This report is the result of the use of the Python 3.4 package Sympy (for symbolic mathematics), as means to translate published models to a common language. It was created by Verónika Ceballos-Núñez (Orcid ID: 0000-0002-0046-1160) on 26/1/2016, and was last modified on lm.
The model depicted in this document considers carbon allocation with a process based approach. It was originally described by Foley et al. (1996).
Here we present a new terrestrial biosphere model (the Integrated Biosphere Simulator - IBIS) which demonstrates how land surface biophysics, terrestrial carbon fluxes, and global vegetation dynamics can be represented in a single, physically consistent modeling framework. In order to integrate a wide range of biophysical, physiological, and ecological processes, the model is designed around a hicrarchical, modular structure and uses a common state description throughout. First, a coupled simulation of the surface water, energy, and carbon fluxes is performed on hourly timesteps and is integrated over the year to estimate the annual water and carbon balance. Next, the annual carbon balance is used to predict changes in the leaf area index and biomass for each of nine plant functional types, which compete for light and water using different ecological strategies. The resulting patterns of annual evapotranspiration, runoff, and net primary productivity are in good agreement with observations. In addition, the model simulates patterns of vegetation dynamics that qualitatively agree with features of the natural process of secondary succession. Comparison of the model's inferred near- equilibrium vegetation categories with a potential natural vegetation map shows a fair degree of agreement. This integrated modeling framework provides a means of simulating hoth rapid biophysical processes and long-term ecosystem dynamics that can be directly incorporated within atmospheric models.
global
| Abbreviation | Source |
|---|---|
| Tropical evergreen trees | Foley et al. (1996) |
The following table contains the available information regarding this section:
| 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\(_i\) |
The following table contains the available information regarding this section:
| Name | Description | Type | Values Tropical evergreen trees |
|---|---|---|---|
| \(NPP_{i}\) | Net Primary Production for PFT\(_i\) | variable | - |
The following table contains the available information regarding this section:
| Name | Description | Type | Values Tropical evergreen trees |
|---|---|---|---|
| \(a_{il}\) | Fraction of annual NPP allocated to leaves for PFT\(_i\) | parameter | \(0.25\) |
| \(a_{is}\) | Fraction of annual NPP allocated to stem for PFT\(_i\) | parameter | \(0.5\) |
| \(a_{ir}\) | Fraction of annual NPP allocated to roots for PFT\(_i\) | parameter | \(0.25\) |
The following table contains the available information regarding this section:
| Name | Description | Type | Values Tropical evergreen trees |
|---|---|---|---|
| \(\tau_{il}\) | Residence time of carbon in leaves for PFT\(_i\) | parameter | - |
| \(\tau_{is}\) | Residence time of carbon in stem for PFT\(_i\) | parameter | - |
| \(\tau_{ir}\) | Residence time of carbon in roots for PFT\(_i\) | parameter | - |
The following table contains the available information regarding this section:
| Name | Description | Expressions |
|---|---|---|
| \(x\) | 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 | \(f_{v}=u\,b+A\,x\) |
| Flux description | |
|---|---|
 Figure 1: Pool model representation |
Input fluxes\(C_{il}: NPP_{i}\cdot a_{il}\) Output fluxes\(C_{il}: \frac{C_{il}}{\tau_{il}}\)\(C_{is}: \frac{C_{is}}{\tau_{is}}\) \(C_{ir}: \frac{C_{ir}}{\tau_{ir}}\) |
\(\left[\begin{matrix}-\frac{C_{il}}{\tau_{il}} + NPP_{i}\cdot a_{il}\\-\frac{C_{is}}{\tau_{is}} + NPP_{i}\cdot a_{is}\\-\frac{C_{ir}}{\tau_{ir}} + NPP_{i}\cdot a_{ir}\end{matrix}\right]\)
\(\left[\begin{matrix}-\frac{1}{\tau_{il}} & 0 & 0\\0 & -\frac{1}{\tau_{is}} & 0\\0 & 0 & -\frac{1}{\tau_{ir}}\end{matrix}\right]\)
\(C_{il} = NPP_{i}\cdot a_{il}\cdot\tau_{il}\)
\(C_{is} = NPP_{i}\cdot a_{is}\cdot\tau_{is}\)
\(C_{ir} = NPP_{i}\cdot a_{ir}\cdot\tau_{ir}\)
\(C_il: 0.25\cdot NPP_{i}\cdot\tau_{il}\), \(C_is: 0.5\cdot NPP_{i}\cdot\tau_{is}\), \(C_ir: 0.25\cdot NPP_{i}\cdot\tau_{ir}\)
\(\lambda_{1}: -\frac{1}{\tau_{is}}\)
\(\lambda_{2}: -\frac{1}{\tau_{ir}}\)
\(\lambda_{3}: -\frac{1}{\tau_{il}}\)
Foley, J. A., Prentice, I. C., Ramankutty, N., Lewis, S., Pollard, D., Sitch, S., & Haxeltine, A. (1996). An integrated biosphere model of land surface processes, terrestrial carbon balance, and vegetation dynamics. Global Biogeochemical Cycles, 10, 603–628. http://doi.org/10.1029/96GB02692