Because of their role in water storage and distribution, mountain environments are of key significance. Modelling 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 several 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 (Jasper et 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 (Braun et al., 2000; Romerio, 2008). Mountainous watersheds are indeed very sensitive to temperature changes which affect rainfall, snowfall and melting processes (Birsan et al., 2005).
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 (Magnusson et 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 investigate the current hydrological regime of a highly glacierized catchment area in the Swiss Alps. A hydrological model has been used to simulate runoff for the Findelen watershed; this is part of the Grande Dixence complex, 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 the impact of climate change on the Findelen catchment area has been conducted in a companion paper (Uhlmann et al., 2012). 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 Jóhannesson 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 methodology enables thus a decoupling of the glacier reaction from the current observed climate trend and a quantification 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.
Hourly air temperatures and precipitation needed as input for the hydrological model are provided by four neighbouring stations (Sion, Viège, Evolène 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 System 3.0 (RS3.0), has been made available by the engineering firm E-dric.ch (www.e-dric.ch). It is a deterministic numerical tool using an object-oriented approach (Hernández, 2007; Jordan, 2007). It also simulates glacier surface area and thickness as model outputs. The considered processes are the spatial interpolation of the temperature and precipitation, the evapotranspiration, the snow melt, the glacier melt, the soil infiltration and the surface 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 outlined. 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 parameterization of evapotranspiration was rudimentary. Finally, each object in the model had a uniform calibration. One limitation 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 precipitation 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 generates 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 conserving, 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 ΔVNGL 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:
where AGLN, degree–day coefficient of transformation of snow into ice [ms−1 m−1]; HN, snow height [m]; S, glacier surface [m2]; Δt, time step [s]. The glacier mass transferred to the downstream glacial elevation band ΔVi, down in m3 is the product of speed, height and width of the upstream elevation band:
where U, glacial flow velocity [m/s]; hi, ice thickness of the ith band [m]; Li, width of the ith band [m]. The melt water volume Vi, out in m3 is defined with the expression:
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:
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 evapotranspiration (PET) and equivalent precipitation—corre- sponding to the sum of liquid and snow melt precipitation—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 outflows, 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 evapotranspiration 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).
Table I. Parameter calibrated in RS3.0
Degree-day snow melt coefficient
mm j−1 m−1
Degree-day coefficient of transformation of snow into ice
Degree-day glacier melt coefficient
Coefficient of linear glacier reservoir
Release coefficient of linear snow reservoir
Capacity of infiltration reservoir
Release coefficient of infiltration reservoir
Despite uncertainties and limitations discussed in other studies (Jordan, 2007; Schaefli et al., 2007; Tobin et al., 2011), RS3.0 has proved to be successful in modelling water discharge (Jordan et al., 2008; Hernández et al., 2010; Jordan et 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, 2012)—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 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 distribution, values close to the mean will be selected more frequently. Likewise, the log-normal distribution of precipitation 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. However, as no direct correlation exists between Tsto and Psto, the series of Tsto is randomly created in association with a series of dew point temperature (Tdsto) as a first step. Subsequently, the hourly value of Psto is null if Tsto − Tdsto > 0 and a positive hourly value of Psto is randomly chosen if Tsto − Tdsto≤0. Similarly to preserve the consistency of the weather pattern, each series is created 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 stations 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.
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 hydrological 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 determination R2, the Nash–Sutcliffe criteria N (Nash and Sutcliffe, 1970) with its logarithmic transformation Nln, and the volume balance Vol (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 predicted data. Nln is also calculated, as it avoids giving too much weight to extreme values as described by Viviroli et al. (2009). Finally, Vol measures the ratio between the simulated and observed discharge. The average values 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 mean Vol score is close to 1, the variability between the different 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 hydrological year 1988–1989 illustrates the good adequacy between the observed and simulated runoff (Figure 3).
Table II. Values of efficiency criteria between the observed and simulated discharge for ten years of calibration and validation
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 Verbunt et al. (2003) or Weber et 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 and Psto sequences 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 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 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; Stahl et 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 hydrological model RS3.0 has demonstrated its ability in simulating 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 climate were to last for more than one century.
The weather generator used for this purpose has generated 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 simulation. 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 surface 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 volume 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 foundation of a companion paper (Uhlmann et al., 2012) 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.