# Weather Based Strawberry Yield Forecasts at Field Scale Using Statistical and Machine Learning Models

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Field Measurement Sensors

#### 2.3. Strawberry Yield Data

#### 2.4. Meteorological Data

#### 2.5. Statistical Analysis

#### 2.5.1. Correlation and Regression Analysis

#### 2.5.2. Principal Component Analysis

#### 2.6. Predictive Models

#### 2.6.1. Predictive Principal Component Regression (PPCR)

#### 2.6.2. Neural Network (NN)

#### 2.6.3. Random Forest (RF)

#### 2.6.4. Performance Strategies

## 3. Results and Discussion

#### 3.1. Statistical Analysis

#### 3.2. Weekly Prediction of Strawberry Yield

#### 3.2.1. Predictive Principal Component Regression (PPCR)

^{2}of 0.42, while the training set showed an adjusted ${R}^{2}$ of 0.92.

#### 3.2.2. Machine Learning Approaches

^{6}, and the error function converged within 2000 iterations. Likewise, the optimal RF model corresponded with 11 ntry and 325 trees. Figure 10 shows the modeled against the observed strawberry yield while Figure 11 shows the time series of the modeled and observed strawberry yield. It is important to note that the best model selected in both approaches corresponded to the model with the least EF values during cross-validation and was used to test the unused dataset.

^{2}(0.95) when compared to the PPCR (250, 0.51) and RF (249, 0.84), respectively.

## 4. Conclusions and Future Research

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location map of the study map together with the CIMIS (California Irigation Managament Information System) station 202 at Nipomo.

**Figure 2.**Flowchart showing the development of the strawberry yield model employing PPCR, NN, and RF.

**Figure 3.**A generic neural network with a single hidden layer used in this study [57].

**Figure 5.**Bar graphs showing the correlations between strawberry yield and other variables as listed in Table 3. The bars below the black line imply that the parameters are insignificant to crop yield. (

**Left**) Daily scale. (

**Right**) Weekly scale.

**Figure 6.**Regression plots for the significant parameters on a daily scale (

**top**) and 7-day moving window (

**bottom**).

**Figure 7.**Multivariate regression model on the top six principal components on a weekly scale. (

**Left**) Time series plot of observed and regressed crop yield. (

**Right**) Observed vs. regressed values.

**Figure 8.**Scatter plots of the observed vs. modeled from a predictive principal component regression (PPCR) model. (

**Left**) Performance of test. (

**Right**) Training.

**Figure 9.**Observed and modeled dynamics of strawberry yield implied by the PPCR model shown in Figure 8. The vertical line separates the sample from the training and testing.

**Figure 10.**Scatter plots of the observed versus the modeled using the neural network, NN (

**top**) entailing. (

**Left**) Testing. (

**Center**) Cross-validation. (

**Right**) Training.

**Figure 11.**Time series plots of strawberry yield overlaid by approximations from NN (

**top**) and RF (

**bottom**). The vertical line separates the sample from the training and testing seven data points.

Neural Network (NN) | Random Forest (RF) |
---|---|

layers: 3 (input, hidden, & neurons) | mtry: varied from $9$ to 27 |

hidden neurons: half of the total parameters | where ${n}_{p}$ is a number of available predictors |

activation function: logistic, hyperbolic tangent and softmax function error function: logistic function | |

algorithm: resilient backpropagation | ntree: 100 to 500 with increment in 25 trees |

learning rate: 0.01 | giving 17 scenarios |

thresholds: 0.05 | |

stepmax: 10^{6} | |

maximum seed = 500 | seed: 100 |

Statistics | Sensor 1 | Sensor 2 | Temperature | Soil Moisture Content | ||||
---|---|---|---|---|---|---|---|---|

Count | Minutes | Count | Minutes | Ambient | Canopy | Soil | ||

$\xb0\mathbf{C}$ | $\xb0\mathbf{C}$ | $\xb0\mathbf{C}$ | ${\mathbf{m}}^{3}/{\mathbf{m}}^{3}$ | |||||

Minimum | 360 | 0 | 436 | 0 | −2 | −1 | 6 | 0.11 |

Average | 450 | 26 | 463 | 55 | 15 | 14 | 17 | 0.13 |

Maximum | 961 | 1960 | 863 | 1998 | 33 | 30 | 32 | 0.32 |

**Table 3.**The measured parameters, current, and lagged weather parameters including the adjusted ${R}^{2}$ for respective linear models.

Id | Parameters | Units | Notation | Daily | Moving Weekly |
---|---|---|---|---|---|

1 | Average leaf wetness minutes | minutes | LWM | 0.004 | 0.041 |

2 | Average leaf wetness count | LWC | 0.120 | 0.274 | |

3 | Average leaf wetness duration | LWD | 0.092 | 0.148 | |

4 | Ambient temperature | °C | ECT1 | 0.460 | 0.505 |

5 | Canopy temperature | °C | ECT2 | 0.030 | 0.116 |

6 | Soil temperature | °C | SMTa | 0.407 | 0.495 |

7 | Volumetric soil moisture | m^{3}/m^{3} | SM | 0.417 | 0.547 |

8 | Daily chill hours | hours | CHDaily | 0.189 | 0.292 |

9 | Cumulated chill hours | hours | cumChill | 0.431 | 0.462 |

10 | Reference evapotranspiration | mm | ETo | 0.338 | 0.585 |

11 | Solar Radiation | Wm-2 | Rs | 0.421 | 0.667 |

12 | Net Radiation | Wm-2 | Rn | 0.439 | 0.656 |

13 | Average vapor pressure | kPa | em | 0.134 | 0.210 |

14 | Average relative humidity | % | RHm | 0.000 | 0.002 |

15 | Dew point | °C | dP | 0.157 | 0.234 |

16 | Average wind speed | ms-1 | uBar | 0.261 | 0.354 |

17 | Penmann-Montieth Evapotranspiration | mm | PMETo | 0.384 | 0.648 |

18 | Fall reference evapotranspiration | mm | ETo.F | 0.244 | 0.356 |

19 | Fall solar radiation | Wm-2 | Rs.F | 0.129 | 0.196 |

20 | Fall net radiation | Wm-2 | Rn.F | 0.242 | 0.300 |

21 | Fall average vapor pressure | kPa | em.F | 0.084 | 0.143 |

22 | Fall average air temperature | °C | aTm.F | 0.270 | 0.449 |

23 | Fall average relative humidity | % | RHm.F | –0.005 | –0.006 |

24 | Fall average wind speed | ms-1 | u.F | 0.020 | 0.055 |

25 | Fall dew point | °C | dP.F | 0.071 | 0.116 |

26 | Fall average soil temperature | °C | STm.F | 0.739 | 0.748 |

Data Set | Statistics | Predictive model | ||
---|---|---|---|---|

PPCR | NN | RF | ||

Training | RMSE, g | 81.83 | 11.47 | 9.87 |

Adjusted${R}^{2}$ | 0.92 | 0.99 | 0.99 | |

EF, % | 16.10 | 2.20 | 1.74 | |

Validation | RMSE, g | 20.85 | 27.49 | |

Adjusted${R}^{2}$ | 0.99 | 0.99 | ||

EF, % | 1.43 | 2.72 | ||

Testing | RMSE, g | 250.90 | 119.58 | 249.07 |

Adjusted${R}^{2}$ | 0.51 | 0.95 | 0.84 | |

EF, % | 30.20 | 15.49 | 29.27 |

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## Share and Cite

**MDPI and ACS Style**

Maskey, M.L.; Pathak, T.B.; Dara, S.K.
Weather Based Strawberry Yield Forecasts at Field Scale Using Statistical and Machine Learning Models. *Atmosphere* **2019**, *10*, 378.
https://doi.org/10.3390/atmos10070378

**AMA Style**

Maskey ML, Pathak TB, Dara SK.
Weather Based Strawberry Yield Forecasts at Field Scale Using Statistical and Machine Learning Models. *Atmosphere*. 2019; 10(7):378.
https://doi.org/10.3390/atmos10070378

**Chicago/Turabian Style**

Maskey, Mahesh L., Tapan B Pathak, and Surendra K. Dara.
2019. "Weather Based Strawberry Yield Forecasts at Field Scale Using Statistical and Machine Learning Models" *Atmosphere* 10, no. 7: 378.
https://doi.org/10.3390/atmos10070378