## 2 Materials and Methods
### Remotely Sensed Measurements
#### 2.3.1 Calculating iAPAR  
We used gap-filled and smoothed daily plot-scale mean NDVI (Figure 2) to calculate iAPAR for each plot on the date of clipping (Figure 3). NDVI data for 2014-2015 came from a Landsat-MODIS fusion (LMF) product created using the STARFM algorithm [33; 34]. NDVI data for 2016-2022 were derived from the Harmonized Landsat Sentinel (HLS) satellite time series [35]. In both cases, we applied a gap-filling and smoothing procedure using linear interpolation followed by 3 rd-order Savitzky-Golay smoothing to arrive at a daily estimate of NDVI at a spatial resolution of 30 m (more details for LMF can be found in [33; 34] and for HLS in [36].  
We converted NDVI to APAR using methods described by [PERSON] et al. (2018) [12]. Briefly, we first converted the daily NDVI time series to fPAR using an exponential function between fPAR and NDVI ([PERSON] et al., 2007 [3]; Equations (1) and (2)).  
\[fPAR=\left(\frac{\text{SR}}{SR_{max}}\right)-\frac{SR_{min}}{\left(SR_{max}-SR_ {min}\right)} \tag{1}\]  
\[SR=\frac{1+NDVI}{1-NDVI} \tag{2}\]  
where SR is the simple ratio index (see [3], and Equation (2)), \(SR_{min}\) = 1.11, based on an average CPER-wide minimum NDVI of 0.05, and \(SR_{max}\) = 11.62, based on [PERSON] et al. (2007) [3].  
To calculate APAR, we multiplied the daily fPAR values by the amount of incoming daily photosynthetically active radiation (PAR) measured at the CPER meteorological station (Equation (3)). We then derived cumulative APAR (iAPAR) by integrating from the start of the season to the quadrat clip date and between the base APAR value and the APAR time series (Equation (4)) (Figure 3). We include the base APAR value in the iAPAR calculation to minimize errors associated with the start of the growing season calculation (see below) and heterogeneity associated with bare soil reflectance values ([PERSON] et al. 2018 [12]).  
\[APAR=fPAR\times PAR \tag{3}\] \[iAPAR=\int_{t=\text{start of season}}^{t=\text{clip date}}(APAR_{t}-APAR_{ base})^{dt} \tag{4}\]  
Figure 2: Example NDVI curves of three grazing management strategies. All pastures are located on a Loamy Plains ecosite. (**A**) NDVI curves for an ungrazed pasture compared to a pasture that was grazed season-long. (**B**) NDVI curves for an ungrazed pasture and a pasture that was pulse-grazed.  
To estimate the start of the season (SOS) for each year and plot, we used the NDVI time series. We calculated the SOS in several steps. First, an NDVI threshold (Threshold 1) was calculated as the 40 th percentile of the NDVI values between 1 April and 19 July (the typical window for SOS). Next, we identified the earliest date after 1 February that NDVI first rose above Threshold 1. We then took a 25-day moving average of the first differential of NDVI values up until the date Threshold 1 was reached. Working backward from this date, we identified the SOS as the latest date that NDVI was below the 35 th percentile of these values. This approach helped avoid \"false stars\" in the growing season that come with small peaks in NDVI observed prior to the sustained increase in NDVI associated with the growing season. Data processing is shown graphically in Figure 4 flowchart.  
Figure 3: Example APAR curves for four grazing management strategies. All pastures are located on a Loamy Plains ecosite in 2019. (**A**) Pasture ungrazed for the entire growing season. (**B**) Pasture experiencing season-long grazing (**C**) Pasture experiencing pulse grazing, (**D**) Pasture considered ungrazed since grazing occurred after the biomass clipping date.