# A Canopy Transpiration Model Based on Scaling Up Stomatal Conductance and Radiation Interception as Affected by Leaf Area Index

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## Abstract

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^{2}= 0.98; p < 0.001) with the predicted values. This was particularly so at lower LAIs. Probable reasons for the discrepancy at higher LAI are explained. Both the predicted and experimental transpiration varied from 0.21 to 0.56 mm h

^{−1}for the range of available LAIs. The physical proportion of the shaded layer exceeded that of the sunlit layer near LAI of 3.0, however, the contribution of the sunlit layer to the total transpiration remains higher throughout the entire growing season.

## 1. Introduction

^{2}= 0.98) when tested at different crop growth stages. The authors concluded that the precision of estimating evapotranspiration and soil evaporation using the “dual-leaf” model was higher than that for the “big-leaf” model and could be an effective substitute for estimating and partitioning evapotranspiration components. However, the model performance was only validated against variable solar radiation, but the impact of variations in canopy coverage or LAI on the magnitude of transpiration was not investigated. Moreover, a single canopy conductance value was calculated for the whole canopy and therefore the potential benefits of assuming a “dual-leaf” configuration was not realized.

## 2. Constructing a Theoretical Model of Canopy Conductance

#### 2.1. Defining the Model Structure

_{b}) in Equation (4). Considering each layer of the canopy as a “big-leaf” in a weighted layer model [8,20] the canopy conductance (g

_{c}) for any of the assumed canopy layers can be written as:

_{s(ab)}= abaxial stomatal conductance (m s

^{−1})

_{s(ad)}= adaxial stomatal conductance (m s

^{−1}), and,

#### 2.2. Modelling Transpiration

_{l}) can be written as:

_{H}and G

_{V}are the total conductance for sensible heat and for water vapour, respectively,

^{−1}),

_{n}= net radiation, (MJ m

^{−2}h

^{−1}),

_{a}= air density, (kg m

^{−3}),

_{p}= specific heat of air, (MJ kg

^{−1}°C

^{−1}),

^{−1}).

_{c}) of the composite canopy can be calculated by combining the adaxial and abaxial stomatal conductances for both the sunlit and shaded layers. In this context, the sensible heat conductance, G

_{H}, (Equation (5)) can be replaced by the surface layer aerodynamic conductance (g

_{a}), and water vapour conductance, G

_{V}, replaced by (1 + g

_{a}/g

_{c}) [3]. A ground heat flux term (G) can also be introduced. The overall canopy evapotranspiration (ET

_{r}) can, therefore, be re-written as [28,30]:

^{−2}h

^{−1}),

_{c}= canopy conductance calculated from stomatal conductance and LAI data, (m s

^{−1}) and

_{a}= aerodynamic conductance, (m s

^{−1}).

_{a}) can be calculated using the following equation:

^{−1}),

_{c}= mean crop height, (m),

_{o}= roughness length of the crop relative to momentum transfer, (m) and

_{o}and d are functions of the mean crop height and can be defined as:

^{−2}s

^{−1}) at the top of the canopy. The constant 0.00173 is the conversion factor used to convert PAR into MJ m

^{−2}h

^{−1}(total radiation energy in all wavelengths), assuming that approximately 45% of the total energy in solar radiation is in the range of 400–700 nm [38,39]. For the sunlit canopy layer, PAR

_{sl}is the measured value at top of the canopy, whereas, for the shaded layer the PAR

_{sh}value is PAR

_{sl}minus the amount that was intercepted by the sunlit portion. The fAPAR

_{LAI}is the fraction of photosynthetically active radiation absorbed by the canopy for a particular LAI. In the model, this is broken up into sunlit and shaded components of the canopy. By introducing fAPAR, the energy that passes through the canopy and is intercepted by the soil is excluded from the model and therefore excludes the soil evaporation component. For each of the sunlit (sl) and shaded (sh) portions, Equation (6) can be re-written in terms of transpiration, T

_{r}, as:

## 3. Materials and Methods

#### 3.1. Establishing and Monitoring the Growing Environment

^{3}self-watering tubs (surface area = 0.02 m

^{2}). Highly permeable peat river sand potting mix (3:1 v/v) was placed as a 1.5 cm thick base layer to facilitate water infiltration into and out of the soil from the underlying water reservoir. The tubs were then filled to within 3 cm of the top with a cracking clay soil (35% clay, bulk density 0.91 g cm

^{−3}) (vertosol) sourced from the Laureldale Field Station (Figure 2).

^{−1}(approx. 2000 seedlings m

^{−2}) on three sowing dates and with four rates of urea/triple superphosphate fertilizer (0, 33, 66 and 100 kg N ha

^{−1}) to achieve a range of growth rates and vegetation coverage during the growing season. All treatments were randomized.

^{−1}, Electus Distribution Pty. Ltd., Rydalmere, Australia).

#### 3.2. Measuring Canopy Transpiration

^{−1}) was calculated from the amount of water loss (amount required to refill), the time elapsed and the pot surface area.

^{−2}of water loss from the tub surface area.

#### 3.3. Measuring Canopy Conductance

## 4. Results and Discussion

_{cb}). A controlled atmosphere experiment involving the same pasture species (tall fescue), where the transpiration was separately calculated through isotopic observation, found that transpiration can be as high as 0.55 mm hr

^{-1}for an LAI of 4, which is also very close to the model-predicted values in this experiment [31].

^{-1}(which mimics the bulk airflow in the centre of the greenhouse bay resulting from the ventilation), yielded a net increase in modelled transpiration of 20%.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic representation of the canopy structure for tall fescue (Festuca arundinacea var. Demeter) and the relevant parameters. The proportion of each layer can be theoretically calculated in terms of leaf area index LAI and varies with canopy LAI.

**Figure 4.**Fraction of sunlit (open circles) and shaded (closed circles) components of LAI as a function of canopy LAI.

**Figure 5.**Measured canopy conductance, g

_{c}(mm s

^{−1}) of adaxial (

**△**, dotted trend line) and abaxial (▲, dashed trend line) leaf surfaces, and net canopy conductance (■, solid trend line) as a function of canopy LAI.

**Figure 6.**Measured (■, dotted line), predicted total transpiration (□, solid line), sunlit transpiration (○, long dashed line) and shaded transpiration (●, short dashed line) for the canopy layers and overall canopy with LAI. All trend curves are significant polynomial fits (p < 0.001).

**Figure 7.**Relationship between actual and calculated transpiration (mm h

^{−1}). The dotted line represents 1:1 equivalence and solid line is the fitted linear equation.

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**MDPI and ACS Style**

Alam, M.S.; Lamb, D.W.; Warwick, N.W.M.
A Canopy Transpiration Model Based on Scaling Up Stomatal Conductance and Radiation Interception as Affected by Leaf Area Index. *Water* **2021**, *13*, 252.
https://doi.org/10.3390/w13030252

**AMA Style**

Alam MS, Lamb DW, Warwick NWM.
A Canopy Transpiration Model Based on Scaling Up Stomatal Conductance and Radiation Interception as Affected by Leaf Area Index. *Water*. 2021; 13(3):252.
https://doi.org/10.3390/w13030252

**Chicago/Turabian Style**

Alam, Muhammad Shahinur, David William Lamb, and Nigel W. M. Warwick.
2021. "A Canopy Transpiration Model Based on Scaling Up Stomatal Conductance and Radiation Interception as Affected by Leaf Area Index" *Water* 13, no. 3: 252.
https://doi.org/10.3390/w13030252