# Global Sensitivity Analysis for CERES-Rice Model under Different Cultivars and Specific-Stage Variations of Climate Parameters

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}level conditions by using the EFAST method; they demonstrated that the orders of the same influential parameters in different climate conditions were different. Roberto et al. [31] also analyzed the parameter sensitivity to the rice model WARM under various environment and climatic conditions and then the necessity of SA within different modeling environments was emphasized.

## 2. Materials and Methods

#### 2.1. Field Experiments

^{−2}. Each cultivar had the same cultivated area with 2.5 m $\times $ 5.5 m. All the experimental cultivars had the same fertilizer treatment with 195 kg ha

^{−1}N, 112 kg ha

^{−1}P

_{2}O

_{5}and 112 kg ha

^{−1}K

_{2}O. Other field management practices followed the local standard procedures for rice production in this region.

#### 2.2. Data Observation

#### 2.3. CERES-Rice Model

#### 2.3.1. Model Description

#### 2.3.2. Crop Modeling

- (1)
- Set parameter range by using the default range (Table A1) in the CERES-Rice model. Uniform parameter distributions were assumed to generate parameter sets. In this study, 10,000 parameter sets were randomly generated by Python 3.6.
- (2)
- Select the observation data including anthesis date, maturity date, and grain yield as our objectives.
- (3)
- Run the CERES-Rice model. The executable file “DSCSM047.exe” was looped called Python 3.6 based on the abovementioned parameter sets.
- (4)
- Calculate the likelihood value. A likelihood function which was described by He et al. [41] was implemented to obtain likelihood values based on simulations and observations.
- (5)
- Calculate the cultivar parameters based on the maximum likelihood value.

#### 2.4. Sensitivity Analysis

#### 2.4.1. Sobol’ Method

#### 2.4.2. Top-Down Concordance Coefficient ($TDCC$)

## 3. Results

#### 3.1. Distribution of Observation Data across Different Cultivars

#### 3.2. Sensitivity Analysis during the Rice Growth Season

#### 3.3. Sensitivity Analysis under Specific-Stage Variations of Climate Parameters

#### 3.3.1. Sensitivity Analysis under the Variation of Climate Parameters at the Vegetative Phase

#### 3.3.2. Sensitivity Analysis under Variation of Climate Parameters at the Panicle-Formation Phase

#### 3.3.3. Sensitivity Analysis under Variation of Climate Parameters at the Ripening Phase

## 4. Discussion

#### 4.1. Sensitivity Analysis of Different Cultivars for Model Outputs during the Rice Growth Season

#### 4.2. Effects of Specific-Stage Variations of Climate Parameters on Sensitivity

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Parameter | Description | Unit | Range |
---|---|---|---|

P1 | Time period in °C above a base temperature of 9 °C during the basic vegetative phase | GDD (°C) | 210–900 |

P2O | Critical photoperiod (in hours) at which the development occurs at a maximum rate | hours | 10.4–13 |

P2R | Extent to which phasic development leading to panicle initiation is delayed for each hour increase in photoperiod above P2O | GDD h^{−1} | 30–200 |

G1 | Potential spikelet number coefficient | -- | 50–80 |

G3 | Tillering coefficient relative to IR64 cultivar under ideal conditions | -- | 0.3–1 |

G4 | Temperature tolerance coefficient | -- | 0.8–1.25 |

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**Figure 1.**Typical workflow for global SA across 30 cultivars in the CERES-Rice model. Strategy 1–4 represent the variations of climate parameters at vegetative phase, panicle-formation phase, ripening phase, and the whole growth season, respectively.

**Figure 2.**Distribution of Sobol’ total order effects ($S{T}_{i}$) for 16 investigated parameters under different cultivar types during the whole rice growth season: (

**a**–

**c**) outputs for ADAP, MDAP, and yield.

**Figure 3.**The mean first order index (${S}_{i}$) and interactions under different cultivar types during the whole rice growth season. The bottom title of each subfigure means the SA for specific outputs (ADAP, MDAP, and yield) under different cultivar types.

**Figure 4.**The mean first order index (${S}_{i}$) and interactions under different cultivar types under variation of climate parameters at the vegetative phase. The bottom title of each subfigure shows the SA for specific outputs (ADAP, MDAP, and yield) under different cultivar types.

**Figure 5.**The mean first order index (${S}_{i}$) and interactions under different cultivar types under the variation of climate parameters at the panicle-formation phase. The bottom title of each subfigure shows the SA for specific outputs (ADAP, MDAP, and yield) under different cultivar types.

**Figure 6.**The mean first order index (${S}_{i}$) and interactions under different cultivar types under variation of climate parameters at the ripening phase. The bottom title of each subfigure shows the SA for specific outputs (ADAP, MDAP, and yield) under different cultivar types.

**Figure 7.**The main total sensitivity indices ($S{T}_{i}$ > 0.05 at the whole growth season) for the model outputs under the specific-stage variations of climate parameters. (

**a**,

**e**,

**i**), (

**b**,

**f**,

**j**), (

**c**,

**g**,

**k**), and (

**d**,

**h**,

**l**) represent the main influential parameters for model outputs (ADAP, MDAP, and yield) under variations of climate parameters for the whole growth season, vegetative phase, panicle-formation phase, and ripening phase, respectively.

Layer (m) | Clay (%) | Silt (%) | OC (%) | TN (%) | LL (%) | DUL (%) | SAT (%) | BD (g cm^{−3}) |
---|---|---|---|---|---|---|---|---|

0–0.2 | 25.96 | 28.6 | 2.13 | 0.18 | 21.4 | 37.0 | 48.3 | 1.26 |

0.2–0.4 | 25.13 | 27.1 | 2.12 | 0.20 | 20.9 | 36.2 | 48.0 | 1.27 |

0.4–0.6 | 23.03 | 25.7 | 1.73 | 0.17 | 18.8 | 32.7 | 46.4 | 1.32 |

0.6–0.8 | 22.99 | 27.9 | 1.51 | 0.19 | 18.2 | 32.0 | 46.2 | 1.33 |

0.8–1.0 | 24.5 | 28 | 1.58 | 0.16 | 19.2 | 33.2 | 46.5 | 1.32 |

Type of Cultivar | Sowing | Transplanting | Initial Heading | Flowering | Full Heading | Maturity |
---|---|---|---|---|---|---|

Mid-season | 15 May | 6 June | 2 August–10August | 4 August–12 August | 7 August–14 August | 10 September–16 September |

Late-season | 24 June | 15 July | 29 August–5 September | 31 August–7 September | 2 September–9 September | 17 October–24 October |

One-season-late | 10 June | 29 June | 24 August–30 August | 26 August–1 September | 29 August–3 September | 10 October–12 October |

Type | Parameter | Description | Unit | Range |
---|---|---|---|---|

Cultivar parameter | P1 | Time period in °C above a base temperature of 9 °C during the basic vegetative phase. | GDD (°C) | $\pm 30\%$ |

P2O | Critical photoperiod (in hours) at which the development occurs at a maximum rate. | hours | $\pm 30\%$ | |

P2R | Extent to which phasic development leading to panicle initiation is delayed for each hour increase in photoperiod above P2O | GDD h^{−1} | $\pm 30\%$ | |

P5 | Time period in °C above a base temperature of 9 °C from beginning of grain filling (3–4 days after anthesis) to physiological maturity. | GDD (°C) | $\pm 30\%$ | |

G1 | Potential spikelet number coefficient | -- | $\pm 30\%$ | |

G2 | Single grain weight (g) under ideal growing conditions | g | $\pm 30\%$ | |

G3 | Tillering coefficient relative to IR64 cultivar under ideal conditions. | -- | $\pm 30\%$ | |

G4 | Temperature tolerance coefficient. | -- | $\pm 30\%$ | |

Species parameter | SHFC | Shock calculation method (1-standard, 2-Salaam) | -- | $\pm 30\%$ |

RWEP | Species coefficient | -- | $\pm 30\%$ | |

PORM | Minimum pore space | -- | 0–0.3 | |

RWMX | Max root water uptake | -- | $\pm 30\%$ | |

RLWR | Root length weight ratio | -- | $\pm 30\%$ | |

Climate parameter | SRAD | Daily solar radiation | MJ m^{−2} day^{−1} | $\pm 30\%$ |

Tavg | Daily average temperature | °C | $\pm 30\%$ | |

RAIN | Daily rainfall | mm day^{−1} | $\pm 30\%$ |

**Table 4.**Distributions of anthesis and maturity dates, and grain yield among mid-season, late-season, and one-season-late rice cultivars in 2018.

Observation Index | Cultivar Type | Number of Cultivars | Statistical Indicators | |||
---|---|---|---|---|---|---|

Mean | Median | 25th Percentile | 75th Percentile | |||

Anthesis date | Mid-season | 12 | 8-August | 8-August | 7-August | 9-August |

Late-season | 9 | 3-September | 2-September | 1-September | 4-September | |

One-season-late | 9 | 29-August | 30-August | 26-August | 30-August | |

Maturity date | Mid-season | 12 | 12-September | 13-September | 10-September | 14-September |

Late-season | 9 | 20-October | 19-October | 18-October | 21-October | |

One-season-late | 9 | 11-October | 12-October | 11-October | 12-October | |

Yield (t ha^{−1}) | Mid-season | 12 | 9.7 | 9.6 | 9.4 | 10.1 |

Late-season | 9 | 8.2 | 7.8 | 8.0 | 8.5 | |

One-season-late | 9 | 9.9 | 9.7 | 9.6 | 10.1 |

**Table 5.**$TDCC$ values based on the results of Sobol’ total order effects ($S{T}_{i}$ ) under the same cultivar type and different cultivar types over the whole growth season.

Model Output | Same Cultivar Type | Different Cultivar Types | ||||
---|---|---|---|---|---|---|

Late-Season | One-Season-Late | Mid-Season | L-O | L-M | O-M | |

ADAP | 0.95 | 0.98 | 0.94 | 0.99 | 0.99 | 0.99 |

MDAP | 0.98 | 0.96 | 0.98 | 0.98 | 0.98 | 0.98 |

Yield | 0.98 | 0.99 | 0.97 | 1.00 | 1.00 | 1.00 |

**Table 6.**$TDCC$ values based on the results of Sobol’ total order effects ($S{T}_{i}$ ) under the same cultivar type and different cultivar types with variation of climate parameters at the vegetative phase.

Model Output | Same Cultivar Type | Different Cultivar Types | ||||
---|---|---|---|---|---|---|

Late-Season | One-Season-Late | Mid-Season | L-O | L-M | O-M | |

ADAP | 0.98 | 0.99 | 0.98 | 1.00 | 1.00 | 1.00 |

MDAP | 0.98 | 0.97 | 0.95 | 0.99 | 0.98 | 0.98 |

Yield | 0.96 | 0.97 | 0.99 | 0.99 | 0.97 | 0.97 |

**Table 7.**$TDCC$ values based on the results of Sobol’ total order effects ($S{T}_{i}$ ) under the same cultivar type and different cultivar types with variation of climate parameters at the panicle-formation phase.

Model Output | Same Cultivar Type | Different Cultivar Types | ||||
---|---|---|---|---|---|---|

Late-Season | One-Season-Late | Mid-Season | L-O | L-M | O-M | |

ADAP | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 |

MDAP | 0.96 | 0.96 | 0.97 | 0.96 | 0.96 | 0.96 |

Yield | 0.96 | 0.98 | 0.97 | 0.98 | 0.98 | 0.98 |

**Table 8.**$TDCC$ values based on the results of Sobol’ total order effects ($S{T}_{i}$ ) under the same cultivar type and different cultivar types with variation of climate parameters at the ripening phase.

Model Output | Same Cultivar Type | Different Cultivar Types | ||||
---|---|---|---|---|---|---|

Late-Season | One-Season-Late | Mid-Season | L-O | L-M | O-M | |

ADAP | 0.99 | 1.00 | 0.99 | 0.99 | 0.99 | 0.99 |

MDAP | 0.96 | 0.97 | 0.97 | 0.96 | 0.95 | 0.95 |

Yield | 0.97 | 0.98 | 0.98 | 0.99 | 0.98 | 0.98 |

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**MDPI and ACS Style**

Ge, H.; Ma, F.; Li, Z.; Du, C.
Global Sensitivity Analysis for CERES-Rice Model under Different Cultivars and Specific-Stage Variations of Climate Parameters. *Agronomy* **2021**, *11*, 2446.
https://doi.org/10.3390/agronomy11122446

**AMA Style**

Ge H, Ma F, Li Z, Du C.
Global Sensitivity Analysis for CERES-Rice Model under Different Cultivars and Specific-Stage Variations of Climate Parameters. *Agronomy*. 2021; 11(12):2446.
https://doi.org/10.3390/agronomy11122446

**Chicago/Turabian Style**

Ge, Haixiao, Fei Ma, Zhenwang Li, and Changwen Du.
2021. "Global Sensitivity Analysis for CERES-Rice Model under Different Cultivars and Specific-Stage Variations of Climate Parameters" *Agronomy* 11, no. 12: 2446.
https://doi.org/10.3390/agronomy11122446