CALCULATION OF LEAF BOUNDARY LAYER PARAMETERS WITH THE TWO-DIMENSIONAL MODEL 2DLEAF AND DATA ON LEAF ANATOMY AND TRANSPIRATION RATES FOR POTATO AND PEANUT LEAVES

Poster Presented at the International Society of Ecological Modeling Meeting in Baltimore, Maryland USA, August 4, 1998

Ludmila B. Pachepsky^1,2, Michael Muschak³, R. Andrés Ferreyra⁴,
Joachim Fisahn³, and B. Acock¹

¹ RSML, ARS, USDA, Beltsville, MD, USA
² Duke University, Durham, NC, USA
³ Max-Plank-Institute for Plant Physiology, Golm, Germany
⁴ CEPROCOR, Córdoba, Argentina

ABSTRACT

The leaf boundary layer, i.e. the layer of air adjacent to a leaf surface in which gas flow is significantly influenced by the leaf, affects leaf gas exchange considerably. Numerous factors, both external conditions and leaf properties, have a strong influence on the characteristics of the boundary layer, and for decades it has been a challenge to develop a reliable model of this link of the leaf gas exchange pathway. Two parameters, the boundary layer thickness, d, and the ratio, B, of the diffusion coefficients of gases in the boundary layer and in the intercellular space, were shown to be sufficient to represent the effect of the boundary layer in the two-dimensional leaf gas exchange model 2DLEAF. An algorithm for calculation of these parameters is presented and applied to simulate the transpiration rates of the leaves of two genotypes of potato (Solanum tuberosum L.) and peanut (Arachis hypogaea L.) plants. Parameters d and B were different for different genotypes and they expressed the real differences in leaf anatomy and leaf surface properties.

INTRODUCTION

Leaf surface significantly affects air movement. The part of the atmosphere near the leaf surface is referred to as the leaf boundary layer (LBL). The idea of the LBL first appeared in 1953 when Bange introduced the concept of a micro "vapor cup" as a region over the stomate where gas flow is different from the surrounding atmosphere. He considered the interactions of these "cups" at very high stomatal frequency. According to a definition by Nobel (1991), the LBL consists of two sub-layers. The surface region nearest the leaf is "dominated by the shearing stresses originated at some surface in a laminar sub-layer of air where movement is parallel to the leaf surface; air movement is arrested at the surface and has increasing speed at increasing distances" from the leaf surface. Farther from the surface, the second sub-layer is a region of turbulent gas movement.

For decades, LBL has been remarkable challenge for both experimentalists and modelers, often causing incomparable and contradicting results of transpiration measurements. Beginning with Brown and Escombe's (1900) experiments conducted in still air, a failure to account for the LBL led to the erroneous conclusion that stomatal aperture had little effect on transpiration. This, in turn, "led to a long and unproductive argument concerning the importance of stomatal control of transpiration" (Kramer & Boyer, 1995) until later experiments summarized by Slatyer (Slatyer, 1967) showed that stomata control transpiration. Numerous attempts to relate stomatal conductance to stomatal dimensions were unsuccessful because the LBL was not accounted for (Pennman & Schofield, 1951).

LBL parameters such as thickness, effective coefficients of gas diffusion, and resistance were shown to be strongly dependent on wind speed (Cowan, 1972; Kramer & Boyer, 1995), intensity of air stirring within a leaf chamber (Nobel, 1991), temperature (Salisbury & Ross, 1991), relative humidity (Monteith, 1995), and leaf properties, i.e., leaf size and shape (Nobel, 1991), stomata size, shape, frequency, and distribution (Bange, 1953; Kramer & Boyer, 1995), stomatal aperture (Parlange & Waggoner, 1970), and roughness of the leaf surface, i. e., how grooved and hairy is it (Larcher, 1995). Many of these factors, like wind speed or stomatal aperture, are highly variable and difficult to control in experiments. This makes measurement of the LBL extremely difficult. Therefore, modeling of the LBL appears to be necessary.

Different models of the LBL have been considered. Nobel (1991) introduced resistance of the LBL as one of several resistances in the gas exchange pathway. The coefficient of diffusion for various gases in the LBL in combination with LBL thickness were used by Jones (1992) and Pachepsky and Acock (1996). Both approaches are approximations to a complete description of gas flow near the leaf surface. The parameters in both models were found to be dependent on environmental conditions.

The objectives of this work were

to determine the minimum number of LBL parameters needed to explicitly account for the boundary layer effect on leaf gas exchange for hypostomatous, Solanum tuberosum L. and amphystomatous, Arachis hypogaea L. plant leaves,
to determine the values of these LBL parameters with data on transpiration and leaf anatomy for normal (cv. Désirée) and transgenic potato plants, and for two Argentine peanut cultivars, and
to formulate an algorithm to quantitatively describe the leaf boundary layer in two-dimensional leaf gas exchange models.

THE 2DLEAF MODEL

The 2DLEAF model is described in detail in (Pachepsky & Acock, 1996). The model simulates a transport of three gases, water vapor, carbon dioxide, and oxygen as a two-dimensional flow in a domain which extends through the leaf cross-section and the boundary layer, BL. The 2DLEAF model can be used for both amphystomatous (Pachepsky et al., 1997) and hypostomatous (Pachepsky & Acock, 1996) leaves. The 2DLEAF model simulates

transport of CO₂ and water vapor in the intercellular spaces and in the boundary layer adjacent to a leaf,
fluxes of CO₂ across cell surfaces due to assimilation, and
fluxes of water vapor from the cell surfaces due to the difference between atmosphere and intercellular water vapor pressure.

The system of equations of the model includes three diffusion equations for CO₂, O₂, and water vapor, and five algebraic carbon assimilation equations as boundary conditions for CO₂ transport, according to the CO₂ assimilation model based on Rubisco kinetics (Farquhar et al., 1980; Harley & Tenhunen, 1991). Boundary conditions are defined also by constant values of [CO₂], [O₂], and water vapor pressure at the outer borders of the BLs. Temperature, air humidity, [CO₂], and light intensity must be known to calculate the coefficients in the system of equations and to set the boundary conditions.

POTATO

Potato plant (Solanum tuberosum L.)

Potato leaf cross-sections, A: cv. Désirée, B: transgenic plant

Schematization of the internal leaf structure for potato, A: cv. Désirée, B: transgenic plant

Transpiration rates calculated for various values of the boundary layer thickness, d, and the ratio of the diffusion coefficients in the boundary layer and in the intercellular space, B, at stomatal aperture values of 1 µm (lower) and 10 µm (upper surface), 70% relative humidity, 20^oC temperature for a potato leaf, A: cv. Désirée, B: transgenic. Arrows show the parameter values and transpiration rates that correspond to the measured transpiration rates.

PEANUT

Peanut plant (Arachis hypogaea L.)

Florman INTA peanut leaf cross-section

Manfredi 393 INTA peanut leaf cross-section

Abaxial leaf surface of Florman INTA leaf

Adaxial leaf surface of Manfredi 393 INTA leaf

Schematization of the leaf internal structure for peanut, A: Manfredi 393 INTA, B: Florman INTA

Leaf transpiration rate as a function of the boundary layer parameters for Florman INTA (a) and Manfredi 393 INTA. Stomatal aperture is equal to 1 (colored surface) and 12 µm (transparent surface). Points represent measured transpiration rates in controlled conditions (a) and in the field (b)

Leaf transpiration rate as a function of stomatal aperture and boundary layer thickness for Florman INTA (colored surface) and Manfredi 393 INTA (transparent surface); Bmult = 1, temperature 25^oC, and 70% relative humidity. Two sets of black points connected with solid lines represent the transpiration rate for the cultivars of Virginia type (Florman INTA), and the set of white points connected with the dashed line represent the transpiration isoline for the Spanish type cultivar (Manfredi 393 INTA).

Leaf boundary layer parameter values at the same transpiration rate, Florman INTA - Tr = 4.1 mmol m^-2 s^-1 at controlled environment conditions (a) and Tr = 7.7 mmol m^-2 s^-1 in the field (b); Manfredi 393 INTA, Tr = 4 mmol m^-2 s^-1 (c ). Upper lines are for stomatal aperture a = 1 µm, lower lines are for stomatal aperture 12 µm (Florman INTA) and 10 µm (Manfredi 393 INTA).

RESULTS

Calibration of the 2DLEAF model for transpiration rates was performed

for normal and transgenic leaves of potato and
leaves of Florman INTA and Manfredi 393 INTA peanut cultivars,

for all possible combinations of reasonable values of d and B at two values (maximal and minimal) of stomatal aperture. The values of the BL thickness, d, were varied over the range 100-2000 µm. This range is based on the estimations by Nobel (1991) for leaves 5 cm long. Parameter B can be greater or less than 1, reflecting the relative thickness of the turbulent (caused by fast air convection, wind, etc.) and laminar (caused by the roughness of leaf surfaces) sub-layers in the BL. If the laminar sub-layer dominates, which could happen under controlled conditions, then B < 1. In field and even greenhouse conditions, the turbulent sub-layer dominates, and then B > 1. Values of B were varied over the range 0.5-5.

Transpiration rate increases when the thickness of the BL decreases, at all values of the parameter B. Transpiration rate is higher for greater values of B. All these qualitative dependencies are consistent with the known mechanisms of the transpiration.

Transpiration rate of Manfredi 393 INTA is always higher than that of Florman due to differences in leaf anatomy. Transpiration rate increases with increasing stomatal aperture, but this dependence is much more pronounced when BL thickness is less than 1000 µm.

A comparison of the leaf anatomical structure for normal and transgenic potato leaves, as well as for two peanut cultivars of different botanical types demonstrated a significant quantitative difference between them.

Two-dimensional modeling based on the analysis of leaf anatomy showed the difference in transpiration processes for these cultivars, expressed as different dependencies of the transpiration rates on the boundary layer parameters.

For both amphystomatous and hypostomatous leaves, two empirical parameters, BL thickness d and the ratio of the coefficients of diffusion in the intercellular space and in the BL, B, are necessary and sufficient to quantitatively describe the effect of the boundary layer on the transpiration rate.

The algorithm of calculating the LBL parameters, d and B, can be described as the three following steps.

Step 1: Estimate the range of d and B values.
Step 2: Calculate transpiration rates with the 2DLEAF model for all possible combinations of the values of d and B, with reasonable steps for both parameters, at two values (maximal and minimal) of stomatal aperture. The corresponding surfaces of transpiration values should be plotted.
Step 3: On these surfaces, the values equal to the measured transpiration values are found, and the corresponding d and B values are the parameters of the BL for the particular experiment.

REFERENCES

Bange, G.G.J. (1953) Acta Botanica Neerlandica 2, 255-297.
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Monteith, J.L. (1995) Plant, Cell and Environ. 18, 357-364.
Nobel, P.S. (1991) Physicochemical and Environmental Plant Physiology. Acad. Press.
Pachepsky, L.B. & Acock B. (1996) Ecological Modelling 93, 1-18.
Parlange, J.Y. and Waggoner P.E. (1970) Plant Physiol. 46, 337-342.
Pennman, H.L. and Schofield R.K. (1951) Symp. Soc. Exp. Biol. 5, 115-129.
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Slatyer, R.O. (1967) Plant-Water Relationships. Academic Press. New York. 366 p.

A little tribute to Vincent Van Gogh

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R. Andrés Ferreyra: aferreyra@iname.com
Ludmila B. Pachepsky: lpachepsky@asrr.arsusda.gov

this page is mirrored on Aug 12 1998 from original site : poster presented at the ISEM worldwide meeting at baltimore, 2.-6. Aug. 1998