## 2 Materials and Methods
### Satellite Data  
A summary of all satellite data used in this study is provided in Table 1. Orbiting Carbon Observatory-2 (OCO-2) SIF data were used to derive SIF metrics for the study. OCO-2  
Figure 1: Map of study area surrounding Natural Bridge State Park, KY, USA. Left shows overview of region within the Eastern United States with shaded area representing the map on the right. The study area lies within black bounding box shown in both maps. was launched in 2014, and it collects high spatial and spectral resolution measurements of solar-induced chlorophyll fluorescence (SIF) globally [68]. OCO-2 collects spectral data 24 times per second, producing eight cross-track spectra covering about 2 km \(\times\) 1.3 km spatially over a swath of approximately 10 km. Although the revisit period is 16 days, through 2 July 2015, each revisit alternated between glint and nadir mode, so the repeat time for nadir was 32 days. After 2 July 2015, the instrument alternated glint and nadir every orbit. While OCO-2 SIF data have high spectral and spatial resolution, individual footprints are noisy; thus, monthly averages across the study area are used in this study [23; 69; 70]. The locations of the SIF footprints in the study area are shown in Figure 2. SIF data were filtered for nadir observations, and footprints were classified as temperate deciduous forests according to the International Geosphere-Biosphere Programme (IGBP) landcover classification category. Instantaneous SIF (SIF\({}_{\rm i}\)) was calculated for each measurement by taking the average of instantaneous SIF measured at 757 nm (SIF\({}_{757}\)) and 771 nm (SIF\({}_{771}\)) times a factor of 1.5 based on the OCO-2 Data Product User's Guide and the previous literature (although the factor in previous studies ranged from 1.4 to 1.7) [20; 45; 69]. Daily average SIF (SIF\({}_{\rm d}\)) was calculated by employing the daily correction factor (DCF) [17; 20; 23; 45; 69]. The DCF is a normalization factor that approximately accounts for the length of day and variability of the solar zenith angle (SZA) using pure geometric incoming light scaling for the location in ten-minute time steps. SIF\({}_{\rm d}\) is calculated with the following equation:  
\[SIF_{d}=\frac{SIF_{i}}{cos(SZA(t_{m}))}\int_{I=t_{m}-12h}^{t=t_{m}+12h}cos(SZA( t))dt \tag{1}\]  
where SZA is the solar zenith angle from the OCO-2 dataset and t\({}_{\rm m}\) is the time of measurement [17; 20; 23; 45; 69; 70; 71; 72]. SIF\({}_{\rm i}\) values, collected at \(\sim\)1330 local time, should have a higher magnitude than SIF\({}_{\rm d}\) because SIF\({}_{\rm d}\) accounts for radiation changes over the daily cycle [23; 70]. Both SIF\({}_{\rm i}\) and SIF\({}_{\rm d}\) values were examined in this study because of the strong influence of changing radiation on SIF. The diurnal variability of SIF and its degree of influence at satellite scales are the focus of several studies [13; 46; 73; 74]. Figure 2: Satellite data locations. The Moderate Resolution Imaging Spectroradiometer (MODIS) gross primary production (GPP), normalized difference vegetation index (NDVI), and enhanced vegetation index (EVI) products were utilized as VI measurements of production. MODIS fraction of photosynthetically active radiation (fPAR) was used as an input to calculate absorbed photosynthetically active radiation (APAR) and \(\text{SIF}_{\text{y}}\) (Section 2.3). MODIS NDVI and EVI MODIS are products that have been used extensively because of their high correlation with phenological changes in vegetation, their relationship to GPP, and their ability to benchmark biophysical parameters and biomass changes (e.g., [50; 75; 76; 77; 78; 79]). The MODIS GPP product (MOD17) model is a semi-empirical GPP product derived using other MODIS products as parameters [77]. The MODIS GPP product is a widely used product that leverages a light use efficiency (LUE) model and generally has shown good performance estimating production [77; 80].