# UNC-Chapel Hill GEOG 595 - Lab 5 Compare Stomatal Conductance Models in Modeling Transpiration (3 pages)

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## Lab 5 Compare Stomatal Conductance Models in Modeling Transpiration

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## Lab 5 Compare Stomatal Conductance Models in Modeling Transpiration

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School:
University of North Carolina at Chapel Hill
Course:
Geog 595 - Ecological Modeling
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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 C a 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 l 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 f T b3 T Tmin Tmax T b4 2 b4 Tmax Topt Tmax Tmin b3 Topt 1 Tmin Tmax Topt b4 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 mol m 2 s The scalar function for vapor pressure deficit D is f D 1 b5 D 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 max is the leaf water potential at which the stomas completely close close 2 3 MPa and l is the leaf water potential at which the stomas remains completely open open 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 l s S b 6 Where s is the soil water potential what the soil is at saturation It depends on soil type In this lab s 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 where is soil volumetric water content and is porosity 0 476 for the soil we are dealing with and 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 7 Cs where gsc is the stomatal conductance for carbon mol m2 s The stomatal conductance for water gsw are related to gsc as gsw 1 56gsc and k is the empirical parameter k 9 31 in Ball et al 1987 A is photosynthesis rate mol m2 s Cs is CO2 concentration at the leaf surface In this study we will assume that Cs Ca in the atmosphere mol mol or ppm and hs is relative humidity g sc kA More recently Leuning 1995 further developed the Ball Berry model as in the following g sc g 0 a 1 A C s 1 D D 0 8 where g0 is the residual conductance g0 0 01 mole m2 s is the CO2 compensation point 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

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