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.