# Monitoring Spatial and Temporal Variabilities of Gross Primary Production Using MAIAC MODIS Data
## 2 Materials and Methods
### Statistical Analysis  
The performance of the RSVIs for the predicting weekly and monthly variabilities of GPP was tested using GPP and RSVI time series, and linear regressions were fitted for each site and index, with GPP as the response variable and the RSVIs as the predictors. Only time series with 60 or more time-steps were considered for both the monthly and weekly analyses. We extracted the variance explained (\(R^{2}\)) from each regression, so we had four models for each site (testing the four RSVIs). We deseasonalised the weekly (monthly) time series of GPP and RSVI by subtracting the average and dividing by the standard deviation for each week (month) and site for each observation (i.e., we calculated the standardised anomalies of the time series) to determine if the relationship between weekly (monthly) GPP and RSVI was preserved when the annual seasonality of the time series was removed. We then performed the same analysis using the standardised anomalies to produce eight additional measures of goodness of fit (i.e., 16 per site in total). We tested the potential effect of snow cover on our results by repeating these analyses using times series without winter values (i.e., weeks 1-12 and 46-52 were removed for the weekly analyses, and December, January, February, and March were removed for the monthly analyses). Weeks were calculated from 1 January. Our results would suggest that the RSVIs were able to track the temporal variability of GPP independently of their seasonal cycle if the models using the standardised anomalies performed as well as those using data with the seasonal component. If the performance using anomalies was dramatically lower than the performance using data with the seasonal component, our results would identify the RSVIs that could track the seasonal component of GPP well, but not its seasonal anomalies (deviations from the mean). We further identified the factors that determined the goodness of fit of the relationship between GPP and RSVIs for each site, using data both with and without the seasonal component (i.e., standardised anomalies). We first calculated several potentially influencing variables for each site such as climatic variables (mean annual temperature (MAT), mean annual precipitation (MAP), mean annual VPD), the seasonalities and interannual variabilities of GPP and the RSVIs, and the variances of GPP and the RSVIs explained by the seasonal cycle (calculated from a linear model such as GPP or RSVI as a function of month (as a factor of 12 levels)). Seasonality (intra-annual variability) was calculated as the proportional variability (PV) index [30; 31] of the averages of a variable for the twelve months of the year. PV is an index of variability, ranging from 0 (no variability) to 1 (very high variability), that assesses the proportional variability of a data set by calculating all pair-wise comparisons between the values of a variable. This index overcomes some of the mathematical issues of the coefficient of variation [30]. The interannual variabilities of GPP and the RSVIs were calculated for each site as the average of the interannual PV for each month. We then identified the factors that were correlated with the goodness of fit of the relationship between GPP and an RSVI (with and without seasonality) using linear models (e.g., NDVI-GPP performance for each site as a function of site GPP seasonality + NDVI seasonality + MAT + MAP + VPD). We calculated (i) the average annual GPP, (ii) the average annual values of the RSVIs across months, and (iii) the average peak-season values of the RSVIs for each site to determine how well the RSVIs explained the spatial variability of GPP. We only used years with data for all 12 months in which both GPP and the RSVIs were recorded. We compared the results using the averages and the peak-season values of the RSVIs to identify artefacts associated with snow, standing water, standing dead vegetation, and other potential confounding factors. Only sites with five or more years of data were used to calculate the annual averages.