3.1 Wavelet coherence and phase for Amazon-scale averaged variables
The wavelet power spectra of spatially averaged P , ET , andTWSA data over the whole Amazon basin reveal, for each data set, a band of maximum power across all years with approximately a 12-month period (Figure 1a, b, and c). For ET the 95% confidence contour band ends around 2010, as there is a substantial change in the ETcycle after 2010. The pattern of a discontinuous maximum power spectrum band for ET can be explained by the drought event in 2010 and its monthly time series with more frequent fluctuations after 2010 than before (Figure 3b). Meanwhile, the global wavelet power spectra identify the main fluctuations of the time series (Figure 1d, e, and f) and show the 12-month peak for all three datasets and a notable, as well as a smaller, 2 – 4 years peak, and some monthly-scale variations in theET power spectrum (Figure 1e). From these analyses it is apparent that the three hydrological fluxes have significant annual cycles. Additionally, the magnitude ofET global power spectra is much less than those of P andTWSA (~100 to ~200 comparing to the order of 104 and 105 forP and TWSA respectively, Figure 1d, e, and f), indicating the periodic intensity of ET is weakened due to its complicated physical and physiological processes of the plants. The non-significant multi-year (2 – 4 years) variation of ET possibly relates to long-term climatic drivers (e.g., El Nino with ~3 - ~7 years periodicity) and its significant intra-annual (~3 months) variability corresponds to the succession of dry and wet seasons, suggesting that multi-climatic drivers and hydrologic responses affect ET in both short-term and long-term timescales, rather than precipitation fluctuations alone.
Larger coherence indicates stronger linear correlation between two time series at the given time scale. Patches of high coherence around 1-year and multi-year periodicities between ET and P and betweenET and TWSA are evident (Figure 2). It can be indicated that ET has a resonant periodicity with both P andTWSA at the annual scale. However, the covariation weakens substantially there since the annual cycle in ET has been interrupted after 2010 (Figure 1b). Between ~2006 and ~2012, the high coherence at a 2 – 4 years period (Figure 2) corresponds to the 2 – 4 years fluctuation in the ETwavelet spectrum (Figure 1b and e). The larger correlation betweenET and TWSA than that between ET and Pindicates the drought events in 2005 and 2010 may have enhanced the effect of TWSA on ET . The cross-wavelet power spectrum between ET and P also shows relatively high values at 2-4 months centered on the dry seasons of most years (Figure 2a). However, this pattern does not occur for coherence between ET andTWSA , indicating that the impact of P on ET is direct (with co-variant at shorter time periods), while the impact ofTWSA on ET at a shorter time scale is intervened by many factors during the deep water extraction from the aquifer by the plants’ root.
For the Amazon basin, \(\phi_{ET-P}^{\text{Amazon}}\) ranges from <1 to ~4 months, and\(\phi_{ET-TWSA}^{\text{Amazon}}\) ranges from ~3 to ~7 months during 2002 to 2013 (Figure 3a), meaning that the impact of P on ET is stronger than that of TWSAon ET on an Amazon-wide. \(\phi_{ET-P}^{\text{Amazon}}\) also reflects how responsive ET is to P . For an area that is strongly water limited, rainfall would quickly become ET , and we expect to see a small lag between ET and P , i.e., a\(\phi_{ET-P}^{\text{Amazon}}\) of around 0. In a real-world, water-limited forest, we must also consider the time it takes for the forest to respond to increasing water supply by growing leaves and roots, which enhances its ability to transpire. Hence, we can expect a small negative \(\phi_{ET-P}^{\text{Amazon}}\) due to the period required for growth and the period with cloud-cover. A positive\(\phi_{ET-P}^{\text{Amazon}}\), on the other hand, is quite intriguing and could possibly suggest the cloud-suppressed forest has adapted to and anticipated the coming dry season and increases leaf allocation toward the end of the rainy season, as suggested by Fu and Li (2004). A large absolute value of \(\phi_{ET-P}^{\text{Amazon}}\)would mean that the system is not water limited, and ET may be suppressed due to too much rainfall and too little radiation relative to its canopy density. The two phases are qualitatively correlated in time, except, for example in 2010, when a severe drought occurred (Figure 3a and c). Both \(\phi_{ET-TWSA}^{\text{Amazon}}\) and\(\phi_{ET-P}^{\text{Amazon}}\) decreased comparing to those in 2009, but after 2010, \(\phi_{ET-TWSA}^{\text{Amazon}}\) increased from ~ 5 month to more than 7 month while\(\phi_{ET-P}^{\text{Amazon}}\) remained relatively constant at ~4 month (Figure 3a). In contrast,\(\phi_{P-TWSA}^{\text{Amazon}}\) and\(\phi_{\ \left(P-ET\right)-TWSA}^{\text{Amazon}}\) have no correlation with \(\phi_{ET-P}^{\text{Amazon}}\), but both of them decreased during the drought period and started to recover after late 2013 (Figure S1). However, the annual flux of ET has remained stable from 2002 to 2013 (Figure 3c). It could also suggest a system that ET will increase even when there is insufficient rainfall. The soil water / groundwater reserves are still maintained at a high level to provide sufficient water for ET during the meteorological dry season.
The basin spatial mean time series may mask important relationships at higher spatial resolutions. Thus, we next explore the behavior of these interactions at 33 sub-basins, 1 km pixel, and three zones based on 1 km pixel spatial scales.