## 2 Instrumentation and Methods
### Empirical Model of Gross Primary Production (EMGPP)  
Based on PAR energy balance at the canopy level, an empirical model of gross primary production (EMGPP) considering 3-factor and 2-factor situations was developed. It was a further application of an empirical model simulating BVOC emission fluxes (EMBEs) that was previously developed for this conifer plantation, a temperate forest and a subtropical bamboo forest in China [27]. This EMBE model can reasonably estimate BVOC emissions for the above forests in China as assessed by different evaluations. At the Qianyanzhou conifer plantation, the measured mean and maximum emission fluxes in 2013 were 0.137 and 1.610 mg m\({}^{-2}\)h\({}^{-1}\) for isoprene, respectively, and 0.474 and 2.711 mg m\({}^{-2}\)h\({}^{-1}\) for monoterenes, respectively. Monoterpene emission fluxes dominated the total BVOC emission fluxes with a contribution of 71.6% of BVOC emission fluxes, displaying clear diurnal variations (higher in the afternoon and lower in the early morning and late evening) and seasonal variations (higher in summer and lower in winter) [35]. Therefore, considering the assuming similarities between the processes and PAR utilization on BVOC emissions (e.g., isoprene production) [68] and GPP, further application of EMBE was investigated, i.e., similar PAR transfer in the atmosphere (absorption, scattering), and different PAR attenuation by BVOCs or CO\({}_{2}\) in the atmosphere, i.e., only one difference in the description of BVOCs and CO\({}_{2}\) term (or GPP term). More specifically, an empirical model development of GPP is reported as follows. The PAR energy balance on a horizontal plane above the canopy level is calculated using three terms (the GPP term and photochemical and scattering terms, representingCO\({}_{2}\) attenuation, GLP attenuation (except CO\({}_{2}\)) and scattering of PAR, respectively) and described as:  
\[\mathrm{PAR}=\mathrm{A}_{1}e^{-0.1\mathrm{aGPPpm}}\times\mathrm{cos}(\mathrm{Z}) +\mathrm{A}_{2}e^{-\mathrm{kWm}}\times\mathrm{cos}(\mathrm{Z})+\mathrm{A}_{3}e^ {-\mathrm{S/Q}}+\mathrm{A}_{0} \tag{1}\]  
Then an empirical model of GPP was developed following procedures similar to those previously used to describe the BVOC emissions at this conifer plantation as well as other forests in China [27; 69; 70], i.e., a further application of the empirical model of BVOC emissions (EMBE):  
\[e^{-0.1\mathrm{aGPPpm}}\times\mathrm{cos}(\mathrm{Z})=\mathrm{B}_{1}\mathrm{ PAR}+\mathrm{B}_{2}e^{-\mathrm{kWm}}\times\mathrm{cos}(\mathrm{Z})+\mathrm{B}_{3}e^{- \mathrm{S/Q}}+\mathrm{B}_{0} \tag{2}\]  
where in the GPP term, \(e^{-0.1\mathrm{aGPPpm}}\), a is the attenuation coefficient for CO\({}_{2}\) in the atmosphere (set to 1 mg CO\({}_{2}\)\({}^{-1}\) m\({}^{2}\) s\({}^{-1}\)), m is the optical thickness of the air mass in the center of the averaging window, GPP is the hourly gross primary production in the sampling period (mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)), t (hour, converted from 0.5 h in CO\({}_{2}\) flux) is the sampling period and 0.1 is a normalizing coefficient for GPP and yields \(e^{-0.1\mathrm{aGPPpm}}\times\mathrm{cos}(\mathrm{Z})<1\). According to the Beer-Lambert law, the GPP term was expressed as \(e^{-0.1\mathrm{aGPPpm}}\). In the photochemical term, \(e^{-\mathrm{kWm}}\), W = 0.021E \(\times\) 60, where E is the mean water vapor pressure (hPa) at ground level during the sampling period and k is the average absorption coefficient of water vapor in the wavelength range of 0.70-2.845 \(\upmu\)m. In the scattering term, \(e^{-\mathrm{S/Q}},S/\mathrm{Q}\) is a scattering factor that objectively describes the relative quantities of GLPs in the atmosphere, including clouds, haze and rain [58]. Cos(Z) = 1/m and Z is the solar zenith angle (degree). A\({}_{\mathrm{i}}\) and B\({}_{\mathrm{i}}\) are coefficients that are determined empirically by using an hourly observational dataset of solar radiation, water vapor pressure and GPP.