The methodological framework adopted in this study is summarised in Fig. . We start from GCM simulations from the CMIP5 archive, dynamically downscaled with MRCM. We apply bias correction to the MRCM output, using observed and ERA-Interim data downscaled with MRCM as the target, which we then feed into a 1 km resolution snow model over our study region to reconstruct snowpack under the various emissions scenarios. Finally, a statistical model is developed for catchment runoff coefficients (RCs), in order to make projections of runoff under future climate conditions.

Annual cycles of reconstructed snow cover as a function of elevation are shown in Fig. . Overall, all models succeed in accurately reproducing snow cover dynamics in the region, although the ERA-Interim simulation tends to have a positive bias at high elevations, particularly above 3000 m (Fig. b), and all simulations have a negative bias at low elevations (Figs. d, e and a, b). The GCM-driven experiments generally show too little snow cover and a later snowpack build-up (Fig. f). December–March average snow cover over the whole modelled area reaches 1460 km2 in MODIS observations but only 1275 km2 in the ERA-Interim-driven run and 1185 km2 in the ensemble mean historical average – a bias largely concentrated at low elevations (Fig. a and b). Still, except for elevations below 2000 m, mean snow cover mostly remains close (±20 %) to MODIS values. The inter-model spread in GCM-driven simulations also generally overlaps with observed snow cover values. Consistent with these results, the spatial distribution of snow-to-precipitation ratio is generally well reproduced in the GCM-driven experiments (Figs. a, d and ), apart from negatives biases at low elevations associated with the underestimation of snow cover (Fig. ). Inter-annual variability in basin-wide snow cover is lower in the simulations compared to MODIS (standard deviation of 220–440 km2 compared to 480 km2 in MODIS), but the discrepancy is mainly due to the negative bias at low elevations, where snow plays a much more limited role in the overall water balance (T20a).

Still in the current climate, we find that annual relative sublimation losses are strongly linked to annual-mean precipitation, a relationship that the GCM experiments are able to capture (Fig. a). Losses from latent heat fluxes are much smaller during wet years as compared to dry years, a relationship robust across all experiments. Wet years indeed bring higher RH over the region, due to enhanced moisture advection from the Atlantic which more than compensates for the larger heat advection and increased air temperatures that also occur in parallel . All experiments also agree reasonably well on the evolution of sublimation losses with elevation (Fig. b). The MPI-ESM-MR and IPSL-CM5A-LR simulations exhibit a slight negative bias but which remains within the uncertainty range in the assimilated run (T20a).

Future projections show a stark decline in snow cover across all the region (Figs.  and ). The greatest relative decline is at low elevations, as expected since they are already seldom above the 0 ∘C line . Above 2500 m, projections still exhibit a 30 %–40 % decrease in snow cover area under RCP4.5 and 50 %–60 % decrease under RCP8.5. Maximum snow cover extent is reached around the beginning of February in all scenarios. However, snowpack build-up and melt occur later and earlier in the season, respectively. The projected decline is even steeper in terms of snowpack water content (Fig. ): SWE is reduced on average by 60 % under RCP4.5 and 80 %–85 % under RCP8.5, bringing the peak SWE value from about 125×106 m3 down to 20×106 m3 (Figs. f and ). Inter-model spread is largest in the RCP4.5 simulations, in which peak SWE ranges from 25 %–60 % of its historical value.

The panel regression and model selection framework are applied to runoff coefficients and selected covariates over the 1982–2011 period. Stepwise regression yields relative humidity and snow fraction as optimal covariates. The adjusted r2 is equal to 0.30, meaning that these two covariates explain nearly a third of inter-annual variability in RC. Fitted RCs are shown against observed ones in Fig. . Consistent with the model r2, fitted values have a much smaller variance. Still, for all the catchments, except Segmine, we observe a significant positive relationship between fitted and observed values. The coefficients for RH and snow fraction are both significant, with βRH>0 and βSF<0 (Table ). In other words, all else being equal, a larger RH yields more runoff and more of the precipitation falling as snow yields less runoff. These results are robust to the choice of the precipitation dataset. When using the CHIRPS dataset, average RCs are generally lower, due to CHIRPS's wet bias compared to TRMM (Fig. ); the optimal RC model includes RH and SF as well but also precipitation as a third variable (Table ). The values of βRH and βSF obtained with CHIRPS data are similar, although βSF is slightly less significant. In addition, for both precipitation datasets, the effect of RH on runoff coefficient, as measured by the respective regression coefficient βRH, is 3–5 times that of snow. Since the input variables were not standardised prior to model fitting, this does not mean however that runoff coefficients are more sensitive to RH variations in the absolute.

Future runoff projections are characterised by consistent, steep declines in runoff coefficients of 5 %–17 % under RCP4.5 and 15 %–30 % under RCP8.5 (Fig. a). The impact of decreasing RH largely dominates over that of declining snow fraction. Tarhat and Chacha, the two watersheds which already receive almost no snow in the present climate, exhibit the greatest relative RC decline, whereas in other watersheds, decreases in snow fraction help limit the decline in RC (Table ). Combining now precipitation and runoff coefficient estimates, we find a 20 %–40 % decrease in runoff in the RCP4.5 experiments, compared to a 50 %–65 % decline under RCP8.5 (Fig. b, c and Table ). Decreases in precipitation drive most of the runoff trends, especially in the RCP8.5 scenario. Projected RC declines are about the same when using CHIRPS data for the analysis although tend to be slightly higher, by 3 %–6 % on average (not shown).

The steep projected decline in snowpack in the High Atlas results both from a decrease in wet-season precipitation and from warming trends which severely reduce the fraction of solid precipitation. This is particularly true at mid-elevations (2000–2500 m), very close to the 0 ∘C line in the current climate, where the relative decline in snow fraction is the highest (Fig. ). At first order, changes in precipitation and rising temperatures each seem to account for about half of the projected SWE trends for the area as a whole. Precipitation goes down by about 25 % under RCP4.5 and 40 %–45 % under RCP8.5 , while the fraction of solid precipitation decreases by 25 % under RCP4.5 and 50 % under RCP8.5 (from ≈19 % in the historical simulations to ≈14 % and ≈9 % annually in the RCP experiments) (Fig. ). Rising temperatures prevent snowpack build-up, not only by increasing the likelihood of liquid precipitation, but also by favouring snowmelt. Snowmelt is already frequent during winter in the High Atlas, even at high elevations , and is thus likely to be even more common in a warmer world. Still, at high elevations, the relative decline in snow fraction is roughly half as small, and consequently the precipitation signal may be dominant in the SWE trends.

Inter-model uncertainty in normalised SWE projections differs across scenarios (Fig. ). It is small in the RCP8.5 simulations: peak SWE declines by 85±3 %. In this scenario, warming is large enough in all the models that regardless of its magnitude, snowpack is projected to disappear almost entirely. All three models agree on a ≈50 % decrease in snow-to-precipitation fraction. This is consistent with observations that in mountain regions, above-freezing temperatures are common, even at high altitudes, where average winter temperatures are not far from freezing . Therefore, under the RCP8.5 scenario, the projected 4 ∘C warming would regularly bring all areas but the very highest peaks well above freezing and prevent seasonal snowpack accumulation. By contrast, uncertainty is high in the RCP4.5 simulations, in which warming and drying are about half as small as under RCP8.5 (Table ). Consequently, the reduction in the snow-to-precipitation fraction projected by the models ranges from 5 % to 35 %. In this scenario, the uncertainty in warming thus appears to be the main factor behind the spread in snowpack projections.

There is also uncertainty in absolute SWE values. As discussed in T20a, the historical SWE peak of 125×106 m3 is subject to caution; experiments with enhanced precipitation or reduced temperatures suggest it may in fact be as high as 200×106 m3. Still, while inter-model spread is large in the historical experiments (≈60×106 m3) and still large (≈40×106 m3) in the RCP4.5 experiment, it is reduced to almost zero under RCP8.5. Again, despite the spread in temperature and precipitation projections among the three models, they all agree on the virtual disappearance of the snowpack by the end of the century under business-as-usual scenarios.

Among the several environmental variables tested, runoff coefficients in the High Atlas appear primarily affected by RH and the fraction of snow in seasonal precipitation. Consistent with previous studies , the higher the RH is, the larger the runoff coefficient. Higher RH in the High Atlas is indeed associated with more precipitation, higher soil moisture levels and a lower evaporative demand. Thus higher RH will lead to reduced relative sublimation losses (Fig. a), but it is also linked to warmer temperatures, which tend to decrease the snow-to-precipitation ratio and lead to lower relative sublimation losses as well. RH is therefore important in our model because it incorporates information on both the energy constraint (evaporative demand) and on the water availability. The snow fraction has an opposite effect: the larger it is, the lower the runoff efficiency. We can understand the influence of snow fraction by noting that a higher snow fraction means more opportunity for sublimation, particularly large at high elevations, and evaporation of melted snow, consistent with our analysis of sublimation losses (Fig. ). Precipitation in the area tends to occur in short and intense storms and quickly saturate the dry soil, leading to rapid overland flow with limited opportunity for evaporation . By comparison, snowmelt is slow and leads to a more gradual surface flow, with the potential for higher evaporative losses in this climate where evaporation tends to be water-limited. More winter snow may also lead to a higher likelihood of rain-on-snow episodes in spring, known to cause rapid flooding due to high runoff efficiencies . Whether this occurs in the High Atlas remains to be shown, but it would nevertheless be consistent with the effect of the snow fraction on runoff efficiencies.

More snow may also mean more opportunity for infiltration and aquifer recharge . It should be noted that karstic areas are also quite frequent within the Oum-Er-Rbia watershed , with important implications for infiltration, aquifer and spring regimes in our study area. Compared to surface runoff, groundwater remains a small fraction of water use in the Oum-Er-Rbia basin (<15 %) and even less of available renewable water since aquifers are largely overdrawn . Groundwater data are quite scarce in this region; we make the choice of purely focusing on surface runoff, keeping in mind that a more complete picture of basin-wide water availability would also require aquifer fluxes to be taken into account. While base flow is negligible in six out of the seven sub-catchments considered here, aquifer discharge may still occur naturally further down the mountains or artificially via direct groundwater pumping in the agricultural plains.

Results indicate a decline in runoff under future climate scenarios, due to a decrease in both runoff efficiency and wet-season precipitation. Precipitation trends play a much larger role than RC changes in runoff projections. In RCP8.5, precipitation decreases by 48 %–57 %, compared to a 15 %–30 % decline in RCs. Our projected runoff trends are consistent with those of , who focused on catchments part of the Sebou watershed, where snow plays a much smaller role than in our region . This is not surprising given the weak impact of the declining snow fraction on runoff coefficients, compared to that of the relative humidity decline. Runoff efficiency is projected to decline mainly due to atmospheric drying (decreasing RH), which more than compensates for the diminishing snow fraction. Under RCP8.5, average relative humidity will decline by 3 %–6 % , which will lead to an average 30 % RC decline across the seven sub-catchments, while the decline in snow fraction increases RCs by only 10 %. Additionally, lower RH implies that sublimation rates will be higher when snow is present. However, because the snow-to-precipitation ratio will also sharply decline due to rising temperatures, the overall loss of annual precipitation by sublimation will tend to decrease by about a third (Fig. b).

The spread in runoff projections is large (Fig. b), due to uncertainties in both RC (Fig. a) and precipitation projections. Despite warming and drying trends being smaller in RCP4.5, the uncertainty in RC changes is just as high as under RCP8.5 (Fig. a), notably because snowpack projections are much more uncertain (Fig. ). Combined with weaker precipitation changes, this translates into larger uncertainty in future runoff under RCP4.5 compared to RCP8.5.

Every modelling framework relies on its own assumptions, which translate into uncertainties. First, it is important to note that our pixel-by-pixel approach to bias correction does not take spatial correlation and inter-variable dependencies into account, for which a more complex method like R2D2 would be required. However, in the present case, it makes little practical difference. To fit the snow model, we rely on average annual cycles of snow cover over which short-term correlations across space and between variables, beyond the seasonal cycle, have little influence. In addition, the target datasets used in the bias correction come from different sources (TRMM, MODIS, etc.), and thus we should be very careful about relying on their correlations when correcting the data. Ideally, one could correct all variables from a single observational dataset that includes all the variables we use, but such a dataset obviously does not exist.

Second, for future climate projections, we rely on a single regional climate model and thus do not explore the full range of uncertainties related to model configuration and parameterisations. Still, the regional simulations we use here have been specifically tailored to the area, particularly the choice of driving GCMs, and validated against a range of observations . The fact that the uncertainty in snowpack projections under RCP8.5 is small could be further explored by using other GCM/RCM combinations, especially ones that lead to less warming than projected in our three-member ensemble. As to the uncertainty in precipitation trends, it is difficult to reconcile. As shown by , the magnitude of future wet-season precipitation in northwestern Africa is mainly determined by that of changes in Mediterranean atmospheric circulation. Spread in dynamical trends is difficult to reduce for this region. A GCM-selection approach based on storylines could be relevant to determine plausible scenarios . In addition, drier soils together with enhanced absorption of solar energy where snowpack disappears will also lead to enhanced warming locally, driving yet further snowpack melt. We do not explicitly take this into account in our model. In particular, the snow albedo effect is largely absent from the MRCM simulations due to their 12 km resolution, which is still too coarse to represent the complex topography. For areas at the highest elevations (near 4000 m) which will still likely be below freezing in future winters, melt may remain largely unchanged in the middle of winter; however, a drier atmosphere will still be associated with reduced precipitation and increased sublimation losses, which will play a critical role in reducing the snowpack.

The advantage of using a statistical regression model to investigate the sensitivity of runoff to climate variables and its changes is its simplicity and interpretability. It allows, for instance, the influence of the snow fraction in the inter-annual variability of RCs to be highlighted. While hydrological models are certainly more comprehensive, they also rely on many parameters, which leaves them vulnerable to overfitting and thus to even more uncertainties. In addition, they suffer from the same drawback as our simple model, which is that there is no guarantee that the relationships obtained in the current climate are directly transferable to the future climate. Still, the large inter-annual variability in climate variables in the present climate helps make the model more robust to large changes in average covariate values. Furthermore, the explanatory variables used in the regression are physical variables; we understand how these mechanistically relate to runoff. The difference with a hydrological model is in the different form of mathematical relations; however the physical relationship between the variables is somewhat respected.

Furthermore, RH and snow fraction only explain 30 % of inter-annual variability in RCs. The rest of the variability may be still explained by climatic variables, which we do not include in our model. Our seasonal approach to defining predictor variables is also quite restrictive; it does not take into account the weekly variability (in RH, temperature, precipitation, etc.), which may affect runoff efficiency. For instance, the details of the daily distribution of precipitation are important to estimate runoff: the more concentrated in time precipitation is, the less opportunity for infiltration and evaporation and therefore the higher the runoff efficiency.

Finally, we focus on climate-driven inter-annual variability in RCs; thus, we do not explain differences in average RCs across catchments, nor can we say anything about long-term variability in RCs forced by non-climatic parameters, like land use change. This last aspect may not be critical in the case of the High Atlas since most of the area under study is uncultivated, naturally lacking tree cover and sparsely populated. It has thus not experienced very significant land use changes in the last few decades. However, climate-change-driven trends in vegetation cover may still affect runoff efficiency in the region. It is also unclear to what extent enhanced groundwater pumping in the Oum-Er-Rbia watershed since the 1980s may have modified the natural water balance and, indirectly, RCs in mountain catchments.