## 5 Conclusions  
Application of PAR balance at the canopy level, 3-factor and 2-factor Re empirical models to describe respirations at different situations were developed at a subtropical coniferous plantation in China. Reasonable Re simulations were obtained in different time scales (hourly, daily, monthly, and annual) during 2013-2016. Then, hourly, daily, monthly, and annual sums of NEPs were calculated using the combined empirical models of GPP and Re, and the simulated NEPs also reasonably agreed with the measurements (within 2 \(\sigma_{\rm obs}\)). The Re and NEP empirical models captured most variation patterns of Re and NEP in 2013-2016 and have better performances for annual sums of Re and NEP In general. As an example, in 4 years, the simulated Re values overestimated the observations by about 30% for mean hourly and annual sums. Similarly, the computed NEPs also overestimated the observations by about 22% and 27% in different time scales for using the 3-factor and 2-factor models, respectively, combined using previously developed 3-factor and 2-factor GPP empirical models. Empirical model simulations of RE, NEP, and GPP can be used to fill the gaps of RE, NEP, and GPP caused by the problems in CO\({}_{2}\) flux measurements. The Re (DR) model has another application for the calibration of longwave radiation sensors.  
The PAR energy balance well-displayed a \"universal\" principle for expressing the energy relationships/main processes associated with Re and NEP, as well as GPP and BVOCs. It can simplify the complex processes of the CO\({}_{2}\) in the atmosphere and biosphere and estimate our concerned key CO\({}_{2}\) parameters. The PAR energy balance method exhibited some advantages, revealed some phenomena and mechanisms associating with Re and GPP that were in line with other extensively used models' studies. It helps us to understand the complicated and multiple interactions/processes fully and deeply among solar radiation, atmosphere, biosphere, and land. Extensive studies deserved to be carried out at this site and other sites in the future.  
Conceptualization, J.B.; Methodology, J.B.; Data curation, F.Y., H.W. and M.X.; Writing--original draft, J.B.; Writing--review & editing, F.Y., H.W. and M.X. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program grant number [No. 2021 YFE0118000], ESA-MOST China Dragon Cooperation, Dragon 4 and 5 projects grant number [ID 32771, ID 59013] and National Natural Science Foundation of China grant number [No. 41275137].  
Not applicable.  
The datasets [GENERATED/ANALYZED] for this study can be found in a Big Earth Data Platform for Three Poles, [[http://poles.tpdc.ac.cn/zh-hans/](http://poles.tpdc.ac.cn/zh-hans/)]([http://poles.tpdc.ac.cn/zh-hans/](http://poles.tpdc.ac.cn/zh-hans/)) (accessed on 1 August 2023).  
The authors thank all reviewers for their beneficial comments and suggestions which contributed to improvement of the manuscript. The authors thank all the people for their great assistance including [PERSON] at the Department of Earth System Science, University of California, Irvine, USA, [PERSON] at 2B Technologies, Inc. Boulder, USA, [PERSON] at National Center for Atmospheric Research, Boulder, USA, [PERSON] at Tufts University, USA; [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] at Qianyanzhou Experimental Station of Red Soil and Hilly Land, CAS, [PERSON], [PERSON] at the Institute of Atmospheric Physics, CAS. The authors thank the Qianyanzhou Experimental Station for providing meteorological and solar radiation data from January to May 2013 and carbon flux data in 2013-2016.  
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.