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).