Description of the LUE-EF model
This model was developed mainly based on the principles of the EC-LUE model ( 48). Specifically, the regulation of water on GPP is represented by the evaporative fraction (EF), taking advantage of the newly available EF products (49). In addition, two new modifiers of GPP were added to the original EC-LUE model. The first modifier considers the impact of cloudiness on GPP. The other modifier addresses the fertilization effect of increased CO2 concentration in the atmosphere.
The LUE-EF model can be expressed as follows:
\begin{equation} \mathbf{\text{GPP}}\mathbf{=}\mathbf{\text{PAR}}\mathbf{\times}\mathbf{\text{FPAR}}\mathbf{\times}\mathbf{F}_{\mathbf{\text{CI}}}\mathbf{\times}\mathbf{F}_{\mathbf{\text{CO}}\mathbf{2}}\mathbf{\times}\mathbf{\text{LUE}}_{\left(\mathbf{\text{MAX}}\right)}\mathbf{\times}\min\left(\mathbf{T}_{\mathbf{S}}\mathbf{,}\mathbf{W}_{\mathbf{S}}\right)\text{\ \ \ \ \ \ \ }\mathbf{(1)}\nonumber \\ \end{equation}
WherePAR is incident photosynthetic active radiation (MJ/m²) over a period of time; FPAR is the fraction of PAR absorbed by the vegetation; FCI is regulation of cloudiness on GPP; FCO2 is the regulation scalar of atmospheric CO2 concentration;LUE(MAX) is maximum light use efficiency;TS and WS are regulation scalars respectively for temperature and water stress on GPP, from which the minimum value is taken, following the Leibig law (9). The determination of models parameters was done as:
FPAR is in practice approximated by EVI (7), since photosynthetically active of vegetation is estimated as a ratio α of EVI , set to be α =1:
\begin{equation} \mathbf{\text{FPAR}}_{\mathbf{\text{EVI}}}=\mathbf{\alpha\ \times EVI}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\mathbf{2})\nonumber \\ \end{equation}
Most previous models underestimates of GPP on cloudy days mainly because photosynthesis can be increased by diffuse radiation under cloudy conditions (28). The regulating effect of cloud cover on GPP was expressed by cloudiness index (CI) as follow:
\begin{equation} \mathbf{F}_{\mathbf{\text{CI}}}=\mathbf{a}\times\mathbf{\text{CI}}+\mathbf{b}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\mathbf{3})\nonumber \\ \end{equation}
Where CI is the ratio of PAR to potential PAR (PPAR) (33). Using the FLUXNET2015 dataset, the coefficients were determined to be a (=2.9) and b (=1.2), using the parameter optimization for nonlinear least-squares (NLS) regression using the ‘nls’ function in R. The robustness of the NLS method was verified by Weibull function sensitivity analysis (4).
For calculating the influence of atmospheric CO2 on GPP, we employed the algorithm in the Frankfurt biosphere model (FBM) (46):
\begin{equation} \mathbf{F}_{\mathbf{\text{CO}}\mathbf{2}}=\mathbf{f}\left(\mathbf{\text{CO}}\mathbf{2},\mathbf{T}\right)=\frac{\mathbf{\text{CCL}}-\left(\mathbf{T}\right)}{\mathbf{\text{CCL}}+\mathbf{2}\left(\mathbf{T}\right)}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\mathbf{4})\nonumber \\ \end{equation}
where CCL is the internal CO2concentration of leaves, and it assumed to be 70% of atmospheric CO2 concentration. Δ(T) is the CO2 compensation point for gross photosynthesis and photorespiration at temperature T(oC) (47):
\begin{equation} \left(\mathbf{T}\right)={\mathbf{40}.\mathbf{6}\mathbf{e}}^{\frac{(\mathbf{9}.\mathbf{46}\times\left(\mathbf{T}-\mathbf{25}\right))}{(\mathbf{T}+\mathbf{273}.\mathbf{2})}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\mathbf{5})\nonumber \\ \end{equation}
Similar argument for eq (4), it always is <1.0 at all T and CO2.
The regulation scalar of water on GPP, WS , was expressed as the evaporative fraction (EF) of the total sensible and latent heat (8):
\begin{equation} \mathbf{W}_{\mathbf{S}}=\mathbf{\text{EF}}=\frac{\mathbf{\text{LE}}}{\mathbf{\text{LE}}+\mathbf{H}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\mathbf{6})\nonumber \\ \end{equation}
where LE is latent heat flux (W m-2), andH is sensible heat flux (W m-2).