## 4 Discussion
### SIF Retrievals with FIREFLY
#### 4.1.1 Indirect Retrievals from Solar and Oxygen Absorption Features
In the example in Figure 22 it can be seen that the reductions in confidence interval are minimal beyond \(6\times 6\) aggregation. There is also separation between groups of absorption features visible in Figure 22b,as a small gap in the vertical distribution of confidence intervals at lower spatial aggregation factors, suggesting that this process could be refined to optimize the set of absorption features to those that would respond best to spatial aggregation. Proceeding with a \(6\times 6\) spatial aggregation based on Figure 22b, Monte Carlo simulation was used (36 samples to represent a \(6\times 6\) spatial aggregation) to introduce expected noise into the absorption  
Figure 16:0 (**a**) Expected variation in valleys (red lines) and peaks (blue lines) relative to a simulated SIF signal (green line); (**b**) expected confidence intervals for valleys (red dots) and peaks (blue dots) at different spatial aggregation factors (functionally, sample sizes); (**c**) example simulated SIF functions (thin green lines) and their sum (thick green line); (**d**) indirect SIF retrievals (red x) fitted to a SIF signal (red line). The true SIF value in each band (green x) is also shown. Note that the vertical axis matches the range of (**e**) for the sake of comparing the fitted functions, and therefore does not show all of the residuals; and (**e**) direct SIF retrievals from valleys (red x) fitted to a SIF signal (red line). The true SIF value in each band (green x) is also shown. features. Then, for each of these simulated samples, a SIF signal with random values for the scaling factors and 740 nm peak (see Section 2.2, and see Appendix A.2 for more details) was simulated (see Figure 22c for examples) and added to the radiance values for the noise-containing valleys and peaks. To complete the process as it would occur in an operational retrieval, estimates of SIF were derived from each simulated absorption feature, and used to fit the SIF simulation function. The independent variables for the fit were the two scaling factors, and the 740 nm peak, with the sum of the squared residuals as the response variable. However, due to the amplification of uncertainty when random noise in applied to indirect retrievals, the resulting fit was extremely poor, and the spatial aggregation factor had to be iteratively increased to \(60\times 60\) (360 pixels) before a reasonable approximation of the true SIF function was achieved (Figure 22d, sum of squared residuals = 39.612 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\)). For comparison, a \(6\times 6\) spatial aggregation of direct SIF retrievals from just the valley bands produced an excellent fit (Figure 22e, sum of squared residuals = 1.357 mW m\({}^{-2}\) sr\({}^{-1}\) nm\({}^{-1}\)). Although further work should be conducted to refine the understanding of noise in FIREFLY, and to formalize the required retrieval standard for particular applications, these findings suggest that indirect SIF retrievals could only reach acceptable levels of uncertainty with a large sample size. Even though this degree of spatial aggregation would reduce the granularity of FIREFLY observations substantially, in turn reducing its usefulness for certain applications such as precision agriculture, in-flight FIREFLY acquisitions could still make indirect SIF retrievals that would be comparable to most satellite retrievals of SIF, with the advantage of controlling the time and conditions of overpasses to investigate many important influences on SIF. The alternative avenue to increasing sample size for indirect retrievals would be to make repeated observations of targets over time. While this would be theoretically possible with consecutive overpasses, it would be more effective to mount FIREFLY on a static platform, such as the tower-based platforms that have shown success for SIF retrievals in other studies [42; 43]. The instrument would also be suitable for other forms of mobile platform that could still facilitate high-repeat acquisitions, such as overhead trans, or unmanned autonomous vehicles [23].