## 4 Results and Discussion
### Relationship between EC GPP, PAW, VPD, and API
The effect of the increase in relative humidity, and decrease in VPD, a full month before the first rains is particularly interesting. This can play the role of an anticipatory mechanism for vegetation that enables it to begin photosynthesis rapidly at, or shortly before, the onset of rain [80]. The second GPP peak (smaller shaded area in Figure 6) can be explained by the second, smaller, rainfall event of that year, which was not sufficient enough to replenish PAW to previous levels. However, it created enough reduction in VPD that stimulated the vegetation to resume C assimilation (Figure 6). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Response = EC GPP** & \multicolumn{4}{c}{**Statistics**} \\ \hline
**Demokeya** & **RMSE** & **R2** & \(n\) & **BIC** \\ \hline API & 1.61 & 0.28 & 97 & 382.04 \\ VPD & 1.22 & 0.59 & 95 & 321.88 \\ PAW & 1.19 & 0.62 & 89 & 298.27 \\ VPD + API & 1.22 & 0.59 & 95 & 326.36 \\ API + PAW & 1.19 & 0.62 & 89 & 301.82 \\ PAW + VPD & 1.12 & 0.66 & 89 & 291.87 \\ \hline
**Wankama Fallow** & **RMSE** & **R2** & \(n\) & **BIC** \\ \hline API & 1.54 & 0.33 & 159 & 605.44 \\ VPD & 0.96 & 0.74 & 157 & 448.70 \\ PAW & 0.91 & 0.76 & 132 & 365.07 \\ VPD + API & 0.94 & 0.75 & 156 & 445.64 \\ API + PAW & 0.91 & 0.77 & 131 & 366.92 \\ PAW + VPD & 0.77 & 0.83 & 129 & 318.23 \\ \hline
**Dahra** & **RMSE** & **R2** & \(n\) & **BIC** \\ \hline API & 2.91 & 0.38 & 161 & 815.93 \\ PAW & 2.51 & 0.59 & 154 & 736.34 \\ VPD & 1.99 & 0.75 & 146 & 631.43 \\ API + PAW & 2.28 & 0.64 & 147 & 680.49 \\ VPD + API & 1.92 & 0.77 & 146 & 624.80 \\ VPD + PAW & 1.88 & 0.77 & 139 & 590.21 \\ \hline
**All Sites** & **RMSE** & **R2** & \(n\) & **BIC** \\ \hline API & 2.37 & 0.33 & 417 & 1888.05 \\ PAW & 2.27 & 0.36 & 375 & 1780.69 \\ VPD & 2.21 & 0.43 & 398 & 1779.50 \\ VPD + API & 2.22 & 0.44 & 390 & 1697.36 \\ API + PAW & 2.18 & 0.45 & 367 & 1652.43 \\ PAW + VPD & 2.06 & 0.47 & 364 & 1624.53 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the regression analysis between eddy covariance gross primary productivity (EC GPP) and three field-measured water stress controls: plant-available water (PAW), vapor pressure deficit (VPD) and antecedent precipitation index (API) for each site. Also shown are the root-mean-square error (RMSE) and Bayesian information criterion (BIC) for each model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Greening Phase**} & \multicolumn{3}{c}{**Browning Phase**} \\
**Response = EC GPP** & \multicolumn{3}{c}{\(n\) = 106**} & \multicolumn{3}{c}{\(n\) = 75} \\ \cline{2-7}  & \(\mathbf{r_{s}}\) & \(\mathbf{t_{s}}\) & \(\mathbf{p}\) & \(\mathbf{r_{s}}\) & \(\mathbf{t_{s}}\) & \(\mathbf{p}\) \\ \hline PAW & 0.44 & 4.950 & \textless{}0.01 & 0.16 & 0.156 & 0.18 \\ VPD & \(-0.24\) & \(-2.525\) & 0.01 & \(-0.52\) & \(-0.523\) & \textless{}0.01 \\ EVI & 0.61 & 7.776 & \textless{}0.05 & 0.60 & 6.289 & \textless{}0.01 \\ LST & \(-0.28\) & \(-2.957\) & \textless{}0.05 & \(-0.34\) & \(-3.074\) & \textless{}0.01 \\ BAND 7 & 0.32 & 3.426 & \textless{}0.05 & 0.22 & 1.920 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of the partial correlation analysis between EC GPP, field, and Earth observation variables during the greening and browning phases. \(r_{s}\) is Spearman’s Rho, \(t_{s}\) is the test statistic, and \(p\) is the significance of the test statistic. Figure 4: Top: Comparison of VPD and EC GPP, with coloring that indicates corresponding values of PAW for each site. Values to the left of the vertical dotted line (GPP \textless{}1\) g C m\({}^{-2}\) d\({}^{-1}\)) and above the horizontal dotted line (VPD \textgreater{}2 kPa) represent the dry season. Bottom: Relationship between the VPD and PAW per corresponding EC GPP values during the dry and growing seasons. The solid black line is the regression line with a 95% confidence interval in light gray shading.