General Overview


Logo

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 24/3/2016.

About the model

The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Luo, Weng, & Yang (2012).

Space Scale

global

Available parameter values

Information on given parameter sets
Abbreviation Description
set1 Original parameters of the publication. Parameter value of GPP corresponds to an annual average

Available initial values

Information on given sets of initial values
Abbreviation Description
_0 original dataset of the publication. Parameter value of GPP corresponds to an annual average
state_variables
Name Description
\(C_{f}\) Carbon in foliage
\(C_{r}\) Carbon in roots
\(C_{w}\) Carbon in woody tissue
photosynthetic_parameters
Name Description Expression Unit
\(t\) - \(day\)
\(GPP\) Photosynthetic rate (Carbon input) at time t - \(gC\cdot day^{-1}\)
\(T\) Temperature - -
\(Q_{10}\) Temperature quotient that describes a change in decomposition rate for evey 10°C difference in temperature - -
\(W\) Volumetric soil moisture - -
\(f_{W}\) Function of W \(f_{W}=\min\left(1, 0.5\cdot W\right)\) -
\(f_{T}\) Function of T \(f_{T}=Q_{10}^{\frac{T}{10} - 1}\) -
\(\epsilon_{t}\) Environmental scalar \(\epsilon_{t}=f_{T}\cdot f_{W}\) \(km^2\)
allocation_coefficients
Name Description
\(\eta_{f}\) Fixed partitioning ratio (fraction) of available carbon allocated to foliage
\(\eta_{r}\) Fixed partitioning ratio (fraction) of available carbon allocated to roots
\(\eta_{w}\) Fixed partitioning ratio (fraction) of available carbon allocated to wood
cycling_rates
Name Description Unit
\(\gamma_{f}\) Foliage turnover rate -
\(\gamma_{r}\) Roots turnover rate -
\(\gamma_{w}\) Wood turnover rate -
components
Name Description Expression
\(x\) vector of states for vegetation \(x=\left[\begin{matrix}C_{f}\\C_{w}\\C_{r}\end{matrix}\right]\)
\(u\) scalar function of photosynthetic inputs \(u=GPP\cdot\epsilon_{t}\)
\(b\) vector of partitioning coefficients of photosynthetically fixed carbon \(b=\left[\begin{matrix}\eta_{f}\\\eta_{w}\\\eta_{r}\end{matrix}\right]\)
\(A\) matrix of turnover (cycling) rates \(A=\left[\begin{matrix}-\gamma_{f} & 0 & 0\\0 & -\gamma_{w} & 0\\0 & 0 & -\gamma_{r}\end{matrix}\right]\)
\(f_{v}\) the righthandside of the ode \(f_{v}=u b + A x\)

Pool model representation


Figure 1
Figure 1: Pool model representation

Input fluxes

\(C_{f}: GPP\cdot Q_{10}^{\frac{T}{10} - 1}\cdot\eta_{f}\cdot\min\left(1, 0.5\cdot W\right)\)
\(C_{w}: GPP\cdot Q_{10}^{\frac{T}{10} - 1}\cdot\eta_{w}\cdot\min\left(1, 0.5\cdot W\right)\)
\(C_{r}: GPP\cdot Q_{10}^{\frac{T}{10} - 1}\cdot\eta_{r}\cdot\min\left(1, 0.5\cdot W\right)\)

Output fluxes

\(C_{f}: C_{f}\cdot\gamma_{f}\)
\(C_{w}: C_{w}\cdot\gamma_{w}\)
\(C_{r}: C_{r}\cdot\gamma_{r}\)

Steady state formulas

\(C_f = \frac{GPP\cdot Q_{10}^{\frac{T}{10} - 1}\cdot\eta_{f}\cdot\min\left(1.0, 0.5\cdot W\right)}{\gamma_{f}}\)

\(C_w = \frac{GPP\cdot Q_{10}^{\frac{T}{10} - 1}\cdot\eta_{w}\cdot\min\left(1.0, 0.5\cdot W\right)}{\gamma_{w}}\)

\(C_r = \frac{GPP\cdot Q_{10}^{\frac{T}{10} - 1}\cdot\eta_{r}\cdot\min\left(1.0, 0.5\cdot W\right)}{\gamma_{r}}\)

References

Luo, Y., Weng, E., & Yang, Y. (2012). Ecosystem ecology, 219–229.