## 5 Conclusions  
Using tower-based spectral measurements in coordination with flux measurements is an efficient way of linking SIF to the photosynthesis status. For the observation of up-welling irradiance, both the conical and the hemispherical configurations have their own advantages, but the footprint of hemispherical observation is much wider than the conical observation, and would surely better match with the footprint of flux measurement. However, the effect of atmospheric radiation transfer for hemispherical observation is more complex. In this paper, we developed and evaluated the models of the footprint and ERTPL of hemispherical spectral observations using a simulated dataset and evaluated the performance of the atmospheric correction by using the modeled ERTPL for simulated tower-based SIF retrieval. First, we developed a method of modeling the footprint of hemispherical spectral observations and found that 90% of the total radiation comes from an FOV of width 72\({}^{\circ}\) (the corresponding radius of the footprint is about 3.1 times the sensor's height above the target surface). For a typical instrument installation height of 20 m above the target surface, and given convective conditions with light winds (0.74 m/s), 90% of the radiation contributing to the hemispherical spectral observations originates from an area that covers 75.68% of the source area of the flux measurements. For conical spectral observations, in contrast, the footprint covers just 1.93% of the flux source area. These results indicate that, when made in conjunction with flux measurements, hemispherical spectral measurements are superior to conical measurements. Second, we built a model to estimate the ERTPL of hemispherical spectral observations. Assuming the surface is isotropic and the transmittance is linearly related to the RTPL, the ERTPL of hemispherical spectral observations with cosine-corrected foreoptic can be estimated as being equal to twice of the sensor's height above the target surface. The modeled ERTPL was evaluated using simulations made by SCOPE and MODTRAN 5. Taking the directional characteristics of up-welling radiance at top of canopy and the non-linear relationship between atmospheric transmittance and RTPL into account, the calculated ERTPL based on the simulations was 1.89H, which is close to the modeled value of 2H. These results indicate that the ERTPL model described in this paper is suitable for making atmospheric corrections to tower-based spectral observations. Furthermore, the SIF retrieval results based on the simulations also indicate that the modeled ERTPL of 2H is acceptable for use in atmospheric correction. The SIF was retrieved by the 3 FLD method using simulated spectra at the top of the canopy, and spectra observed at a height of 20 m without atmospheric correction and with atmospheric corrections using an RTPL of H and 2H. The SIF values retrieved using spectra atmospherically corrected using an RTPL of 2H matched the reference SIF values well--the RRMSE was 18.22%. For the SIF retrieved from spectra that were atmospherically corrected using an RTPL of H and from spectra without atmospheric correction, the RRMSEs were 133.71% and 293.79%, respectively, indicating totally unreliable results. Therefore, the ERTPL model proposed in this paper is helpful for SIF retrieval based on hemispherical spectral measurements. In conclusion, considering the match between the footprints of spectral and flux measurements, the hemispherical configuration for the observation of up-welling irradiance has advantage, and the RETPL for hemispherical observation can be estimated as twice of the sensor's height above the surface. **Acknowledgments:** The authors gratefully acknowledge the financial support provided by the Key Deployment Projects of Chinese Academy of Sciences (KFZD-SW-310), and the National Natural Science Foundation of China (41671349).