Geog 595 Ecological Modeling

Geog 595 Ecological Modeling Spring 2010 Due: March 17, 2010

Lab 5 Compare Stomatal Conductance Models in Modeling Transpiration

1. Objectives (1) Understanding three stomatal conductance models in modeling transpiration: Jarvis (1976), Ball-Berry (1987) and Lenuing (1995). (2) Implement the models in C programs.

2. Theory Water is an essential resource for plants. No plant physiological process can happen without water. Plants lose water during the photosynthesis process when stomas open to absorb CO2 in the atmosphere. Plants lose more water when the stomas are more open. Physiologists use stomatal conductance (gsw) to describe the openness of stomas. It is essential for modelers to numerically describe how stomatal conductance change in difference environmental conditions as it controls the rate of transpiration as well as the rate of photosynthesis. Jarvis (1976) provided an empirical model that describe stomatal conductance as in the following

g sw  g s max f (T) f (PAR) f (VPD) f ( l ) f (Ca ) , (1)

where gsmax is the maximum stomatal conductance for the leaves under study, i.e. stomatal conductance with no environmental constrains, and the f(·) are scalar functions that evaluate between 0 and 1 for temperature (T), photosynthetically active radiation (PAR), vapor pressure deficit (VPD), leaf water potential (ψl) and CO2 concentration in the atmosphere (Ca). A common maximum conductance value used in the literature is 0.006m/s. Since the Jarvis model was published, there are numerous variation of f(·) which have been used in the literature. We will use more recent and simpler scalar functions in this lab.

b4 f (T )  b3 (T  Tmin )(Tmax  T ) , (2)

b4  (Tmax  Topt )(Tmax  Tmin ) 1 b  3 b4 (Topt  Tmin )(Tmax  Topt )

where Tmin, Topt and Tmax are minimum, optimal and maximum temperature for stomatal opening, respectively. For most vegetations, Tmin=5.0, Topt=25.0 and Tmax=40.0 degrees Celsius.

A simpler scalar function for PAR will be used as

f (PAR)  PAR /(PPFD50  PAR) (3) where PPFD50 is the PAR intensity at half stomotal closure, PPFD50 =75 μmol/m2/s. The scalar function for vapor pressure deficit (D) is

f (D)  1 b5D (4)

where b5 is an empirical parameter, b5=0.19. Note, hear D is in kPa. f(D) set to 0 is Eq (4) is less than zero, and set to 1 if Eq (4) evaluates to greater than 1. The scalar function for leaf water potential is

f ( l )  1 exp(b6 (l  max )) (5)

where ψmax is the leaf water potential at which the stomas completely close, ψclose= -2.3 MPa, and ψl is the leaf water potential at which the stomas remains completely open, ψopen= -0.6 MPa. Leaf water potential is determined by soil water potential, which in turn is determined by soil type, porosity and volumetric soil water content.

b  l  s S (6)

Where ψs is the soil water potential what the soil is at saturation. It depends on soil type. In this lab, ψs=-0.008 MPa for silt loam soil in the Duke Forest at the loblolly pine site. The empirical parameter, b, also depends on soil type, b=-5.3 for the silt loam. The degree of saturation, S, indicates percent of pores filled with water. S=θ/φ, where θ is soil volumetric water content, and φ is porosity (φ=0.476 for the soil we are dealing with) and θ will be obtained from measurements.

In most cases, f(Ca) is set to unity based on the data provided in this paper.

A second model for stomatal conductance was proposed by Ball et al. (1987) that linked photosynthesis with transpiration as in

hs gsc  kA (7) Cs 2 where gsc is the stomatal conductance for carbon (mol/m /s). The stomatal conductance for water (gsw) are related to gsc as: gsw=1.56gsc, and k is the empirical 2 parameter (k=9.31 in Ball et al., 1987). A is photosynthesis rate (μmol/m /s). Cs is CO2 concentration at the leaf surface. In this study, we will assume that Cs=Ca in the atmosphere (μmol/mol or ppm) and hs is relative humidity.

More recently, Leuning (1995) further developed the Ball-Berry model as in the following.

A gsc  g0  a1 (8) (Cs Γ)(1  D/D0 ) 2 where g0 is the residual conductance (g0=0.01 mole/m /s). Γ is the CO2 compensation point (Γ=4.4 ppm in this lab). D0 is the vapor pressure deficit at which stomas are half open (D0=1500 pa in this lab). The empirical parameter, a1, varies significantly as shown in Leuning’s paper. We will have to estimate it based on observation data.

3. Lab Report Using the default parameter values set in the program, we will run the model. The out put include the stomatal conductances for the three models and the corresponding ET modeled with Penman-Monteith equation. a. Make two scatter plots with x being the stomatal conductance from Ball-Berry model, and y-axis being the Leuning stomatal conductance and Jarvis stomatal conductance, respectively. Add trend line, regression equations and R2 to the plots. Please discuss the differences among the models and the implications. b. Make another two scatter plots similar to a) above, but for ET. Please discuss the difference among the models with reference to the stomatal conductance above.