## Materials and Methods
### Data Preprocessing  
In 2014, we had 15,135 instantaneous radiance/irradiance observations, which covered the spectral range of 678.6-775.6 nm. It is important to note that energy received by our sensor (downwelling) contains contribution from emitted SIF and reflected solar radiation. However, they can be separated at the Fraunhofer lines and telluric oxygen absorption lines of the solar spectrum--hereafter referred to as absorption lines [47]. We used SIF emission at the O\({}_{2}\)-A band which is centered at approximately 761 nm in this study (referred to as SIF\({}_{760}\) hereafter). The Spectral Fitting Method (SFM) based on polynomial functions [48; 49] was used to extract SIF emission at 760 nm. In this study, SFM was set so that both reflected solar radiation and SIF emission can be expressed by Taylor polynomials with the terms of second order in each absorption line. See the study by [PERSON] et al. [49] for the detailed steps in the application of the SFM method. These instantaneous SIF\({}_{760}\) measurements were first averaged into hourly SIF measurements. Further, daily daytime SIF emission was calculated as the mean of hourly SIF between 07:00 a.m. and 5:00 p.m. local time. Days with more than 4 hourly SIF observations missed were excluded from the further analysis. Monthly GOME-2 data were linearly interpolated into a daily time step. To reduce the effect of scene illumination, original RGB digital numbers (DN) obtained from the PhenoCam in the region of interest (ROI) were extracted and converted into RGB Chromatic Coordinates [50; 51] which are defined as:  
\[\text{GCC}=\ \frac{G}{(R+G+B)} \tag{2}\]  
The green chromatic coordinate (GCC) was used to determine plant phenological phase [52; 53]. We used photos taken during daytime period (06:00 a.m.-6:00 p.m. local time). Furthermore, we used the 90 th percentile of the GCC (GCC90) within a 3-day moving window to remove uncertainties caused by weather conditions such as very cloudy and very sunny days [15; 54]. After producing 8-day NDVI time series from the MODIS reflectance product, we removed NDVI values with poor quality or filled values according to their quality assurance flags. NDVI values contaminated by clouds or snow, or acquired under conditions of low levels of radiation were also removed from MODIS NDVI time series (NDVI\({}_{\text{MODIS}}\)). All the smoothed time series were linearly interpolated into daily time scale. We then used the moving average approach to reduce noise in these time series. Specifically, values that deviated from the mean in a 5-day moving window by more than 25% are excluded and missing values were filled by interpolated values of adjacent \"clean\" points in time series using the inverse distance weighting method. In this study, we used a nonlinear least squares regression to fit the double sigmoid functions [4] to these smoothed daily time series:  
\[g(t)=a+\ \frac{b}{\left[1+e^{c-dt}\right]*\left[1+e^{e-ft}\right]} \tag{3}\]  
where \(g(t)\) represents the selected daily time series; \(t\) is time (in days); and \(a\)-\(f\) are fit parameters: \(a\) and \(b\) decide the minimum and maximum limits of the function, respectively; \(c\) and \(d\) control the timing and slope of the increasing part of the time series which corresponds to the leaf development phase, respectively; and \(e\) and \(f\) control the timing and slope of the decreasing part of the time series that corresponds to the leaf senescence phase, respectively. By tracking rate of local extrema in the rate of change of curvature [55; 56], we can have 3 spring metrics (S1, S2 and S3) and 3 autumn metrics (A1, A2 and A3) from the fitted time series (Figure 1). S1, S2 and S3 represent the start of spring, middle of spring and end of spring, respectively; and A1, A2 and A3 stand for the start of autumn, middle of autumn and end of autumn, respectively. However, previous studies [57; 58] showed that S2 and A2 derived from curvature change rates may be sensitive to dynamic of understory, canopy coverage and structure.