## 3 Results
### Forward Modelling  
The results from the characterization of FIREFLY with GLAMR, the integrating sphere, controlled acquisitions, and in-flight data were used to parameterize various forward models that related instrument specifications, and other potential sources of uncertainty, to downstream error in SIF retrievals. For the most part, these modelling efforts were conducted to contextualize specific discussion points, and their outcomes can be found in the subsequent sections. However, some general relationships between the types of sources of uncertainty and SIF retrieval error that were prevalent in the modelling efforts can be demonstrated here. These relationships are mostly intuitive, given the principles of SIF retrieval outlined in the method, and can be summarized as follows:  
1. Uniform influences on spectra intended for SIF retrieval will result in one-to-one error in both direct and indirect SIF retrievals (Figure 3).
2. Non-uniform sloped influences produce one-to-one error in direct retrievals (Figure 3).
3. All non-uniform influences produce amplified errors in indirect SIF retrievals (the magnitude of the error is higher than the sum of the influences on the relevant bands) (Figure 3).
4. Sloped influences produce positive errors in indirect SIF retrievals if the direction of the slope increases the valley radiance relative to the peak radiance, and negative errors if the peak is increased relative to the valley.
5. Sloped influences produce higher magnitude errors in indirect SIF retrievals when there is a steeper slope; when the spectral distance between the valley band and the peak band is greater; or when the absorption feature is shallower (the proportional depth is higher) (Figure 14).
6. Random influences produce one-to-one error in each band used for direct retrievals (Figure 3).  
Figure 13: The proportional response of FIREFLY bands to a range of wavelengths of light emitted by the GLAMR laser. Note the non-linear, categorical color-ramp.  
Random influences that are expected to be normally distributed (such as shot noise) produce bimodal error distributions in indirect SIF retrievals (Figure 15).  
Figure 14: **(a)** Modelled relationship between error in an indirect SIF retrieval, the gradient of a sloped influence, and the spectral distance between a valley and a peak for an absorption feature of 0.9 proportional depth. For context, the approximate steepness of the leaf reflectivity (yellow line), and the SIF function (red line) at 730 nm, based on Figure A, are shown. Spectral distance equivalent to 1, 2, and 3 band intervals of FIREFLY (blue lines) are shown. **(b)** Modelled relationship between error in an indirect SIF retrieval, the gradient of a sloped influence, and the proportional depth of an absorption feature.  
Figure 15: **(a)** Monte Carlo simulation of 10,000 pairs of random influences applied to a peak and a valley for indirect SIF retrieval, drawn from normal distributions (black lines) based on measured  
FIREFLY shot noise; (**b**) SIF retrieval error plotted against the sum of absolute influences applied to the valley and peak bands (black dots); and (**c**) distributions of sum of absolute influences and resulting errors in indirect SIF retrieval.