Validation Using Independent Data Sets

Figure 8.7 shows time series of soil water, groundwater, and surface water averaged over the entire Mississippi River Basin, as well as river discharge for one example station

0 2 4 6 8 10 12 10

15 20

Month in 2005

Maximum daily potential

evapotranspiration [mm/day] 0 2 4 6 8 10 12 5 10 15 20 Month in 2005

Critical precipitation for

groundwater recharge [mm/day]

0 2 4 6 8 10 12 0.5 1 1.5 2 Month in 2005

Root depth multiplier [-]

0 2 4 6 8 10 12 0 0.02 0.04 0.06 0.08 0.1 Month in 2005

Groundwater outflow coef

ficient [1/day] 0 2 4 6 8 10 12 -4 -2 0 2 4 Month in 2005

Snow melt temperature [´°]

Mode Limits Ensemble Calibrated a)

c)

b)

d)

e) _f)

Figure 8.6: Time series of calibrated parameters (ensemble mean) and ensemble members that are found to be most sensitive in chapter 6. The initial parameter ensemble is shown for month "0".

(GRDC station number 4123400). The simulated water changes from the standard WGHM variant (WGHM_MRB-1) and the C/DA variants (EnKF_MRB-1 and EnKF_MRB-2) are compared to independent observations.

In-situ observations and model simulations of soil water changes are spatially averaged over the entire Mississippi River Basin (Fig. 8.7 a). Estimates of soil water changes become better during the C/DA phase. The correlation of model outputs and in-situ soil moisture measurements from SCAN is improved from 0.81 for WGHM_MRB-1 to 0.97 and 0.93 in case of EnKF_MRB-1 and EnKF_MRB-2, respectively. This indicates a better repre- sentation of the seasonal phase of the observations. However, in the validation phase, the correlations drop from 0.83 to 0.75 and 0.78. In terms of RMSE, which is used to test the

8.1. Test Region: Mississippi River Basin 117

reproducibility of the seasonal amplitude, only during the C/DA phase of EnKF_MRB-2 the simulation of soil water changes are improved (36 mm instead of 40 mm). This can be explained by the very dry conditions in 2005 that might not reflect the hydrological conditions for the three following years. This leads to an underestimation of the seasonal amplitudes of the soil water storage. Thus, only adapting the model parameters in 2005 does not guarantee improvements between 2006-2008. Uncertainty information for the soil moisture measurements are not available. Instead, the time series of the in-situ ob- servations at all 29 stations in the Mississippi River Basin are shown in Fig. 8.7 a, which illustrates the high spatial variability of soil moisture in the basin. Soil water changes are also averaged over the four major sub-basins of the Mississippi River Basin to investigate the influence of GRACE data assimilation on a smaller spatial scale. During the C/DA phase, the correlation of EnKF_MRB-1 and EnKF_MRB-2 with in-situ soil moisture was increased up to 0.41 in three of four sub-basins but was not improved in the validation phase.

The observed groundwater time series from USGS, prepared for investigations in Rodell et al. (2007), and the study period overlap only for the year 2005. A comparison of the ob- served and simulated basin averaged time series (Fig. 8.7 b) shows that WGHM_MRB-1 underestimates the annual amplitude by a factor of 2.2 (17 mm instead of 38 mm). In case of EnKF_MRB-1 the representation of the annual amplitude has not considerably changed, while EnKF_MRB-2 leads to a larger amplitude. This seems to disagree with the reduction of the annual amplitude that is found for TWSA. However, while integra- tion of GRACE into WGHM results in larger amplitudes for groundwater, the ampli- tudes of soil water changes are considerably reduced (see Fig. 8.7 a). Nonetheless, the observed groundwater amplitude is still underestimated by EnKF_MRB-2 by a factor of 1.9. WGHM_MRB-1 shows a high correlation of 0.95 for the Mississippi River Basin. When basin-averaged or gridded TWSA are assimilated, the correlation decreased to 0.36 and 0.80. The sub-basin averages are also analyzed. These time series are shown in Fig. 8.7 b as well, since their values were spatially averaged to determine the basin averaged time series. The investigations showed higher agreements with the measurements in two of four sub-basins in case of EnKF_MRB-2. Compared to previous GRACE data assimilation experiments into NASA’s catchment land surface model for the Mississippi River Basin improvements in terms of correlations also for two or three of the four sub-basins were reported (Houborg et al., 2012, Zaitchik et al., 2008).

Simulated river discharge at seven stations was validated against measurements provided by GRDC. In Fig. 8.7 c, for example, the time series at one particular river discharge sta- tion (GRDC station number 4123400) located in the eastern part of the Ohio/Tennessee Basin (Fig. 8.2) is shown. Uncertainty information is not available for the river discharge observations. WGHM_MRB-1 overestimates the high flows occurring in spring dramati- cally, while the low flows are represented almost perfectly. In case of EnKF_MRB-1, the simulation of high flows is nudged to the observed river discharge. Even further improve- ments are achieved in case of EnKF_MRB-2 in terms of the Nash-Sutcliffe coefficient (NSC). In the C/DA phase, NSC is improved from -1.48 to -0.22, which still represents a poor fit with the observations. Then, during the validation phase, the NSC increases from 0.43 to 0.63 (Fig. 8.7 c). Since NSC is very sensitive to high flows, better values are achieved for EnKF_MRB-1 and EnKF_MRB-2, although the low flows are better repre- sented by WGHM_MRB-1. A perfect fit between simulated and observed river discharge

a)

b)

c)

d)

Figure 8.7: Time series of a) soil water and b) groundwater changes, c) river discharge at GRDC station 4123400, and d) normalized surface water changes and extent are shown from the standard and C/DA variants of WGHM averaged over the entire Mississippi River Basin (except for river discharge). Corresponding independent measurements are also shown, which are used for validation.

8.1. Test Region: Mississippi River Basin 119

would result in a NSC of 1. The investigations indicate that the simulation of river dis- charge during the C/DA phase is improved for up to five stations for both C/DA variants and for four stations in case of EnKF_MRB-2, even during the validation phase. C/DA of TWSA into WGHM shows potential to also exhibit a positive impact on water fluxes. Figure 8.7 d presents the time series for surface water bodies (summarizing lakes, wet- lands, reservoirs and rivers) for 2005-2007 averaged over the entire Mississippi River Basin. The time series of the individual grid cells that contribute to the basin average are also shown. Since WGHM simulates water storage changes, represented as equivalent water heights (in mm), and GIEMS specifies the area of a grid cell that is inundated (in km2_),

the time series are normalized and their correlation coefficients are computed following Papa et al. (2008). A high correlation of 0.90 exists in the C/DA phase and a moderate correlation of 0.64 in the validation phase between WGHM_MRB-1 and GIEMS. These values are found to be higher than the correlation of 0.51 that was reported in Papa et al. (2008), who compared surface water extent from GIEMS to model simulations from WGHM for the Mississippi River Basin for 2003-2004. Papa et al. (2008) explained the low to moderate correlations by snow melt in the northern part of the basin (Missouri, Upper Mississippi, and northern part of Ohio/Tennessee) which causes spring floods that complicate the hydrological processes within the basin. Assimilation of GRACE TWSA results in decreased correlation coefficients of 0.85 and 0.66 during the C/DA phase, while improvements in the validation period are achieved (0.74 and 0.71). Analyzing the four sub-basins of the Mississippi River Basin shows that in each case of the C/DA variants two sub-basins were improved during the assimilation phase. Then, the surface water sim- ulation of two sub-basins for EnKF_MRB-1 and three for EnKF_MRB-2 were enhanced in the validation phase.