Model input data

In order to delineate a catchment, digital terrain model (DTM), stream network and catchment divide are required. Data on the land use type, vegetation or soil types can facilitate establishing prior ranges of some parameters (e.g. CN, CAN^max, soil-related parameters).

Data required for a model run include:

 Precipitation depths [mm Δt ^-1],

 Potential evapotranspiration [mm Δt ^-1],

 Temperature [°C],

 Observed flows [m³/s].

13In this research impact of model structure on the Pareto-optimaltimal parameter temporal variability is analysed (chapter 1.6). Therefore, the results of the distributed model version are compared to the results of the semi-lumped one.

Input time series should be (dis)aggregated to match the computational time step (e.g.

mean daily temperatures or flows).

Semi-lumped versions of the model. Since topography of the catchments considered in this research (chapter 2.6) considerably varies in elevation, model forcings (such as precipitation or temperature) are adjusted for elevation and different input vectors are estimated for every elevation zone of a catchment.

In this research, every catchment is divided into an arbitrary number of elevation zones of approximately equal spans. Each elevation zone is represented by its mean elevation, total area and mean slope. Precipitation depths and temperature are estimated for every zone, depending on the difference between the mean zone elevation and the reference altitude zMS. The reference altitude zMS is assessed as the weighted mean elevation of the meteorological stations following the methodology presented by Panagoulia (1995):

MS

where Ns is number of meteorological stations, zi and ωi are the elevation and the weight of the i^th meteorological station, respectively. Station weights are obtained by applying the Thiessen polygon method.

In general, temperature exhibits a rather constant lapse rate i.e. decrease with elevation, while the increase in precipitation depths lessens with the elevation (Bardossy & Das, 2008; Hundecha & Bárdossy, 2004). However, the constant gradients of both variables with elevation are adopted in this research.

Mean precipitation depth

P





can be estimated based on the slope of a linear regression between annual precipitation depths and meteorological station elevations. Some recommendations on increase in precipitation with elevation may be found in the literature. For example, Uhlenbrook et al. (2000) estimated an increase of 6% / 100 m, while Seibert and Vis (2012) recommended increase of 10% / 100 m for simulations.

Similarly, mean temperature in an elevation zone is calculated as:

MS

MS 100 lapse

z zc

T T  ^ T (2.1.92)

where TMS is the mean catchment temperature calculated by applying the Thiessen polygon method. T^lapse is a temperature lapse rate (in °C/100 m). The value of this parameter is commonly assumed to be approximately -0.6 °C/100 m (e.g. U.S. A.C.E., 1994; Uhlenbrook et al., 2000; Seibert and Vis, 2012).

In this research α and T^lapse are free model parameters to be estimated in the calibration procedure. Their prior ranges are assessed for every catchment according to long-term observations at the meteorological stations.

The PET time series can be calculated externally and introduced into the model as the input time series, or within the model following the Hargreaves method (Hargreaves and Samani, 1982; Lu et al., 2005, Oudin et al., 2005; Trajkovic and Kolakovic, 2009; Tabari et al., 2011). To account for changes with elevation, PET rates are estimated for every elevation zone independently, using the obtained mean zone temperatures. Since only the temperature data were available for PET assessment, the PET rates had to be calculated by some of the temperature- or radiation-based methods, which have modest data requirement (Maidment, 1993).

Oudin et al. (2005) examined influence of the method for PET assessment on performance of hydrologic models. They simulated runoff at a lot of catchments using 27 methods for PET estimation and four lumped, conceptual hydrologic models. They demonstrated that the use of the temperature- or radiation-based methods may result in the same model performance as the use of more complex methods (e.g. Penman-Monteith). For example, models that used the McGuinness, Jensen-Haise (radiation-based) or Hamon methods

(temperature-based) outperformed models that used the Penman-Monteith method both in calibration and validation periods. Considering the results of Lu et al. (2005), Trajkovic and Kolakovic (2009), Rao et al. (2011) and Tabari et al. (2011), the Hamon method is selected for use in this study. Application of this method for hydrologic modelling purposes is reported in the literature by Fenicia et al. (2008), Gharari et al. (2012); Gharari et al. (2013) and Osuch et al. (2014).

According to the Hamon method (Hamon, 1961), daily PET rates are calculated for every elevation zone as:

2

12 exp 16

Ta

PET DL   (2.1.93)

where Ta is a mean daily temperature in an elevation zone and DL is a daytime length (time from sunrise to sunset, in h day^-1), which depends on latitude φ and declination of the Sun δ, both in expressed in radians (Spitters et al., 1986):

 

24arccos tan ( ) tan ( )

DL  

   (2.1.94)

 

0.4093sin 2 284

365 Dⁿ

 ^  ^ (2.1.95)

where Dn denotes a day of a year.

In the semi-lumped versions of the 3DNet-Catch model vertical water balance (surface runoff and percolation into the groundwater reservoir) is simulated independently for every elevation zone by using a single parameter set common to all zones, with precipitation, temperature and PET rates estimated for each particular zone. Simulated surface runoff and percolation generated in individual zones are summed and routed through the reservoirs at the catchment outlet.

In this research, however, the catchment elevation zones are considered HRUs. The input data obtained for semi-lumped versions of the model are therefore used in the distributed version as well.

Figure 28. The inverse-distance weighting for estimating mean precipitation depths or temperature for a HRU in the 3DNet-Catch model.