# Adjustments to SIF Aid the Interpretation of Drought Responses at the Caatinga of Northeast Brazil
## 3 Results
### SIF and Climate: Linear Mixed Model Analysis
Results suggest that vegetation at the Northern Sertaneja Depression (Figure 6a) and eastern ecoregions Borborema Plateau (Figure 6a), Minor Southern Sertaneja Depression (Figure 6h) and Raso da Catarina (Figure 6g) were the most sensitive to environmental influences. Temperature had significant negative effects on \(\text{SIF}_{FR}\) measured from the vegetation of most ecoregions. Ecoregion-specific models using \(\text{SIF}_{FR}\)-Yield as their response variable showed a decrease in the significance of temperature and, an increase in temperature and soil moisture interaction (\"T : SM\") fixed effect slopes (Figure 6), in relation to models using \(\text{SIF}_{FR}\). Comparing the land cover classification results (Figure 3) and the correspondent ecoregion's LMM slopes (Figure 6) we noticed that sensitivity to environmental variables increased in areas where land cover had smaller percentages of forest formations. To test this, we added relative cover percentage values of the different forest physiognonies (closed, open, deciduous and evergreen) and performed Kendall rank correlation tests between total forest cover percentage and the correspondent fixed effect slopes of ecoregion-specific \(\text{SIF}_{FR}\) and \(\text{SIF}_{FR}\)-Yield models. These tests showed that drought sensitivity (fixed effect slope declivity) was negatively correlated to forest physiognonies cover percentages (Table 4). \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Response Var.** & **Fixed Effect** & \(\mathbf{\tau}\) & \(\mathbf{p}\) & \\ \hline \multirow{2}{*}{\(\text{SIF}_{FR}\)} & Soil Moisture (SM) & \(-0.56\) & \(0.045\) & * \\  & Temperature (T) & \(-0.61\) & \(0.025\) & * \\  & SM : T & \(-0.67\) & \(0.013\) & * \\ \hline \multirow{2}{*}{\(\text{SIF}_{FR}\)-Yield} & Soil Moisture (SM) & \(-0.50\) & \(0.075\) & \multirow{2}{*}{\({}^{\prime}\)} \\  & Temperature (T) & \(-0.44\) & \(0.119\) & \\  & SM : T & \(-0.72\) & \(0.006\) & ** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Kendall rank correlation tests between the GlobCover 2009 forest physiognonies cover and Linear Mixed Model fixed effect slopes, per ecoregion. \(\tau\) (tau) is the correlation rank and \(p\) is the probability value of [PERSON]’s test. \(\text{SIF}_{FR}\) is Sun-induced Fluorescence at the far-red wavelength peak and \(\text{SIF}_{FR}\)-Yield is the quotient of Sun-induced Fluorescence at the far-red wavelength peak by NDVI; \(n=9\) per fixed effect. Significance levels are marked according to the following legend: ** for \(p<0.01\), * for \(p<0.05\) and \({}^{\prime}\) for \(p<0.1\). \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Metric** & \(\text{SIF}_{FR}\) & \(\mathbf{d}\text{SIF}_{FR}\) & \(\text{SIF}_{FR}\)-Prod & \(\text{SIF}_{FR}\)-SZA & \(\text{SIF}_{FR}\)-Yield & \(\text{SIF}_{R}\) & \(\text{SIF}_{FR}\) \\ \hline R\({}^{2}\) (marginal) & \(0.678\) & \(0.648\) & \(0.745\) & \(0.705\) & \(0.478\) & \(0.539\) & \(0.012\) \\ R\({}^{2}\) (conditional) & \(0.867\) & \(0.867\) & \(0.905\) & \(0.862\) & \(0.735\) & \(0.783\) & \(0.035\) \\ RMSE & \(0.364\) & \(0.365\) & \(0.306\) & \(0.158\) & \(0.504\) & \(0.443\) & \(0.978\) \\ REML & \(1340\) & \(1366\) & \(982\) & \(-588\) & \(2035\) & \(1165\) & \(2145\) \\ BIC & \(1446\) & \(1472\) & \(1088\) & \(-482\) & \(2141\) & \(1265\) & \(2244\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Linear Mixed Models’ Goodness of Fit—R\({}^{2}\) is the coefficient of determination; RMSE is Root Mean Square Error, REML is Restricted Maximum Likelihood and BIC is Bayesian Information Criterion.