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\begin{document}

\title{Spatial and temporal variations of evapotranspiration, groundwater and
precipitation in Amazonia}



\author[1]{Juan Zhang}%
\author[1]{Jie Niu}%
\author[2]{Chaopeng Shen}%
\author[3]{John Melack}%
\author[1]{Jin Zhang}%
\author[4]{Han Qiu}%
\author[1]{Bill Hu}%
\author[5]{William Riley}%
\affil[1]{Jinan University}%
\affil[2]{Pennsylvania State University}%
\affil[3]{University of California Santa Barbara}%
\affil[4]{Pacific Northwest National Laboratory}%
\affil[5]{Lawrence Berkeley National Laboratory}%


\vspace{-1em}



  
  \date{May 08, 2024}


\begingroup
\let\center\flushleft
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\selectlanguage{english}
\begin{abstract}
The relationships and seasonal-to-annual variations among
evapotranspiration (ET), precipitation (P), and groundwater dynamics
(total water storage anomaly, TWSA) are complex across the Amazon basin,
especially the water and energy limitation mechanism for ET. To analyze
how ET is controlled by P and TWSA, we used wavelet coherence analysis
to investigate the effects of P and TWSA on ET at sub-basin, kilometer,
regional, and whole basin scales in the Amazon basin. The Amazon-scale
averaged ET has strong correlations with P and TWSA at the annual
periodicity. The phase lag between ET and P (\selectlanguage{greek}ϕ\selectlanguage{english}\_(ET-P)) is
\textasciitilde{}1 to \textasciitilde{}4 months, and between ET and TWSA
(\selectlanguage{greek}ϕ\selectlanguage{english}\_(ET-TWSA)) is \textasciitilde{}3 to \textasciitilde{}7 months. The
phase pattern has a south-north divide due to the significant variation
in climatic conditions. The correlation between \selectlanguage{greek}ϕ\selectlanguage{english}\_(ET-P) and
\selectlanguage{greek}ϕ\selectlanguage{english}\_(ET-TWSA) is affected by the aridity index, of each sub-basin, as
determined using the Budyko framework at the sub-basin level. In the
southeast Amazon during a drought year (e.g., 2010), both phases
decreased, while in the subsequent years, \selectlanguage{greek}ϕ\selectlanguage{english}\_(ET-TWSA) increased. The
area of places where ET is limited by water continues to decrease over
time in the southern Amazon basin. These results suggest immediate
strong groundwater subsidy to ET in the following dry years in the
water-limited area of Amazon. The water storage has more control on ET
in the southeast but little influence in the north and southwest after a
drought. The areas of ET limited by energy or water are switched due to
the variability in weather conditions.%
\end{abstract}%



\sloppy


Spatial and temporal variations of evapotranspiration, groundwater and
precipitation in Amazonia

Juan Zhang\textsuperscript{1}, Jie Niu\textsuperscript{1}, Chaopeng
Shen\textsuperscript{2}, John M. Melack\textsuperscript{3}, Jin
Zhang\textsuperscript{1}, Han Qiu\textsuperscript{4}, Bill X.
Hu\textsuperscript{1}, and William J. Riley\textsuperscript{5}

\textsuperscript{1}Institute of Groundwater and Earth Science, Jinan
University, Guangzhou 510632, China

\textsuperscript{2}Civil and Environmental Engineering, Pennsylvania
State University, PA

\textsuperscript{3}Earth Research Institute, University of California,
Santa Barbara, CA

\textsuperscript{4}Joint Global Change Research Institute, Pacific
Northwest National Lab, College Park, MD 20740, USA

\textsuperscript{5}Earth Sciences Division, Lawrence Berkeley National
Lab, Berkeley, CA

Correspondence to: J. Niu, jniu@jnu.edu.cn

\textbf{Abstract}

The relationships and seasonal-to-annual variations among
evapotranspiration (\emph{ET} ), precipitation (\emph{P} ), and
groundwater dynamics (total water storage anomaly, \emph{TWSA} ) are
complex across the Amazon basin, especially the water and energy
limitation mechanism for \emph{ET} . To analyze how \emph{ET} is
controlled by \emph{P} and \emph{TWSA} , we used wavelet coherence
analysis to investigate the effects of \emph{P} and \emph{TWSA}
on\emph{ET} at sub-basin, kilometer, regional, and whole basin scales in
the Amazon basin. The Amazon-scale averaged \emph{ET} has strong
correlations with \emph{P} and \emph{TWSA} at the annual periodicity.
The phase lag between \emph{ET} and \emph{P} (\(\phi_{ET-P}\)) is
\textasciitilde{}1 to \textasciitilde{}4 months, and between
\emph{ET}and \emph{TWSA} (\(\phi_{ET-TWSA}\)) is \textasciitilde{}3 to
\textasciitilde{}7 months. The phase pattern has a south-north divide
due to the significant variation in climatic conditions. The correlation
between \(\phi_{ET-P}\) and \(\phi_{ET-TWSA}\) is affected by the
aridity index, of each sub-basin, as determined using the Budyko
framework at the sub-basin level. In the southeast Amazon during a
drought year (e.g., 2010), both phases decreased, while in the
subsequent years, \(\phi_{ET-TWSA}\) increased. The area of places where
\emph{ET} is limited by water continues to decrease over time in the
southern Amazon basin. These results suggest immediate strong
groundwater subsidy to \emph{ET} in the following dry years in the
water-limited area of Amazon. The water storage has more control
on\emph{ET} in the southeast but little influence in the north and
southwest after a drought. The areas of \emph{ET} limited by energy or
water are switched due to the variability in weather conditions.

\textbf{Running head:} Evapotranspiration, groundwater and precipitation
variation in Amazon

\textbf{Keywords:} Evapotranspiration (\emph{ET} ), Wavelet coherence,
Amazon basin, Phase lag, Budyko framework

\textbf{1. Introduction}

Climate change is accompanied by increasing variability in seasonal
rainfall (Feng et al., 2013) and alters rainfall regimes, where water
availability and timing are key factors controlling primary productivity
(Briggs \& Knapp, 1995; Weltzin et al., 2003; Huxman et al., 2004) and
the phenology of growth and reproduction (Dirzo et al., 2011; Walther et
al., 2002). Evapotranspiration (\emph{ET} ) links regional climate and
forest function and plays an important role in the hydrological cycle.
It is also an internal connection with CO\textsubscript{2} flux during
the transpiration process and an indicator for ecosystem function. It is
broadly known that the Amazon basin transfers large amounts of water
from the land surface to the atmosphere by \emph{ET} every day, which
has a huge impact on the global energy budget (Christoffersen et al.,
2014; Hasler \& Avissar, 2006; Restrepo-Coupe et al., 2016). Therefore,
any impact on the \emph{ET} over the Amazon tropical forest may affect
the global carbon cycle and provide further feedback to climate change.
Nonetheless, the spatio-temporal variation of \emph{ET} across the
Amazon basin, as well as the relative contributions of multiple drivers
to this process, are still uncertain. Thus, assessing the factors
controlling \emph{ET} in the Amazon basin is fundamentally important and
largely depends on how tropical vegetation processes available energy
and water (Nepstad et al., 1994; Saleska et al., 2003).

Controls of \emph{ET} across the Amazon basin vary. Based on
observations and model syntheses, the response of forest cover to
seasonal disparities in both water availability and solar radiation can
reduce drought susceptibility by temporally adjusting net leaf flush
(Jones et al., 2014). Wagner et al. (2016) found that the seasonal
variation of canopy photosynthetic capacity is positively correlated
with precipitation (\emph{P} ) (water-limited forests) when rainfall is
less than \textasciitilde{}2000 mm yr\textsuperscript{-1}, and
negatively correlated with radiation (light-limited forests). Costa et
al. (2010) concluded that \emph{ET} in the dry season is larger than
that in the wet season and that surface net radiation is the main
controller of \emph{ET} in wet equatorial sites. Some models (Baker et
al., 2008; da Rocha et al., 2009; Kleidon \& Heimann, 2000; Werth \&
Avissar, 2004) predict water-limited \emph{ET} seasonality that
resembles \emph{P} variations. Considering the large scale of previous
studies, the evaluation of \emph{ET} drivers has not been conclusive in
some cases, or only analyzed for the whole Amazon basin. Malhi et al.
(2002) were the first to measure a full annual trend of latent heat flux
for the Cuieiras forest close to Manaus. Their regression results
indicate that water limitation and stomatal control were the main
factors driving seasonal \emph{ET} . Nemani et al. (2003) concluded that
light is more limiting than water for tropical forest productivity,
consistent with greening of Amazon forests during the dry season from
satellite data (Brando et al., 2010; Doughty \& Goulden, 2008; Huete et
al., 2006; Myneni et al., 2007; Samanta et al., 2012). By evaluating
potential mechanisms for the seasonal green-up phenomenon, Morton et al.
(2014) found that the light-limited net primary production in Amazon
forest and enhanced forest growth during drought conditions are
influenced by the stability of Amazon forest structure and reflectance
over seasonal timescales. Recent studies based on eddy flux measurements
indicate seasonal \emph{ET} is driven by radiation, rather than water
availability, in the Amazon (da Rocha et al., 2009; Ju\selectlanguage{ngerman}árez et al., 2007)
and across the tropics (Fisher et al., 2009). Maeda et al. (2017)
suggested that both annual mean and seasonality of \emph{ET} are driven
by a combination of energy and water availability, as rainfall or
radiation alone could not explain \emph{ET} patterns. This led to
continued controversy regarding the seasonality of \emph{ET} and its
control. Therefore, more detailed studies are needed to explore the
factor driving \emph{ET} (i.e., radiation or water availability).

The modeling results from Verbeeck et al. (2011) show that forests in
some regions of the Amazon maintain high transpiration during the dry
season. Therefore, the flux of \emph{ET} will also be changed by various
external conditions, resulting in great uncertainty for
\emph{ET}measurements that are sparse and often indirect due to the
limited spatial coverage and the complex plant components (Culf et al.,
2008). Moreover, there are systematic biases of hydrologic and carbon
fluxes and responses in Earth system models. For example, Tang et al.
(2015) found that \emph{ET} predicted using CLM4.5 at the Tapajos forest
site in the Amazon basin compares poorly and is out of phase with MODIS
data (MOD16A2). The latest MOD16 global \emph{ET} product agrees well
with measurements from Amazon tropics eddy flux towers (Mu et al.,
2011), and shows higher \emph{ET} in the dry season and lower \emph{ET}
in the wet season. On the one hand, \emph{ET} includes contributions
from the evaporation of the ground or other wet surfaces, as well as
transpiration flux from plants. Thus, \emph{ET} reflects aspects of the
aspiration functioning of plants (Swann et al., 2017) and is largely
affected by precipitation, as the vegetation canopy of the Amazon
rainforest is highly sensitive to changes in precipitation patterns.
Reduction in rainfall has diminished vegetation greenness, which
coincides with the decline in terrestrial water storage (Hilker et al.,
2014). This pattern is supported by severe drought suppressed
photosynthesis (Doughty et al., 2015). On the other hand, groundwater
has a strong influence on hydrologic responses in the Amazon (Tomasella
et al., 2010). Previous empirical studies indicate that errors result if
groundwater is not included in hydrologic balances (Leopoldo et al.,
1995; Lesack, 1993). Several modeling studies have also concluded that
surface runoff is rare and groundwater plays a key role in Amazon
hydrology (Hodnett et al., 1997b, 1997a; Leopoldo et al., 1995;
Miguez-Macho \& Fan, 2012a), and groundwater has significant influence
on soil moisture and \emph{ET}(Miguez-Macho \& Fan, 2012b). Our recent
analysis with a three-dimensional hydrologic model applied to Amazon
watersheds (Niu et al., 2017) demonstrated that lateral fluxes,
especially groundwater flows, have a large impact on hydrologic
responses.

To detect and analyze oscillations of different hydrologic components on
a given scale, wavelet coherence analysis qualitatively estimates the
temporal evolution of the degree of linearity of the relationship
between two signals (Labat, 2005). Wavelet spectral and correlation
analyses have been applied widely in previous studies to identify the
annual periodicity of the hydrologic and climate fluxes and detect their
long-term trends (Andreo et al., 2006); to detect potential flood
triggering conditions (Schaefli et al., 2007); and to extract
significant information and the characteristic time scale of the
dominant hydrologic processes (Molénat et al., 1999; Zhang et al.,
2016). The method has also been applied to Amazon River monthly
discharges to suggest physical explanations for time-scale dependent
relationships (Labat et al., 2005). To the best of our knowledge, due to
the scarcity of observations, especially of water table depth, no
previous studies using wavelet spectral has analyzed the relationships
between \emph{P} and \emph{ET} , or groundwater and \emph{ET,} in the
Amazon. The phase difference of wavelet analysis can obtain the dynamic
correlation among hydrological components, and its application is
relatively rare. In addition, the Budyko curve framework is a classic
empirical approach to analyze annual hydrological budgets and their
inter-annual variability (Bukydo, 1974). The Budyko framework has been
used to evaluate the inter-annual variability of annual water balances
(Yang et al., 2007; Wang, 2012). A recent study found that the errors
between observations and the traditional Budyko curve could be reduced
if the equation was corrected using information extracted from the
Gravity Recovery and Climate Experiment (GRACE) terrestrial water
storage anomalies (\emph{TWSA} ) (Fang et al., 2016).

In this paper, we explore the relationships and seasonal-to-annual
variations among \emph{P} , \emph{ET} , and \emph{TWSA} across the
Amazon basin using wavelet analysis. By analyzing the phase differences
among\emph{P} (\emph{TWSA} ) and \emph{ET} , we can explore the
interaction between \emph{ET} fluxes and rainfall (groundwater) at
different scales (for sub-basins, the individual grid cells, different
climatic zones, and averaged for the whole Amazon basin), including the
effects of drought. The purpose is to dynamically analyze the main
factors controlling \emph{ET} across the Amazon basin. We also apply the
Budyko framework to evaluate the annual hydrological budgets in
sub-basins of the Amazon and analyze the degree of radiation and
rainfall limitation, as well as their interactive effects on \emph{ET} .
With these tools we address the following hypotheses: (1) in years with
sufficient \emph{P} ,\emph{ET} is energy limited, while during drought
years, plants have sufficient water supply from groundwater to maintain
photosynthesis and\emph{ET} compared to normal years; (2) after a
drought year, the groundwater system recovers, and the phases between
\emph{ET} and\emph{P} , and between \emph{ET} and \emph{TWSA,} reflect
this recovery; and (3) the above two hypotheses vary spatially and the
spatial heterogeneity of the water-energy balance account for their
spatial variation. Hypotheses (1) and (2) were addressed using wavelet
coherence phase analysis for the whole Amazon (Section 3.1), sub-basins
(Section 3.2), and sub-regions (Section 3.5). The analyses at different
scales (from Section 3.2 to Section 3.5) help address hypothesis (3),
specifically, applying the wavelet coherence phase for analyzing the
individual grid cells and the Bydyko framework for analyzing each
sub-basin.

\textbf{2. Methods}

\textbf{2.1 Data Sources}

The Tropical Rainfall Measuring Mission (TRMM, available from NASA,
http://trmm.gsfc.nasa.gov/) 3B42 V7 daily data with 0.25-degree spatial
resolution were used for \emph{P} . MODIS 16 monthly data (MODIS 16A2;
Mu et al., 2007) were used for
\emph{ET}(http://www.ntsg.umt.edu/project/mod16) at 1 km resolution for
the global vegetated land areas and cover the period 2002 to 2013. The
latest \emph{ET} product (Mu et al., 2011) implements the
improved\emph{ET} algorithm in Mu et al. (2007) and agrees well with
measurements from 46 eddy flux towers, including two towers in the
Amazon basin. The most recent release of the spherical harmonics
GRACE\emph{TWSA} (RL05) was downloaded from the Jet Propulsion
Laboratory (available at http://grace.jpl.nasa.gov/). This distributed
GRACE product has been ``destriped'' and smoothed using a 300 km wide
Gaussian filter to minimize north-south stripes, and is appropriate for
land hydrology applications (Landerer \& Swenson, 2012; Swenson \& Wahr,
2006). The resolution of GRACE and \emph{TWSA} data are 1-degree.

The sub-basin delineation map applied here was obtained from a
topography-independent analysis method (Mayorga et al., 2005) using the
vector river network from the Digital Chart of the World (DCW, Danko,
1992). The map includes the sub-basin boundaries of the major
tributaries to the main stem of the Amazon River
(http://daac.ornl.gov/LBA/guides/CD06\_CAMREX.html).

\textbf{2.2 Wavelet Analysis}

The concepts of wavelet analysis have been reviewed in previous
publications (Daubechies, 1990; Labat, 2005; Torrence \& Comp, 1998).
Briefly, similar to Fourier analysis, wavelet analysis extracts
frequency information (called scales) from time series. Wavelet analysis
also reveals the timing of the features. For this work, we adopted the
algorithm of wavelet transform from Torrence and Compo (1998). The
wavelet power spectrum is then defined as\(\left|W_{n}\left(s\right)\right|^{2}\) and the
phase angle is\(atan2\left(\frac{\text{Imag}\left\{W_{n}\left(s\right)\right\}}{\text{Real}\left\{W_{n}\left(s\right)\right\}}\right)\), where \emph{atan2} is the
four-quadrant inverse tangent function,\(\text{Real}\left\{W_{n}\left(s\right)\right\}\) is the real
part of the continuous wavelet transform \(W_{n}\left(s\right)\),
and\(\text{Imag}\left\{W_{n}\left(s\right)\right\}\) denotes the imaginary part. The wavelet power
spectrum provides insight into the temporal-scale variability of the
time series.

The global wavelet spectrum is defined as the time-averaged wavelet
spectrum over all the local wavelet spectra:

\({\overset{\overline{}}{\mathbf{W}}}^{\mathbf{2}}\left(\mathbf{s}\right)\mathbf{=}\frac{\mathbf{1}}{\mathbf{N}}\sum_{\mathbf{n=0}}^{\mathbf{N-1}}\left|\mathbf{W}_{\mathbf{n}}\left(\mathbf{s}\right)\right|^{\mathbf{2}}\). (1)

where \emph{N} is the number of points in the time series.

Given two time series \emph{X} and \emph{Y} , with wavelet
transforms\(W_{n}^{X}\left(s\right)\) and \(W_{n}^{Y}\left(s\right)\), the cross-wavelet
spectrum is defined as:

\(\mathbf{W}_{\mathbf{n}}^{\mathbf{\text{XY}}}\left(\mathbf{s}\right)\mathbf{=}\mathbf{W}_{\mathbf{n}}^{\mathbf{X}}\left(\mathbf{s}\right)\mathbf{W}_{\mathbf{n}}^{\mathbf{Y}^{\mathbf{*}}}\left(\mathbf{s}\right)\)(2)

where \(W_{n}^{Y^{*}}\left(s\right)\) is the complex conjugate of\(W_{n}^{Y}\left(s\right)\).
The cross-wavelet power is\(\left|W_{n}^{\text{XY}}\left(s\right)\right|\), and indicates covariance
between the time series at all time scales. The wavelet coherence is
defined as the square of the cross-spectrum,\(\left|W_{n}^{\text{XY}}\left(s\right)\right|^{2}\)
normalized by the individual power spectra. The wavelet coherence ranges
between 0 and 1 and provides a qualitative estimator of the temporal
evolution of the degree of linearity of the relationship between two
signals on a given temporal scale. The coherence phase is therefore
defined as\(\text{atan}\left(\frac{\text{Imag}\left\{W_{n}^{\text{XY}}\left(s\right)\right\}}{\text{Real}\left\{W_{n}^{\text{XY}}\left(s\right)\right\}}\right)\).

To derive the phase, \(\phi\), the difference in timing
between two time series at their maximum power spectrum, we multiplied
the coherence phase in proportion to 2\(\pi\) by their
coherent period at their maximum cross wavelet power spectrum band:

\(\mathbf{\phi=atan}\mathbf{2}\left(\frac{\mathbf{\text{Imag}}\left\{\mathbf{W}_{\mathbf{n}}^{\mathbf{\text{XY}}}\left(\mathbf{s}_{\mathbf{\max}}\right)\right\}}{\mathbf{\text{Real}}\left\{\mathbf{W}_{\mathbf{n}}^{\mathbf{\text{XY}}}\left(\mathbf{s}_{\mathbf{\max}}\right)\right\}}\right)\frac{\mathbf{S}_{\mathbf{\max}}}{\mathbf{2}\mathbf{\pi}}\)(3)

where \(\mathbf{s}_{\mathbf{\max}}\) means the time scale (or period) of the
maximum cross wavelet power spectrum band. And the values range
of\(atan2\) is {[}--\(\pi\),
\(\pi\){]}. Although the phase difference has been defined
when the cross-wavelet analysis method was developed, there are few
studies on its application and to the best of the authors' knowledge,
there was no previous research used this technique to analyze the
relationships among \emph{P} , \emph{ET} , and \emph{TWSA} in Amazon.

We performed wavelet analyses for \emph{ET} , \emph{P} , and
\emph{TWSA}and their coherences for four spatial resolutions: (1)
averaged across the Amazon basin, (2) for 33 watersheds within the
Amazon basin, (3) for individual 1 km scale grid cells, and (4) averaged
for three zones in the Amazon basin. The underlying resolutions of
\emph{P} , \emph{ET} , and\emph{TWSA} are 0.25-degree, 1 km, and
1-degree respectively as described in Section 2.1, but \emph{P} and
\emph{TWSA} were interpolated to the same 1 km resolution as \emph{ET}
to calculate the 1 km scale phases. Comparisons among these spatial
averaging units allow us to analyze the behavior of the coherences at
different spatial scales. Hereafter, we define the phases between
\emph{ET} and \emph{P} at the different spatial scales
as\(\phi_{ET-P}^{\text{Amazon}}\),\(\ \phi_{ET-P}^{\text{subbas}},\)\(\phi_{ET-P}^{1km}\), and
\(\phi_{ET-P}^{\text{Zone}}\), and the phases between \emph{ET} and \emph{TWSA}
as\(\phi_{ET-TWSA}^{\text{Amazon}}\),\(\phi_{ET-TWSA}^{\text{subbas}},\ \phi_{ET-TWSA}^{1km}\), and\(\phi_{ET-TWSA}^{\text{Zone}},\) for
the whole Amazon basin, sub-basins, the individual grid cells, and three
zones, respectively. A positive \(\phi_{ET-P}^{\text{Amazon}}\) would mean that
\emph{ET}signal leads that of \emph{P} .

For simplicity and convenience, the time scales and wavelet power
spectrum are presented using the 2-based logarithmic scale in all
figures shown in the results sections below.

\textbf{2.3 Budyko framework}

The Budyko hypothesis assumes that the long-term (annual scale)
partitioning of \emph{P} into \emph{ET} and runoff can be determined
from available water measured as precipitation and available energy
measured as potential evapotranspiration (\(E_{P}\)). Based on
the Budyko hypothesis, the ratio between actual evapotranspiration
(\(E_{A}\)) and \emph{P} is related to the aridity index (the
ratio between \emph{E\textsubscript{P}} and \emph{P} ,
\(\frac{E_{P}}{P}\)), or the climate dryness index (Budyko, 1974):

\(\frac{\mathbf{E}_{\mathbf{A}}}{\mathbf{P}}\mathbf{=}\left\{\frac{\mathbf{E}_{\mathbf{P}}}{\mathbf{P}}\mathbf{\tanh}\left(\frac{\mathbf{E}_{\mathbf{P}}}{\mathbf{P}}\right)\left[\mathbf{1-cosh}\left(\frac{\mathbf{P}}{\mathbf{E}_{\mathbf{P}}}\right)\mathbf{+sinh}\left(\frac{\mathbf{P}}{\mathbf{E}_{\mathbf{P}}}\right)\right]\right\}^{\mathbf{0.5}}\)(4)

\textbf{3. Results and Discussion}

\textbf{3.1 Wavelet coherence and phase for Amazon-scale averaged
variables}

The wavelet power spectra of spatially averaged \emph{P} , \emph{ET} ,
and\emph{TWSA} 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 \emph{ET} the 95\% confidence
contour band ends around 2010, as there is a substantial change in the
\emph{ET}cycle after 2010. The pattern of a discontinuous maximum power
spectrum band for \emph{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 the\emph{ET} power spectrum (Figure 1e). From these
analyses it is apparent that the three hydrological fluxes have
significant annual cycles. Additionally, the magnitude of\emph{ET}
global power spectra is much less than those of \emph{P} and\emph{TWSA}
(\textasciitilde{}100 to \textasciitilde{}200 comparing to the order of
10\textsuperscript{4} and 10\textsuperscript{5} for\emph{P} and
\emph{TWSA} respectively, Figure 1d, e, and f), indicating the periodic
intensity of \emph{ET} is weakened due to its complicated physical and
physiological processes of the plants. The non-significant multi-year (2
-- 4 years) variation of \emph{ET} possibly relates to long-term
climatic drivers (e.g., El Nino with \textasciitilde{}3 -
\textasciitilde{}7 years periodicity) and its significant intra-annual
(\textasciitilde{}3 months) variability corresponds to the succession of
dry and wet seasons, suggesting that multi-climatic drivers and
hydrologic responses affect \emph{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 \emph{ET} and \emph{P} and
between\emph{ET} and \emph{TWSA} are evident (Figure 2). It can be
indicated that \emph{ET} has a resonant periodicity with both \emph{P}
and\emph{TWSA} at the annual scale. However, the covariation weakens
substantially there since the annual cycle in \emph{ET} has been
interrupted after 2010 (Figure 1b). Between \textasciitilde{}2006 and
\textasciitilde{}2012, the high coherence at a 2 -- 4 years period
(Figure 2) corresponds to the 2 -- 4 years fluctuation in the
\emph{ET}wavelet spectrum (Figure 1b and e). The larger correlation
between\emph{ET} and \emph{TWSA} than that between \emph{ET} and
\emph{P}indicates the drought events in 2005 and 2010 may have enhanced
the effect of \emph{TWSA} on \emph{ET} . The cross-wavelet power
spectrum between \emph{ET} and \emph{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
\emph{ET} and\emph{TWSA} , indicating that the impact of \emph{P} on
\emph{ET} is direct (with co-variant at shorter time periods), while the
impact of\emph{TWSA} on \emph{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 \textless{}1 to
\textasciitilde{}4 months, and\(\phi_{ET-TWSA}^{\text{Amazon}}\) ranges from
\textasciitilde{}3 to \textasciitilde{}7 months during 2002 to 2013
(Figure 3a), meaning that the impact of \emph{P} on \emph{ET} is
stronger than that of \emph{TWSA}on \emph{ET} on an Amazon-wide.
\(\phi_{ET-P}^{\text{Amazon}}\) also reflects how responsive \emph{ET} is to \emph{P}
. For an area that is strongly water limited, rainfall would quickly
become \emph{ET} , and we expect to see a small lag between \emph{ET}
and \emph{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
\emph{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 \textasciitilde{} 5 month to
more than 7 month while\(\phi_{ET-P}^{\text{Amazon}}\) remained relatively constant
at \textasciitilde{}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 \emph{ET} has
remained stable from 2002 to 2013 (Figure 3c). It could also suggest a
system that \emph{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 \emph{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.

\textbf{3.2 Phase lag for sub-basins of the Amazon}

To further analyze the relationship between phase lags and other
climatic indicators, sub-basins within the Amazon basin are examined
(Figure 4). Sub-basin \#1 is narrow, crosses almost the entire Amazon
basin horizontally, and closely conforms to the Amazon River (cross
hatched in Figure 4). The sub-basin delineation from Mayorga et al.
(2005) is not accurate for sub-basin \#1 since it only approximates the
floodplain of the main stem of Amazon River and includes minor
catchments bordering the floodplain. Thus, the results for this
sub-basin will not be discussed.

Inter-annual variability in \(\phi_{ET-P}^{\text{subbas}}\) (blue lines) and
\(\phi_{ET-TWSA}^{\text{subbas}}\) (red lines) differs among the sub-basins, although
coherent patterns are evident (Figure 4).\(\phi_{ET-P}^{\text{subbas}}\) ranges from
5 to 8 months, generally. However, some sub-basins have either larger
(10 -- 12 months) (\#5, \#9, \#16, \#20, and \#25) or much smaller (\#32
and \#33) values of phase lag. Since the periodicity for all data sets
is \textasciitilde{} 12 months, a phase lag close to 12 months is
equivalent to a small lag. Thus, \(\phi_{ET-P}^{\text{subbas}}\) for those sub-basins
with larger values (10 -- 12 months) are equivalent to -2 -- 0 months,
about the same as those sub-basins with smaller lags, and they are all
smaller than those of other sub-basins with normal 5 -- 8 months lag.
Only the sub-basins mentioned above with smaller\(\phi_{ET-P}^{\text{subbas}}\) (or
10 -- 12 months ones) have positive \(\phi_{ET-TWSA}^{\text{subbas}}\). All these
sub-basins are located in the south of the Amazon basin, which are
generally water limited comparing to other sub-basins (Figure 5). The
remaining sub-basins, with 5 \textasciitilde{} 8
months\(\phi_{ET-P}^{\text{subbas}}\), all have negative\(\phi_{ET-TWSA}^{\text{subbas}}\), ranging
from approximate -5 to -3 months. These sub-basins are located in the
north of the Amazon basin, which are energy limited (Figure 5). For
these sub-basins \emph{ET} may be suppressed by excessive rainfall and
low radiation. In the southern basins, the linear correlations
between\(\phi_{ET-P}^{\text{subbas}}\) and\(\phi_{ET-TWSA}^{\text{subbas}}\) are higher (Figure 4)
than those of the northern basins (red is more obvious for southern
basins, meaning the correlation coefficients are larger in those
basins), and the correlation is also more significant (\emph{p} is
significantly less than \emph{0.05} ). It indicates that rainfall and
water storage have mutual constraints in affecting \emph{ET} . \emph{ET}
decreases as rainfall decreases. Nonetheless, the trend of \emph{ET} has
resumed before the peak of the dry season and increased with the
increase of solar radiation, showing that trees can obtain soil water /
groundwater even during the peak of the dry season.

Qualitatively, north-to-south patterns of phase lag are obvious due to
these sub-basins vary considerably in topography and rainfall patterns.
For example, the elevation and the surface slope of the Andes mountain
area and southern basins are obviously higher than those of the Amazon
River basin. \emph{P} (Figure S2) and \emph{ET} (Figure S3) present
different seasonality in each subbasin. And the intensity of rainfall in
each subbasin also varies (Figure S4), which also present north-south
pattern. We explore the light and water limitations in the sub-basins by
using Budyko analysis in the following Section.

\textbf{3.3 Budyko analysis for sub-basins}

To analyze the phase lag patterns across the sub-basins, we applied the
Budyko framework (Figure 5). Since Budyko analysis is only applicable
over annual or longer time frames and for large-scale watersheds, we
analyzed the annual averaged data for each sub-basin. Almost all the
sub-basins are energy limited, but some sub-basins (\#5, \#9, \#16, and
\#33) in some years are water limited, which are located in the south of
Amazon (subplots on the bottom row of Figure 5).
Plotting\(\phi_{ET-P}^{\text{subbas}}\) and\(\phi_{ET-TWSA}^{\text{subbas}}\) against \emph{PET} /
\emph{P} shows that the northern and southern basins are clearly
separated (Figures S5 and S6). Except for sub-basins \#2, \#4, \#6, and
\#13, where \emph{PET}/ \emph{P} is greater than \textasciitilde{}0.65,
the correlations between \(\phi_{ET-P}^{\text{subbas}}\) and\(\phi_{ET-TWSA}^{\text{subbas}}\) are
statistically significant (Figure S7). When the linear correlation
coefficients are greater than \textasciitilde{}0.6, the correlations are
significant (\emph{p \textless{} 0.05} ) (Figure S8).

Water-limited sub-basins tend to have smaller\(\phi_{ET-P}^{\text{subbas}}\)
(southern basins, Figures 4 and 5), which implies a less delayed
\emph{ET} after \emph{P} . For these southern basins, the linear
correlations between\(\phi_{ET-P}^{\text{subbas}}\) and\(\phi_{ET-TWSA}^{\text{subbas}}\) are more
statistically significant, indicating that if the immediate supply from
\emph{P} is insufficient to maintain \emph{ET} , groundwater plays an
important role. However, if the sub-basin is not water limited, the
correlation between the phase lags is not statistically significant,
thus groundwater is less effectively affecting \emph{ET} than in those
water limited sub-basins.

\textbf{3.4 Phase for kilometer scale variables}

By downscaling \emph{P} and \emph{TWSA} to the same resolution
as\emph{ET} , we calculated 1 km spatial scale phase relationships
between\emph{ET} and \emph{P} (\(\phi_{ET-P}^{1km}\); Figure 6) and
\emph{ET}and \emph{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 \(\phi_{ET-P}^{1km}\) (\textasciitilde{}6 month) in the middle
latitudes of the Amazon basin (-5° \textasciitilde{} -10°) that varies
to the negative \(\phi_{ET-P}^{1km}\) (\textasciitilde{}-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 \emph{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 (\textasciitilde{}-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 \emph{ET} and \emph{P} (\emph{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
CO\textsubscript{2} growth rate is closely related to \emph{TWSA} .
Considering that plant transpiration is related to
CO\textsubscript{2}absorption through leaf stomata, the variability of
\emph{ET} is also closely associated with \emph{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 \emph{ET} is snow and ice cover, and
\emph{ET} should mostly be driven by solar radiation. Thus, in these
areas \emph{ET} is unaffected by groundwater depth and the timing
for\emph{ET} 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 \textasciitilde{}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 of\emph{ET} , \emph{P} , or
\emph{TWSA} alone. Across the basin, the spatial standard deviation of
annual \emph{ET} is negatively correlated to that of \(\phi_{ET-P}^{1km}\)
(Figure 8; \emph{r = -0.92} and\emph{R\textsuperscript{2} = 0.85} ).
Since the inter-annual variation of\emph{ET} is small (Figure 3c), in
some areas \emph{ET} and the aridity index may remain about the same
regardless of annual precipitation. When the areas with low \emph{ET} in
dry years have recovered from water limitation, indicating \emph{ET}
possibly increased in these areas and the values become close to those
in the unaffected areas, the overall spatial standard deviation of
\emph{ET} decreases, but the spatial variation of \(\phi_{ET-P}^{1km}\)
becomes larger due to the generally small variation in \emph{ET} (Figure
8). This relationship implies that the spatial variation of \emph{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 of\emph{ET} means the change of \emph{ET}
spatial heterogeneity.

\textbf{3.5 Phase lag for three zones' averaged variables}

As can be noted from the spatial variations of phases,\(\phi_{ET-P}^{1km}\)
and \(\phi_{ET-TWSA}^{1km}\), there are north-south and east-west patterns.
These patterns could indicate that there are spatially varied
differences in the interaction mechanism of\emph{ET} , \emph{P} , and
\emph{TWSA} . To further analyze the differences, we calculated the
phases for zone-averaged variables based on kilometer scale phases
(Figures 6 and 7). The detailed method for zone partitioning is
described in the supporting information (SI). Zone 1 and Zone 2 are
marked by the negative phase (blue) and positive phase (yellow),
respectively, while Zone 3 is for the phase approaching zero (green)
(Figure S9). Zone 1 covers the north half of the Amazon basin with some
scattered regions in the mid-south area. The south half part (except the
scattered area of Zone 1) and some northern-most regions constitute Zone
3 except for the southwest Andes mountain and the areas with low
vegetation cover, which are marked by Zone 2. The results of the phase
lag for the three zones' averaged variables are shown in Figures 9, 10,
and 11, respectively.

For Zone 1, the trends of \(\phi_{ET-P}^{Zone\ 1}\) and\(\phi_{ET-TWSA}^{Zone\ 1}\) are
both relatively stable during 2002 to 2013 (Figure 9a). The monthly peak
and trough of \emph{P} and \emph{ET}are out of phase (Figure 9b). The
annual \emph{P} in this zone is larger than those in other zones
(Figures 9c, 10c, and 11c), which implies that larger \emph{P} (and less
radiation) suppresses \emph{ET} . In addition, the phases slight
increase in drought years, suggesting the suppression of \emph{P} on
\emph{ET} decreases along with the reduction of \emph{P}and cloud-cover.
The small variations of two phases relate to sufficient\emph{P} ,
indicating the drought events may have weak impact on the\emph{ET} in
Zone 1. The suppression of \emph{ET} in Zone 1 is most likely that the
cloudy conditions limit the energy available to drive\emph{ET} . Thus,
this area is considered to be light limited.

As Zone 2 has mountain areas that are covered by low vegetation, snow
and ice, and therefore \emph{ET} is mainly driven by solar radiation.
The drought event in 2005 promotes the impact of rainfall on
\emph{ET}(Figure 10a), indicating that Zone 2 was also water limited,
which corresponds to the Budyko analysis. The time series of \emph{P}
and\emph{ET} are resonant before 2005. However, the monthly peak and
trough of \emph{P} and \emph{ET} time series are offset and the
amplitude of\emph{TWSA} variation slightly increases after 2005 (Figure
10b). These patterns could indicate that \emph{P} has a positive effect
on \emph{ET}before 2005, and suppresses \emph{ET} after 2005.

The variations of phases for Zone 3 averaged variables correspond well
to the drought events (Figure 11). This is the regime with higher
aridity index (the lowest annual averaged \emph{P} among three zones),
where \emph{P} is not large enough to suppress \emph{ET} and is
therefore water limited, and this is corroborated in the Section 3.3.
The variations of phases for Zone 3 are also relatively similar to those
at the whole Amazon scale (Figure 3). The close response
of\(\phi_{ET-P}^{Zone\ 3}\) to the variation of the annual \emph{P}supports the
hypothesis that when \emph{P} is small, \emph{ET} relies on rapid
evaporation of rainfall. The large variation and the similar response of
\(\phi_{ET-TWSA}^{Zone\ 3}\) to the annual\emph{P} indicate that groundwater
supports \emph{ET} during the dry periods (Figure 11a) via water supply
mechanism (rooting depth and groundwater) and vegetation water
requirement (Christoffersen et al., 2014).

\emph{ET} presents different seasonality in different zones (Figure S9).
In August and September, it peaks in Zone 1 while is lowest in Zone 2
with the largest variation. In Zone 3, the lowest \emph{ET} occurs in
June (Figure S10). The seasonality of precipitation in Zone 2 and 3 are
similar, but it is slightly different in Zone 1 (Figure S11). The
precipitation in Zone 3 is much more intense as there are many more days
with daily rainfall larger than 20 mm, which is not the case for Zones 1
and 2. Therefore, controls of \emph{ET} across the different area of the
Amazon basin vary. Evaporation demand (especially net radiation) plays a
more important role in wetter forests, and soil moisture (or \emph{P} )
has larger affects in the relative drier area (Rocha et al., 2009). The
soil water storage still remains relatively large after the start of the
dry season (i.e. when rainfall is small). When the soils reach their
lower water storage capacity, 3 months after the peak of the dry season,
the rainy season has already started to provide enough water supply for
plants. Therefore, the annual flux of \emph{ET} remains relatively
stable in dry years.

\textbf{4. Conclusions}

Using wavelet coherence analysis, we found that Amazon-scale averaged
evapotranspiration (\emph{ET} ) has strong correlations with
precipitation (\emph{P} ) and the total water storage anomaly
(\emph{TWSA} ) at the annual and multi-year (\textasciitilde{}2 to
\textasciitilde{} 4 year) periodicities. But the strong annual
periodicity was no longer significant due to irregular short-term
pattern of \emph{ET} after 2010 (drought event). Moreover, at multi-year
scale the correlation from 2006 to 2012, possibly indicating that
external climate drivers (drought and El Nino events) have enhanced the
impact of groundwater on \emph{ET} . The spatial distributions
of\(\phi_{ET-P}^{1km}\) and \(\phi_{ET-TWSA}^{1km}\) across the Amazon basin have
clear large south-north and small east-to-west patterns, and our Budyko
framework analysis demonstrates that the water and energy limitation
conditions vary significantly between the northern and southern
sub-basins of the Amazon. Although the Amazon basin is generally energy
limited, some southern sub-basins are water limited in some
years.\(\ \phi_{ET-P}^{\text{subbas}}\) and\(\phi_{ET-TWSA}^{\text{subbas}}\) are also well correlated
in the southern Amazon. The strength and significance of their
correlations are affected by the aridity index (\emph{PET} / \emph{P} )
of each sub-basin. The spatial heterogeneity of \(\phi_{ET-P}^{1\ km}\) is
negatively correlated with the spatial variation of annual \emph{ET} ,
which implies that the spatial variation of \emph{ET} is the primary
cause for the changing pattern of \(\phi_{ET-P}^{1\ km}\)
inter-annually.\(\phi_{ET-P}^{1\ km}\) and \(\phi_{ET-TWSA}^{1km}\) show the
dynamic changes of the spatiotemporal correlation among \emph{ET}
,\emph{P} , and \emph{TWSA} . The water limited area gradually decreases
due to the frequent deforestation in the southern Amazon basin.

The results of the three zones analysis also confirm that the effect of
drought on \emph{ET} has the south-north patterns. The drought events
have weak impact on \emph{ET} with sufficient annual \emph{P} in the
northern Amazon basin, and in the southwest Amazon basin as well, where
the main source of \emph{ET} in the mountain areas is snow and ice
cover. But the variation of phase in the southeast Amazon basin is
closely related to the drought events. During the drought year (2010),
the decreased phases (\(\phi_{ET-P}^{\text{Amazon}}\) and\(\phi_{ET-TWSA}^{\text{Amazon}}\)) likely
indicate that \emph{ET} was supported by both rainfall and groundwater
to maintain the same yield compared to the years with sufficient
\emph{P} . After the drought year, when the watershed was no longer
water limited,\(\phi_{ET-TWSA}^{\text{Amazon}}\) increased rapidly, possibly implying
the groundwater system had recovered and \emph{ET} was not immediately
supported by groundwater but by \emph{P} , since\(\phi_{ET-P}^{\text{Amazon}}\) is
much smaller than\(\phi_{ET-TWSA}^{\text{Amazon}}\) during this recovery period. Thus,
Amazon-wide annual \emph{ET} is possibly not limited by rainfall
availability since groundwater plays an important role during dry years.

The energy and water limitations are switched in some regions over time.
Whether \emph{ET} is driven by light-limited or water-limited needs to
be studied separately in specific areas. This work expounds a deeper
understanding of the control of \emph{ET} in different regions in the
Amazon basin by studying the phase lag between two variables at
different scales. However, in most cases, the seasonality of \emph{ET}is
driven by the balance between radiation, rainfall, and vegetation
regulations, rather than being completely limited by any one of these
factors. Vegetation phenology further increases the complexity of
studying the relative importance of controlling \emph{ET} factors in the
Amazon basin. Future, we expect to add datasets about radiation and
vegetation to further analyze the factors of controlling \emph{ET} in
the Amazon basin.

\textbf{Acknowledgements}

This research was partially supported by NSF project of Guangdong, China
under Contract 2018A030313165, and by the Director, Office Science,
Office of Biological and Environmental Research of the U.S. Department
of Energy under Contract DE-0010620 as part of their Earth System
Modeling and NGEE-Tropics Program.

\textbf{Data Availability Statement}

All data used in this study are publicly available online and can be
accessed through the links provided in the manuscript. All models or
code generated or used during the study are available from the
corresponding author by request.

\textbf{References:}

Andreo, B., Jimenez, P., Duran, J. J., Carrasco, F., Vadillo, I., \&
Mangin, A. (2006). Climatic and hydrological variations during the last
117 -- 166 years in the south of the Iberian Peninsula, from spectral
and correlation analyses and continuous wavelet analyses. \emph{Journal
of Hydrology} , \emph{324} , 24--39. https://doi.org/10.1016/j.
jhydrol.2005.09.010

Bonan, G. B., Levis, S., Kergoat, L., \& Oleson, K. W. (2002).
Landscapes as patches of plant functional types: An integrating concept
for climate and ecosystem models. \emph{Global Biogeocheical Cycles}
,\emph{16} , 5-1-5-23. https://doi.org/10.1029/2000GB001360

Brando, P. M., Goetz, S. J., Baccini, A., Nepstad, D. C., Beck, P. S.
A., \& Christman, M. C. (2010). Seasonal and interannual variability of
climate and vegetation indices across the Amazon. \emph{Proceedings of
the National Academy of sciences of the United States of America}
,\emph{107} , 14685--14690. https://doi.org/ 10.1073/pnas.0908741107

Briggs, J. M., \& Knapp, A. K. (1995). Interannual Variability in
Primary Production in Tallgrass Prairie: Climate, Soil Moisture,
Topographic Position, and Fire as Determinants of Aboveground
Biomass.\emph{American Journal of Botany} , \emph{82} , 1024-1030.
https://doi.org/10.2307/2446232

Budyko, M. I. (1974). Climate and Life. Academic Press, New York.

Carabajal, C. C., \& Harding, D. J. (2006). SRTM C-Band and ICEsat Laser
Altimetry Elevation Comparisons as a Function of Tree Cover and
Relief.\emph{Photogrammetric Engineering \& Remote Sensing} , \emph{72}
, 287--298. https://doi.org/10.14358/PERS.72.3.287

Christoffersen, B. O., Restrepo-Coupe, N., Arain, M. A., Baker, I. T.,
Cestaro, B. P., Ciais, P., Fisher, J. B., Galbraith, D., Guan, X. D.,
Gulden, L., Hurk, B. V. D., Ichii, K., Imbuzeiro, H., Jain, A., Levine,
N., Miguez-Macho, G., Poulter, B., Roberti, D. R., Sakaguchi, K., Sahoo,
A., Schaefer, K., Shi, M., Verbeeck, H., \& Yang, Z. L. (2014).
Mechanisms of water supply and vegetation demand govern the seasonality
and magnitude of evapotranspiration in Amazonia and
Cerrado.\emph{Agricultural and Forest Meteorology} , \emph{191} , 33-50.
https://doi.org/ 10.1016/j.agrformet.2014.02.008

Costa, M. H., Biajoli, M. C., Sanches, L., Malhado, A., Hutyra, L. R.,
\& Da Rocha, H. R. (2010). Atmospheric. versus vegetation controls of
Amazonian tropicalrain forest evapotranspiration: are the wet and
seasonally dry rain forests any different? \emph{Journal of Geophysical
Research: Biogeosciences} , \emph{115} , 1--9. https://doi.org/
10.1029/2009JG001179

Culf, A. D., Foken, T., \& Gash, J. H. C. (2008). The energy balance
closure problem: an overview. \emph{Ecological Applications} , \emph{18}
, 1351-1367. https://doi.org/10.1890/06-0922.1

Danko, D. M. (1992). The digital chart of the
world.\emph{Photogrammetric Engineering and Remote Sensing} , \emph{58}
. https://doi.org/10.1016/0924-2716(92)90041-7

Daubechies, I. (1990). The wavelet transform, time-frequency
localization and signal analysis. Information Theory, IEEE Transactions
on \emph{36} , 961--1005. https://doi.org/10.1063/1.4928520

Doughty, C. E., \& Goulden, M. L. (2008). Seasonal patterns of tropical
forest leaf area index and CO\textsubscript{2} exchange. \emph{Journal
of Geophysical Research-Biogeoscience} \emph{113} , n/a-n/a.
https://doi/org/10.1029/2007JG000590

Doughty, C. E., Metcalfe, D. B., Girardin, C. A. J., Amézquita, F. F.,
Cabrera, D. G., Huasco, W. H., Silva-Espejo, J. E., Araujo-Murakami, A.,
da Costa, M. C., Rocha, W., Feldpausch, T. R., Mendoza, A. L. M., da
Costa, A. C. L., Meir, P., Phillips, O. L., \& Malhi, Y. (2015). Drought
impact on forest carbon dynamics and fluxes in Amazonia. \emph{Nature}
,\emph{519} , 78--82. https://doi.org/10.1038/nature14213

Fan, Y., Li, H., \& Miguez-Macho, G. (2013). Global Patterns of
Groundwater Table Depth. \emph{Science} , \emph{339} , 940--943.
https://doi.org/10.1126/science.1229881

Feng, X., Porporato, A., \& Rodriguez-Iturbe, I. (2013). Changes in
rainfall seasonality in the tropics. \emph{National Climate Change}
,\emph{3} , 811--815. https://doi.org/10.1038/nclimate1907

Franken, W., \& Leopoldo, P. R. (1984). The Amazon-Limnology and
landscape ecology of a mighty tropical river and its basin. Dr W. Junk
Publishers. https://doi.org/10.1007/978-94-009-6542-3\_27

Fu, R., \& Li, W. (2004). The influence of the land surface on the
transition from dry to wet season in Amazonia. \emph{Theoretical and
Applied Climatology} , \emph{78} , 97--110.
https://doi.org/10.1007/s00704-004-0046-7

Guber, A. K., Pachepsky, Y. A., van Genuchten, M. T., Rawls, W. J.,
Simunek, J., Jacques, D., Nicholson, T. J., \& Cady, R. E. (2006).
Field-Scale Water Flow Simulations Using Ensembles of Pedotransfer
Functions for Soil Water Retention. \emph{Vadose Zone Journal} ,\emph{5}
, 234-247. https://doi.org/10.2136/vzj2005.0111

Hasler, N., \& Avissar, R. (2006). What controls evapotranspiration in
the amazon basin? \emph{Journal of Hydrometeorology} , \emph{8} ,
380-395. https://doi.org/10.1175/JHM587.1

Hilker, T., Lyapustin, A. I., Tucker, C. J., Hall, F. G., Myneni, R. B.,
Wang, Y., Bi, J., Mendes de Moura, Y., \& Sellers, P. J. (2014).
Vegetation dynamics and rainfall sensitivity of the
Amazon.\emph{Proceedings of the National Academy of sciences of the
United States of America} , \emph{111} , 16041--16046.
https://doi.org/10.1073/ pnas.1404870111

Hodnett, M. G., Vendrame, I., Filho, A. D. O. M., Oyama, M. D., \&
Tomasella, J. (1997). Soil water storage and groundwater behaviour in a
catenary sequence beneath forest in central Amazonia: i. comparisons
between plateau, slope and valley floor. \emph{Hydrology and Earth
System Sciences} , \emph{1} , 279--290. https://doi.org/
10.5194/hess-1-265-1997

Huete, A. R., Didan, K., Shimabukuro, Y. E., Ratana, P., Saleska, S. R.,
Hutyra, L. R., Yang, W., Nemani, R. R., \& Myneni, R. (2006). Amazon
rainforests green-up with sunlight in dry season. \emph{Geophysical
Research Letters} , \emph{33} , 272-288.
https://doi.org/10.1029/2005GL025583

Humphrey, V., Zscheischler, J., Ciais, P., Cudmundsson, L., Sitch, S.,
\& Seneviratne, S. I. (2018). Sensitivity of atmospheric
CO\textsubscript{2} growth rate to observed changes in terrestrial water
storage. \emph{Nature} , \emph{560} , 628-631. https://
doi.org/10.1038/s41586-018-0424-4

Huxman, T. E., Snyder, K. A., Tissue, D., Leffler, A. J., Ogle, K.,
Pockman, W. T, Sandquist, D. R., Potts, D. L., \& Schwinning, S. (2004).
Precipitation pulses and carbon fluxes in semiarid and arid
ecosystems.\emph{Oecologia} , \emph{141} , 254--268.
https://doi.org/10.1007/s00442-004-1682-4

Jones, M. O., Kimball, J. S., \& Nemani, R. R. (2014). Asynchronous
Amazon forest canopy phenology indicates adaptation to both water and
light availability. \emph{Environmental Research Letters} , \emph{9} ,
124021. https://doi.org/ 10.1088/1748-9326/9/12/124021

Kleidon, A., \& Heimann, M. (2000). Assessing the role of deep rooted
vegetation in the climate system with model simulations: mechanism,
comparison to observations and implications for Amazonian
deforestation.\emph{Climate Dynamics} , \emph{16} , 183--199.
https://doi.org/10.1007/s003820050012

Labat, D. (2005). Recent advances in wavelet analyses: Part 1. A review
of concepts. \emph{Journal of Hydrology} , \emph{314} , 275--288.
https://doi.org/10.1016/j.jhydrol.2005.04.003

Labat, D., Ronchail, J., \& Guyot, J. L. (2005). Recent advances in
wavelet analyses: Part 2---Amazon, Parana, Orinoco and Congo discharges
time scale variability. \emph{Journal of Hydrology} , \emph{314} ,
289--311. https://doi. org/10.1016/j.jhydrol.2005.04.004

Lai, C. T., \& Katul, G. (2000). The dynamic role of root-water uptake
in coupling potential to actual transpiration. \emph{Advances in Water
Resources,} \emph{23} , 427--439.
https://doi.org/10.1016/S0309-1708(99)00023-8

Landerer, F. W., \& Swenson, S. C. (2012). Accuracy of scaled GRACE
terrestrial water storage estimates. \emph{Water Resources Research}
,\emph{48} , 4531. https://doi.org/10.1029/2011WR011453

Leopoldo, P. R., Franken, W. K., \& Villa Nova, N. A. (1995). Real
evapotranspiration and transpiration through a tropical rain forest in
central Amazonia as estimated by the water balance method. \emph{Forest
Ecology \& Management} , \emph{73} , 185--195.
https://doi.org/10.1016/0378-1127(94)03487-H

Lesack, L. F. W. (1993). Water balance and hydrologic characteristics of
a rain forest catchment in the central Amazon Basin. \emph{Water
Resources Research} , \emph{29} , 759--773.
https://doi.org/10.1029/92WR02371

Lettau, H., Lettau, K., \& Molion, L. C. B. (1979). Amazonia's
Hydrologic Cycle and the Role of Atmospheric Recycling in Assessing
Deforestation Effects. \emph{Monthly Weather Review} , \emph{107} , 227.
https://doi.org/10.1175/
1520-0493(1979)107\textless{}0227:AHCATR\textgreater{}2.0.CO;2

Maeda, E. E., Ma, X., Wagner, F. H., Kim, H., Oki, T., Eam D., \& Huete,
A. (2017). us, Evapotranspiration seasonality across the Amazon
Basin.\emph{Earth System Dynamics Discussions} , \emph{8} , 439--454.
https://doi.org/ 10.5194/esd-2016-75

Malhi, Y., Pegoraro, E., Nobre, A. D., Pereira, M. G. P., Grace, J.,
Culf, A. D., \& Clement, R. (2002). Energy and water dynamics of a
central Amazonian rain forest. \emph{Journal of Geophysical Research:
Atmospheres} , \emph{107} , 8061. https://doi.org/10.1029/2001JD000623

Mayorga, E., Logsdon, M. G., Ballester, M. V. R., \& Richey, J. E.
(2005). Estimating cell-to-cell land surface drainage paths from digital
channel networks, with an application to the Amazon basin. \emph{Journal
of Hydrology} , \emph{315} , 167-182.
https://doi.org/10.1016/j.jhydrol.2005.03.023

Miguez-Macho, G., \& Fan, Y. (2012a). The role of groundwater in the
Amazon water cycle: 1. Influence on seasonal streamflow, flooding and
wetlands. \emph{Journal of Geophysical Research: Atmospheres}
,\emph{117} , 1--30. https://doi.org/10.1029/2012JD017539

Miguez-Macho, G., \& Fan, Y. (2012b). The role of groundwater in the
Amazon water cycle: 2. Influence on seasonal soil moisture and
evapotranspiration. \emph{Journal of Geophysical Research: Atmospheres}
,\emph{117} , D15114. https://doi.org/10.1029/2012JD017540

Molénat, J., Davy, P., Gascuel-Odoux, C., \& Durand, P. (1999). Study of
three subsurface hydrologic systems based on spectral and cross-spectral
analysis of time series. \emph{Journal of Hydrology} , \emph{222} ,
152--164. https://doi.org/ 10.1016/S0022-1694(99)00107-9

Mooney, H. A., Dirzo, R., Ceballos, G., \& Young, H. S. (2011).
Seasonally dry tropical forests: ecology and
conservation.\emph{Seasonally Dry Tropical Forests} .

Morton, D.C., Nagol, J., Carabajal, C.C., Rosette, J., Palace, M., Cook,
B.D., Vermote, E.F., Harding, D.J., North, P.R.J., 2014. Amazon forests
maintain consistent canopy structure and greenness during the dry
season. \emph{Nature} , \emph{506} , 221--224.
https://doi.org/10.1038/nature13006

Mu, Q., Heinsch, F.A., Zhao, M., Running, S.W., 2007. Development of a
global evapotranspiration algorithm based on MODIS and global
meteorology data. \emph{Remote Sensing of Environment} , \emph{106} ,
285--304. https://doi.org/10.1016/j.rse.2006.07.007

Mu, Q., Zhao, M., Running, S.W., 2011. Improvements to a MODIS global
terrestrial evapotranspiration algorithm. \emph{Remote Sensing of
Environment} , \emph{115} , 1781--1800.
https://doi.org/10.1016/j.rse.2011.02.019

Myneni, R. B., Yang, W., Nemani, R. R., Huete, A. R., Dickinson, R. E.,
Knyazikhin, Y., Didan, K., Fu, R., Negron Juarez, R. I., Saatchi. S. S.,
Hashimoto, H., Ichii, K., Shabanov, N. V., Tan, B., Ratana, P.,
Privette, J. L., Morisette, J. T., Vermote, E. F., Roy, D. P., Wolfe, R.
E., Friedl, M. A., Running, S. W., Votava, P., El-Saleous, N., Devadiga,
S., Su, Y., \& Salomonson, V. V. (2007). Large seasonal swings in leaf
area of Amazon rainforests. \emph{Proceedings of the National Academy of
sciences of the United States of America} , \emph{104} , 4820--4823.
https://doi.org/10.1073/pnas.0611338104

Nemani, R.R., 2003. Climate-Driven Increases in Global Terrestrial Net
Primary Production from 1982 to 1999. \emph{Science} , \emph{300} ,
1560--1563. https://doi.org/10.1126/science.1082750

Nepstad, D. C., de Carvalho, C. R., Davidson, E. A., Jipp, P. H.,
Lefebvre, P. A., Negreiros, G. H., da Silva, E. D., Stone, T. A.,
Trumbore, S. E., \& Vieira, S. (1994). The role of deep roots in the
hydrological and carbon cycles of Amazonian forests and
pastures,\emph{Nature} , \emph{372} , 666--669.
https://doi.org/10.1038/372666a0

Niu, J., Shen, C., Chambers, J. Q., Melack, J. M., \& Riley, W. J.
(2017). Interannual Variation in Hydrologic Budgets in an Amazonian
Watershed with a Coupled Subsurface - Land Surface Process
Model.\emph{Journal of Hydrometeorology} , \emph{18} , 2597-2617.
https://doi.org/10.1175/JHM-D-17-0108.1

Nobre, A. D., Cuartas, L. A., Hodnett, M., Rennó, C. D., Rodrigues, G.,
Silveira, A., Waterloo, M., \& Saleska, S. (2011). Height Above the
Nearest Drainage - a hydrologically relevant new terrain
model.\emph{Journal of Hydrology} , \emph{404} , 13--29.
https://doi.org/10.1016/j.jhydrol.2011.03.051

Oleson, K. W., Lawrence, D. M., Bonan, G. B., Drewniak, B., Huang ,M.,
Charles, D., Levis, S., Li, F., Riley, W. J., Zachary, M., Swenson, S.
C., Thornton, P. E., Bozbiyik, A., Fisher, R., Heald, C. L., Kluzek, E.,
Lamarque, F., Lawrence, P. J., Leung, L. R., Muszala, S., Ricciuto, D.
M., \& Sacks, W. (2013). Technical description of version 4.5 of the
Community Land Model (CLM). \emph{National Central Atmosphere Research
Boulder} , CO 420pp. https://doi.org/10.5065/D6RR1W7M

Piao, S., Ito, A., Li, S., Huang, Y., Ciais, P., Wang, X., Peng, S.,
Andres, R. J., Fang, J., Jeong, S., Mao, J., Mohammat, A., Muraoka, H.,
Nan, H., Peng, C., Peylin, P., Shi, X., Sitch, S., Tao, S., Tian, H.,
Xu, M., Yu, G., Zeng, N., \& Zhu, B. (2012). The carbon budget of
terrestrial ecosystems in East Asia over the last two
decades.\emph{Biogeosciences} , \emph{9} , 4025--4066.
https://doi.org/10.5194/bg-9-3571-2012

Restrepo-Coupe, N., Levine, N. M., Christoffersen, B. O., Albert, L. P.,
Wu, J., Costa, M. H., Galbraith, D., Imbuzeiro, H., Martins, G., da
Araujo, A. C., Malhi, Y. S., Zeng, X., Moorcroft, P., \& Saleska, S. R.
(2016). Do dynamic global vegetation models capture the seasonality of
carbon fluxes in the Amazon basin? A data-model
intercomparison.\emph{Global Change Biology} , 1--18.
https://doi.org/10.1111/gcb.13442

Rocha, H. R. D., Manzi, A. O., Cabral, O. M., Miller, S. D., Goulden, M.
L., \& Saleska, S. R. (2015). Patterns of water and heat flux across a
biome gradient from tropical forest to savanna in brazil. \emph{Journal
of Geophysical Research Biogeosciences} , \emph{114} , 579-581.
https://doi.org/10.1029/2007JG000640

Salati, E., Dall'Olio, A., Matsui, E., \& Gat, J. R., (1979). Recycling
of water in the Amazon Basin: An isotopic study. \emph{Water Resources
Research} , \emph{15} , 1250. https://doi.org/10.1029/WR015i005p01250

Saleska, S. R., Miller, S. D., Matross, D. M., Goulden, M. L., Wofsy, S.
C., da Rocha, H. R., de Camargo, P. B., Crill, P., Daube, B. C., de
Freitas, H. C., Hutyra, L., Keller, M., Kirchhoff, V., Menton, M.,
Munger, J. W., Pyle, E. H., Rice, A. H., \& Silva, H. (2003). Carbon in
Amazon forests: unexpected seasonal fluxes and disturbance-induced
losses. \emph{Science} , \emph{302} , 1554--1557.
https://doi.org/10.1126/science.1091165

Samanta, A., Knyazikhin, Y., Xu, L., Dickinson, R. E., Fu, R., Costa, M.
H., Saatchi, S. S., Nemani, R. R., \& Myneni, R. B. (2012). Seasonal
changes in leaf area of Amazon forests from leaf flushing and
abscission. \emph{Journal of Geophysical Research Biogeosciences}
,\emph{117} , 75-81. https://doi.org/10.1029/2011JG001818

Schaefli, B., Maraun, D., \& Holschneider, M. (2007). What drives high
flow events in the Swiss Alps? Recent developments in wavelet spectral
analysis and their application to hydrology. \emph{Advances in Water
Resources} , \emph{30} , 2511--2525.
https://doi.org/10.1016/j.advwatres.2007.06.004

Shen, C., Niu, J., \& Phanikumar, M. S. (2013). Evaluating controls on
coupled hydrologic and vegetation dynamics in a humid continental
climate watershed using a subsurface-land surface processes
model.\emph{Water Resources Research} , \emph{49} , 552--2572.
https://doi.org/10.1002/wrcr.20189

Shen, C., \& Phanikumar, M.S. (2010). A process-based, distributed
hydrologic model based on a large-scale method for surface--subsurface
coupling. \emph{Advances in Water Resources} , \emph{33} , 1524--1541.
https://doi.org/ 10.1016/j.advwatres.2010.09.002

Simard, M., Pinto, N., Fisher, J. B., \& Baccini, A. (2011). Mapping
forest canopy height globally with spaceborne lidar. \emph{Journal of
Geophysical Research Biogeosciences} , \emph{116} , 1--12.
https://doi.org/10.1029/ 2011JG001708

Spracklen, D. V., Arnold, S. R., \& Taylor, C. M. (2012). Observations
of increased tropical rainfall preceded. by air passage over forests.
Nature, 489, 282-285. https://doi.org/10.1038/nature11390

Swann, A. L. S., \& Koven, C. D. (2017) A direct estimate of the
seasonal cycle of evapotranspiration over the amazon.
basin.\emph{Journal of Hydrometeorology} .
https://doi.org/10.1175/JHM-D-17-0004.1

Swenson, S. C., \& Wahr, J. (2006). Post-processing removal of
correlated errors in GRACE data. \emph{Geophysical Research Letters}
,\emph{33} , L08402. https://doi.org/10.1029/2005GL025285

Tang, J., Riley, W. J., \& Niu, J. (2015). Incorporating root hydraulic
redistribution in CLM4.5: Effects on predicted site and global
evapotranspiration, soil moisture, and water storage. \emph{Journal of
Advances in Modeling Earth Systems} , \emph{7} , 1828-1848.
https://doi.org/10.1002/2015MS000484

Tomasella, A. J., \& Hodnett, M. G. (1998). Estimating soil water
retention characteristics from limited data in Brazilian
Amazonia.\emph{Soil Science} , \emph{163} , 190-202.
https://doi.org/10.1097/00010694-199803000-00003

Torrence, C., \& Compo, G. P. (1998). A Practical Guide to Wavelet
Analysis. \emph{Bulletin of the American Meteorological Society}
,\emph{79} , 61--78.
https://doi.org/10.1175/1520-0477(1998)079\textless{}0061:APGTWA\textgreater{}2.0.
CO;2

van Genuchten, M. T. (1980). A Closed-form Equation for Predicting the
Hydraulic Conductivity of Unsaturated Soils1. \emph{Soil Science Society
of America Journal} . https://doi.org/10.2136/sssaj1980.0361599500440005
0002x

Wagner, F. H., Hérault, B., Bonal, D., Stahl, C., Anderson, L. O.,
Baker, T. R., Becker, G. S., Beeckman, H., Boanerges Souza, D., Botosso,
P. C., Bowman, D. M. J. S., Bräuning, A., Brede, B., Brown, F. I.,
Camarero, J. J., Camargo, P. B., Cardoso, F. C. G., Carvalho, F. A.,
Castro, W., Chagas, R. K., Chave, J., Chidumayo, E. N., Clark, D. A.,
Costa, F. R. C., Couralet, C., da Silva Mauricio, P. H., Dalitz, H., de
Castro, V. R., de Freitas Milani, J. E., de Oliveira, E. C., de Souza
Arruda, L., Devineau, J-L., Drew, D. M., Dünisch, O., Durigan, G.,
Elifuraha, E., Fedele, M., Ferreira Fedele, L., Figueiredo Filho, A.,
Finger, C. A. G., Franco, A. C., Freitas Júnior, J. L., Galvão, F.,
Gebrekirstos, A., Gliniars, R., Graça, P. M. L., de, A., Griffiths, A.
D., Grogan, J., Guan, K., Homeier, J., Kanieski, M. R., Kho, L. K.,
Koenig, J., Kohler, S. V., Krepkowski, J., Lemos-Filho, J. P.,
Lieberman, D., Lieberman, M. E., Lisi, C. S., Longhi Santos T, López
Ayala, J. L., Maeda, E. E., Malhi, Y., Maria, V. R. B., Marques, M. C.
M., Marques, R., Maza, C. H., Mbwambo, L., Melgaço, K. L. L.,
Mendivelso, H. A., Murphy, B. P., O'Brien, J. J., Oberbauer, S. F.,
Okada, N., Pélissier, R., Prior, L. D., Roig, F. A., Ross, M., Rossatto,
D. R., Rossi, V., Rowland, L., Rutishauser, E., Santana, H., Schulze,
M., Selhorst, D., Silva, W. R., Silveira, M., Spannl, S., Swaine, M. D.,
Toledo, J. J., Toledo, M. M., Toledo, M., Toma, T., Tomazello, F. M.,
Valdez Hernández, J. I., Verbesselt, J., Vieira, S. A., Vincent, G.,
Volkmer de Castilho, C., Volland, F., Worbes, M., Zanon, M. L. B., \&
Aragão, L. E. O. C. (2016). Climate seasonality limits leaf carbon
assimilation and wood productivity in tropical
forests.\emph{Biogeoscience} , \emph{13} , 2537--2562.
https://doi.org/10.5194/bg-13-2537-2016

Wang, D. (2012). Evaluating interannual water storage changes at
watersheds in Illinois based on long-term soil moisture and groundwater
level data. \emph{Water Resources Research} , \emph{48} , n/a-n/a.
https://doi.org/10.1029/ 2011wr010759

Weltzin, J. F., Loik, M. E., Schwinning, S., Williams, D. G., Fay, P.
A., Haddad, B. M., Harte, J., Huxman, T. E., Knapp, A. K., Lin, G.,
Pockman, W. T., Shaw, M. R., Small, E. E., Smith, M. D., Smith, S. D.,
Tissue, D. T., \& Zak, J. C. (2003). Assessing the Response of
Terrestrial Ecosystems to Potential Changes in
Precipitation.\emph{Bioscience} . \emph{53} , 941-952.
https://doi.org/10.1641/0006-3568(2003)053{[}0941:ATROTE{]}2.0. CO;2

Werth, D., \& Avissar, R. (2004). The regional evapotranspiration of the
Amazon. \emph{Journal of Hydrometeorology} , 5,100--109.
https://doi.org/10.1175/1525-7541(2004)005\textless{}0100:TREOTA\textgreater{}2.0.CO;2

Wilson, K., Glodstein, A., Falge, E., Aubinet, M., Baldocchi, D.,
Berbigier, P., Bernhofer, C., Ceulemans, R., Dolman, H., Field, C.,
Grelle, Grelle, A., Ibrom, A., Law, B. E., Kowalski, A., Meyers, T.,
Moncrieff, J., Monson, R., Oechel, W., Tenhunen, J., Valentini, R., \&
Verma, S. (2002). Energy balance closure at fluxnet
sites.\emph{Agricultural and Forest Meteorology} , \emph{113} , 223-243.
https://doi.org/10.1016/S0168-1923(02)00109-0

Yang, D., Sun, F., Liu, Z., Cong, Z., Ni, G., \& Lei, Z. (2007).
Analyzing spatial and temporal variability of annual water-energy
balance in nonhumid regions of China using the Budyko
hypothesis.\emph{Water Resources Research} , \emph{43} , 436-451.
https://doi.org/10.1029/2006WR005224

Zemp, D. C., Schleussner, C. F., Barbosa, H. M. J., \& Rammig, A.
(2017). Deforestation effects on Amazon. forest
resilience.\emph{Geophysical Research Letters} , \emph{44} .
https://doi.org/10.1002/2017GL072955

Zhang, J., Hao, Y., Hu, X., Huo, X., \& Hao, P. (2016). The effects of
monsoons and climate teleconnections on the Niangziguan Karst Spring
discharge in North China. \emph{Climate Dynamics} , \emph{48} , 53.
https://doi.org/10.1007/ s00382-016-3062-2

Zhang, L., Dawes, W. R., \& Walker, G. R. (2001). Response of mean
annual evapotranspiration to vegetation. changes at catchment scale.
Water Resources Research, 37, 701-708. https://doi.org/10.1029/2000WR
900325

\textbf{Figures}

\textbf{Figure 1.} Contour plots of wavelet power spectra of
precipitation (a), \emph{ET} (b), and \emph{TWSA} (c), and global
wavelet spectra of precipitation (d), \emph{ET} (e) and \emph{TWSA} (f).
The x-axes of subplots (a), (b), and (c) represent the time, the y-axis
represents the periodicity scale, and the color represents the magnitude
of the wavelet coefficient. The contour lines enclose regions of greater
than 95\% confidence (Torrence \& Compo, 1998). The x-axes of subplots
(d), (e), and (f) represent the power of global wavelet spectrum.

\textbf{Figure 2.} Cross wavelet power spectra of \emph{ET} and
\emph{P}(a), and \emph{ET} and \emph{TWSA} (b). The contour plots
represent the power of cross spectra and are shown as blank when the
values are smaller than 2\textsuperscript{-8}. The arrows represent the
phase relationship between these time series and are only presented when
the wavelet power is greater than 2\textsuperscript{-2}.

\textbf{Figure 3.} Plots of phase lags (a) between \emph{ET} and\emph{P}
(\(\phi_{ET-P}^{\text{Amazon}}\)), and between \emph{ET} and\emph{TWSA}
(\(\phi_{ET-TWSA}^{\text{Amazon}}\)); monthly time series data (b) of \emph{P} ,
\emph{TWSA} , and \emph{ET} ; and annual averaged data (c) of \emph{P} ,
\emph{ET} , and \emph{P -- ET} . All time series data are
spatially-averaged over the Amazon, and the phase lags are calculated
based on the spatially-averaged monthly time series data.

\textbf{Figure 4.} Sub-basins of Amazon (center subplot) and the phase
lags between \emph{ET} and \emph{P} (\(\phi_{ET-P}^{\text{subbas}}\)), and between
\emph{ET} and \emph{TWSA}(\(\phi_{ET-TWSA}^{\text{subbas}}\)) (subplots 1 -- 33). The
color saturation in the center sub-plot indicates the linear correlation
coefficients between \(\phi_{ET-P}^{\text{subbas}}\) and\(\phi_{ET-TWSA}^{\text{subbas}}\). Darker
means higher correlation as shown in the legend. The location of
subplots 1 -- 33 are generally corresponding to the geographical
position as shown in the center subplot. Subplots 1 -- 33 also show the
linear correlation coefficients and \emph{p} -values for testing the
hypothesis of no correlation against the alternative that there is a
nonzero correlation. If \emph{p} is small (i.e., \emph{p \textless{}
0.05} ), then the correlation is significantly different from zero. The
x-axes of subplots 1 -- 33 are the time (year), the left y-axes of them
are\(\phi_{ET-P}^{\text{subbas}}\) and the right ones are\(\phi_{ET-TWSA}^{\text{subbas}}\).

\textbf{Figure 5.} The Budyko framework applied to 33 sub-basins of
Amazon. In each subplot, the x-axes are the ratio between potential
evapotranspiration and precipitation (\emph{PET / P} ); the y-axes are
the ratio between actual ET and precipitation (\emph{ET / P} ); the
solid horizontal line indicates water limitation (i.e., annual \emph{ET}
= annual \emph{P} ); the 1:1 line indicates energy limitation
(annual\emph{ET} = annual \emph{PET} ); the dashed vertical line
indicates the boundary between these limitations; and the dots are the
annual averaged data for each sub-basin. The label of each subplot
corresponds to the index of each sub-basin (see Figure 4) and the
positions of them are generally corresponding to the geographical
location of each sub-basin.

\textbf{Figure 6.} Map of the pixel-by-pixel phase lag between
\emph{ET}and \emph{P} (\(\phi_{ET-P}^{1\ km}\)) for each year from 2002 to
2013. Different colors represent different phase lags in time (month) as
shown in the legend. Missing data from either \emph{ET} or \emph{P} are
shown as blank.

\textbf{Figure 7.} Map of the pixel-by-pixel phase lag between
\emph{ET}and \emph{TWSA} (\(\phi_{ET-TWSA}^{1\ km}\)) for each year from 2002 to
2013. Different colors represent different phase lags in time (month) as
shown in the legend. Missing data from either \emph{ET} or\emph{TWSA}
are shown as blank.

\textbf{Figure 8.} Correlation plot of the spatial standard deviation of
the pixel-by-pixel annual averaged phase lag between \emph{ET}
and\emph{P} (\(\selectlanguage{greek}\text{σϕ}\selectlanguage{english}_{ET-P}^{\text{pixel}}\)) and the standard deviation of annual
averaged \emph{ET} (\selectlanguage{greek}σ\selectlanguage{english}ET). The dots are the data and the
solid line is the fitting curve.

\textbf{Figure 9.} Plots of (a) phases between \emph{ET} and
\emph{P}(\(\phi_{ET-P}^{Zone\ 1}\)), and between \emph{ET} and
\emph{TWSA}(\(\phi_{ET-TWSA}^{Zone\ 1}\)); (b) monthly time series of \emph{P}
,\emph{TWSA} , and \emph{ET} ; and (c) annual averages of \emph{P}
,\emph{ET} , and \emph{P -- ET} . All time series data are spatially
averaged over Zone 1, and the phases are calculated based on the
spatially averaged monthly variables of Zone 1.

\textbf{Figure 10.} Plots of (a) phases between \emph{ET} and
\emph{P}(\(\phi_{ET-P}^{ZOne\ 2}\)), and between \emph{ET} and
\emph{TWSA}(\(\phi_{ET-TWSA}^{Zone\ 2}\)); (b) monthly time series of \emph{P}
,\emph{TWSA} , and \emph{ET} ; and (c) annual averages of \emph{P}
,\emph{ET} , and \emph{P -- ET} . All time series data are spatially
averaged over Zone 2, and the phases are calculated based on the
spatially averaged monthly variables of Zone 2.

\textbf{Figure 11.} Plots of (a) phases between \emph{ET} and
\emph{P}(\(\phi_{ET-P}^{Zone\ 3}\)), and between \emph{ET} and
\emph{TWSA}(\(\phi_{ET-TWSA}^{Zone\ 3}\)); (b) monthly time series of \emph{P}
,\emph{TWSA} , and \emph{ET} ; and (c) annual averages of \emph{P}
,\emph{ET} , and \emph{P -- ET} . All time series data are spatially
averaged over Zone 3, and the phases are calculated based on the
spatially averaged monthly variables of Zone 3.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/Figures-20200730/Figures-20200730}

\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\end{document}

