## 2 Instrumentation and Methods
### Empirical Model of Respiration (EMRe)  
Based on PAR balance at canopy level, an empirical model of BVOC emissions (EMBE) was developed for some representative forests (a subtropical coniferous forest, a subtropical bamboo forest, and a temperate forest) in China [55]. Further application of PAR balance principle and EMBE, an empirical model of GPP (EMGPP) was developed in Qianyanzhou subtropical forest with reasonable performance [45], considering the similarities of PAR use in the processes of BVOC emissions and GPP, in which CO\({}_{2}\) (GPP) was replaced by BVOCs in the EMGPP. Furthermore, these experiences were used in empirical model developments of respiration and NEP in this study. Briefly, EMGPP (Equation (1)) considers the following three main processes: PAR attenuation by CO\({}_{2}\) in the atmosphere (GPP term); PAR attenuation by atmospheric gases, liquids, and particles (GLPs, except CO\({}_{2}\), photochemical term); PAR scattering by GLPs (scattering term [45; 55]). At a canopy level, these three processes contribute to PAR balance. After adjustment, the EMGPP is described as follows:  
\[e^{-0.1\mathrm{a}\mathrm{GPP}\mathrm{tm}}\,\times\,\mathrm{cos}(Z)=\mathrm{A }_{1}\mathrm{PAR}+\mathrm{A}_{2}e^{-kWm}\,\times\,\mathrm{cos}(Z)+\mathrm{A}_{ 3}e^{-S/Q}+\mathrm{A}_{0} \tag{1}\]  
where a = 1 mgCO\({}_{2}\)\({}^{-1}\) m\({}^{2}\) s\({}^{-1}\) is an attenuation coefficient for CO\({}_{2}\) in the atmosphere, m is the optical thickness, GPP is the hourly GPP in the sampling period (mgCO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\)), sampling period t = 1 h, and 0.1 is a normalizing coefficient. W = 0.021E \(\times\) 60, E is the average water vapor pressure (hPa) at the ground in the sampling time period, and k is the mean absorption coefficient of water vapor in 0.70-2.845 \(\upmu\)m. Scattering factor (S/Q) represents the atmospheric GLP amounts [47]. Z is the solar zenith angle (degree), and \(\mathrm{Cos}(Z)\) = 1/m. Coefficients A\({}_{\mathrm{i}}\) are determined using observational dataset (solar radiation, water vapor pressure, GPP, etc.). It is known that GPP = Re + NEP, and Re is ecosystem respiration. Then, it is necessary to calculate ecosystem respiration. Firstly, an empirical model of daytime respiration (mgCO\({}_{2}\) m\({}^{-2}\) s\({}^{-1}\), Equation (2), 3-factor) (under conditions of light) was developed and named as Re (LR) method. \[e^{-0.1\mathrm{b}\mathrm{Re}\mathrm{tm}}\,\times\,\mathrm{cos}(Z)=\mathrm{B}_ {1}\mathrm{PAR}+\mathrm{B}_{2}e^{-kWm}\,\times\,\mathrm{cos}(Z)+\mathrm{B}_{ 3}e^{-S/Q}+\mathrm{B}_{0} \tag{2}\]  
where, we set b = 1, m = 1 and \(\mathrm{cos}(Z)\) = 1 for daytime estimation. Coefficients B\({}_{\mathrm{i}}\) (i = 1, 2, 3) and B\({}_{0}\) were determined by analyzing observational data (data criteria, Section 2.3) in the daytime (Re, solar radiation, water vapor). \(e^{-0.1\mathrm{b}\mathrm{Re}\mathrm{tm}}\,\times\,\mathrm{cos}(Z)>\) 1 was used in Re model development. The 3-factor and 2-factor EMRe models were developed for two atmospheric situations (S/Q \(<\) 0.5 and S/Q \(\geq\) 0.5, representing low atmospheric GLPs, high solar radiation and air temperature, and high GLPs, low solar radiation and air temperature, respectively), which were similar to EMGPP and EMBE models [45; 55]. In view of the fact there are no measurement of global direct or diffuse radiation at some stations in China, the 3-factor Re empirical model was adjusted to the 2-factor Re model, i.e., the scattering term was removed in Equation (2). Secondly, nighttime Re, dark respiration was developed by further application of EMGPP (Equation (1)) or Re (LR) (Equation (2)) from daytime to nighttime and named the Re (DR) method. \[E^{-0.1\mathrm{bReturn}}\times\cos(\mathrm{Z})=\mathrm{C_{1}}e^{-\mathrm{kWm}} \times\cos(\mathrm{Z})+\mathrm{C_{0}} \tag{3}\]  
Similarly, we set b = 1, m = 1 and \(\cos(\mathrm{Z})=1\) for nighttime Re simulation. Coefficients C\({}_{1}\) and C\({}_{0}\) were obtained by analyzing nighttime measurements (Re, water vapor).