## 3 Results  
### Examine Time Series and Annual Cycles  
All productivity metrics (SIFi, SIFd, SIFy, GPP, NDVI, and EVI) and intermediate variables (fPAR and LAI) display seasonal cycles each year, with the highest values occurring in summer and the lowest values occurring in winter months, except for SIFy. (Figure 3). SIFi, SIFd, and GPP peak values occurred most often in May (2015, 2016, and 2017), except in 2018, when GPP still peaked in May but SIFi and SIFd peaked in June (Figure 3a-c). While the peak month for EVI tended to be in June rather than May (Figure 3), the trend of sharp peaks was similar to SIFi, SIFd, and GPP (Figure 3f). NDVI did not exhibit sharp peaks; rather, it remained at similar values for the summer months before dropping quickly to low levels during the winter months (Figure 3d). NDVI peaked in different months for each year of the analysis: July 2015, May 2016, August 2017, and June 2018 (Figure 3d). GPP, NDVI, and EVI values declined to low values mainly in January or February, after which they increased into the summer (Figure 3b,d,f). SIFi and SIFd, however, reached low values in the fall and then experienced a relatively small peak once each winter (Figure 3a,c). SIFy displays little indication of seasonality matching the other measures of productivity and large standard deviations in portions of the time series compared to SIFy values, i.e., SIF signal is composed largely of fPAR and the remaining information is noisy (Figure 3e). LAI and fPAR, the intermediate variables, display patterns of high values in the summer months and low values in the winter months, similar to the other MODIS products (Figure 3g,h). In January 2017, the monthly mean LAI and fPAR were higher than in December 2016 and February 2017, but with a particularly high standard deviation in these metrics. A time series of LST, T\({}_{\text{can}}\), T\({}_{\text{air}}\), and VPD highlights the seasonal variation of these environmental factors in the temperate deciduous forest in all cases (Figure 4). The T\({}_{\text{can}}\) and T\({}_{\text{air}}\) patterns were the same. The peak months of VPD matched the peak months of T\({}_{\text{can}}\) and T\({}_{\text{air}}\), but the patterns during the winter and spring were more distinct for VPD than for T\({}_{\text{can}}\) and T\({}_{\text{air}}\). Generally, there was a slower increase in VPD relative to the peak month of VPD than for LST, T\({}_{\text{can}}\), and T\({}_{\text{air}}\), which sharply rose after winter and remained closer to their peak for a few more months, and then declined more sharply in the fall. The monthly LST from MODIS reflected a similar pattern to T\({}_{\text{can}}\) and T\({}_{\text{air}}\), and, although the overall range of the temperature was similar, the values of LST were higher than those for T\({}_{\text{can}}\) and T\({}_{\text{air}}\). All the time series, including productivity metrics, intermediate variables, and environmental factors, were examined for anomalies and extreme values, but none were found for the study period. The annual average cycles (normalized) represented typical seasonal behavior and show that the peak values of productivity occur in June for all measures except \(\text{SIF}_{\text{y}}\), which peaks in May (Figure 5a). \(\text{SIF}_{\text{i}}\), \(\text{SIF}_{\text{d}}\), and \(\text{SIF}_{\text{y}}\) reach their minimum values in March; NDVI and EVI reach their minimum values in February, but GPP reaches its minimum value in January, a likely result of the minimum values of LAI and fPAR occurring in February and December, respectively (Figure 5a,b). \(\text{SIF}_{\text{i}}\) and \(\text{SIF}_{\text{d}}\) have the most similar trend. EVI trends similarly to \(\text{SIF}_{\text{i}}\) and \(\text{SIF}_{\text{d}}\) from the peak months to October and November. GPP trends with EVI and NDVI in the spring, although it increases more rapidly in March, peaks with everything except \(\text{SIF}_{\text{y}}\) in June, and declines more rapidly in August.