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SUPPLEMENTARY MATERIAL
The supplementary material contains detailed explanations of some aspects described in the text
and additional results. Sections and figures are referred to in the text with the notation S before the
number.
S1. Stations selected for the study
Discharge data was provided by the French HYDRO2 and Swiss Federal Office for the
Environment (FOEN) databases, from which 37 stream gauges were selected (Table S1) with data series
systematically covering the period 1960-2012.
Table S1: Stations selected for the study, code from the HYDRO2 and FOEN data bases, river, name of
the station and drainage area in km2.
Code
SHN2009
SH2606
2028
Station
Drainage
area (km2)
Porte du Scex
5220
Halle de l’Ile
7987
Sécheron
7987
Pont Des Favrands
205
River
Rhone (lake
inflow)
Rhone (lake
outflow)
Geneva Lake
(water level)
V0002010
Arve
V0032010
Arve
Sallanches
514
V0222010
Arve
Pont-Notre-Dame
1664
V1214010
Fier
Dingy-Saint-Clair
222
V1264010
Fier
Vallieres
1350
V1504010
Guiers Mort
Saint-Laurent-Du-Pont
89
V1515010
Guiers Mort
Pont Saint-Martin
114
V2024010
Saine
Foncine-Le-Bas
55.8
V2202010
Ain
Chalain
650
V2322010
Ain
Vouglans
1120
V2712010
Ain
Pont-D'ain
2760
V2942010
Ain
Chazey-Sur-Ain
3630
U1004010
L'ognon
Fourguenons
73.5
U1044010
L'ognon
Chassey-Les-Montbozon
866
U1054010
L'ognon
Beaumotte-Aubertans
1250
U1084010
L'ognon
Pesmes
2038
U2604030
Loue
Vuillafans
478
U2624010
Loue
Chenecey-Buillon
1300
U2634010
Loue
Champagne-Sur-Loue
1509
U2654010
Loue
Parcey
1922
U0020010
Saone
Monthureux-Sur-Saone
228
U0230010
Saone
Cendrecourt
1130
U0610010
Saone
Ray-Sur-Saone
3740
U0820010
Saone
Gray
5390
U1120010
Saone
Auxonne
8746
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17
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22
23
24
25
26
27
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33
U1420010
Saone
Pagny-La-Ville
11673
U3120010
Saone
Chalon-Sur-Saone
20807
U3310010
Saone
Tournus
22740
U4300010
Saone
Macon
26058
V1020010
Rhone
Injoux-Genissiat
10910
V1440020
Rhone
Brens
13960
V1630020
Rhone
Lagnieu
15380
V3000015
Rhone
Lyon
20300
V3130020
Rhone
Ternay
50560
S2. Long-term analysis of past discharge
The first step of the study was based on the identification of changes in runoff regimes based on the
following criteria:


Change in seasonal behaviour of monthly Pardé coefficients,
Change in extreme values of monthly Pardé coefficients (min, max), resulting in an increase or decrease
of the seasonal variability of runoff (= change in amplitude),
 Change in the timing of extreme values of monthly Pardé coefficients, indicating an inter-annual shift of
dominant hydrological processes,
The monthly Pardé coefficient (PC) gives the relation between mean monthly (MQmonth) and mean
annual (MQyear) runoff. The Pardé coefficient therefore describes the mean monthly distribution of runoff
over the year.
Depending on the number of maxima of the monthly Pardé coefficients over the year, Pardé (1933)
distinguished between unimodal (one maximum) and complex (e.g., bimodal) runoff regimes. In addition,
he differentiated between pluvial, nival and glacial runoff regimes depending on the dominant feeding
mechanism. In case of complex runoff regimes, combinations of two or three feeding mechanisms are
assumed. The difference between the maximum (PCmax) and the minimum (PCmin) values of monthly Pardé
coefficients is called amplitude (A). It characterises the inter-annual variability of mean monthly flow.
Figure S1 shows some of the results (explained in the text in section 4.1).
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For all available time series, trends in the mean and extreme (minimum and maximum) annual
runoff can be computed for identification of possible significant trends. These trends can be classified
according to their significance:
 tendency, a statistically still unproven development
 trend, a statistically proven development (at least 80% significance)
 strong trend, a statistically well-founded development (at least 95% significance)
Trend analyses in this study are conducted by the nonparametric Mann–Kendall (MK) test. The
application of the MK test to hydrological series has been discussed in detail by Kundzewicz and Robson
(2004), and is summarised as follows:
Considering a sample (x1, . . . , xn) with size n. The MK statistic, S, is given by
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Under the null hypothesis that there is no trend within the time series:
E(S) = 0,
Var(S) = n(n−1)(2n+5)/18.
The test statistic is the standardised value calculated as
Figure S1: Temporal variability of flow regime in a multi-decadal scale for the recent past (19601979) and current situation (1980-2009) for the main flow regimes in the area: (A) nivo-glacial in the
Arve; (B) pluvial regime in the Ain; (C) pluvial Loue at Parcey (in the region of the Doubs); and (D) in
the Rhône at Ternay (outlet of the studied basin).
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Typically, the hypothesis of stationarity is rejected at the α significance level if |Z| > u1−α/2, where
u1−α/2 is the (1–α/2) quantile of the standard normal distribution.
Detrending was accomplished by using the so called Zhang’s method (described in Yue and Wang,
2002 and Yue et al., 2003).
The MK Z statistic was calculated from the available time series for each indicator, for every
possible combination of start and end year over the analysis period. Trend tests are generally less reliable
for shorter periods (with at least n = 10 recommended for the MK test); therefore, a minimum window
length of 20 yr was applied.
S3. Climate change scenarios
According to CMIP5, the projected changes in temperature, precipitation and evaporation for the
studied area point to a slight decrease in precipitation (depending on the RCP) as well as increases both in
temperature and evaporation (Figure S2).
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Figure S2: Precipitation, temperature and evaporation annual change for the study area (45º-48ºN, 3º9ºE) for the period 1980-2010 (reference period 1980-2010) and the full CMIP5 ensemble. On the left,
for each scenario one line per model is shown plus the multi-model mean, on the right percentiles of the
whole dataset for projected changes and values: the box extends from 25% to 75%, the whiskers from 5%
to 95% and the horizontal line denotes the median (50%).
Different models have been chosen to catch the variability and uncertainty of the climate responses.
We selected the four runs closest to the percentiles (grey shade in the graph of Figure S3). These four
scenarios represent the range of almost no-change, warm-dry, wet and warm-wet future climates
projected for the studied area.
Figure S3: Projected changes in temperature and precipitation for the study region (i.e. 3-9°E and 43-45°N) and for
RCP 2.6 and 5.8 based on all GCM runs. Values indicate differences between the baseline period (1980-2010) and
projected future evolutions for the period 2080-2100. The range between the 10th and 90th percentiles is shaded in
grey and the runs highlighted with circles are those considered for further analysis.
These final climate projections assumed a change in temperature between -8 to 51%, from -10% to
-27% for precipitation and between 1.3% to 33% for evaporation (Figure S4).
Figure S4: Comparison between monthly mean observed values (baseline period 1980-2010) and
projected averaged values for the studied basin for temperature, precipitation and evaporation for the
period up to 2100.
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S4. Downscaled data series performance
The delta-change approach was used to obtain the final corrected and downscaled time series. We
checked the performance of the approach comparing the historical data series observed in the basin with
the corrected and downscaled series we obtained. The result of this validation in the control period was
satisfactory, with the best adjustment in temperature, and the lowest in precipitation (Figure S5).
Figure S5: Comparison between monthly mean observed values and corrected and downscaled averaged
values for the studied basin for temperature, precipitation and evaporation for the baseline period 19802010.
The error estimated for each variable ranges between 0.05% and 27%. It is ranging between 9 and
17% for temperature, -18 and -27% for precipitation and -0.05 and 11% for evaporation. The temporal
distribution from monthly to daily was also validated for the control period. The resulted time series were
reproducing the observed daily values (Figure S6).
Figure S6: Daily observed values for precipitation and corrected and downscaled daily values for
the control period (1980-2010). Red line is the linear regression and grey line is the line 1:1.
S5. Geneva Lake management scenarios
We used as boundary condition for the hydrological simulation the outlet discharge from Lake
Geneva in order to link both parts of the Rhone basin (the Upper-Swiss watershed and the French part).
Since the outlet of the Lake is managed and artificially regulated, it is not possible to project or anticipate
the management strategy. However, and according to future projections, the discharge of the Rhône
upstream Geneva Lake will be reduced between -50% to -75% by 2100 (Beniston et al., 2012). Lake
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management strategy should change accordingly. For this study, we defined two scenarios; one scenario
was assuming that the discharge will be the same as in the baseline period, which is a strong assumption
(based on future projections). On the other hand, a more reliable scenario, assuming that the discharge
will be affected as well by climate change. In this scenario the management strategy will remain the same
as in the baseline period but the discharge is reduced by a coefficient of 0.5 (Figure S7).
Figure S7: Outlet discharge from Lake Geneva. Red is the managed discharge for the period 1980-2010
(and assumed to be one scenario for the future), and blue is the same strategy management but reduced
by 50%.
S6. Model calibration and validation
TETIS model was calibrated and validated and its performance evaluated for the most recent past.
The model’s performance both during calibration and validation was measured with the Nash–
Sutcliffe Efficiency (NSE) coefficient (Nash and Sutcliffe, 1970). The NSE coefficient is defined as:
where Qo is the mean of observed discharges, and Qm is modelled discharge. Qot is observed
discharge at time t. Nash–Sutcliffe efficiencies can range from −∞ to 1. An efficiency of 1 (NSE = 1)
corresponds to a perfect match of modelled discharge to the observed data. An efficiency of 0 (NSE = 0)
indicates that the model predictions are as accurate as the mean of the observed data, whereas an
efficiency less than zero (NSE < 0) occurs when the observed mean is a better predictor than the model
or, in other words, when the residual variance (described by the numerator in the expression above), is
larger than the data variance (described by the denominator). Essentially, the closer the model efficiency
is to 1, the more accurate the model is.
The visual fit of model simulations shows a good agreement between observations and simulations
for most flood events, for which the model accurately represents the timing and magnitude of peaks and
the recession limb of the hydrographs (the Figure S8 shows some examples).
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Figure S8: (A) Model calibration at the outlet of the basin for the calibration period (2003-2008)
with NSE =0.701. (B) Detail of the model calibration for the Loue River basin, for which NSE = 0.805;
(C) Model validation at Saone for the period 2008-2012 with a NSE = 0.68.
S7. Climate scenarios impacts on the Rhone discharge
At Lyon, the reduction in mean annual flows is projected to be between -46% and -63% by the end
of the century and for the scenario in which runoff from Lake Geneva is reduced by 50%. The reduction
is in the order of -38 to -57% in case that outlet discharge of Lake Geneva would remain unchanged
(Table S2).
Table S2: Annual mean discharge for the Rhone River at Ternay, for the baseline period (1980-2010) and
for the future climate projections (2070-2100) and the two Lake management scenarios.
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Mean discharge (m3·s-1)
RCP 2.6
GISS
RCP 2.6
MRI
Baseline period
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176
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178
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180
RCP 8.5
FGOALS
RCP 8.5
CSIRO
1053
Future (100% outlet discharge from the Lake)
652
518
585
452
Future (50% outlet discharge from the Lake)
520
427
385
560
Discharge at Ternay is likely to decrease significantly by the end of the century, low flows will
become more extreme whereas less severe low flows can be expected in the rest of the sub-basins. With
respect to floods, high flows show a general tendency of decrease and possible upwards are limited to the
more extreme, yet less frequent floods. Table S3 shows the summary of the impacts on discharge for all
the Rivers analysed.
Table S3: Summary of climate change impacts on discharge in the French Rhone basin upstream Lyon
(Ternay). Percentages show the potential change in mean flows as compared to the baseline period
(1980-2010) (mean value and deviation), DOWN and UP mean downward and upward trend,
respectively. Changes are for the period 2070-2100.
Mean flow
Low flows
High flows
Extreme
floods
-55% (±8%)
DOWN
DOWN
UP
4% (±18%)
UP (tendency)
DOWN
UP
Ain (V2712010)
15% (±19%)
UP
DOWN
DOWN
Arve (V0222010)
-46% (±11%)
DOWN
DOWN
UP
Loue
(U2654010)
-26% (17%)
UP
DOWN
UP
River
Rhone
(V3130020)
Saone
(U0610010)
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