in the ensemble mean of about 2 cm in groundwater and TWS compared to the standard model run (Fig. 6.2 a, b). To handle this, the PDF of the groundwater baseflow coefficient with 0.01 as mode and 0.006 and 0.1 as limits is modified to keep the difference between the ensemble mean and the standard model run less than 1 cm for total and individual water storage changes (Fig. 6.2 c, d). The mode of the new triangular distribution is empirically determined as 0.006 with 0.006 and 0.018 being the lower and upper limit values. In this case, the mode and the lower limit of the distribution coincide. This modified PDF results in lower baseflow and more groundwater storage, which might be a good choice given that WGHM tends to underestimate seasonality. However, a selection of other PDFs would have been possible.
In addition, the a priori limits of the triangular distribution of wetland depth are modified from 1 m and 20 m to 0.5 m and 5 m. Only in exceptional cases like the Amazon River Basin, a wetland depth of 20 m might occur. Therefore, the modified PDF fits better in most regions of the world, but this would not work for the Amazon River Basin.
Jan 20030 Jan 2004 Jan 2005 100
200 300
Time [years]
TWS [mm]
Jan 2003 Jan 2004 Jan 2005 -60
-40 -20 0 20
Time [years]
Groundwater [mm]
WGHM Standard Run Ensemble mean Ensemble members
a) c)
b) d)
Figure 6.2: Time series of a) groundwater and b) TWS averaged over the entire Mississippi River Basin are shown, while using the a priori PDF in Tab. 2.1 to generate realizations of the groundwater outflow coefficients. Time series of c) groundwater, as well as d) TWS are shown, while using the modified PDF in section 6.2.1.
6.2.2 Sensitivity of Individual Water Storage Changes
To identify sensitive WGHM parameters, which predominantly influence the water stor-age compartments, the SI, SRCC, and CC between the water states averstor-aged over the Mississippi River Basin and each model parameter for each month in 2002-2009 are de-termined (see Fig. 6.1). As an example in Fig. 6.3, the time evolution of the SI and CC
6.2. Covariance and Sensitivity Analysis 91
between the averaged snow and soil water storage and all model parameters are shown for 2008 (see also Schumacher et al., 2016a). Figure 6.3 a shows that considering SI as a measure of sensitivity, the snow storage is identified to be highly sensitive with respect to changes in the snow melt temperature (IN=13), the precipitation multiplier (IN=22) and the net radiation multiplier (IN=6) parameters. This can be understood by consid-ering the physical meaning of these parameters: the precipitation multiplier represents a multiplication factor applied to the input forcing fields after interpolation to daily rainfall values; snow melts when the actual temperature exceeds the snow melt temperature; and the net radiation multiplier is used to scale solar radiation, which controls the potential evapotranspiration from land and water bodies. Note that between May and November no sensitivity is observed for the snow compartment, since there is usually no snow in the basin at this time.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.8 13
226 1412 816
2 4 6 8 10 12
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
month in 2008
correlation
16 9 -0.8
-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
correlation
1322
a) c)
16b) d)
2 4 6 8 10 12
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
month in 2008 61
227 9
Figure 6.3: Time evolution of the SI between the 22 model parameters and the basin mean of the a) snow and b) soil compartment, and of the CC for the c) snow and d) soil compartment.
The parameters with the highest correlations to the averaged compartment states are listed in the legend. The gray lines belong to the other parameters. See Tab. 2.1 for parameter names.
This figure is taken from Schumacher et al. (2016a).
The CC confirms the high sensitivity of the snow storage change to the snow melt tempera-ture and the precipitation multiplier (Fig. 6.3 c). However, high correlations are also found between the snow storage and the groundwater factor multiplier (IN=16). This parameter does not exhibit a direct physical relationship to the snow compartment. It appears this correlation is introduced through joint dependence of other perturbed parameters, and thus is only captured by CC and not by SI. The magnitude of the correlations is found to be different, e.g., the maximum correlation value for the snow melt temperature varies
between 0.5 in case of SI and 0.8 in case of CC and SRCC. However, the overall interpre-tation of all metrics leads to the same result: the snow melt temperature (IN=13) is the most important parameter with respect to the snow storage (see also Tab. 6.1).
For the soil compartment, the SI approach identifies high dependencies between soil water changes and the net radiation multiplier (IN=6), the root depth multiplier (IN=1), and the precipitation multiplier (IN=22) for the year 2008 (Fig. 6.3 b). The sensitive parameters for the soil water storage are confirmed by evaluating the CC and the SRCC (Fig. 6.3 d, here shown for CC).
Storage changes in the other individual compartments show lower variability of the SI, SRCC, and CC during the year 2008. Therefore, their time series are not shown here. The most sensitive parameters based on the analysis of SI, SRCC, and CC (temporal averaged during 2002-2009) are summarized in Tab. 6.1 as ISI, ISRCC, and ICC.
Table 6.1: Most sensitive parameters are indicated for the Mississippi River Basin corresponding to the ten individual water storage compartments of WGHM. The identification numbers of the parameters (i=IN) can be found in Tab. 2.1. The overline denotes the temporal average. In case that only one parameter is provided, the index is zero for all other parameters.
Three most sensitive parametersi Compartment j ISI(i, j) ISRCC(i, j) ICC(i, j)
canopy 10 10, 6, 7 10, 6, 7
snow 13, 22, 6 13, 22, 16 13, 22, 16
soil 6, 1, 22 1, 6, 3 1, 6, 9
local lake 3, 5, 6 3, 7, 6 3, 7, 6
local wetland 4, 5, 22 4, 5, 22 4, 22, 5
global lake 3 3, 7, 2 3, 7, 5
global wetland 4 4, 22, 9 4, 22, 5
reservoir 22, 6, 7 22, 6, 1 22, 6, 7
river 2, 6, 22 2, 6, 22 2, 6, 22
groundwater 6, 21, 17 21, 6, 7 19, 6, 21
Changes in the maximum canopy water height (IN=10), as well as the net radiation multiplier (IN=6), and the Priestley-Taylor coefficient for humid areas (IN=7) consider-ably influence the canopy water storage. All metrics suggest that the lake and wetland compartments are mostly sensitive to changes in the lake and wetland depth (IN=3 and IN=4), respectively. The precipitation multiplier (IN=22) and the surface water outflow coefficient (IN=5) also exhibit a high impact on the water storage in surface water bodies.
Furthermore, the river storage is most sensitive to the river roughness coefficient (IN=2), the net radiation (IN=6) and the precipitation multiplier (IN=22), whereas the multipliers also show a high influence on reservoirs. For the groundwater compartment, all metrics indicate high influences of the net radiation (IN=6) and net groundwater abstraction multiplier (IN=21).
6.2. Covariance and Sensitivity Analysis 93
6.2.3 Sensitivity of TWSA
In Schumacher et al. (2016a), a sensitivity analysis for the 33 largest river basins world-wide was performed. For this, the SRCC between the calibration parameters and monthly GRACE TWSA averaged over the 33 basins were calculated. Different parameters were identified for these basins that exhibit the most dominant influence on simulated TWSA (Fig. 3, 4 in Schumacher et al., 2016a). Numerous river basins (e.g., the Mississippi River Basin) were found to react very sensitive to changes in the net radiation multiplier, the river roughness coefficient and the precipitation multiplier. Thus, it is concluded that these calibration parameters have an overall strong influence.
In Güntner et al. (2007) and Werth and Güntner (2010), a sensitivity study of WGHM parameters was reported. Their study used the WGHM version 2.1 f that is calibrated for 724 river basins. WGHM was forced by time series of the Climate Research Unit (CRU TS 2.0). In contrast, CRU TS 3.2 and precipitation data from GPCC are used in this thesis (see section 2.2.2.2). In Güntner et al. (2007) and Werth and Güntner (2010), Ne = 2000 ensemble members were generated from uniform, triangular and normal distributions for 36 calibration parameters (Kaspar, 2004), as well as for climate input fields comprising precipitation, the number of rain days, temperature and sunshine duration. The SRCC was used as a measure of sensitivity and was determined between the calibration parameters and the mean annual amplitude of TWS as a measure for sensitivity for the 22 largest river basins world-wide. To make the presented investigations comparable to their results, the global sensitivity analysis is repeated for the mean annual amplitude of TWS. However, the 33 largest river basins world-wide are considered and the climate input fields are not perturbed.
The parameters, that are found to be sensitive in this study, confirm some of the sensitive parameters that were listed in Güntner et al. (2007) as well as Werth and Güntner (2010) but not all of them. The reason for this is not clear but it might be explained due to differences in the study set-ups. As an example, for the Mississippi River Basin, the snow melt temperature (IN=13), the precipitation multiplier (IN=22), the groundwater baseflow coefficient (IN=19), the root depth multiplier (IN=1), the critical precipitation for groundwater recharge in semi-arid and arid regions (IN=18), and the maximum daily potential evapotranspiration (IN=9) are identified as most sensitive. Only the root depth multiplier and the snow melt temperature were also found to be sensitive in Güntner et al.
(2007) as well as Werth and Güntner (2010). For the Murray-Darling River Basin, it was found that the net radiation multiplier (IN=6), the precipitation multiplier (IN=22), the root depth multiplier (IN=1), the Priestley-Taylor coefficient for arid areas (IN=8), the net abstraction surface water multiplier (IN=20), and the temperature gradient (IN=15) have a high impact on the simulation of TWSA. However, from these parameters only the Priestley-Taylor coefficient for arid areas was found to be sensitive in the study of Güntner et al. (2007) as well as Werth and Güntner (2010). In summary, the results of the global comparison only confirm some of those parameters with large model sensitivity in the world’s largest river basins that were found in Güntner et al. (2007) as well as Werth and Güntner (2010). In their studies, parameters that govern radiation were identified as most sensitive, while in this study precipitation and net radiation multipliers are identified.
Thus, a strong overall dependence of TWS on climate input is found in all investigated studies.