Modeling the Footprint and Equivalent Radiance Transfer Path Length for Tower-Based Hemispherical Observations of Chlorophyll Fluorescence

The measurement of solar-induced chlorophyll fluorescence (SIF) is a new tool for estimating gross primary production (GPP). Continuous tower-based spectral observations together with flux measurements are an efficient way of linking the SIF to the GPP. Compared to conical observations, hemispherical observations made with cosine-corrected foreoptic have a much larger field of view and can better match the footprint of the tower-based flux measurements. However, estimating the equivalent radiation transfer path length (ERTPL) for hemispherical observations is more complex than for conical observations and this is a key problem that needs to be addressed before accurate retrieval of SIF can be made. In this paper, we first modeled the footprint of hemispherical spectral measurements and found that, under convective conditions with light winds, 90% of the total radiation came from an FOV of width 72°, which in turn covered 75.68% of the source area of the flux measurements. In contrast, conical spectral observations covered only 1.93% of the flux footprint. Secondly, using theoretical considerations, we modeled the ERTPL of the hemispherical spectral observations made with cosine-corrected foreoptic and found that the ERTPL was approximately equal to twice the sensor height above the canopy. Finally, the modeled ERTPL was evaluated using a simulated dataset. The ERTPL calculated using the simulated data was about 1.89 times the sensor's height above the target surface, which was quite close to the results for the modeled ERTPL. Furthermore, the SIF retrieved from atmospherically corrected spectra using the modeled ERTPL fitted well with the reference values, giving a relative root mean square error of 18.22%. These results show that the modeled ERTPL was reasonable and that this method is applicable to tower-based hemispherical observations of SIF.