2.1 The river catchments

In the current study, the futurization approach is applied over three Mediterranean watersheds with different characteristics and external influences. The Lez, Aude and Muga catchments displayed in Fig. 1 are frequently subject to flash floods that cause considerable damage to surrounding areas and cities.

The upstream part of the Lez watershed, shown in red in Fig. 1, is located 15 km north of the city of Montpellier and covers 114 km². The landscape is dominated by garrigue vegetation, very common in the Mediterranean countries. The spring of the Lez River is the resurgence of a karstic aquifer of about 380 km². The karst aquifer plays an important role in water resources in the basin, and the karst outcrops actively participate in flash flood dynamics (Raynaud et al., 2016). Cumulative annual rainfall is around 909 mm, which, on average, falls 60 days per year (Coustau, 2011; Harader, 2015). The Lez catchment is frequently subject to flash floods caused by extreme precipitation episodes regionally known as the “Cévenols” events (Ducrocq et al., 2008; Nuissier et al., 2008, 2011). Cumulative extreme precipitation can locally reach 600 mm in 24 h within the river catchment (Boudevillain et al., 2011).

The Aude watershed, shown in brown in Fig. 1, covers more than 5000 km² upstream the nearby city of Narbonne. The Aude River springs at the Pyrenees and flows along the catchment for 223 km before entering the Mediterranean Sea. The Orbieu and the Fresquel are its major tributaries. The Aude catchment is surrounded by several mountain chains such as the Cevennes massif to the north and the Pyrenees to the south. The catchment is mainly dominated by a Mediterranean climate, but large climate contrasts can be found over its sub-watersheds. A severe flash flood episode occurred in November 1999 (more than 200 mm of rain in 24 h over a major part of the catchment) and caused severe damage over an extended region (Aude, Tarn, Pyrénées Orientales, Hérault; Estupina, 2004; Bechtold and Bazille, 2001; Ducrocq et al., 2003; Gaume et al., 2004).

Finally, the Muga catchment (shown in purple in Fig. 1) located in northeastern Spain over Catalonia covers 854 km². The Muga River is about 58 km long, between the Pyrenees (maximum altitude of the catchment, 1214 m) and the Gulf of Roses. This catchment is usually affected by heavy precipitation associated with convective events, with annual precipitation average between 700 mm in the upper part and 530 mm at the mouth, and daily precipitation of 200 mm for return period of 10 years (Llasat et al., 2009, 2014). The previously mentioned November 1999 flash flood event led to a historical peak discharge recorded near the mouth of the Muga River, with 925 m³ s⁻¹ compared to an average value of 3.34 m³ s⁻¹. The Muga catchment was affected by 26 severe flood events between 1982 and 2010 (Llasat et al., 2014).

It should be noted that, in this paper, statistical analysis is carried out over the Lez, Aude and Muga catchment areas as well as over more extended regional boxes also displayed in Fig. 1.

Table 1The parameterization and physics scheme related to the RCM (0.11^∘) used in the present study are presented in the five first lines. The lateral boundary conditions (LBCs) for each type of simulations are presented with four different GCMs of CMIP5. The last row lists the name used for each GCM–RCM pair throughout this study.

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2.2 RCM Euro-Mediterranean CORDEX simulations

The set of EMCORDEX simulations used in this study are summarized in Table 1. The five RCMs used are presented with the main reference papers (in particular with respect to boundary layer and convection schemes). The EMCORDEX community has provided three types of RCM simulations with driving conditions (also detailed in Table 1) issued from either ERA-Interim or GCMs simulations over past and future periods:

• The evaluation simulations (EVAL hereinafter). The lateral boundary conditions (LBCs) are driven by ERA-Interim reanalysis (Dee et al., 2011) over 1981–2010. These simulations are used to evaluate the RCM intrinsic biases.

• The historical simulations (HIST hereinafter). The LBCs are issued from numerical experiments performed with four different GCMs and extracted from the CMIP5 historical archive. These historical simulations represent the climate conditions over 1976–2005.

• The future climate scenario simulations (RCP hereinafter). In this case, the LBCs correspond to four future climate scenarios (from four different GCMs from CMIP5) under RCP4.5 and RCP8.5 (Clarke et al., 2007; Riahi et al., 2007; Meinshausen et al., 2011; van Vuuren et al., 2011) over 2011–2040, 2041–2070 and 2071–2100. These simulations cover 30-year time slice periods like the HIST simulation. Thus they can be statistically compared to assess future changes.

This results in eight pairs of RCM–GCM simulations analyzed in this study, for HIST and RCP as indicated in the last row of Table 1. Only simulations at 12 km for which EVAL, HIST and both RCP experiments were available at the beginning of the study were considered.

2.3 The reference data set: SAFRAN

SAFRAN reanalysis provides daily precipitation data for the period 1958–2008 over France and Spain on an 8 and 5 km grid, respectively (Vidal et al., 2010, Quintana-Seguí et al., 2016a, b). SAFRAN-France was built by using data from 3675 selected rain gauges that were gridded through an optimal interpolation algorithm described in Quintana-Seguí et al. (2008). The great number of rain gauges considered in SAFRAN and its high spatial resolution produce more accurate precipitation analyses over France and Spain than those proposed by other products commonly used for model assessments, such as CRU (Harris et al., 2014) and E-OBS (Haylock et al., 2008). A recent study shows that, for precipitation, the performance of SAFRAN is very similar to that of Spain02 (Quintana-Seguí et al., 2016b). SAFRAN data set has been evaluated using the Météo-France and Spanish State Meteorological Agency (AEMET) gauging station network as well as independent data (Quintana-Seguí et al., 2008, 2016a, b; Vidal et al., 2010).

SAFRAN product is used here as a reference data set to evaluate the simulated precipitation from EVAL and HIST ensembles. For that purpose, the 12 km RCM outputs and also SAFRAN Spain were regridded on the 8 km SAFRAN-France grid using the ESMF (Earth System Modeling Framework) bilinear regridding method. The impact of interpolation has been largely investigated in the literature, for instance in Diaconescu et al. (2015), and it should be quantified before interpretation of interpolated fields. In the present study, the impact of a bilinear scheme for the interpolation of precipitation fields from 12 km simulation grid to 8 km SAFRAN grid was assessed from an analytical test case based on the cosine function of longitude and latitude. The comparison is achieved by mapping the analytical field onto the 12 km fields and interpolated it onto an 8 km grid with the analytical field mapped onto the 8 km. The quadratic error reaches 5.10⁻⁵; the impact of interpolation was thus neglected in the following.

2.4 Statistical metrics to evaluate RCM performance

Given the small size of the Lez, Aude and Muga catchments (3, 84 and 11 SAFRAN grid points, respectively), and in order to allow for proper statistical analysis, the evaluation of mean precipitation (seasonal and annual cycle) was achieved on larger regional boxes (excluding sea grid points) shown in Fig. 1. These regional boxes have been selected according to regions of homogeneous climate conditions. In the particular case of the Lez catchment, the RCM precipitation is evaluated over the entire Cevennes region. However for all three catchments, extreme precipitation metrics are computed over grid points that are strictly inside the catchments. The precipitation extremes are analyzed with respect to the 90th to 99.9th quantiles of the daily precipitation distribution discretized as follows:

• one point per 1 quantile rank from 90 to 95th;

• one point per 0.5 quantile rank from 95 to 98th;

• one point per 0.2 quantile rank from 98 to 99th;

• one point per 0.1 quantile rank from 99 to 99.9th.

Short-term observed precipitation events are thereby completely covered and evenly distributed with this quantile discretization (not shown). Quantiles are computed considering all the days (rainy days and dry days), thus allowing for a comparison of precipitation quantiles between the different RCM–GCM pairs (Giorgi et al., 2016; Schär et al., 2016). However, it should be noted that when precipitation is below 0.1 mm day⁻¹, the precipitation is set to 0 so that the cumulative precipitation is not affected by overrepresentation of light rainy days in the models (Harader et al., 2015; Tramblay et al., 2013, Paxian et al., 2015).

In addition to the classical metrics (spatial bias, annual cycle bias, quantile–quantile plot), two original metrics are used in this study. First, assuming additivity between GCM and RCM errors, the impact of the GCM bias on the RCM solution can be diagnosed by computing the difference ΔB between the HIST and the EVAL precipitation bias with respect to SAFRAN:

The ΔB criteria corresponds to the bias in the annual cycle of precipitation simulated with the RCMs that is strictly related to the influence of the lateral boundary condition imposed by the GCM. A high positive value indicates overestimation of the total monthly precipitation, and a negative value indicates underestimation of the total monthly precipitation.

Secondly, in the present study, change coefficients between the past (HIST) and future precipitation (RCP) quantile distributions are computed. For that purpose, precipitation from HIST and RCPs is quantile-ranked, and for each quantile rank “qi”, a change coefficient “Aqi” for precipitation intensities between HIST and RCP is computed as follows:

where Pqi(RCP) and Pqi(HIST) represent the values of the quantiles for HIST and RCP, respectively.

All metrics are computed on a seasonal basis, considering hereinafter four seasons: autumn (September, October and November), winter (December, January and February), spring (March, April and May) and summer (June, July and August). Only autumn and spring results are presented in the following section.

3.1 Spatial bias pattern

Figure 1 shows the spatial distribution of the cumulative precipitation normalized difference between each RCM from the EVAL ensemble and SAFRAN, averaged over the previous 30 years in autumn. The top-left panel in Fig. 1a displays the mean cumulative precipitation for SAFRAN-France and SAFRAN-Spain reference data sets. Large values of the cumulative precipitation (greater than 400 mm season⁻¹) are observed over mountainous regions, in particular the Cevennes and the Pyrenees chains. Lower cumulative precipitation values are observed in the valleys (Garonne, Aude) and over the coastal regions.

In general, the cumulative precipitation is overestimated for most RCMs over the mountainous regions (+30 %) and underestimated over the Mediterranean coastal region (−30 %), as shown in Fig. 1b to f, most likely because of imperfect representation of the orography as well as the parameterization of the convection scheme. Note that the RACMO22E pattern of precipitation bias differs from the other RCM patterns. Indeed, slight overestimation is observed over the south of the Pyrenees and the Cevennes (+20 %), and almost no bias is observed over the valleys.

We focus now on the precipitation bias over river catchments that are analyzed in the present study: for Cevennes, the cumulative precipitation is overestimated by 20 % in the southwest mountainous region and underestimated by 30 % in the northeast valley region for all RCMs (Fig. 1b, c, e, f) except for RACMO22E (Fig. 1d).

For the Aude region, no relevant bias is presented by ALADIN52 (Fig. 1b), ALADIN53 (Fig. 1c) and RACMO22E (Fig. 1d). A positive bias (+40 %) is presented by RCA4 (Fig. 1e) in the western region under continental influence, while no relevant bias is presented in the eastern region under Mediterranean influence. HIRHAM5 (Fig. 1f) displays a strong positive bias (+50 %) in the high-elevation areas (Pyrenees in the southwest, and Black mountain in the northwest) and a strong negative bias elsewhere.

The mean cumulative precipitation is underestimated (−30 %) by all RCMs over the Muga region, except for RACMO22E.

For other seasons, the mean cumulative precipitation pattern tends to be overestimated over all three regions in spring (not shown), and a strong positive bias (+50 %) is presented by ALADIN52 and ALADIN53 over the Pyrenees in summer (not shown).

Figure 2(a) Annual cycle of precipitation over Aude box with SAFRAN data set (b). Bias of the annual cycle of precipitation simulated by the five RCMs with respect to SAFRAN's annual cycle of precipitation for the period 1981–2010 (no units), over the Aude box. The colored lines with different markers represent the biases of RCM-simulated precipitation with respect to SAFRAN data set (black line).

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3.2 Annual cycle of precipitation bias

The 30-year climatology for the monthly cumulative precipitation is spatially averaged over each region of interest and normalized by the SAFRAN monthly climatology. Figure 2a displays the annual cycle of precipitation over the Aude box for SAFRAN data set. Figure 2b displays the bias of the annual cycle over the Aude region for each RCM. Globally speaking, the RCM bias and the inter-model spread are smaller in autumn than in summer. This can be explained by the influence of the large-scale atmospheric circulation being weaker in summer, the control exerted by the LBCs on the RCM is reduced in this season and the RCM solution has more degrees of freedom to deviate from the large-scale forcing (Déqué et al., 2012; Lucas-Picher et al., 2008).

ALADIN52 and ALADIN53 clearly overestimate the cumulative monthly precipitation in late spring and summer. This is likely due to a large presence of low precipitation days in the RCM precipitation distribution (0 to 10 mm day⁻¹) compared to SAFRAN distribution (not shown). This behavior is also observed over the Cevennes and Muga regions (not shown). Consistent with Fig. 1d, RACMO22E displays a low bias in the annual cycle. Similar behavior is observed for HIRHAM5, suggesting an error compensation between positive and negative spatial biases displayed in Fig. 1f. For the Muga and the Cevennes boxes (not shown), HIRHAM5 presents a negative bias. Finally, RCA4 simulates a large positive bias (+30 %) for the entire annual cycle that tends to intensify over the Alps and the western Pyrenees.

3.3 Extreme precipitation bias

The ability of the EVAL simulations to represent the extreme of precipitation is investigated through a quantile–quantile analysis with respect to SAFRAN. This analysis is performed for each grid point within the Lez, Aude and Muga catchments. The highest-order quantiles (95 to 99th) are displayed in Fig. 3 for each RCM and SAFRAN in autumn.

For the Lez, Aude and Muga catchments, the RCMs underestimate the higher-order quantiles. This underestimation is more important for the Muga catchment, where the extreme precipitation intensities are stronger.

ALADIN52 underestimates the upper precipitation quantiles; for instance, the intensity of the 99th quantiles only reaches 70 mm day⁻¹ compared to 140 mm day⁻¹ for SAFRAN. ALADIN53 performance is slightly improved with respect to ALADIN52, especially for the Aude and Muga catchments. RACMO22E and RCA4 underestimate the extreme precipitation above the 99.5th quantiles. HIRHAM5 provides a satisfactory description of all extreme quantiles for the three catchments.

3.4 Summary of means and extremes analysis

The mean and extreme precipitation is investigated over the Aude, Lez and Muga catchments. Largest biases in mean precipitation simulated by the regional climate models are located over the mountainous (positive bias) and coastal (negative bias) regions. These biases are stronger during the summer season, when the control exerted by the LBCs on the RCM is weaker, due to a reduction of the large-scale circulation and North Atlantic inflow. Overall, while the climate variability is covered by the spread of EMCORDEX ensemble of RCMs, each RCM simulates plausible precipitation.

These results are coherent with specific studies for mean and extreme precipitation as cited hereafter. ALADIN52 precipitation biases are consistent with those obtained by Harader (2015), and slightly reduced in ALADIN53. The RCA4 overestimation of mean precipitation is in accordance with the results showed in Prein et al. (2016). The underestimation of extreme precipitation diagnosed in our study is possibly even more severe than our reference, SAFRAN, found to underestimate observed extreme precipitation (Quintana-Seguí et al., 2008a). This last point was confirmed through a comparison between pluviometer data and SAFRAN over our catchments of interest.

Parameterization and physical processes that are involved in the generation of low precipitation differ from those involved in stronger precipitation events. Thus the precipitation bias varies according to the precipitation intensity. Quantile classification is thereby relevant for the determination of past/future precipitation change.

Figure 3Quantile–quantile diagram of daily precipitation in the cells of the three catchments for the period 1981–2010. EVAL-simulated precipitation (colored lines with different markers) is compared to SAFRAN (black line). The x axis represents the precipitation quantile values with respect to the SAFRAN reference data. The y axis represents the precipitation intensity simulated by the EMCORDEX models for the same quantiles. If a colored line is above/below the black line, the corresponding RCM over/underestimates quantile intensities with respect to SAFRAN. Units are in mm day⁻¹. The colored dots represent, from left to right, the 90, 95, 97, 99, 99.5 and 99.9th quantiles.

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4.1 Annual cycle of precipitation bias

Figure 4 displays the annual cycle of ΔB over the Aude watershed for each GCM–RCM pairs. The color code refers to the GCM (for instance for CNRM-CM5 forcing), while the markers refer to the RCM (for instance star for ALADIN53). From Fig. 4 it is evident that CNRM-CM5 forcing leads to systematic overestimation of summer precipitation, hence proving that the positive precipitation bias identified in EVAL (Sect. 3, Fig. 2 for ALADIN52, ALADIN53 and RCA4) is enhanced in HIST simulations.

ICHEC large-scale conditions induce no significant changes on RACMO22E and RCA4 errors, while they lead to strong overestimation of the HIRHAM5 precipitation. Except when forced by CNRM-CM5, the bias of GCM–RCA4 pairs is similar to the intrinsic bias of RCA4, as displayed for all three, MPI, MOHC and HIRHAM5. Illustration is provided for the Aude box in Fig. 4, but similar results are obtained for the Cevennes and the Muga boxes.

It should be noted that previous results might also be explained by bias compensation between GCM impacts and RCM intrinsic bias. Despite the GCM–RCM deficiencies shown here, all the GCM–RCM pairs display plausible precipitation and are then considered in the following for future change analysis over mean precipitation annual cycle.

Figure 5Quantile–quantile diagram of daily precipitation in the cells of the three catchments for the period 1981–2010. HIST-simulated precipitation (colored lines) is compared to SAFRAN (black line). The x axis represents the precipitation quantile values with respect to the SAFRAN reference data. The y axis represents the precipitation intensity simulated by the EMCORDEX models for the same quantiles. If a colored line is above/below the black line, the corresponding RCM over/underestimates quantile intensities with respect to SAFRAN. Units are in mm day⁻¹. The colored dots represent, from left to right, the 90th, 95th, 97th, 99th, 99.5th and 99.9th quantiles.

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4.2 Extreme precipitation bias

Figure 5 is the counterpart of Fig. 3; it displays quantile–quantile diagrams of precipitation in autumn for the HIST ensemble over the Lez, Aude and Muga catchments. First, the spread amongst the HIST simulations displayed in Fig. 5 is larger, except for the Muga catchment, larger than the one generated by the EVAL ensemble (Fig. 3) that the EVAL ones (Fig. 3), and extreme quantiles tend to be systematically underestimated over all three catchments of interest.

Generally, CNRM-CM5 forcing leads to underestimation of SAFRAN quantiles, thus enhancing the RCMs' intrinsic biases displayed in Fig. 3. MPI and ICHEC provide good quantile distribution for all RCMs except beyond 99.5th quantile. In more detail, ICHEC-RCA4 extreme quantiles are slightly overestimated over the Aude catchment, and in good agreement with SAFRAN over the Muga catchment. MOHC-RCA4 provides good statistics over Aude and Muga catchments, while it overestimates all quantiles over the Lez catchment.

To conclude, the impact of the GCM on RCMs tends to systematically intensify the underestimation of extreme precipitation values. However, the HIST ensemble remains consistent with SAFRAN statistics and thus will be used in the following step, in order to estimate future changes over extreme precipitation over the different catchments.

Figure 6Annual cycle of mean precipitation (mm month⁻¹) simulated in the three regional boxes (Cevennes, Aude, Muga; see Fig. 1). Solid lines represent the ensemble means computed amongst the eight GCM–RCM pairs. The shaded areas represent the ensemble spreads characterized by the standard deviation. HIST ensemble mean (1976–2005) is plotted in blue. RCP4.5 and RCP8.5 ensemble means (2071–2100) are respectively plotted in green and red. SAFRAN annual cycle computed over 1981–2010 is plotted in black.

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5.1 Annual cycle of precipitation

Figure 6 presents the precipitation annual cycle simulated for HIST computed over 1976–2005 period and the scenario RCP4.5 and RCP8.5 computed over 2071–2100 period, for the Cevennes, Aude and Muga boxes.

The results reveal stronger mean precipitation change between RCP4.5 and RCP8.5 than for the 2011–2040 and 2041–2070 periods. The annual cycle of the RCP4.5 ensemble is similar to HIST one in terms of mean and spread, suggesting that radiative forcing in RCP45 seems to have a weak impact on monthly averaged precipitation. In contrast, the annual cycle of the RCP8.5 ensemble displays a general decrease in mean precipitation from April to October for the three river catchments. These results are consistent with the conclusions from the study of Jacob et al. 2013 over EMCORDEX domain. As previously mentioned the spread of the ensemble is larger in summer when the LBCs exert a weaker control in the RCM domain. It should be noted that these results hold for the three boxes of interest that are of significantly different sizes. This suggests that the high-resolution EMCORDEX simulations can be confidently used to investigate precipitation at local scale.

As mentioned in the previous section, the analysis of the annual cycle of HIST simulations emphasized that the association of GCM and RCM models induces a different precipitation bias that the intrinsic RCM biases (comparison between black and blue curve in Fig. 6). Nevertheless, the precipitation field issued from HIST is not bias corrected here. They are used, together with the RCP simulations, to estimate the change coefficient between past and future values of the quantile of the precipitation distribution.

5.2 Change coefficients for extreme precipitation

The change coefficients between quantile-ranked precipitation presented in Eq. (2) are displayed in Fig. 7. They allow the estimation of the changes between the past (HIST) and future precipitation (RCP) quantile distributions

Following Eq. (2), a change/transfer coefficient greater than 1 for a given quantile indicates an increase of the future precipitation value associated with this quantile. On the other hand, Aqi <1 means a decrease in RCP precipitation with respect to HIST.

Figure 7Change coefficients (Aqi) over the 90–99.9 quantile range computed for each GCM–RCM pairs over the Lez, Aude and Muga catchments during the autumn season (SON). The no change line (ai = 1) is also displayed in solid black. The thick solid lines represent the ensemble mean for (Aqi), and the associated ensemble spread is presented by the shaded areas (standard deviation). RCP4.5 and RCP8.5 are respectively plotted in blue and red. For clarity purposes, the scale of the x axis was distorted according to the quantile discretization.

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The Aqi coefficients are computed for each GCM–RCM pair over the Lez, Aude and Muga catchments. The multi-model approach adopted here allows for estimating an uncertainty in the values of the change coefficients. The Aqi coefficients are represented in Fig. 7 over the upper level quantile range (90–99.9) for RCP4.5 and RCP8.5 in autumn for the three river catchments and for 2041–2070 and 2071–2100 future time periods. The ensemble mean for Aqi computed amongst the GCM–RCM pairs is compared to the associated ensemble spread (standard deviation) in Fig. 7.

The interesting result here is that while RCP simulations tend to decrease mean precipitation with respect to HIST simulation (Fig. 6), extreme precipitation events are intensified for both time periods over the three catchments. Globally speaking, the mean change coefficient for RCP4.5 and RCP8.5 is similar except for the Lez (2041–2070) and the Muga (2071–2100) catchments, where RCP8.5 displays biggest changes. The ensemble spread from RCP8.5 is smaller than the one from RCP4.5, meaning that the change in extreme precipitation displays higher level of certainty under RCP8.5 scenario, which can be explained by stronger radiative forcing in RCP85 compared to RCP45. Few models indicate a decrease in extreme precipitation for RCP4.5 over 2041–2070 period. In contrast, for 2071–2100, all the GCM–RCM members agree on an increase in extreme precipitation for both RCP4.5 and RCP8.5 scenarios. For instance, the mean change coefficient over 2071–2100 reaches 1.15 for the 99.5th quantile over the Aude catchment for both RCPs, while RCP4.5 spread is about 0.3, versus 0.1 for RCP8.5. In terms of precipitation, a change coefficient of 1.35 over the Lez catchment for the 99.9th quantile of RCP8.5 represents an increase from 140 to 189 mm day⁻¹.