## 5 Conclusions  
The initial simulations conducted using the existing Fluspect model without the FQE inversion code could not efficiently reproduce the fluorescence under natural conditions, and the fluorescence was always overestimated on both the upward and downward sides of the leaves. The peak values of the simulated fluorescence were higher than those of the observations.  
These results are due to the RTM inversion model retrieving only six plant parameters. These parameters can show the chlorophyll content, but the FQE parameters are set to their default values, depending on the status of the photosystems. The fluorescence spectrum cannot be simulated efficiently with default values, since photosystems vary with the solar light under natural conditions.  
The setting of the parameters to default will lead to overestimation or underestimation of fluorescence by the model simulation. To verify this, FQE II and I were set as 0.01 and 0.002, respectively. With these values, the results of the simulated fluorescence for leaves with different chlorophyll contents were higher than those of the measured data.  
There was an obvious decrease in these overestimated values after being retrieved by the FQE inversion code. This indicates that the model accurately simulated the fluorescence under natural conditions upon the addition of the inversion code. This is also confirmed by the validation for each wavelength and two peaks. The different percentages of upward fluorescence for the high-chlorophyll-content leaves between the simulation results and the measured data in the first peak reduced from over 150% to 20%. For the low-chlorophyll-content leaves, the differential percentage of the upward fluorescence decreased by 20%. For the second peak of the fluorescence in both the high- and low-chlorophyll-content leaves, the percentage difference decreased to 20% for both the upward and downward sides. The primary limitation of this study is that the significance of FQE is not yet fully understood. The major hurdle for measuring FQE is that the signals of PS II and PS I overlap but are distinguishable. The FQE values also depend on the weather, and retrieved values of FQE need to be tested and verified.  
This study demonstrated that the Fluspect model can simulate fluorescence under natural conditions; however, the initial FQE values must be set to very accurate levels to achieve satisfactorily accurate simulations. Depending on the weather conditions and the features of the plant species, PS II and PS I will vary. After the addition of the FQE inversion code, the RTM inversion model gives more accurate FQE values. In future studies, variations in FQE I and FQE II with illumination and temperature under natural conditions should be simulated, which will require realistic reference values.  
Conceptualization, [PERSON] and J.Z.; coding, T.Z.; writing--original draft preparation, T.Z.; supervision, J.Z.; writing--reviewing and editing, [PERSON] Both authors have read and agreed to the published version of the manuscript.  
The fieldwork was funded by the Netherlands Organization for Scientific Research (NWO) in the frame of the Earth and Life Sciences (ALW) division, project ALW-GO/13-32. The fieldwork was further supported by FLEX-EU campaign funded by the European Space Agency (ESA) (contract no. 4000107143/12/NIL/FF/I). The research time of [PERSON] had been funded by the National Key R&D Program of China (2017 YFC0406004) and the National Natural Science Foundation of China (NSFC) (41271004).  
Published dataset with the leaf fluorescence data: [[https://doi.org/10.17026/dans-xym-hhq](https://doi.org/10.17026/dans-xym-hhq)]([https://doi.org/10.17026/dans-xym-hhq](https://doi.org/10.17026/dans-xym-hhq)).  
The data utilized herein were collected by [PERSON] at Forschungszentrum Julich. We send our sincere thanks to [PERSON] and [PERSON] of the University of Twente for their cooperation with us on data analysis.  
The authors declare no competing non-financial/financial interests.