To determine which parameters have the largest influence on the modelled discharge, a sensitivity analysis was conducted on a broad selection of parameters in the model (see Table 2.3). The parameter selection was made such that the main hydrological pro- cesses were represented and included 28 VIC parameters from the three different sec- tions. Sensitivity analysis was conducted using the Distributed Evaluation of Local Sensi- tivity Analysis (DELSA) method (Rakovec et al., 2014). DELSA is a hybrid local-global sen-
sitivity analysis method. It evaluates parameter sensitivity based on the gradients of the objectivefunctionforeachindividualparameteratseveralpointsthroughouttheparam- eterspace. Notethatthismethodonlyprovidesfirst-ordersensitivitiesandthusdoesnot account for parameter interaction.
A base set of 100 parameter samples was created. For each parameterkthat is accounted
for in the analysis, the base set of parameter samples is perturbed. In total, including the base set, this leads to (number of parameters+1)×100 parameter samples that need to
be evaluated. To save computation time, the sensitivity analysis was conducted on the lumped VIC model for the Thur. To study the effect of spatial scale on sensitivity, also two lumped models for sub-catchments of the Thur have been constructed: The Jonschwil catchment(495km2)andtheRietholzbachcatchment(3.3km2). TheRietholzbachcatch-
ment is nested inside the Jonschwil catchment, which is again nested in the Thur catch- ment(Figure2.4). Thethreecatchmentshavecomparablelanduse. Threeobjectivefunc-
Rietholzbach 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.5 1 Jonschwil 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.5 1 Thur 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 0.5 1 DELSA sensitivity [−] Parameter number 0.2 0.3 0.5 0.6 0.8 0.9 0.1 quantiles 0.7 0.4 hourly daily
Figure 2.11: DELSA parameter sensitivity (scaled from 0 to 1) for three nested catchments with a different size (Rietholzbach; 3.3 km2, Jonschwil; 493 km2, Thur; 1703 km2). The numbers on
thex-axis refer to the parameters in Table 2.3. The sensitivity as shown in this figure is based on NSE(Q) as objective function. Results are shown based on a daily and hourly time interval.
2.3. Parameter sampling strategy
Table 2.3: Description and bounds of VIC parameters that have been considered in the DELSA sen- sitivity analysis.
Parameter Units Lower
value Uppervalue Description Soil parameter file
1 bi - 10-5 0.4 Variable infiltration curve parameter
2 ds - 10-4 1 Fraction ofdmwhere non-linear base flow
starts
3 dm mm d−1 1 50 Maximum base flow
4 ws - 0.5 1 Fraction of maximum soil moisture where
non-linear base flow starts
5 c - 1 4 Exponent used in the base flow curve
6 expt0 - 4 30 Exponent of the Brooks-Corey drainage
equation layer 0
7 expt1 - 4 30 Exponent of the Brooks-Corey drainage
equation layer 1
8 expt2 - 4 30 Exponent of the Brooks-Corey drainage
equation layer 2
9 Ksat0 mm d−1 100 1000 Saturated hydrologic conductivity layer 0
10 Ksat1 mm d−1 100 1000 Saturated hydrologic conductivity layer 1 11 Ksat2 mm d−1 100 1000 Saturated hydrologic conductivity layer 2
12 Depth0 m 0.01 0.5 Thickness of soil layer 0
13 †Depth
1 m Depth0+0.1 Depth0+4 Thickness of soil layer 1
14 Depth2 m 0.1 4 Thickness of soil layer 2
15 bulk density0 kg m−3 1500 2685 Bulk density of soil layer 0 16 bulk density1 kg m−3 1500 2685 Bulk density of soil layer 1 17 bulk density2 kg m−3 1500 2685 Bulk density of soil layer 2
18 Wcr-FRACT0 - 0.30 0.47 Fractional soil moisture content at critical point layer 0
19 Wcr-FRACT1 - 0.30 0.47 Fractional soil moisture content at critical point layer 1
20 Wcr-FRACT2 - 0.30 0.47 Fractional soil moisture content at critical point layer 2
21 snow-rough m 5·10-5 0.5 Surface roughness of the snow pack
Vegetation parameter file
22 Root depth 0 m 0.1 3 Root zone thickness layer 0
23 Root depth 1 m 0.1 3 Root zone thickness layer 1
24 Root depth 2 m 0.1 3 Root zone thickness layer 2
Vegetation library file
25 rmin s m-1 30 300 Minimum stomatal resistance of vegetation
26 ?LAI - 0.7 1.3 Leaf Area Index
Global parameter file
27 Tmin ◦C -1.5 0.0 Minimumtemperatureatwhichraincanfall
28 †T
max ◦C Tmin+0.5 Tmin+1.5 Maximum temperature at which snow can fall
†Value of this parameter must be greater than the related parameter mentioned in the parameter boundaries.
tions were used to assess the sensitivity of the parameters: • The Kling-Gupta Efficiency (KGE) (Gupta et al., 2009):
KGE(Q)= 1−p(r−1)2+ (α−1)2+ (β−1)2, (2.11)
whereristhecorrelationbetweenobserveddischargeQoandmodelleddischarge
Qm,αis the standard deviation ofQmdivided by the standard deviation ofQo, andβis the mean ofQm(Qm) divided by the mean ofQo(Qo) .
• The Nash-Sutcliffe Efficiency (NSE) of the discharge to describe the model perfor- mance for the higher discharge regions (Nash and Sutcliffe, 1970):
NSE(Q)= 1− PT t=1(Q t o−Q t m) 2 PT t=1(Qto−Qo)2 = 2·α·r−α2−βn2, (2.12)
in whichβnis the bias normalized by the standard deviation.
• The Nash-Sutcliffe Efficiency of the logarithm of the discharge NSE(logQ) to test the model performance for low discharges (Krause et al., 2005).
The analysis showed that parameter sensitivity did not notably change over the assessed scales: thesameparameterswerefoundtobemostsensitive,butinaslightlydifferentor- der (see Figure 2.11). There are four parameters which, for all scales and for all objective functions, proved to be highly sensitive: The parameter describing variable infiltration (bi), the parameter that defines the fraction ofdmwhere non-linear base flow starts (ds), the maximum base flow (dm) and the exponent of the Brooks-Corey relation (B2p +3, expt1, see Equation 2.8). Other parameters that showed sensitivity in some cases were
the depth and bulk density of soil layer 1, the depth and bulk density of soil layer 2, and the rooting depth of layer 0. The selection of sensitive parameters closely resembles the results ofDemaria et al.(2007), who applied a sensitivity analysis on VIC over different
hydro-climatological regimes. Next to the four identified most sensitive parameters,De- maria et al.(2007) found that the depth of soil layer 1 (Depth1) was highly sensitive.