## 3 Results and Discussion  
### Inter-Hydrological Unit Analysis  
We first conduct a trend analysis of changes to the water budget components and vegetation greening at the hydrological unit scale to assess variability within the study region. The trend magnitudes can be estimated using different approaches, including [PERSON]'s slope estimator or the ordinary least squares regression [39,40]. A two-tailed hypothesis test is used to determine the significance of these trends at the 95% confidence level. Time series of (P-Ru) from 1901-2008, dS/dt(gw) from 1955-2011 and NDVI from 1982-2009 are displayed in Figure 2 for each hydrological unit, and quantitative results of the trend and significance tests are provided in Table 1. The longest possible time series for each variable is used, given the available data. Hydrological unit 6 is considerably smaller in spatial scale than the other hydrological units in our study region. Therefore, in order to compare hydrological units of similar size, hydrological unit 6 and the adjacent hydrological unit 3 have been combined and are considered as one hydrological unit for the purpose of this analysis. We use the Kendall-Sen slope estimator and the linear regression methods to estimate the magnitude of the trends for each individual hydrological unit. Both methods produce similar estimates. In all but one of the hydrological units (HU7), (P-Ru) trends are positive and statistically significant at the 95% confidence interval, indicating that P is increasing, and more so than Ru (Table 1). The largest increases in (P-Ru) occur in the eastern-most hydrological units, while HU's 7 and 9, in the northwestern-most region of the study domain exhibit the smallest trends. Generally, however, P-Ru trends are similar across the hydrological units. In all but one hydrological unit, dS/dt(gw) trends are insignificant in the statistical sense, while NDVI trends are positive and significant for all hydrological units (Table 1). While some variability exists between the different hydrological units, the water budget components and vegetation trends are consistent across the study region, and inter-hydrological unit variability is limited. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{2}{c}{**P-Ru**} & \multicolumn{2}{c}{**dS/dt(gw)**} & \multicolumn{2}{c}{**NDVI**} \\ \cline{2-7}  & Linear & Kendall & Linear & Kendall & Linear & Kendall \\  & slope & slope & slope & slope & slope \\ \cline{2-7}  & [\(p\)-value] & [\(p\)-value] & [\(p\)-value] & [\(p\)-value] & [\(p\)-value] \\ \hline \multirow{2}{*}{HU01} & 0.47 & 0.43 & \(-\)0.31 & \(-\)0.22 & 0.01 & 0.01 \\  & [0.0013] & [0.0041] & [0.1935] & [0.3182] & [1.91(10)\({}^{-9}\)] & [7.77(10)\({}^{-9}\)] \\ \hline \multirow{2}{*}{HU02} & 0.56 & 0.52 & 0.25 & 0.3 & 0.01 & 0.01 \\  & [0.0002] & [0.0013] & [0.2140] & [0.1464] & [8.59(10)\({}^{-13}\)] & [2.05(10)\({}^{-11}\)] \\ \hline \multirow{2}{*}{HU03+06} & 1.27 & 1.23 & 0.15 & 0.16 & 0.01 & 0.01 \\  & [1.33(10)\({}^{-12}\)] & [1.96(10)\({}^{-11}\)] & [0.3474] & [0.4366] & [1.58(10)\({}^{-9}\)] & [1.40(10)\({}^{-6}\)] \\ \hline \end{tabular}
\end{table} 
Table 1: The rate of change in the difference between precipitation and runoff (P-Ru) in mm\(\cdot\)yr\({}^{-1}\), groundwater storage (dS/dt(gw)) in mm\(\cdot\)yr\({}^{-1}\) and Normalized Difference Vegetation Index (NDVI) in yr\({}^{-1}\), for each Hydrological Unit (HU) considered in our study region. Linear regression and Kendall-Sen methods are used to estimate slopes. Significance is considered at the 95% confidence level. Figure 2: Time series of P-Ru (mm\(\cdot\)yr\({}^{-1}\)) from 1901–2008, dS/dt(gw) (mm\(\cdot\)yr\({}^{-1}\)) from 1955–2011 (primary axis) and annual total NDVI (yr\({}^{-1}\)) from 1982–2009 (secondary axis) for each hydrological unit (HU) considered in the study region. Linear regression trend lines and R\({}^{2}\) coefficients are displayed. Red-boxed numbers identify which HU each subplot corresponds to. Note, HU3 and HU6 are considered together as one hydrological unit.