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 (ET ) links regional climate and forest function and plays an important role in the hydrological cycle. It is also an internal connection with CO2 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 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 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 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 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 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 (P ) (water-limited forests) when rainfall is less than ~2000 mm yr-1, and negatively correlated with radiation (light-limited forests). Costa et al. (2010) concluded that ET in the dry season is larger than that in the wet season and that surface net radiation is the main controller of 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 ET seasonality that resembles P variations. Considering the large scale of previous studies, the evaluation of 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 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 ET is driven by radiation, rather than water availability, in the Amazon (da Rocha et al., 2009; Juárez et al., 2007) and across the tropics (Fisher et al., 2009). Maeda et al. (2017) suggested that both annual mean and seasonality of ET are driven by a combination of energy and water availability, as rainfall or radiation alone could not explain ET patterns. This led to continued controversy regarding the seasonality of ET and its control. Therefore, more detailed studies are needed to explore the factor driving 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 ET will also be changed by various external conditions, resulting in great uncertainty for ETmeasurements 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 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 ET product agrees well with measurements from Amazon tropics eddy flux towers (Mu et al., 2011), and shows higher ET in the dry season and lower ET in the wet season. On the one hand, ET includes contributions from the evaporation of the ground or other wet surfaces, as well as transpiration flux from plants. Thus, 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 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 P and ET , or groundwater and 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 (TWSA ) (Fang et al., 2016).
In this paper, we explore the relationships and seasonal-to-annual variations among P , ET , and TWSA across the Amazon basin using wavelet analysis. By analyzing the phase differences amongP (TWSA ) and ET , we can explore the interaction between 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 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 ET . With these tools we address the following hypotheses: (1) in years with sufficient P ,ET is energy limited, while during drought years, plants have sufficient water supply from groundwater to maintain photosynthesis andET compared to normal years; (2) after a drought year, the groundwater system recovers, and the phases between ET andP , and between ET and 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.