Figures
Figure 1. Contour plots of wavelet power spectra of
precipitation (a), ET (b), and TWSA (c), and global
wavelet spectra of precipitation (d), ET (e) and 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.
Figure 2. Cross wavelet power spectra of ET and P(a), and ET and TWSA (b). The contour plots represent the
power of cross spectra and are shown as blank when the values are
smaller than 2-8. The arrows represent the phase
relationship between these time series and are only presented when the
wavelet power is greater than 2-2.
Figure 3. Plots of phase lags (a) between ET andP (\(\phi_{ET-P}^{\text{Amazon}}\)), and between ET andTWSA (\(\phi_{ET-TWSA}^{\text{Amazon}}\)); monthly time series
data (b) of P , TWSA , and ET ; and annual averaged
data (c) of P , ET , and 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.
Figure 4. Sub-basins of Amazon (center subplot) and the phase
lags between ET and P (\(\phi_{ET-P}^{\text{subbas}}\)),
and between ET and 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 p -values for testing the hypothesis of no correlation against
the alternative that there is a nonzero correlation. If p is
small (i.e., p < 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\(\phi_{ET-TWSA}^{\text{subbas}}\).
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 (PET / P ); the y-axes are
the ratio between actual ET and precipitation (ET / P ); the solid
horizontal line indicates water limitation (i.e., annual ET =
annual P ); the 1:1 line indicates energy limitation (annualET = annual 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.
Figure 6. Map of the pixel-by-pixel phase lag between ETand 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 ET or P are
shown as blank.
Figure 7. Map of the pixel-by-pixel phase lag between ETand 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 ET orTWSA are shown as blank.
Figure 8. Correlation plot of the spatial standard deviation of
the pixel-by-pixel annual averaged phase lag between ET andP (\(\text{σϕ}_{ET-P}^{\text{pixel}}\)) and the standard
deviation of annual averaged ET (σET). The dots are
the data and the solid line is the fitting curve.
Figure 9. Plots of (a) phases between ET and P(\(\phi_{ET-P}^{Zone\ 1}\)), and between ET and TWSA(\(\phi_{ET-TWSA}^{Zone\ 1}\)); (b) monthly time series of P ,TWSA , and ET ; and (c) annual averages of P ,ET , and 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.
Figure 10. Plots of (a) phases between ET and P(\(\phi_{ET-P}^{ZOne\ 2}\)), and between ET and TWSA(\(\phi_{ET-TWSA}^{Zone\ 2}\)); (b) monthly time series of P ,TWSA , and ET ; and (c) annual averages of P ,ET , and 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.
Figure 11. Plots of (a) phases between ET and P(\(\phi_{ET-P}^{Zone\ 3}\)), and between ET and TWSA(\(\phi_{ET-TWSA}^{Zone\ 3}\)); (b) monthly time series of P ,TWSA , and ET ; and (c) annual averages of P ,ET , and 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.