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Iterative solution to Ball-Berry stomatal conductance simultaneous equations (Simile V3+) - Model catalogue - Simulistics.com

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Iterative solution to Ball-Berry stomatal conductance simultaneous equations (Simile V3+)

Model : ballberry1
Simile version : 3.1+
Date added : 2003-07-27
Keywords : Ecophysiology ; Stomatal conductance ; Evapotranspiration ; Technique ;

Description

Here’s an example of a model with two simultaneous equations implemented in Simile. It is a version of the Ball-Berry stomatal conductance model where assimilation (photosynthesis) is a function of stomatal conductance and stomatal conductance is a function of assimilation.

Where there is a big change in stomatal conductance (Gs) more iterations are needed to reach a certain accuracy.

The iteration submodel is at time step #2. This and its contained submodels have a time step of 0.01 in the run control. The rest of the model has a time step of 1. The iteration thus runs 100 times for each time step of the container submodel.

Files

Model file

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ballberry1.sml

Diagram

Equations

Equations in Desktop

Equations in Assimilation
 
Variable   A : Assimation (umol CO2 m^-2 s^-1)
	A = A_Q*last(Gs_0) 
	Where:
		Gs_0=../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 

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 Iteration
 
Variable   Gs : Stomatal conductance (mol m^-2 s^-1)
	Gs = if time()==time then Gs else g_0+g_1*A*H/C_a 
	Where:
		A=Assimilation/A
		time=../time
		H=../../Environment/H
		C_a=../../Environment/C_a
		g_0=../g_0
		g_1=../g_1
		Gs=../Gs 
	Comments:
		Ball-Berry equation 
 
Variable   errorGs
	errorGs = Gs_0-last(Gs_0) 
	Where:
		Gs_0=Gs 

Equations in Ball-Berry
 
Variable   A
	A = A 
	Where:
		A=Iteration/Assimilation/A 
 
Variable   Gs
	Gs = if time()==0 then g_0 else last(Gs_0) 
	Where:
		Gs_0=Iteration/Gs 
 
Variable   errorGs
	errorGs = last(errorGs_0) 
	Where:
		errorGs_0=Iteration/errorGs 
 
Variable   g_0 : Stomatal conductance in the dark (mol m^-2 s^-1)
	g_0 = 0.01 
 
Variable   g_1 : Ball-Berry stomatal conductance coefficient
	g_1 = 23 
 
Variable   time
	time = time()

Results

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This first pair of graphs shows the calculated Stomatal Conductance and Assimilation on an hour-by-hour basis throughout the day.

This second pair shows the internal model representation of the two variables converging on the required hourly value. Note that when the magnitude of changes in the variables is large, as it is around time()==10 units, the convergence takes longer.

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Web links

  • Vincent P. Gutschick : Regularities in Plant Control of Evapotranspiration and Carbon Gain Across Sites: Tests with Scaling Up and Modelling Consequences for Water and Carbon Balances

References

J. T. Ball, I. E. Woodrow, J. A. Berry. 1987. A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: Progress in Photosynthesis Research, ed. J. Biggins. M. Nijhoff Publishers, Dordrecht. Vol. 4, pp 221-224.

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