3.2. Data and methods
4.2.3. 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 snowmelt, 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 homogenous calibration.
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 archieved 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 4.2a together with the diagram of the glacier sub-model (Fig. 4.2b) 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 critical ice melt temperature [°C]. As a result, the ge neral equation of glacier mass variation for an elevation band is the following:
down
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 – corresponding 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.
Bedrock 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 4.1), 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; 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.
Table 4.1. Parameter calibrated in RS3.0.
Sub-model Parameter Unit Description
Snow AN m s-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 m s-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