The Rhône–Mediterranean district covers all the Mediterranean coastal rivers and the French part of the Rhône river basin, from the outlet of Lake Geneva to its mouth (Fig. 1). Climate is rather varied, with a temperate influence in the north, a continental influence in the mountainous areas, and a Mediterranean climate with dry and hot summers dominating in the south and along the coast. In the mountainous part (in both the Alps and the Pyrenees) the snowmelt-fed regimes are observed in contrast to the northern part under oceanic climate influences, where seasonal variations in evaporation and precipitation drive the monthly runoff pattern (Sauquet et al., 2008).

Water is globally abundant but uneven between the mountainous areas and the northern and southern parts of the RM district, and water resources are under high pressure due to water abstractions. For the period 2008–2013, annual total water withdrawal was around 6×109 m3 (excluding any water abstraction for energy such as cooling nuclear plants and hydropower) with more used for irrigation (3.4×109 m3, including 2×109 m3 for channel conveyance). Use for public and industrial supply is 1.6×109 and 1×109 m3, respectively. Because of an intense competition for water between different users – agricultural, municipal and industrial – and the environment, some areas within the RM district can be vulnerable during low-flow periods. Around 40 % of the RM district suffers from water stress and scarcity (http://www.rhone-mediterranee.eaufrance.fr/gestion/gestion-quanti/problematique.php, last access: 1 August 2019) and has been identified by the French RM Water Agency as areas with persistent imbalance between water supply and water demand.

DMPs define specific actions to be undertaken to enhance preparedness and increase resilience to drought. In France DMPs include regulatory frameworks to be applied in case of drought, called arrêtés cadres sécheresse. The past and operating DMPs and the water-restriction orders were inspected in the 28 departments of the RM district. They were obtained from the following:

the database of the DREAL Auvergne-Rhône-Alpes (“Direction Régionale de l'Eau, de l'Alimentation et du Logement” in French), including water-restriction levels (WRLs) and duration at the catchment scale available over the period 2005–2016 within the RM district,

The hydrological observation dataset is a subset of the 632 French near-natural catchments identified by Caillouet et al. (2017). Daily flow data from 1958 to 2013 were extracted from the French HYDRO database (http://hydro.eaufrance.fr/, last access: 1 August 2019). Time series with more than 30 % missing values or more than 30 % null values were disregarded. Finally, the total dataset consists of 106 gauged catchments located in the RM district, with minor human influence and with high-quality data. The selected catchments are benchmark catchments where near-natural drought events are observed and current water availability is monitored. Water can be abstracted from other nearby streams.

A selection of 15 evaluation catchments (Table 1) were used to calibrate and to evaluate the WRL (WR level) modelling framework (Sect. 4), selected because (i) they have complete records of stated water restriction, including dates and levels of restrictions – which was not the case in other catchments – and (ii) they are located in areas where water-restriction decisions are frequent. To facilitate interpretation, the 15 catchments were ordered along the north–south gradient. The Ouche and Argens river basins (no. 1 and 15 in Table 1) are the northernmost and the southernmost gauged basins, respectively. The 15 catchments encompass a large variety of river flow regimes according to the classification suggested by Sauquet et al. (2008; see Appendix A) that can be observed in the RM district (e.g. the Ouche – 1 in Table 1, pluvial regime; Roizonne – 3, transition regime; and Argens – 15, snowmelt-fed regime – river basins).

Baseline climate data were obtained from the French near-surface Safran meteorological reanalysis (Quintana-Seguí et al., 2008; Vidal et al., 2010) onto an 8 km resolution grid from 1 August 1958 to 2013. Exposure data were based on the regional projections for France (Table 2) available from the DRIAS French portal (http://www.drias-climat.fr/, last access: 1 August 2019, Lémond et al., 2011). Catchment-scale data were computed as a weighted mean for temperature and the sum for precipitation based on the river network described by Sauquet (2006).

Traditionally, hydrological impact studies are often based on “top-down” (scenario-driven) approaches and easy to interpret, but with associated conclusions becoming outdated as new climate projections are produced. In addition scenario-based studies may fail to match decision-making needs, since the implication in terms of water management is usually ignored (Mastrandrea et al., 2010). As a substitute to the scenario-driven approach, the scenario-neutral approach (Brekke et al., 2009; Prudhomme et al., 2010, 2013a, b, 2015; Brown et al., 2012; Brown and Wilby, 2012; Culley et al., 2016; Danner et al., 2017) has been developed to better address risk-based decision issues. The suggested framework shifts the focus to the current vulnerability of the system affected by changes and to critical thresholds above which the system starts to fail to identify possible maladaptation strategies (Broderick et al., 2019). Applied to water management issues, the scenario-neutral studies (Weiß, 2011; Wetterhall et al., 2011; Brown et al., 2011; Whateley et al., 2014) aim at improving the knowledge of the system's vulnerability to changes and at bridging the gap between scientists and stakeholders facing needs in relevant adaptation strategy. Prudhomme et al. (2010) have suggested combining of the sensitivity framework with top-down projections through climate response surfaces. This approach has been applied to low flows in the UK (Prudhomme et al., 2015), and its interests have been discussed as a support tool for drought management decisions.

The risk-based framework adopted contains three independent components (Fig. 4): i.

Sensitivity analysis (Fronzek et al., 2010) is based on simulations under a large spectrum of perturbed climates to (a) quantify how policy-relevant variables respond to changes in different climate factors and (b) identify the climate factors that the system is the most sensitive to. Addressing (a) and (b) may help modellers in checking the relevance of their model (e.g. unexpected sensitivity to a climate factor regarding the known processes influencing the rainfall–runoff transformation). From an operational viewpoint, it may encourage stakeholders to monitor, with priority, the variables that affect the system of interest (reinforcement of the observation network, literature monitoring, etc.).

The sensitivity analysis was conducted by applying a water-restriction modelling framework. Climate conditions were generated by applying incremental changes to historical data (precipitation and temperature) and introduced as inputs in the developed models to derive occurrence and severity of water restriction under modified climates. The tool chosen here to display the interactions between water restriction and the parameters that reflect the climate changes is a two-dimensional response surface, with axes represented by the main climate drivers. This representation is commonly used in scenario-neutral approach. For example, in both Culley et al. (2016) and Brown et al. (2012), the two axes were defined by the changes in annual precipitation and temperature. When changes affect numerous attributes of the climate inputs, additional analyses (e.g. elasticity concept combined with regression analysis – Prudhomme et al., 2015; the Spearman rank correlation and Sobol sensitivity analyses – Guo et al., 2017) may be required to point out the key variables with the largest influence on water restriction that form thereafter the most appropriate axes for the response surfaces.

Performance assessment is a challenging task for hydrologists, since it requires information on the impact of extreme hydrometeorological past events on stakeholders' activities. Simonovic (2010) used observed past events selected with local authorities on a case study in southwestern Ontario (Canada), chosen for their past impact (flood peak associated with a top-up of the embankments of the main urban centre; level 2 drought conditions of the low water response plan). Schlef et al. (2018) set the threshold to the worst modelled event under current conditions. Whateley et al. (2014) assessed the robustness of a water supply system, and the threshold is fixed to the cumulative cost penalties due to water shortage evaluated under the current conditions. Brown et al. (2012) and Ghile et al. (2014) suggested selecting thresholds according to expert judgment of unsatisfactory performance of the system by stakeholders, whilst Ray and Brown (2015) use results from cost–benefit analyses. The spatial coverage of a large area, such as the RM district, and the heterogeneity in water use (domestic needs, hydropower, recreation, irrigation, etc.) make it challenging for a systematic, consistent and comparable stakeholder consultation to be conducted and for a relevant critical threshold Tc to be fixed for all the users. Facing this complexity, only the irrigation water use will been examined here, since it is the sector which consumes most water at the regional scale, with a critical threshold defined for this single water use.

Exposure to changes here is measured using regional projections, visualized graphically by positioning the regional projections in the coordinate system of the climate response surfaces and identifying the associated likelihood of failure relative to Tc. Note that, to update the risk assessment, only the exposure component has to be examined (including the latest climate projections available onto the response surfaces).

The conceptual lumped rainfall–runoff model GR6J was adopted for simulating daily discharge at 106 selected catchments of the RM district. The GR6J model is a modified version of GR4J originally developed by Perrin et al. (2003), which is well suited to simulate low-flow conditions (Pushpalatha et al., 2011). The four-parameter version of the model GR4J has been progressively modified. Le Moine (2008) has suggested a new groundwater exchange function and a new routing store representing long-term memory in the GR5J model. Pushpalatha et al. (2011) finally introduced in the GR6J model an exponential store parallel to the existing store of the GR5J model. Considering additional routing stores is consistent regarding the natural complexity of hydrological processes, and in particular, the dynamics of flow components in low flows (Jakeman et al., 1990).

The GR6J model has six parameters to be fitted (Fig. 5): the capacity of soil moisture reservoir (X1) and of the routing reservoir (X3), the time base of a unit hydrograph (X4), two parameters of the groundwater exchange function F (X2 and X5), and a coefficient for emptying the exponential store (X6). The GR6J model is combined here with the CemaNeige semi-distributed snowmelt runoff component (Valéry et al., 2014). The catchment is divided into five altitudinal bands of equal area on which snowmelt and snow accumulation processes are represented. For each band, daily meteorological inputs – including solid fractions of precipitation – are extrapolated using elevation as a covariate, and the snow routine is calculated separately. Finally, its outputs are then aggregated at the catchment scale to feed GR6J. The two parameters of CemaNeige, S1 and S2, control the snowpack inertia and the snowmelt, respectively. S1 is used to compute the thermal state of the snowpack eTG, which is an equivalent to the internal snowpack temperature (∘C). eTG(t) at day t is a weighted linear combination of the value of eTG(t-1) (×S1) and the air temperature at the day t (×(1-S1)). S2 is the snowmelt degree-day factor used to calculate the daily snowmelt depth by multiplying the air temperature when it exceeds 0 ∘C, with S2. The splitting coefficient (SC) of effective rainfall between the two stores (in Fig. 5) has been fixed to 0.4 by Pushpalatha et al. (2011), since calibrating the SC leads to only slightly better performance. The allocation of the outflow from the soil moisture reservoir, with 90 % being percolation and 10 % being surface and sub-surface runoff in the GR6J model, is the result of previous studies. The GR6J model was selected for its good performance across a large spectrum of river flow regimes (e.g. Hublart et al., 2016; Poncelet et al., 2017).

No routine to simulate water management (e.g. reservoir) was considered here, since discharges of the 106 gauging stations are weakly altered by human actions or naturalized discharges (i.e. flows corrected from the effects of water use). The eight parameters (six from the GR6J model and two from the CemaNeige module) were calibrated against the observed discharges using the baseline Safran reanalysis as input data and the Kling–Gupta efficiency criterion (Gupta et al., 2009) KGESQRT calculated on the square root of the daily discharges as an objective function. The KGESQRT criterion was used to place less emphasis on extreme flows (both low and high flows). As the climate sensitivity space includes unprecedented climate conditions (including colder climate conditions around the current-day condition), the CemaNeige module was run for all the 106 catchments, even for those not currently influenced by snow.

The two-step procedure suggested by Caillouet et al. (2017) was adopted for the calibration: first the eight free parameters were fitted only for the catchments significantly influenced by snowmelt processes – i.e. when the proportion of snowfall to total precipitation less than 10 % – and second, for the other catchments, the medians of the CemaNeige parameters were fixed, and the six remaining parameters were then calibrated. Calibration is carried out over the period 1 January 1973 to 30 September 2006, with a 3-year spin-up period to limit the influence of reservoir initialization on the calibration results. The criterion KGESQRT and the Nash–Sutcliffe efficiency criterion on the log-transformed discharge NSELOG (Nash and Sutcliffe, 1970) were calculated over the whole period 1958–2013 for the subset of 15 evaluation catchments (Table 1), showing KGESQRT and NSELOG values are above 0.80 and 0.70, respectively. These two goodness-of-fit statistics indicate that GR6J adequately reproduces observed river flow regime, from low- to high-flow conditions. The less satisfactory performances of GR6J are observed for the Tarn and Roizonne river basins, both characterized by smallest drainage areas and highest elevations of the dataset. These lowest performances are likely to be linked to their location in mountainous areas (snowmelt processes are difficult to reproduce) and to their size (the grid resolution of the baseline climatology fails to capture the climate variability in the headwaters).

The WRL modelling framework developed aims to identify periods when the hydrological monitoring indicator is consistent with legally binding water restrictions. Only physical components (mainly hydrological drought severity) leading to WR decisions are considered, with no sociopolitical factor accounted for to model water restrictions.

To enable comparison of results across all catchments – in particular to combine response surfaces obtained from different catchments (see Sect. 5.1) – the same drought-monitoring indicators and regulatory thresholds were adopted in all the catchments (see Sect. 3 for details), selected as the most commonly used in the 28 DMPs across the RM district, specifically choosing VC3 as a monitoring indicator and 10d-VCN3(T) with return periods T of 2, 5, 10 and 20 years as regulatory thresholds. Each regulatory threshold is defined for a 10 d calendar period between 1 April and 31 October, resulting in 21 sets of four thresholds. Water restrictions are decided after consulting drought committees that convene irregularly depending on hydrological conditions over a time window, i.e. the last N days. Here a time window for analysis of N=10 d was decided, which is consistent with the prefectural decision-making time frame (frequency of updates in water-restriction statements). The WRL modelling time step is finally fixed to 10 d, and a representative value of WRL is given to the twenty-one 10 d calendar periods from April to October. Thus WRL is thus computed as follows:

VC3(t) is computed from daily discharge Qdaily(t) every day t.

The WRL modelling framework can be applied to both observed and simulated time series. For the latter, outputs from GR6J are used for simulations under current and modified climate conditions. Regulatory thresholds are derived from simulated discharge using the Safran baseline meteorological reanalysis as input to moderate the possible effect of bias in rainfall–runoff modelling.

The WRL modelling framework was verified in the 15 evaluation catchments (Table 1). WRL simulations based on modelled (hereafter GR6J) and observed (hereafter HYDRO) discharge were compared graphically to official WR measures (OBS). A further assessment was conducted using the Sensitivity and Specificity scores (Jolliffe and Stephenson, 2003) to examine how well the WRL modelling framework can discriminate WR severity levels (Table 4). The Sensitivity score assesses the probability of event detection; the Specificity score calculates the proportion of “no” events that are correctly identified. An event was defined as any legally binding water restriction of at least level 1, and a “non-event” was described as a period where WRL is zero or without WR. Comparisons were made over the 2005–2013 period, corresponding to the common period of availability for OBS, HYDRO and GR6J.

Figure 6 shows years with severe simulated WRLs (e.g. 2005 and 2011) and years with no or few simulated WRs (e.g. 2010 and 2013). Both GR6J and HYDRO simulations are generally consistent with OBS, even if misses are found (e.g. basins 9 to 11 during the year 2005). There is no systematic bias, with some overestimations (e.g. 2005 using GR6J in basins 1 and 15; 2007 using HYDRO in basin 15), underestimations (e.g. 2009 in basin 6–8) and misses (e.g. 2005 using HYDRO in basin 1).

Sensitivity and Specificity scores computed with OBS considered to be a benchmark (Fig. 7) show a large variation across the catchments, in particular for Sensitivity. Specificity scores are around 0.85 for both GR6J and HYDRO, suggesting that more than 85 % of the observed non-events were correctly simulated by the WRL modelling framework. The median of WRL Sensitivity score with HYDRO is around 45 %, indicating that for half the catchments, fewer than 45 % of observed events are detected based on HYDRO discharges, but this increases to 68 % of events detected when WRLs are simulated based on GR6J discharge. Using GR6J is more effective for detecting legally binding restriction than using observed discharges, while it is less efficient for predicting periods without restriction for most of the catchments. There is a compensatory effect, which is not easy to detect graphically, since Sensitivity scores are more sensitive than Specificity scores due to the reduced number of observed days with adopted restrictions. No evidence of systematic bias associated with catchment location or river flow regime was found: northern (blue) and southern (red) catchments are uniformly distributed in the Sensitivity and Specificity space.

Sensitivity and Specificity scores using HYDRO as a benchmark in the contingency table were also used to compare simulations from GR6J discharge with those obtained from HYDRO discharge. Median values reach 84 % (Sensitivity) and 92 % (Specificity), showing high consistency between HYDRO and GR6J. No statistical link between the hydrological model and WRL model performance was found, with R2 between NSELOG and Sensitivity or NSELOG and Specificity lower than 7 %. In addition, the similar skill scores of GR6J and HYDRO modelling suggest that possible biases in rainfall–runoff modelling does not impact on the ability of the WRL modelling framework to correctly simulate declared or undeclared WRs.

Choosing the same definitions for the monitoring indicator and regulatory thresholds is a simplifying assumption and may partly explain the deviations between simulated (HYDRO or GR6J) and adopted (HYDRO) WR measures. Before stating for VC3 and 10d-VCN3 the four prevalent modalities found in the current DMPs have been tested to reproduce the observed WR, and results have shown weak variables considered in the WR modelling framework. The mains reasons are that all the indicators and thresholds are derived from Qdaily time series and are highly correlated and thus share, above all, the same information on the dynamics and on the severity of drought.

Heterogeneity in basin characteristics and rules imposed by the DMPs should not result in a systematic difference in the Sensitivity and Specificity score between GR6J and HYDRO identified for most of the 15 evaluation catchments. Simulations were made on near-pristine catchments, and thus water uses are unlikely to be the main reason. Other causes of higher Sensitivity scores obtained when simulated discharges are used as input have been investigated in the WRL modelling framework. However, results of this analysis have not been conclusive. The aforementioned tests with the four prevalent modalities have all led to a higher Sensitivity score using GR6J and a higher Specificity score using HYDRO, demonstrating that the choice of the monitoring indicator and regulatory thresholds is probably not involved. A “smoothing” introduced by the hydrological modelling was also suspected, but autocorrelation in observed and GR6J-simulated VC3 time series was found to be very similar. Future works may reinvestigate these aspects. They will need to explore new aspects (e.g. the way WRL is derived from the daily values wrl for each 10 d period) using a longer verification period with a not necessarily uniform but fixed regulatory framework. Indeed some catchments have experienced only 3 years with legally binding water restrictions and DMPs were frequent during the 2005–2013 period (see the black vertical segments in Fig. 6).

Discrepancy between simulated and adopted WR measures is most likely due to the other factors involved in the decision-making process. When regulatory thresholds are crossed, restrictive measures should follow the DMPs. In reality, the measures are not automatically imposed but are the result of a negotiating process. This process includes for example some expert-judgment factors such as (i) the evolution of low-flow monitoring indicators and thresholds over the years – e.g. annual revision for the Ouche and irregular revision for the Isère (38), Gard (30), Alpes-de-Haute-Provence (04) and Lozère (48) departments (last one in 2012); (ii) the role of drought committees in negotiating a delay in WRL applications to limit economic damages or to harmonize responses across different administrative sectors sharing the same water intake; and (iii) the local expertise, especially regarding the uncertainty in flow measurements (Barbier et al., 2007) impacting the low-flow monitoring indicators, e.g. Côte d'Or (21) and Lozère (48) in the northern and southwestern parts of the RM district, respectively. Note that where WR decisions are not uniquely based on hydrological indicators but also involve a negotiation process, the results of the WRL modelling framework should be interpreted as potential hydrological conditions for stating water restrictions.

Results of our sample study on 15 evaluation catchments show deviations for most catchments but links between order restrictions and hydrological drought severity. These deviations may partly be attributed to the use of the same monitoring indicator and regulatory thresholds across the catchments in the modelling (whilst it is not true in reality) as a necessary assumption for a regional-scale analysis. Tests with QC7 as low-flow monitoring variable combined with the two dominant modalities for the regulatory thresholds show a weak sensitivity of the WRL modelling skill to the choice of the indicators (with a slight increase in Specificity score – ∼90 % – while the Sensitivity score is reduced – <50 % – using GR6J). Whilst the developed WRL modelling framework does not account for the expert decision made by drought committees – and hence is not designed to simulate the exact WR decisions – its ability to simulate 68 % of the stated restrictions over the period 2005–2013 demonstrates its usefulness as a tool to objectively simulate the potential of drought restrictions based on hydrological drought physical processes. The methodology was applied to the 106 catchments of the RM district under climate perturbations to assess the potential impact of climate change on water restriction in the region. The resulting analysis focuses on water-restriction level higher than 1, denoted thereafter as WR*.

The generation of climate response surfaces relies on synthetic climate time series representative of each explore climate condition and used as input to the impact modelling chain (here hydrological model and WRL modelling framework). Methods based on stochastic weather simulation have been used (Steinschneider and Brown, 2013; Cipriani et al., 2014; Guo et al., 2016, 2017), but it can be complex to apply them in a region with such a heterogeneous climate as the RM district. Alternatively, the simple “delta-change” method (Arnell, 2003) has been commonly used to provide a set of perturbed climates in a scenario-neutral approach (Paton et al., 2013; Singh et al., 2014) and was used here, similar to Prudhomme et al. (2010, 2013a, b, 2015).

Following Prudhomme et al. (2015), monthly correction factors ΔP and ΔT are calculated using single-phase harmonic functions: 1ΔP(i)=P0+AP⋅cos⁡(i-φP)⋅π6,2ΔT(i)=T0+AT⋅cos⁡(i-φT)⋅π6, with P0 and T0 as mean annual changes in precipitation (Eq. 1) and temperature (Eq. 2), respectively, i as the indicator of the month (from 1 to 12), φ as the phase parameter, and A as the semi-amplitude of change (e.g. half the difference between highest and lowest values) for precipitation (Eq. 1) and temperature (Eq. 2). These correction factors were applied to the baseline climate datasets to create perturbed daily forcings: 3P*(d)=P(d)⋅[PM‾(month(d))+ΔP(month(d))]/PM‾(month(d)),4T*(d)=T(d)+ΔT(month(d)), with P(d) and T(d) representing baseline precipitation and temperature values for day d, P*(d) and T*(d) representing the corrected (or perturbed) values for day d, and PM¯(month(d)) representing average monthly baseline precipitation for month(d). Corrected potential evapotranspiration PET* time series were derived from temperature values using the formula suggested by Oudin et al. (2005): 5PET*(d)=max[PET(d)+Ra28.5ΔT(month(d))100;0], with PET(d) as baseline potential evapotranspiration values for day d; Ra is the extraterrestrial global radiation for the catchment.

The baseline climate (precipitation and temperature) time series were extracted from the Safran reanalysis over the period 1958–2013 (56 years), and perturbed time series were generated for the same length. The range of climate change factors to generate the perturbed series were chosen to encompass both the range and the seasonality of RCM-based (RCM – regional climate model) changes in projections in France. A set of 45 precipitation and 30 temperature scenarios was created (Fig. 8), spanning the range of potential future climate suggested by Terray and Boé (2013) and combined independently, resulting in a total of 1350 precipitation and temperature perturbations pairs used to define the climate sensitivity space. In this application, the following applies:

P0 (mm) = -20+20/3×(j-1), j=1, …, 9,

Water uses and the feedbacks between use and available resources are not explicitly addressed in this application either under current or future conditions. This should not be considered to be a limitation for basins where hydrological modelling has been implemented. Indeed, the 106 basins under study have been carefully chosen, since they are currently influenced little or are not influenced by human actions. These catchments are benchmark catchments where natural water availability is monitored for the statement of restriction orders. Water can be abstracted from other neighbouring rivers. Water needs will probably evolve in the coming decades. The water requirement for irrigation may increase parallel to air temperature or may decrease due to adaptive actions (e.g. farmers may choose to plant specific crops less sensitive to water shortages). Water needs and sensitivity to water restrictions depend on socio-economic and institutional pathways. Forward-looking studies have been recently carried out with the involvement of local experts but at the local scale (Grouillet et al., 2015 for the Hérault river basin; Andrews and Sauquet, 2017 for the Durance river basin). The distinct underlying assumptions make it difficult to combine and to extend the prospective scenarios over the RM district. Thus, the water-restriction modelling framework considers, in this application, the “business-as-usual” scenario, which assumes that only minor change in water demand behaviour will occur. In particular, no major alteration of the river flow regime is projected for the 106 catchments. Despite being unrealistic, maintaining the current conditions allows for the assessment of the impact of climate change regardless of any other human-induced changes. The advantage is that results are easier to understand and to embrace by stakeholders than those obtained with complex multi-sectorial scenarios that they may not identify with.

The 1350 sets of perturbed precipitation, temperature and PET time series were each fed into the WRL modelling framework for each of the 106 catchments. Both VC3 (monitoring indicators) and 10d-VCN3(T) (regulatory thresholds) were computed from GR6J 56-year discharge simulations. For each scenario, the number of 10 d periods under a water restriction of at least level 1 (WR*) was calculated and expressed as a deviation from the simulated baseline value, ΔWR*, hence removing the effect of any systematic bias from the WRL modelling framework. Results are shown as WR response surfaces built with x and y axes that represent key climate drivers. Because different climate perturbation combinations share the same values of the key climate drivers, hence being represented at the same location of the response surface, the median ΔWR* from all relevant combinations is displayed as a colour gradient, with the standard deviation (SD) of ΔWR* shown as the size of the symbol.

Response surfaces based on different climate variables for x (precipitation) and y (temperature) were generated over the whole or part of the water-restriction period (April to October – AMJJASO; March to June – MAMJ; and July to October – JASO, the latter coinciding with the highest temperatures) and visually inspected to identify the greatest signal pattern, combined with the smallest dispersion around the surface response (i.e. analysis of the median and the maximum of SD values over the grid cells).

The response surfaces are exemplified on three of the 15 evaluation catchments (Table 1, Fig. 9):

the Argens river basin, along the Mediterranean coast, where severe low flows occur in summer and actual evapotranspiration is limited by water availability in the soil;

Following Köplin et al. (2012) and Prudhomme et al. (2013a), the 106 response surfaces were classified to define typical response surfaces, designed as tools to help in prioritizing actions for adapting water management rules to future climate conditions in the RM district. Here a hierarchical clustering based on Ward's minimum variance method and Euclidian distance as similarity criteria (Ward Jr., 1963) was applied, and four classes were identified after inspection of the agglomeration schedule and silhouette plots (Rousseeuw, 1987). A manual reclassification was conducted for the few catchments with negative individual silhouette coefficients to ensure higher intra-class homogeneity. For each class, a mean response surface and associated SD were computed, and main climate drivers associated with WR changes were identified (Table 5).

All suggest an increase in the occurrence of legally binding water restrictions when precipitation decreases or when temperature increases (Fig. 10). An additional temperature increase and its associated PET increase can compensate for precipitation increase and lead to a decrease in ΔWR*, with intra-class differences emerging in the magnitude of changes. The identified four typical water restriction response surfaces show a weak regional pattern and common features. Class 4 (including the Roizonne river basin) regroups snowmelt-fed river flow regimes in the Alps, whilst basins of Class 1 are mainly Mediterranean river flow regimes. Class 2 (including the Ouche river basin) and Class 3 catchments are partly influenced by both precipitation and temperature, with ΔWR* in Class 2 catchments being less sensitive to climatic changes (flatter WR response surface) than catchments of Class 3. The flow regime of Class 2 to 3 ranges from rainfall-fed regimes with high flow in winter and low flow in summer in the northern part of the RM district to regimes partly influenced by snowmelt, with high flows in spring in the Alps and in the Cevennes.

To further the regional analysis and help sensitivity assessment at unmodelled catchments, basin descriptors were investigated as possible discriminators of the four classes. A set of potential discriminators – which included measures of the severity, frequency, duration, timing and rate of change in low-flow events (Table 6); the drainage area and the median elevation for the catchment; and one climate descriptor (mean annual precipitation and mean annual potential evapotranspiration used to compute an aridity index – AI) – were introduced in a CART model (Classification And Regression Trees; Breiman et al., 1984), aimed at performing successive binary splits of a given dataset according to decision variables. Through a set of “if–then” logical conditions the algorithm automatically identifies the best possible predictors of group membership, starting from the most discriminating decision variable to the less important factors. The optimal choices are fixed recursively by increasing the homogeneity within the two resulting clusters. At each step, one of the clusters (node) is divided into two non-overlapping parts. Here, to free results from catchment size influence, descriptors related to severity were expressed in millimetres per year, millimetres per month or millimetres per day.

Results show three top discriminators, with the aridity index being the strongest:

the AI given by the mean annual precipitation divided by the mean annual potential evapotranspiration (UNEP, 1993),

CART overall misclassification (18 %) suggests a satisfactory performance in the classification method, characterized by a parsimonious algorithm (five nodes and three variables) with the potential for a first-guess assessment of the WR response to disruptions and evaluation of the robustness of existing water restriction at the department-level scale. For each class, Fig. 11 shows the empirical distribution of the three main discriminators, the mean timing θ of daily discharge below Q95 and its dispersion r, which is based on circular statistics, where Q95 is the 95th quantile derived from the flow duration curve.

The classification discriminates catchments primarily on the seasonality of low-flow conditions and the aridity index, with the extreme classes (1 and 4) being particularly well discriminated.

Geographically, Class 1 catchments are mainly located along the Mediterranean coast and include the Argens river basin; ΔWR* is mainly driven by changes in precipitation in spring and early summer. Class 1 gathers water-limited basins with small values of the AI and a weak sensitivity to climate change in summer. In these dry water-limited basins, the mid-year period exhibits the minimal ratio P / PET, and changes in summer precipitation have hence only a moderate impact on low flows; spring is the only season when PET changes are likely to result in both actual evapotranspiration and discharge changes. WRLs are more likely controlled by antecedent soil moisture conditions in spring and early summer. This behaviour is typical of the basins under Mediterranean conditions and was discussed in the context of a scenario-neutral study in Australia (Guo et al., 2016). For those catchments, climate drivers computed in spring (over the period MAMJ) are used to describe the x and y axes of the response surface, fully consistent with water-limited basin processes.

Catchments of both Class 2 and 3 have a similar CI, hence suggesting that flow variability is not a proxy for low-flow response to climatic deviation. However, BFI values for Class 3 are lower than for Class 2, while Class 3 is characterized by high values for the AI. Despite higher capability to sustain low flows (see BFI values) the response surface representative of Class 2 is more contrasted than that of Class 3; a possible reason could be drier conditions under current conditions (the median of the AI equals 2.5 for Class 3 compared to 1.6 for Class 2). The monthly perturbation factors (see Sect. 5.1) are the same for all the classes, but the changes in relative terms are less significant regarding the current climate conditions for Class 3 than for Class 2 and may explain the limited changes in river flow patterns.

Class 4 regroups catchments with low flows in winter and significant snow storage. The BFI values are high, and due to smooth flow duration curves, the CI demonstrates also high values.

The risk-based framework has been applied to the irrigation water use, since annual net total water withdrawal for agriculture purposes is ranked first at the regional scale. Note that in the Rhône–Mediterranean district around 90 % and 10 % of water used for irrigation originates from surface water and groundwater, respectively. To complement water needs irrigators may also have access to small reservoirs (storage capacity usually less than 1×106 m3). Most of the reservoirs are filled by surface water in winter and release water later in the following summer. Water restrictions are not imposed to these reservoirs, but it is assumed here that during severe drought events the majority of them are empty, and thus the existence of potential sources auxiliary to surface water on the conclusions has limited influence on the conclusions.

We assumed here that irrigated farming is globally under failure if the duration with limited or suspended abstraction is above a critical threshold Tc that causes insufficient water for crops. The catchment or area i will be considered more vulnerable than the catchment or area j if the likelihood of failure (i.e. exceeding Tc) for catchment or area i is more than the likelihood of failure for catchment or area j. The critical threshold Tc is a value of total number of days with legally binding water restrictions that needs to be fixed. To move closer to reality and following Simonovic (2010), the value of Tc is based on the analysis of past events. A possible way to fix Tc is to simulate historic drought events observed during the period 2005–2012 and the effects of water restrictions on crop yield and quality and on economic losses. Computing water deficits was considered rather tricky at the farming scale – partly due to the high heterogeneity in crop and soil types, watering systems, conveyance efficiencies, etc., across the RM district – and we have investigated the use of “agricultural disaster” notifications as proxies to identify the damaging conditions instead.

Specifically the agricultural disaster notifications are issued by the agriculture ministry following recommendations from the prefecture to each department affected by extreme hydrometeorological events and applied uniformly over the RM district. Whilst the agricultural disaster status is a global index that may mask heterogeneity in crop losses within each department, and that reflects losses related to both agricultural and hydrological droughts, it has the advantage of being directly related to the economic impact and uniformly applied across the RM district, hence being suitable for a regional-scale analysis. The national system of compensation to farmers is initiated for areas classified under the agricultural disaster status.

Over 2005–2012, only one agriculture disaster was declared, in 2011, and this applied to 70 of the 95 departments in continental France and to 16 of the 28 departments fully or partly located in the RM district. Data are collected by the French Ministry of Agriculture and Food, and they are not publicly available. The year 2011 was the only year when the national system of compensation was triggered between 1958 and 2013, and the analysis of simulated water restrictions for this year fixed the value for Tc. The duration of water restrictions was calculated individually for each catchment and converted into anomalies ΔWR* (2011) with respect to the benchmark value (mean over the period 1958–2013). For consistency with the indicators used in the response surfaces, this threshold ΔWR* (2011) is derived from GR6J outputs.

The RCM-based projections of all the catchments of the class for the three time slices 2021–2050, 2041–2070 and 2071–2100 were superimposed to the representative response surfaces to assess the risk of failure (Fig. 4). Finally the vulnerability resulting from the combination of the three components of sensitivity, performance and exposure was measured by the proportion of RCM-based projections leading to critical situations, similarly to Prudhomme et al. (2015). Technically this vulnerability index (VI), calculated as the proportion of exposure simulations that fail below the critical threshold Tc, is the complement to the “climate-informed” robustness index (CRI; Whateley et al., 2014). Given one specific climate projection, a catchment or a group of catchments could be determined vulnerable if on average Tc is exceeded. VI is introduced here to account for the uncertainty in climate projections in risk assessment. This index should be interpreted as conditional probability (risk) with respect to a specified ensemble of future climates.

Figure 12 shows an application to the Ouche river basin, north of the RM district (1 in Fig. 1 and Table 1) and declared under the agricultural disaster status in 2011. The black dotted lines are isopleths connecting points of the response surface with ΔWR*=ΔWR*(2011)=Tc (seven 10 d periods for this catchment) and delimit the climate space, leading to median climatic situations more severe than 2011 (ΔWR*>ΔWR* (2011); above left) or less severe than 2011 (ΔWR*<ΔWR* (2011); below right) ΔWR* (2011). As reference, the black solid line (ΔWR*=0) delimits the climate space associated with more (above left) or fewer (bottom right) water restrictions compared with the whole period average (1958–2013). Basin-scale exposure projections (Table 2) were plotted onto the WR response surface for three time periods, 2021–2050, 2041–2070 and 2071–2100 (grey symbols), showing a warmer trend but no total precipitation signal. Whilst by the end of the century, projections move towards the critical threshold ΔWR* (2011) climate space, pointing out a significant increase in more severe low flows, a large spread in signal remains (dispersion of the grey symbols), and the vulnerability index equals zero for this catchment.

Following the methodology applied to the Ouche river basin, ΔWR* (2011) values were calculated for individual catchments and averaged to produce a value of Tc relevant for each class (Table 7). Class variation in ΔWR* (2011) is large, with Class 2 and 3 showing thresholds of at least seven 10 d periods, whilst they are close to zero for Class 1 and Class 4. The scatter in the ΔWR* (2011) values is certainly due to heterogeneity in crops, in irrigation systems, in climate conditions, etc., at the regional scale, leading to locally differentiated sensitivity to water restrictions as well as to biases in WR modelling. Since information on agricultural disaster notifications is only available for the year 2011, it is difficult to come to conclusions on the origins of the dispersion (natural or non-natural). However the distribution and absolute values of the critical thresholds reflect the spatial pattern of WR enforced from May to September 2011 well, with southern regions and the French Alps moderately affected by lack of rainfall in spring compared to the northern and western regions of the RM district (Fig. 13). Surprisingly negative values for ΔWR* (2011) are found for some catchments of Class 1 and 4, providing no evidence to support their agricultural disaster status that year. At the RM scale, average ΔWR* (2011) equals 38 d when considering all catchments and increases to 66 d when considering only catchments under agricultural disaster status. Simplified but realistic assumptions are imposed by the lack of detailed information; thus only one value was considered at the regional scale despite high dispersion in ΔWR* (2011) values (Table 7): the critical threshold Tc was set to the average of the ΔWR* (2011) values computed on all catchments in departments under agricultural disaster status in 2011 (6.6 10 d periods) and was used thereafter for all classes. Note that this value of Tc seems realistic: it represents a significant period with restrictions (66 d or 30 % of the time between 1 April and 31 October).

Using the class WR response surface as a diagnostic tool, exposure information (grey symbols) and thresholds (ΔWR*=0, solid; ΔWR* (2011), dashed black lines) were displayed (Fig. 14), and the VI was calculated (Table 7). The location of the two isopleths ΔWR*=ΔWR* (2011) (black dotted line) and ΔWR*=0 (black straight line) in the WR response surface depends on the shape of the response surface and differs from one class to another. The portion of the WR response surface associated with ΔWR*<0 is gradually lower from Class 1 to Class 4, suggesting that catchments of Class 4 are more subject to an increase in water-restriction occurrence than catchments of the other classes. Class 1 and 4, the most extreme responses classes, contain fewer catchments, whilst Class 2 and 3, characterized by an intermediate response, have the most of the catchments. Because of the large geographical spread of catchments of Class 2 and 3, an expert-based division was done to distinguish catchments with continental (northern sectors, Class 2-N) and Mediterranean (southern sectors, Class 2-S) climate in terms of exposure. This is to better capture the predominantly north–south gradient in future projections of both temperature and rainfall, as they have a differing impact on the river flow regime (e.g. Boé et al., 2009; Chauveau et al., 2013; Dayon et al., 2018). For all classes, vulnerability increases with lead time, with Class 4 showing the largest vulnerability and Class 1 being the less vulnerable despite its location in the Mediterranean area. In Class 2 and 3, vulnerability increases from north to south in the RM district (VI = 13 % for Class 2-N compared to 32.9 % for Class 2-S at the end of the century). These contrasting results are mainly explained by the difference between exposure characterizations, since a common value of the threshold Tc was adopted.

In 2011, France adopted a general framework for action – the “French National Climate Change Impact Adaptation Plan” (“Plan National d'Adaptation au Changement Climatique – PNACC” in French) – with numerous recommendations related to research and observation. Five priorities of the first “PNACC” related to water resources have been highlighted. The “PNACC” was recently reviewed, and the “PNACC2” published in December 2018 confirms the place of DMPs as tools for monitoring water resources and water allocation and for driving greater public and stakeholder awareness (https://www.ecologique-solidaire.gouv.fr/adaptation-france-au-changement-climatique, last access: 1 August 2019).

However, until now, impacts of future climate change are not accounted for in DMPs. The development of DMPs has helped to ease past conflicts at the departmental scale. Water users are now facing more frequent water restrictions – more than half of France has departments experiencing WRL ≥ 1 between 2011 and 2018 (Fig. 15) – and the timing and the level of the restrictions vary from one year to another: the highest number of French departments with WRL ≥ 1 was observed in summer in both 2015 and 2017, while the year 2018 was characterized by late water restrictions (mostly in autumn). Stakeholders are now questioning the DMP implementation but only in the short term – the impact of climate change is not yet a topic. One of their main concerns is the heterogeneity in current restriction levels and timing from one department to another or from the upstream to the downstream part of the catchment. One of the options being considered to address this challenge in southeastern France is to harmonize the definition of the regulatory thresholds at the regional scale. Results obtained here show that the standardization will probably not fix the problem due to the balance between sociopolitical and hydrological factors in the final WR statement.

The map displaying the class membership could be a convenient tool for local authorities to discuss the spatial heterogeneity in terms of impact to drought on water restrictions under both current and future climate conditions. Despite operating rules uniformly applied, there is high variability in catchment responses within the department (see the southernmost department in Fig. 10). Therefore, any investigation on DMPs at the department level disregarding this heterogeneity will be biased. The sensitivity analysis provides information for local authorities to better understand the differences in catchment responses to observed droughts in areas, which fall within their responsibility. For instance, water management in basins of Class 4 could be more problematic during a year with a severe heat wave, while it could be more problematic for a year with a pronounced precipitation deficit for catchments of Class 1. It is likely that the differences in the impact of droughts on WR will persist if stakeholders do not question the assumption of a uniform definition for the hydrological indicators within the department.

DMPs have been recognized in the “PNACC” as relevant water management tools, and our findings also have implications for adaptation strategies. We have shown that the climate change effects could be felt more acutely during the irrigation period by an increase in water restriction. Thus, relying on surface water to compensate deficits is highly hazardous. Options under consideration are saving water, enhancing water storage by building new small dams or securing water access by transferring water from the Rhône river (e.g. Ruf, 2012), which is considered to be an “overabundant” river within the RM district. Saving water is the solution favoured by the RM Water Agency. Creating new storages is increasingly considered to be a potential solution to secure water for agriculture, since they are not subject to water restrictions. Authorizing new water storages may also reduce the sense of unfairness among users in areas with no secured access. Most of the small reservoirs are filled by surface water in winter, release water later in summer for irrigation purposes and then limit the pressure on water resources during crises. However, there is actually a wide discussion about these hydraulic structures in France, since their cumulative impacts on the ecosystem and their efficiency are not well known (Habets et al., 2018). Building adaptation strategies for additional water storage may lead to maladaptation, since natural inflows will probably decrease and delay the mutation of agricultural practices and conservation measures. In addition, there is actually no guarantee that these reservoirs will be filled and that their storage capacity will be enough to cope with severe droughts.

The RM Water Agency has taken other the objectives of “PNACC” at the regional scale and has initiated an unprecedented major initiative that provides guidance for the “River Basin Management Plan” (2016–2021). The adaptation strategy partly relies on an analysis of the vulnerability in different water-related sectors (water resources, soil-moisture, biodiversity and water quality) within the RM district to climate change. The study complements this former analysis by focusing here on agricultural uses and meets the requirements for vulnerability assessment carried out by the RM Water Agency: it covers the same area, and the methodology is uniformly applied across the area of interest. It may help the RM Water Agency in identifying when and where actions and investments are the most needed to mitigate the effects of climate change (probably in catchments of Class 4 from the short perspective and later for the other areas).