# Simultaneous Calibration of Grapevine Phenology and Yield with a Soil–Plant–Atmosphere System Model Using the Frequentist Method

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Observational Data

#### 2.1.1. Field Measurements on Grapevine

#### 2.1.2. Weather and Soil Inputs

#### 2.2. Brief Description of STICS Grapevine Modules

#### 2.3. Calibration Setup

#### 2.3.1. Identification of the Calibrated Parameters

#### 2.3.2. Establishment of the Unit of Simulation (USM) and Objective Function

_{ij}is the number of USM where the response variable j was measured (i.e., an equally 6-year measurement for both phenology and yield at each plot); ${Y}_{{j}_{mean}}$ is the mean observation for the response variable j; and ${\omega}_{j}$ is the user-defined weight for each response variable. The weight given to each variable determines the priority given to the prediction accuracy of that response variable, i.e., a higher weight for a higher priority [25]. We followed here an equal-weight approach (${\omega}_{j}$ = 1), thus giving equal importance to phenology and yield.

_{flower}+ nRMSE

_{harvest}+ nRMSE

_{yield}for each studied variety–training system. The normalization by the mean observation, rather than the range, is widely used in crop modelling communities [6,29,42], thus facilitating comparisons between studies. Furthermore, in standard regression analysis, the MSE of the prediction already integrated the effects of parameter uncertainties and variance in model error [10]. In this study, the total prediction variability was caused by parameter variability, where the total variability included a fixed contribution of the model error term. For a given subject (i.e., variety–training system), the fixed model error term (for every calculated nRMSE) included the uncertainties from the model structure (e.g., equations not exhaustively included all explanatory variables), input variables (limited accuracy in gridded datasets), and the measurement errors.

#### 2.3.3. Assumption of Error Distributions

#### 2.3.4. Parameter Uncertainty and Sensitivity Analysis

#### 2.4. Evaluations of Calibrated Parameters

#### 2.4.1. Goodness-Of-Fit of the Estimated Parameters

#### 2.4.2. Evaluations Using Additional Published Data

#### 2.5. Data Process and Software Environment

## 3. Results and Discussion

#### 3.1. General Assessment of Testing Parameters

#### 3.1.1. Total Spread of Prediction Uncertainties

#### 3.1.2. Error Dependence and Homoscedasticity Test

#### 3.2. Calibration Results

#### 3.2.1. Calibrated Parameters and Associated Uncertainties

#### 3.2.2. Sensitivity Analysis and Interpretation of Calibrated Parameters

#### 3.2.3. Comparison between Multivariate and Univariate Function

#### 3.3. Variations in the Best-Performing Parameters among Variety–Training Systems

#### 3.4. Evaluations Using Additional Data

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Spread of the STICS model prediction uncertainties (nRMSE, %) for each variety–training system on flower and harvest DOY, yield (kg/ha) and the objective function (combined phenology and yield), respectively. Spread over (

**a**) all the tested parameter vectors (684,375 effective combinations); and (

**b**) selected parameter vectors resulting in an nRMSE (%) below 30% (dash line), where the figures in the brackets indicate the corresponding number of available vectors. Refer to Figure S2 for the boxplot definition. TN: Touriga Nacional; TF: Touriga Franca (TF).

**Figure 2.**Minimum value of the STICS model prediction uncertainties (nRMSE, %) based on the combined variable (i.e., objective function) under each parameter value (fix a given parameter value and test the remaining combinations). (

**a**) Touriga Nacional (TN) with the single-cordon training system; (

**b**) Touriga Nacional (TN) with the double-cordon training system; (

**c**) Touriga Franca (TF) with the single-cordon training system; (

**d**) Touriga Franca (TF) with the double-cordon training system. The parameter abbreviations are denoted for each subplot (see Table 2 for detailed parameter descriptions). The associated boxplots are shown in Figures S2–S5. The calibrated parameters are BN: Box number; FF: Fruit filling thermal requirement; FS: Fruit setting thermal requirement; FN: Fruit number formation potential per degree day

^{−1}per cluster; FW: Fruit (berry) weight potential; RG: Thermal requirement between budbreak and reproductive onset; SS: Source sink ratio threshold; VG: Thermal requirement between juvenile onset and veraison onset; WD: Thermal requirement between reproductive onset and fruit water dynamic onset.

**Figure 3.**Range of STICS model prediction uncertainties (nRMSE, %) based on the combined variable (i.e., objective function) under each parameter value (fix a given parameter value and test the remaining combinations). (

**a**) Touriga Nacional (TN) with the single-cordon training system; (

**b**) Touriga Nacional (TN) with the double-cordon training system; (

**c**) Touriga Franca (TF) with the single-cordon training system; (

**d**) Touriga Franca (TF) with the double-cordon training system. The range (spread) is calculated as four times the inter-quartile range (the associated boxplots are shown in Figures S2–S5).

**Figure 4.**The variance-based sensitivity index is calculated for each variety–training system combination based on the variance of the total prediction uncertainty (nRMSE, %) over the response variable of (

**a**) flowering date; (

**b**) harvest date; (

**c**) yield; (

**d**) combined variable (i.e., objective function). The index denotes the main effect index, which can rank the relative importance of each parameter in terms of its individual effect on the total variance of the prediction uncertainty (nRMSE, %). Parameter abbreviations are labelled on the x-axis with detailed parameter descriptions in Table 2.

**Figure 5.**Parallel coordinate plot for the overall distribution of prediction uncertainties (nRMSE, %) based on all tested parameter vectors (684,375) over the combined variable (i.e., objective function). For each variety–training system (with a specific color), (

**a**) the best-performing parameter vector and (

**b**) the top 5% (percentile) best-performing vectors are presented. The background grey shade represents the range of results over all the parameter vectors.

**Table 1.**Summary of the measured parameters in the four experimental vineyard plots from 2014 to 2019. The indicated figures and the figures in the brackets (where applicable) are the mean and the coefficient variation (CV) of the 6-year measurements in each plot, respectively. The yearly values for the measured cluster weight and cluster number per vine at harvest are taken from the median of the measurements over 20 random replicates (vines) at each plot (refer to Table S1 for more details). Note the measured individual harvestable cluster weight (kg) is independent from the training system, and mainly determined by variety. The training system parameters are mostly empirically determined according to a local expert´s experience.

Vineyard Parameters | Plot S | Plot D | Plot O | Plot M | ||
---|---|---|---|---|---|---|

Touriga Nacional with a Single Cordon | Touriga Nacional with a Double Cordon | Touriga Franca with a Single Cordon | Touriga Franca with a Double Cordon | |||

Lat: 41.137° N Lon: −7.262° W | Lat: 41.215° N Lon: −7.538° W | Lat: 41.040° N Lon: −7.037° W | Lat: 41.153° N Lon: −7.623° W | |||

Target parameters | Flowering day (Julian day) | 132 (6%) | 139 (7%) | 135 (4%) | 140 (9%) | |

Harvest day (Julian day) | 261 (3%) | 262 (5%) | 261 (6%) | 261 (4%) | ||

Yield (kg/ha) | 5156 (37%) | 6871 (27%) | 5793 (11%) | 5263 (24%) | ||

Growth parameters | Individual cluster weight at harvest (kg) | 0.109 (19%) | 0.108 (23%) | 0.180 (22%) | 0.185 (20%) | |

Cluster number per vine at harvest | 11 (27%) | 19 (14%) | 8 (18%) | 10 (20%) | ||

Training system parameters | Planting density (vines/ha) | 4132 | 3344 | 4040 | 3030 | |

Trunk height (m) | 0.6 | 0.6 | 0.6 | 0.6 | ||

Inter-row distance (m) | 2.2 | 2.2 | 2.2 | 2.2 | ||

Maximum canopy height (include trunk height) (m) | 1.6 | 1.6 | 1.6 | 1.6 | ||

Maximum canopy width (m) | 0.5 | 0.6 | 0.5 | 0.6 | ||

Initial state (assumed at dormancy) | Initial plant carbon (kg/ha) | 3175 | 2801 | 3105 | 2538 | |

Initial plant nitrogen (kg/ha) | 47.5 | 42.1 | 46.5 | 38.2 |

**Table 2.**List of tested STICS model parameters (description and value range) for calibration. Each genotype-dependent parameter was tested with five different values while the two generic (plant-specific) parameters were tested with three different values. In total, there are 703,125 parameter combinations (684,375 effective combinations) involved in the model calibration.

STICS Codes | Parameter Abbreviations | Description | Units | Min | Max | Interval | |
---|---|---|---|---|---|---|---|

Genotype-dependent parameters | stdrpnou | FS | Fruit setting thermal requirement | degree day^{−1} | 50 | 350 | 75 |

afruitpot | FN | Potential fruit number formation per degree day^{−1} per cluster accumulated during fruit setting | / | 0.5 | 2.5 | 0.5 | |

dureefruit | FF | Fruit filling thermal requirement | degree day^{−1} | 700 | 1500 | 200 | |

pgrainmaxi | FW | Genetic potential dry fruit (berry) weight | g | 0.5 | 1.7 | 0.3 | |

stamflax | VG | Thermal requirement between juvenile onset and veraison onset | degree day^{−1} | 600 | 1400 | 200 | |

stlevdrp | RG | Thermal requirement between budbreak onset and reproductive onset | degree day^{−1} | 250 | 450 | 50 | |

stdrpdes | WD | Thermal requirement between reproductive onset and fruit water dynamic onset | degree day^{−1} | 100 | 300 | 50 | |

Generic or plant-dependent parameters | nboite | BN | Box number or fruit age class | / | 5 | 15 | 5 |

spfrmin | SS | Source sink ratio threshold that affects fruit setting | / | 0.25 | 0.75 | 0.25 |

**Table 3.**List of parameters that respectively minimize the sum of the nRMSE based on the multivariate objective function (combined phenology and yield), and the nRMSE for phenology and yield separately based on the univariate function. Since RG is the only parameter that affects flowering date, a possible difference in values that minimize the nRMSE between the flowering and harvest date is indicated (F: flowering date; H: harvest date). The parameters with the proposed stable calibration are highlighted in bold, whereas the unstable calibrated parameters are underlined (see Section 2.3.4 for details).

Grapevine Parameter Abbreviation | Touriga Nacional with a Single Cordon | Touriga Nacional with a Double Cordon | Touriga Franca with a Single Cordon | Touriga Franca with a Double Cordon | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

To Minimize | To Minimize | To Minimize | To Minimize | |||||||||||||

Objective Function | Phenology | Yield | Objective Function | Phenology | Yield | Objective Function | Phenology | Yield | Objective Function | Phenology | Yield | |||||

FS | 200 | 275 | 50 | 125 | 50 | 125 | 350 | 275 | 125 | 125 | 350 | 50 | ||||

FN | 0.5 | 2.5 | 2.5 | 1.0 | 0.5 | 1.0 | 1.5 | 2.5 | 2.5 | 1.5 | 2.5 | 1.0 | ||||

FF | 700 | 700 | 700 | 1500 | 700 | 1500 | 1500 | 700 | 1500 | 1300 | 700 | 1500 | ||||

FW | 0.5 | 1.1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 1.7 | 1.1 | 0.5 | 1.7 | 1.4 | ||||

VG | 800, 1000 | 800 | 1000 | 600 | 600, 800 | 600 | 600 | 1000, 1200 | 600 | 600 | 600 | 600 | ||||

RG | 250 | 300 (F) | 450 (H) | 450 | 300 | 300 (F) | 250 (H) | 450 | 300 | 300 (F) | 450 (H) | 450 | 300 | 300 (F) | 400 (H) | 450 |

WD | 300 | 100 | 100–300 | 250, 300 | 300 | 150–300 | 150, 200 | 100 | 150–300 | 300 | 100 | 150–300 | ||||

BN | 5 | 5 | 5 | 15 | 15 | 10 | 15 | 5 | 15 | 10 | 5 | 15 | ||||

SS | 0.25, 0.5, 0.75 | 0.75 | 0.25 | 0.25 | 0.25, 0.5, 0.75 | 0.25 | 0.25 | 0.75 | 0.25 | 0.75 | 0.75 | 0.5 |

**Table 4.**Summary of various goodness-of-fit measures on the parameter combinations identified from the multivariate objective function, which is highlighted in bold, and from the univariate function that minimize the nRMSE for flowering date, harvest date and yield separately (highlighted in italic). MBE denotes Mean Biased Error; MAE denotes Mean Absolute Errors; RMSE denotes Root Mean Squared Errors; Rsd denotes the ratio of standard deviation of simulations to that of the observations.

Goodness-Of-Fit Statistics for the Study Variables | Touriga Nacional with a Single Cordon | Touriga Nacional with a Double Cordon | Touriga Franca with a Single Cordon | Touriga Franca with a Double Cordon | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Objective Function | Univariate Function | Objective Function | Univariate Function | Objective Function | Univariate Function | Objective Function | Univariate Function | ||||||||||

Flower | Harvest | Yield | Flower | Harvest | Yield | Flower | Harvest | Yield | Flower | Harvest | Yield | ||||||

Flower Date | MBE | 4 | −3 | −22 | −22 | 1 | 1 | 8 | −18 | 1 | 1 | −16 | −16 | 2 | 2 | −11 | −18 |

MAE | 4 | 4 | 22 | 22 | 4 | 4 | 8 | 18 | 4 | 4 | 16 | 16 | 4 | 4 | 11 | 18 | |

RMSE | 6 | 5 | 22 | 22 | 4 | 4 | 10 | 18 | 6 | 6 | 17 | 17 | 4 | 4 | 12 | 18 | |

nRMSE | 4% | 4% | 16% | 16% | 3% | 3% | 7% | 13% | 5% | 5% | 12% | 12% | 3% | 3% | 8% | 13% | |

Rsd | 1.5 | 1.5 | 1.3 | 1.3 | 1.2 | 1.2 | 1.3 | 1.1 | 1.7 | 1.7 | 1.6 | 1.6 | 0.9 | 0.9 | 0.9 | 0.9 | |

Harvest Date | MBE | −2 | 14 | −2 | 5 | −1 | −4 | 1 | −2 | −1 | 21 | 2 | −4 | −2 | 4 | −2 | 2 |

MAE | 6 | 14 | 3 | 6 | 3 | 5 | 3 | 4 | 10 | 21 | 5 | 9 | 12 | 11 | 3 | 8 | |

RMSE | 6 | 16 | 4 | 8 | 4 | 6 | 3 | 5 | 10 | 25 | 6 | 11 | 12 | 11 | 4 | 10 | |

nRMSE | 2% | 6% | 1% | 3% | 1% | 2% | 1% | 2% | 4% | 10% | 2% | 4% | 5% | 4% | 1% | 4% | |

Rsd | 1.4 | 1.8 | 0.9 | 1.6 | 0.8 | 0.8 | 0.9 | 0.8 | 0.6 | 1.1 | 0.8 | 0.6 | 1.4 | 1.4 | 0.9 | 1.0 | |

Yield (kg/ha) | MBE | −232 | −8317 | −3865 | 236 | −16 | 4853 | 4533 | 209 | 104 | −4382 | −1301 | −158 | 159 | −9265 | −6612 | 258 |

MAE | 1168 | 8317 | 3865 | 980 | 1417 | 4853 | 4533 | 1249 | 1294 | 4382 | 2822 | 1117 | 1226 | 9265 | 6612 | 1104 | |

RMSE | 1255 | 8720 | 4808 | 1060 | 1718 | 5290 | 4941 | 1544 | 1478 | 4984 | 3217 | 1258 | 1611 | 10435 | 8159 | 1315 | |

nRMSE | 24% | 169% | 93% | 21% | 25% | 77% | 72% | 22% | 26% | 86% | 56% | 22% | 31% | 198% | 155% | 25% | |

Rsd | 0.7 | 1.8 | 1.9 | 1.1 | 0.7 | 0.3 | 0.3 | 0.7 | 1.8 | 3.8 | 4.5 | 1.5 | 0.7 | 3.8 | 3.7 | 0.6 |

**Table 5.**Evaluations of the selected parameter vectors identified from the objective function (listed in Table 3) using additional, independent observations. Observational data were obtained from an experimental vineyard (Lat: 41.15° N, Lon: −7.75° W) in the Douro Demarcated Region between 2012 and 2014 for Touriga Nacional (double-cordon system) and between 2012 and 2013 for Touriga Franca (double-cordon system) (Fraga et al., 2015). MBE denotes Mean Biased Error; MAE denotes Mean Absolute Errors; RMSE denotes Root Mean Squared Errors; Rsd denotes the ratio of standard deviation of simulations to that of the observations.

Evaluation Statistics of Studied Variables | Touriga Nacional with a Double Cordon | Touriga Franca with a Double Cordon | |
---|---|---|---|

Flowering Date | MBE (days) | 10 | 3 |

MAE (days) | 10 | 3 | |

RMSE (days) | 11 | 3 | |

nRMSE (%) | 7% | 2% | |

Rsd | 1.7 | 1.5 | |

Harvest Date | MBE (days) | 0 | −15 |

MAE (days) | 11 | 15 | |

RMSE (days) | 12 | 17 | |

nRMSE (%) | 4% | 6% | |

Rsd | 1.3 | 0.9 | |

Yield | MBE (kg/ha) | −466 | 619 |

MAE (kg/ha) | 1196 | 619 | |

RMSE (kg/ha) | 1208 | 730 | |

nRMSE (%) | 16% | 11% | |

Rsd | 1.0 | 0.6 |

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**MDPI and ACS Style**

Yang, C.; Menz, C.; Fraga, H.; Reis, S.; Machado, N.; Malheiro, A.C.; Santos, J.A.
Simultaneous Calibration of Grapevine Phenology and Yield with a Soil–Plant–Atmosphere System Model Using the Frequentist Method. *Agronomy* **2021**, *11*, 1659.
https://doi.org/10.3390/agronomy11081659

**AMA Style**

Yang C, Menz C, Fraga H, Reis S, Machado N, Malheiro AC, Santos JA.
Simultaneous Calibration of Grapevine Phenology and Yield with a Soil–Plant–Atmosphere System Model Using the Frequentist Method. *Agronomy*. 2021; 11(8):1659.
https://doi.org/10.3390/agronomy11081659

**Chicago/Turabian Style**

Yang, Chenyao, Christoph Menz, Helder Fraga, Samuel Reis, Nelson Machado, Aureliano C. Malheiro, and João A. Santos.
2021. "Simultaneous Calibration of Grapevine Phenology and Yield with a Soil–Plant–Atmosphere System Model Using the Frequentist Method" *Agronomy* 11, no. 8: 1659.
https://doi.org/10.3390/agronomy11081659