## 2 Instrumentation and Methods
### Applications of Empirical Models of GPP, Re, and NEP  
On the basis of the PAR balance principle, the empirical models (EMGPP, Equation (1); EMRe, Equation (2); EMNEP, combined Equations (1) and (2), NEP = GPP\(-\)Re) in Qianyanzhou subtropical coniferous forest have been developed using the hourly observational data (fluxes measured by the Qianyanzhou station, PAR, S/Q, and meteorological parameters measured by [PERSON]'s group) from 22 May 2013-31 December 2014. These empirical models were then used to calculate GPP, Re, and NEP from 1 January 2013-31 December 2016, also using hourly solar radiation and meteorological parameters measured by [PERSON]'s group. Their simulations were compared and evaluated in different ways (from hourly to daily, monthly, and annual values in different years, 2013-2016) and showed reasonable performances (the statistical metrics, including coefficient of determination (R\({}^{2}\)), average and maximum of the absolute relative bias, normalized mean square error (NMSE), standard deviations of calculated and observed fluxes, mean absolute deviations (MAD), and root mean square errors (RMSE)) of GPP, Re, and NEP (including the hourly, daily, monthly, and annual values), and reproducibility of their seasonal and annual variations from 2013-2016 [40; 41]. Considering the limitation of direct or diffuse solar radiation at stations in China, 2-factor empirical models of GPP, Re, and NEP (i.e., without scattering term) were also developed for their practical applications. Generally, the simulations of GPP, Re, and NEP were in reasonable agreement with the measurements (e.g., 20-50% for CO\({}_{2}\) flux measurements) and popular used models (e.g., standard deviations of calculated and observed fluxes, RMSE). The RMSE simulated using the Yale Interactive Terrestrial Biosphere (YIB) model was 3.21 gC m\({}^{-2}\) day\({}^{-1}\) (57 evergreen coniferous forests), which is in good line with that of 3.55 and 3.44 gC m\({}^{-2}\) day\({}^{-1}\) from 2013-2016, which was calculated using 3-factor and 2-factor EMGPP [40]. Annual GPP, RE, and NEP estimates overestimated the observations from 2013-2016 by 31% and 29% for GPP, 30% for Re, and 22.0% and 27.0% for NEP, respectively, using the 3-factor and 2-factor models [40; 41]. In more detail, the empirical models (EMGPP, EMRe, and EMNEP) considered the two atmospheric conditions (described by a scattering factor, S/Q), S/Q! 0.5 and S/Q! 0.5, representing low or high gas, liquid, and particle (GLP) loads in the atmosphere, corresponding to a clean atmosphere (low amounts of clouds, aerosols, etc., along with strong solar radiation and high air temperature) or misty atmosphere (a large number of clouds, aerosols, etc., as well as low solar radiation and air temperature), respectively, and combined them together for the simulations of GPP, RE, and NEP under realistic atmospheric conditions (S/Q = 0-1). \[e^{-0.1\mathrm{aGFPtm}}\,\times\,\cos\,(\mathrm{Z})=\mathrm{A_{1}PAR}+ \mathrm{A_{2}}e^{-\mathrm{kWm}}\,\times\,\cos\,(\mathrm{Z})+\mathrm{A_{3}}e^{ -\mathrm{S/Q}}+\mathrm{A_{0}} \tag{1}\]  
\[e^{-0.1\mathrm{bReturn}}\,\times\,\cos\,(\mathrm{Z})=\mathrm{B_{1}PAR}+ \mathrm{B_{2}}e^{-\mathrm{kWm}}\,\times\,\cos\,(\mathrm{Z})+\mathrm{B_{3}}e^{ -\mathrm{S/Q}}+\mathrm{B_{0}} \tag{2}\]  
where in the GPP term (\(e^{-0.1\mathrm{aGFPtm}}\)), the attenuation coefficient for CO\({}_{2}\) in the atmosphere a is 1 mg CO\({}_{2}\)\({}^{-1}\) m\({}^{2}\) s\({}^{-1}\)), m is the optical air mass, GPP (mg CO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)) is the hourly GPP in the sampling period (t, h), and 0.1 is a normalizing coefficient for GPP. In the photochemical term (\(e^{-\mathrm{kWm}}\)), W = 0.021E \(\times\) 60, E is the average water vapor pressure (hPa) at ground during the sampling period and k is the mean absorption coefficient of water vapor (0.70-2.845 um). In the scattering term (\(e^{-\mathrm{S/Q}}\)), S/Q describes the relative amounts of atmospheric GLPs. b = 1 mg CO\({}_{2}\)\({}^{-1}\) m\({}^{2}\) s\({}^{-1}\).