3.4 Phase for kilometer scale variables
By downscaling P and TWSA to the same resolution asET , we calculated 1 km spatial scale phase relationships betweenET and P (\(\phi_{ET-P}^{1km}\); Figure 6) and ETand TWSA \((\phi_{ET-TWSA}^{1km}\); Figure 7). Large south-to-north and small east-to-west gradients occur for both phase lags across all years analyzed (2002 – 2013). There is a band of the positive \(\phi_{ET-P}^{1km}\) (~6 month) in the middle latitudes of the Amazon basin (-5° ~ -10°) that varies to the negative \(\phi_{ET-P}^{1km}\) (~-6 month) in north-south extent across years (Figure 6), indicating that the leaf area in this area is reduced due to deforestation activities and that cloudy conditions limit the available energy driving ET(Zhang et al., 2001; Spracklen et al., 2012). Meanwhile, the location of this band of positive \(\phi_{ET-P}^{1km}\) generally corresponds to negative \(\phi_{ET-TWSA}^{1km}\) values (~-6 month). The importance of plant controlling should be considered in the water balance accounting of forests in the Amazon basin, as these evergreen trees have deep root systems and can extract water from the aquifer to meet the atmospheric water demand (Maeda et al., 2017). However, deforestation interrupts the water absorption path of roots from groundwater (Zemp et al., 2017). \(\phi_{ET-P}^{1km}\) and\(\phi_{ET-TWSA}^{1km}\) have zero-to-positive and zero-to-negative variation patterns from 2002 to 2013, which indicate that the correlation between ET and P (TWSA ) has decreased in the central of Amazon region due to deforestation during the observation period (Figure 7). The increase in deforestation has weakened the carbon sink of terrestrial ecosystems. Meanwhile, Humphrey et al. (2018) proved that the inter-annual variability of the CO2 growth rate is closely related to TWSA . Considering that plant transpiration is related to CO2absorption through leaf stomata, the variability of ET is also closely associated with TWSA . A consistently positive\(\phi_{ET-P}^{1km}\) and \(\ \phi_{ET-TWSA}^{1km}\) occur in the southwest Amazon basin with high elevation. Here, in the Andes with low vegetation cover, the only source for ET is snow and ice cover, and ET should mostly be driven by solar radiation. Thus, in these areas ET is unaffected by groundwater depth and the timing forET and groundwater variation may remain relatively constant inter-annually. The drastic transition could be artificial and regarded as the unchanged absolute value of the phase since the periodicity for all data sets is ~12 months. For example, a negative 6-month phase lag is the same as a positive 6-month lag. Overall, the water-limiting areas (green) of the Amazon basin continue to shift to energy-limiting areas (blue). It could also suggest a system that switches between water and energy limitation with a growth cycle that coincidentally appears to lead rainfall, among other possibilities.
Across all 1 km grid cells, \(\phi_{ET-P}^{1km}\) and\(\phi_{ET-TWSA}^{1km}\) are not well correlated to the values ofET , P , or TWSA alone. Across the basin, the spatial standard deviation of annual ET is negatively correlated to that of \(\phi_{ET-P}^{1km}\) (Figure 8; r = -0.92 andR2 = 0.85 ). Since the inter-annual variation ofET is small (Figure 3c), in some areas ET and the aridity index may remain about the same regardless of annual precipitation. When the areas with low ET in dry years have recovered from water limitation, indicating ET possibly increased in these areas and the values become close to those in the unaffected areas, the overall spatial standard deviation of ET decreases, but the spatial variation of \(\phi_{ET-P}^{1km}\) becomes larger due to the generally small variation in ET (Figure 8). This relationship implies that the spatial variation of ET is the primary cause for the changing spatial pattern of \(\phi_{ET-P}^{1km}\) inter-annually, but this relationship does not hold for \(\phi_{ET-TWSA}^{1km}\) (data not shown). Thus, the variation of the spatial standard deviation ofET means the change of ET spatial heterogeneity.