Report of the model: Integrated Biosphere Simulator (IBIS), version: 2.6

This report is the result of the use of the python package bgc_md, as means to translate published models to a common language. The underlying yaml file was created by Verónika Ceballos-Núñez (Orcid ID: 0000-0002-0046-1160) on 22/3/2016.

About the model

The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Castanho et al. (2013).

Space Scale

state_variables
Name	Description
\(C_{il}\)	Carbon in leaves of plant functional type (PFT) \(i\)
\(C_{is}\)	Carbon in transport tissue (mainly stems) of PFT\(_{i}\)
\(C_{ir}\)	Carbon in fine roots of PFT\(_{i}\)

state_variables

\(C_{il}\)

Carbon in leaves of plant functional type (PFT) \(i\)

\(C_{is}\)

Carbon in transport tissue (mainly stems) of PFT\(_{i}\)

\(C_{ir}\)

Carbon in fine roots of PFT\(_{i}\)

additional_variables
Name	Description	Unit
\(S\)	Percent sand in soil	\(percentage\)

additional_variables

\(S\)

Percent sand in soil

\(percentage\)

photosynthetic_parameters
Name	Description
\(NPP_{i}\)	Net Primary Production for PFT\(_{i}\)

photosynthetic_parameters

\(NPP_{i}\)

Net Primary Production for PFT\(_{i}\)

allocation_coefficients
Name	Description	Expression
\(a_{il}\)	Fraction of annual NPP allocated to leaves for PFT\(_{i}\)	\(a_{il}=0.44 - 0.0025\cdot S\)
\(a_{ir}\)	Fraction of annual NPP allocated to roots for PFT\(_{i}\)	\(a_{ir}=0.0039\cdot S + 0.137\)
\(a_{is}\)	Fraction of annual NPP allocated to stem for PFT\(_{i}\)	\(a_{is}=- a_{il} - a_{ir} + 1\)

allocation_coefficients

\(a_{il}\)

Fraction of annual NPP allocated to leaves for PFT\(_{i}\)

\(a_{il}=0.44 - 0.0025\cdot S\)

\(a_{ir}\)

Fraction of annual NPP allocated to roots for PFT\(_{i}\)

\(a_{ir}=0.0039\cdot S + 0.137\)

\(a_{is}\)

Fraction of annual NPP allocated to stem for PFT\(_{i}\)

\(a_{is}=- a_{il} - a_{ir} + 1\)

cycling_rates
Name	Description	Unit
\(\tau_{il}\)	Residence time of carbon in leaves for PFT\(_{i}\)	-
\(\tau_{is}\)	Residence time of carbon in stem for PFT\(_{i}\)	-
\(\tau_{ir}\)	Residence time of carbon in roots for PFT\(_{i}\)	-

cycling_rates

\(\tau_{il}\)

Residence time of carbon in leaves for PFT\(_{i}\)

\(\tau_{is}\)

Residence time of carbon in stem for PFT\(_{i}\)

\(\tau_{ir}\)

Residence time of carbon in roots for PFT\(_{i}\)

components
Name	Description	Expression
\(x\)	vector of states for vegetation	\(x=\left[\begin{matrix}C_{il}\\C_{is}\\C_{ir}\end{matrix}\right]\)
\(u\)	scalar function of photosynthetic inputs	\(u=NPP_{i}\)
\(b\)	vector of partitioning coefficients of photosynthetically fixed carbon	\(b=\left[\begin{matrix}a_{il}\\a_{is}\\a_{ir}\end{matrix}\right]\)
\(A\)	matrix of turnover (cycling) rates	\(A=\left[\begin{matrix}-\frac{1}{\tau_{il}} & 0 & 0\\0 & -\frac{1}{\tau_{is}} & 0\\0 & 0 & -\frac{1}{\tau_{ir}}\end{matrix}\right]\)
\(f_{v}\)	the righthandside of the ode	\(f_{v}=u b + A x\)

components

\(x\)

vector of states for vegetation

\(x=\left[\begin{matrix}C_{il}\\C_{is}\\C_{ir}\end{matrix}\right]\)

\(u\)

scalar function of photosynthetic inputs

\(u=NPP_{i}\)

\(b\)

vector of partitioning coefficients of photosynthetically fixed carbon

\(b=\left[\begin{matrix}a_{il}\\a_{is}\\a_{ir}\end{matrix}\right]\)

\(A\)

matrix of turnover (cycling) rates

\(A=\left[\begin{matrix}-\frac{1}{\tau_{il}} & 0 & 0\\0 & -\frac{1}{\tau_{is}} & 0\\0 & 0 & -\frac{1}{\tau_{ir}}\end{matrix}\right]\)

\(f_{v}\)

the righthandside of the ode

\(f_{v}=u b + A x\)

Pool model representation

Input fluxes

\(C_{il}: NPP_{i}\cdot\left(0.44 - 0.0025\cdot S\right)\)
\(C_{is}: NPP_{i}\cdot\left(0.423 - 0.0014\cdot S\right)\)
\(C_{ir}: NPP_{i}\cdot\left(0.0039\cdot S + 0.137\right)\)

Output fluxes

\(C_{il}: \frac{C_{il}}{\tau_{il}}\)
\(C_{is}: \frac{C_{is}}{\tau_{is}}\)
\(C_{ir}: \frac{C_{ir}}{\tau_{ir}}\)

Steady state formulas

References

Castanho, A. D. A., Coe, M. T., Costa, M. H., Malhi, Y., Galbraith, D., & Quesada, C. A. (2013). Improving simulated amazon forest biomass and productivity by including spatial variation in biophysical parameters. Biogeosciences, 10(4), 2255–2272. http://doi.org/10.5194/bg-10-2255-2013