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Model : BallBerry4a
Simile version : 4.0
Date added : 20041125
Keywords :
Stomatal conductance ;
Evapotranspiration ;
Ecophysiology ;
Technique ;
Iteration ;
The BallBerry stomatal conductance poses a problem for conventional System Dynamics modelling tools because it depends upon the solution of the following pair of simultaneous equations.
Gs = g_{0} + g_{1} * A * H / C_{a}
A = Gs * A_{Q}
Apart from the external parameters, g0, g1, H, Ca and AQ, the equation for Gs depends only on A, and the equation for A depends only on Gs. In this implementation, the loop is opened, by introducing a placeholder for Gs, called Gs_0. This variable is calculated from A. A is calculated using Gs. A guess is made for the initial value of Gs. Subsequently, Gs is set to the last calculated value of Gs_0. The influence arrow from Gs_0 to Gs is dashed, indicating that the value from the previous iteration is to be used. The alarm symbol terminates the iterative loop when Gs and Gs_0 differ by less than one part in one thousand.
That’s all there is to it, except that it’s worth noting what to do if the iteration does not converge. It is necessary to use the new “Abort Execution” command in the “Model” menu of the model diagram window (i.e. NOT in the run control window).
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BallBerry4aP.sml 
Equations in BallBerry4aP Equations in Environment Variable C_a : Carbon dioxide concentration (umol CO2 (mol air)^1) C_a = graph(time()) Comments: Typical diurnal curve in forest canopy Variable H : Relative humidity (proportion) H = graph(time()) Comments: Typical diurnal graph (24 hour) Variable Q : Photon flux density (umol m^2 s^1) Q = graph(time()) Comments: Graph for a sunny day (24 hours) Equations in BallBerry Variable Gs_start Gs_start = if time()==0 then g_0 else last(Gs_0) Where: Gs_0=Iteration time step/Gs_0 Variable g_0 : Stomatal conductance in the dark (mol m^2 s^1) g_0 = 0.01 Variable g_1 : BallBerry stomatal conductance coefficient g_1 = 23 Equations in Iteration time step Alarm Variable Gs Gs = if loop_count==0 then Gs_start else Gs_0 Where: Gs_start=../Gs_start Variable Gs_0 : Stomatal conductance (mol m^2 s^1) Gs_0 = g_0+g_1*A*H/C_a Where: A=Assimilation/A H=../../Environment/H C_a=../../Environment/C_a g_0=../g_0 g_1=../g_1 Comments: BallBerry equation Variable loop_count loop_count = iterations(al1) Equations in Assimilation Variable A : Assimation (umol CO2 m^2 s^1) A = A_Q*Gs Where: Gs=../Gs Variable A_Q : Assimilation light response curve A_Q = graph(Q) Where: Q=../../../Environment/Q Comments: Relationship of Assimilation with photon flux density (light) when stomatal conductance (Gs) is maximum
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