Volume 123, Issue 1 p. 207-225
Research Article
Free Access

Comparison of Big-Leaf, Two-Big-Leaf, and Two-Leaf Upscaling Schemes for Evapotranspiration Estimation Using Coupled Carbon-Water Modeling

Xiangzhong Luo

Corresponding Author

Xiangzhong Luo

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

Lawrence Berkeley National Laboratory, Berkeley, CA, USA

Correspondence to: X. Luo and J. M. Chen,

[email protected];

[email protected]

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Jing M. Chen

Corresponding Author

Jing M. Chen

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

Correspondence to: X. Luo and J. M. Chen,

[email protected];

[email protected]

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Jane Liu

Jane Liu

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

School of Atmospheric Sciences, Nanjing University, Nanjing, China

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T. Andrew Black

T. Andrew Black

Faculty of Land and Food Systems, University of British Columbia, Vancouver, British Columbia, Canada

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Holly Croft

Holly Croft

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

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Ralf Staebler

Ralf Staebler

Air Quality Processes Research Section, Environment Canada, Toronto, Ontario, Canada

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Liming He

Liming He

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

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M. Altaf Arain

M. Altaf Arain

School of Geography and Earth Sciences and McMaster Centre for Climate Change, McMaster University, Hamilton, Ontario, Canada

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Bin Chen

Bin Chen

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

International Institute for Earth System Science, Nanjing University, Nanjing, China

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Gang Mo

Gang Mo

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

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Alemu Gonsamo

Alemu Gonsamo

Department of Geography and Planning, University of Toronto, Toronto, Ontario, Canada

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Harry McCaughey

Harry McCaughey

Department of Geography, Queen's University, Kingston, Ontario, Canada

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First published: 09 January 2018
Citations: 62

Abstract

Evapotranspiration (ET) is commonly estimated using the Penman-Monteith equation, which assumes that the plant canopy is a big leaf (BL) and the water flux from vegetation is regulated by canopy stomatal conductance (Gs). However, BL has been found to be unsuitable for terrestrial biosphere models built on the carbon-water coupling principle because it fails to capture daily variations of gross primary productivity (GPP). A two-big-leaf scheme (TBL) and a two-leaf scheme (TL) that stratify a canopy into sunlit and shaded leaves have been developed to address this issue. However, there is a lack of comparison of these upscaling schemes for ET estimation, especially on the difference between TBL and TL. We find that TL shows strong performance (r2 = 0.71, root-mean-square error = 0.05 mm/h) in estimating ET at nine eddy covariance towers in Canada. BL simulates lower annual ET and GPP than TL and TBL. The biases of estimated ET and GPP increase with leaf area index (LAI) in BL and TBL, and the biases of TL show no trends with LAI. BL miscalculates the portions of light-saturated and light-unsaturated leaves in the canopy, incurring negative biases in its flux estimation. TBL and TL showed improved yet different GPP and ET estimations. This difference is attributed to the lower Gs and intercellular CO2 concentration simulated in TBL compared to their counterparts in TL. We suggest to use TL for ET modeling to avoid the uncertainty propagated from the artificial upscaling of leaf-level processes to the canopy scale in BL and TBL.

Key Points

  • Big-leaf scheme underestimates GPP and ET due to its incorrect simulation of leaf light environment
  • Two-big-leaf and two-leaf scheme implement sunlit-shaded radiation regime and show advantages for ET modeling
  • Two-leaf scheme is recommended as it applies tight water-carbon coupling at the leaf level

1 Introduction

Land surface evapotranspiration (ET) plays a critical role in the water and energy exchanges between the biosphere and the atmosphere. It accounts for 60% of the terrestrial precipitation (Oki & Kanae, 2006) and consumes 50% of the solar energy absorbed by the land surface (Trenberth et al., 2009). In the past decades, the Penman-Monteith (PM) equation has provided a sound foundation for estimating ET from the site to the global scales (Bonan, 1996; Dickinson et al., 1993; Moran et al., 1996; Mu et al., 2011; Sellers et al., 1986; Wang & Dickinson, 2012; Weiß & Menzel, 2008).

The PM equation perfectly combines the physical constraints and the biophysical constraints into one simple equation for ET estimations (Monteith & Unsworth, 2013). However, the simplicity of the PM equation also leads to a potential imperfection: in order to calculate canopy conductance (Gc), the PM equation has to use a big leaf assumption, which abstracts the whole canopy into a one-layer source. This assumption is in conflict with the complex structures of canopies in reality, where the leaf distribution varies by clumping (Chen et al., 1997), light environments (Norman, 1982), leaf angles and canopy heights (Baldocchi & Meyers, 1998), and consequently influence the canopy transpiration rates.

However, a considerable number of studies have used Gc to produce reliable ET results regardless of the potential defect of the PM equation, hence corroborated the validity of the big-leaf scheme (BL) underlying the PM equation (Dickinson et al., 1991; Monteith & Unsworth, 2013; Moran et al., 1996; Mu et al., 2011; Yan et al., 2012). These studies regarded ET as an independent process, and Gc for the PM equation can be freely tuned with experience to fit the ET measurements. Gc is usually acquired through either a top-down or a bottom-up method. In the top-down method, Gc is derived by inverting the PM equation using near-surface measurements of the latent heat flux and meteorological variables (Kelliher et al., 1995; Lai et al., 2000; Monteith & Unsworth, 2013; Phillips & Oren, 1998; Stewart, 1988). The reciprocal of Gc value represents the bulk resistance enforced collectively by leaf stomata and soil to transport water (Paw & Meyers, 1989; Raupach & Finnigan, 1988). Process models used for large-scale ET simulations are often equipped with the bottom-up method, which identifies “two layers” for ET, namely, the transpiration from vegetation and the evaporation from soil. An integrated canopy stomatal conductance (Gs) is used to represent the control of vegetation in such two-layer models (Norman et al., 1995). Several theoretical and experimental studies have suggested that Gs is not equivalent to Gc, though the value of Gs would be close to Gc for dense vegetation (Baldocchi & Meyers, 1998; Kelliher et al., 1995). Gs is directly used in the PM equation to calculate canopy transpiration.

However, with the emergence of process-based Terrestrial Biosphere models (TBMs) that consider carbon and water exchange as a coupled process, Gs acquired from BL should be able to satisfy the simulation of ET as well as the simulation of carbon uptake. The statistical model or semiempirical models that quantify Gc or Gs by inversing ET measurements or using empirical indices would no longer suffice for TBMs. The concept of Gc and Gs may not be appropriate anymore because photosynthesis model (Farquhar et al., 1980) is only developed for leaves not for canopies. Ball et al. (1987) and Leuning (1990) discovered that stomatal conductance (gs) is linearly tuned by the carbon assimilation rate (A) of leaves, denoted “Ball-Woodrow-Berry model” here. Sellers et al. (1992) and Amthor (1994) made the first efforts to update BL for TBMs. They assumed that A decreases from the top to the bottom of a canopy following either the foliage nitrogen gradient or long-term solar radiation gradient, and so does gs. These gradients are expressed in a form of an exponential function dependent on the canopy depth which is quantified using the accumulated LAI from the canopy top. Afterward, the canopy total photosynthesis (Ac, aka GPP (gross primary productivity)) can be easily upscaled from A using these functions and then Gs is calculated through the Ball-Woodrow-Berry stomatal conductance model.

BL designed for the carbon-water coupled TBMs was shown to perform well at some sites, but many researchers reported an underestimation of GPP by these models, since A is more sensitive to the instantaneous solar radiation on leaves, while nitrogen and the long-term radiation gradient cannot explain the rapid changes in A as described in BL (De Pury & Farquhar, 1997; Friend, 2001). For example, a leaf at the bottom of a canopy in a sun fleck will instantaneously receive far more radiation for photosynthesis than the average radiation that Beer's law would predict. To describe the instantaneous radiation intercepted by leaves, a two-leaf radiation regime was developed (Chen et al., 1999; De Pury & Farquhar, 1997; Norman, 1982; Sinclair et al., 1976). It separates a canopy into a group of sunlit leaves and a group of shaded leaves. A of a sunlit leaf tends to be light saturated by receiving both direct and diffuse solar radiation, while A of a shaded leaf is capped by the amount of diffuse radiation on leaves. Based on the two-leaf radiation regime, a hierarchy of upscaling schemes including the multilayer scheme, the two-big-leaf scheme (TBL), and the two-leaf scheme (TL) are developed for TBMs.

Leuning et al. (1995) and Baldocchi and Harley (1995) developed the multilayer scheme, in which a canopy is separated into layers, and every layer is divided into sunlit and shaded segments. The multilayer scheme considers the ecological processes inside the canopy in great detail: leaf nitrogen, leaf photosynthetic capacity, and even leaf inclination angles can be prescribed independently. In this scheme, the leaf photosynthesis and transpiration are calculated for each segment and then integrated into the canopy-scale GPP and ET by multiplying by the LAI of each segment. Though the multilayer scheme is regarded as the most accurate way to upscale fluxes from leaf to canopy, its expensive computational demand for large-scale applications drives the need to use simple upscaling schemes in TBMs (Wang & Leuning, 1998).

Some studies then developed an upscaling scheme which is classified as TBL, inheriting the idea of BL and using the two-leaf radiation regime (Dai et al., 2004; De Pury & Farquhar, 1997; Ryu et al., 2011; Wang & Leuning, 1998). Ac and Gs for sunlit and shaded canopies are simulated respectively in TBL, and Gs of each leaf group is then used in the PM equation to calculate ET. In order to calculate Ac and Gs, TBL requires the biochemical parameters of leaves to be upscaled to their canopy counterparts. Since the biochemical model (i.e., Farquhar's biochemical model) is originally developed to simulate leaf-level photosynthesis, the direct application of it at the canopy scale can bring unexpected uncertainties in simulation when the physiological behavior of an imaginary “big leaf” surpasses the explanatory ability of a leaf-level model.

Chen et al. (1999, 2012) developed TL as an alternative to the multilayer scheme and TBL. TL separates the canopy into sunlit and shaded segments and calculate the A and gs of a representative leaf for each segment. A representative leaf is the average status of all leaves in each segment. This method takes advantage of the two-leaf radiation regime and avoids the use of canopy parameters (i.e., Gs) in TBMs. It is conceptually rigorous in running the Farquhar's biochemical model, the Ball-Woodrow-Berry stomatal conductance model, and the PM equation simultaneously at the leaf level, since the first two were developed using leaf-level measurements.

Since the application of the two-leaf radiation regime in TBMs in 1990s, some studies have strived to evaluate the performance of different upscaling schemes with flux measurements. The advantage of TBL over BL has been proved at two flux sites for GPP modeling (Medlyn et al., 2003; Mercado et al., 2006), and TL has been validated with data from 11 eddy covariance (EC) towers and proved its advantage over BL on GPP modeling (Sprintsin et al., 2012). However, there is a lack of attention on the effects of upscaling schemes for ET simulations in carbon-water coupled models. Vogel et al. (1995) has used a TBM with the multilayer scheme to simulate ET and compared it with a hierarchy of less-sophisticated ET models over a well-irrigated cropland and suggested no advantage of using the two-leaf radiation regime for ET modeling. The conclusion may not be applicable for TBMs since the parameters for those less-sophisticated ET models can be freely tuned to fit the measurements, whereas the parameters of TBMs are simulated based on the physiological principle of carbon-water coupling. Currently, we still lack a clear understanding of the effects of upscaling schemes in TBMs for ET simulations and how these effects vary across sites. In addition, there is a need to clarify the definitions of the two-leaf radiation regime, TBL and TL, because of their interchangeable uses in previous studies (De Pury & Farquhar, 1997; Wang & Leuning, 1998). Therefore, the objective of this research is to compare BL, TBL, and TL over a spectrum of flux sites and analyze their influences on ET modeling.

2 Data and Method

2.1 Description of the Model

The Boreal Ecosystems Productivity Simulator (BEPS) is an enzyme kinetic, two-layer (i.e., vegetation and soil), and dual-source (sunlit and shaded) model first developed to estimate carbon uptake and the water cycle over the Canadian landmass (Liu et al., 2003). It is characterized by a two-leaf radiation regime (Norman, 1982) and an analytic daily integration scheme (Chen et al., 1999). Several intermodel comparisons and site-level validations have shown that BEPS can produce reasonable GPP and ET estimates (Amthor et al., 2001; Grant et al., 2006; Liu et al., 2003; Potter et al., 2001). Its usage has expanded from boreal ecosystems to other plant functional types in the past decade (Chen et al., 2012; Gonsamo et al., 2013; Wang et al., 2004), and BEPS has been updated to support simulations at hourly and half-hourly steps (Chen et al., 2007).

In BEPS, ET from the land surface mainly consists of three components: transpiration from leaves, evaporation (sublimation) from the wet canopy, and evaporation (sublimation) from the soil surface. Since this study focuses on leaf-to-canopy upscaling methodologies and their effects on ET estimation, we will primarily describe the transpiration-related processes in BEPS.

According to TL, BEPS simulates the photosynthetic rate of a representative sunlit leaf (Asunlit) and a shaded leaf (Ashaded) first and then obtains the canopy photosynthetic productivity (Ac) as the sum of the photosynthesis of leaves (equation 1). Similar to the calculation of Ac, the transpiration of the canopy (Tc) is the sum of transpiration from these two groups of leaves (equation 2). TL assumes that all sunlit leaves (shaded leaves) are exposed to the same environment (i.e., irradiance, temperature, and vapor pressure deficit) and have the same physiological features (i.e., urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0001), and therefore, the transpiration and photosynthesis of the whole leaf group can be predicted using one representative leaf.
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0002(1)
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0003(2)
where Asunlit and Ashaded are the photosynthetic rates of a representative sunlit leaf and a representative shaded leaf, respectively. They are acquired from an analytic solution derived from a leaf biochemical model and a mass transfer equation (Baldocchi, 1994). The maximum carboxylation velocity ( urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0004) and the maximum electron transport capacity ( urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0005) at 25°C for sunlit and shaded leaves are calculated based on a nitrogen gradient in the canopy (Appendix A) to parameterize the biochemical processes in BEPS. Tsunlit and Tshaded are the transpiration from sunlit leaf and shaded leaf, respectively. LAIsunlit and LAIshaded are the LAI of sunlit leaves and shaded leaves, respectively. The values of LAIsunlit and LAIshaded are calculated following the stratification scheme of Norman (1982) and Chen et al. (1999).
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0006(3)
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0007(4)
where θ is the solar zenith angle, LAItot is the total leaf area index of the canopy, and Ω is the clumping index.
Then, the PM equation is employed to calculate T of a sunlit or shaded leaf (equation 5).
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0008(5)
where λ is the latent heat of evaporation of water, Rn is the net radiation at the leaf surface (Appendix B), G is the heat storage of the leaf which can be neglected, ρ is the density of air, cp is the specific heat of air, VPD is the vapor pressure deficit of the ambient air, γ is the psychrometric constant, gV is leaf boundary layer conductance for water vapor, Δ is the slope of the saturation vapor pressure curve at air temperature, and gs is the stomatal conductance of the representative sunlit or shaded leaf.
A modified Ball-Woodrow-Berry model is then used to calculate the gs of sunlit or shaded leaves (Chen et al., 2012), respectively.
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0009(6)
where m is the dimensionless Ball-Woodrow-Berry coefficient set at 8 for C3 plants, RH is the relative humidity, Cs is the carbon dioxide concentration on the leaf surface, g0 is the minimum conductance at night, and A is the rate of photosynthesis (μmol/m2/s) of the representative sunlit or shaded leaf. The variable fw, which is the soil water stress factor, is added to overcome the inability of the Ball-Woodrow-Berry equation to close the stomata during drought spells. It is widely employed as a complementary parameter to represent the regulation of the conductance of water through stomata (Sala & Tenhunen, 1996; Xu & Baldocchi, 2003). BEPS has developed a mechanistic module to simulate soil moisture and fw (Ju et al., 2006). However, sometimes the performance of the soil moisture module is biased because the module requires accurate parameterization of soil texture for multiple layers. To minimize the possible deviations in gs caused by the soil moisture simulation, we replaced the soil moisture module with measured soil moisture in this study and applied a simple equation to calculate fw (Appendix C). The incorporation of measured surface soil moisture also reduces the errors in the estimates of surface evaporation. With this modification, the overall change in ET between schemes is mainly attributed to the transpiration, and in turn be attributed to the corresponding upscaling scheme.

3 Modeling Schemes

3.1 Big-Leaf Scheme

BL developed by Sellers et al. (1992) and Sellers (1997) is one of the first attempts to simulate water and carbon fluxes simultaneously, in which.
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0010(7)
where A0 is the photosynthetic rate of the leaves at the top of the canopy and Ac is the total canopy photosynthesis rate. Since BL assumes an optimal nitrogen gradient following the long-term solar radiation gradient, k is the extinction coefficient for both solar radiation and nitrogen gradients in a canopy and it is set as 0.5. After obtaining Ac, Gs for the big leaf is then acquired using the Ball-Woodrow-Berry equation introduced in equation 6. To facilitate our analysis, Gs is simplified into the form of
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0011(8)
where gs0 is the stomatal conductance of the leaves on top of the canopy.

3.2 Two-Big-Leaf Scheme

TBL applies a different way of describe the dual sources than TL (Figure 1). TBL scheme requires an artificial upscaling of leaf-level physiological parameters urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0012 and urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0013 to their counterparts for each leaf group (i.e., urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0014, urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0015, urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0016, and urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0017). By incorporating these canopy-scale parameters into Farquhar's model and the Ball-Woodrow-Berry equation, we are able to obtain Ac and Gs for the sunlit and shaded leaf groups, respectively. For the purpose of this study, TBL is added to existing BEPS to compute the Gs of sunlit leaves (Gs_sunlit) and Gs of shaded leaves (Gs_shaded) (Dai et al., 2004; Ryu et al., 2011; Wang & Leuning, 1998). The calculation of the canopy-scale urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0018 in TBL is introduced in Appendix D.

Details are in the caption following the image
Schematic descriptions of the three upscaling schemes: BL, TBL, and TL. In reality, gs of each leaf is different. BL integrates gs into Gs; TBL integrates gs into Gs for sunlit and shaded leaves, respectively; TL uses the average of gs of each leaf group and avoids the calculation of Gs.

3.3 Two-Leaf Scheme

The default BEPS uses TL to estimate the transpiration of a representative sunlit leaf and a representative shaded leaf first and then upscales the leaf-level transpiration to canopy level by multiplying by the corresponding LAI values (equation 2) (see section 2.1 for a more detailed description of TL). This method avoids the use of Gs and canopy-level photosynthetic parameters, so it is described as TL.

4 Validation Sites and Input Data

The data used to drive the model are obtained from Fluxnet (http://fluxnet.ornl.gov/). Nine sites in Canada are selected, mainly because they have some measured leaf area index (LAI), clumping index (Ω), and soil moisture data (Table 1). Using these measurements can effectively constrain the uncertainty for ET simulation. The input meteorology data include incident solar irradiance (W/m2), air temperature (°C), precipitation (mm/h), relative humidity (%), wind speed (m/s), and soil water content (m3/m3). Overstory LAI (LAIo) data were measured during some growing seasons at these sites. We use the reflectance data of the Moderate-resolution Imaging Spectroradiometer to extrapolate the LAI measurements to daily LAIo sequences (Gonsamo & Chen, 2014). Except for an old aspen site (CaOas), the understorey LAI (LAIu) is calculated using an empirical equation, urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0019 (Liu et al., 2003). Since CaOas has an LAIu comparable to LAIo (Barr et al., 2004), its LAIu is calculated as 90% of LAIo. The clumping index (Ω) is also a critical canopy structural parameter, as it defines the nonrandomness of the foliage distribution in a canopy (i.e., the overlapping of the leaves and aggregations of the needles in a shoot) (He et al., 2012). Ω ranges from 0 to 1, with a higher number indicating the canopy is closer to a random distribution.

Table 1. Features of the Selected Canada Carbon Program Flux Tower Sites
Site code Latitude Longitude Year Land covera Overstorey main genera Maximum overstorey LAIb Clumping indexc urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0020(μmol m−2 s−1)f Number of LAI measurements Reference
CaCa2 49.8705 −125.2909 2002–2010 ENF Pseudotsuga menziesii 4.45 0.48d 38.8 26 Chen et al. (2009)
CaCa3 49.5346 −124.9004 2002–2010 ENF Pseudotsuga Menziesii 8.15 0.532 38.8 31 Chen et al. (2009)
CaCbo 44.3185 −79.9342 2008–2013 DBF Acer rubrum, Populus tremuloides 4.96 0.72e 62 30h Froelich et al. (2015)
CaGro 48.2173 −82.1555 2005–2011 MF Picea mariana 3.87 0.821 40 6 Gökkaya et al. (2013)
CaOas 53.6289 −106.1978 2002–2010 DBF Populus Tremuloides 2.43 0.87 62.5g 9 Barr et al. (2004)
CaObs 53.9872 −105.1178 2002–2010 ENF Picea Mariana 3.45 0.662 39.4 6 Bergeron et al. (2007)
CaOjp 53.9163 −104.6920 2005–2010 ENF Pinus banksiana 2.01 0.599 31 12 Barr et al. (2006)
CaTp3 42.7068 −80.3483 2009–2013 ENF Pinus strobus 7.17 0.518 31 15 Peichl et al. (2010)
CaTp4 42.7098 −80.3574 2009–2013 ENF Pinus Strobus 8.10 0.513 31 15 Arain and Restrepo-Coupe (2005)
  • a The land cover type is adopted from the site introductions on the Fluxnet. The selected sites include deciduous broadleaf forests (DBF), evergreen needleleaf forests (ENF), and mixed forests (MF).
  • b The maximum value of the available LAI measurements on the Fluxnet. These values refer total LAI of the overstorey.
  • c Chen et al., (2006).
  • d Canada Carbon Program.
  • e He et al. (2012).
  • f urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0021 values refer to the maximum carboxylation capacity at 25°C for leaves on top of canopies, and they are derived based on the values provided by Groenendijk et al. (2011). We assume that same species should have similar urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0022 values. For all the Douglas fir (Pseudotsuga menziesii) sites in British Columbia, urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0023 ranges from 20.5 to 54.1 μmol m−2 s−1 (Groenendijk et al., 2011). In this study, the median urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0024 (38.8 μmol m−2 s−1) of all these sites is assigned to site CaCa2 and CaCa3; CaCbo uses the average urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0025 of all temperate deciduous forest; CaGro uses the average urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0026 of all temperate mixed forest; CaObs uses the value that is provided. Since the dominate species of CaGro and CaObs are black spruce (Picea mariana), their urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0027 should be similar. CaTp4 is the only pine (Pinus) site with a known urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0028 of 31 μmol m−2 s−1. Since CaTp3 and CaOjp are also pine sites, they are also assigned a Vmax value of 31 μmol m−2 s−1.
  • g He et al. (2014).
  • h Croft et al. (2015).
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0029 is a critical parameter in Farquhar's photosynthesis model. urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0030 for each site is obtained from previous data assimilation work (Groenendijk et al., 2011; He et al., 2014). The temporal variation in urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0031 is also considered by assuming that the seasonal patterns of urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0032 follows the season patterns of LAI (Ryu et al., 2011). In this study, the urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0033 value on a given day in growing seasons is calculated using an empirical equation:
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0034(9)
where Lmax, Lmin, and Lc are maximum, minimum, and current LAI values over the year, respectively. The empirical variables α and β are set as 0.30 and 0.75, respectively. The ratio term urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0035 should range between 0 and 1.

5 Results

5.1 Difference Between Simulations and Measurements Among Three Schemes

Three versions of BEPS using different upscaling schemes (BL, TBL, and TL) are used to simulate ET and GPP at nine eddy covariance (EC) sites, and results from each scheme are evaluated against tower measurements (Figure 2 and Appendix E).

Details are in the caption following the image
Simulated and measured annual ET at the studied sites, as well as the ET components obtained using BL, TBL, and TL.

According to Figure 2, the annual ET are 286 mm yr−1, 318 mm yr−1, 340 mm yr−1, and 325 mm yr−1 for BL, TBL, TL, and EC measurements across the sites, respectively. The annual ET estimated by BL and TBL are 16% and 7% lower compared to TL. BL, TBL, and TL produce similar evaporative fluxes from soil, indicating that soil evaporation is largely determined by the total radiation incident on the ground. Most of the difference between TL and TBL is caused by shaded leaves, where the average difference in ET estimates between TL and TBL is 24 mm yr−1, while the difference between sunlit ET estimates of TBL and TL is only about −2 mm yr−1.

Figure 3 demonstrates that GPP is underestimated by BL at all sites, while the GPP estimates from TBL and TL show a complex relationship. Five out of the nine sites have smaller GPP estimates from TBL than those from TL, while four sites show the opposite results. The pattern is clearer when partitioning GPP into its sunlit and shaded components: at eight out of the nine sites, TL produces higher sunlit GPP than TBL; and at seven sites, shaded GPP from TL is smaller than that from TBL. Averaged across all sites, the total GPP are 922 g C m−2 yr−1, 1,250 g C m−2 yr−1, 1,232 g C m−2 yr−1, and 1,165 g C m−2 yr−1 for BL, TBL, TL, and EC measurements, respectively. Compared to TL, BL underestimates annual GPP by 25% and TBL overestimates GPP slightly by 1.5%.

Details are in the caption following the image
Simulated and measured annual GPP at the study sites, as well as the GPP components obtained using BL, TBL, and TL.

BL has been used in several carbon-water coupled TBMs (Alton et al., 2007; Cramer et al., 2001). Some studies have noticed the underestimation of GPP by BL, but the accompanying underestimation of ET has been less reported and inadequately studied across sites. The differences between the ET and GPP estimates by TL and TBL have not been studied as well. Figure 4 demonstrates the biases of annual ET and GPP estimates from BL, TBL, and TL and their relationships with LAI.

Details are in the caption following the image
The biases of annual ET and GPP estimates along with site mean LAI for each upscaling scheme.

According to Figure 4, BL underestimates both GPP and ET, and TBL tends to underestimate ET but overestimate GPP. The biases in ET and GPP estimation by BL and TBL increase significantly (p < 0.05) with LAI, indicating that the sites with dense foliage tend to create large errors in ET and GPP estimates by BL and TBL. In contrast, the biases in ET and GPP estimation by TL are small and insensitive to LAI. For those low LAI sites, the difference between the simulations of TBL and TL are negligible, but their differences amplify with increasing LAI. These results suggest existence of errors in the modeling structures of BL and TBL that induce larger biases at higher LAI. In addition, the errors incurred by TBL are smaller than those by BL for ET and GPP estimation.

5.2 Difference Between the Radiation Regimes in BL and TBL (TL)

BL uses Beer's law to describe the radiation distribution inside a canopy, while TBL and TL both use the two-leaf radiation regime to describe the radiation distribution. The amount of intercepted radiation of leaves affects the photosynthetic rates of leaves and consequently influences conductance and ET. Figure 5 demonstrates the amount of light-saturated leaves for a given sunny day at the nine sites.

Details are in the caption following the image
The amount of light-saturated leaves (LAI) at each site using BL and TBL (TL). The light saturation point is fixed at 400 W/m2 for this analysis. coordinated universal time (UTC) is used for abscissas.

Figure 5 shows that BL usually classifies more leaves as light-saturated leaves than TBL and TL. Considering that light-saturated leaves have high photosynthetic rates, the GPP and ET contributed by light-saturated leaves are larger in BL than in TBL and TL. However, the total GPP and ET estimates are smaller in BL than in TBL and TL according to Figures 2-4, indicating that the underestimation in BL are mainly attributed to the underestimation of fluxes from light-unsaturated leaves. Light-unsaturated leaves includes all shaded leaves and the sunlit leaves with low solar irradiance. Because high LAI often indicates high percentage for shaded leaves, the underestimation of fluxes in BL increases with LAI.

5.3 Difference Between TBL and TL

TBL and TL both implement the two-leaf radiation regime, so the differences in their ET and GPP estimation are not caused by the simulation of radiation. Though TBL tends to simulate lower total ET and higher total GPP relative to TL, we found that the sunlit and shaded parts of the canopies are affected differently using TBL (Figure 6).

Details are in the caption following the image
The differences in (a) ET and (b) GPP estimation between TBL and TL for sunlit and shaded leaves. Negative values mean TBL underestimates fluxes relatively to TL; positive values mean TBL overestimates fluxes relatively to TL.

Figure 6 demonstrates that for sunlit leaves, ET estimated by TBL and TL are similar to each other, while sunlit GPP is underestimated by TBL relative to estimates of TL. For shaded leaves, TBL underestimates ET at all sites with the ET underestimation amplifying with LAI. TBL overestimates shaded GPP at five sites and underestimates at four sites, and the difference between the GPP estimates of TBL and TL displays significant correlation with LAI. The difference between the estimated GPP and ET for shaded leaves is more pronounced than that for sunlit leaves.

In order to identify the reasons for the different estimates between TBL and TL, the simulation of ET is expressed in the form of diffusion equations:
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0036(10)
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0037(11)
and for GPP simulation these equations are
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0038(12)
urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0039(13)
where j refers to sunlit or shaded leaves, ea is the atmospheric water vapor pressure, es is the saturated water pressure in plant cells, Ca is the atmospheric CO2 concentration, and Ci is the intercellular CO2 concentration.

According to equations 10 and 11, the difference between the ET estimates of TBL and TL is driven by the difference between Gs and the value of gs × LAI. Figure 7 compares Gs values from TBL with the corresponding gs × LAI values from TL for all nine sites.

Details are in the caption following the image
Comparison between the average daytime Gs obtained from TBL and the gs × LAI obtained from TL for sunlit and shaded leaves.

Figure 7 shows that the TBL Gs is smaller than the gs × LAI obtained from TL. Shaded leaves generally show larger gaps between TBL Gs and the corresponding TL gs × LAI value than sunlit leaves. The difference between the Gs and the gs × LAI suggests a potential caveat in the process of calculating Gs in TBL. The relatively low value of Gs in TBL could cause an underestimation of GPP and ET relative to TL.

However, Figure 6 has shown that TBL only underestimates ET for shaded leaves and GPP for sunlit leaves, while shaded GPP are sometimes even overestimated by TBL. This conflict indicates that there is another factor that drives the difference between TL and TBL for GPP simulation. Based on equations 12 and 13, we expect the Ci values estimated by TL and TBL are different (Figure 8).

Details are in the caption following the image
Comparison between the daytime average Ci:Ca obtained from TBL and TL for sunlit and shaded leaves.

Figure 8 shows that Ci simulated by TBL is smaller than that of TL for both sunlit and shaded leaves. The smaller Ci in TBL leads to a greater gradient to drive the CO2 to diffuse from the atmosphere to the inside of leaves and consequently compensates for the underestimation of Gs in TBL for GPP estimations. In addition, the underestimation of Ci by TBL is usually stronger at sites with large LAI values (e.g. CaCa3, CaTp3, and CaTp4), and thus, this compensation effect at those sites is even able to incur the overestimations of GPP by TBL (Figure 4).

6 Discussion

For the first time, our results demonstrate the differences between TBL and TL in estimating biosphere-atmosphere carbon and water exchanges. The underestimations of Gs and Ci in TBL are responsible for the difference between the fluxes estimated by TBL and TL. The structure of TL and TBL models is briefly demonstrated in Figure 9 to explore the driver for the underestimations of Gs and Ci in TBL.

Details are in the caption following the image
A schematic description of the difference between TL and TBL models. The nonlinear processes in models determine that the product of gs from TL and LAI does not equal to Gs from TBL, for either sunlit or shaded leaves.

Process-based TBMs usually consider various linear and nonlinear biochemical and biophysical processes in simulating GPP and ET (Figure 9). In TL, all these processes are performed at the leaf level, then the estimated fluxes of leaves are upscaled to the canopy scale by timing LAI. In TBL, these processes are simulated at the canopy scale through upscaling the key biochemical and biophysical parameters from leaf to canopy. If all the processes considered in TBMs were linear, TL would be equivalent to TBL, and Gs = gs × LAI. However, due to Jensen's inequality, Gs cannot be expressed as a linear function of gs and LAI.

Ci is dynamically adjusted in plants shown in Figure 9 until the model realizes an optimal water use efficiency (WUE; Medlyn et al., 2011; Sellers, 1997; Wang et al., 2017). With an artificially upscaled urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0040, a big leaf is apparently more capable of assimilating CO2 compared to the leaves in reality in the same environment, and thus driving Ci to be lower in the big leaf. With the change of photosynthesis by using the big leaf, the WUE is expected to be adjusted accordingly to obtain an optimal value. This big leaf WUE is different from the WUE acquired directly from leaf level simulations.

Figure 10 shows that the WUE acquired from TBL is similar to that from TL for sunlit leaves, while for shaded leaves the WUE acquired from TBL is larger than its counterpart in TL. Based on the separation of sunlit and shaded LAI described by equations 3 and 4, we know that the sunlit LAI could not be larger than 2 and the remaining LAI are assigned to shaded leaves. Therefore, the difference between the WUE of a shaded big leaf and a shaded leaf is stronger than that for sunlit leaves. The WUE estimated by TBL also is positively correlated with LAI, which may raise doubts on the analysis of WUE trend in the context of climate change using TBL.

Details are in the caption following the image
WUE for sunlit and shaded leaves estimated by TBL and TL.

At last, considering that most biochemical and biophysical processes in TBMs are originally developed based on leaf-level measurements, we suggest that it is conceptually correct to apply TL to TBMs which uses gs in the mathematical formulations of these processes and avoids the uncertainties propagated from the derivation of the canopy-scale parameters as intermediate variables. Though the results from TL models may not be superior to the results from TBL due to a range of reasons such as observational uncertainty of inputs, uncertainty of flux measurements, and the uncertainty of leaf-level parameters, the difference between the estimates from TBL and TL is worth noting since estimates from TBL show systematically increasing bias with LAI. With a given set of input parameters, the systematic differences between TL and TBL models at all test sites suggest that more attention should be given to model structure in addition to improving model parameters. In fact, using a model with correct structure and processes should be a prerequisite to tuning model parameters in the quest to understand the complex processes governing the carbon and water fluxes of terrestrial ecosystems.

7 Conclusion

The big leaf concept is widely used to describe the bulk control of plant canopies on transporting water and carbon molecules. It is characterized by the use of canopy conductance in the Penman-Monteith equation. In order to consider the physiological principle of carbon-water coupling, some state-of-the-art TBMs expand the big leaf concept by upscaling leaf-level photosynthetic parameters to their canopy-level counterparts, and directly using of leaf-level biochemical models at the canopy scale. Gs is then calculated in BL for ET simulation. However, BL has been reported to incur some biases in GPP estimation, and TBL has been developed to address the problem (e.g., De Pury & Farquhar, 1997). Meanwhile, less attention has been paid to the uncertainties underlying the artificial upscaling process for Gs and other biochemical parameters in BL and TBL. In this study, we aim to promote the use of TL in TBMs built on the carbon-water coupling principle and to avoid the use of Gc and Gs in the Penman-Monteith equation. The performance of BL, TBL, and TL in estimating ET and GPP are evaluated with flux measurements from nine eddy covariance towers. Our conclusions are as follows:
  1. BL underestimates ET and GPP across all sites because the radiation gradient calculated based on Beer's law fails to describe the instantaneous radiation distribution in the canopy. Increasing LAI leads to the increasing underestimations of ET and GPP in BL, mainly due to the underestimation of fluxes from shaded leaves.
  2. TBL and TL demonstrate improved ET and GPP estimations by implementing the sunlit-shaded radiation regime. TBL and TL produce very similar total GPP and ET values when LAI is low but amplified difference when LAI is high. This difference is attributed to the lower Gs and Ci simulated in TBL than their counterparts in TL.
  3. The nonlinear biophysical and biochemical processes make it questionable to use any form of big leaf (i.e., TBL and BL) in carbon-water coupled TBMs, through using Gc or Gs. Conceptually, TL is appropriate for carbon-water coupled TBMs since it couples the water flow with the carbon flow at the leaf level by directly using the stomatal conductance derived from leaf biochemical models for ET modeling.

Acknowledgments

The authors wish to thank the efforts of researchers in Canadian Carbon Program for maintaining the sites and collecting data. This study is financially supported by a Discovery Grant and a Strategic Grant from the Natural Science and Engineering Research Council of Canada and a Canada Research Chair to J. M. Chen. L. He is supported by the Canadian Space Agency grant (14SUSMAPTO). We would like to thank Dennis Baldocchi for his insightful comments on the paper. The data used could be obtained from Fluxnet (http://fluxnet.ornl.gov/). The codes of BEPS model using BL, TBL, and TL are stored at https://github.com/JChen-UToronto/BEPS_H

    Appendix A: Nitrogen-Weighted urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0041 and urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0042 for Sunlit and Shaded Leaves

    Chen et al. (2012) combined the “two-leaf” separation scheme and a nitrogen gradient to derive the urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0043 and urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0044 values for the sunlit and shaded leaves separately. Leaf nitrogen content per leaf area N(L) generally decreases exponentially from the top to the bottom in a canopy (equation A1):
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0045(A1)
    where the extinction coefficient kn = 0.3 used in BEPS is adopted from De Pury and Farquhar (1997), N0 is the nitrogen content at top of the canopy, and L is the canopy depth described in total LAI. On the other hand, the leaf maximum carboxylation rate at 25°C ( urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0046) is proportional to the leaf nitrogen content therefore it can be expressed as:
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0047(A2)
    where urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0048 is the urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0049 of the leaves at the top of the canopy and χn quantifies the relative change of urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0050 to the leaf nitrogen content in the canopy. χn has units of m2/g while N(L) has units of g/m2. The value of χn, the mean value of N and its standard deviation, and the standard deviation of urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0051 are provided according to the plant functional types (Chen et al., 2012). N0 is taken as the mean N value plus one standard deviation; urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0052 is taken as the input urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0053value plus one standard deviation.
    The fraction of the sunlit and shaded leaves in the canopy change with the canopy depth:
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0054(A3)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0055(A4)
    where k = G(θ)Ω/ cos θ. G(θ) is the projection coefficient of the canopy, and it is 0.5 assuming a spherical leaf angle distribution. Ω is the clumping index, and θ is the solar zenith angle. We assume the urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0056 of a representative sunlit or shaded leaf is equal to the mean urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0057 value of the sunlit or shaded leaves' group. Therefore, the urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0058 of a representative sunlit or shaded leaf is obtained by the following integrations:
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0059(A5)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0060(A6)
    After the urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0061 values of the representative sunlit and shaded leaves are obtained, the maximum electron transport rate at 25°C ( urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0062) is obtained using the following equations (Medlyn et al., 1999).
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0063(A7)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0064(A8)

    Appendix B: Leaf Energy Budget

    In the absence of rainfall and snow coverage over leaves, the leaf energy budget is composed of the net radiation on leaf (Rn), the sensible heat (Q), and the latent heat (LE) from the leaf in every hourly step, during which period the heat storage of leaf is negligible.
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0065(B1)

    B1. Net Radiation on a Leaf

    In BEPS the whole canopy was divided into four groups of leaves based on the location and radiation features of the leaves, namely, sunlit leaves in the overstorey, shaded leaves in the overstorey, sunlit leaves in the understorey, and shaded leaves in the understorey (Chen et al., 1999; Liu et al., 2003). The leaves in each group have identical features, so BEPS could use one leaf to represent a group. Net radiation on a leaf comprises three sources:
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0066(B2)
    where Rn is the total net radiation on a given leaf, Rdir, Rdif, and Rl refers to the net direct incoming solar radiation, net diffuse solar radiation, and net longwave radiation on the leaf. The subscript i refers to one of the four types of leaves. For a shaded leaf, Rdir = 0.
    In order to differentiate the incoming solar radiation into a direct and diffuse part, a semiempirical equation is applied:
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0067(B3)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0068(B4)
    where Sg, Sdir, and Sdif are incident solar irradiance, incoming direct solar radiation, and diffuse solar radiation, respectively. r is a parameter used to quantify the cloudiness of the sky.
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0069(B5)
    where S0 is the solar constant set as 1,362 W/m2 and θ is the solar zenith angle.
    The net direct solar radiation on the sunlit representative leaf in the overstorey or understorey of the canopy is
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0070(B6)
    where αL is the albedo of the leaves. But in BEPS, αL is different for the overstorey and the understorey because snow coverage varies with canopy depth. The parameter α is the mean leaf-sun angle which is fixed at 60° when the canopy has a spherical leaf distribution.
    On the other hand, the net diffuse solar radiation on the four groups of the leaves are approximated, respectively, as
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0071(B7)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0072(B8)
    where LAIo and LAIu are the LAI value of the overstorey and the understorey and Co and Cu are used to quantify the multiple scattering of the direct solar radiation from the leaf (Chen et al., 1999)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0073(B9)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0074(B10)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0075 and urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0076 are the representative zenith angles for diffuse radiation transmission of the overstorey and understorey leaves and slightly dependent on the corresponding LAI (Liu et al., 2003):
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0077(B11)
    The net longwave radiation on these leaves is calculated as
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0078(B12)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0079(B13)
    where σ is the Stephen-Boltzmann constant equals to 5.67 × 10−8 W m−2 K−4. εa, εo, εu, and εg are the emissivity of the atmosphere, overstorey, understory, and ground surface, respectively. εo, εu, and εg are prescribed as 0.98, 0.98, and 0.95, respectively, according to (Chen et al., 1989; Chen & Zhang, 1989), and εa is computed as urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0080(Brutsaert, 1982), where ea and Ta are water vapor pressure in mbar and temperature of the atmosphere in K. To, Tu, and Tg are the temperatures of the overstorey, the understorey, and ground, respectively, in kelvin, and To and Tu are calculated as the weighed average temperature of sunlit leaves and shaded leaves in overstorey and understorey, respectively.

    B2. Sensible Heat From a Leaf

    The sensible heat is calculated for overstorey sunlit leaves, overstorey shaded leaves, understorey sunlit leaves, and understorey shaded leaves, respectively.
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0081(B14)

    where i refers to the type of the leaf, ρ is the density of air, cp is the specific heat of air, and gH is total conductance of heat from the leaf surface to the atmosphere, which equals to the reciprocal of the leaf boundary layer resistance and aerodynamic resistance in tandem.

    B3. Latent Heat From a Leaf

    Latent heat is calculated using the Penman-Monteith equation (equation 5), which was simplified into a linear function of leaf temperature (Campbell & Norman, 2012) in BEPS:
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0082(B15)
    where i, ρ and cp have the same meaning as above, VPD is the vapor pressure deficit of the ambient air, γ is the psychrometric constant, Δ is the slope of the saturation vapor pressure curve at air temperature, and gw is total conductance of water vapor from leaf interior to the atmosphere, which equals to the reciprocal of the tandem of the leaf boundary layer resistance, aerodynamic resistance, and leaf stomatal resistance (1/gs). gs is obtained from the carbon assimilation module using Farquhar's model and the Ball-Woodrow-Berry equation.

    Ultimately, the three components of leaf energy budget are expressed as a function of leaf temperature. We reiterate the processes above until the leaf temperature converge to realize the leaf energy balance.

    Appendix C: Quantification of the Soil Water Stress Factor

    To account for the effect of the soil water deficit on stomatal conductance, a soil water stress factor (fw) based on the ratio of the measured available water in the soil to the maximum plant available water (Chen et al., 2005; Wang & Leuning, 1998; Wigmosta et al., 1994) was calculated as follows:
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0083(C1)
    where θsw(z) is the soil water content of layer z and z often refers to the top 30 cm based on the availability of the soil water measurements. θwp and θfc are the wilting point and the field capacity, respectively, (m3/m3) of the soil layer. θwp and θfc are derived from the soil texture information provided by Fluxnet (http://fluxnet.ornl.gov/), the patterns of multiyear soil moisture measurements and the algorithm developed by Saxton and Rawls (2006).

    Appendix D: Parameterization for TBL

    According to literature (Dai et al., 2004; Ryu et al., 2011; Wang & Leuning, 1998), TBL will upscale the leaf-level urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0084 to its canopy counterpart first, then it will calculate Ac and Gs directly without the derivation of the parameter A and gs. In this case,
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0085(D1)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0086(D2)
    urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0087(D3)
    where urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0088, urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0089, and urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0090 are the canopy-level urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0091 for the whole canopy, sunlit canopy, and shaded canopy, respectively. N(L) is the nitrogen gradient in canopy, and fsun(L)and fsh(L) are the fraction of sunlit and shaded leaves in the canopy that change with the canopy depth (Appendix A).

    Through using the canopy-scale urn:x-wiley:21698953:media:jgrg20954:jgrg20954-math-0092 in Farquhar's biochemical model and the Ball-Woodrow-Berry stomatal conductance model, we obtain the Gs and Ac for the sunlit canopy and shaded canopy, respectively.

    Appendix E: Correlations Between the Simulated Hourly ET (GPP) and Measured Hourly ET (GPP) Under All Schemes

    Table E1 shows that on average, simulations using BL, TBL, and TL explains about 67%, 70%, and 71% of the variance in the ET measurements, respectively. Linear correlations between the simulations and the measurements indicate that TL performs best in capturing the temporal patterns of ET with a regression slope of 0.91, while BL and TBL underestimate ET with slopes of 0.72 and 0.83, respectively. Average root-mean-square errors (RMSEs) between simulated and measured ET are 0.055, 0.055 and 0.051 mm/h using BL, TBL, and TL, respectively.

    Table E1. Correlations Between the Simulated Hourly ET (GPP) and Measured Hourly ET (GPP) Under All Schemes
    Site ID Year Upscaling schemes ET GPP
    r2 Slope Intercept (mm/h) RMSE (mm/h) r2 Slope Intercept (g/m2/h) RMSE (g/m2/h)
    CaCa2 2002–2010 BL 0.71 0.76 0.006 0.04 0.78 0.72 0.015 0.10
    TBL 0.73 0.89 0.003 0.04 0.84 1.02 0.009 0.09
    TL 0.74 0.92 0.004 0.04 0.85 0.98 0.015 0.08
    CaCa3 2002–2009 BL 0.69 0.71 0.007 0.05 0.72 0.69 0.018 0.14
    TBL 0.72 0.84 0.004 0.05 0.84 1.05 0.013 0.12
    TL 0.76 0.98 0.005 0.04 0.84 0.99 0.016 0.11
    CaCbo 2008–2013 BL 0.55 0.52 0.025 0.09 0.65 0.62 0.047 0.22
    TBL 0.65 0.62 0.021 0.08 0.77 0.89 0.052 0.18
    TL 0.65 0.71 0.023 0.08 0.78 0.87 0.054 0.18
    CaGro 2005–2011 BL 0.69 0.76 0.016 0.05 0.77 0.66 0.011 0.13
    TBL 0.72 0.89 0.011 0.06 0.82 0.92 0.007 0.11
    TL 0.73 0.94 0.011 0.05 0.84 0.90 0.009 0.10
    CaOas 2002–2010 BL 0.73 0.80 0.013 0.05 0.82 0.82 0.017 0.12
    TBL 0.79 0.89 0.010 0.05 0.90 0.98 0.006 0.09
    TL 0.80 0.91 0.009 0.05 0.90 0.98 0.011 0.09
    CaObs 2002–2009 BL 0.62 0.89 0.015 0.06 0.61 0.68 0.006 0.11
    TBL 0.62 1.03 0.012 0.06 0.67 0.99 −0.001 0.11
    TL 0.65 1.08 0.012 0.06 0.69 0.96 0.005 0.11
    CaOjp 2005–2010 BL 0.57 0.67 0.020 0.04 0.69 0.63 0.011 0.08
    TBL 0.57 0.74 0.019 0.05 0.67 0.82 0.008 0.08
    TL 0.57 0.76 0.020 0.05 0.72 0.85 0.013 0.07
    CaTp3 2009–2013 BL 0.74 0.65 0.016 0.05 0.82 0.54 0.034 0.17
    TBL 0.77 0.78 0.011 0.04 0.88 0.87 0.046 0.11
    TL 0.79 0.90 0.012 0.04 0.88 0.80 0.045 0.11
    CaTp4 2008–2013 BL 0.71 0.68 0.010 0.06 0.82 0.60 0.019 0.15
    TBL 0.73 0.75 0.007 0.06 0.89 0.98 0.027 0.11
    TL 0.74 0.95 0.006 0.06 0.89 0.87 0.025 0.10

    In the linear regressions between simulated GPP and measured GPP, the mean r2 values are 0.69, 0.81, and 0.82, and the mean slopes are 0.66, 0.95, and 0.92 for BL, TBL, and TL, respectively. Moreover, the mean RMSEs are 0.135, 0.112, and 0.107 g/m2/h for BL, TBL, and TL, respectively. TBL and TL simulate GPP with similar accuracies, while BL significantly underestimates GPP. The variations of these statistics across the sites are smaller for TL or TBL than for BL, suggesting that TL or TBL is more suitable for large-scale applications.