## 4 Discussion
### SIF Retrievals with FIREFLY
#### 4.1.1 Indirect Retrievals from Solar and Oxygen Absorption Features
Since noise has a non-linear relationship with radiance (Figures 9 and 21), it is suggested that decisions about absorption features in an operational product would be made on a per-acquisition, or possibly even per-pixel basis. Additionally, Figure 21 shows that both indirect and direct retrievals can be expected to show an attenuation of noise influence with repeated independent samples, and confirms that indirect retrievals will have a much stronger response to the influence of random noise than direct retrievals (as suggested in Figure 3). Mitigating the effects of noise by increasing sample size is a potentially promising avenue to improve indirect SIF retrievals. Generally, in spectroscopy, equivalent benefits to sample size increase are achieved by amalgamation, either spectrally (spectral binning), or spatially (spatial aggregation). Spectral binning faces some challenges for its application to indirect SIF retrievals, particularly because the expected shape of SIF is quite nuanced (Figure 1). Since variation in the properties of the SIF spectral shape are of direct ecological interest, and because they can reveal vegetation composition, condition, and stress, it would not be ideal to have to assume aspects of SIF shape in order to implement spectral binning. Additionally, the relatively narrow FWHM, and high spectral sampling resolution (0.051 nm) of FIREFLY result in closely-packed absorption features that could be obscured by spectral binning, with a mean of 2.09 absorption features per nanometer across the spectral range of FIREFLY. The high spectral sampling resolution also makes FIREFLY effective at capturing local minima and maxima to increase the proportional depth of absorption features. Simulated spectra with half the spectral sampling resolution of FIREFLY (0.12 nm) showed absorption features losing a mean of 39.83% of their proportional depth, with some absorption features losing over 90% of their depth. Even this simple look at the benefits of the spectral sampling resolution of FIREFLY advises against spectral binning as a solution to shot noise. Spatial aggregation also encounters some interesting challenges when applied to SIF retrieval. Spatial aggregation is functionally equivalent to drawing additional random samples from combined populations with similar variances, to estimate the combined mean. However, when retrieving SIF at the spatial resolution of FIREFLY, especially in mixed land-cover and land-use areas, it is reasonable to expect that many ground targets will not contain SIF. In the context of a SIF retrieval, non-SIF-containing ground targets contain only noise. Therefore, including ground targets that do not contain SIF in a spatially aggregated SIF estimate could actually be harmful to the uncertainty of the retrieval. One approach could be to filter observations to only include those expected to contain SIF in spatial aggregations. Such filtering could be achieved for FIREFLY acquisitions by using vegetation indices such as NVDI (Figure 19). Obviously, the caveat to this approach is that it would introduce a guaranteed negative bias in the SIF retrievals, and result in a product that was actually an estimate of minimum SIF for each given area. Another consideration for the implementation of spatial aggregation in SIF retrievals is that the shape of the SIF signal is expected to vary even between adjacent SIF-containing pixels. In fact, some of the most desirable applications for SIF retrievals, such as monitoring of vegetation stress in agriculture or forestry, rely on the detection of such differences in SIF shape on a fine spatial-scale. Figure 22 demonstrates an indirect SIF retrieval process with FIREFLY. The selected absorption features are modelled for their expected noise (a), and combined to simulate spatial aggregation at different scales up to \(12\times 12\) FIREFLY pixels (b). Forward modelling of the expected noise using the information from these studies could help choose spatial aggregation factors in an operational product.