These are the states and parameters as defined in Table 1 of Braswell et al. (2005) for the SIPNET model.
The model description is in Appendix A but not reproduced here.
| Symbol | Definition | Units |
|---|---|---|
| Initial pool values | ||
| \(C_{W,0}\) | Initial plant wood C content | g C m\(^{-2}\) |
| \(C_{L,0}\) | Initial plant leaf C content | g C m\(^{-2}\) |
| \(C_{S,0}\) | Initial soil C content | g C m\(^{-2}\) |
| \(W_0\) | Initial soil moisture content | cm (precipitation equivalent) |
| Photosynthesis parameters | ||
| \(A_{\text{max}}\) | Maximum net CO2 assimilation rate | nmol CO2 g\(^{-1}\) (leaf) s\(^{-1}\) |
| \(A_d\) | Avg. daily max photosynthesis as fraction of \(A_{\text{max}}\) | (no units) |
| \(K_F\) | Foliar maintenance respiration as fraction of \(A_{\text{max}}\) | (no units) |
| \(T_{\text{min}}\) | Minimum temperature for photosynthesis | \(^{\circ}\text{C}\) |
| \(T_{\text{opt}}\) | Optimum temperature for photosynthesis | \(^{\circ}\text{C}\) |
| \(K_{\text{VPD}}\) | Slope of VPD–photosynthesis relationship | kPa\(^{-1}\) |
| \(\text{PAR}_{1/2}\) | Half saturation point of PAR–photosynthesis relationship | Einsteins m\(^{-2}\) day\(^{-1}\) |
| \(k\) | Canopy PAR extinction coefficient | (no units) |
| \(D_{\text{on}}\) | Day of year for leaf out | day of year |
| \(D_{\text{off}}\) | Day of year for leaf drop | day of year |
| \(L_{\text{max}}\) | Maximum leaf area index obtained | m\(^2\) (leaf) m\(^{-2}\) (ground) |
| Respiration parameters | ||
| \(K_A\) | Wood respiration rate at 0 \(^{\circ}\text{C}\) | g C g\(^{-1}\) C yr\(^{-1}\) |
| \(Q_{10v}\) | Vegetation respiration Q10 | (no units) |
| \(K_H\) | Soil respiration rate at 0 \(^{\circ}\text{C}\) and moisture-saturated soil | g C g\(^{-1}\) C yr\(^{-1}\) |
| \(Q_{10s}\) | Soil respiration Q10 | (no units) |
| Moisture parameters | ||
| \(f\) | Fraction of soil water removable in 1 day | (no units) |
| \(K_{\text{WUE}}\) | VPD–WUE relationship | mg CO2 kPa g\(^{-1}\) H2O |
| \(W_c\) | Soil water holding capacity | cm (precipitation equivalent) |
| Tree physiological parameters | ||
| SLW | Density of leaves | g m\(^{-2}\) |
| \(C_{\text{frac}}\) | Fractional C content of leaves | g C g\(^{-1}\) |
| \(K_W\) | Turnover rate of plant wood C | g C g\(^{-1}\) C yr\(^{-1}\) |
One additional parameter, \(T_{\text{max}}\), the maximum temperature for photosynthesis, was calculated by assuming a symmetric function around the optimum photosynthetic temperature, \(T_{\text{opt}}\). That is, for any values of \(T_{\text{opt}}\) and \(T_{\text{min}}\), \(T_{\text{max}} = T_{\text{opt}} + (T_{\text{opt}} - T_{\text{min}})\). SIPNET, simplified PnET model; VPD, vapor pressure deficit; PAR, photosynthetically active radiation; WUE, water use efficiency; SLW, specific leaf weight.
Any reason to have this list? State variables indexed w/ 0 e.g.
Rates of decomposition, nitrification, denitrification, and methanogenesis are depend on temperature and soil moisture.
Used for photosynthesis (eq A9):
\[ f_{T}=\max\left(\frac{(T_{max} - T_{air})(T_{air} - T_{min})}{\left(\frac{(T_{max} - T_{min})}{2}\right)^2}, 0\right) \]
\[ f_{temp} = Q_{10}^{(T - 20)/10} \]
Might need to find a function with an optimal W\(_S\) != 1
\[ f_{W} = 1 - \frac{W_{S}}{W_{c}} \]
\[ d_{anaer} = \frac{W_{S}}{W_{c}} \]
\[ R_{nh4_fert} = \textrm{provided as a driver} \]
\[ R_{no3_fert} = \textrm{provided as a driver} \]
\[ R_{org_fert} = \textrm{provided as a driver} \]
\[ R_{dec} = K_{dec} \cdot f_{T} \cdot f_{W} \]
\[ R_{min} = R_{dec} \cdot N_{S} \cdot f_{T} \cdot f_{W} \]
\[ R_{nitr} = K_{nitr} \cdot NH_4 \cdot f_{T} \cdot f_{W} \]
\[ R_{denitr} = K_{denitr} \cdot NO_3 \cdot f_{T} \cdot f_{anaer} \]
Need to modify this for to account for diffusion, ebullition, and plant transport
\[ R_{meth} = K_{meth} \cdot C_S \cdot f_{anaer} \]
\[ R_{methox} = K_{methox} \cdot CH_4 \cdot f_{T} \cdot f_{W} \]
if a nitrogen fixing plant is present, N fixation is represented as a function of plant growth, needs to have a carbon cost to the plant
\[ R_{fix} = K_{fix} \cdot R_{growth} \]
TBD
\[ \frac{dC_S}{dt} = -R_{dec} \cdot C_S \]
\[ \frac{dN_S}{dt} = -R_{dec} \cdot N_S + R_{fix} + R_{updake} \]
\[ \frac{dNH_4}{dt} = R_{min} \cdot N_S + R_{nh4fert} - R_{nitr} \]
\[ \frac{dNO_3}{dt} = R_{nitr} + R_{nh4fert} - R_{denitr} \]
\[ \frac{dN_2O}{dt} = f_{N2O_{nitr}} \cdot R_{nitr} + f_{N2O_{denitr}} \cdot R_{denitr} \]
\[ \frac{dCH_4}{dt} = R_{meth} - R_{methox} \]
Braswell, Bobby H., William J. Sacks, Ernst Linder, and David S. Schimel. 2005. Estimating Diurnal to Annual Ecosystem Parameters by Synthesis of a Carbon Flux Model with Eddy Covariance Net Ecosystem Exchange Observations. Global Change Biology 11 (2): 335–55. https://doi.org/10.1111/j.1365-2486.2005.00897.x.
Manzoni, Stefano, and Amilcare Porporato. 2009. Soil Carbon and Nitrogen Mineralization: Theory and Models across Scales. Soil Biology and Biochemistry 41 (7): 1355–79. https://doi.org/10.1016/j.soilbio.2009.02.031.
Parton, W. J., E. A. Holland, S. J. Del Grosso, M. D. Hartman, R. E. Martin, A. R. Mosier, D. S. Ojima, and D. S. Schimel. 2001. Generalized Model for NOx and N2O Emissions from Soils. Journal of Geophysical Research: Atmospheres 106 (D15): 17403–19. https://doi.org/10.1029/2001JD900101.