## 3 Results and Discussion
### Evaportranspiration and Vegetation Greening  
We also examined to what extent vegetation greening, and consequently increases in ET, could be explained by increases in the \"excess water\" (P-Ru). Although coherent satellite observations of vegetation greening do not exist over the entire period of analysis, the longest available time series of AVHRR-observed NDVI [34] shows evidence of vegetation greening from 1982-2009 over all eight hydrological units considered in this study. A linear regression trend analysis showed that the average annual NDVI has a statistically significant positive trend of 0.004 per year over the 1982 to 2009 period (Table 2). These trends are in agreement with measurements made by the United States Forest Service, as documented in [52]. These observations indicated that vegetation density in timberland area, which makes up the majority of U.S. forests, has been increasing since 1953 in the Northeast and Southeast. The referenced findings incorporated measurements of growing stock, or the volume of living vegetation. Therefore, similar to our NDVI calculations, this positive trend only represents vegetation greening of previously existing plant life, and not an increase of vegetation areal extent. The data show a statistically significant (\(p=0.004\)) lag-correlation between changes in NDVI and excess water (P-Ru), where NDVI was lagged by one year to account for the natural response of NDVI to precipitation. A lag of weeks or months is a more accurate representation of the physical lag between available water and vegetation greening, and may have resulted in a higher correlation, but we are limited to annual runoff data given the time and space scale of our study. A lag of one year has been used in a similar fashion in previous work ([53; 54]). The lag-correlation also shows that (P-Ru) explains only about 20% of the total variance in NDVI, reflecting the fact that other variables (e.g., temperature, nutrients, vegetation composition, growing season length and solar radiation) also control NDVI trends. Furthermore, NDVI is only indicative of an increase in transpiration and interception loss of water from the canopy, whereas the \"excess water\" contributes not just to evaporation from the canopy, but also to soil evaporation. Biophysical modeling of evapotranspiration shows that over the study area, the canopy-dependent components of evaporation represent approximately 65% of the total evapotranspiration rate [55], in agreement with a multi-model average of 64% [56], suggesting that over vegetated lands, an increase in ET is largely due to vegetation growth through transpiration and interception loss. On the other hand, the relationship between vegetation CO\({}_{2}\) uptake and transpiration is controlled by stomatal conductance. Increased CO\({}_{2}\) reduces stomatal conductance, yet this reductionis not associated with similar change in stomatal density. Under elevated CO\({}_{2}\), vegetation exhibits down-regulation characterized by a reduction in the initial CO\({}_{2}\)-enhanced rates of photosynthesis that results from a decrease in the activity and the amount of Rubisco [16]. In model simulations [12], down-regulation reduced the canopy conductance beyond the reduction caused by the radiative and physiological effects of CO\({}_{2}\) leading to increased water availability which could be diverted to increase leaf density beyond increases caused by climate changes and CO\({}_{2}\)-induced water use efficiency. However, the exact moisture stressing mechanisms in the soil, plant and atmosphere are difficult to assess due to the strong nonlinear correlations among environmental forcing variables on transpiration [57], which could explain why the \"excess water\" can only explain a fraction of the variance in NDVI, even though a strong correlation exists between the two variables (\(r=0.45\)). Our results merely hint at the possibility of a physical relationship. Further analysis is necessary to draw more robust conclusions.