## 2 The 3-PG Model
### Data Inputs  
The main input parameters required are site factors and species-specific data of the species of interest (Table 1). The site factors include latitude, maximum available soil water (\(ASW_{x}\): mm), soil texture (sandy, sandy loam, clay, or clay loam), and fertility rating (\(FR\)). Species-specific parameter values are adjusted for each species. If the parameter values for a species do not exist, parameterization of the new site-specific parameter is necessary. Another input is meteorological variables, including mean air temperature (\(T_{a}\): \(\mathrm{\SIUnitSymbolC}\)), mean solar radiation (\(SR\): MJ m\({}^{-2}\) day\({}^{-1}\)), total precipitation (\(R\): mm), frost days (\(d_{F}\): days per month), and vapor pressure deficit (\(VPD\): mbar). If \(VPD\) is not available, it can be calculated from the maximum and minimum temperatures (\(T_{x}\) and \(T_{n}\): \(\mathrm{\SIUnitSymbolC}\)) as half the difference between the saturated vapor pressure at \(T_{x}\) and \(T_{n}\). The meteorological inputs can be actual monthly data or long-term monthly averages. \begin{table}
\begin{tabular}{l c c} \hline
**Description of parameter** & **Symbol** & **Units** \\ \hline
**Biomass partitioning and turnover** & & \\ _Allometric relationships \& partitioning_ & \\ Ratio of foliage:stem partitioning at \(B=2\) cm & \(p_{2}\) & – \\ Ratio of foliage:stem partitioning at \(B=20\) cm & \(p_{20}\) & – \\ Constant in stem mass \(v\) diam. relationship & \(a_{S}\) & – \\ Power in stem mass \(v\) diam. relationship & \(n_{S}\) & – \\ Maximum fraction of NPP to roots & \({}_{Rx}\) & – \\ Minimum fraction of NPP to roots & \({}_{Rn}\) & – \\ _Litterfall \& root turnover_ & \\ Litterfall rate at \(t=0\) & \({}_{F0}\) & month\({}^{-1}\) \\ Litterfall rate for mature stands & \({}_{F1}\) & month\({}^{-1}\) \\ Age at which litterfall rate has median value & \({}_{F}\) & month \\ Average monthly root turnover rate & \({}_{R}\) & month\({}^{-1}\) \\
**Growth modifiers** & & \\ _Temperature modifier_ & & \\ Minimum temperature for growth & \(T_{n}\) & \(\mathrm{\SIUnitSymbolC}\) \\ Optimum temperature for growth & \(T_{opt}\) & \(\mathrm{\SIUnitSymbolC}\) \\ Maximum temperature for growth & \(T_{x}\) & \(\mathrm{\SIUnitSymbolC}\) \\ _Frost modifier_ & & \\ Number of days production lost for each frost day & \(kF\) & days \\ \hline \end{tabular}
\end{table} 
Table 1: List of all parameters of species specific with descriptions, symbols and unit. **Table 1.**_Cont._  
**Description of parameter**  
**Symbol**  
**Units**  
_Fertility modifiers_  
Value of \(m\) when \(FR=0\)  
Value of \(f_{N}\) when \(FR=0\)  
Power of (1-_FR_) in \(f_{N}\)  
_VPD modifier_  
Defines stomatal response to VPD  
_Soil water modifier_  
Moisture ratio deficit which gives \(f_{\theta}=0.5\)  
Power of moisture ratio deficit in \(f_{\theta}\)  
_Age modifier_  
Maximum stand age used to computer relative age  
Power of relative age in \(f_{age}\)  
Relative age to give \(f_{age}=0.5\)  
**Conductance**  
Canopy LAI for maximum canopy conductance  
Canopy boundary layer conductance  
**Canopy structure and processes**  
_Specific leaf area_  
Specific leaf area at stand age 0  
Specific leaf area for mature aged stands  
Age at which specific leaf area = \(\
icefrac{{1}}{{2}}(\sigma_{0}+\sigma_{1})\)  
_Rainfall interception_  
Maximum fraction of rainfall intercepted by canopy  
LAI for maximum rainfall interception  
_Light interception, production and respiration_  
Extinction coefficient for PAR absorption by canopy  
Age at full canopy cover  
Maximum canopy quantum efficiency  
Ratio NPP/GPP  
**Wood and stand properties**  
_Basic density_  
Minimum basic density--for young trees  
Maximum basic density--for older trees  
Age at which \(\rho=\
icefrac{{1}}{{2}}\) density of old and young trees  
**Conversion factors**  
Intercept of net radiation and solar radiation relationship  
Slope of net radiation and solar radiation relationship  
Molecular weight of dry matter  
Conversion of solar radiation to PAR