## 4 Discussion
### SIF Retrievals with FIREFLY
#### 4.1.2 Direct Retrievals
Forward modelling efforts to understand the influence of noise in potential FIREFLY SIF retrievals produced favorable results for a direct retrieval approach. Although it is a somewhat arbitrary standard, Figure 21d shows 95% confidence intervals of direct retrievals falling well within the magnitude of simulated SIF signals, even without the aid of repeated samples. Figure 22 demonstrates direct retrievals with propagated noise recovering an excellent estimation of a simulated SIF signal, albeit with some repeated sampling via simulated spatial aggregation. The oxygen features provide some of the best opportunities for direct retrievals. The key advantage of using oxygen features for SIF retrievals, as discussed in the previous subsection, is the expectation that there will be a comparatively high ratio of SIF to radiance, and therefore noise, in these regions. Additionally, the underlying SIF emission spectrum has peaks at 685 nm (FIREFLY band 296) and 740 nm (FIREFLY band 1372), close to the oxygen B feature at 688 nm (FIREFLY band 333), and the oxygen A feature at 761 nm (FIREFLY band 1774). Indeed, the observed radiances for the oxygen features from in-flight acquisitions, and the modelled expected noise, compared favorably to the expected levels of SIF (see Section 4.1.1). While oxygen features are an appealing subject for an initial operational SIF product, it is also hard to detect error in direct SIF retrievals from oxygen features without experimentation in a controlled environment; robust validation data; or least a simulation environment where error can be traced back to its specific source. Obscuration of the presence and provenance of error arises because oxygen features typically contain so little total energy that retrieved estimates of SIF more frequently fall within plausible bounds for SIF values by chance alone. This tendency prompts particular caution when spectra are being processed by techniques that scale, or put bounds on radiance, such as atmospheric and reflectivity models, and is the primary reason that this study focuses on propagating error explicitly, rather than working backwards from retrieval efforts to estimates of error. Direct retrievals with FIREFLY are further facilitated by this study with the characterization of dark current characterization, and resulting correction (Figure 8), and the characterization of response and linearity (Figure 7). Some uncertainty does remain in the fit of the response function, with the residuals having a standard deviation of 1.6 DN mW\({}^{-1}\) m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\), and the following relationship with wavelength:  
\[U=2\times 10^{-4}\cdot W-0.1005 \tag{7}\]  
where \(U\) is the uncertainty in DN and \(W\) is the wavelength in nanometers. Over the spectral range of FIREFLY, this is equivalent to a band radiance uncertainty of between 3.5% and 5.1%, meaning that a future characterization of band response with a larger sample size could be useful. Another essential characterization in this study was of the stray light behavior of FIREFLY. The FWHM characterization captures the influence of directly neighboring spectral regions on each band, but confirming that there were no far-field stray light effects in FIREFLY was also a particular concern. Far-field stray light would act much like a random influence (Figure 3), adding considerable uncertainty to SIF retrievals, while also being extremely difficult to detect in in-flight acquisitions. The investigation of FIREFLY with GLAMR revealed no evidence of far-field stray light (Figure 13), but it would be recommended to repeat far-field stray light checks periodically. There are several other instrument attributes that are displayed as potential sources of uncertainty in Figure 2, but were primarily investigated initially through in-flight acquisitions in this study. One example is spatial stray light, which would arise if the point spread function (PSF) of FIREFLY extended beyond the boundaries of each spatial pixel on the detector array.