Canopy-scale biophysical controls of transpiration and evaporation in the Amazon Basin

Abstract

Canopy and aerodynamic conductances ($g_{\text{C}}$ and $g_{\text{A}})$ are two of the key land surface biophysical variables that control the land surface response of land surface schemes in climate models. Their representation is crucial for predicting transpiration ($E_{\text{T}}$) and evaporation ($\mathit{\lambda }{E}_{\text{E}}$) flux components of the terrestrial latent heat flux ($\mathit{\lambda }E$), which has important implications for global climate change and water resource management. By physical integration of radiometric surface temperature ($T_{\text{R}}$) into an integrated framework of the Penman–Monteith and Shuttleworth–Wallace models, we present a novel approach to directly quantify the canopy-scale biophysical controls on$\mathit{\lambda }{E}_{\text{T}}$ and $\mathit{\lambda }{E}_{\text{E}}$ over multiple plant functional types (PFTs) in the Amazon Basin. Combining data from six LBA (Large-scale Biosphere-Atmosphere Experiment in Amazonia) eddy covariance tower sites and a $T_{\text{R}}$-driven physically based modeling approach, we identified the canopy-scale feedback-response mechanism between $g_{\text{C}}$,$\mathit{\lambda }{E}_{\text{T}}$, and atmospheric vapor pressure deficit ($D_{\text{A}}$), without using any leaf-scale empirical parameterizations for the modeling. The $T_{\text{R}}$-based model shows minor biophysical control on$\mathit{\lambda }{E}_{\text{T}}$ during the wet (rainy) seasons where$\mathit{\lambda }{E}_{\text{T}}$ becomes predominantly radiation driven and net radiation ($R_{\text{N}}$) determines 75 to 80 % of the variances of$\mathit{\lambda }{E}_{\text{T}}$. However, biophysical control on $\mathit{\lambda }{E}_{\text{T}}$ is dramatically increased during the dry seasons, and particularly the 2005 drought year, explaining 50 to 65 % of the variances of$\mathit{\lambda }{E}_{\text{T}}$, and indicates $\mathit{\lambda }{E}_{\text{T}}$ to be substantially soil moisture driven during the rainfall deficit phase. Despite substantial differences in $g_{\text{A}}$ between forests and pastures, very similar canopy–atmosphere “coupling” was found in these two biomes due to soil moisture-induced decrease in $g_{\text{C}}$ in the pasture. This revealed the pragmatic aspect of the $T_{\text{R}}$-driven model behavior that exhibits a high sensitivity of $g_{\text{C}}$ to per unit change in wetness as opposed to $g_{\text{A}}$ that is marginally sensitive to surface wetness variability. Our results reveal the occurrence of a significant hysteresis between$\mathit{\lambda }{E}_{\text{T}}$ and $g_{\text{C}}$ during the dry season for the pasture sites, which is attributed to relatively low soil water availability as compared to the rainforests, likely due to differences in rooting depth between the two systems. Evaporation was significantly influenced by$g_{\text{A}}$ for all the PFTs and across all wetness conditions. Our analytical framework logically captures the responses of $g_{\text{C}}$ and$g_{\text{A}}$ to changes in atmospheric radiation, $D_{\text{A}}$, and surface radiometric temperature, and thus appears to be promising for the improvement of existing land–surface–atmosphere exchange parameterizations across a range of spatial scales.

Introduction

The Amazon rainforest is one of the world's most extensive natural ecosystems, influencing the Earth's water, energy, and carbon cycles (Malhi, 2012), and is also a major source of global terrestrial evapotranspiration ($E$) or latent heat flux ($\mathit{\lambda }E$) (Costa et al., 2010; Harper et al., 2014). An intensification of the Amazon hydrological cycle was observed in the past 2 decades (Cox et al., 2000; Huntingford et al., 2008; Gloor et al., 2013). Recent Amazonian droughts have gained particular attention due to the sensitivity of the tropical forest $\mathit{\lambda }E$ to climate change (Hilker et al., 2014). If persistent precipitation extremes become more prevalent (Hilker et al., 2014), the Amazon rainforest may increasingly become a net source of carbon as a result of both the suppression of net biome exchange by drought and carbon emissions from fires (Gatti et al., 2014). Changes in land cover due to conversion of tropical forest to pastures significantly alter the energy partitioning by decreasing $\mathit{\lambda }E$ and increasing sensible heat fluxes ($H$) over pasture sites (e.g., Priante Filho et al., 2004). This will ultimately lead to severe consequences for the water balance in the region, with changes to river discharge already observed in some parts of the basin (Davidson et al., 2012). Evaluating the $\mathit{\lambda }E$ response to changing climate and land use in the Amazon Basin is critical to understanding the stability of the tropics within the Earth system (Lawrence and Vandecar, 2015). The control of $\mathit{\lambda }E$ can be viewed as complex supply–demand interactions, where net radiation and soil moisture represent the supply and the atmospheric vapor pressure deficit represents the demand. This supply–demand interaction accelerates the biophysical feedbacks in $\mathit{\lambda }E$, and understanding these biophysical feedbacks is necessary to assess the terrestrial biosphere response to water availability. Therefore, quantifying the critical role of biophysical variables on $\mathit{\lambda }E$ will add substantial insight to assessments of the resilience of the Amazon Basin under global change.

The aerodynamic and canopy conductances ($g_{\text{A}}$ and $g_{\text{C}}$ hereafter) (unit m s${}^{-\mathrm{1}}$) are the two most important biophysical variables regulating the evaporation ($\mathit{\lambda }{E}_{\text{E}}$) and transpiration ($\mathit{\lambda }{E}_{\text{T}})$ flux components of $\mathit{\lambda }E$ (Monteith and Unsworth, 2008; Dolman et al., 2014; Raupach, 1995; Colaizzi et al., 2012; Bonan et al., 2014). While $g_{\text{A}}$ controls the bulk aerodynamic transfer of energy and water through the near-surface boundary layer, $g_{\text{C}}$ represents the restriction on water vapor flow through the aggregated conductance from stomata of the leaves, in the case of a vegetated surface. In the case of partial vegetation cover, $g_{\text{C}}$ also includes the soil surface conductance for evaporation. At a small $g_{\text{C}}$ / $g_{\text{A}}$ ratio, the vapor pressure deficit close to the canopy source/sink height ($D_{\mathrm{0}}$) approximates the atmospheric vapor pressure deficit ($D_{\text{A}}$) due to aerodynamic mixing and/or low transpiration. This results in a strong canopy–atmosphere coupling, and such conditions are prevalent under soil moisture deficits, which prevails under conditions of soil moisture deficit. By contrast, a large $g_{\text{C}}$ / $g_{\text{A}}$ ratio influences the gradients of vapor pressure deficit just above the canopy, such that $D_{\mathrm{0}}$ tends towards zero and thus remains different from $D_{\text{A}}$ (Jarvis and McNaughton, 1986). This situation reflects a weak canopy–atmosphere coupling, and such situations prevail under predominantly wet conditions and/or poor aerodynamic mixing due to wetness-induced low aerodynamic roughness. The Penman–Monteith (PM) equation is a physically based scheme for quantifying such biophysical controls on canopy-scale $\mathit{\lambda }{E}_{\text{E}}$ and $\mathit{\lambda }{E}_{\text{T}}$ from terrestrial ecosystems, treating the vegetation canopy as “big-leaf” (Monteith, 1965, 1981). Despite its development based on biophysical principles controlling water vapor exchange, quantifying the $g_{\text{A}}$ and $g_{\text{C}}$ controls on $\mathit{\lambda }E$ through the PM equation suffers from the continued longstanding uncertainty in the aggregated stomatal and aerodynamic behavior within the soil–plant–atmosphere continuum (Matheny et al., 2014; Prihodko et al., 2008).

One of the major sources of uncertainties in modeling $g_{\text{A}}$ is associated with the empirical (and uncertain) parameterizations of near-surface boundary-layer dynamics, which is invariably confounded by space–time variability in atmospheric stability (van der Tol et al., 2009; Shuttleworth, 1989; Gibson et al., 2011). For example, the Monin–Obukhov similarity theory (MOST) used for $g_{\text{A}}$ modeling appears to be only valid over uniform, extensive, and flat surfaces (Monteith and Unsworth, 2008; van der Tol et al., 2009; Holwerda et al., 2012), and its application to complex “real” canopy systems is problematic due to chaotic interactions between turbulence, canopy roughness, and topography (Raupach and Finnigan, 1995; Shuttleworth, 2007; Holwerda et al., 2012). Similarly, $g_{\text{C}}$ varies in space and time due to variations in plant species, photosynthetic capacity, soil moisture variability, and environmental drivers (Monteith and Unsworth, 2008; van der Tol et al., 2009). Despite the existence of several semi-mechanistic and empirical parameterizations for $g_{\text{C}}$ (e.g., Ball et al., 1987; Leuning, 1995; Tuzet et al., 2003; Medlyn et al., 2011), the adaptive tendencies of plant canopies severely compromise the efficacy of such approaches (Matheny et al., 2014), limiting their applicability over most landscapes. Thus, debate on the most appropriate model for the canopy conductance has endured for decades.

Previous studies in the Amazon Basin focused on developing an observational understanding of the biogeochemical cycling of energy, water, carbon, trace gases, and aerosols in Amazonia (Andreae et al., 2002; Malhi et al., 2002; da Rocha et al., 2009), model-based understanding of surface ecophysiological behavior and seasonality of $\mathit{\lambda }E$ (Baker et al., 2013; Christoffersen et al., 2014), modeling the environmental controls on $\mathit{\lambda }E$ (Hasler and Avissar, 2007; Costa et al., 2010), understanding the seasonality of photosynthesis and of $\mathit{\lambda }E$ (da Rocha et al., 2004; Restrepo-Coupe et al., 2013), and the impact of land use on hydrometeorology (Roy and Avissar, 2002; von Randow et al., 2012). However, the combination of climatic and ecohydrological disturbances will significantly affect stomatal functioning, the partitioning of $\mathit{\lambda }{E}_{\text{E}}$ $-$ $\mathit{\lambda }{E}_{\text{T}}$, and carbon–water–climate interactions of tropical vegetation (Cox et al., 2000; Mercado et al., 2009). Hence, investigation of the effects of drought and land cover changes on conductances, $\mathit{\lambda }{E}_{\text{E}}$ and $\mathit{\lambda }{E}_{\text{T}}$, is a topic requiring urgent attention (Blyth et al., 2010) both because of the cursory way it is handled in the current generation of parametric models (Matheny et al., 2014) and because of the centrality of $g_{\text{A}}$ and $g_{\text{C}}$ in controlling modeled flux behaviors (Villagarcía et al., 2010). The persistent risk of deforestation is likely to alter the radiation interception, surface temperature, surface moisture, associated meteorological conditions, and vegetation biophysical states of different plant functional types (PFTs). Conversion from forest to pasture is expected to change the $g_{\text{C}}$ / $g_{\text{A}}$ ratio of these ecosystems and impact the evapotranspiration components. Besides inverting the PM equation using field measurements of $\mathit{\lambda }E$, to date either photosynthesis-dependent modeling or leaf-scale experiments were performed to directly quantify $g_{\text{C}}$ (Ball et al., 1987; Meinzer et al., 1993, 1997; Monteith, 1995; Jones, 1998; Motzer et al., 2005). However, an analytical or physical retrieval for $g_{\text{A}}$ and $g_{\text{C}}$ is required not only to better understand the role of the canopy in regulating evaporation and transpiration, but also to enable our capability to characterize the conductances using remote observations, across large spatial domains where in situ observations are not available. This paper aims to leverage this emerging opportunity by exploring data from the Large-scale Biosphere-Atmosphere Experiment in Amazonia (LBA) eddy covariance (EC) observations (e.g., de Goncalves et al., 2013; Restrepo-Coupe et al., 2013) using a novel analytical modeling technique, the Surface Temperature Initiated Closure (STIC) (Mallick et al., 2014, 2015), in order to quantify the biophysical control on $\mathit{\lambda }{E}_{\text{E}}$ and $\mathit{\lambda }{E}_{\text{T}}$ over several representative PFTs of the Amazon Basin.

STIC (STIC1.0 and STIC1.1) provides a unique framework for simultaneously estimating $g_{\text{A}}$ and $g_{\text{C}}$, surface energy balance fluxes, and $\mathit{\lambda }{E}_{\text{E}}$ and $\mathit{\lambda }{E}_{\text{T}}$. It is based on finding analytical solutions for $g_{\text{A}}$ and $g_{\text{C}}$ by physically integrating radiometric surface temperature ($T_{\text{R}})$ information (along with radiative fluxes and meteorological variables) into the PM model (Mallick et al., 2014, 2015). The direct estimates of canopy-scale conductances and $\mathit{\lambda }E$ obtained through STIC are independent of any land surface parameterization. This contrasts with the multi-layer canopy models that explicitly parameterize the leaf-scale conductances and perform bottom-up scaling to derive the canopy-scale conductances (Baldocchi et al., 2002; Drewry et al., 2010). A primary advantage of the approach on which STIC is based is the ability to directly utilize remotely sensed $T_{\text{R}}$ to estimate $E$, thereby providing a capability to estimate $E$ over large spatial scales using a remotely sensed variable that is central to many ongoing and upcoming missions. This study presents a detailed examination of the performance of STIC to better understand land–atmosphere interactions in one of the most critical global ecosystems and addresses the following science questions and objectives.

• How realistic are canopy-scale conductances when estimated analytically (or non-parametrically) without involving any empirical leaf-scale parameterization?

• What are the controls of canopy-scale $g_{\text{A}}$ and $g_{\text{C}}$ on evaporation and transpiration in the Amazon Basin, as evaluated using STIC?

• How do the STIC-based canopy-scale conductances compare with known environmental constraints?

• Is the biophysical response of $g_{\text{C}}$ consistent with the leaf-scale theory (Jarvis and McNaughton, 1986; McNaughton and Jarvis, 1991; Monteith, 1995)?

The following section describes a brief methodology to retrieve $g_{\text{C}}$, $g_{\text{A}}$, $\mathit{\lambda }{E}_{\text{E}}$, and $\mathit{\lambda }{E}_{\text{T}}$. The data sources used for the analysis are described after the methodology and will be followed by a comparison of the results with fluxes derived from EC measurements. A detailed discussion of the results and potential applicability of the method with implications for global change research are elaborated at the end. A list of symbols and variables used in the present study is given in Table 1.

Methodology

Theory

The retrievals of $g_{\text{A}}$, $g_{\text{C}}$, and $\mathit{\lambda }E$ are based on finding a “closure” of the PM equation (Eq. 1 below) using the STIC framework (Fig. A1) (Mallick et al., 2015). STIC is a physically based single-source surface energy balance scheme that includes internally consistent estimation of $g_{\text{A}}$ and $g_{\text{C}}$ (Mallick et al., 2014, 2015). Originally designed for application to thermal remote sensing data from Earth observation sensors, the STIC framework exploits observations of radiative ($T_{\text{R}}$) and environmental variables, including net radiation ($R_{\text{N}}$), ground heat flux ($G$), air temperature ($T_{\text{A}}$), relative humidity ($R_{\text{H}}$), or vapor pressure ($e_{\text{A}}$) at a reference level above the surface.

Variables and symbols and their description used in the present study.

Variables	Description
and
symbols
$\mathit{\lambda }E$	Evapotranspiration (evaporation $+$ transpiration) as latent heat flux (W m${}^{-\mathrm{2}}$)
$H$	Sensible heat flux (W m${}^{-\mathrm{2}}$)
$R_{\text{N}}$	Net radiation (W m${}^{-\mathrm{2}}$)
$G$	Ground heat flux (W m${}^{-\mathrm{2}}$)
$\mathit{\varphi }$	Net available energy (W m${}^{-\mathrm{2}}$)
$T_{\text{A}}$	Air temperature (${}^{\circ }$C)
$T_{\text{D}}$	Dew-point temperature (${}^{\circ }$C)
$T_{\text{R}}$	Radiometric surface temperature (${}^{\circ }$C)
$R_{\text{H}}$	Relative humidity (%)
$e_{\text{A}}$	Atmospheric vapor pressure at the level of $T_{\text{A}}$ measurement (hPa)
$D_{\text{A}}$	Atmospheric vapor pressure deficit at the level of $T_{\text{A}}$ measurement (hPa)
$u$	Wind speed (m s${}^{-\mathrm{1}}$)
$u^{*}$	Friction velocity (m s${}^{-\mathrm{1}}$)
$T_{\text{SD}}$	Dew-point temperature at the source/sink height (${}^{\circ }$C)
$T_{\mathrm{0}}$	Aerodynamic temperature or source/sink height temperature (${}^{\circ }$C)
$e_{\text{S}}$	“Effective” vapor pressure of evaporating front near the surface (hPa)
$e_{\text{S}}^{*}$	Saturation vapor pressure of the surface (hPa)
$e_{\mathrm{0}}^{*}$	Saturation vapor pressure at the source/sink height (hPa)
$e_{\mathrm{0}}$	Atmospheric vapor pressure at the source/sink height (hPa)
$D_{\mathrm{0}}$	Atmospheric vapor pressure deficit at the source/sink height (hPa)
$\mathit{\lambda }{E}_{\text{eq}}$	Equilibrium latent heat flux (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{imp}}$	Imposed latent heat flux (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{E}}$	Evaporation as flux (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{T}}$	Transpiration as flux (W m${}^{-\mathrm{2}}$)
$E$	Evapotranspiration (evaporation $+$ transpiration) as depth of water (mm)
$\mathit{\lambda }{E}^{*}$	Potential evaporation as flux (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{T}}^{*}$	Potential transpiration as flux (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{W}}$	Wet environment evaporation as flux (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{P}}^{*}$	Potential evaporation as flux according to Penman (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{PM}}^{*}$	Potential evaporation as flux according to Penman–Monteith (W m${}^{-\mathrm{2}}$)
$\mathit{\lambda }{E}_{\text{PT}}^{*}$	Potential evaporation as flux according to Priestley–Taylor (W m${}^{-\mathrm{2}}$)
$E^{*}$	Potential evaporation as depth of water (mm)
$E_{\text{P}}^{*}$	Potential evaporation as depth of water according to Penman (mm)
$E_{\text{PM}}^{*}$	Potential evaporation as depth of water according to Penman–Monteith (mm)
$E_{\text{PT}}^{*}$	Potential evaporation as depth of water according to Priestley–Taylor (mm)
$E_{\text{W}}$	Wet environment evaporation as depth of water (mm)
$g_{\text{A}}$	Aerodynamic conductance (m s${}^{-\mathrm{1}}$)
$g_{\text{C}}$	Stomatal/surface conductance (m s${}^{-\mathrm{1}}$)
$g_{\text{M}}$	Momentum conductance (m s${}^{-\mathrm{1}}$)
$g_{\text{B}}$	Quasi-laminar boundary-layer conductance (m s${}^{-\mathrm{1}}$)
$g_{\text{Cmax}}$	Maximum stomatal/surface conductance (m s${}^{-\mathrm{1}}$) ($=$ $g_{\text{C}}/M$)
$M$	Surface moisture availability (0–1)
$s$	Slope of saturation vapor pressure vs. temperature curve (hPa K${}^{-\mathrm{1}})$ (estimated at $T_{\text{A}}$)
$s_{\mathrm{1}}$	Slope of the saturation vapor pressure and temperature between ($T_{\text{SD}}$ $-$ $T_{\text{D}})$
	vs. ($e_{\mathrm{0}}$ $-$ $e_{\text{A}}$) (approximated at $T_{\text{D}})$ (hPa K${}^{-\mathrm{1}}$)
$s_{\mathrm{2}}$	Slope of the saturation vapor pressure and temperature between ($T_{\text{R}}$ $-$ $T_{\text{D}})$
	vs. ($e_{\text{S}}^{*}$ $-$ $e_{\text{A}})$ (hPa K${}^{-\mathrm{1}}$), estimated according to Mallick et al. (2015)
$s_{\mathrm{3}}$	Slope of the saturation vapor pressure and temperature between ($T_{\text{R}}$ $-$ $T_{\text{SD}})$
	vs. ($e_{\text{S}}^{*}$ $-$ $e_{\text{S}}$) (approximated at $T_{\text{R}}$) (hPa K${}^{-\mathrm{1}}$)
$k$	Ratio between ($e_{\mathrm{0}}^{*}$ $-$ $e_{\text{A}}$) and ($e_{\text{S}}^{*}$ $-$ $e_{\text{A}}$)
$\mathit{\lambda }$	Latent heat of vaporization of water (J kg${}^{-\mathrm{1}}$ K${}^{-\mathrm{1}}$)
$z_{\text{R}}$	Reference height (m)

Continued.

Variables	Description
and
symbols
$z_{\text{M}}$	Effective source–sink height of momentum (m)
$z_{\mathrm{0}}$	Roughness length (m)
$d$	Displacement height (m)
$\mathit{\gamma }$	Psychrometric constant (hPa K${}^{-\mathrm{1}}$)
$\mathit{\rho }$	Density of air (kg m${}^{-\mathrm{3}}$)
$c_p$	Specific heat of dry air (MJ kg${}^{-\mathrm{1}}$ K${}^{-\mathrm{1}}$)
$\mathrm{\Lambda }$	Evaporative fraction (unitless)
$\mathit{\beta }$	Bowen ratio (unitless)
$\mathit{\alpha }$	Priestley–Taylor parameter (unitless)
$\mathrm{\Omega }$	Decoupling coefficient (unitless)
Sc	Schmidt number (unitless)
Pr	Prandtl number (unitless)
$\mathit{\kappa }$	von Kármán constant (0.4)

The foundation of the development of STIC is based on the goal of finding an analytical solution of the two unobserved “state variables” ($g_{\text{A}}$ and $g_{\text{C}}$) in the PM equation while exploiting the radiative ($R_{\text{N}}$ and $G)$, meteorological ($T_{\text{A}}$, $R_{\text{H}}$), and radiometric surface temperature ($T_{\text{R}}$) as external inputs. The fundamental assumption in STIC is the first-order dependence of $g_{\text{A}}$ and $g_{\text{C}}$ on the aerodynamic temperature ($T_{\mathrm{0}}$) and soil moisture (through $T_{\text{R}}$). This assumption allows a direct integration of $T_{\text{R}}$ into the PM equation while simultaneously constraining the conductances through $T_{\text{R}}$. Although the $T_{\text{R}}$ signal is implicit in $R_{\text{N}}$, which appears in the numerator of the PM equation (Eq. 1), it may be noted that $R_{\text{N}}$ has a relatively weak dependence on $T_{\text{R}}$ (compared to the sensitivity of $T_{\text{R}}$ to soil moisture and $\mathit{\lambda }E$). Given that $T_{\text{R}}$ is a direct signature of the soil moisture availability, inclusion of $T_{\text{R}}$ in the PM equation also works to add water-stress controls in $g_{\text{C}}$. Until now the explicit use of $T_{\text{R}}$ in the PM model was hindered due to the unavailability of any direct method to integrate $T_{\text{R}}$ into this model, and, furthermore, due to the lack of physical models expressing biophysical states of vegetation as a function of $T_{\text{R}}$. Therefore, the majority of the PM-based $\mathit{\lambda }E$ modeling approaches strongly rely on surface reflectance and meteorology while exploiting the empirical leaf-scale parameterizations of the biophysical conductances (Prihodko et al., 2008; Bonan et al., 2014; Ershadi et al., 2015).

The PM equation is commonly expressed as $$\mathit{\lambda }E={\displaystyle \frac{s\mathit{\varphi }+\mathit{\rho }{c}_P{g}_{\text{A}}{D}_{\text{A}}}{s+\mathit{\gamma }\left(\mathrm{1},+,\frac{g_{\text{A}}}{g_{\text{C}}}\right)}},$$ where $\mathit{\rho }$ is the air density (kg m${}^{-\mathrm{3}}$), $c_P$ is the specific heat of air (J kg${}^{-\mathrm{1}}$ K${}^{-\mathrm{1}}$), $\mathit{\gamma }$ is the psychrometric constant (hPa K${}^{-\mathrm{1}}$), $s$ is the slope of the saturation vapor pressure vs. air temperature (hPa K${}^{-\mathrm{1}}$), $D_{\text{A}}$ is the saturation deficit of the air (hPa) or vapor pressure deficit at the reference level, and $\mathit{\varphi }$ is the net available energy (W m${}^{-\mathrm{2}}$) (the difference between $R_{\text{N}}$ and $G$). The units of all the surface fluxes and conductances are in W m${}^{-\mathrm{2}}$ and m s${}^{-\mathrm{1}}$, respectively. For a dense canopy, $g_{\text{C}}$ in the PM equation represents the canopy surface conductance. Although it is not equal to the canopy stomatal conductance, it contains integrated information on the stomata. For a heterogeneous landscape, $g_{\text{C}}$ in the PM equation is an aggregated surface conductance containing information on both canopy and soil. Traditionally, the two unknown “state variables” in Eq. (1) are $g_{\text{A}}$ and $g_{\text{C}}$, and the STIC methodology is based on formulating “state equations” for these conductances that satisfy the PM model (Mallick et al., 2014, 2015). The PM equation is “closed” upon the availability of canopy-scale measurements of the two unobserved biophysical conductances, and if we assume the empirical models of $g_{\text{A}}$ and $g_{\text{C}}$ to be reliable. However, neither $g_{\text{A}}$ nor $g_{\text{C}}$ can be measured at the canopy scale or at larger spatial scales. Furthermore, as shown by some recent studies (Matheny et al., 2014; Van Dijk et al., 2015), a more appropriate $g_{\text{A}}$ and $g_{\text{C}}$ model is currently not available. This implies that a true “closure” of the PM equation is only possible through an analytical estimation of the conductances.

State equations

By integrating $T_{\text{R}}$ with standard surface energy balance (SEB) theory and vegetation biophysical principles, STIC formulates multiple “state equations” that eliminate the need for exogenous parametric submodels for $g_{\text{A}}$ and $g_{\text{C}}$, associated aerodynamic variables, and land–atmosphere coupling. The state equations of STIC are as follows and their detailed derivations are described in Appendix A1. $$\begin{array}{}& & g_{\text{A}}={\displaystyle \frac{\mathit{\varphi }}{\mathit{\rho }{c}_P\left[\left(T_{\mathrm{0}},-,T_{\text{A}}\right),+,\left(\frac{e_{\mathrm{0}}-e_{\text{A}}}{\mathit{\gamma }}\right)\right]}}& & g_{\text{C}}=g_{\text{A}}{\displaystyle \frac{\left(e_{\mathrm{0}},-,e_{\text{A}}\right)}{\left(e_{\mathrm{0}}^{*},-,e_{\mathrm{0}}\right)}}& & T_{\mathrm{0}}=T_{\text{A}}+\left({\displaystyle \frac{e_{\mathrm{0}}-e_{\text{A}}}{\mathit{\gamma }}}\right)\left({\displaystyle \frac{\mathrm{1}-\mathrm{\Lambda }}{\mathrm{\Lambda }}}\right)& & \mathrm{\Lambda }={\displaystyle \frac{\mathrm{2}\mathit{\alpha }s}{\mathrm{2}s+\mathrm{2}\mathit{\gamma }+\mathit{\gamma }\frac{g_{\text{A}}}{g_{\text{C}}}(\mathrm{1}+M)}}\end{array}$$ Here, $T_{\mathrm{0}}$ is the temperature (${}^{\circ }$C) at the source/sink height (or at the roughness length ($z_{\mathrm{0}}$) or in-canopy air stream), $e_{\mathrm{0}}$ is the atmospheric vapor pressure (hPa) at the source/sink height, $e_{\mathrm{0}}^{*}$ is the saturation vapor pressure (hPa) at the source/sink height, $\mathrm{\Lambda }$ is the evaporative fraction (the ratio of $\mathit{\lambda }E$ and $\mathit{\varphi }$), $\mathit{\alpha }$ is the Priestley–Taylor parameter (unitless) (Priestley and Taylor, 1972), and $M$ is a unitless quantity that describes the relative wetness (or moisture availability) of the surface. $M$ controls the transition from potential to actual evaporation and hence is critical for providing a constraint against which the conductances can be estimated ($M$ estimation is explained in Appendix A2). Given values of $R_{\text{N}}$, $G$, $T_{\text{A}}$, and $R_{\text{H}}$ or $e_{\text{A}}$, the four state equations (Eqs. 2–5) can be solved simultaneously to derive analytical solutions for the four state variables. This also produces a “closure” of the PM model, which is independent of empirical parameterizations for both $g_{\text{A}}$ and $g_{\text{C}}$. However, the analytical solutions to the above state equations have four accompanying unknowns, $M$ (surface moisture availability), $e_{\mathrm{0}}$ (vapor pressure at the source/sink height), $e_{\mathrm{0}}^{*}$ (saturation vapor pressure at the source/sink height), and the Priestley–Taylor coefficient ($\mathit{\alpha }$), and as a result there are four equations with eight unknowns. Consequently an iterative solution is needed to determine the four unknown variables (as described in Appendix A2), which is a further modification of the STIC1.1 framework (Mallick et al., 2015). The present version of STIC is designated as STIC1.2 and its uniqueness is the physical integration of $T_{\text{R}}$ into a combined structure of the PM and Shuttleworth–Wallace (SW, hereafter) (Shuttleworth and Wallace, 1985) models to estimate the source/sink height vapor pressures (Appendix A2). In addition to physically integrating $T_{\text{R}}$ observations into a combined PM–SW framework, STIC1.2 also establishes a feedback loop describing the relationship between $T_{\text{R}}$ and $\mathit{\lambda }E$, coupled with canopy–atmosphere components relating $\mathit{\lambda }E$ to $T_{\mathrm{0}}$ and $e_{\mathrm{0}}$. To estimate $M$, the radiometric surface temperature ($T_{\text{R}}$) is extensively used in a physical retrieval framework, thus treating $T_{\text{R}}$ as an external input. In Eq. (5), the Priestley–Taylor coefficient ($\mathit{\alpha }$) appeared due to the use of the advection–aridity (AA) hypothesis (Brutsaert and Stricker, 1979) for deriving the state equation of $\mathrm{\Lambda }$ (Supplement S1). However, instead of optimizing $\mathit{\alpha }$ as a “fixed parameter”, we have developed a physical equation of $\mathit{\alpha }$ (Eq. A15) and numerically estimated $\mathit{\alpha }$ as a “variable”. The derivation of the equation for $\mathit{\alpha }$ is described in Appendix A2. The fundamental differences between STIC1.2 and earlier versions are described in Table A1.

In STIC1.2, $T_{\mathrm{0}}$ is a function of $T_{\text{R}}$, and they are not assumed equal ($T_{\mathrm{0}}$ $\ne$ $T_{\text{R}}$). The analytical expression of $T_{\mathrm{0}}$ is dependent on $M$ and the estimation of $M$ is based on $T_{\text{R}}$. To further elaborate this point on the inequality of $T_{\mathrm{0}}$ and $T_{\text{R}}$, we show an intercomparison of retrieved $T_{\mathrm{0}}$ vs. $T_{\text{R}}$ for forest and pasture (Fig. A2). This indicates the distinct difference of the retrieved $T_{\mathrm{0}}$ from $T_{\text{R}}$ for the two different biomes.

Partitioning $\mathit{\lambda }E$

The terrestrial latent heat flux is an aggregate of both transpiration ($\mathit{\lambda }{E}_{\text{T}}$) and evaporation ($\mathit{\lambda }{E}_{\text{E}}$) (sum of soil evaporation and interception evaporation from the canopy). During rain events the land surface becomes wet and $\mathit{\lambda }E$ tends to approach the potential evaporation ($\mathit{\lambda }{E}^{*}$), while surface drying after rainfall causes $\mathit{\lambda }E$ to approach the potential transpiration rate ($\mathit{\lambda }{E}_{\text{T}}^{*}$) in the presence of vegetation, or zero without any vegetation. Hence, $\mathit{\lambda }E$ at any time is a mixture of these two end-member conditions depending on the degree of surface moisture availability or wetness ($M$) (Bosveld and Bouten, 2003; Loescher et al., 2005). Considering the general case of evaporation from an unsaturated surface at a rate less than the potential, $M$ is the ratio of the actual to potential evaporation rate and is considered as an index of evaporation efficiency during a given time interval (Boulet et al., 2015). Partitioning of $\mathit{\lambda }E$ into $\mathit{\lambda }{E}_{\text{E}}$ and $\mathit{\lambda }{E}_{\text{T}}$ was performed according to Mallick et al. (2014) as follows: $$\mathit{\lambda }E=\mathit{\lambda }{E}_{\text{E}}+\mathit{\lambda }{E}_{\text{T}}=M\mathit{\lambda }{E}^{*}+(\mathrm{1}-M)\mathit{\lambda }{E}_{\text{T}}^{*}.$$ The estimates of $\mathit{\lambda }{E}_{\text{E}}$ in the current method consist of an aggregated contribution from both interception and soil evaporation, and no further attempt is made to separate these two components. In the Amazon forest, soil evaporation has a negligible contribution, while the interception evaporation contributes substantially to the total evaporative fluxes, and therefore the partitioning of $\mathit{\lambda }E$ into $\mathit{\lambda }{E}_{\text{E}}$ and $\mathit{\lambda }{E}_{\text{T}}$ is crucial. After estimating $g_{\text{A}}$, $\mathit{\lambda }{E}^{*}$ was estimated according to the Penman equation (Penman, 1948) and $\mathit{\lambda }{E}_{\text{T}}$ was estimated as the residual in Eq. (6).

In this study, we use the term “canopy conductance” instead of “stomatal conductance” given that the term “stomata” is applicable at the leaf scale only. As stated earlier, for a heterogeneous surface, $g_{\text{C}}$ should principally be a mixture of the canopy surface (integrated stomatal information) and soil conductances. However, given the high vegetation density of the Amazon Basin, the soil surface exposure is negligible, and hence we assume $g_{\text{C}}$ to be the canopy-scale aggregate of the stomatal conductance. Similarly, a different $g_{\text{A}}$ exists for soil–canopy, sun–shade, and dry–wet conditions (Leuning, 1995), which are currently integrated into a lumped $g_{\text{A}}$ (given the big-leaf nature of STIC). From the big-leaf perspective, it is generally assumed that the aerodynamic conductance of water vapor and heat are equal (Raupach, 1998). However, to obtain partitioned aerodynamic conductances, explicit partitioning of $\mathit{\lambda }E$ is needed, which is beyond the scope of the current paper.

Evaluating $g_{\text{A}}$ and $g_{\text{C}}$

Due to the lack of direct canopy-scale $g_{\text{A}}$ measurements, a rigorous evaluation of $g_{\text{A}}$ cannot be performed. To evaluate the STIC retrievals of $g_{\text{A}}$ ($g_{\text{A-STIC}}$), we adopted three different methods.

• a.

  By using the measured friction velocity ($u^{*}$) and wind speed ($u$) at the EC towers and using the equation of Baldocchi and Ma (2013) ($g_{\text{A-BM13}}$) in which $g_{\text{A}}$ was expressed as the sum of turbulent conductance and canopy (quasi-laminar) boundary-layer conductance as$$g_{\text{A-BM13}}={\left[\left(u,/,u^{{*}^{\mathrm{2}}}\right),+,\left(\mathrm{2},/,k,u^{{*}^{\mathrm{2}}}\right),(,\mathit{\text{Sc}},/,\mathit{\text{Pr}},{)}^{0.67}\right]}^{-\mathrm{1}},$$where $\mathit{\kappa }$ is the von Kármán constant, 0.4; Sc is the Schmidt number; Pr is the Prandtl number, and their ratio is generally considered to be unity. Here the conductances of momentum, sensible, and latent heat fluxes are assumed to be identical (Raupach, 1998).

• b.

  By inverting $\mathit{\lambda }E$ observations for wet conditions, hence assuming $\mathit{\lambda }E$ $\cong$ $\mathit{\lambda }{E}^{*}$ and estimating $g_{\text{A}}$ ($g_{\text{A-INV}}$) as$$g_{\text{A-INV}}=\mathit{\gamma }\mathit{\lambda }E/\mathit{\rho }{c}_P{D}_{\text{A}}.$$

• c.

  By inverting the aerodynamic equation of $H$ and estimating a hybrid $g_{\text{A}}$ ($g_{\text{A-HYB}}$) from observed $H$ and STIC $T_{\mathrm{0}}$ as ($T_{\text{0-STIC}}$),$$g_{\text{A-HYB}}=H/\mathit{\rho }{c}_P\left(T_{\text{0-STIC}},-,T_{\text{A}}\right).$$Like $g_{\text{A-STIC}}$, direct verification of STIC $g_{\text{C}}$ ($g_{\text{C-STIC}}$) could not be performed, as canopy-scale $g_{\text{C}}$ observations are not possible with current measurement techniques. Although leaf-scale $g_{\text{C}}$ measurements are relatively straightforward, these values are not comparable to values retrieved at the canopy scale. However, assuming $u^{*}$-based $g_{\text{A}}$ as the baseline aerodynamic conductance, we have estimated canopy-scale $g_{\text{C}}$ by inverting the PM equation ($g_{\text{C-INV}}$) (Monteith, 1995) to evaluate $g_{\text{C-STIC}}$ by exploiting $g_{\text{A-BM13}}$ in conjunction with the available $\mathit{\varphi }$, $\mathit{\lambda }E$, $T_{\text{A}}$, and $D_{\text{A}}$ measurements from the EC towers.

Decoupling coefficient and biophysical controls

The decoupling coefficient or “Omega” ($\mathrm{\Omega }$) is a dimensionless coefficient ranging from 0.0 to 1.0 (Jarvis and McNaughton, 1986) and is considered as an index of the degree of stomatal control on transpiration relative to the environment. The equation of $\mathrm{\Omega }$ is as follows: $$\mathrm{\Omega }={\displaystyle \frac{\frac{s}{\mathit{\gamma }}+\mathrm{1}}{\frac{s}{\mathit{\gamma }}+\mathrm{1}+\frac{g_{\text{A}}}{g_{\text{C}}}}}.$$ Introducing $\mathrm{\Omega }$ into the Penman–Monteith (PM) equation for $\mathit{\lambda }E$ results in $$\begin{array}{}& & \mathit{\lambda }E=\mathrm{\Omega }\mathit{\lambda }{E}_{\text{eq}}+(\mathrm{1}-\mathrm{\Omega })\mathit{\lambda }{E}_{\text{imp}},& & \mathit{\lambda }{E}_{\text{eq}}={\displaystyle \frac{s\mathit{\varphi }}{s+\mathit{\gamma }}},& & \mathit{\lambda }{E}_{\text{imp}}={\displaystyle \frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}}{g}_{\text{C}}{D}_{\text{A}},\end{array}$$ where $\mathit{\lambda }{E}_{\text{eq}}$ is the equilibrium latent heat flux, which depends only on $\mathit{\varphi }$ and would be obtained over an extensive surface of uniform moisture availability (Jarvis and McNaughton, 1986; Kumagai et al., 2004). $\mathit{\lambda }{E}_{\text{imp}}$ is the imposed latent heat flux, which is “imposed” by the atmosphere on the vegetation surface through the effects of vapor pressure deficit (triggered under limited soil moisture availability), and $\mathit{\lambda }E$ becomes proportional to $g_{\text{C}}$.

When the $g_{\text{C}}/g_{\text{A}}$ ratio is very small (i.e., water-stress conditions), stomata principally control the water loss, and a change in $g_{\text{C}}$ will result in a nearly proportional change in transpiration. Such conditions trigger a strong biophysical control on transpiration. In this case the $\mathrm{\Omega }$ value approaches zero and vegetation is believed to be fully coupled to the atmosphere. In contrast, for a high $g_{\text{C}}$ / $g_{\text{A}}$ ratio (i.e., high water availability), changes in $g_{\text{C}}$ will have little effect on the transpiration rate, and transpiration is predominantly controlled by $\mathit{\varphi }$. In this case the $\mathrm{\Omega }$ value approaches unity, and vegetation is considered to be poorly coupled to the atmosphere.

Given that both $g_{\text{A}}$ and $g_{\text{C}}$ are the independent estimates in STIC1.2, the concept of $\mathrm{\Omega }$ was used to understand the degree of biophysical control on $\mathit{\lambda }{E}_{\text{T}}$, which indicates the extent to which the transpiration fluxes are approaching the equilibrium limit. However, the biophysical characterization of $\mathit{\lambda }{E}_{\text{T}}$ and $\mathit{\lambda }{E}_{\text{E}}$ through STIC1.2 significantly differs from previous approaches (Ma et al., 2015; Chen et al., 2011; Kumagai et al., 2004), and the fundamental differences are centered on the specifications of $g_{\text{A}}$ and $g_{\text{C}}$ (as described in Table A2). While the estimation of $g_{\text{A}}$ in previous approaches was based on $u$ and $u^{*}$, the estimation of $g_{\text{C}}$ was based on inversion of observed $\mathit{\lambda }E$ based on the PM equation (e.g., Stella et al., 2013). However, none of these approaches allow independent quantification of biophysical controls of $\mathit{\lambda }E$, as $g_{\text{C}}$ is constrained by $\mathit{\lambda }E$ itself.

Datasets

Eddy covariance and meteorological quantities

We used the LBA (Large-Scale Biosphere-Atmosphere Experiment in Amazonia) data for quantifying the biophysical controls on the evaporative flux components. LBA was an international research initiative conducted during 1995–2005 to study how Amazonia functions as a regional entity within the larger Earth system, and how changes in land use and climate will affect the hydrological and biogeochemical functioning of the Amazon ecosystem (Andreae et al., 2002).

Overview of the LBA tower sites. Here, (–) refers to (S) and (W) for latitude and longitude, respectively.

Biome	PFT	Site	LBA	Data	Latitude	Longitude	Tower	Annual
			code	availability	(${}^{\circ }$)	(${}^{\circ }$)	height	rainfall
				period			(m)	(mm)
Forest	Tropical	Manaus	K34	Jun 1999 to	$-$2.609	$-$60.209	50	2329
	rainforest	KM34		Sep 2006
	(TRF)
Forest	Tropical	Santarem	K67	Jan 2002 to	$-$2.857	$-$54.959	63	1597
	moist	KM67		Jan 2006
	forest
	(TMF)
Forest	Tropical	Santarem	K83	Jul 2000 to	$-$3.018	$-$54.971	64	1656
	moist	KM83		Dec 2004
	forest
	(TMF)
Forest	Tropical	Reserva	RJA	Mar 1999 to	$-$10.083	$-$61.931	60	2354
	dry forest	Biológica		Oct 2002
	(TDF)	Jarú
Pasture	Pasture	Santarem	K77	Jan 2000 to	$-$3.012	$-$54.536	18	1597
	(PAS)	KM77		Dec 2001
Pasture	Pasture	Fazenda	FNS	Mar 1999 to	$-$10.762	$-$62.357	8.5	1743
	(PAS)	Nossa		Oct 2002
		Senhora

Examples of monthly averages of the diurnal time series of canopy-scale (a) $g_{\text{A}}$ and (b) $g_{\text{C}}$ estimated for two different biomes (forest and pasture) in the Amazon Basin (LBA sites K34 and FNS). The time series of four different $g_{\text{A}}$ estimates and their corresponding $g_{\text{C}}$ estimates are shown here.

[Figure omitted. See PDF]

A network of eddy covariance (EC) towers was operational during the LBA experiment, such that data from nine EC towers were obtained from the ORNL Distributed Archive Active Centre (ftp://daac.ornl.gov/data/lba/carbon_dynamics/CD32_Brazil_Flux_Network/). These are the quality-controlled and harmonized surface flux and meteorological data from the Brazilian Amazon flux network. Time series of surface fluxes ($\mathit{\lambda }E$, $H$, $G$), radiation ($R_{\text{N}}$, shortwave and longwave), thermal ($T_{\text{R}}$), meteorological quantities ($T_{\text{A}}$, $R_{\text{H}}$, wind speed) as well as soil moisture and rainfall were available from six (out of nine) EC towers. Three of the EC towers had numerous missing data and were not included in the analysis. The surface energy balance was closed by applying the Bowen ratio (Bowen, 1926) closure as described in Chavez et al. (2005) and later adopted by Anderson et al. (2007) and Mallick et al. (2015). In the absence of $G$ measurements, $\mathit{\varphi }$ was assumed to be equal to the sum of $\mathit{\lambda }E$ and $H$ with the assumption that a dense vegetation canopy restricts the energy incident on the soil surface, thereby allowing us to assume negligible ground heat flux. For the present analysis, data from six selected EC towers (Table 2) represent two different biomes (forest and pasture) covering four different PFTs, namely, tropical rainforest (TRF), tropical moist forest (TMF), tropical dry forest (TDF), and pasture (PAS), respectively. A general description of the datasets can be found in Saleska et al. (2013). For all sites, monthly averages of the diurnal cycle (hourly time resolution) were chosen for the present analysis.

Results

Evaluating $g_{\text{A}}$, $g_{\text{C}}$, and surface energy balance fluxes

Examples of monthly averages of the diurnal cycles of the four different $g_{\text{A}}$ estimates and their corresponding $g_{\text{C}}$ estimates over two different PFTs (K34 for forest and FNS for pasture) reveal that $g_{\text{A-STIC}}$ and $g_{\text{C-STIC}}$ tend to be generally higher for the forest than their counterparts, varying from 0 to 0.06 m s${}^{-\mathrm{1}}$ and 0 to 0.04 m s${}^{-\mathrm{1}}$ respectively (Fig. 1a and b). The magnitude of $g_{\text{A-STIC}}$ varied between 0 and 0.025 m s${}^{-\mathrm{1}}$ for the pasture (Fig. 1a), while $g_{\text{C-STIC}}$ values were less than half of those estimated over the forest (0–0.01 m s${}^{-\mathrm{1}}$) (Fig. 1b). The conductances showed a marked diurnal variation expressing their overall dependence on net radiation, vapor pressure deficit, and surface temperature. Despite the absolute differences between the conductances from the different retrieval methods, their diurnal patterns were comparable.

The canopy-scale evaluation of $g_{\text{A-STIC}}$ is illustrated in Fig. 2a (and Table 3), combining data from the four PFTs. Estimated values range between zero and 0.1 m s${}^{-\mathrm{1}}$ and show modest correlation ($R^{\mathrm{2}}$ $=$ 0.44) ($R^{\mathrm{2}}$ range between 0.22 [$\pm$0.18] and 0.55 [$\pm$0.12]) between $g_{\text{A-BM13}}$ and $g_{\text{A-STIC}}$, with regression parameters ranging from 0.81 ($\pm$0.023) to 1.07 ($\pm$0.047) for the slope and 0.0019 ($\pm$0.0006) to 0.0006 ($\pm$0.0006) m s${}^{-\mathrm{1}}$ for the offset (Table 3). The root mean squared deviation (RMSD) varied between 0.007 (TDF) and 0.013 m s${}^{-\mathrm{1}}$ (TRF). Statistical comparisons between $g_{\text{A-STIC}}$ and $g_{\text{A-HYB}}$ revealed relatively low RMSD and high correlation between them (RMSD $=$ 0.007 m s${}^{-\mathrm{1}}$ and $R^{\mathrm{2}}$ $=$ 0.77) as compared to the error statistics between $g_{\text{A-STIC}}$ and $g_{\text{A-INV}}$ (RMSD $=$ 0.011 m s${}^{-\mathrm{1}}$ and $R^{\mathrm{2}}$ $=$ 0.50) (Fig. 2b and c). The residuals between $g_{\text{A-STIC}}$ and $g_{\text{A-BM13}}$ are plotted as a function of $u$ and $u^{*}$ in Fig. 2d with the aim of ascertaining whether significant biases are introduced by ignoring wind and shear information within STIC1.2. As illustrated in Fig. 2d, there appears to be a weak systematic relationship between the residual $g_{\text{A}}$ difference with either $u^{*}$ or $u$ ($r$ $=$ $-$0.26 and $-$0.17). However, a considerable relationship was found between wind- and shear-driven $g_{\text{A}}$ (i.e., $g_{\text{A-BM13}}$) vs. $\mathit{\varphi }$, $T_{\text{R}}$, and $D_{\text{A}}$ ($r$ $=$ 0.83, 0.48, and 0.42) (Fig. 2e and f), which indicates that these three energy and water constraints can explain 69, 23, and 17 % variance of $g_{\text{A-BM13}}$, respectively.

Canopy-scale evaluation of hourly $g_{\text{C}}$ is presented in Fig. 3a (and Table 3), combining data from the four PFTs. Estimated values range between zero and 0.06 m s${}^{-\mathrm{1}}$ for $g_{\text{C-STIC}}$ and show reasonable correlation ($R^{\mathrm{2}}$ $=$ 0.39) ($R^{\mathrm{2}}$ range between 0.14 [$\pm$0.04] and 0.58 [$\pm$0.12]) between $g_{\text{C-STIC}}$ and $g_{\text{C-INV}}$, with regression parameters ranging between 0.30 ($\pm$0.022) and 0.85 ($\pm$0.025) for the slope and between 0.0024 ($\pm$0.0003) and 0.0097 ($\pm$0.0007) m s${}^{-\mathrm{1}}$ for the offset (Table 3). The RMSD varied between 0.007 (PAS) and 0.012 m s${}^{-\mathrm{1}}$ (TRF and TDF). Given that $g_{\text{A}}$ significantly controls $g_{\text{C}}$, we also examined whether biases in $g_{\text{C}}$ are introduced by ignoring wind and shear information within STIC. The scatter plots between the residual $g_{\text{C}}$ difference ($g_{\text{C-STIC}}$ $-$ $g_{\text{C-INV}}$) vs. both $u$ and $u^{*}$ (Fig. 3b) showed $g_{\text{C}}$ residuals to be evenly distributed across the entire range of $u$ and $u^{*}$, and no systematic pattern was evident.

(a) Comparison between STIC-derived $g_{\text{A}}$ ($g_{\text{A-STIC}}$) with an estimated aerodynamic conductance based on friction velocity ($u^{*}$) and wind speed ($u$) according to Baldocchi and Ma (2013) ($g_{\text{A-BM13}}$), (b) comparison between $g_{\text{A-STIC}}$ with an inverted $g_{\text{A}}$ ($g_{\text{A-INV}}$) based on EC observations of $\mathit{\lambda }E$ and $D_{\text{A}}$, (c) comparison between $g_{\text{A-STIC}}$ with a hybrid $g_{\text{A}}$ ($g_{\text{A-HYB}})$ based on EC observations of $H$ and estimated $T_{\mathrm{0}}$ over the LBA EC sites, (d) comparison between residual $g_{\text{A}}$ differences vs. $u$ and $u^{*}$, and (e, f) relationship between wind- and shear-derived $g_{\text{A}}$ vs. $\mathit{\varphi }$, $T_{\text{R}}$, and $D_{\text{A}}$ over the LBA EC sites.

[Figure omitted. See PDF]

(a) Comparison between STIC-derived $g_{\text{C}}$ ($g_{\text{C-STIC}}$) and $g_{\text{C}}$ computed by inverting the PM model ($g_{\text{C-INV}}$) over the LBA EC sites, where $g_{\text{A-BM13}}$ was used as aerodynamic input in conjunction with tower measurements of $\mathit{\lambda }E$, radiation and meteorological variables, and (b) residual $g_{\text{C}}$ differences vs. wind speed ($u$) and friction velocity ($u^{*}$) over the LBA EC sites.

[Figure omitted. See PDF]

Comparison between STIC-derived (a) $\mathit{\lambda }E$ and (b) $H$ over four different PFTs in the Amazon Basin (LBA tower sites). MAPD is the percent error defined as the mean absolute deviation between the predicted and observed variables divided by the mean observed variable.

[Figure omitted. See PDF]

The reliability of STIC1.2-based $g_{\text{A}}$ and $g_{\text{C}}$ retrievals was further verified by evaluating $\mathit{\lambda }E$ and $H$ estimates (Fig. 4). Both the predicted $\mathit{\lambda }E$ and $H$ are generally in good agreement with the observations, with substantial correlation ($r$) ($R^{\mathrm{2}}$ from 0.61 to 0.94), reasonable RMSD of 33 and 37 W m${}^{-\mathrm{2}}$, and mean absolute percent deviation (MAPD) of 14 and 32 % between the observed and STIC fluxes (Fig. 4), respectively. Regression parameters varied between 0.96 ($\pm$0.008) and 1.14 ($\pm$0.010) for the slope and between $-$16 ($\pm$2) and $-$2 ($\pm$2) W m${}^{-\mathrm{2}}$ for the offset for $\mathit{\lambda }E$ (Table 4), whereas for $H$, these were 0.60 ($\pm$0.025) to 0.89 ($\pm$0.035) for the slope and 9 ($\pm$1) to 29 ($\pm$2) W m${}^{-\mathrm{2}}$ for the offset (Table 3), respectively. The RMSD in $\mathit{\lambda }E$ varied from 20 to 31 W m${}^{-\mathrm{2}}$ and from 23 to 34 W m${}^{-\mathrm{2}}$ for $H$ (Table 3).

The evaluation of the conductances and surface energy fluxes indicates some efficacy for the STIC-derived fluxes and conductance estimates that represent a weighted average of these variables over the source area around the EC tower.

Canopy coupling, transpiration, and evaporation

From Fig. 5a an overall weak to moderate relationship ($r$ $=$ $-$0.31 to $-$0.42) is apparent between the coupling (i.e., 1 $-$ $\mathrm{\Omega }$) and $\mathit{\lambda }{E}_{\text{T}}$, where $\mathit{\lambda }{E}_{\text{T}}$ is negatively related to the coupling for all the PFTs, thus indicating the influence of weak to moderate biophysical controls on $\mathit{\lambda }{E}_{\text{T}}$ throughout the year in addition to radiative controls. The biophysical control was substantially enhanced in TRF ($r$ increased from $-$0.36 to $-$0.53 and $-$0.60) (47 to 67 % increase) and TMF ($r$ increased from $-$0.31 to $-$0.53 and $-$0.58) (70 to 85 % increase) during the dry seasons (July–September) (Fig. 5a). A profound increase in the biophysical control on $\mathit{\lambda }{E}_{\text{T}}$ during the dry season was also found in TDF (52 % increase) and PAS (37 % increase) (Fig. 5a). The negative relationship ($r$ $=$ $-$0.29 to $-$0.45) between (1 $-$ $\mathrm{\Omega }$) and $\mathit{\lambda }{E}_{\text{E}}$ (Fig. 5b) in all four PFTs indicated the role of aerodynamic control on $\mathit{\lambda }{E}_{\text{E}}$. The aerodynamic control was also enhanced during the dry seasons, as shown by the increased negative correlation ($r$ $=$ $-$0.50 to $-$0.69) (Fig. 5b) between (1 $-$ $\mathrm{\Omega }$) and $\mathit{\lambda }{E}_{\text{E}}$.

Correlation of coupling (1 $-$ $\mathrm{\Omega }$) with (a) transpiration ($\mathit{\lambda }{E}_{\text{T}})$ and (b) evaporation ($\mathit{\lambda }{E}_{\text{E}}$) and over four different PFTs by combining data for all the years, only during dry seasons for all the years, and during drought year 2005. Data for 2005 were not available for TDF and PAS. (c)–(e) Examples of the diurnal pattern of $\mathrm{\Omega }$ (black lines), $\mathit{\lambda }{E}_{\text{E}}$ (grey dotted lines) and $\mathit{\lambda }{E}_{\text{T}}$ (grey solid lines) estimated over two ecohydrologically contrasting biomes (K34 for forest and FNS for pasture) in the Amazon Basin (LBA tower sites) during wet and dry seasons.

[Figure omitted. See PDF]

Illustrative examples of the diurnal variations of $\mathit{\lambda }{E}_{\text{E}}$, $\mathit{\lambda }{E}_{\text{T}}$, and $\mathrm{\Omega }$ for two different PFTs with different annual rainfall (2329 mm in rainforest, K34, and 1597 mm in pasture, FNS) for 3 consecutive days during both dry and wet seasons are shown in Fig. 5c–f. This shows the morning rise of $\mathrm{\Omega }$ and a near-constant afternoon $\mathrm{\Omega }$ in the wet season (Fig. 5c and 5d), thus indicating no biophysical controls on $\mathit{\lambda }{E}_{\text{E}}$ and $\mathit{\lambda }{E}_{\text{T}}$ during this season. By contrast, during the dry season, the morning rise in $\mathrm{\Omega }$ is followed by a decrease during noontime (15 to 25 % increase in coupling in forest and pasture) (Fig. 5e and f) due to dominant biophysical control, which is further accompanied by a transient increase from mid-afternoon till late afternoon, and steadily declines thereafter. Interestingly, coupling was relatively higher in pasture during the dry seasons, and the reasons are detailed in the following section and discussion.

$g_{\text{C}}$ and $g_{\text{A}}$ vs. transpiration and evaporation

Scatter plots between $\mathit{\lambda }{E}_{\text{T}}$ and $\mathit{\lambda }{E}_{\text{E}}$ vs. $g_{\text{C}}$ and $g_{\text{A}}$ showed a triangular pattern that became wider with increasing conductances (Fig. 6). To explain this behavior of $\mathit{\lambda }{E}_{\text{T}}$ vs. $g_{\text{C}}$ and $g_{\text{A}}$, we further examined the entire mechanism of conductance–$\mathit{\lambda }{E}_{\text{T}}$ interactions through two-dimensional scatters between $\mathit{\lambda }{E}_{\text{T}}$ and conductances for two consecutive diurnal cycles during wet and dry seasons over rainforest and pasture sites with different annual rainfall (e.g., K34 as a wet site and FNS as a dry site, annual rainfall 2329 and 1597 mm) (Fig. 7). Our results confirm the occurrence of diurnal hysteresis between $g_{\text{C}}$ $-$ $g_{\text{A}}$ and $\mathit{\lambda }{E}_{\text{T}}$ and explain the reason for the shape of the curves obtained in Fig. 6. During the wet season, a distinct environmental control is detectable on $g_{\text{C}}$ and $\mathit{\lambda }{E}_{\text{T}}$ in the morning hours (Fig. 7a and b) in both the PFTs where $g_{\text{C}}$ and $\mathit{\lambda }{E}_{\text{T}}$ increased as a result of increasing $R_{\text{N}}$, $T_{\text{R}}$, and $D_{\text{A}}$. From the late morning to afternoon, a near-constant (forest) or negligible (pasture) increase in $\mathit{\lambda }{E}_{\text{T}}$ is observed despite substantial reduction of both $g_{\text{C}}$ and $g_{\text{A}}$ (25 to 50 % decrease), after which $\mathit{\lambda }{E}_{\text{T}}$ starts decreasing. This behavior of $\mathit{\lambda }{E}_{\text{T}}$ was triggered due to the concurrent changes in $R_{\text{N}}$ (15 to 50 % change), $D_{\text{A}}$ (20 to 60 % change), and $T_{\text{R}}$ (5 to 14 % change), which indicates the absence of any dominant biophysical regulation on $\mathit{\lambda }{E}_{\text{T}}$ during the wet season (Fig. 7a and b). On the contrary, in the dry season, although the morning rise in $\mathit{\lambda }{E}_{\text{T}}$ is steadily controlled by the integrated influence of environmental variables, a modest to strong biophysical control is found for both PFTs during the afternoon, where $\mathit{\lambda }{E}_{\text{T}}$ substantially decreased with decreasing conductances (Fig. 7c and d). This decrease in $\mathit{\lambda }{E}_{\text{T}}$ is mainly caused by the reduction in $g_{\text{C}}$ as a result of increasing $D_{\text{A}}$ and $T_{\text{R}}$ (as seen later in Fig. 8a and c). In the dry season, the area under the hysteretic relationship between $\mathit{\lambda }{E}_{\text{T}}$, $g_{\text{C}}$, and environmental variables was substantially wider in pasture (Fig. 7d) than for the rainforest (Fig. 7c), which is attributed to a greater hysteresis area between $R_{\text{N}}$ and $D_{\text{A}}$ in pasture as a result of reduced water supply. The stronger hysteresis effects in pasture during the dry season (Fig. 7d) ultimately led to the stronger relationship between coupling and $\mathit{\lambda }{E}_{\text{T}}$ (as seen in Fig. 5a).

Scatter plots of transpiration ($\mathit{\lambda }{E}_{\text{T}}$) and evaporation ($\mathit{\lambda }{E}_{\text{E}}$) vs. $g_{\text{C}}$ and $g_{\text{A}}$ over four different PFTs in the Amazon Basin (LBA tower sites).

[Figure omitted. See PDF]

Illustrative examples of the occurrence of diurnal hysteresis of transpiration ($\mathit{\lambda }{E}_{\text{T}}$) during wet and dry seasons with canopy and environmental controls over two different sites with different annual rainfall (2329 and 1597 mm, respectively) in the Amazon Basin (LBA tower sites K34 and FNS).

[Figure omitted. See PDF]

(a) Response of retrieved $g_{\text{C}}$ to atmospheric vapor pressure deficit ($D_{\text{A}}$) for different classes of net radiation ($R_{\text{N}}$), (b) response of retrieved $g_{\text{C}}$ to transpiration for different classes of $D_{\text{A}}$, (c) response of retrieved $g_{\text{C}}$ to radiometric surface temperature ($T_{\text{R}}$) for different classes $D_{\text{A}}$, and (d) relationship between retrieved $g_{\text{A}}$ and radiometric surface temperature and air temperature difference ($T_{\text{R}}$ $-$ $T_{\text{A}}$) in the Amazon Basin (LBA tower sites).

[Figure omitted. See PDF]

Factors affecting variability of $g_{\text{C}}$ and $g_{\text{A}}$

The sensitivity of stomatal conductance to vapor pressure deficit is a key governing factor of transpiration (Ocheltree et al., 2014; Monteith, 1995). We examined whether the feedback or feed-forward response hypothesis (Monteith, 1995; Farquhar, 1987) between $g_{\text{C}}$, $D_{\text{A}}$, and $\mathit{\lambda }{E}_{\text{T}}$ is reflected in our canopy-scale $g_{\text{C}}$ retrievals. Combining data of all the PFTs, we found an exponential decline of $g_{\text{C}}$ in response to increasing $D_{\text{A}}$ regardless of the variations of net radiation (Fig. 8a). High $g_{\text{C}}$ is consistent with high humidity and low evaporative demand. Five negatively logarithmic scatters fit the data with $r$ values of 0.38 (0 $<$ $R_{\text{N}}$ $<$ 150 W m${}^{-\mathrm{2}}$), 0.63 (150 $<$ $R_{\text{N}}$ $<$ 300 W m${}^{-\mathrm{2}}$), 0.73 (300 $<$ $R_{\text{N}}$ $<$ 450 W m${}^{-\mathrm{2}}$), 0.78 (450 $<$ $R_{\text{N}}$ $<$ 600 W m${}^{-\mathrm{2}}$), and 0.87 ($R_{\text{N}}$ $>$ 600 W m${}^{-\mathrm{2}}$). The sensitivity of $g_{\text{C}}$ to $D_{\text{A}}$ was at the maximum in the high $R_{\text{N}}$ range beyond 600 W m${}^{-\mathrm{2}}$ and the sensitivity progressively declined with declining magnitude of $R_{\text{N}}$ (0–150 W m${}^{-\mathrm{2}}$).

Scatter plots between $g_{\text{C}}$ and $\mathit{\lambda }{E}_{\text{T}}$ for different levels of $D_{\text{A}}$ revealed a linear pattern between them for a wide range of $D_{\text{A}}$ (20 $>$ $D_{\text{A}}$ $>$ 0 hPa) (Fig. 8b). Following Monteith (1995), isopleths of $R_{\text{N}}$ are delineated by the solid lines passing through $\mathit{\lambda }{E}_{\text{T}}$ on the $x$ axis and through $g_{\text{C}}$ on the $y$ axis. Isobars of $D_{\text{A}}$ (dotted lines) pass through the origin because $\mathit{\lambda }{E}_{\text{T}}$ approaches zero as $g_{\text{C}}$ approaches zero. Figure 8b shows substantial reduction of $g_{\text{C}}$ with increasing $D_{\text{A}}$ without any increase in $\mathit{\lambda }{E}_{\text{T}}$, like an inverse hyperbolic pattern to $D_{\text{A}}$ (Monteith, 1995; Jones, 1998). For all the PFTs, an active biological (i.e., stomatal) regulation maintained almost constant $\mathit{\lambda }{E}_{\text{T}}$ when $D_{\text{A}}$ was changed from low to high values (Fig. 8b). At high $D_{\text{A}}$ (above 10 hPa), after an initial increase in $\mathit{\lambda }{E}_{\text{T}}$ with $g_{\text{C}}$, $g_{\text{C}}$ approached a maximum limit and remained nearly independent of $\mathit{\lambda }{E}_{\text{T}}$ (Fig. 8b). Among all the $D_{\text{A}}$ levels, the maximum control of $g_{\text{C}}$ on $\mathit{\lambda }{E}_{\text{T}}$ variability (62 to 80 %) was found at high atmospheric water demand (i.e., 30 hPa $>$ $D_{\text{A}}$ $>$ 20 hPa). The scatter plots between $g_{\text{C}}$ and $T_{\text{R}}$ (Fig. 8c) for different levels of $D_{\text{A}}$ revealed an exponential decline in $g_{\text{C}}$ with increasing $T_{\text{R}}$ and atmospheric water demand. When retrieved $g_{\text{A}}$ was plotted against the radiometric surface temperature and air temperature difference ($T_{\text{R}}$ $-$ $T_{\text{A}}$), an exponential decline in $g_{\text{A}}$ was found in response to increasing ($T_{\text{R}}$ $-$ $T_{\text{A}}$) (Fig. 8d). High $g_{\text{A}}$ is persistent with low ($T_{\text{R}}$ $-$ $T_{\text{A}}$) irrespective of the variations in $R_{\text{N}}$ (with the exception of very low $R_{\text{N}}$). Four negatively logarithmic scatters fit the $g_{\text{A}}$ vs. ($T_{\text{R}}$ $-$ $T_{\text{A}}$) relationship with $r$ values of 0.28 (150 $<$ $R_{\text{N}}$ $<$ 300 W m${}^{-\mathrm{2}}$), 0.55 (3000 $<$ $R_{\text{N}}$ $<$ 450 W m${}^{-\mathrm{2}}$), 0.64 (450 $<$ $R_{\text{N}}$ $<$ 600 W m${}^{-\mathrm{2}}$), and 0.77 ($R_{\text{N}}$ $>$ 600 W m${}^{-\mathrm{2}}$).

(a) Scatter plots between source/sink height (or in-canopy) vapor pressure deficit ($D_{\mathrm{0}}$) and atmospheric vapor pressure deficit ($D_{\text{A}}$) for two different classes of $g_{\text{C}}$ / $g_{\text{A}}$ ratios over four PFTs, which clearly depicts a strong coupling between $D_{\mathrm{0}}$ and $D_{\text{A}}$ for low $g_{\text{C}}$ / $g_{\text{A}}$ ratios. (b) Histogram distribution of $g_{\text{C}}$ / $g_{\text{A}}$ ratios over the four PFTs in the Amazon Basin (LBA tower sites). (c) Scatter plots between $g_{\text{C}}$ / $g_{\text{A}}$ ratio vs. surface air temperature difference ($T_{\text{R}}$ $-$ $T_{\text{A}}$) for the four PFTs during the wet season and dry season in the Amazon Basin (LBA tower sites).

[Figure omitted. See PDF]

Discussion

Evaluating $g_{\text{A}}$, $g_{\text{C}}$, and surface energy balance fluxes

The aerodynamic conductance retrieved with STIC1.2 showed acceptable correlation and valid estimates of $g_{\text{A}}$ when compared against an empirical model that uses $u^{*}$ and $u$ to derive $g_{\text{A}}$ (Figs. 1 and 2a) and two other inversion-/hybrid-based $g_{\text{A}}$ estimates. The differences between $g_{\text{A-STIC}}$ and $g_{\text{A-BM13}}$ were mainly attributed to the structural differences and empirical nature of the parameterization for the near-surface boundary-layer conductance ((2/$k{u}^{{*}^{\mathrm{2}}}$)(Sc/Pr)${}^{0.67}$) in $g_{\text{A-BM13}}$, which results in some discrepancies between $g_{\text{A-STIC}}$ and $g_{\text{A-BM13}}$, particularly in the pasture (Fig. 2a). The extent to which the structural discrepancies between $g_{\text{A-STIC}}$ and $g_{\text{A-BM13}}$ relate to actual differences in the conductances for momentum vs. heat is beyond the scope of this paper, and a detailed investigation using data on atmospheric profiles of wind speed, temperature, etc. are needed to actually quantify such differences. Momentum transfer is associated with pressure forces and is not identical to heat and mass transfer (Massman, 1999). In STIC1.2, $g_{\text{A}}$ is directly estimated and is a robust representative of the conductances to heat (and water vapor) transfer, whereas $g_{\text{A-BM13}}$ estimates based on $u^{*}$ and $u$ are more representative of the momentum transfer. Therefore, the difference between the two different $g_{\text{A}}$ estimates (Fig. 2) can be largely attributed to the actual difference in the conductances for momentum and heat (water vapor). The turbulent conductance equation ($u^{{*}^{\mathrm{2}}}$/$u$) in $g_{\text{A-BM13}}$ is also very sensitive to the uncertainties in the sonic anemometer measurement (Contini et al., 2006; Richiardone et al., 2012). However, the evidence of a weak systematic relationship between the $g_{\text{A}}$ residuals and $u$ (Fig. 2d) and the capability of the thermal ($T_{\text{R}})$, radiative ($\mathit{\varphi }$), and meteorological ($T_{\text{A}}$, $D_{\text{A}})$ variables in capturing the variability of $g_{\text{A-BM13}}$ (Fig. 2e and f) indicates the diagnostic potential $g_{\text{A-STIC}}$ estimates to explain the wind-driven $g_{\text{A}}$ variability. Excluding $u$ might introduce errors in cases where wind is the only source of variations in $g_{\text{A}}$ and surface fluxes (Mallick et al., 2015). In general, the accuracies in commonly used parametric $g_{\text{A}}$ estimates based on $u$ and surface roughness parameters several meters distant from canopy foliage are limited due to the uncertainties concerning the attenuation of $u$ close to the vegetation surface (Meinzer et al., 1997; Prihodko et al., 2008). The magnitude of $u$ near the foliage can be substantially lower than that measured considerably away at some reference location above or within the canopy (Meinzer et al., 1997). Notwithstanding the inequalities of $g_{\text{A}}$ estimated with different methods, it is challenging to infer the accuracy of the different estimates. It is imperative to mention that $g_{\text{A}}$ is one of the main anchors in the PM–SW model because it not only appears in the numerator and denominator of these models, but also provides feedback to $g_{\text{C}}$, $T_{\mathrm{0}}$, and $D_{\mathrm{0}}$ (the seminal paper of Jarvis and McNaughton, 1986). Therefore, the estimates of $\mathit{\lambda }E$ in the PM–SW framework are very sensitive to parameterization of $g_{\text{A}}$ and stable $\mathit{\lambda }E$ estimates might be possible if $g_{\text{A}}$ estimation is unambiguous (Holwerda et al., 2012; Van Dijk et al., 2015). Given the lack of consensus in the community on the “true” $g_{\text{A}}$ and from the nature of surface flux validation results (Fig. 4), it appears that $g_{\text{A-STIC}}$ tends to be the appropriate aerodynamic conductance that satisfies the PM–SW equation. Discrepancies between $g_{\text{C-STIC}}$ and $g_{\text{C-INV}}$ originated from the differences in $g_{\text{A}}$ estimates between the two methods.

Comparative statistics for the STIC- and tower-derived hourly $g_{\text{A}}$ and $g_{\text{C}}$ for a range of PFTs in the Amazon Basin (LBA tower sites). Values in parentheses are $\pm$1 standard deviation (standard error for correlation).

	$g_{\text{A-STIC}}$ vs. $g_{\text{A-BM13}}$					$g_{\text{C-STIC}}$ vs. $g_{\text{C-INV}}$
PFTs	RMSD	$R^{\mathrm{2}}$	Slope	Offset		RMSD	$R^{\mathrm{2}}$	Slope	Offset	$N$
	(m s${}^{-\mathrm{1}}$)			(m s${}^{-\mathrm{1}}$)		(m s${}^{-\mathrm{1}}$)			(m s${}^{-\mathrm{1}}$)
TRF	0.013	0.41	1.07	0.0031		0.012	0.14	0.39	0.0097	1159
		($\pm$0.03)	($\pm$0.047)	($\pm$0.0008)			($\pm$0.04)	($\pm$0.039)	($\pm$0.0007)
TMF	0.012	0.55	0.81	0.0006		0.009	0.55	0.85	0.0032	1927
		($\pm$0.12)	($\pm$0.023)	($\pm$0.0006)			($\pm$0.12)	($\pm$0.025)	($\pm$0.0005)
TDF	0.007	0.49	0.89	0.0019		0.012	0.33	0.30	0.0050	787
		($\pm$0.15)	($\pm$0.041)	($\pm$0.0006)			($\pm$0.19)	($\pm$0.022)	($\pm$0.0005)
PAS	0.012	0.22	1.03	0.0059		0.007	0.58	0.65	0.0024	288
		($\pm$0.18)	($\pm$0.083)	($\pm$0.0007)			($\pm$0.12)	($\pm$0.025)	($\pm$0.0003)
Mean	0.012	0.44	0.76	0.0047		0.010	0.39	0.63	0.0046	4161
		($\mathbf{\pm }$0.10)	($\mathbf{\pm }$0.016)	($\mathbf{\pm }$0.003)			($\mathbf{\pm }$0.08)	($\mathbf{\pm }$0.016)	($\mathbf{\pm }$0.0003)

$N$: number of data points; RMSD: root mean square deviation between predicted ($P$) and observed ($O$) variables $={\left[\frac{\mathrm{1}}{N},,\sum _{i=\mathrm{0}}^N,{\left(P_i,-,O_i\right)}^{\mathrm{2}}\right]}^{\mathrm{2}}$.

Comparative statistics for the STIC- and tower-derived hourly $\mathit{\lambda }E$ and $H$ for a range of PFTs in the Amazon Basin (LBA tower sites). Values in parentheses are $\pm$1 standard deviation (standard error for correlation).

	$\mathit{\lambda }E$					$H$
PFTs	RMSD	$R^{\mathrm{2}}$	Slope	Offset		RMSD	$R^{\mathrm{2}}$	Slope	Offset	$N$
	(W m${}^{-\mathrm{2}}$)			(W m${}^{-\mathrm{2}}$)		(W m${}^{-\mathrm{2}}$)			(W m${}^{-\mathrm{2}}$)
TRF	28	0.96	1.10	$-$16		34	0.52	0.60	29	1159
		($\pm$0.007)	($\pm$0.008)	($\pm$2)			($\pm$0.030)	($\pm$0.025)	($\pm$2)
TMF	20	0.98	1.08	$-$11		23	0.71	0.61	20	1927
		($\pm$0.004)	($\pm$0.004)	($\pm$1)			($\pm$0.019)	($\pm$0.014)	($\pm$1)
TDF	26	0.96	0.96	$-$7		30	0.66	0.89	20	787
		($\pm$0.009)	($\pm$0.008)	($\pm$2)			($\pm$0.032)	($\pm$0.035)	($\pm$3)
PAS	31	0.96	1.14	$-$2		33	0.88	0.67	9	288
		($\pm$0.009)	($\pm$0.010)	($\pm$2)			($\pm$0.016)	($\pm$0.011)	($\pm$1)
Mean	33	0.94	1.04	$-$1		37	0.61	0.58	24	4161
		($\mathbf{\pm }$0.005)	($\mathbf{\pm }$0.005)	($\mathbf{\pm }$1)			($\mathbf{\pm }$0.021)	($\mathbf{\pm }$0.009)	($\mathbf{\pm }$2)

Despite the good agreement between the measured and predicted $\mathit{\lambda }E$ and $H$ (Fig. 4, Table 4), the larger error in $H$ was associated with the higher sensitivity of $H$ to the errors in $T_{\text{R}}$ (due to poor emissivity correction) (Mallick et al., 2015). Since the difference between $T_{\text{R}}$ and $T_{\text{A}}$ is considered to be the primary driving force of $H$ (van der Tol et al., 2009), the modeled errors in $H$ are expected to arise due to the uncertainties associated with $T_{\text{R}}$.

Canopy coupling, $g_{\text{C}}$, and $g_{\text{A}}$ vs. transpiration and evaporation

The correlation analysis between 1 $-$ $\mathrm{\Omega }$ and $\mathit{\lambda }{E}_{\text{T}}$ revealed the extent of biophysical and radiative controls on $\mathit{\lambda }{E}_{\text{T}}$ (Fig. 5). The degree of biophysical control is a function of the ratio of $g_{\text{C}}$ to $g_{\text{A}}$. Minor biophysical control on $\mathit{\lambda }{E}_{\text{T}}$ was apparent for forest and pasture during the wet seasons (Fig. 5c and d) as a result of a high $g_{\text{C}}$ / $g_{\text{A}}$ ratio along with increasing $\mathit{\lambda }{E}_{\text{T}}$. Such conditions stimulate local humidification of air surrounding the canopy and uncoupling of the in-canopy vapor pressure deficit ($D_{\mathrm{0}}$) from that in the air above (i.e., $D_{\mathrm{0}}$ $<$ $D_{\text{A}}$) (Meinzer et al., 1997; Motzer et al., 2005) (Fig. 9a), which implies that $\mathit{\lambda }{E}_{\text{T}}$ becomes largely independent of $g_{\text{C}}$. By contrast, an enhanced biophysical control on $\mathit{\lambda }{E}_{\text{T}}$ was apparent during the dry season and drought year 2005 during the period of reduced water supply, particularly over PAS (Figs. 5e, f, and 7). Such a condition leads to a relatively dry canopy surface and substantially high $g_{\text{A}}$ compared to $g_{\text{C}}$, thus resulting in low $g_{\text{C}}$/$g_{\text{A}}$ ratios regardless of their absolute values (Meinzer et al., 1993; McNaughton and Jarvis, 1991). Here, a fractional change in $g_{\text{C}}$ results in an equivalent fractional change in $\mathit{\lambda }{E}_{\text{T}}$. This impedes transpiration from promoting local equilibrium of $D_{\mathrm{0}}$ and minimizing (or maximizing) the gradient between $D_{\mathrm{0}}$ and atmospheric vapor pressure deficit ($D_{\text{A}}$) (i.e., $D_{\mathrm{0}}$ $\cong$ $D_{\text{A}}$ or $D_{\mathrm{0}}$ $>$ $D_{\text{A}}$) (Eq. A10) (Fig. 9a), thereby resulting in strong coupling between $D_{\mathrm{0}}$ and $D_{\text{A}}$ (Meinzer et al., 1993; Jarvis and McNaughton, 1986). Besides, a supplemental biophysical control on $\mathit{\lambda }{E}_{\text{T}}$ might have been imposed as a consequence of a direct negative feedback of $D_{\text{A}}$ and $D_{\mathrm{0}}$ on $g_{\text{C}}$ (McNaughton and Jarvis, 1991; Jarvis, 1986). An increase in $D_{\text{A}}$ (or $D_{\mathrm{0}}$) beyond a certain limit decreases $g_{\text{C}}$ (Figs. 7 and 8), resulting in a low and narrow increase in $\mathit{\lambda }{E}_{\text{T}}$, despite a steady increase in $g_{\text{A}}$ and $R_{\text{N}}$. The combination of a negative feedback response between $D_{\text{A}}$ and $g_{\text{C}}$ with the overall radiative–aerodynamic coupling significantly dampens the variation of transpiration in PAS and TDF in the dry season, thus featuring increased biophysical control in these PFTs. These results are in agreement with von Randow et al. (2012), who found enhanced biophysical control on $\mathit{\lambda }{E}_{\text{T}}$ for the pasture during the dry season. For the wet season, evidence of minor biophysical control indicates the dominance of $R_{\text{N}}$-driven equilibrium evaporation in these PFTs (Hasler and Avissar, 2007; da Rocha et al., 2009; Costa et al., 2010). In the TRF and TMF, 94 and 99 % of the retrieved $g_{\text{C}}$ / $g_{\text{A}}$ ratios fall above 0.5, and only 1 and 6 % of the retrieved $g_{\text{C}}$ / $g_{\text{A}}$ ratios fall below the 0.5 range (Fig. 9b). In contrast, 90 and 73 % of the $g_{\text{C}}$ / $g_{\text{A}}$ ratios range above 0.5, and 10 to 27 % of the $g_{\text{C}}$ / $g_{\text{A}}$ ratios were below 0.5 for TDF and PAS, respectively (Fig. 9b). This shows that, although radiation control is prevailing in all the sites, biophysical control is relatively stronger in TDF and PAS as compared to the other sites. For large $g_{\text{C}}$ / $g_{\text{A}}$ ratios, the conditions within the planetary boundary layer (PBL) become decoupled from the synoptic scale (McNaughton and Jarvis, 1991) and the net radiative energy becomes the important regulator of transpiration. For small $g_{\text{C}}$ / $g_{\text{A}}$ ratios (e.g., in the dry season), the conditions within the PBL are strongly coupled to the atmosphere above by rapid entrainment of air from the capping inversion and by some ancillary effects of sensible heat flux on the entrainment (McNaughton and Jarvis, 1991). These findings substantiate the earlier theory of McNaughton and Jarvis (1991), who postulated that large $g_{\text{C}}$ / $g_{\text{A}}$ ratios result in minor biophysical control on canopy transpiration due to the negative feedback on the canopy from the PBL. The negative relationship between 1 $-$ $\mathrm{\Omega }$ and $\mathit{\lambda }{E}_{\text{E}}$ (Fig. 5b) over all the PFTs is due to the feedback of $g_{\text{A}}$ on $g_{\text{C}}$. However, over all the PFTs, a combined control of $g_{\text{A}}$ and environmental variables on $\mathit{\lambda }{E}_{\text{E}}$ again highlighted the impact of realistically estimated $g_{\text{A}}$ on $\mathit{\lambda }{E}_{\text{E}}$ (Holwerda et al., 2012).

It is important to mention that forests are generally expected to be better coupled to the atmosphere as compared to the pastures, which is related to generally higher $g_{\text{A}}$ of the forests (due to high surface roughness). This implies that forests exhibit stronger biophysical control on $\mathit{\lambda }{E}_{\text{T}}$. However, due to the broad leaves of the rainforests (larger leaf area index) and higher surface wetness (due to higher rainfall amounts), the wet surface area is much larger in the forests than in the pastures. This results in much higher $g_{\text{C}}$ values for forests than for pastures during the wet season ($g_{\text{C}}$ $\approx$ $g_{\text{A}}$), and $g_{\text{C}}$ / $g_{\text{A}}$ $\to$ 1. Consequently, no significant difference in coupling was found between them during the wet season (Fig. 5c and d). Despite the absolute differences in $g_{\text{A}}$ and $g_{\text{C}}$ between forest and pasture, the high surface wetness is largely offsetting the expected $\mathrm{\Omega }$ difference between them. Although the surface wetness is substantially lower during the dry season, the high water availability in the forests due to the deeper root systems helps in maintaining a relatively high $g_{\text{C}}$ compared to the pastures. Hence, despite $g_{\text{A}}$ (forest) $>$ $g_{\text{A}}$ (pasture) during the dry season, substantially lower $g_{\text{C}}$ values for the pasture result in a lower $g_{\text{C}}$ / $g_{\text{A}}$ ratio for the pasture compared to the forest, thus causing more biophysical control on $\mathit{\lambda }{E}_{\text{T}}$ during the dry season. The relatively better relationship between coupling vs. $\mathit{\lambda }{E}_{\text{T}}$ in PAS and TDF during the dry season was also attributed to high surface air temperature differences ($T_{\text{R}}$ $-$ $T_{\text{A}}$) in these PFTs that resulted in low $g_{\text{C}}$ / $g_{\text{A}}$ ratios (Fig. 9c).

Factors affecting $g_{\text{C}}$ and $g_{\text{A}}$ variability

The stomatal feedback-response hypothesis (Monteith, 1995) also became apparent at the canopy scale (Fig. 8a and b), which states that a decrease in $g_{\text{C}}$ with increasing $D_{\text{A}}$ is caused by a direct increase in $\mathit{\lambda }{E}_{\text{T}}$ (Monteith, 1995; Matzner and Comstock, 2001; Streck, 2003), and $g_{\text{C}}$ responds to the changes in the air humidity by sensing $\mathit{\lambda }{E}_{\text{T}}$ rather than $D_{\text{A}}$. This feedback mechanism is found because of the influence of $D_{\text{A}}$ on both $g_{\text{C}}$ and $\mathit{\lambda }{E}_{\text{T}}$, which in turn changes $D_{\text{A}}$ by influencing the air humidity (Monteith, 1995). The change in $g_{\text{C}}$ is dominated by an increase in the net available energy, which is partially offset by an increase in $\mathit{\lambda }{E}_{\text{T}}$. After the net energy input in the canopy exceeds a certain threshold, $g_{\text{C}}$ starts decreasing even if $\mathit{\lambda }{E}_{\text{T}}$ increases. High $\mathit{\lambda }{E}_{\text{T}}$ increases the water potential gradient between guard cells and other epidermal cells or reduces the bulk leaf water potential, thus causing stomatal closure (Monteith, 1995; Jones, 1998; Streck, 2003). The control of soil water on transpiration also became evident from the scatter plots between $g_{\text{C}}$ vs. $\mathit{\lambda }{E}_{\text{T}}$ and $T_{\text{R}}$ for different $D_{\text{A}}$ levels (Figs. 8b, c, and 7). Denmead and Shaw (1962) hypothesized that reduced $g_{\text{C}}$ and stomatal closure occurs at moderate to higher levels of soil moisture (high $\mathit{\lambda }{E}_{\text{T}}$) when the atmospheric demand of water vapor increases (high $D_{\text{A}})$. The water content in the immediate vicinity of the plant root depletes rapidly at high $D_{\text{A}}$, which decreases the hydraulic conductivity of soil, and the soil is unable to efficiently supply water under these conditions. For a given evaporative demand and available energy, transpiration is determined by the $g_{\text{C}}$ / $g_{\text{A}}$ ratio, which is further modulated by the soil water availability. These combined effects tend to strengthen the biophysical control on transpiration (Leuzinger and Kirner, 2010; Migletta et al., 2011). The complex interaction between $g_{\text{C}}$, $T_{\text{R}}$, and $D_{\text{A}}$ (Fig. 8c) explains why different parametric $g_{\text{C}}$ models produce divergent results.

Although $\mathit{\lambda }{E}_{\text{T}}$ and $\mathit{\lambda }{E}_{\text{E}}$ estimates are interdependent on $g_{\text{C}}$ and $g_{\text{A}}$ (as shown in Figs. 6–8), the figures reflect the credibility of the conductances as well as transpiration estimates by realistically capturing the hysteretic behavior between biophysical conductances and water vapor fluxes, which is frequently observed in natural ecosystems (Zhang et al., 2014; Renner et al., 2016) (also Zuecco et al., 2016). These results are also compliant with the theories postulated earlier from observations that the magnitude of hysteresis depends on the radiation–vapor pressure deficit time lag, while the soil moisture availability is a key factor modulating the hysteretic transpiration–vapor pressure deficit relation as soil moisture declines (Zhang et al., 2014; O'Grady et al., 1999; Jarvis and McNaughton, 1986). This shows that despite being independent of any predefined hysteretic function, the interdependent conductance–transpiration hysteresis is still captured in STIC1.2.

Figure 8d is in accordance with the existing theory that under conditions of extremely high atmospheric turbulence (i.e., high $g_{\text{A}}$), a close coupling exists between the surface and the atmosphere, which causes $T_{\text{R}}$ and $T_{\text{A}}$ to converge (i.e., $T_{\text{R}}$ $-$ $T_{\text{A}}$ $\to$ 0). When $g_{\text{A}}$ is low, the difference between $T_{\text{R}}$ and $T_{\text{A}}$ increases due to poor vertical mixing of the air.

Conclusions

By integrating the radiometric surface temperature ($T_{\text{R}}$) into a combined structure of the PM–SW model, we have estimated the canopy-scale biophysical conductances and quantified their control on the terrestrial evapotranspiration components in a simplified SEB modeling perspective that treats the vegetation canopy as “big-leaf”. The STIC1.2 biophysical modeling scheme is independent of any leaf-scale empirical parameterization for stomata and associated aerodynamic variables.

Stomata regulate the coupling between terrestrial carbon and water cycles, which implies that their behavior under global environmental change is critical to predicting vegetation functioning (Medlyn et al., 2011). The combination of variability in precipitation (Hilker et al., 2014) and land cover change (Davidson et al., 2012) in the Amazon Basin is expected to increase the canopy–atmosphere coupling of pasture or forest systems under drier conditions by altering the ratio of the biological and aerodynamic conductances. An increase in biophysical control will most likely be an indicator of shifting the transpiration from an energy-limited to a water-limited regime (due to the impact of $T_{\text{R}}$, $T_{\text{A}}$, and $D_{\text{A}}$ on the $g_{\text{C}}$ / $g_{\text{A}}$ ratio), with further consequences for the surface water balance and rainfall recycling. At the same time, a transition from forest to pasture or agriculture lands will substantially reduce the contribution of interception evaporation in the Amazon; hence, it will affect the regional water cycle. This might change the moisture regime of the Amazonian Basin and affect the moisture transport to other regions. In this context, STIC1.2 provides a new quantitative and internally consistent method for interpreting the biophysical conductances and is able to quantify their controls on the water cycle components in response to a range of climatic and ecohydrological conditions (excluding rising atmospheric CO${}_{\mathrm{2}}$) across a broad spectrum of PFTs. It could also provide the basis for improving existing land surface parameterizations for simulating vegetation water use at large spatial scales.

It should also be noted that although the case study described here provides general insights into the biophysical controls of $\mathit{\lambda }E$ and associated feedback between $g_{\text{C}}$, $D_{\text{A}}$, $T_{\text{R}}$, and $\mathit{\lambda }{E}_{\text{T}}$ in the framework of the PM–SW equation, there is a tendency to overestimation of $g_{\text{C}}$ due to the embedded evaporation information in the current single-source composition of STIC1.2. For accurate characterization of canopy conductance, explicit partitioning of $\mathit{\lambda }E$ into transpiration and evaporation (both soil and interception) is one of the further scopes for improving STIC1.2, and this assumption needs to be tested further.

Data availability

The LBA eddy covariance datasets are available through ftp://daac.ornl.gov/data/lba/carbon_dynamics/CD32_Brazil_Flux_Network/ (Saleska et al., 2013).

Description of STIC1.2

Derivation of “state equations” in STIC 1.2

Neglecting horizontal advection and energy storage, the surface energy balance equation is written as follows: $$\mathit{\varphi }=\mathit{\lambda }E+H.$$ Figure A1 shows that, while $H$ is controlled by a single aerodynamic resistance ($r_{\text{A}}$) (or 1/$g_{\text{A}}$); $\mathit{\lambda }E$ is controlled by two resistances in series, the surface resistance ($r_{\text{C}}$) (or 1/$g_{\text{C}}$) and the aerodynamic resistance to vapor transfer ($r_{\text{C}}$ $+$ $r_{\text{A}}$). For simplicity, it is implicitly assumed that the aerodynamic resistance of water vapor and heat are equal (Raupach, 1998), and both the fluxes are transported from the same level from near surface to the atmosphere. The sensible and latent heat flux can be expressed in the form of aerodynamic transfer equations (Boegh et al., 2002; Boegh and Soegaard, 2004) as follows: $$\begin{array}{}& & H=\mathit{\rho }{c}_P{g}_{\text{A}}\left(T_{\mathrm{0}},-,T_{\text{A}}\right)& & \mathit{\lambda }E={\displaystyle \frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}}{g}_{\text{A}}\left(e_{\mathrm{0}},-,e_{\text{A}}\right)={\displaystyle \frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}}{g}_{\text{C}}\left(e_{\mathrm{0}}^{*},-,e_{\mathrm{0}}\right)\end{array}$$ where $T_{\mathrm{0}}$ and $e_{\mathrm{0}}$ are the air temperature and vapor pressure at the source/sink height (i.e., aerodynamic temperature and vapor pressure) or at the so-called roughness length ($z_{\mathrm{0}}$), where wind speed is zero. They represent the vapor pressure and temperature of the quasi-laminar boundary layer in the immediate vicinity of the surface level (Fig. A1), and $T_{\mathrm{0}}$ can be obtained by extrapolating the logarithmic profile of $T_{\text{A}}$ down to $z_{\mathrm{0}}$. $e_{\mathrm{0}}^{*}$ is the saturation vapor pressure at $T_{\mathrm{0}}$ (hPa).

By combining Eqs. (A1)–(A3) and solving for $g_{\text{A}}$, we get the following equation. $$g_{\text{A}}={\displaystyle \frac{\mathit{\varphi }}{\mathit{\rho }{c}_P}}\left[\left(T_{\mathrm{0}},-,T_{\text{A}}\right),+,\left({\displaystyle \frac{e_{\mathrm{0}}-e_{\text{A}}}{\mathit{\gamma }}}\right)\right]$$

Combining the aerodynamic expressions of $\mathit{\lambda }E$ in Eq. (A3) and solving for $g_{\text{C}}$, we can express $g_{\text{C}}$ in terms of $g_{\text{A}}$, $e_{\mathrm{0}}^{*}$, $e_{\mathrm{0}}$, and $e_{\text{A}}$. $$g_{\text{C}}=g_{\text{A}}{\displaystyle \frac{\left(e_{\mathrm{0}},-,e_{\text{A}}\right)}{\left(e_{\mathrm{0}}^{*},-,e_{\mathrm{0}}\right)}}$$

While deriving the expressions for $g_{\text{A}}$ and $g_{\text{C}}$, two more unknown variables are introduced ($e_{\mathrm{0}}$ and $T_{\mathrm{0}}$), thus there are two equations and four unknowns. Therefore, two more equations are needed to close the system of equations.

An expression for $T_{\mathrm{0}}$ is derived from the Bowen ratio ($\mathit{\beta }$) (Bowen, 1926) and evaporative fraction ($\mathrm{\Lambda }$) (Shuttleworth et al., 1989) equation. $$\begin{array}{}& & \mathit{\beta }=\left({\displaystyle \frac{\mathrm{1}-\mathrm{\Lambda }}{\mathrm{\Lambda }}}\right)={\displaystyle \frac{\mathit{\gamma }\left(T_{\mathrm{0}},-,T_{\text{A}}\right)}{\left(e_{\mathrm{0}},-,e_{\text{A}}\right)}}& & T_{\mathrm{0}}=T_{\text{A}}+\left({\displaystyle \frac{e_{\mathrm{0}}-e_{\text{A}}}{\mathit{\gamma }}}\right)\left({\displaystyle \frac{\mathrm{1}-\mathrm{\Lambda }}{\mathrm{\Lambda }}}\right)\end{array}$$

Schematic representation of the one-dimensional description of STIC1.2. In STIC1.2, a feedback is established between the surface-layer evaporative fluxes and source/sink height mixing and coupling, and the connection is shown in dotted arrows between $e_{\mathrm{0}}$, $e_{\mathrm{0}}^{*}$, $g_{\text{A}}$, $g_{\text{C}}$, and $\mathit{\lambda }E$. Here, $r_{\text{A}}$ and $r_{\text{C}}$ are the aerodynamic and canopy (or surface in the case of partial vegetation cover) resistances, $g_{\text{A}}$ and $g_{\text{C}}$ are the aerodynamic and canopy conductances (reciprocal of resistances), $e_{\text{S}}^{*}$ is the saturation vapor pressure of the surface, $e_{\mathrm{0}}^{*}$ is the saturation vapor pressure at the source/sink height, $T_{\mathrm{0}}$ is the source/sink height temperature (i.e., aerodynamic temperature) that is responsible for transferring the sensible heat ($H$), $e_{\mathrm{0}}$ is the source/sink height vapor pressure, $e_{\text{S}}$ is the vapor pressure at the surface, $z_{\mathrm{0}}$ is the roughness length, $T_{\text{R}}$ is the radiometric surface temperature, $T_{\text{SD}}$ is the source/sink height dew-point temperature, $M$ is the surface moisture availability or evaporation coefficient, $R_{\text{N}}$ and $G$ are net radiation and ground heat flux, $T_{\text{A}}$, $e_{\text{A}}$, and $D_{\text{A}}$ are temperature, vapor pressure, and vapor pressure deficit at the reference height ($z_{\text{R}}$), $\mathit{\lambda }E$ is the latent heat flux, and $H$ is the sensible heat flux, respectively.

[Figure omitted. See PDF]

Aerodynamic temperature obtained from STIC1.2 ($T_{\text{0-STIC}}$) vs. radiometric surface temperature ($T_{\text{R}}$) over two different biomes in the Amazon Basin. The regression equation of line of best fit is $T_{\text{0-STIC}}$ $=$ 0.67 ($\pm$0.10) $T_{\text{R}}$ $+$ 10.59 ($\pm$2.79) with $r$ $=$ 0.65.

[Figure omitted. See PDF]

This expression for $T_{\mathrm{0}}$ introduces another new variable ($\mathrm{\Lambda }$); therefore, one more equation that describes the dependence of $\mathrm{\Lambda }$ on the conductances ($g_{\text{A}}$ and $g_{\text{C}}$) is needed to close the system of equations. In order to express $\mathrm{\Lambda }$ in terms of $g_{\text{A}}$ and $g_{\text{C}}$, we had adopted the advection–aridity (AA) hypothesis (Brutsaert and Stricker, 1979) with a modification introduced by Mallick et al. (2015). The AA hypothesis is based on a complementary connection between the potential evaporation ($E^{*}$), sensible heat flux ($H$), and $E$; and leads to an assumed link between $g_{\text{A}}$ and $T_{\mathrm{0}}$. However, the effects of surface moisture (or water stress) were not explicit in the AA equation, and Mallick et al. (2015) implemented a moisture constraint in the original AA hypothesis while deriving a “state equation” of $\mathrm{\Lambda }$ (Eq. A8 below). A detailed derivation of the “state equation” for $\mathrm{\Lambda }$ is described in Supplement S1 (also see Mallick et al., 2014, 2015). Estimation of $e_{\mathrm{0}}$, $e_{\mathrm{0}}^{*}$, $M$, and $\mathit{\alpha }$ is described in Appendix A2. $$\mathrm{\Lambda }={\displaystyle \frac{\mathrm{2}\mathit{\alpha }s}{\mathrm{2}s+\mathrm{2}\mathit{\gamma }+\mathit{\gamma }\frac{g_{\text{A}}}{g_{\text{C}}}(\mathrm{1}+M)}}$$

Iterative solution of $e_{\mathrm{0}}$, $e_{\mathrm{0}}^{*}$, $M$, and $\mathit{\alpha }$ in STIC 1.2

In STIC1.0 and 1.1 (Mallick et al., 2014, 2015), no distinction was made between the surface and source/sink height vapor pressures. Therefore, $e_{\mathrm{0}}^{*}$ was approximated as the saturation vapor pressure at $T_{\text{R}}$ and $e_{\mathrm{0}}$ was empirically estimated from $M$ based on the assumption that the vapor pressure at the source/sink height ranges between extreme wet–dry surface conditions. However, the level of $e_{\mathrm{0}}$ and $e_{\mathrm{0}}^{*}$ should be consistent with the level of the aerodynamic temperature ($T_{\mathrm{0}}$) from which the sensible heat flux is transferred (Lhomme and Montes, 2014). The predictive use of the PM model could be hindered by neglecting of the feedbacks between the surface-layer evaporative fluxes and source/sink height mixing and coupling (McNaughton and Jarvis, 1984) and their impact on the canopy-scale conductances. Therefore, in STIC1.2, we have used physical expressions for estimating $e_{\mathrm{0}}$ and $e_{\mathrm{0}}^{*}$ followed by estimating $T_{\text{SD}}$ and $M$ as described below. The fundamental differences between the STIC1.0, 1.1, and 1.2 modeling philosophies are described in Table A1.

An estimate of $e_{\mathrm{0}}^{*}$ is obtained by inverting the aerodynamic transfer equation of $\mathit{\lambda }E$. $$e_{\mathrm{0}}^{*}=e_{\text{A}}+\left[{\displaystyle \frac{\mathit{\gamma }\mathit{\lambda }E\left(g_{\text{A}},+,g_{\text{C}}\right)}{\mathit{\rho }{c}_P{g}_{\text{A}}{g}_{\text{C}}}}\right]$$

Following Shuttleworth and Wallace (1985) (SW), the vapor pressure deficit ($D_{\mathrm{0}}$) ($=$ $e_{\mathrm{0}}^{*}$ $-$ $e_{\mathrm{0}}$) and vapor pressure ($e_{\mathrm{0}}$) at the source/sink height are expressed as follows. $$\begin{array}{}& & D_{\mathrm{0}}=D_{\text{A}}+\left[{\displaystyle \frac{\mathit{\{}s\mathit{\varphi }-(s+\mathit{\gamma }\left)\mathit{\lambda }E\mathit{\right\}}}{\mathit{\rho }{c}_P{g}_{\text{A}}}}\right]& & e_{\mathrm{0}}=e_{\mathrm{0}}^{*}-D_{\mathrm{0}}\end{array}$$

A physical equation of $\mathit{\alpha }$ is derived by expressing the evaporative fraction ($\mathrm{\Lambda }$) as a function of the aerodynamic equations of $H$ [$\mathit{\rho }{c}_P{g}_{\text{A}}(T_{\mathrm{0}}$ $-$ $T_{\text{A}})$] and $\mathit{\lambda }E$ [$\frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}\frac{g_{\text{A}}{g}_{\text{C}}}{g_{\text{A}}+g_{\text{C}}}(e_{\mathrm{0}}^{*}$ $-$ $e_{\text{A}})$] as follows. $$\begin{array}{}& \mathrm{\Lambda }& ={\displaystyle \frac{\mathit{\lambda }E}{H+\mathit{\lambda }E}}& & ={\displaystyle \frac{\frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}\frac{g_{\text{A}}{g}_{\text{C}}}{g_{\text{A}}+g_{\text{C}}}\left(e_{\mathrm{0}}^{*},-,e_{\text{A}}\right)}{\mathit{\rho }{c}_P{g}_{\text{A}}\left(T_{\mathrm{0}},-,T_{\text{A}}\right)+\frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}\frac{g_{\text{A}}{g}_{\text{C}}}{g_{\text{A}}+g_{\text{C}}}\left(e_{\mathrm{0}}^{*},-,e_{\text{A}}\right)}}& & ={\displaystyle \frac{g_{\text{C}}\left(e_{\mathrm{0}}^{*},-,e_{\text{A}}\right)}{\left[\mathit{\gamma },\left(T_{\mathrm{0}},-,T_{\text{A}}\right),\left(g_{\text{A}},+,g_{\text{C}}\right),+,g_{\text{C}},\left(e_{\mathrm{0}}^{*},-,e_{\text{A}}\right)\right]}}\end{array}$$

Combining Eqs. (A14) and (A8) (eliminating $\mathrm{\Lambda }$), we can derive a physical equation of $\mathit{\alpha }$. $$\mathit{\alpha }={\displaystyle \frac{g_{\text{C}}\left(e_{\mathrm{0}}^{*},-,e_{\text{A}}\right)\left[\mathrm{2},s,+,\mathrm{2},\mathit{\gamma },+,\mathit{\gamma },\frac{g_{\text{A}}}{g_{\text{C}}},(,\mathrm{1},+,M,)\right]}{\mathrm{2}s\left[\mathit{\gamma },\left(T_{\mathrm{0}},-,T_{\text{A}}\right),\left(g_{\text{A}},+,g_{\text{C}}\right),+,g_{\text{C}},\left(e_{\mathrm{0}}^{*},-,e_{\text{A}}\right)\right]}}$$

Following Venturini et al. (2008), $M$ can be expressed as the ratio of the vapor pressure difference to the vapor press deficit between the surface and atmosphere as follows. $$M={\displaystyle \frac{\left(e_{\mathrm{0}},-,e_{\text{A}}\right)}{\left(e_{\mathrm{0}}^{*},-,e_{\text{A}}\right)}}={\displaystyle \frac{\left(e_{\mathrm{0}},-,e_{\text{A}}\right)}{k\left(e_{\text{S}}^{*},-,e_{\text{A}}\right)}}={\displaystyle \frac{s_{\mathrm{1}}\left(T_{\text{SD}},-,T_{\text{D}}\right)}{k{s}_{\mathrm{2}}\left(T_{\text{R}},-,T_{\text{D}}\right)}},$$ where $T_{\text{SD}}$ is the dew-point temperature at source/sink height and $T_{\text{D}}$ is the air dew-point temperature; $s_{\mathrm{1}}$ and $s_{\mathrm{2}}$ are the psychrometric slopes of the saturation vapor pressure and temperature between the ($T_{\text{SD}}$ $-$ $T_{\text{D}}$) vs. ($e_{\mathrm{0}}$ $-$ $e_{\text{A}}$) and ($T_{\text{R}}$ $-$ $T_{\text{D}}$) vs. ($e_{\text{S}}^{*}$ $-$ $e_{\text{A}}$) relationship (Venturini et al., 2008), and $k$ is the ratio between ($e_{\mathrm{0}}^{*}$ $-$ $e_{\text{A}}$) and ($e_{\text{S}}^{*}$ $-$ $e_{\text{A}}$). Despite $T_{\mathrm{0}}$ driving the sensible heat flux, the comprehensive dry–wet signature of the underlying surface due to soil moisture variations is directly reflected in $T_{\text{R}}$ (Kustas and Anderson, 2009). Therefore, using $T_{\text{R}}$ in the denominator of Eq. (A16) tends to give a direct signature of the surface moisture availability ($M$). In Eq. (A16), $T_{\text{SD}}$ computation is challenging because both $e_{\mathrm{0}}$ and $s_{\mathrm{1}}$ are unknown. By decomposing the aerodynamic equation of $\mathit{\lambda }E$, $T_{\text{SD}}$ can be expressed as follows. $$\begin{array}{}& & \mathit{\lambda }E={\displaystyle \frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}}{g}_{\text{A}}\left(e_{\mathrm{0}},-,e_{\text{A}}\right)={\displaystyle \frac{\mathit{\rho }{c}_P}{\mathit{\gamma }}}{g}_{\text{A}}{s}_{\mathrm{1}}\left(T_{\text{SD}},-,T_{\text{D}}\right)& & T_{\text{SD}}=T_{\text{D}}+{\displaystyle \frac{\mathit{\gamma }\mathit{\lambda }E}{\mathit{\rho }{c}_P{g}_{\text{A}}{s}_{\mathrm{1}}}}\end{array}$$

In the earlier STIC versions, $s_{\mathrm{1}}$ was approximated at $T_{\text{D}}$, $e_{\mathrm{0}}^{*}$ was approximated at $T_{\text{R}}$, $T_{\text{SD}}$ was estimated from $s_{\mathrm{1}}$, $T_{\text{D}}$, $T_{\text{R}}$, and related saturation vapor pressures (Mallick et al., 2014, 2015), and $M$ was estimated from Eq. (A16) (estimation of $T_{\text{SD}}$ and $M$ was stand-alone earlier). However, since $T_{\text{SD}}$ depends on $\mathit{\lambda }E$ and $g_{\text{A}}$, an iterative procedure is applied to estimate $T_{\text{SD}}$ and $M$ as described in the following paragraph.

(a) Convergence of the iteration method for retrieving the source/sink height (or in-canopy) vapor pressures ($e_{\mathrm{0}}$ and $D_{\mathrm{0}}$) and Priestley–Taylor coefficient ($\mathit{\alpha }$). (b) Convergence of the iteration method for retrieving the surface wetness ($M$) and source/sink height dew-point temperature ($T_{\text{SD}}$). The initial values of $\mathit{\lambda }E,g_{\text{A}}$, $g_{\text{C}}$, and $T_{\mathrm{0}}$ were determined with $\mathit{\alpha }$ $=$ 1.26. The process is then iterated by updating $\mathit{\lambda }E$, $e_{\mathrm{0}}$, $D_{\mathrm{0}}$, $M$, $T_{\text{SD}}$, and $\mathit{\alpha }$ in subsequent iterations with the previous estimates of $g_{\text{A}}$, $g_{\text{C}}$, and $T_{\mathrm{0}}$.

[Figure omitted. See PDF]

In STIC1.2, an initial value of $\mathit{\alpha }$ is assigned as 1.26 and initial estimates of $e_{\mathrm{0}}^{*}$ and $e_{\mathrm{0}}$ are obtained from $T_{\text{R}}$ and $M$ as $e_{\mathrm{0}}^{*}$ $=$ 6.13753$e^{\frac{17.27T_{\text{R}}}{\left(T_{\text{R}},+,237.3\right)}}$ and $e_{\mathrm{0}}$ $=$ $e_{\text{A}}$ $+$ $M(e_{\mathrm{0}}^{*}$ $-$ $e_{\text{A}})$. Initial $T_{\text{SD}}$ and $M$ were estimated as described in Mallick et al. (2014, 2015). With the initial estimates of these variables, first estimates of the conductances, $T_{\mathrm{0}}$, $\mathrm{\Lambda }$, and $\mathit{\lambda }E$ are obtained. The process is then iterated by updating $e_{\mathrm{0}}^{*}$ (using Eq. A9), $D_{\mathrm{0}}$ (using Eq. A10), $e_{\mathrm{0}}$ (using Eq. A11), $T_{\text{SD}}$ (using Eq. A17 with $s_{\mathrm{1}}$ estimated at $T_{\text{D}}$), $M$ (using Eq. A16), and $\mathit{\alpha }$ (using Eq. A15), with the first estimates of $g_{\text{C}}$, $g_{\text{A}}$, and $\mathit{\lambda }E$, and recomputing $g_{\text{C}}$, $g_{\text{A}}$, $T_{\mathrm{0}}$, $\mathrm{\Lambda }$, and $\mathit{\lambda }E$ in the subsequent iterations with the previous estimates of $e_{\mathrm{0}}^{*}$, $e_{\mathrm{0}}$, $M$, and $\mathit{\alpha }$ until the convergence of $\mathit{\lambda }E$ is achieved. Stable values of $\mathit{\lambda }E$, $e_{\mathrm{0}}^{*}$, $e_{\mathrm{0}}$, $T_{\text{SD}}$, $M$, and $\mathit{\alpha }$ are obtained within $\sim$ 25 iterations. Illustrative examples of the convergence of $e_{\mathrm{0}}^{*}$, $e_{\mathrm{0}}$, $T_{\text{SD}}$, $M$, and $\mathit{\alpha }$ are shown in Fig. A3.

To summarize, the computational steps of the conductances and evaporative fluxes in STIC are

• Step 1: analytical solution of the conductances, $T_{\mathrm{0}}$ and $\mathrm{\Lambda }$, by solving the “state equations” (Eqs. 2–5);

• Step 2: initial estimates of the conductances ($g_{\text{C}}$ and $g_{\text{A}}$), $T_{\mathrm{0}}$, $\mathrm{\Lambda }$, $\mathit{\lambda }E$, and $H$;

• Step 3: simultaneous iteration of $\mathit{\lambda }E$, $e_{\mathrm{0}}^{*}$, $e_{\mathrm{0}}$, $T_{\text{SD}}$, $M$, and $\mathit{\alpha }$, and final estimation of the conductances ($g_{\text{C}}$ and $g_{\text{A}}$), $T_{\mathrm{0}}$, $\mathrm{\Lambda }$, $\mathit{\lambda }E$, and $H$; and

• Step 4: partitioning $\mathit{\lambda }E$ into $\mathit{\lambda }{E}_{\text{T}}$ and $\mathit{\lambda }{E}_{\text{E}}$.

Differences in the modeling philosophies of source/sink height vapor pressures ($e_{\mathrm{0}}$, $e_{\mathrm{0}}^{*}$) and dew-point temperature ($T_{\text{SD}}$), surface wetness ($M$), and $\mathit{\alpha }$ between STIC1.0, STIC1.1, and STIC1.2.

Variable	Principles
estimation	STIC1.0	STIC1.1	STIC1.2
	(Mallick et al., 2014)	(Mallick et al., 2015)	(this study – Mallick et al., 2016)
Saturation	$e_{\mathrm{0}}^{*}$ was approximated as the	Same as STIC1.0	$e_{\mathrm{0}}^{*}$ is estimated through numerical
vapor	saturation vapor pressure at		iteration by inverting the aerodynamic
pressure at	$T_{\text{R}}$.		equation of $\mathit{\lambda }E$ (as described in Appendix A2).
source/sink			$e_{\mathrm{0}}^{*}$ $=$ $e_{\text{A}}$ $+$ $\left[\frac{\mathit{\gamma }\mathit{\lambda }E\left(g_{\text{A}},+,g_{\text{C}}\right)}{\mathit{\rho }{c}_P{g}_{\text{A}}{g}_{\text{C}}}\right]$
height ($e_{\mathrm{0}}^{*}$)
Actual vapor	$e_{\mathrm{0}}$ was empirically estimated	Same as STIC1.0	$e_{\mathrm{0}}$ is estimated as $e_{\mathrm{0}}$ $=$ $e_{\mathrm{0}}^{*}$ $-$ $D_{\mathrm{0}}$, where $D_{\mathrm{0}}$
pressure at	from $M$ based on the		was iteratively estimated by combining
source/sink	assumption that the vapor		PM with the Shuttleworth–Wallace
height ($e_{\mathrm{0}}$)	pressure at the source/sink		approximation (as described in Appendix A2).
	height ranges between		$D_{\mathrm{0}}$ $=$ $D_{\text{A}}$ $+$ $\left[\frac{\mathit{\{}s\mathit{\varphi }-(s+\mathit{\gamma }\left)\mathit{\lambda }E\mathit{\right\}}}{\mathit{\rho }{c}_P{g}_{\text{A}}}\right]$
	extreme wet–dry surface
	conditions.
Dew-point	$T_{\text{SD}}$ $=$ $\frac{\left(e_{\text{S}}^{*},-,e_{\text{A}}\right)-s_{\mathrm{3}}{T}_{\text{R}}+s_{\mathrm{1}}{T}_{\text{D}}}{\left(s_{\mathrm{1}},-,s_{\mathrm{3}}\right)}$	Same as STIC1.0	$T_{\text{SD}}$ is estimated through numerical
temperature at	$s_{\mathrm{1}}$ and $s_{\mathrm{3}}$ are the slopes of		iteration by inverting the aerodynamic
source/sink	saturation vapor pressures at		equation of $\mathit{\lambda }E$ (as described in Appendix A2).
height ($T_{\text{SD}}$)	temperatures, approximated at		$T_{\text{SD}}$ $=$ $T_{\text{D}}$ $+$ $\frac{\mathit{\gamma }\mathit{\lambda }E}{\mathit{\rho }{c}_P{g}_{\text{A}}{s}_{\mathrm{1}}}$
	$T_{\text{D}}$ and $T_{\text{R}}$, respectively.
Surface	As a stand-alone equation,	Same as STIC1.0	A feedback of $M$ into $\mathit{\lambda }E$ is introduced
moisture	without any feedback to $\mathit{\lambda }E$.		and $M$ is iteratively estimated after
availability			estimating $T_{\text{SD}}$ (as described in Appendix A2).
($M$)
Priestley–	As fixed parameter (1.26).	A physical equation	A physical equation of $\mathit{\alpha }$ is derived as a
Taylor		of $\mathit{\alpha }$ is derived as a	function of the conductances and $\mathit{\alpha }$ is
parameter ($\mathit{\alpha }$)		function of the	numerically estimated as a variable
		conductances and $\mathit{\alpha }$	(Eq. A15) (as described in Appendix A2).
		is numerically
		estimated as a
		variable.

Fundamental differences in the modeling principles between STIC1.2 and previous approaches for characterizing the biophysical controls on $\mathit{\lambda }E$ components.

Biophysical	Modeling principles
states	Parametric modeling	STIC1.2
	(Ma et al., 2015; Chen et al., 2011;
	Kumagai et al., 2004)
$g_{\text{A}}$	Either $g_{\text{A}}$ is assumed to be the momentum	Analytically retrieved by solving “$n$” state
	conductance ($g_{\text{M}}$) or estimated as a sum of $g_{\text{M}}$ and	equations and “$n$” unknowns, with explicit
	quasi-laminar boundary-layer conductance ($g_{\text{B}}$).	convective feedback and without any wind
		speed ($u$) information.
	1/$g_{\text{A}}$ $=$ 1/$g_{\text{M}}$ $+$ 1/$g_{\text{B}}$	In a hallmark paper by Choudhury and
	$g_{\text{M}}$ $=$ $(u^{*}{)}^{\mathrm{2}}/u$	Monteith (1986), it is clearly stated that
	$g_{\text{B}}$ $=$ $f$ $\mathit{\{}$Nusselt number, leaf dimension, thermal	“aerodynamic conductance determined by wind
	conductivity of air in the boundary layer, $u$, kinematic	speed and roughness is assumed to be
	viscosity, Reynolds number$\mathit{\}}$	unaffected by buoyancy. Strictly, the
		aerodynamic conductance should be replaced
	If $u^{*}$ is available from EC tower, it is directly	by a term that accounts for radiative as well
	used, otherwise $u^{*}$ is parametrized using Monin–	as convective heat transfer”. The role of $g_{\text{A}}$ is
	Obukhov Similarity Theory (MOST).	associated with the role of convection
		(Choudhury and Monteith, 1986) according to
	Disadvantages: (1) MOST is only valid for an	the surface energy balance principle as
	extended, uniform, and flat surface (Foken,	reflected in the derivation of Eq. (A4). Wind
	2006). MOST tends to fail over rough surfaces	is generated as a result of the differences in
	due to breakdown of the similarity relationships	atmospheric pressure that is a result of
	for heat and water vapor transfer in the roughness	uneven surface radiative heating. Therefore,
	sub-layer, which results in an underestimation of	the aerodynamic conductance (and wind as
	the “true” $g_{\text{A}}$ by a factor of 1–3 (Thom et al., 1975;	well) is an effect of net radiative heating and
	Chen and Schwerdtfeger, 1989; Simpson et al.,	there should be a physical relationship between
	1998; Holwerda et al., 2012). (2) In the state-of-the-	these two.
	art $\mathit{\lambda }E$ modeling, the parametric $g_{\text{A}}$ sub-models
	are stand-alone and empirical, and do not provide	Advantages: (1) STIC1.2 consists of a
	any feedback to $g_{\text{C}}$, aerodynamic temperature	feedback describing the relationship between
	($T_{\mathrm{0}}$), and aerodynamic vapor pressures ($e_{\mathrm{0}}$ and	$T_{\text{R}}$ and $\mathit{\lambda }E$, coupled with canopy–atmosphere
	$D_{\mathrm{0}}$). (3) Additional challenges in grid-scale or	components relating $\mathit{\lambda }E$ to $T_{\mathrm{0}}$ and $e_{\mathrm{0}}$.
	spatial-scale $g_{\text{A}}$ estimation are the requirements	(2) Supports the findings of Villani et al. (2003)
	of numerous site-specific parameters (e.g.,	which stated that during unstable surface-layer
	vegetation height, measurement height,	conditions the major source of net available
	vegetation roughness, leaf size, soil roughness),	energy is located at the canopy top and drives
	and coefficients needed to correct the	the convective motion in the layers above.
	atmospheric stability conditions (Raupach,
	1998).
$g_{\text{C}}$	(a) If $\mathit{\lambda }E$ measurements are available from the EC	Analytically retrieved by solving “$n$” state
	towers, $g_{\text{C}}$ is estimated by inverting the PM	equations and “$n$” unknowns where physical
	equation. None of these approaches allow	feedbacks of $g_{\text{A}}$, soil moisture, and vapor
	independent quantification of biophysical	pressure deficit are embedded (as explained in
	controls of $\mathit{\lambda }E$ as $g_{\text{C}}$ is constrained by $\mathit{\lambda }E$ itself.	STIC1.2 equations in the Appendix).
	(b) Sometimes $g_{\text{C}}$ is modeled either by coupled
	leaf-scale photosynthesis models (Ball et al.,
	1987; Leuning, 1995) or $g_{\text{C}}$ is estimated from
	stand-alone empirical models (Jarvis, 1976)

The Supplement related to this article is available online at doi:10.5194/hess-20-4237-2016-supplement.

Acknowledgements

This study was funded by the Luxembourg Institute of Science and Technology (LIST). The developed modeling framework contributes to the Catchments As Organized Systems (CAOS) Phase-2 research group (FOR 1598) funded by the German Science Foundation (DFG) and to the HiWET (High-resolution modelling and monitoring of Water and Energy Transfers in wetland ecosystems) consortium funded by BELSPO and FNR. We sincerely thank Andrew Jarvis (Lancaster University, UK), Monica Garcia (Technical University of Denmark, Denmark), and Georg Wohlfahrt (University of Innsbruck, Austria) for very helpful discussions and edits of the manuscript. We are grateful to all Brazilian and international collaborators and all the funding agencies that have contributed to the Large-scale Biosphere Atmosphere Experiment in Amazônia (LBA). The authors are indebted to Pavel Kabat, Antônio Ocimar Manzi, David R. Fitzjarrald, Julio Tota, Humberto Ribeiro da Rocha, Michael Goulden, Maarten J. Waterloo, and Luiz Martinelli for planning, coordinating, conducting, and evaluating the eddy covariance, meteorological, and leaf–gas exchange measurements at the LBA sites. We are particularly grateful to all field technicians whose hard work was the key ingredient to establishing the quality of the datasets used in this paper. The authors declare no conflict of interest. Darren T. Drewry acknowledges the support of the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Edited by: P. Saco Reviewed by: four anonymous referees