ModelId:

BallBerry4a

SimileVersion:

5.9

The Ball-Berry 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}

Equations:

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 Ball-Berry

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 : Ball-Berry 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:

Ball-Berry 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

Results:

Plot of stomatal conductance versus time Plot of assimilation versus time