# Grapevine Phenology in Four Portuguese Wine Regions: Modeling and Predictions
## 3 Results
### Development of Generalized Models  
As previously mentioned, and according to Table S1, an individual model was estimated for each grape variety, phenological stage, and wine region. For the sake of succinctness, the parameters \(d\) and  
Figure 3: Simulation of the veraison of cv. _Touriga Nacional_ from the Lisboa wine region. (**a**) sigmoid model response function. (**b**) Chronogram of the observed and predicted veraison dates (Julian calendar day of the year, DOY) from 1990 to 2018 (cf. legend). for all of the studied varieties and wine regions are displayed in Figure 4, along with the corresponding centroids (averaged parameters \(d\) and \(e\)). For budburst and for all the selected varieties, the parameter values are within the range from \(-0.3\) to \(-0.7\) (parameter\(-d\)) and from \(6.3\) to \(11.6\) (parameter\(-e\)). Hence, according to parameter\(-e\), cv. _Espadeiro_/Lisboa and _cv. Baga_/Dao present the lowest mid-curve (sigmoid response function value of \(0.5\)) temperature of \(6.3\)\({}^{\circ}\)C, while other varieties such as cv. _Jaen_/Dao present mid-curve temperatures as high as \(11.6\)\({}^{\circ}\)C. As expected, the intermediate varieties are closer to the centroid, such as cv. _Dona Maria_, _Merlot_ and _Tinta Francisca_/Lisboa, with parameter\(-e\) of approximately \(8.6\)\({}^{\circ}\)C. For flowering, the parameters range between \(-0.3\) and \(-1.0\) (parameter\(-d\)) and \(10.0\) to \(20.0\) (parameter\(-e\)). The cv. _Espadeiro_/Vinhos Verdes shows the lowest parameter\(-e\) (\(10.0\)\({}^{\circ}\)C), while cv. _Aragomez_/Douro shows a mid-curve temperature (parameter\(-e\)) of \(20.0\)\({}^{\circ}\)C. The varieties closer to the corresponding centroid are now cv. _Trajadura_, _Sauvignon_ and _Gouveio_/Lisboa, with a mid-curve temperature of \(13.7\)\({}^{\circ}\)C. Lastly, for veraison, the range of the parameters is between \(-0.2\) and \(-0.8\) for parameter\(-d\), and \(7.5\) and \(21.0\) for parameter\(-e\). Therefore, there is a clear tendency for lower parameter\(-e\) values (mid-curve temperatures) for budburst when compared with flowering or veraison. On the other hand, flowering and veraison, which depict very similar mid-curves temperatures, reveal differences in terms of the parameter\(-d\). In fact, there is a clear tendency for less steep response curves for veraison than for flowering, which suggests a less defined threshold for temperature accumulation in veraison than in flowering or in budburst, thus highlighting that step-models (e.g., GDD) are not suitable for simulating veraison. The subsequent step was to test the application of the three GSM on the basis of the centroid parameters. The performance of the GSM was also compared to the individual SM so as to assess whether the former is still useful. The resulting GSM response functions are shown in Figure 5, which demonstrates the aforementioned differences between the response functions of the phenological stages (mid-curve temperature lower in budburst and less steep curve in veraison). For budburst, the GSM parameters \(d\) and \(e\) are equal to \(-0.6\) and \(8.6\), respectively. For flowering, these same parameters are of \(-0.6\) and \(13.7\). Finally, for veraison, they are of \(-0.5\) and \(13.2\). After applying these GSM and cross-validation, the model performance metrics (RSMEP and EF*) were assessed. As expected, a slight increase of the RMSEP exists for the GSM with respect to the individual SM, but most of the values are still below seven days. The model performances in terms of the EF* metrics (EF after cross-validation) remain above \(0.05\) in \(140\) out of \(153\) (\(51\) varieties \(\times\)\(3\) phenological stages) calibrated models (Table S2). The exceptions are: for budburst, all six varieties in the Vinhos Verdes wine region, cv. _Touriga Franca_, _Moscatel Galego_ and _Aragomez_, in the Douro wine  
Figure 4: Scatterplot of the sigmoid model (SM) parameters \(d\) and \(e\) and the corresponding centroids for the three phenological stages (budburst, flowering, and veraison) in red.