Article
Reference
Modelling runoff in a Swiss glacierized catchment - part I:
methodology and application in the Findelen basin under a long-lasting stable climate
UHLMANN-SCHNEITER, Bastienne, JORDAN, Frédéric, BENISTON, Martin
Abstract
The complex topography of the Alps makes detailed hydrological modelling a real challenge. It is yet an essential task to improve the insight of hydrological processes in the context of intensification of renewable energy use and under the constraints of climate change. In this perspective and as a case study, the runoff of a small highly glacierized basin in the Swiss Alps – namely the Findelen catchment area – has been modelled with a hydrological model (Routing System 3.0; RS3.0). It is a conceptual model, based on object-oriented programming and it computes snow-melt, glaciers, infiltration and runoff processes. As input, it requires hourly air temperatures and precipitation, and the geomorphologic features of the catchment area and glacier. RS3.0 has proven to be very efficient in reproducing discharge. To evaluate the impacts of climate change on runoff – the final objective of the study addressed in a companion paper – a stochastic meteorological data generator has been developed to reproduce a sequence of air temperature and precipitation over more than one century. In this way, a continuous series of [...]
UHLMANN-SCHNEITER, Bastienne, JORDAN, Frédéric, BENISTON, Martin. Modelling runoff in a Swiss glacierized catchment - part I: methodology and application in the Findelen basin under a long-lasting stable climate. International Journal of Climatology , 2013, vol. 33, no. 5, p.
1293-1300
DOI : 10.1002/joc.3501
Available at:
http://archive-ouverte.unige.ch/unige:21644
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1 / 1
Int. J. Climatol.(2012)
Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/joc.3501
Modelling runoff in a Swiss glacierized catchment – part I:
methodology and application in the Findelen basin under a long-lasting stable climate
Bastienne Uhlmann,
a* Fr´ed´eric Jordan
band Martin Beniston
aaClimatic Change and Climate Impacts, University of Geneva, Carouge/GE, Switzerland
bE-dric.ch, Le Mont-sur-Lausanne, Switzerland
ABSTRACT:The complex topography of the Alps makes detailed hydrological modelling a real challenge. It is yet an essential task to improve the insight of hydrological processes in the context of intensification of renewable energy use and under the constraints of climate change. In this perspective and as a case study, the runoff of a small highly glacierized basin in the Swiss Alps – namely the Findelen catchment area – has been modelled with a hydrological model (Routing System 3.0; RS3.0). It is a conceptual model, based on object-oriented programming and it computes snow-melt, glaciers, infiltration and runoff processes. As input, it requires hourly air temperatures and precipitation, and the geomorphologic features of the catchment area and glacier. RS3.0 has proven to be very efficient in reproducing discharge. To evaluate the impacts of climate change on runoff – the final objective of the study addressed in a companion paper – a stochastic meteorological data generator has been developed to reproduce a sequence of air temperature and precipitation over more than one century. In this way, a continuous series of daily discharge values has been simulated by RS3.0 with the stochastic input data. This methodology has also enabled an assessment of the glacier response time to a stable climate. Indeed, if the climatic conditions of the standard reference period 1961-1990 were to be preserved throughout the 21st century, the simulation shows that the watershed would be slow to adapt: the glaciers would be balanced with the atmospheric conditions and the water discharge would reach a lower stable value in more than 40 years. However, the glacierized area would lose only 3.5% of its surface. Copyright 2012 Royal Meteorological Society
KEY WORDS discharge; glacier; hydrological modelling; Alps; stable climate; stochastic weather generator Received 2 December 2011; Revised 26 March 2012; Accepted 1 April 2012
1. Introduction
Because of their role in water storage and distribution, mountain environments are of key significance. Mod- elling the hydrology that characterizes such areas is useful not only to reproduce the complexity of the region itself but also because of its impacts on lowland areas for the water supplied in terms of irrigation, hydropower or drinking water. Alpine countries indeed benefit in sev- eral ways from the time lag of released discharge of winter precipitation locked as snow or ice, as well as from the enhanced precipitation related to the orographic effect (Hagg and Brown, 2005). In addition, glaciers that still cover a large part of the Alps have a strong influence on the amount of runoff in rivers originating in the mountains (Jasperet al., 2004; Farinotti et al., in press). Changes in their shape and mass due for instance to climate change can have immediate consequences, in particular economic (Braunet al., 2000; Romerio, 2008).
Mountainous watersheds are indeed very sensitive to tem- perature changes which affect rainfall, snowfall and melt- ing processes (Birsanet al., 2005).
∗Correspondence to: B. Uhlmann, Climatic Change and Climate Impacts, University of Geneva, Carouge/GE, Switzerland.
E-mail: Bastienne.Uhlmann@gmail.com
Other contributions found in the literature for instance by Schaefli et al. (2005), Abbaspour et al. (2007) or Viviroli et al. (2009) aim at modelling runoff. Some of these papers focus on largely ice-covered catchments (Paul et al., 2007; Konz and Seibert, 2010) and ice melt runoff dynamics (Magnussonet al., 2011; Kobierska et al., 2011). This paper lies within the same general framework and adds to the list of case studies that can improve the understanding of high mountain hydrology.
Besides, this study aims also at quantifying the effect of glacier imbalance on present discharge and at analysing how the system would evolve under stationary climate.
The first objective of the paper is therefore to investi- gate the current hydrological regime of a highly glacier- ized catchment area in the Swiss Alps. A hydrological model has been used to simulate runoff for the Finde- len watershed; this is part of the Grande Dixence com- plex, a much larger basin whose discharge is largely exploited for electricity production. The calibration and the performance of the model have been assessed through quantitative measures of its hydrographs and by means of various efficiency criteria (Legates and McCabe, 1999;
Krause et al., 2005).
The second objective is to prepare the study of assessing runoff in a warmer climate. The analysis of
B. UHLMANNet al.
Findelen glacier Outlet
Findelen watershed 45°58'N 1 km
SWITZERLAND
Figure 1. Map of Switzerland showing the Findelen catchment area.
the impact of climate change on the Findelen catchment area has been conducted in a companion paper (Uhlmann et al., this issue). As described by Braun et al. (2000), each timescale needs to be considered when exploring the influence of global warming on runoff of a particular basin. The daily variations in weather for a given region of complex topography are indeed as important as the sequence of long-term atmospheric conditions that can affect the mass balance and spatial extent of a glacier for instance. To keep this refinement, an existing stochastic weather generator (Perroud and Goyette, 2009) of hourly atmospheric data has been further developed to simulate a series of more than one hundred years. The generated values have then been used as inputs for the hydrological model, reproducing a theoretical ‘stable’ climate: the analysis of the watershed under such circumstances can give indications on the hydrological evolution that would be expected if the current warming trends were to cease (i.e. if climate were to remain constant over coming decades).
Finally, as established by J´ohannesson et al. (1989), Oerlemans (2005) or Hay and Elliott (2007), glaciers’
response times to be in equilibrium with the atmospheric conditions may vary from years to decades. This method- ology enables thus a decoupling of the glacier reaction from the current observed climate trend and a quantifica- tion of this response time for Findelen glacier. The latter part of the study will therefore report on long-term runoff trends and glacier evolution for a ‘stable climate’.
2. Experimental setup 2.1. Study area
The Findelen basin is located in the southern part of the Canton of Valais in the Swiss Alps, close to Zermatt (Figure 1). Its altitude ranges from 2439 to 4190 m and its surface area is 21.18 km2. Despite the fact that it represents only about 5% of the large Grande Dixence watershed, its interest lies in that 73% of the basin is
ice-covered by Findelen Glacier, which is one of the 20 largest glaciers in Switzerland. Therefore, the Findelen basin is a valuable example of a basin with runoff dominated by ice meltwater.
2.2. Data
Hourly air temperatures and precipitation needed as input for the hydrological model are provided by four neighbouring stations (Sion, Vi`ege, Evol`ene and Zermatt) of the automatic ANETZ network of the Swiss weather service, MeteoSwiss. Extended time series are available up to now, but only 10 years (1982–1991) cover the period prior to the intense warming trend of the past 20 years. As the principal aim of the study is to model runoff that is representative of the baseline climate (1961–1990), only the data for the years 1982–1991 were selected. The annual mean values for the baseline climate in Zermatt are 3.5°C for temperature and a sum of 611 mm for precipitation. Observed hourly discharge data at the outlet were provided by the hydropower company Grande Dixence S.A. During winter, there is no discharge, whereas the flows can reach a peak of discharge of about 12 m3/s in summer. The mean yearly runoff approximates 1.25 m3/s for the baseline climate period. A digital elevation model of the area with a resolution of 25 m (DHM25) has been obtained from the Swiss Federal Office of Topography. The Laboratory of Hydraulics, Hydrology and Glaciology (VAW) at ETH- Zurich provided also flow velocities estimations as well as a DHM25 of the bedrock, enabling the extractions of values for ice thicknesses for the years 1981 and 1990.
2.3. Hydrological model
The hydrological model used in this study, Routing Sys- tem 3.0 (RS3.0), has been made available by the engi- neering firm E-dric.ch (www.e-dric.ch). It is a determin- istic numerical tool using an object-oriented approach (Hern´andez, 2007; Jordan, 2007). It also simulates glacier
Copyright2012 Royal Meteorological Society Int. J. Climatol.(2012)
Bedrock Glacial band i+1
Glacial band i
Snow
Glacial band i-1 (5)
(1)
(2) (3)
(4) Glacial
band i+1
Glacial band i
Glacial band i-1 S
U
L
h
(a) (b)
Figure 2. Three-dimensional scheme of the glacial bands modelled by RS3.0 (a) and diagram of the glacier sub-model (b).
surface area and thickness as model outputs. The consid- ered processes are the spatial interpolation of the temper- ature and precipitation, the evapotranspiration, the snow melt, the glacier melt, the soil infiltration and the sur- face runoff. RS3.0 is consequently composed of a snow, a glacier, an infiltration and a runoff sub-model and consists in an extension of the GSM-SOCONT Model (Schaefli et al., 2005). A short description of the four sub-models is given below where the enhancements of RS3.0 compared to the published core model will be out- lined. In the previous version of the hydrological model, the glacier mass was constant and unlimited, as it was unrelated to melt and no mass transfer of snow to ice was computed. Besides, the general water balance was mainly adjusted by glacier melt and the parameteriza- tion of evapotranspiration was rudimentary. Finally, each object in the model had a uniform calibration. One limi- tation of RS3.0 is that it does not consider solar radiation in its formulation.
The Findelen watershed is separated in three sub- basins, corresponding to the three parts of Findelen Glacier. These parts are further divided into 300 m glacial and non-glacial elevation bands that can be, henceforth in RS3.0, calibrated separately. A spatial interpolation of the input meteorological variables is computed for the
‘centre of gravity’ of each elevation band according to an inverse-distance weighting method (Shepard, 1968).
The interpolation also integrates a vertical linear lapse rate both for temperature and precipitation. In the present study, discharge simulations by RS3.0 are carried out at an hourly time step but archived daily.
The snow sub-model computes the evolution of the snow pack as a function of temperature and precipita- tion with a degree–day equation. It is composed of two reservoirs that represent the snow stock and the water content of snow respectively. Thus, the snow melt gen- erates an equivalent precipitation that is used as an input variable by the soil infiltration or glacier sub-models.
Without snow, precipitation is directly transferred to the infiltration sub-model.
The glacier sub-model, when the basin becomes snow free, begins to produce water discharge with a degree–day relationship as well. This sub-model was
improved by integrating an approach that is mass con- serving, transfers the snow mass to the ice mass and computes the gravity flow of the glacier. The scheme of the glacial bands is illustrated in Figure 2a together with the diagram of the glacier sub-model (Figure 2b) where the numbers refer to the expressions stated hereafter. The mass transfer VNGL in m3 from the snow pack to the glacier is proportional to the snow height present on the glacier band and is computed as follows:
VNGL =AGLN×HN×S×t (1) where AGLN, degree–day coefficient of transformation of snow into ice [ms−1 m−1]; HN, snow height [m];
S, glacier surface [m2]; t, time step [s]. The glacier mass transferred to the downstream glacial elevation band
Vi,down in m3 is the product of speed, height and width
of the upstream elevation band:
Vi,down=U×hi+hi−1
2 ×Li +Li−1
2 ×t (2)
Vi,in=Vi+1,down (3)
where U, glacial flow velocity [m/s];hi, ice thickness of theith band [m];Li, width of theith band [m]. The melt water volumeVi,outin m3 is defined with the expression:
Vi,out=AGL×(T −Tc)×S×t (4)
where AGL, degree–day glacier melt coefficient [ms−1
°C−1]; T, air temperature [°C]; Tc, critical ice melt temperature [°C]. As a result, the general equation of glacier mass variation for an elevation band is the following:
V =VNGL+Vin−Vout−Vdown (5) The resulting glacier discharge is added to the final flow at the outlet of the catchment and the glacier surface and thickness is modified at each time step and for each elevation band.
Without ice on the elevation band, potential evapo- transpiration (PET) and equivalent precipitation – corre-
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sponding to the sum of liquid and snow melt precipita- tion – are introduced in the linear infiltration sub-model.
PET is calculated according to the Turc method (Turc, 1961). This sub-model computes the slow contribution of soil and underground water. It has two possible out- flows, the base flow and actual evapotranspiration that are dependent on the soil saturation.
Finally, the surface runoff sub-model computes the quick flow component by a non-linear storage-discharge relationship and by solving a kinematic wave on an inclined plane. The main parameter of this sub-model is the surface roughness. The total runoff from the non ice-covered part of the catchment corresponds to the sum of the quick and base flow. All the contributions of the elevation bands are added to provide the total discharge at the outlet of the watershed. Consideration of evapotran- spiration and glacier mass, as well as precipitation and snow melt, enables a complete assessment of the different runoff contributions.
Many parameters can be potentially calibrated in the different sub-models. It is therefore a tedious task to test every combination of parameters for every elevation bands. As a consequence, analyses have been done to select constant values for a set of parameters and a manual calibration procedure has been followed for the remaining ones (Table I), thanks to the rather non- simultaneous flow processes (Jordan, 2007). For example, the snow melt parameters can be isolated in spring and those of ice from July to September. The adjustment order of parameters falls thus within the following steps: first ensuring the spring balance (snow melt), then the summer one (ice melt), adjusting the annual balance (infiltration) and finally set the model nervousness (quick flow).
Despite uncertainties and limitations discussed in other studies (Jordan, 2007; Schaefliet al., 2007; Tobinet al., 2011), RS3.0 has proved to be successful in modelling water discharge (Jordan et al., 2008; Hern´andez et al., 2010; Jordanet al., 2010). Its low data input requirements as well as its ice and snow sub-models make it convenient for the analysis of long-time series discharge in a mountainous environment.
2.4. Stochastic weather generator
In order to assess the response of water discharge and the extent of the glacier to a long lasting stable climate, as well as to assess the impact of climate change on runoff – the complementary objective of the study addressed in a companion paper (Uhlmann et al, this issue) – datasets of hourly temperature (Tsto) and precipitation (Psto) have been created using a stochastic weather generator for the four weather stations. It is based on previous work of Perroud and Goyette (2009) and further expanded to generate long-term precipitation.
The length of these series extend for more than a century, enabling a spread large enough to reproduce meteorological data representative of the conditions of the baseline climate (1961–1990) through to the end of the 21st century. The data have been generated in
Table I. Parameter calibrated in RS3.0.
Sub- model
Parameter Unit Description
Snow AN ms−1 °C−1 Degree-day snow melt coefficient
AGLN mm j−1 m−1 Degree-day coefficient of transformation of snow into ice
Glacier AGL ms−1 °C−1 Degree-day glacier melt coefficient
KGL l/s Coefficient of linear glacier reservoir KN l/s Release coefficient of
linear snow reservoir Infiltration hmax m Capacity of infiltration
reservoir
k l/s Release coefficient of infiltration reservoir Runoff Ks m1/3 s−1 Strickler coefficient
order to fit the statistical properties of the observations in terms of monthly mean, monthly mean intra-day standard deviation and monthly mean inter-day standard deviation of temperature and precipitation. Despite the fact that the results show more disparities for precipitation because of the inherently fluctuating character of the variable from one year to another, observations and generated random data show a rather good agreement.
The general concept that governs the generator is based on the Markov process (Gardiner, 1985): it chooses each hourly value according to the conditions that precedes it. In addition, as temperature follows a normal distri- bution, values close to the mean will be selected more frequently. Likewise, the log-normal distribution of pre- cipitation induces a more frequent selection of lower values. To preserve the consistency of the atmospheric conditions, the procedure used by the generator has also been extended to force a link between temperature and humidity: for example, a warm air mass must be able to contain more moisture than a cold air mass. How- ever, as no direct correlation exists between Tsto and Psto, the series of Tsto is randomly created in associa- tion with a series of dew point temperature (T dsto) as a first step. Subsequently, the hourly value ofPstois null if Tsto−T dsto>0 and a positive hourly value ofPstois ran- domly chosen if Tsto−T dsto≤0. Similarly to preserve the consistency of the weather pattern, each series is cre- ated conjointly for the four weather stations. The control station is Zermatt as it is the closest to the investigated site and exerts the greatest influence in the hydrological model. It implies that the hourly values of the other sta- tions are randomly selected within their own distribution but based on the probability of occurrence of the values for Zermatt. As an analysis of the evolution of extreme events lies beyond the framework of the present study, all values are generated within the bounds of the observed datasets.
Copyright2012 Royal Meteorological Society Int. J. Climatol.(2012)
Table II. Values of efficiency criteria between the observed and simulated discharge for ten years of calibration and validation.
Year R2 N Nln V ol
1982–1983 0.93 0.92 0.92 1.05
1983–1984 0.85 0.83 0.91 1.07
1984–1985 0.88 0.86 0.77 1.06
1985–1986 0.89 0.89 0.91 0.98
1986–1987 0.83 0.81 0.88 0.99
1987–1988 0.91 0.89 0.72 0.84
1988–1989 0.96 0.85 0.74 1
1989–1990 0.9 0.9 0.78 0.9
1990–1991 0.87 0.87 0.89 0.96
1991–1992 0.91 0.9 0.81 1.06
Mean 0.9 0.87 0.83 0.99
3. Results and discussion 3.1. Calibration and validation
RS3.0 has simulated 10 years of daily runoff with observed input: it has been calibrated for the hydrolog- ical years 1982–1983 to 1985–1986 and then validated over the years 1987–1992. Efficiency criteria that reflect the adequacy between observed and simulated flows have been computed, namely the Pearson coefficient of deter- mination R2, the Nash–Sutcliffe criteria N (Nash and Sutcliffe, 1970) with its logarithmic transformationNln, and the volume balanceV ol (Table II). N compares the error of the hydrological model to the one resulting from the average of the observed data; an efficiency of 1 would correspond to a perfect match between observed and pre- dicted data.Nln is also calculated, as it avoids giving too much weight to extreme values as described by Viviroli et al. (2009). Finally, V ol measures the ratio between the simulated and observed discharge. The average val- ues over ten years for R2 and N equal 0.9 and 0.87, respectively. When considering years individually, both criteria always reach values higher than 0.8.Nln exhibits relatively lower values indicating that discrepancies are
more frequent for medium flows. Whereas the meanV ol score is close to 1, the variability between the differ- ent years is higher than for the other criteria. However, the modelled discharge is in close agreement with the observed one. The hydrograph reproduced for the hydro- logical year 1988–1989 illustrates the good adequacy between the observed and simulated runoff (Figure 3).
The ice melt contribution to total runoff can also be assessed by RS3.0. It equals 22 % when averaged on the ten-year period, while snow melt and precipitation constitute the remaining components of water balance simulated by RS3.0. These results are in close agreement with those found by Verbuntet al. (2003) or Weberet al.
(2010) for high mountain catchments.
In order to analyse the ability of the model to reproduce observed discharge statistics (mean and variance) when driven by the stochastic weather data, 10 decades of Tsto andPstosequences have been generated. The simulations conducted with these series provide 10 hydrographs of decadal mean daily runoff. Each of them reproduces accurately the dominant patterns of observed discharge and lies inside the daily extrema found within the 10- year measurements (Figure 4). The major disagreements are found for the mid-summer months but if simulated values are generally slightly under-estimated, they are still found between the bounds of observations.
Therefore, the efficiency of the hydrological model has been established with observed and stochastic input data and RS3.0 can be used with stochastic input sequences to simulate water discharge over a longer period.
3.2. Discharge and glacier in a stable climate
Simulation of daily runoff with stochastic input data has been conducted to the end of the 21st century (Figure 5, black curve). The graph illustrates the average yearly discharge of the Findelen catchment keeping atmospheric conditions identical to the baseline climate. The figure illustrates the fact that the discharge first slowly declines during more than 40 years (further stated as the ‘decrease
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
0 2 4 6 8 10 12
Discharge (m3/s)
Time (day) Observation
Simulation
Figure 3. Example of observed (black curve) and simulated (dashed curve) discharge for the hydrological year 1988–1989.
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Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep
0 2 4 6 8 10 12 14 16
Time (month) Observed mean
Observed minimum and maximum Stochastic mean
Discharge (m3/s)
Figure 4. Mean daily discharge per decade obtained from a 100-year simulation driven with random temperature and precipitation (dotted line) compared to mean and extreme daily discharge obtained from a 10-year simulation driven with observed temperature and precipitation
(1982–1991).
0.50 0.75 1.00 1.25 1.50
1 2 3 4 5 6 7 8 9 10 11
Time (decade)
Average annual discharge (m3/s) Glacier surface (m2)
20×106 19×106 18×106 17×106 16×106 15×106 14×106 13×106
Figure 5. Discharge and total glacier surface obtained with stochastic weather data in RS3.0 during 11 decades: in black, smoothed averaged annual discharge; surface in grey, glacier surface area.
period’) before starting to stabilize at lower discharge levels (stabilization period). The difference between the average discharge of the first three decades and the one of the last three decades equals −15%. This decrease was expected since a glacier is rarely in equilibrium with climate – and this was indeed not the case during the baseline climate. Therefore, the contribution of the ice- melt runoff decreases regularly until the entire system finds a new equilibrium with the stable climate. From about the beginning of the fifth decade onwards, the melt water of this idealized glacier contributes little to runoff, compared to snow-melt and rain. As a consequence, the discharge quantities depend mostly on the variability of weather patterns at the end of the simulation and less on the presence of the glacier. Concerning the year- to-year variations, no marked trend is to be observed.
This confirms the fact that no forcing has been added to input data in the hydrological model that could have induced more or less variability on discharge, thereby demonstrating that RS3.0 does not drift when run over a long period.
In order to analyse the potential change in seasonality, the average daily runoff for the control run, the decrease and stabilization period has been compared (Figure 6).
The larger amount of water available for the control run throughout the year is clearly outlined. Besides, the timing of the snow melt season during late spring remains largely synchronous between the three curves.
On the contrary, less water is made available from ice melting during the decrease period and especially during the stabilization period in summer and at the beginning of fall: the influence of the glacier is less preponderant and most of the variations can be attributed to the given atmospheric conditions. No other major shift in seasonality can be observed during the three simulated periods, while the general convex shape of the curves is preserved throughout the simulations.
Some aspects of the morphology of Findelen Glacier can also be analysed. In a stable climate, the ice cover tends to find its optimal configuration and evolves towards an established geometry. Therefore, the glacier surface decreases until it reaches a new level of
Copyright2012 Royal Meteorological Society Int. J. Climatol.(2012)
Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep 0
1 2 3 4 5 6 7 8
Time (day) Control run
Decrease period Stabilization period
Discharge (m3/s)
Figure 6. Average daily discharge for the control run (black curve), the decrease period (dotted curve) and the stabilization period (grey curve).
stabilization (Figure 5, grey surface). From this point on, the equilibrium line altitude has theoretically reached a steady-state and, as a consequence, the glacier neither grows nor shrinks. According to RS3.0, the glacier loses 3.5% of its surface in about 40 years before stabilizing.
This rather long response time value corresponds to other findings for middle-size glaciers (Leysinger Vieli and Gudmundsson, 2004; Joerin et al, 2006; Hoelzle et al., 2007; Stahlet al., 2008). The close relationship between the evolution of the glacier surface and that of the water discharge is clearly seen by comparing the curves of both graphs.
4. Conclusions and outlook
Despite the complex topography of the Alps, the hydro- logical model RS3.0 has demonstrated its ability in simu- lating water discharge. Not only the favourable efficiency criteria but also the visual adequacy of the observed and simulated runoff curves attests to the quality of the model runs for the highly glacierized Findelen basin. These results were naturally the prerequisite for exploring the implications for runoff and glacier area/volume if the atmospheric conditions of the baseline 1961–1990 cli- mate were to last for more than one century.
The weather generator used for this purpose has gener- ated a long-term series of temperature and precipitation that have successfully reproduced not only the general statistical properties of the observed weather distributions but also those of the water discharge quantities. RS3.0 was therefore run with stochastic generated sequence of meteorological data over more than a century and has shown consistency throughout the long period of simula- tion. The results indicate that discharge would decrease during the first four to five decades before stabilizing to the end of the studied time period. The glacier sur- face follows this same general trend. This methodology enables therefore a quantification of the response time
for Findelen Glacier to find its balance with the climate if the atmospheric conditions remain stable. In such a context, it would need a little less than half a century to achieve equilibrium between runoff or glacier vol- ume and climate. However, a limited decrease in runoff of 15% is observed and the glacier loses only 3.5% of its surface. The simulations also indicate that discharge resulting from glacier melt is rarely in equilibrium with the current climate.
The findings presented here contribute to the founda- tion of a companion paper (Uhlmann et al., this issue) that investigates the impacts of climate change on runoff and glacier evolution in the Findelen catchment area. The same kind of study applied to the entire basin of the Grande Dixence, at an hourly resolution for runoff and taking into account solar radiation in the model or the impacts of extreme events could be an area of future investigation to provide further information of use to water managers and hydropower utilities.
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