## 4 Discussion
### SIF Retrievals with FIREFLY
#### 4.1.2 Direct Retrievals  
A direct retrieval of SIF involves removing all the non-SIF components of the radiance observed in a band or bands, with the remaining energy treated as the SIF signal (see Section 2.1). Exactly which components need to be accounted for and removed, and the supplementary requirements for estimating these components, varies greatly depending on instrument properties, and by spectral region. The influences at work in various spectral regions have already been discussed in the context of indirect retrievals (Section 4.1.1 and Figure 16), but for direct retrievals the requirements are even more stringent, since every estimation of a component of a radiance measurement can contribute uncertainty to the retrieval of a SIF signal that is only a small proportion of the total radiance in any given band (Figures 1 and 21). The focus of this study was characterizing the attributes of the FIREFLY instrument itself that would influence SIF retrievals, but for the following discussions it is important to bear in mind that an operational product utilizing direct SIF retrievals would also have to account for irradiance conditions, atmospheric conditions, and target reflectivity shapes, which could contribute additional uncertainties of various types (see Figure 3). However, FIREFLY could benefit from coincident data from the other instruments mounted on G-LiHT when it comes to estimating non-SIF components for direct retrievals. For example, the downwelling radiometer could give an estimate of irradiance conditions, and the lidar could provide an accurate path-length to each spatial pixel on the ground (Figure 18). In SIF retrieval efforts with other instruments, the challenges of using the full spectral range have been met by the use of spectral fitting methods. By utilizing explicit estimates of particular spectral components, such as atmospheric water vapor, and reflectivity profiles, or by deriving their influence implicitly through principle component analysis, or singular vector decomposition, other studies have demonstrated the ability to retrieve SIF from the amalgamated information from many absorption features [19; 28; 29]. Such approaches could be a promising avenue for SIF retrievals from FIREFLY, especially considering the wealth and variety of coincident data available from G-LiHT instruments, and will the subject of future studies. In terms of FIREFLY attributes characterized in this study, it is important for direct retrievals that a thorough characterization of FWHM was performed (Figure 5), since knowledge of FWHM is essential to predict the interaction of irradiance conditions with target reflectivity profiles. There is some uncertainty remaining in the FWHM estimation which could encourage some further refinement in the characterization. The standard deviation of the residuals of the fit of the observations to the FWHM function (Figure 5) is equivalent to a relatively large potential uncertainty in SIF estimates. Although a future characterization effort with a larger number of repetitions could prove beneficial, the FWHM function in its current form seems to explain cross-track patterning observed in test SIF retrievals in in-flight acquisitions. Moreover, there is a clear heteroscedasticity in the residuals that may be inflating the apparent variation, while actually being an artefact of characterizing the spatial and spectral variation in FWHM separately. The high spectral sampling resolution of FIREFLY (0.051 nm) is helpful for direct SIF retrievals since it can either provide a higher sample size to mitigate noise (2160 total bands), or allow very specific filtering by spectral region. The FWHM of FIREFLY, combined with the spectral sampling resolution, does lead to considerable overlap in the spectral sampling of adjacent bands. However, in spectroscopy, this is not typically treated as a problem to the assumptions of independent sampling required by some statistical analyses.