## 4 Discussion
### The Application of Re (DR) Model and Calibration of Longwave Radiation Sensor  
The PAR balance equation can be obtained from EMGPP (Equation (1)) by replacing GPP with isoprene (one dominant species of BVOCs), or converted from the EMBE (Section 5.4 in [55]):  
\[\text{PAR}=\text{C}_{1}e^{-\text{a}}\text{1}^{\text{ISOm}}\times\cos(\text{Z })+\text{C}_{2}e^{-\text{kWm}}\times\cos(\text{Z})+\text{C}_{3}e^{-\text{S/ Q}}+\text{C}_{0} \tag{4}\]The computed PAR at the top of the atmosphere (TOA) is C\({}_{1}\)+ C\({}_{2}\)+ C\({}_{3}\) + \(\mid\) C\({}_{0}\) \(\mid\) and is equal to the PAR at the TOA measured by the satellites and airplanes (PAR\({}_{\rm TOA}\)). This method can be used to calibrate the PAR sensor by the ratio of PAR\({}_{\rm TOA}\)/(C\({}_{1}\)+ C\({}_{2}\)+ C\({}_{3}\) + \(\mid\) C\({}_{0}\) \(\mid\)).  
Similarly, the Re (DR) model (Equation (3)) also exhibited an energy balance at the canopy level. Based on the Beer-Lambert law, C\({}_{1}\) represents the longwave radiation at the TOA associated with the individual atmospheric GLPs, and C\({}_{0}\) represents that emitted from the surface (i.e., vegetation). The processes and their associated energy are divided and quantified by separate terms in empirical equations. So, C\({}_{1}\) + \(\mid\)C\({}_{0}\) \(\mid\) = 357.22 and 368.06 W m\({}^{-2}\) is the estimated total longwave radiation contributed by the atmosphere and the surface for 2013 and 2014 night (using half-hour flux and other corresponding data in this section, \(n\) = 4412, 4445, respectively). The detailed meaning of C\({}_{1}\) + \(\mid\)C\({}_{0}\) \(\mid\) is described in studies [55; 78]. It should be noted that the longwave radiation of the GLPs at the TOA is isotropy. According to the canopy temperature measured at the flux tower (23.6 m), forest emissivity = 0.95 [79] and Stefan-Boltzmann law, the estimated longwave radiation emitted by vegetation canopy were 379.87 and 379.91 W m\({}^{-2}\) with relative biases of 5.96% and 3.12% for 2013 and 2014 night, respectively. This estimated longwave radiation can be used as a reference at TOA, and the ratios of 0.940 and 0.969 can be selected as calibration factors. Compared this estimated total longwave radiation to that emitted from the canopy measured at the tower (41.6 m) (398.19 and 399.29 W m\({}^{-2}\)), their relative biases were 10.28% and 7.82%, respectively.  
The attenuating rates of CO\({}_{2}\) and photochemical terms using Equation (3) were 1.39% and 77.60% for 2013, respectively, and 1.42% and 77.40% for 2014, indicating the longwave radiation absorption by CO\({}_{2}\) was much lower than that of atmospheric components, and can be neglected, considering its low concentration compared with other GLPs. These were in good agreement with the studies [80; 81].  
The annual averages of downward longwave radiation at the canopy level were computed using Equation (3), and a longwave radiation that was remitted by the atmospheric GLPs after they absorb the longwave radiation emitted from the canopy, \(\mid\) C\({}_{0}\) \(\mid\) \(\times\) (1 \(-\) e\({}^{-\rm kWm}\)\(\times\) cos(Z)) were added. Then, their annual averages were 352.30 and 358.55 Wm\({}^{-2}\) for the 2013 and 2014 night, respectively, the corresponding values measured at 41.6 m were 362.31 and 362.01 Wm\({}^{-2}\), respectively. Their relative biases were 0.29% and 1.22% for 2013 and 2014, respectively.  
In a summary, the Re (DR) model showed a good performance for the estimations of the downward and upward longwave radiation. It was a new piece of evidence to demonstrate the reasonability and potential application of the Re (DR) model.