Figure 2.9: Overview of the processes incorporated in the Variable Infiltration Capacity (VIC) mo- del. Source: http://vic.readthedocs.org.
TheVICmodel(Liang et al.,1994,1996)wasinitiallydevelopedforlargescaleapplications,
to couple climate models to hydrological processes. It is a land-surface model that solves both the water and the energy balance. Sub-grid land use variability is accounted for by providing vegetation tiles that each cover a certain percentage of the total surface area. Three different types of evaporation are considered by the VIC model: Evaporation from thebaresoil(Eb), transpirationbythevegetation(T), consideredpervegetationtile, and evaporation from interception (Ei). The total evapotranspiration is the area-weighted sum of the three evaporation types. The fraction of land that is not assigned to a partic- ular land use type is considered to be bare soil. Evaporation from bare soil only occurs at the top layer (layer 0). If layer 0 is saturated, bare soil evaporation is at its potential rate. Potential evaporation is obtained with the Penman-Monteith equation. If the top layer is not saturated, an Arno-formulation (Francini and Pacciani, 1991), which uses the structure
of the Xinanjiang model (Zhao et al., 1980), is used to reduce the evaporation.
For the upper two soil layers, the Xinanjiang formulation (Zhao et al., 1980) is used to de-
an area. Surface runoff occurs when precipitation intensity exceeds the local infiltration capacity of the soil. Moisture transport from layer 0 to layer 1 and from layer 1 to layer 2 is gravity-driven and only dictated by the moisture level of the upper layer. It is assumed thatthereisnodiffusionbetweenthedifferentlayers. Layer2characterizesthelongterm soilmoistureresponse,e.g. seasonality. Itonlyrespondstoshort-termrainfallwhenboth top layers are fully saturated. The gravity-driven moisture movement is regulated by the Brooks-Corey relationship: Qi,i+1=Ksat,i W i−Wr,i Wic−Wr,i expti . (2.8)
Qi,i+1is the flow (L T-1) from layerito layeri+ 1.Ksat,iis the saturated hydraulic con- ductivity of layeri,Wiis the soil moisture content in layeri,Wicis the maximum soil moisture content in layeri,Wr,ithe residual moisture content in layeri. The exponent of the Brooks-Corey relation, expti, is defined as follows:B2p+3, in whichBpis the pore size distribution index. The exponent as a whole is often calibrated.
Base flow is determined based on the moisture level of layer 2. Base flow generation fol- lows the conceptualization of the Arno model (Francini and Pacciani, 1991). This formula-
tion consists of a linear part (lower moisture content regions) and a quadratic part (in the higher moisture regions). Base flow is modelled as follows:
Qb= dsdm wsW2c ·W2 if 0≤W2< wsW c 2 dsdm wsW2c ·W2+ dm−dswdm s W2−wsW2c Wc 2−wsW2c g if W2≥wsW2c (2.9)
In this equation,Qbis the total base flow over the model time step,dmis the maximum base flow,dsthe fraction ofdmwhere non-linear base flow begins,wsis the fraction of soil moisture where non-linear base flow starts.W2cis the maximum soil moisture con-
tent in layer 2, calculated as a product of porosity and depth. The exponentgis by default
set to two (Liang et al., 1996).
Since the grid-size of the VIC model is often larger than the characteristic scale of snow processes, sub-gridvariabilityisaccountedforbymeansofelevationbands. Foreachgrid cell the percentage of area within certain altitude ranges is provided. The snow model is applied for each elevation band and land use type separately; the weighted average pro- vides the output per grid cell. This output consists of the Snow Water Equivalent (SWE) andthesnowdepth. Thesnowmodelisatwo-layeraccumulation-ablationmodel,which solves both the energy- and the mass balance. At the top layer of the snow cover the en- ergy exchange takes place. A zero energy flux boundary is assumed at the snow-ground interface.
In order to apply VIC in a distributed fashion, a routing model is required to transport the water between the different grid cells. Therefore, the mizuRoute routine (Mizukami
2.3. Parameter sampling strategy
et al., 2016) was implemented. The routing is based on the same concept as the default
VIC-routing developed byLohmann et al.(1996), except that in mizuRoute the response is
determined per sub-catchment instead of per grid cell. With the linearised St. Venant equation,
∂Q ∂t =D ∂2Q ∂x2 −C ∂Q ∂x, (2.10)
water is transported from the boundary of the sub-catchment to the next sub-catchment and finally to the outlet. In Equation 2.10,D(L2T-1) represents the diffusion coefficient
andC(L T-1) the advection coefficient.
In the default VIC routing ofLohmann et al.(1996), water is routed per grid cell and there-
fore dependent on the spatial resolution of the VIC model. By applying mizuRoute based on pre-defined sub-catchments (~1 km2), the effect of the spatial resolution on the rout-
ing process is excluded.
2.3
Parameter sampling strategy
For the VIC model, described in the previous section, a GLUE-based approach (Beven and Binley, 1992) was employed for parameter sampling. This approach requires that the mo-
del is run with a large number of parameter sets (preferably covering the complete pa- rameter space). Subsequently only the behavioural runs are selected. Different defi- nitions for ‘behavioural’ can be adopted, dependent on the goal of the study. In Chap- ter 4 for example, a different definition is used than in Chapter 6, because in the first one mainly a sensitivity analysis is conducted, while in the latter model confirmation is needed to estimate model credibility.
The VIC model has a large number of parameters, divided over three sections: soil pa- rameters, vegetation parameters, and snow parameters. Sampling all parameters com- pletely would be a heavy computational burden (see Figure 2.10a for a 3-parameter mo-
P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3 P3 P2 P1 P2 P3 P3 P2 a b c d
Figure 2.10: Parameter sampling strategy. (a) Example situation when sampling for a model with three parameters. (b) Sensitivity analysis can be conducted to decrease the dimensions of the sam- pling space. (c) Latin Hypercube sampling is structured and more efficient: one sample in each row and each column, as indicated with the bands. The number of samples has to be determined beforehand. (d) Hierarchical Latin Hypercube sampling allows to extend the sample if necessary, while conserving Latin Hypercube structure.
del example). Therefore, several strategies have been combined to make the sampling more efficient. The number of parameter samples needed to cover the full parameter space can decrease significantly by selecting only the most sensitive parameters (see Fig- ure 2.10b), as described in the next section. The number of parameter sets can be further reduced by choosing an efficient sampling strategy (Figure 2.10c and d).