# Adjustments to SIF Aid the Interpretation of Drought Responses at the Caatinga of Northeast Brazil
## 2 Materials and Methods
### Statistics and Software  
All available data discussed above were used in tests for the period from February 2007 to December 2017, with the exception of GOME-2 SIF\({}_{R}\). While red SIF was available for the period from February 2007 until December 2015, only the period from February 2007 to December 2013 was analyzed. Considering that SIF\({}_{R}\) is also produced from MetOP-A data and therefore, it also subject to the above mentioned degradation problem, we decided to include a period similar to that of MetOP-A SIF\({}_{FR}\) data to maintain correspondence of SIF at both wavelengths. Specific tested periods will also be declared at the Results section to aid interpretation. The overall study design and data application is illustrated in Figure 2.  
To evaluate the seasonality and the long-term tendencies of all data we carried out time-series decomposition with Locally Estimated Scatterplot Smoothing (LOESS) [67; 68]. This statistical technique also known as STL decomposition, separates the data into three components: a seasonal component, a trend component and the remainder which can be generally interpreted as random variation or white noise [68]. To test the coherence between SIF and SVIs, we carried out several ecoregion-specific correlation analysis. These were made using data detrended and deseasonalized through time-series decomposition [67; 68]. Hence, all correlation tests have been applied to the remainders of time-series. Furthermore, we chose to use Kendall's rank correlation test since it doesn't assume parametric data distribution and is more conservative than the popular Pearson's Product Moment Correlation Coefficient [69]. To study the effects of environmental variables over SIF and other predictors we employed Linear Mixed Models (LMM), fitting one holistic model to all ecoregions (per response variable) and a series of simpler ecoregion-specific models, parameterized according to our data and to model quality limitations inferred from model diagnostics. The various response variables used in model selection are presented in previous sections and listed in Table 1. The selected holistic model was defined with each given response variable as a Gaussian function of \"Surface Temperature\", \"Soil Moisture\" (and interaction \begin{table}
\begin{tabular}{l l l} \hline \hline
**Variable Label** & **Description** & **Data Source** \\ \hline SIF\({}_{FR}\) & Sun-induced chlorophyll fluorescence at the far-red wavelength peak. & GOME-2 MetOP-A + MetOP-B \\ SIF\({}_{R/FR}\) & Sun-induced chlorophyll fluorescence at the red wavelength peak. & GOME-2 MetOP-A \\ SIF\({}_{R/FR}\) & The ratio between SIF at both wavelength peaks. & GOME-2 MetOP-A \\ \(d\)SIF\({}_{FR}\) & Daily average of SIF\({}_{R}\) based on a clear sky PAR proxy. & GOME-2 MetOP-A + MetOP-B \\ SIF\({}_{R}\)SZA & The quotient of SIF\({}_{R}\) by the cosine of the Sun’s zenith angle (SZA). & GOME-2 MetOP-A + MetOP-B and MODIS \\ SIF\({}_{FR}\)-Yield & The quotient of SIF\({}_{FR}\) by NDVI—nolog to “real fluorescence”. & GOME-2 MetOP-A + MetOP-B and MODIS \\ SIF\({}_{FR}\)-Prod & The product of SIF\({}_{FR}\) by NDVI—well correlated to GPP. & GOME-2 MetOP-A + MetOP-B and MODIS \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of SIF response variables used in this study. For detailed description of these variables, their source and calculation, please refer to the Introduction section and to the Sun-Induced Fluorescence sub-section of Materials and Methods. between these continuous variables) and \"Ecoregion\". Random factors were \"Month\" individually and \"Month\" nested into \"Year\" to ensure adequate error structure [70; 71]. Ecoregion-specific models were parameterized differently due to limitations imposed by a smaller number of observations than were available for holistic models.