# Phenological Model Intercomparison for Estimating Grapevine Budbreak Date (Vitis vinifera L.) in Europe

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Observations

#### 2.2. Phenological Models

#### 2.2.1. GDD

#### 2.2.2. WANG

#### 2.2.3. UNIFORC

#### 2.2.4. BRIN

#### 2.2.5. UNICHILL

#### 2.2.6. UNIFIED

#### 2.3. Model Fitting and Validation

#### 2.3.1. Outliers Removal

#### 2.3.2. Parameters’ Range and Starting Date

#### 2.3.3. Model Fitting, Validation and Application

#### 2.4. Statistical Analysis

^{2}, Equation (10), [53]); Akaike information criterion (AIC, Equation 11, [54]); Root Mean Squared Error (RMSE, Equation (12), [55]) and modeling efficiency coefficient (EF, Equation (13), [56]), each defined as follows:

_{i}is the observed value, $\overline{O}$ is the average of the observed values, ${P}_{i}$ is the predicted value, $n$ is the number of observations, $k$ is the number of parameters in the model, and $\widehat{L}$ is the maximized value of the likelihood function of the predicted model.

## 3. Results

#### 3.1. Overall Model Behavior in Fitting and Validation

^{2}= 0.74; AIC = 150.42; RMSE = 4.22, Val, R

^{2}= 0.61; AIC = 111.64; RMSE = 5.79) compared to F models (Fit, R

^{2}= 0.61; AIC = 160.62; RMSE = 5.51; Val, R

^{2}= 0.59; AIC = 112.01; RMSE = 6.10). Among all models (Figure 3 and Table S1), the highest performances were achieved by UNIFIED model (Fit, R

^{2}= 0.77; AIC = 147.60; RMSE = 3.96; Val, R

^{2}= 0.64; AIC = 110.74; RMSE = 5.42), while the lowest were obtained by the WANG model (Fit, R

^{2}= 0.61; AIC = 161.15; RMSE = 5.60) and GDD model (Val, R

^{2}= 0.58; AIC = 112.59; RMSE = 6.25). Moreover, higher performances were found for those models in which the starting date was fixed at 1st September in CF models (Fit, R

^{2}= 0.74; AIC = 150.24; RMSE = 4.21; Val, R

^{2}= 0.61; AIC = 111.59; RMSE = 5.75) and at 1st January in F models (Fit, R

^{2}= 0.66; AIC = 159.20; RMSE = 5.53; Val, R

^{2}= 0.63; AIC = 111.10; RMSE = 6.15). Finally, concerning grapevine varieties, Chardonnay was best fitted by the models (Fit, R

^{2}= 0.90; AIC = 138.66; RMSE = 4.90; Val, R

^{2}= 0.89; AIC = 101.54; RMSE = 5.97), while the poorest results were obtained for Touriga Nacional (Fit, R

^{2}= 0.42; AIC = 147.09; RMSE = 6.23; Val, R

^{2}= 0.31; AIC = 105.40; RMSE = 7.74) and Touriga Franca in terms of AIC values (Fit = 180.19; Val = 127.35).

#### 3.2. HP versus AV

^{2}and AIC) of the model fitting and validation (symbols) and the applications of the different parameterizations on all validation subsamples (boxplot) obtained by considering all grapevine varieties and starting dates. In detail, the selected parameter sets with highest performances (HP; filled symbols with different shapes according to the starting dates) were the result of the highest rank value of R

^{2}and AIC and the minimum discrepancy between fitting (red) and validation (blue) models. By contrast, the AV parameter sets (boxplots in shadow area) were the application of the average parameterization obtained for all subsamples. Despite that similar performances for HP and AV parameter sets were evidenced in Figures S1–S7, higher discrepancy was found in the behavior of CF and F models. In Figures S1–S4 (CF models), no differences were observed when different starting dates were set during model fitting and application. On the other hand, high discrepancy was found in model performances when different starting dates were adopted in Figures S5–S7 (F models). This trend is also evidenced by the correlations between observed and simulated DOYs in Figure 4, Figures S8 and S9. The results of model fitting showed accurate performances for all selected HP, with more discrepancy between starting dates of F models (yellow and green correlations) compared to those used in CF models (blue and red correlations). The values of R

^{2}also highlighted the higher performances obtained with some varieties compared to others (Chardonnay vs. Touriga Nacional).

^{2}= 11.99%, AIC = 3.36%, RMSE = 22.20%) compared to F models (R

^{2}= 5.73%, AIC = 1.51%, RMSE = 8.16%). Among CF models, UNICHILL model showed the lowest difference between HP and AV in terms of R

^{2}and AIC (R

^{2}= 6.20%, AIC = 2.70%), while it evidenced the highest difference in terms of RMSE (40.02%). Considering F models, WANG showed the highest difference (R

^{2}= 7.07%, AIC = 2.25%, RMSE = 9.38%) and UNIFORC, the lowest (R

^{2}= 4.21%, AIC = 0.84%, RMSE = 7.13%). Following the same trend, the starting dates 1st September and 1st August (R

^{2}= 3.89%, AIC = 0.86%, RMSE = 15.62%) showed bigger differences compared to 1st January and 1st March (R

^{2}= 2.96%, AIC = 0.72%, RMSE = 7.62%). In particular, 1st September showed a lower difference in terms of AIC and RMSE (AIC = 0.86%, RMSE = 13.53%) compared to 1st August in CF models while 1st January showed the highest difference in F models (R

^{2}= 2.88%, AIC = 0.65%, RMSE = 7.23%). Finally, regarding grapevine varieties, the highest difference was found for Touriga Nacional (R

^{2}= 23.96%, RMSE = 24.20%) while the lowest was shown by Chardonnay in terms of R

^{2}(1.89%) and by Touriga Franca in terms of AIC and RMSE (1.10% and 9.55%, respectively).

#### 3.3. Model Applications on Other Independent Datasets

^{2}= 0.55, AIC = 57.97, RMSE = 9.41) and AV (R

^{2}= 0.54, AIC = 58.37, RMSE = 9.26) parameter sets. However, this difference slightly increased when CF (R

^{2}= 0.56, AIC = 59.05, RMSE = 8.75) and F models (R

^{2}= 0.52, AIC = 57.01, RMSE = 10.01) were compared without distinguishing between HP and AV parameterizations. Therefore, CF models showed better results in terms of R

^{2}(+8%) and RMSE (−15%) compared to F models while lower results of AIC value were obtained for CF compared to F models (+3.44%). A detailed analysis revealed that the CF models with highest performances (R

^{2}and AIC) were UNICHILL (R

^{2}= 0.64, AIC = 56.74) and UNIFIED (R

^{2}= 0.58, AIC = 56.61) models, while, in F models, the better results were provided by UNIFORC (R

^{2}= 0.54, AIC = 55.98). However, in terms of RMSE, highest performances were found for BRIN hourly (8.37, CF) and GDD (9.67, F). Concerning the starting dates, similar results were found when the 1st September (R

^{2}= 0.58, AIC = 58.92, RMSE = 8.55) and 1st of August (R

^{2}= 0.57, AIC = 59.17, RMSE = 8.95) were analyzed, with the 1st September showing better performance (R

^{2}= +1.83%, AIC = −0.44% and RMSE = −4.68%). Instead, higher differences were found when the 1st January (R

^{2}= 0.55, AIC = 60.47, RMSE = 7.74) and 1st of March (R

^{2}= 0.49, AIC = 52.57, RMSE = 12.47) were compared, evidencing the most relevant performances for 1st January (R

^{2}= +10.83% and RMSE = −61.23%, with the exception of AIC = +14.15%).

_{0}= −121 and −152, respectively) and end of February (e.g., Riesling: DOY 56 and 57 for t

_{0}= −121 and −152, respectively). More specifically, the period of endo-dormancy fulfilment was similarly reached regardless of starting date (1st September/August), allowing the next forcing unit accumulation during the eco-dormancy period to be correctly satisfied (differences in days from 0 to 3 days). The analysis further highlighted that the endo-dormancy release occurs later at northern than at southern latitudes and this is consistent with results obtained using F approach. These demonstrate that a late starting date (1st of March) for forcing unit accumulation is more suitable for budbreak simulation of varieties collected in Northern Europe (e.g., Gewürztraminer, Riesling and Pinot Gris), whose endo-dormancy release is simulated by CF late in the season (54 DOY on average). Conversely, an early starting date (1 January) provided the best results in simulating budbreak for grapevine varieties collected in Southern Europe (e.g., Touriga Franca and Nacional, Cabernet Sauvignon, Grenache and Chardonnay), which are characterized by an early end of endo-dormancy as simulated by CF models (13 DOY on average).

## 4. Discussion

^{2}and AIC), the average error (RMSE) between observed and simulated data was relatively high (from 4 to 19 days). This situation was exacerbated in F models where the reliability in simulating budbreak is dependent to the use of a specific starting date (1st of January/1st of March) and thus the original observed dataset. The discrepancy between the two starting dates raises the question of which initial date to choose for forcing unit accumulation when simulations are conducted on a European scale [31,64].

## 5. Conclusions

## Supplementary Materials

^{2}and AIC values of the BRIN Daily model obtained for all fitted and average models, grapevine varieties and starting dates. The symbols (points and triangles) show the model results at two starting dates (in this example t

_{0}= −121 and −152 DOY), while the two colours represent fitting (red) and validation (blue) procedure, respectively. The filled symbols constitute the R

^{2}and AIC values of the models obtained by the selected HP parameter sets, while the dashed (fitting) and dotted (validation) lines depict the average R

^{2}and AIC values for both starting dates (in this example orange line = −121 DOY and green line = −152 DOY). The boxplots represent the R

^{2}and AIC values distribution for HP (orange and light blue: HP model application on all validation subsamples for t

_{0}= −121 and t

_{0}= −152 DOY, respectively) and AV (boxplot in the shaded area, orange and light blue: AV application on all validation subsamples for t0 = −121 and t0 = −152 DOY, respectively). The outliers represent all values out of the 1.5*InterQuartile Range (IQR) of the boxplot. Figure S2: R

^{2}and AIC values of the BRIN Hourly model obtained for all fitted and average models, grapevine varieties and starting dates. The symbols (points and triangles) show the model results at two starting dates (in this example t

_{0}= −121 and −152 DOY), while the two colours represent fitting (red) and validation (blue) procedure, respectively. The filled symbols constitute the R

^{2}and AIC values of the models obtained by the selected HP parameter sets, while the dashed (fitting) and dotted (validation) lines depict the average R

^{2}and AIC values for both starting dates (in this example orange line = −121 DOY and green line = −152 DOY). The boxplots represent the R

^{2}and AIC values distribution for HP (orange and light blue: HP model application on all validation subsamples for t

_{0}= −121 and t

_{0}= −152 DOY, respectively) and AV (boxplot in the shaded area, orange and light blue: AV application on all validation subsamples for t

_{0}= −121 and t

_{0}= −152 DOY, respectively). The outliers represent all values out of the 1.5*InterQuartile Range (IQR) of the boxplot. Figure S3: R

^{2}and AIC values of the UNICHILL model obtained for all fitted and average models, grapevine varieties and starting dates. The symbols (points and triangles) show the model results at two starting dates (in this example t

_{0}= −121 and −152 DOY), while the two colours represent fitting (red) and validation (blue) procedure, respectively. The filled symbols constitute the R

^{2}and AIC values of the models obtained by the selected HP parameter sets, while the dashed (fitting) and dotted (validation) lines depict the average R

^{2}and AIC values for both starting dates (in this example orange line = −121 DOY and green line = −152 DOY). The boxplots represent the R

^{2}and AIC values distribution for HP (orange and light blue: HP model application on all validation subsamples for t

_{0}= −121 and t

_{0}= −152 DOY, respectively) and AV (boxplot in the shaded area, orange and light blue: AV application on all validation subsamples for t

_{0}= −121 and t

_{0}= −152 DOY, respectively). The outliers represent all values out of the 1.5*InterQuartile Range (IQR) of the boxplot. Figure S4: R

^{2}and AIC values of the UNIFIED model obtained for all fitted and average models, grapevine varieties and starting dates. The symbols (points and triangles) show the model results at two starting dates (in this example t

_{0}= −121 and −152 DOY), while the two colours represent fitting (red) and validation (blue) procedure, respectively. The filled symbols constitute the R

^{2}and AIC values of the models obtained by the selected HP parameter sets, while the dashed (fitting) and dotted (validation) lines depict the average R

^{2}and AIC values for both starting dates (in this example orange line = −121 DOY and green line = −152 DOY). The boxplots represent the R

^{2}and AIC values distribution for HP (orange and light blue: HP model application on all validation subsamples for t

_{0}= −121 and t

_{0}= −152 DOY, respectively) and AV (boxplot in the shaded area, orange and light blue: AV application on all validation subsamples for t

_{0}= −121 and t

_{0}= −152 DOY, respectively). The outliers represent all values out of the 1.5*InterQuartile Range (IQR) of the boxplot. Figure S5: R

^{2}and AIC values of the UNIFORC model obtained for all fitted and average models, grapevine varieties and starting dates. The symbols (points and triangles) show the model results at two starting dates (in this example t

_{0}= 1 and 60 DOY), while the two colours represent fitting (red) and validation (blue) procedure, respectively. The filled symbols constitute the R

^{2}and AIC values of the models obtained by the selected HP parameter sets, while the dashed (fitting) and dotted (validation) lines depict the average R

^{2}and AIC values for both starting dates (in this example orange line = 1 DOY and green line = 60 DOY). The boxplots represent the R

^{2}and AIC values distribution for HP (orange and light blue: HP model application on all validation subsamples for t

_{0}= 1 and t

_{0}= 60 DOY, respectively) and AV (boxplot in the shaded area, orange and light blue: AV application on all validation subsamples for t

_{0}= 1 and t

_{0}= 60 DOY, respectively). The outliers represent all values out of the 1.5*InterQuartile Range (IQR) of the boxplot. Figure S6: R

^{2}and AIC values of the GDD model obtained for all fitted and average models, grapevine varieties and starting dates. The symbols (points and triangles) show the model results at two starting dates (in this example t

_{0}= 1 and 60 DOY), while the two colours represent fitting (red) and validation (blue) procedure, respectively. The filled symbols constitute the R

^{2}and AIC values of the models obtained by the selected HP parameter sets, while the dashed (fitting) and dotted (validation) lines depict the average R

^{2}and AIC values for both starting dates (in this example orange line = 1 DOY and green line = 60 DOY). The boxplots represent the R

^{2}and AIC values distribution for HP (orange and light blue: HP model application on all validation subsamples for t

_{0}= 1 and t

_{0}= 60 DOY, respectively) and AV (boxplot in the shaded area, orange and light blue: AV application on all validation subsamples for t

_{0}= 1 and t

_{0}= 60 DOY, respectively). The outliers represent all values out of the 1.5*InterQuartile Range (IQR) of the boxplot. Figure S7: R

^{2}and AIC values of the WANG model obtained for all fitted and average models, grapevine varieties and starting dates. The symbols (points and triangles) show the model results at two starting dates (in this example t

_{0}= 1 and 60 DOY), while the two colours represent fitting (red) and validation (blue) procedure, respectively. The filled symbols constitute the R

^{2}and AIC values of the models obtained by the selected HP parameter sets, while the dashed (fitting) and dotted (validation) lines depict the average R

^{2}and AIC values for both starting dates (in this example orange line = 1 DOY and green line = 60 DOY). The boxplots represent the R

^{2}and AIC values distribution for HP (orange and light blue: HP model application on all validation subsamples for t

_{0}= 1 and t

_{0}= 60 DOY, respectively) and AV (boxplot in the shaded area, orange and light blue: AV application on all validation subsamples for t

_{0}= 1 and t

_{0}= 60 DOY, respectively). The outliers represent all values out of the 1.5*InterQuartile Range (IQR) of the boxplot. Figure S8: Correlations between observed and simulated budbreak Days of Year (DOY) of the UNIFORC and UNICHILL models. The results were obtained for all grapevine varieties and starting dates using the HP parameter set. Figure S9: Correlations between observed and simulated budbreak Days of Year (DOY) of the WANG and BRIN Daily models. The results were obtained for all grapevine varieties and starting dates using the HP parameter set. Figure S10: Highest-Performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Cabernet sauvignon variety. Figure S11: Highest-Performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Gewürztraminer variety. Figure S12: Highest-Performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Grenache variety. Figure S13: Highest-Performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Pinot Gris variety. Figure S14: Highest-Performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Riesling variety. Figure S15: Highest-Performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Touriga Franca variety. Figure S16: Highest-Performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Touriga Nacional variety. Figure S17: Statistical results (R

^{2}, AIC and RMSE) of the comparison between CF (black bars) and F (red bars) models in model fitting and application for all grapevine varieties using AV parameters’ set. The differences between CF and F models in model fitting and applications were displayed using green and yellow bars, respectively. CS = Cabernet Sauvignon, CH = Chardonnay, GE = Gewürztraminer, GR = Grenache, PG = Pinot Gris, RS = Riesling, TF = Touriga Franca, TN = Touriga Nacional. Table S1: Statistical indices (RMSE, EF, R

^{2}, AIC) obtained for all models, varieties and starting dates after model fitting and validation on all subsamples.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Map of the vineyards and weather stations situated in three European countries (Luxembourg, France and Portugal). The vineyards are displayed with triangles and points in relation to the use of phenological data for model fitting or application. The arrows indicate that both vineyards and weather stations are located in the same site. 10 weather stations and 10 vineyards are situated in Douro valley (Portugal).

**Figure 2.**Workflow of the methodology adopted in this study. Random subsamples = Random distribution of the phenological observed data in subsample; Fitting and Validation = Model fitting on the selected 60% of the observed data and model validation on the remaining 40%; Applications = Model application on all validation and independent datasets. Fit = model fitting; Val = model validation; HP = highest-performance models; AV = average models; RS(n) = random subsamples; ID = independent datasets.

**Figure 3.**Statistical performances (R

^{2}, AIC, RMSE, EF) of all combinations of the six phenological models, eight grapevine varieties and different starting dates during fitting and validation. The results of forcing (F) and chilling-forcing (CF) models (different bar colours) are displayed at the top and bottom of the figure, respectively. The two bars identify the model fitting (no bar texture) and validation (line bar texture). CS = Cabernet Sauvignon, CH = Chardonnay, GE = Gewürztraminer, GR = Grenache, PG = Pinot Gris, RS = Riesling, TF = Touriga Franca, TN = Touriga Nacional.

**Figure 4.**Correlations between observed and simulated budbreak Days of Year (DOY) of the GDD and UNIFIED models. The results were obtained for all grapevine varieties and starting dates using the HP parameter set.

**Figure 5.**Highest-performance (HP) and average (AV) parameters’ set applied on the independent datasets by considering all phenological models and starting dates. The example of Chardonnay variety.

**Figure 6.**Statistical results (R

^{2}, AIC and RMSE) of the comparison between CF (black bars) and F (red bars) approaches in model fitting and application for all grapevine varieties using HP parameter set. The differences between CF and F models (CF-F) in both fitting and applications are displayed using green and yellow bars, respectively. CS = Cabernet Sauvignon, CH = Chardonnay, GE = Gewürztraminer, GR = Grenache, PG = Pinot Gris, RS = Riesling, TF = Touriga Franca, TN = Touriga Nacional.

**Table 1.**Observed weather (daily maximum and minimum air temperature, °C) and budbreak data of eight grapevine varieties used for model fitting, validation and application in different locations across Europe. The geographical positions of all weather stations and vineyards are identified with the latitude (Lat) and longitude (Long) coordinates (degrees).

Variety × Site | Weather Data | Budbreak Data | |||||||
---|---|---|---|---|---|---|---|---|---|

Procedure | Variety | Country | Weather Station | Period | Vineyard | Period | Cases | ||

Lat | Long | Years | Lat | Long | Years | Number | |||

Fitting & Validation | Cabernet Sauvignon | France | 43.58 | 3.96 | 1950–2017 | 43.33 | 3.56 | 1951–2012 | 39 |

Luxembourg | 49.50 | 6.35 | 2016–2018 | 49.50 | 6.35 | 2017–2018 | 2 | ||

Chardonnay | France | 43.58 | 3.96 | 1950–2017 | 43.33 | 3.56 | 1951–2012 | 33 | |

Luxembourg | 49.50 | 6.35 | 2010–2018 | 49.50 | 6.35 | 2011–2018 | 8 | ||

Gewürztraminer | Luxembourg | 49.50 | 6.35 | 1970–2018 | 49.50 | 6.35 | 1972–2018 | 50 | |

Grenache | France | 43.58 | 3.96 | 1950–2017 | 43.33 | 3.56 | 1951–2012 | 41 | |

Pinot Gris | Luxembourg | 49.50 | 6.35 | 1970–2018 | 49.50 | 6.35 | 1971–2018 | 51 | |

Riesling | Luxembourg | 49.50 | 6.35 | 1970–2018 | 49.50 | 6.35 | 1971–2018 | 50 | |

Touriga Franca | Portugal | 39.04 | −9.18 | 1994–2014 | 39.04 | −9.18 | 1995–2014 | 20 | |

41.81 | −8.41 | 2004–2009 | 41.81 | −8.41 | 2005–2009 | 5 | |||

41.25 | −7.11 | 2013–2018 | 41.25 | −7.11 | 2014–2018 | 5 | |||

41.19 | −7.54 | 2013–2018 | 41.19 | −7.54 | 2014–2018 | 5 | |||

41.04 | −7.04 | 2013–2017 | 41.04 | −7.04 | 2014–2017 | 4 | |||

41.17 | −7.56 | 2013–2017 | 41.17 | −7.56 | 2014–2017 | 4 | |||

41.15 | −7.62 | 2013–2018 | 41.15 | −7.62 | 2014–2018 | 5 | |||

41.17 | −7.55 | 2014–2018 | 41.17 | −7.55 | 2015–2018 | 4 | |||

Touriga Nacional | Luxembourg | 49.50 | 6.35 | 2016–2018 | 49.50 | 6.35 | 2017–2018 | 2 | |

Portugal | 39.04 | −9.18 | 1989–2014 | 39.04 | −9.18 | 1990–2014 | 19 | ||

41.81 | −8.41 | 2004–2009 | 41.81 | −8.41 | 2005–2009 | 5 | |||

41.21 | −7.43 | 2013–2018 | 41.21 | −7.43 | 2014–2018 | 5 | |||

41.24 | −7.76 | 2014–2017 | 41.24 | −7.76 | 2015–2017 | 3 | |||

41.22 | −7.54 | 2013–2018 | 41.22 | −7.54 | 2014–2018 | 5 | |||

41.15 | −7.76 | 2015–2018 | 41.15 | −7.76 | 2016–2018 | 3 | |||

Application | Cabernet Sauvignon | France | 44.79 | −0.58 | 2012–2019 | 44.79 | −0.58 | 2013–2019 | 7 |

Chardonnay | France | 48.55 | 7.64 | 1950–2017 | 48.22 | 7.35 | 1976–1990 | 15 | |

Gewürztraminer | France | 48.55 | 7.64 | 1950–2017 | 48.22 | 7.35 | 2006–2009 | 4 | |

Grenache | France | 48.55 | 7.64 | 1950–2017 | 48.22 | 7.35 | 1976–1990 | 13 | |

Pinot Gris | France | 48.55 | 7.64 | 1950–2017 | 48.22 | 7.35 | 1976–1990 | 15 | |

Riesling | France | 48.55 | 7.64 | 1950–2017 | 48.22 | 7.35 | 2006–2009 | 4 | |

Touriga Franca | France | 44.79 | −0.58 | 2012–2019 | 44.79 | −0.58 | 2013–2019 | 7 | |

Touriga Nacional | France | 44.79 | −0.58 | 2012–2019 | 44.79 | −0.58 | 2013–2019 | 7 |

**Table 2.**HP (highest-performance) parameter sets for each combination of models, grapevine varieties and starting dates. C

_{crit}= critical amount of chilling and F

_{crit}= critical amount of forcing.

GDD | WANG | UNIFORC/UNICHILL/UNIFIED | BRIN h/BRIN d | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Variety | t_{0} | F_{crit} | T_{b} | F_{crit} | T_{opt} | T_{min} | T_{max} | C_{crit} | F_{crit} | a | b | c | d | e | w | z | C_{crit} | F_{crit} | Q_{10c} | T_{l} | T_{h} |

Cabernet Sauvignon | 1 −121 | 763.47 | 0 | 67.32 | 18.15 | 0 | 45 | - | 16.39 | - | - | - | −0.21 | 16.47 | - | - | 190.14 184.86 | 6636.2 295.3 | 1.54 1.54 | 5.07 4.45 | 25 |

142.36 | 26.54 | 0.15 | −23.61 | −20.41 | −0.19 | 11.80 | - | - | |||||||||||||

151.14 | 20.62 | 1.31 | −31.06 | −1.45 | −0.20 | 12.44 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 286.89 | 1.18 | 19.49 | 23.96 | 0 | 45 | - | 7.74 | - | - | - | −0.21 | 16.45 | - | - | 217.53 206.55 | 6597.1 272.1 | 1.52 1.59 | 5.07 4.84 | 25 | |

178.96 | 23.19 | 0.16 | −15.33 | −24.24 | −0.25 | 11.83 | - | - | |||||||||||||

175.24 | 20.40 | 0.91 | −26.60 | −1.63 | −0.14 | 14.69 | −0.00025 | 21.05 | |||||||||||||

Chardonnay | 1 −121 | 432.23 | 2.34 | 14.63 | 30.42 | 0 | 45 | - | 8.58 | - | - | - | −0.21 | 18.46 | - | - | 148.48 148.34 | 5194.0 238.3 | 1.54 1.54 | 5.86 4.99 | 25 |

132.02 | 17.55 | 0.72 | −29.03 | −17.19 | −0.24 | 12.56 | - | - | |||||||||||||

123.96 | 19.71 | 0.85 | −32.05 | −2.20 | −0.28 | 11.79 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 49.18 | 7.21 | 4.00 | 31.26 | 0 | 45 | - | 1.33 | - | - | - | −0.30 | 18.36 | - | - | 173.38 172.90 | 5276.9 211.9 | 1.54 1.54 | 5.81 5.44 | 25 | |

165.85 | 19.05 | 0.46 | −19.82 | −13.84 | −0.24 | 11.93 | - | - | |||||||||||||

172.71 | 19.63 | 1.19 | −34.66 | 0.22 | −0.25 | 10.46 | −0.00025 | 21.05 | |||||||||||||

Grenache | 1 −121 | 645.68 | 0 | 47.27 | 21.91 | 0 | 45 | - | 13.40 | - | - | - | −0.21 | 16.48 | - | - | 177.23 158.40 | 3769.3 312.9 | 1.67 1.55 | 6.63 4.02 | 25 |

156.67 | 8.05 | 0.61 | −20.19 | −11.39 | −0.19 | 16.94 | - | - | |||||||||||||

157.54 | 20.94 | 0.55 | −30.18 | −10.31 | −0.26 | 9.98 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 85.11 | 5.99 | 5.17 | 30.40 | 0 | 45 | - | 4.17 | - | - | - | −0.21 | 16.49 | - | - | 215.25 210.27 | 5029.4 319.2 | 1.53 1.54 | 5.27 2.80 | 25 | |

186.21 | 4.73 | 0.79 | −26.99 | −7.35 | −0.18 | 21.33 | - | - | |||||||||||||

186.89 | 20.41 | 1.04 | −30.11 | −1.81 | −0.28 | 9.72 | −0.00025 | 21.05 | |||||||||||||

Gewürrtztraminer | 1 −121 | 137.17 | 7.10 | 12.11 | 31.26 | 0 | 45 | - | 9.37 | - | - | - | −0.21 | 18.50 | - | - | 283.90 280.72 | 3961.1 181.3 | 1.53 1.54 | 6.19 5.39 | 25 |

186.01 | 17.05 | 0.17 | −32.51 | −12.74 | −0.35 | 10.79 | - | - | |||||||||||||

172.62 | 20.42 | 1.18 | −34.32 | −10.15 | −0.23 | 11.48 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 255.89 | 3.61 | 9.17 | 31.26 | 0 | 45 | - | 8.43 | - | - | - | −0.23 | 16.45 | - | - | 312.24 311.34 | 4159.1 182.5 | 1.53 1.54 | 5.98 5.36 | 25 | |

161.74 | 12.51 | 1.62 | −34.01 | −6.44 | −0.33 | 12.71 | - | - | |||||||||||||

214.68 | 20.29 | 0.50 | −31.89 | −10.95 | −0.28 | 10.28 | −0.00025 | 21.05 | |||||||||||||

Pinot Gris | 1 −121 | 122.16 | 7.39 | 12.15 | 31.26 | 0 | 45 | - | 9.63 | - | - | - | −0.21 | 18.49 | - | - | 285.01 284.32 | 4633.1 225.9 | 1.53 1.55 | 5.22 4.11 | 25 |

183.87 | 14.70 | 0.56 | −23.01 | −19.53 | −0.25 | 12.67 | - | - | |||||||||||||

183.25 | 20.45 | 0.95 | −30.94 | −10.68 | −0.28 | 10.26 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 250.48 | 3.91 | 9.36 | 31.23 | 0 | 45 | - | 9.44 | - | - | - | −0.21 | 16.54 | - | - | 314.40 314.75 | 6374.7 218.9 | 1.53 1.54 | 3.52 4.29 | 25 | |

174.41 | 12.60 | 1.13 | −25.39 | −8.01 | −0.33 | 12.02 | - | - | |||||||||||||

211.57 | 20.26 | 0.36 | −11.66 | −7.14 | −0.28 | 10.31 | −0.00025 | 21.05 | |||||||||||||

Riesling | 1 −121 | 156.14 | 6.74 | 12.60 | 31.26 | 0 | 45 | - | 9.90 | - | - | - | −0.21 | 18.46 | - | - | 267.03 280.95 | 4980.8 208.2 | 1.53 1.56 | 5.44 4.93 | 25 |

150.99 | 5.33 | 1.39 | −27.15 | −5.31 | −0.18 | 21.68 | - | - | |||||||||||||

173.34 | 20.47 | 1.09 | −28.42 | −10.79 | −0.21 | 11.23 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 279.34 | 3.46 | 11.80 | 30.29 | 0 | 45 | - | 10.14 | - | - | - | −0.22 | 16.45 | - | - | 297.05 313.12 | 5022.2 221.8 | 1.53 1.53 | 5.41 4.68 | 25 | |

168.39 | 10.63 | 1.08 | −23.72 | −7.63 | −0.29 | 13.89 | - | - | |||||||||||||

163.61 | 20.58 | 1.00 | −19.62 | −5.65 | −0.26 | 10.30 | −0.00025 | 21.05 | |||||||||||||

Touriga Franca | 1 −121 | 743.93 | 0 | 36.53 | 26.70 | 0 | 45 | - | 16.61 | - | - | - | −0.21 | 16.45 | - | - | 158.30 144.69 | 7933.9 493.9 | 1.53 1.52 | 4.80 2.89 | 25 |

142.03 | 24.35 | 0.83 | −21.47 | −1.62 | −0.32 | 10.79 | - | - | |||||||||||||

141.22 | 20.61 | 0.42 | −14.45 | −10.02 | −0.27 | 12.24 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 149.08 | 2.86 | 7.61 | 28.57 | 0 | 45 | - | 4.84 | - | - | - | −0.21 | 16.45 | - | - | 180.41 183.23 | 6998.5 293.1 | 1.52 1.52 | 5.79 5.28 | 25 | |

171.91 | 24.24 | 0.33 | −18.24 | −25.30 | −0.23 | 11.70 | - | - | |||||||||||||

159.86 | 20.53 | 0.38 | −13.35 | −5.10 | −0.19 | 14.67 | −0.00025 | 21.05 | |||||||||||||

Touriga Nacional | 1 −121 | 688.00 | 1.06 | 35.57 | 26.38 | 0 | 45 | - | 16.11 | - | - | - | −0.21 | 16.46 | - | - | 133.81 123.57 | 13,660.2 774.2 | 1.59 1.54 | 2.15 0.92 | 25 |

117.39 | 21.11 | 0.19 | −22.31 | −18.25 | −0.21 | 15.44 | - | - | |||||||||||||

124.23 | 19.76 | 0.47 | −27.59 | −0.002 | −0.14 | 17.19 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 199.94 | 0.80 | 8.19 | 28.71 | 0 | 45 | - | 5.20 | - | - | - | −0.21 | 16.45 | - | - | 165.37 144.19 | 12,985.3 823.9 | 1.57 1.55 | 2.40 0.42 | 25 | |

148.45 | 20.97 | 0.61 | −22.96 | −6.80 | −0.21 | 15.47 | - | - | |||||||||||||

150.90 | 20.54 | 0.26 | −8.36 | −0.72 | −0.14 | 17.87 | −0.00025 | 21.05 |

**Table 3.**AV (average) parameter sets for each combination of models, grapevine varieties and starting dates. C

_{crit}= critical amount of chilling and F

_{crit}= critical amount of forcing.

GDD | WANG | UNIFORC/UNICHILL/UNIFIED | BRIN h/BRIN d | ||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Variety | t_{0} | F_{crit} | T_{b} | F_{crit} | T_{opt} | T_{min} | T_{max} | C_{crit} | F_{crit} | a | b | c | d | e | w | z | C_{crit} | F_{crit} | Q_{10c} | T_{l} | T_{h} |

Cabernet Sauvignon | 1 −121 | 765.16 | 0 | 68.54 | 17.99 | 0 | 45 | - | 16.42 | - | - | - | −0.21 | 16.45 | - | - | 182.31 177.95 | 11,075.3 508.7 | 1.54 1.55 | 2.07 1.49 | 25 |

145.70 | 24.79 | 0.18 | −20.62 | −20.10 | −0.19 | 11.91 | - | - | |||||||||||||

152.62 | 20.60 | 0.94 | −23.60 | −2.86 | −0.22 | 12.08 | -0.00025 | 21.05 | |||||||||||||

60 −152 | 225.25 | 3.16 | 11.83 | 28.64 | 0 | 45 | - | 7.31 | - | - | - | −0.21 | 16.46 | - | - | 196.01 193.98 | 11,942.8 496.5 | 1.56 1.61 | 1.91 1.80 | 25 | |

176.29 | 25.03 | 0.18 | −21.03 | −18.95 | −0.19 | 11.89 | - | - | |||||||||||||

180.78 | 20.59 | 0.87 | −27.91 | −4.13 | −0.19 | 12.69 | -0.00025 | 21.05 | |||||||||||||

Chardonnay | 1 −121 | 527.48 | 0.91 | 22.21 | 28.11 | 0 | 45 | - | 11.02 | - | - | - | −0.22 | 16.91 | - | - | 150.00 167.46 | 6316.0 254.1 | 1.61 1.54 | 4.97 4.63 | 25 |

127.15 | 14.36 | 0.57 | −22.95 | −14.48 | −0.25 | 14.42 | - | - | |||||||||||||

130.52 | 20.32 | 0.88 | −24.70 | −2.52 | −0.27 | 11.40 | -0.00025 | 21.05 | |||||||||||||

60 −152 | 47.34 | 7.24 | 4.10 | 21.26 | 0 | 45 | - | 1.50 | - | - | - | −0.30 | 18.30 | - | - | 171.33 184.56 | 5931.7 266.4 | 1.61 1.55 | 5.35 4.44 | 25 | |

160.41 | 17.18 | 0.65 | −27.13 | −13.07 | −0.25 | 13.11 | - | - | |||||||||||||

163.81 | 20.45 | 0.85 | −28.65 | −3.25 | −0.26 | 11.35 | -0.00025 | 21.05 | |||||||||||||

Grenache | 1 −121 | 653.93 | 0 | 54.66 | 19.74 | 0 | 45 | - | 13.61 | - | - | - | −0.21 | 16.50 | - | - | 184.09 172.80 | 6316.6 286.7 | 1.58 1.66 | 4.31 3.87 | 25 |

126.06 | 8.07 | 1.04 | −26.44 | −8.24 | −0.26 | 16.68 | - | - | |||||||||||||

151.30 | 20.59 | 0.78 | −24.27 | −5.82 | −0.24 | 10.49 | -0.00025 | 21.05 | |||||||||||||

60 −152 | 113.43 | 4.85 | 6.61 | 29.66 | 0 | 45 | - | 3.96 | - | - | - | −0.23 | 17.10 | - | - | 182.40 198.81 | 8882.5 324.5 | 1.67 1.60 | 2.97 3.11 | 25 | |

150.54 | 10.30 | 0.90 | −28.01 | −10.48 | −0.24 | 16.05 | - | - | |||||||||||||

173.87 | 20.58 | 0.80 | −25.81 | −5.45 | −0.24 | 11.04 | -0.00025 | 21.05 | |||||||||||||

Gewürrtztraminer | 1 −121 | 178.85 | 6.24 | 11.97 | 31.26 | 0 | 45 | - | 8.95 | - | - | - | −0.23 | 18.17 | - | - | 251.39 264.22 | 5324.3 228.9 | 1.71 1.60 | 5.01 4.53 | 25 |

154.79 | 13.62 | 0.88 | −28.20 | −14.15 | −0.26 | 14.32 | - | - | |||||||||||||

149.42 | 20.26 | 0.89 | −23.75 | −8.10 | −0.25 | 11.17 | -0.00025 | 21.05 | |||||||||||||

60 −152 | 314.55 | 2.55 | 12.43 | 29.91 | 0 | 45 | - | 9.12 | - | - | - | −0.22 | 16.46 | - | - | 280.20 291.30 | 5274.6 232.9 | 1.66 1.62 | 5.05 4.44 | 25 | |

157.90 | 12.92 | 0.93 | −26.85 | −13.41 | −0.25 | 14.65 | - | - | |||||||||||||

176.90 | 20.45 | 0.71 | −25.17 | −8.95 | −0.26 | 10.95 | −0.00025 | 21.05 | |||||||||||||

Pinot Gris | 1 −121 | 126.62 | 7.39 | 12.26 | 31.26 | 0 | 45 | - | 7.61 | - | - | - | −0.25 | 18.35 | - | - | 271.42 269.51 | 6580.6 287.7 | 1.56 1.59 | 3.75 3.29 | 25 |

169.54 | 14.04 | 0.89 | −27.31 | −13.36 | −0.23 | 14.11 | - | - | |||||||||||||

173.20 | 20.38 | 0.69 | −22.47 | −9.57 | −0.25 | 10.82 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 359.67 | 1.77 | 15.09 | 28.93 | 0 | 45 | - | 9.48 | - | - | - | −0.21 | 16.47 | - | - | 292.53 299.62 | 6507.2 290.8 | 1.61 1.57 | 3.86 3.24 | 25 | |

188.72 | 14.01 | 0.85 | −25.77 | −12.46 | −0.24 | 14.19 | - | - | |||||||||||||

184.87 | 20.47 | 0.77 | −21.17 | −8.63 | −0.27 | 10.65 | −0.00025 | 21.05 | |||||||||||||

Riesling | 1 −121 | 156.13 | 6.78 | 12.43 | 31.26 | 0 | 45 | - | 8.51 | - | - | - | −0.23 | 18.47 | - | - | 267.92 270.05 | 6755.6 317.7 | 1.65 1.63 | 3.75 2.84 | 25 |

167.21 | 13.93 | 0.94 | −25.59 | −11.82 | −0.24 | 14.39 | - | - | |||||||||||||

166.51 | 20.56 | 0.95 | −24.12 | −8.63 | −0.26 | 10.92 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 416.44 | 0.93 | 16.95 | 28.35 | 0 | 45 | - | 9.76 | - | - | - | −0.21 | 16.65 | - | - | 294.27 296.64 | 6967.0 297.4 | 1.66 1.66 | 3.58 3.20 | 25 | |

176.49 | 13.62 | 0.99 | −27.07 | −12.29 | −0.27 | 13.61 | - | - | |||||||||||||

174.36 | 20.30 | 1.03 | −25.01 | −7.57 | −0.26 | 10.71 | −0.00025 | 21.05 | |||||||||||||

Touriga Franca | 1 −121 | 759.41 | 0.07 | 36.55 | 26.40 | 0 | 45 | - | 15.97 | - | - | - | −0.21 | 16.87 | - | - | 154.21 149.90 | 8897.4 363.8 | 1.54 1.57 | 4.39 4.42 | 25 |

137.46 | 19.81 | 0.69 | −22.91 | −8.82 | −0.24 | 14.33 | - | - | |||||||||||||

137.41 | 20.48 | 0.73 | −23.67 | −6.05 | −0.23 | 13.26 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 143.12 | 3.71 | 7.49 | 28.97 | 0 | 45 | - | 4.96 | - | - | - | −0.21 | 16.46 | - | - | 178.92 178.72 | 8466.3 387.1 | 1.54 1.56 | 4.63 4.20 | 25 | |

148.81 | 24.27 | 0.63 | −25.76 | −11.79 | −0.22 | 14.28 | - | - | |||||||||||||

165.50 | 20.42 | 0.64 | −22.47 | −5.83 | −0.21 | 13.90 | −0.00025 | 21.05 | |||||||||||||

Touriga Nacional | 1 −121 | 710.02 | 0.77 | 37.39 | 26.29 | 0 | 45 | - | 16.73 | - | - | - | −0.21 | 16.49 | - | - | 106.82 118.99 | 15,757.2 694.1 | 1.81 1.58 | 2.14 1.98 | 25 |

108.60 | 19.98 | 0.59 | −23.76 | −7.24 | −0.22 | 15.56 | - | - | |||||||||||||

108.85 | 20.33 | 0.72 | −24.30 | −2.98 | −0.16 | 16.91 | −0.00025 | 21.05 | |||||||||||||

60 −152 | 176.18 | 1.89 | 9.42 | 26.87 | 0 | 45 | - | 4.86 | - | - | - | −0.21 | 16.66 | - | - | 134.59 140.60 | 16,289.3 691.0 | 1.71 1.65 | 1.86 1.92 | 25 | |

123.73 | 20.27 | 0.62 | −23.51 | −12.11 | −0.22 | 15.53 | - | - | |||||||||||||

139.52 | 20.67 | 0.82 | −25.39 | −3.31 | −0.16 | 16.66 | −0.00025 | 21.05 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Leolini, L.; Costafreda-Aumedes, S.; A. Santos, J.; Menz, C.; Fraga, H.; Molitor, D.; Merante, P.; Junk, J.; Kartschall, T.; Destrac-Irvine, A.; van Leeuwen, C.; C. Malheiro, A.; Eiras-Dias, J.; Silvestre, J.; Dibari, C.; Bindi, M.; Moriondo, M. Phenological Model Intercomparison for Estimating Grapevine Budbreak Date (*Vitis vinifera* L.) in Europe. *Appl. Sci.* **2020**, *10*, 3800.
https://doi.org/10.3390/app10113800

**AMA Style**

Leolini L, Costafreda-Aumedes S, A. Santos J, Menz C, Fraga H, Molitor D, Merante P, Junk J, Kartschall T, Destrac-Irvine A, van Leeuwen C, C. Malheiro A, Eiras-Dias J, Silvestre J, Dibari C, Bindi M, Moriondo M. Phenological Model Intercomparison for Estimating Grapevine Budbreak Date (*Vitis vinifera* L.) in Europe. *Applied Sciences*. 2020; 10(11):3800.
https://doi.org/10.3390/app10113800

**Chicago/Turabian Style**

Leolini, Luisa, Sergi Costafreda-Aumedes, João A. Santos, Christoph Menz, Helder Fraga, Daniel Molitor, Paolo Merante, Jürgen Junk, Thomas Kartschall, Agnès Destrac-Irvine, Cornelis van Leeuwen, Aureliano C. Malheiro, José Eiras-Dias, José Silvestre, Camilla Dibari, Marco Bindi, and Marco Moriondo. 2020. "Phenological Model Intercomparison for Estimating Grapevine Budbreak Date (*Vitis vinifera* L.) in Europe" *Applied Sciences* 10, no. 11: 3800.
https://doi.org/10.3390/app10113800