# Global Optimization of Cultivar Trait Parameters in the Simulation of Sugarcane Phenology Using Gaussian Process Emulation

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

^{2}0.93–0.98; normalized root mean squared error: 5–22%; Willmott’s agreement index: 0.87–0.99). The best parametrization was obtained under the lowest water stressed conditions. Based on these results, we suggest that GP emulation can be efficiently implemented for the parameterization of computationally expensive simulators.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Field

#### 2.2. APSIM Simulation

- sowing: from sowing to sprouting;
- sprouting: from sprouting to emergence;
- emergence: from emergence to the beginning of cane growth;
- begin cane: from the beginning of cane growth to flowering;
- flowering: from flowering to the end of the crop;
- end of the crop: crop is not currently in the simulated system.

_{SIM}, experiment B1 was denoted as B1

_{SIM}and experiment B2 was denoted as B2

_{SIM}. Biomass and CDW at different DAP (indicated in Table 1: Observed data) were selected as the outputs of each simulation. These simulations were used in building emulators (described in Section 2.3.2), emulator accuracy evaluation (described in Section 2.3.3) and checking the goodness of the optimization process (described in Section 2.5).

#### 2.3. Emulation

**m**) to reduce the cost of training runs. Whenever a simulation run is needed at a point (e.g.,

**q**), a fast prediction from a metamodel $\widehat{\mathit{m}}$

**(q)**can be used to replace the costly value

**m**(

**q**).

#### 2.3.1. Gaussian Process-Based Emulation

_{1}, x

_{2}, …, x

_{p}]), then Y is a random function in a Bayesian framework. According to Kennedy and O’Hagan [37], GP can be considered to be a flexible and convenient class of distributions that can be used to represent prior understanding about f(X). A prior distribution can therefore be assumed to be a multi-variate normal function that is characterized by a linear additive mean (Equation (1)) and a covariance function (Equation (2)). The covariance function is specified to characterize the smoothness of the output.

_{1}, x

_{2}, …, x

_{p}]) and $\beta $

_{0}, $\beta $

_{1}, …, $\beta $

_{p}are unknown coefficients. $cov\left(f\left(x\right),f\left(x\right){}^{\prime}\right)$ is the covariance function of any pair of joint probability distribution $\left(f\left(x\right),f\left(x\right){}^{\prime}\right)$, ${r}_{i}$ is a scaling parameter determining how rough the function is with respect to the ith input and ${\sigma}^{2}$ is the overall variance of the mean function.

_{1}, x

_{2}, …, x

_{p}]).

#### 2.3.2. Building Emulators

_{SIM}, B1

_{SIM}and B2

_{SIM}(described in Section 2.2) producing 500 simulations per single experiment. Required scripts were created using the jsonlite [39], DBI [40] and RSQLite [41] packages of R.

#### 2.3.3. Emulator Accuracy Evaluation

^{2}), leave-one-out cross-validated root-mean-squared standardized error (CV

_{RMSSE}) and sigma-squared value (σ

^{2}).

^{2}was calculated between the APSIM-simulated values and the emulator-predicted values. While developing each emulator, the remaining 200 parameter ensembles that were not used to generate emulators (described in Section 2.3.2) were used in the GEM-SA for obtaining the emulator-predicted outputs. Additionally, corresponding APSIM simulated outputs of the 200 parameter ensembles mentioned in Section 2.3.2 were used here as simulator predicted outputs. Then, both the emulator and simulator predictions were graphed to determine the R

^{2}between them. The emulators with R

^{2}values close to 1.0 were considered to be highly accurate. R

^{2}of emulator accuracy is hereafter denoted by ${R}_{emu}^{2}$.

_{RMSSE}and σ

^{2}were computed internally by the GEM-SA while building emulators with 300 training data points. To calculate CV

_{RMSSE}in GEM-SA, leave-one-out-cross-validation was used. In briefly, it fits the emulator by leaving one data point from the training data and, the missing point is predicted from the fitted emulator. This is repeated for all combinations of training data to provide overall effectiveness of the emulator as CV

_{RMSSE}. According to Qin et al. [43] and Sexton [44], the emulator variance is considered to have accurately estimated the actual error variance if the CV

_{RMSSE}is close to 1; overestimation and underestimation are indicated by lower and higher values, respectively.

_{RMSSE}as follows:

_{i}is the true output for the ith training run, $\widehat{y}$ is the corresponding emulator approximation, s

_{i}is the standard deviation calculated with the ith training point removed and n is the number of runs” [45].

^{2}value effectively measures the nonlinearity of an emulator via indicting the emulator variance after the output standardization. For a linear model, the σ

^{2}value is close to 0, whereas moderately to highly nonlinear models have greater σ

^{2}values (without a defined cutoff value).

#### 2.4. Global Optimization

_{i}) of the next successive generation, three random parameter vectors of the existing population (x

_{r0}, x

_{r1}and x

_{r2}) are selected, and v

_{i}is generated by using ${v}_{i}\dot{=}{x}_{ro}+F\xb7\left({x}_{r1}-{x}_{r2}\right)$, where F is a differential weighting factor, effective values of which are typically between 0 and 1. After the first mutation, the remaining parameter vectors of successive generations are created by continuing the mutation with a crossover probability $CR\in \left[0,1\right]$. The fraction of the parameter values that are copied from a mutant is controlled by the CR. During the process, all elements of the vector are created with respect to the defined lower and upper bounds of the parameters. The corresponding values of the objective function with respect to each trial vector are then determined. The previous vector in the population is replaced if the objective function value of a particular trial vector is equal to or lower than the previous vector; otherwise, the previous vector is retained.

_{i}is the value of the ith observation, Ep

_{i}is the emulator-predicted value of the ith observation, and n is the number of observations.

_{i}).

#### 2.5. Validation of Optimized Parameters

#### 2.5.1. Validation—Step One

_{i}) were obtained. Then, Ep

_{i}, Sp

_{i}, and O

_{i}were graphed together, and the normalized root mean square error (NRMSE), R

^{2}, and Willmott’s agreement index (AI) were calculated to evaluate the accuracy of the optimized results. The R

^{2}was calculated from the linear regression between the observed and simulated values (Ep

_{i}and Sp

_{i}). The NRMSE (Equation (5)) was equated to the RMSE divided by the output range and was reported as a percentage. The AI is a measure of non-parametric goodness of fit (Equation (6)), and the desired value is close to one.

_{i}indicates ith simulated value, O

_{i}indicates the value of ith observation, and ${O}_{max}-{O}_{min}$ is the range of observed values.

^{2}and AI of the first validation step are hereafter denoted by NRMSE

_{opt}, ${R}_{opt}^{2}$ and AI

_{opt}, respectively. Results of the validation step one was indicated under Section 3.2.1.

#### 2.5.2. Validation—Step Two

^{2}, NRMSE, and AI between the observed values and simulator predictions. Comparing all optimized parameter ensembles based on the validation results of step one and two, an optimal parameter ensemble was selected for each cultivar to parameterize APSIM-Sugarcane for estimating biomass and CDW. Validation process of step two was showed in Figure 2.

^{2}and AI of second validation step are hereafter denoted by NRMSE

_{val}, ${R}_{val}^{2}$ and AI

_{val}, respectively. Results were depicted using box diagrams and dot plots under Section 3.2.2. Finally, the selected optimal parameter ensembles were compared.

## 3. Results and Discussion

#### 3.1. Emulator Accuracy

^{2}(Figure 4), and the CV

_{RMSSE}values (Figure 5).

^{2}and CV

_{RMSSE}values to assess the performances of the emulators.

^{2}values ranged between 0.06 and 1.64 for all emulators (Figure 4). We observed relatively high σ

^{2}values for the early stages of CDW (e.g., 96_DAP of experiment A and 99_DAP of experiment B1). This pattern was consistent with the observations of low ${R}_{emu}^{2}$ values under those conditions. The computed values of CV

_{RMSSE}of the emulators were ranged between 0.74 and 1.01 (Figure 5).

^{2}values for their emulators ranged between 0.13 and 1.6, Qin et al. [43] have reported that the σ

^{2}values for their emulators ranged between 0.6 and 2.1 and the parameters they used showed only moderate deviation from the linearity. Gunarathna et al. [30] have indicated that their emulators showed good to moderate linearity with σ

^{2}values that ranged from 0.10 to 1.43. It can hence be concluded that good linearity was shown by our emulators under all considered environmental and management condition.

_{RMSSE}values obtained by Gunarathna et al. [30], Kennedy and Petropoulos [45] and Petropoulos et al. [46] the values we obtained were lower, and the fact that they were close to 1.0 in all the experiments suggested that the built emulators could represent the true model well.

#### 3.2. Validation of Optimized Parameters

#### 3.2.1. Validation—Step One

_{opt}percentages and the AI

_{opt}values between sugarcane yields simulations obtained with the optimized parameter ensembles and observed sugarcane yields.

_{opt}values and the NRMSE

_{opt}percentages fell in the ranges 0.95–1, 0.97–1 and 1–11.32%, respectively. The indication was that all parameter ensembles obtained from the optimization could probably be used to approximate observed values using APSIM.

#### 3.2.2. Validation—Step Two

_{val}and AI

_{val}values among cultivars and parameter ensembles (Figure 8).

_{val}percentages and AI

_{val}values of the parameter ensembles P3 of cultivar KK3 (NRMSE

_{val}%: 8–14%, AI

_{val}: 0.94–0.99), P5 of cultivar LK92-11 (NRMSE

_{val}%: 6–22%, AI

_{val}: 0.87–0.99%) and the P3 of cultivar 02-2-058 (NRMSE

_{val}%: 5–19%, AI

_{val}: 0.95–0.99) indicated relatively high performance (Table 4). They could therefore be selected as the best parameter ensemble to parametrize the APSIM-Sugarcane model for cultivars KK3, LK92-11 and 02-2-058. All NRMSE

_{val}percentages were dispersed closer to 0 than other parameter ensembles (Figure 8). Moreover, those parameter ensembles corresponded to the lowest AI

_{val}values, and the data points were dispersed closer to 1 than the data points of the other parameter ensembles of the respective cultivars (Figure 8).

_{val}%), where optimized parameter ensembles (P1 and P2) for experiment A resulted in comparatively high NRMSE

_{val}percentages when estimating the observed sugarcane yield of experiment B1. To explain this pattern, we simulated the “soil water deficit factor for photosynthesis (swdef_photo)” in the APSIM for each experiment. For instance, the swdef_photo and the observed sugarcane biomass yields of experiments A, B1 and B2 of cultivar KK3 are indicated in Figure 9. We observed that water stress conditions were most apparent in experiment A (swdef_photo near 0), than experiment B1 and B2. Due to that the lowest sugarcane yield was also observed in experiment A. Therefore, when the parameters were optimized in experiment A, the parameters were estimated to result in lower yields than in experiment B1 and B2. Use of parameters estimated to result in low yields under severe water stress conditions may lead to poor performances under low water stress conditions.

_{val}% in Figure 8. The optimized parameter ensembles for experiment B1 (P3 and P4) resulted in comparatively low NRMSE

_{val}values in the estimates of the observed sugarcane yields for experiment A. Because in APSIM-Sugarcane, parameter rue is previously identified as a highly sensitive parameter for the estimation of biomass and CDW of sugarcane [27,28,29,30]. Therefore, when optimizing parameters under low water stress conditions (B1), the estimated value of rue could be increased to estimate higher yields. When those optimized parameter ensembles are used for simulations under severe water stress conditions (A), APSIM-Sugarcane will reduce the rue because in APSIM-Sugarcane, rue tends to be reduced whenever a soil water shortage condition is met [9,51].

#### 3.3. Comparison of Optimized Parameters

_{val}: 18.14%, Exp. A_ CDW = NRMSE

_{val}: 21.61% [Figure 8: cultivar LK92-11, NRMSE

_{val}% of P5]). However, parameter ensembles of the remaining cultivars indicated satisfactory results under the same conditions (Figure 8, cultivars KK3 and 02-2-058: P3). Our results were similar to the results obtained by Preecha et al. [6] using the same field experiments and are consistent with Peerasak [52], who reported that LK92-11 was less sensitive to water shortage than KK3. Cha-um et al. [53] have also indicated that LK92-11 is tolerant to water deficit.

## 4. Conclusions

^{2}, σ

^{2}and CV

_{RMSSE}values, the emulators we built for the optimization showed satisfactory results. The indication is that these emulators can approximate the original simulator (APSIM-Sugarcane) successfully. Via the GP-based emulator optimization, we could obtain acceptable parameter ensembles for parametrization of Thai cultivars KK3, LK92-11 and 02-2-058 by using the APSIM-Sugarcane model. The optimized parameters evidenced satisfactory results during the validation under the environmental and management conditions found in KK, Thailand. Based on our validation results, we suggest that GP emulation can be efficiently implemented for parameterization of computationally expensive simulators. Future studies will be needed to reach more robust conclusions concerning the use of emulation for parameter optimization with APSIM-Sugarcane.

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Monthly weather data for Khon Kaen (KK) during 2010/12–2012/12; Rain: mean monthly rainfall (mm); Radn: daily solar radiation (MJ/m

^{2}); Maxt: daily maximum temperature (°C); Mint: daily minimum temperature (°C).

**Figure 2.**Process flow diagram of validation—step two. P1, P2, P3, P4, P5 and P6 represent the optimized parameter ensembles of each cultivar. A

_{SIM}, B1

_{SIM}and B2

_{SIM}represent the APSIM simulations described in Section 2.2.

**Figure 3.**Relationship between APSIM-simulated values and emulator-predicted values of biomass and CDW in experiment B1 at each reporting frequency at days after planting (DAP): 99, 128, 185, 238, 267, 299, 329, 360 and 390. Solid lines indicate linear fit to the APSIM-simulated values and emulator-predicted values of biomass and CDW. : Biomass and : CDW. ${R}_{emu}^{2}$_Biomass and ${R}_{emu}^{2}$ CDW were calculated by using 200 data points.

**Figure 4.**Heat maps of σ

^{2}values of the emulators built for biomass and CDW at each reporting frequency of three experiments: Experiment A, Experiment B1 and Experiment B2. Color ranges from dark blue to white represent values from 0 to higher values.

**Figure 5.**Heat maps of CV

_{RMSSE}values of the emulators built for biomass and CDW at each reporting frequency of three experiments: Experiment A, Experiment B1 and Experiment B2. Color ranges from dark blue to light blue represent values from 1 to lower values and 1 to higher values.

**Figure 6.**Comparison between simulated (both from emulator and APSIM) and observed biomass and CDW for cultivar KK3 in experiments A, B1 and B2. NRMSE

_{opt}%: Normalized root mean square error percentage, ${R}_{opt}^{2}$: Coefficient of determination and AI

_{opt}: Agreement index.

**Figure 7.**Box plots of ${R}_{val}^{2}$ values obtained during the validation of the parameter ensembles (P1, P2, P3, P4, P5 and P6) under each experimental condition corresponding to cultivars (

**a**) KK3, (

**b**) LK92-11, and (

**c**) 02-2-058. Each parameter ensemble of the box plots indicated ${R}_{val}^{2}$ values calculated between observed and simulated yields for six different cases (A_Biomass, A_CDW, B1_Biomass, B1_CDW, B2_Biomass, and B2_CDW) of a single cultivar (see Figure 2 for more details). The median is indicated by thick black lines, the interquartile range (IQR) is indicated by the boxes, 1.5 times the IQR is indicated by the whiskers, and the outliers beyond 1.5 times the IQR are indicated by points in black color.

**Figure 8.**Dot plots of NRMSE

_{val}percentages and AI

_{val}values obtained during the validation of the parameter ensembles (P1, P2, P3, P4, P5 and P6) under each experimental condition corresponding to cultivars KK3, LK92-11, or 02-2-058. Each parameter ensemble of the dot plots indicated NRMSE

_{val}percentages and AI

_{val}values calculated between observed and simulated yields for six different cases (A_Biomass, A_CDW, B1_Biomass, B1_CDW, B2_Biomass and B2_CDW) of a single cultivar (see Figure 2).

**Figure 9.**Observed biomass weight (g m

^{−2}), APSIM-simulated soil water deficit factor (0 = full stress and 1 = no stress) for photosynthesis (swdef_photo) and nitrogen deficit factor (0 = full stress and 1 = no stress) for photosynthesis (nfact_photo) of cultivar KK3 in experiments A, B1 and B2 from planting to harvesting.

**Figure 10.**Observed biomass weight (gm

^{−2}) of selected parameter ensembles of each cultivar under optimized experimental conditions. Cultivars KK3 and 02-2-058: observed biomass yield in experiment B1 and cultivar LK92-11: observed biomass yield in experiment B2. Growth stages were obtained from the APSIM-Sugarcane simulations using the corresponding parameter ensemble and APSIM simulation files.

Experiment A | Experiments B1 and B2 | |
---|---|---|

Planting date | 1/12/2010 | 28/11/2011 |

Harvesting date | 20/12/2011 | 22/12/2012 |

Cultivars | 02-2-058, KK3, LK92-11 | |

Water supply | Rainfed ^{a} (A) | Irrigated ^{b} (B1) and Rainfed ^{a} (B2) |

Fertilizer | 93.5:40.80:77.62 kg of N:P:K per hectare | |

Observed data | Biomass and CDW of experiment A were recorded at; 96, 117, 147 173, 244, 29 and 388 days after planting (DAP) and experiment B1 and B2 at; 99, 128, 185, 238, 267, 299, 329, 360 and 390 DAP |

^{a}Amount of water applied: 24 mm per week from planting to 45 DAP,

^{b}Amount of water applied: 24 mm per week from planting to harvest.

Soil Depth (cm) | Texture Class * | Wilting Point (mm/mm) | Field Capacity (mm/mm) | Saturation (mm/mm) | Hydraulic Conductivity (mm/day) | Bulk Density (g/cm^{3}) |
---|---|---|---|---|---|---|

0–20 | Loamy soil | 0.075 | 0.206 | 0.357 | 3336 | 1.52 |

20–50 | Sandy loam | 0.116 | 0.236 | 0.395 | 2232 | 1.61 |

50–100 | Sandy clay loam | 0.124 | 0.238 | 0.410 | 2232 | 1.57 |

Function of Parameters | Parameter Name | Description | Level | Code | Units | Parameter Space * |
---|---|---|---|---|---|---|

Canopy development | leaf_size | Area of the respective leaf | leaf_size_no = 1 | LS1 | mm^{2} | 500–2000 |

leaf_size_no = 14 | LS2 | mm^{2} | 20,000–70,000 | |||

leaf_size_no = 20 | LS3 | mm^{2} | 20,000–70,000 | |||

green_leaf_no | Maximum number of fully expanded green leaves | GLN | No. | 9–15 | ||

tillerf_leaf_size | Tillering factors according to the leaf numbers | Tiller_leaf_size_no = 1 | TLS1 | mm^{2}/mm^{2} | 1–6 | |

Tiller_leaf_size_no = 4 | TLS2 | mm^{2}/mm^{2} | 1–6 | |||

Tiller_leaf_size_no = 10 | TLS3 | mm^{2}/mm^{2} | 1–6 | |||

Tiller_leaf_size_no = 16 | TLS4 | mm^{2}/mm^{2} | 1–6 | |||

Tiller_leaf_size_no = 26 | TLS5 | mm^{2}/mm^{2} | 1–6 | |||

Partitioning of assimilates | cane_fraction | Fraction of accumulated biomass partitioned to cane | CF | g/g | 0.65–0.80 | |

sucrose_fraction_stalk | Fraction of accumulated biomass partitioned to sucrose | SF1 | g/g | 0.40–0.70 | ||

stress_factor_stalk | Stress factor for sucrose accumulation | SF2 | n/a | 0.2–1.0 | ||

sucrose_delay | Sucrose accumulation delay | SD | g/m^{2} | 0–600 | ||

min_sstem_sucrose | Minimum stem biomass before partitioning to sucrose commences | MSS | g/m^{2} | 400–1500 | ||

Phenological development based on thermal time | min_sstem_sucrose_redn | Reduction to minimum stem sucrose under stress | MSSR | g/m^{2} | 0–20 | |

tt_emerg_to_begcane | Accumulated thermal time from emergence to beginning of cane | EB | °C day | 1200–1900 | ||

tt_begcane_to_flowering | Accumulated thermal time from beginning of cane to flowering | BF | °C day | 5400–6600 | ||

tt_flowering_to_crop_end | Accumulated thermal time from flowering to end of the crop | FC | °C day | 1750–2250 | ||

Dry matter assimilation | transp_eff_cf | Transpiration efficiency coefficient | From sowing to sprouting | TEC1 | kg kPa/kg | 0.006–0.014 |

From sprouting to emergence | TEC2 | |||||

From emergence to the beginning of cane growth | TEC3 | |||||

From the beginning of cane growth to flowering | TEC4 | |||||

From flowering to the end of the crop | TEC5 | |||||

At the end of the crop | TEC6 | |||||

rue | Radiation use efficiency | From emergence to the beginning of cane growth | RUE3 | g/MJ | 0.74–2.5 | |

From the beginning of cane growth to flowering | RUE4 | |||||

From flowering to the end of the crop | RUE5 |

Parameter Name | Code | Unit | Cultivar | ||
---|---|---|---|---|---|

KK3 (P3) | LK92-11 (P5) | 02-2-058 (P3) | |||

leaf_size | LS1 | mm^{2} | 1566 | 1792 | 1790 |

LS2 | 62,686 | 56,809 | 20,252 | ||

LS3 | 47,681 | 68,364 | 61,664 | ||

cane_fraction | CF | g/g | 0.65 | 0.66 | 0.68 |

sucrose_fraction_stalk | SF1 | g/g | 0.7 | 0.6 | 0.5 |

stress_factor_stalk | SF2 | n/a | 0.9 | 0.9 | 0.9 |

sucrose_delay | SD | g/m^{2} | 582 | 563 | 137 |

min_sstem_sucrose | MSS | g/m^{2} | 432 | 1097 | 1420 |

min_sstem_sucrose_redn | MSSR | g/m^{2} | 19 | 0.26 | 2 |

tt_emerg_to_begcane | EB | °C day | 1537 | 1874 | 1397 |

tt_begcane_to_flowering | BF | °C day | 5404 | 5748 | 6523 |

tt_flowering_to_crop_end | FC | °C day | 2138 | 2153 | 1794 |

green_leaf_no | GLN | No. | 14 | 15 | 14 |

tillerf_leaf_size | TLS1 | mm^{2}/mm^{2} | 5 | 4 | 3 |

TLS2 | 3 | 4 | 3 | ||

TLS3 | 1 | 1 | 1 | ||

TLS4 | 4 | 5 | 3 | ||

TLS5 | 3 | 3 | 5 | ||

transp_eff_cf | TEC1 | kg kPa/kg | 0.008 | 0.014 | 0.010 |

TEC2 | 0.007 | 0.014 | 0.011 | ||

TEC3 | 0.013 | 0.013 | 0.012 | ||

TEC4 | 0.014 | 0.009 | 0.014 | ||

TEC5 | 0.014 | 0.013 | 0.013 | ||

TEC6 | 0.011 | 0.014 | 0.010 | ||

rue | RUE3 | g/MJ | 2.50 | 2.24 | 2.49 |

RUE4 | 2.46 | 2.34 | 2.48 | ||

RUE5 | 1.14 | 2.40 | 1.84 |

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**MDPI and ACS Style**

Bandara, W.B.M.A.C.; Sakai, K.; Nakandakari, T.; Kapetch, P.; Anan, M.; Nakamura, S.; Setouchi, H.; Rathnappriya, R.H.K. Global Optimization of Cultivar Trait Parameters in the Simulation of Sugarcane Phenology Using Gaussian Process Emulation. *Agronomy* **2021**, *11*, 1379.
https://doi.org/10.3390/agronomy11071379

**AMA Style**

Bandara WBMAC, Sakai K, Nakandakari T, Kapetch P, Anan M, Nakamura S, Setouchi H, Rathnappriya RHK. Global Optimization of Cultivar Trait Parameters in the Simulation of Sugarcane Phenology Using Gaussian Process Emulation. *Agronomy*. 2021; 11(7):1379.
https://doi.org/10.3390/agronomy11071379

**Chicago/Turabian Style**

Bandara, W. B. M. A. C., Kazuhito Sakai, Tamotsu Nakandakari, Preecha Kapetch, Mitsumasa Anan, Shinya Nakamura, Hideki Setouchi, and R. H. K. Rathnappriya. 2021. "Global Optimization of Cultivar Trait Parameters in the Simulation of Sugarcane Phenology Using Gaussian Process Emulation" *Agronomy* 11, no. 7: 1379.
https://doi.org/10.3390/agronomy11071379