Non-linear intensification of Sahel rainfall as a possible dynamic response to future warming

Abstract. Projections of the response of Sahel rainfall to future global warming diverge significantly. Meanwhile, paleoclimatic records suggest that Sahel rainfall is capable of abrupt transitions in response to gradual forcing. Here we present climate modeling evidence for the possibility of an abrupt intensification of Sahel rainfall under future climate change. Analyzing 30 coupled global climate model simulations, we identify seven models where central Sahel rainfall increases by 40 to 300 % over the 21st century, owing to a northward expansion of the West African monsoon domain. Rainfall in these models is non-linearly related to sea surface temperature (SST) in the tropical Atlantic and Mediterranean moisture source regions, intensifying abruptly beyond a certain SST warming level. We argue that this behavior is consistent with a self-amplifying dynamic– thermodynamical feedback, implying that the gradual increase in oceanic moisture availability under warming could trigger a sudden intensification of monsoon rainfall far inland of today’s core monsoon region.

highest Representative Concentration Pathway (van Vuuren et al., 2011), RCP8.5. Individually, some of the models project a much stronger rainfall increase, while others even project an overall decrease. This uncertainty in future projections raises questions about potential mechanisms of change that may be present in some models but not others, and that may be responsible for the large differences between models. In particular, paleoclimatic records suggest that Sahel rainfall is capable of abrupt transitions in response to gradual forcing (DeMenocal et al., 2000;McGee et al., 5 2013); and theoretical studies have demonstrated that such a non-linear response can in principle arise from internal monsoon dynamics (Levermann et al., 2009;Seshadri, 2016). In this study, we examine Sahel rainfall in state-of-the art climate model simulations and show that in those models that exhibit the strongest rainfall increase, this increase is non-linearly related to the SST warming in the tropical North Atlantic and Mediterranean moisture source regions. We argue that this behaviour is consistent with the theory and paleoclimatic evidence mentioned above. Considering that this non-linear rainfall response may 10 be more pronounced in some models than in others may contribute to understanding the differences between the models' future projections.

Methods and Results
We investigated Sahel rainfall in 30 Coupled Model Intercomparison Project phase 5 (CMIP5) global climate models under RCP8.5 (see Appendix A). Three models (MIROC-ESM-CHEM, MIROC-ESM, BNU-ESM) project an increase of over 100% 15 in average summer (July-September) rainfall across the central and eastern Sahel by the end of the 21 st century (Fig. 1). Some other models (notably FGOALS-g2, MIROC5, CanESM2, NorESM1-M) project slightly smaller rainfall increases but with similar patterns as the three wettest models: a pronounced rainfall increase north and east of the present core monsoon region (Fig. 2; notice that while CanESM2 has only a moderate wetting trend over the central Sahel region analyzed in Fig. 1, it shows a strong rainfall increase in the eastern Sahel). This is in contrast to the majority of models which do not show a marked rainfall 20 increase outside the present-day monsoon region (Supplementary Figures). We select the above-mentioned seven modelshereafter referred to as the "Wet7" subset-for further investigation, in order to elucidate possible mechanisms behind the strong rainfall increase in presently dry regions. We note that the Wet7 can largely account for the positive rainfall trend that has been found in the CMIP5 ensemble as a whole (cf. Roehrig et al., 2013;Park et al., 2015): The Wet7 multi-model mean shows a doubling of average summer rainfall by 2100 (Fig. 3). In contrast, the mean over the 23 other models exhibits only a 25 weak wetting trend of less than 20%; trends in the individual models are small and some models even show a drying trend.
Although we focus here on the future projections, we also note that the Wet7 models perform better than average in reproducing the magnitude of the 1970-1989 drought period, the three MIROC models especially being very close to observed values (orange lines in Fig. 1, and inset in Fig. 3). This observation is consistent with a more comprehensive analysis of the CMIP5 models for the historical period (Biasutti, 2013), which found that past multi-decadal variability is underestimated by 30 all except a few models, one MIROC model among them. It may serve as an additional motivation to further study the future projections by these models, which we do in the following. We point out, however, that there is much variation among the Wet7 models themselves in terms of past and projected rainfall changes, and the dynamical features discussed below may be more or less developed in different models. We use the wettest model, MIROC-ESM-CHEM, to illustrate our discussion, and show the other six models as evidence that our findings are not exclusive to just one model.
The seasonal distribution of the rainfall change in the Wet7 shows a clear monsoonal shape, despite considerable spread in its magnitude (Fig. 3). Generally, the rainfall increase occurs over a broad region between 10 and 20 • N, i.e., extending into today's Sahara desert (Fig. 4). Conversely, rainfall decreases somewhat in the more humid regions around the Gulf of 5 Guinea and the West coast. This pattern corresponds to an inland shift compared to the present-day rainfall regime. At the same time, the near-surface, southwesterly winds intensify in the northern and eastern parts of the Sahel, near the positive rainfall anomaly, while they do not change much near the coast (Fig. 5). This suggests that the rainfall increase is not simply a consequence of thermodynamic changes (higher water-holding capacity of warmer air), but goes together with a shift in West African monsoon circulation dynamics. 10 Sahel rainfall has been linked to Atlantic as well as Mediterranean SSTs via evaporation rate and moisture supply (e.g. Giannini et al., 2003;Rowell, 2003). In order to examine temporal patterns of rainfall and SST change more closely, we average each model's summer rainfall over a rectangular subregion of the Sahel (solid boxes in Fig. 4 and 5). The subregions are chosen to encompass an area where the rainfall increase is substantial in both absolute (Fig. 4) and relative terms (Fig. 5), and to be similar in size and location across the different models' grids (except for CanESM2 where the rainfall increase is 15 located further east than in the other models). Thus, the subregions are generally located northward of the present-day core monsoon regions, which also see rainfall increases but less pronounced in relative terms. Similarly, we identify for each model one region in the tropical North Atlantic ocean and one in the Mediterranean Sea (dashed boxes in Fig. 4) as the main sources of additional moisture influx into the Sahel, based on the lower-troposphere moisture flux changes (arrows in Fig. 4).
Moisture influx from both sources into North Africa is projected to increase in the Wet7 models (Fig. 2). However, moisture 20 flux from the Atlantic into the Sahel subregion increases more strongly than from the Mediterranean by the end of the 21 st century ( Fig. 2 and 6). Moreover, only the Atlantic branch is accompanied by an increase in near-surface wind speed (Fig. 5).
Thus, while the increased moisture import from the Mediterranean appears to be due to higher SST and evaporation alone, increased wind speed further amplifies moisture import from the Atlantic; a mechanism already proposed by Rowell (2003).
Sahel rainfall generally increases as the surface of the oceanic moisture source regions warms ( Fig. 7 and 8). But this relation 25 is not linear. Rainfall shows little response to SST changes within a range of approx. 1 • C around the present-day value; but when SST increases beyond this point, rainfall shifts abruptly to a stronger level, where it then keeps increasing as SST rises further. Given the convex shape of the temperature forcing over time, the abruptness of the rainfall response is expected to be less apparent in the time domain; nonetheless, rainfall appears relatively stable over the historical period, before it begins increasing strongly in the 21 st century (Fig. 9). 30 Numerous paleoclimatic reconstructions reveal abrupt shifts in monsoon systems in Asia (Gupta et al., 2003;Wang et al., 2008) and Africa (DeMenocal et al., 2000;McGee et al., 2013;Weldeab et al., 2007) before and throughout the Holocene.
In those cases, external forcing through changes in solar insolation was much more gradual than that associated with modern anthropogenic climate change. A physical mechanism has been proposed to explain such abrupt shifts in large-scale monsoon rainfall in response to gradual forcing (Levermann et al., 2009(Levermann et al., , 2016: While the summer monsoon circulation is initiated 35 by differential warming of land and ocean in spring, it is latent heat release from precipitation that maintains the land-sea atmospheric temperature contrast throughout the summer and thus drives the monsoon winds into the continental interior. The monsoon winds in turn supply the moisture necessary to maintain precipitation. Summer monsoon rainfall is thus powered by a positive feedback between moisture inflow and atmospheric heating. This positive moisture-advection feedback gives rise to a threshold behaviour with respect to external quantities that govern the energy budget of the monsoon; in particular, in 5 this simplified theory, there is a minimum atmospheric humidity in the oceanic moisture source region below which such a monsoon circulation cannot be maintained (Schewe et al., 2012). This framework has been used to explain abrupt variations in monsoon strength documented in Asian speleothem (Schewe et al., 2012) and pollen records (Herzschuh et al., 2014), but has not yet been applied to modern monsoon systems. We suggest that it is also useful for understanding the projected Sahel rainfall changes in the Wet7 models. Today, the West African 10 monsoon is most active between the Gulf of Guinea coast and the southern edge of the Sahel (Nicholson, 2013). Rainfall declines towards the continental interior, and while central and eastern Sahel rainfall still exhibits a clear seasonality, it is relatively weak and erratic (compared to e.g. the Indian monsoon with its intense rainfall throughout much of the subcontinent).
An increase in evaporation due to ocean warming in the tropical North Atlantic and the Mediterranean increases moisture availability. Once atmospheric humidity exceeds the monsoon threshold even in the more continental parts of the Sahel, the 15 moisture-advection feedback can amplify the monsoon response by enhancing the westerly monsoon winds and thus the moisture influx from the North Atlantic. These inland regions thereby become increasingly connected with the oceanic moisture source, and benefit from further increases in oceanic evaporation.
This framework can explain the observed shape of the rainfall response in both the time and SST domains (Fig. 10): The functional form of the rainfall-SST relationship found in the Wet7 models (most prominently in MIROC-ESM-CHEM) re-20 sembles the concave form and threshold behaviour that arises from the above theory; given the convex form of mean SST forcing under global warming, the resulting pattern of rainfall over time is one where rainfall is relatively stable and low up to a certain point and then starts rising quasi-linearly.

Discussion and Conclusions
This explanation of an abrupt intensification of inland monsoon rainfall in the Sahel region is consistent with studies suggesting 25 a substantially wetter Sahel, and Sahara, region in past climates compared to today (DeMenocal et al., 2000;Gasse, 2000).
It is also consistent with theories linking rainfall changes in the Sahel to a combination of a local (through radiative forcing changes) and a remote (through tropical SST impacts on atmospheric stability) forcing mechanism (Giannini, 2010;Giannini et al., 2013;Seth et al., 2010). In a warming world, the remote mechanism would increase atmospheric stability especially in places with oceanic influence, and make it harder for convection to set in. Acting in the other direction, the local mechanism 30 would directly warm the surface and decrease vertical stability over land. The mechanism we suggest here would act on top of these two mechanisms, and help explain the abruptness of the Sahel rainfall response to global warming seen in some models. It would particularly affect the more continental parts of the region. We note that part of the increased moisture influx is through westerly winds near 10 • N, a flow called the West African Westerly Jet Cook, 2010, 2012). While its intraseasonal dynamics are somewhat distinct from the more southerly monsoon flow across the Gulf of Guinea, on a seasonal timescale both are driven by the pressure-and thus, temperature-gradient between the eastern Atlantic and the Sahel, and would be subject to the dynamical feedback mechanism described above. Our analysis also provides further evidence for the role of the Mediterranean Sea as a contributor to enhanced Sahelian moisture availability, which then further amplifies inflow from the 5 North Atlantic through latent heating over the Sahel.
We have found a strong, non-linear Sahel rainfall increase only in a minority of the CMIP5 models, and we do not mean to imply that these particular model simulations are more realistic than others. Consideration of the mechanism demonstrated here may, however, help to make sense of the diversity of model projections, and eventually establish a more consistent understanding of the Sahel's future climate in a warming world. We also note that the marked increase in Sahel rainfall begins at 10 remarkably similar levels of SST change across the Wet7 models: Mostly at around, or just below 1 • C of SST warming (Fig. 7).
In order to put these regional climatic changes in the context of global anthropogenic warming, we also show the projected Sahel rainfall changes over global mean temperature (GMT) change (Fig. 11). Given the different regional distribution of the warming signal in different models and the fact that GMT and SST do not necessarily co-vary on an annual time scale, there is not as clear an association of the rainfall change with GMT change as with SST change: The GMT level at which Sahel rainfall 15 begins to increase strongly is somewhat different across the models. However, it may be noted that in many of the models the "Paris range" of 1.5-2.0 • C of global warming (UNFCC, 2015) presents an approximate dividing line between the historical Sahel climate regime and a substantially wetter future climate.   Sissoko, K., Keulen, H., Verhagen, J., Tekken, V., and Battaglini, A.: Agriculture, livelihoods and climate change in the West African Sahel, Reg. Environ. Chang., 11, 119-125, doi:10.1007/s10113-010-0164-y, http://link.springer.com/10.1007/s10113-010-0164-y, 2010.       Figure 6. As top panel in Fig. 2 but showing absolute moisture flux in the 20 th century (1900-1999, top)     and are identical to the data shown in the top panels of Fig. 7 and 9; they are shown here without labels to emphasize the functional form.
Orange lines (with blue axes) show illustrative functional forms that qualitatively match those of the simulation data, and are consistent with analytical results from a minimal monsoon model (Schewe et al., 2012): The moisture-advection feedback implies that no continental monsoon exists below a certain threshold (blue tick mark) in the energy budget-here controlled by sea surface temperature (SST)-, whereas above the threshold, monsoon intensity is a concave function of SST (top). In combination with a convex SST evolution (middle), this behaviour can give rise to the observed rainfall evolution over time, where rainfall is relatively stable and low up to a certain point and then starts rising quasi-linearly.