## 3 Methods  
We first analyzed the temporal and spatial dynamics of GPP, SIF, APAR\({}_{\text{N}}\)DVI and APAR\({}_{\text{E}VI}\) for the 2009 drought event and compared the drought responses of vegetation proxies for the main vegetation types in Victoria. We applied monthly relative anomalies and the normalized anomaly of all the aforementioned variables to assess drought stress-related signals. The relative anomaly (\(\Delta\)) and normalized anomaly (\(\delta\)) can be calculated as below:  
\[\Delta(i,k)=\left(\text{P}\left(i,k\right)-\text{P}\left(i\right)_{\text{ mean}}\right)\,/\,\text{P}\left(i\right)_{\text{\it{m}}} \tag{3}\]  
\[\delta(i,k)=\left(\text{P}\left(i,k\right)-\text{P}\left(i\right)_{\text{ mean}}\right)\,/\,\text{P}\left(i\right)_{\text{\it{std}}} \tag{4}\]  
where \(\text{P}\left(i,k\right)\) stands for different variables (e.g., GPP, SIF, APAR and other meteorological variables) for month \(i\) of year \(k\), and the multiyear mean \(\text{P}\left(i\right)_{\text{\it{m}}}\) and standard deviation \(\text{P}\left(i\right)_{\text{\it{std}}}\) are established from 2007 to 2013 for all data sets.  
To further explore the feasibility of SIF in interpreting drought effects on vegetation productivity in Victoria, we estimated the response of vegetation to drought-related meteorology anomalies in a relatively long period (2007-2013). Because the sensitivity of vegetation productivity to high temperature is variable in different seasons [50], we first analyzed the relationship between the temperature from stations and GPP over 1982-2013 and obtained the annual-temperature-sensitive period when GPP decreased with increasing temperature. Based on the determined annual-temperature-sensitive period, we applied the autoregressive with exogenous terms (ARx) model [48; 51] to estimate the sensitivities of GPP and vegetation proxies to meteorology anomalies and examined the correlations of the GPP anomaly with the anomalies of vegetation proxies. The ARx model is an auto-regressive model with exogenous inputs [51]. We used the GPP as an example to illustrate the ARx model:  
\[\delta\text{GPP}_{\text{t}}=\text{a}^{\text{T}}\times\delta\text{T}_{\text{t }}+\text{a}^{\text{W}}\times\delta\text{W}_{\text{t}}+\text{a}^{\text{P}} \times\delta\text{P}_{\text{t}}+\text{a}^{\text{M}}\times\delta\text{GPP}_{ \text{t}-1}+\varepsilon \tag{5}\]  
where \(\delta\text{GPP}_{\text{t}}\), \(\delta\text{T}_{\text{t}}\), \(\delta\text{W}_{\text{t}}\) and \(\delta\text{P}_{\text{t}}\) represent the normalized anomalies of GPP, ECMWF temperature, water availability and PAR, respectively, at month t; \(\delta\text{GPP}_{\text{t}-1}\) is the normalized GPP anomaly at month t-1. The one-month-lagged normalized GPP anomaly was used to investigate potential memory effects. Time series were normalized to assure comparability of the coefficients. \(\text{a}^{\text{T}}\), \(\text{a}^{\text{W}}\) and \(\text{a}^{\text{P}}\) represent the estimated sensitivity of GPP changes to the respective meteorology-forcing factors while \(\text{a}^{\text{M}}\) is related to memory effects and \(\varepsilon\) is the residual error term. The coefficient of determination (R\({}^{2}\)) value of model result and the significance of the model's coefficients were used to assess the quality of the fitting. We used the partial least squares method (PLS) to solve the parameters in Equation (5) to avoid multicollinearity of the forcing factors.  
Note that all the analyses were made for general Victoria region, crop land and evergreen broadleaf forest land to consider potential different behaviors of different vegetation types during drought conditions.  
Figure 2: Spatial pattern of temperature and rainfall stations in Victoria.