration at the time they occur. However, we do not know how much each of the forcings affects the AHP intensities. To look into this we perform simulations according to the factor separation method of and implement its equations (see Appendix ) using the model output for annual means of temperature, precipitation and the vegetation fraction in the Sahara region. Because the separation method depends on the chosen simulation target, we carry out two analyses: one of them isolates the contributions of the forcing factors to attain an Eemian-like strong AHP response (i.e. interglacial perspective), while the other one does it for an LGM-like non-AHP response (i.e. glacial perspective).

Both target responses for the two separation analyses are represented in simulations EI7 and EG7. Simulation EI7 from the interglacial perspective has all three forcing factors fixed at interglacial conditions (using the Eemian as reference). In this simulation, annual mean Saharan temperature stays for all times at 21.8 ∘C, precipitation at 1.3 mmd-1 and the vegetation cover fraction at 95.8 %. These values resemble those around the Eemian peak (about 125 ka) in the control simulation E0 (see Fig. ). Simulation EG7 from the glacial perspective has forcings fixed at glacial conditions (using the LGM as reference). In this simulation, annual mean Saharan temperature remains for all times at 15.2 ∘C, precipitation at 0.2 mmd-1 and the vegetation cover fraction at 0.0 %. These values resemble those around the LGM (about 21 ka) in the control simulation E0 (see Fig. ). Therefore, the interglacial-perspective experiment EI7 keeps a permanent strong Eemian-like AHP for the entire simulation, whereas the glacial EG7 keeps none. Through the factor separation method we then estimate how much each of the forcings is contributing at all times to the differences between the control experiment E0 and targets EI7 (strong AHP) and EG7 (no AHP).

Results of the separation analysis from the interglacial perspective are shown in Fig.  for AHP temperature, precipitation and the vegetation cover fraction. With the forcing factors fixed at interglacial levels, the modelled response in EI7 (Eemian-like AHP) always deviates positively from the control experiment E0 for the three climatic variables. This is as expected since the resulting values of EI7 in the previous paragraph are higher than those in the control E0 at all times (only the Eemian in E0 is close to EI7). The slight offset between E0 and EI7 at MIS 5e occurs because the combination of prescribed forcings in EI7 happens closely around MIS 5e but not exactly at the same time during the control experiment E0. The relevant outcome of the separation method lies in the colours (and patterns) in Fig. , which show how the forcings contribute to the EI7–E0 difference. For AHP temperature (Fig. a) the individual contribution of each forcing is directly proportional to the change in the forcing. To see this it is necessary to compare differences between the control forcing values in the transient series in Fig.  and the interglacial reference level in that same figure. For instance, at MIS 6b the largest contribution to temperature change comes from the GHG radiative forcing change (Fig. a) since that is the forcing with the largest difference between the transient series and the interglacial horizontal line (see also Fig. a). For the AHP temperature response the synergistic effects are small in comparison to the individual contributions. Averaging the contributions to AHP temperature for the whole time series in Fig. a shows that GHGs add about 1.6 ∘C (41.1 % of change from E0), ice sheets 0.8 ∘C (19.9 % of change from E0) and the orbital forcing 1.8 ∘C (45.9 % of change from E0). The synergy between GHGs and the orbital forcing is small but is the synergy with the largest effect, adding on average about -0.2 ∘C (-4.9 % of change from E0).

The AHP precipitation case in the separation analysis is different to the temperature one. Figure b shows that the AHP precipitation response largely depends on the orbital forcing (substantial blue colour). Not only is the individual contribution of this forcing the largest for all times, but also its synergies with the other two forcings have relatively large effects. The individual contribution of the GHG radiative forcing to changes in AHP precipitation is small. The individual effects of ice sheets on AHP precipitation are negligible as well. No synergistic effects seem to exist between the ice sheet forcing and the GHG radiative forcing. Averaging the contributions to AHP precipitation for the whole time series in Fig. b, we find that GHGs add about 0.1 mmd-1 (6.7 % of change from E0), ice sheets close to 0.0 mmd-1 (2.2 % of change from E0) and the orbital forcing about 0.6 mmd-1 (59.3 % of change from E0). Both synergies of the orbital forcing with GHGs and ice sheets round up to 0.2 mmd-1 (each about 15 % of change from E0). This means the effects of the orbital forcing and these two synergies with GHGs and ice sheets amount to about 90.9 % of the change from E0.

AHP vegetation results in Fig. c are similar to the AHP precipitation case, although the individual effect of the orbital forcing is much more conspicuous (predominant blue colour). The negative synergistic effects seen in the vegetation changes should be an artefact of the separation analysis method because vegetation is a bounded quantity. Consider, for example, the time around 150 ka during MIS 6b, when the Sahara is much greener, close to a 100 % vegetation cover, in simulation EI7 than in simulation E0 (Fig. c). The individual contribution of orbital forcing (blue colour) would make some 90 % of the Sahara green and the GHG forcing (green colour) some 50 %. If both forcings are active, then the pure contributions cannot be superposed (do not add linearly) because the Sahara cannot be more than 100 % covered with vegetation. Therefore, the synergy between these forcings (pink colour and dot pattern) has to be negative. Average contributions to AHP vegetation for the whole series in Fig. c are about 5.8 % from GHGs (6.4 % of change from E0), 2.2 % from ice sheets (2.4 % of change from E0) and 72.6 % from the orbital forcing (79.5 % of change from E0). The synergy (when positive) between GHGs and orbital forcing adds on average about 4.0 % (4.4 % of change from E0) and the synergy (when positive) between ice sheets and orbital forcing about 5.3 % (5.8 % of change from E0). The orbital forcing and all of its synergies account for about 90.4 % of vegetation change from E0.

From the glacial perspective in the additional separation analysis, we do not find anything significantly new; hence details are to be found in Appendix . Figure  shows that in this case the deviations in EG7 from the control E0 are always negative for the three climatic variables and the effects of the ice sheet changes are larger than those of the GHGs. Nonetheless, the same behaviour for temperature is observed, with changes being proportional to the changes in the forcings. This analysis demonstrates that it is the relatively low maxima in orbital forcing that result in the absence of AHP conditions at MIS 6b, 4 and 3a – rather than the low GHG radiative forcing or the large ice sheets. From this perspective synergies are more difficult to assess because of the lower bounds in precipitation (0 mmd-1) and the vegetation cover fraction (0 %).

When computing the monsoon forcing index for the next 100 kyr (millennia after present) we see that the onset threshold range of past AHPs (15–20 Wm-2 in the model) will not be crossed within the next ca. 60 kyr (Fig. a). The amplitude in the monsoon forcing index (proxy for orbital forcing) is much smaller than that of past times (see Fig. ) due to low eccentricity in the Earth's orbit. Only for the time around 66 kyrAP does the monsoon forcing index approach the onset threshold range. From the sensitivity simulation EI1 in which the GHG radiative forcing change is set to an interglacial level, we find that an increase in GHG forcing by some 2 Wm-2 can lower the threshold in the monsoon forcing index by some 5 Wm-2 (Fig. b). Hence we expect that in a climate with much stronger GHG forcing and much warmer global temperatures (Fig. b and c), the threshold might decrease even further. The simulations F0–5 corroborate the lesson learnt from the study of the past; Fig. d shows AHP responses for monsoon forcing indices below 10 Wm-2.

The modelled vegetation response in Fig. d shows the potential effects of increased GHG radiative forcing for climate in the Sahara. The no-emissions scenario F0 (0 GtC) predicts that no AHP should occur before the next 60 kyr. For this scenario only at 66 kyrAP (named peak M4) is the threshold range of the monsoon forcing index crossed slightly at 16.5 Wm-2, and we see a vegetation response of about 54.1 %. However, for the moderate emissions scenario F1 (1000 GtC) we see already that additional vegetation responses begin to occur at earlier monsoon forcing index peaks. These are still quite small responses since the average change in GHG radiative forcing stays close to 1 Wm-2 for this scenario, and according to our estimate from the past simulations, this means the threshold range only decreases by 2.5 Wm-2 from its original position at 15–20 Wm-2; thus it remains higher than most peaks in the monsoon forcing index in Fig. a. Such mild responses are amplified as the GHG radiative forcing increases with the other scenarios. For instance, for the large emissions scenario F5 (5000 GtC) the vegetation cover response at 9 kyrAP (peak M1) with a monsoon forcing index of only 9.2 Wm-2 is already at about 89.9 %, which is higher than that of the strongest monsoon forcing index peak M4 for any scenario. In this case the average GHG forcing change is close to 6 Wm-2, which according to our calculations should lower the threshold range in the monsoon forcing index to about 2–7 Wm-2 (lowered by 13 Wm-2), and this would explain why with only 9.2 Wm-2 of the monsoon forcing index do we see such a strong response. Therefore we see that the effect of the large GHG radiative forcing in the early 60 kyrAP of simulation is compensating for the low monsoon forcing index values during this time. Nonetheless, this effect is only seen at the monsoon forcing index peaks; therefore the orbital forcing is still the triggering mechanism for the AHP response.