# Using the Bayesian Network to Map Large-Scale Cropping Intensity by Fusing Multi-Source Data

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. The Study Area

#### 2.2. The Data and Preprocessing

## 3. Method

#### 3.1. Bayesian Network

#### 3.2. Cropping Intensity Index

#### 3.3. BNPK Model

#### 3.3.1. Fusing Time-Series MODIS Data

#### 3.3.2. Adding Zone Information as Prior Knowledge

#### 3.4. Validation of the Model

_{j}is the probability predicted for class j; and n is the number of states for which the training data provides a value for the classification variable.

^{2}, root mean square error (RMSE), intercept a and slope b of the simple linear regression with respect to the validation samples. After the validation tests, the BN model was complete and could then be applied to the mapping of CII in the study area.

## 4. Results and Analysis

#### 4.1. Model Calibration

^{2}of 0.44 and 0.79 and the p-value of 0.59 and 0.14 for the two models was obtained at the 95% confidence level. The BN model had poor prediction because it ignored the intra-class variations in the MODIS time-series. The BNPK model predicted CII better than BN with a R

^{2}of 0.79 because of its full consideration of prior knowledge.

^{2}for the BNPK model approached 0.84, while the BN reached a R

^{2}maxima of 0.679 in HRV. Overall, the BNPK based estimates were better than that of BN in all of the sample areas.

#### 4.2. Accuracy Validation

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The research area, the sample areas (covered by five Landsat scenes), and the cropping frequency distribution in 2015 (Resource and Environment Data Cloud Platform, (http://www.resdc.cn/DOI, 2017. DOI:10.12078/2017122201). Regions A-D represent the Songliao Plain, North China Plain, Middle-Upper Hanjiang River Valley, and the Middle–Lower Yangtze River Valley, respectively.

**Figure 4.**The initial Bayesian network model. L1, L2, etc., represent the enhanced vegetation index time-series.

**Figure 5.**The BNPK model (Bayesian network fusing zone data as prior knowledge). SP1, SP2, NCP, HRV, and YRV represent the five sample areas. L1, L2, etc., represent the EVI time-series. (

**a**) CPT when adding a zone node as prior knowledge. We simply assigned codes 1–5 to the five sample areas. After adding this node, all the CPTs in other nodes updated automatically. The intra-class variations on CII could be observed, which were consistent with the fact of regional differentiation. (

**b**) CPT when giving evidence of zone information. If we provide evidence of zone type as NCP at 100% probability, all the child nodes update the CPT through the propagation of probabilities. This CPT is locally trained and exclusively for NCP.

**Figure 6.**Trend line of the modeled and the referenced CII at pixel level, (

**a**) BN model, and (

**b**) BNPK model.

**Figure 7.**Comparison of the modeled and sample CII. (

**a**) and (

**b**) SP1; (

**c**) and (

**d**) SP2; (

**e**) and (

**f**) NCP; (

**g**) and (

**h**) HRV; and (

**i**) and (

**j**) YRV.

**Figure 8.**Trend line of the modeled and the referenced data at block level. (

**a**) SP1, (

**b**) SP2, (

**c**) NCP, (

**d**) HRV, and (

**e**) YRV.

**Figure 9.**EVI profiles of the cropland pixels in three sample areas. About 100 representative pixels with a CII value of 0.7 were selected randomly for each sample area (using NCP, HRV, and YRV as examples), and the mean values of the EVI time-series were calculated to plot this figure.

Paths/Rows | Acquisition Date | Cloud Cover (%) |
---|---|---|

118/027 | 16/06/2015 | 1.76 |

120/031 | 10/03/2015 | 3.47 |

26/03/2015 | 3.48 | |

13/05/2015 | 0.02 | |

123/034 | 15/03/2015 | 9.02 |

18/05/2015 | 0.26 | |

124/037 | 17/01/2015 | 0.04 |

09/05/2015 | 19.94 | |

124/039 | 01/012015 | 12.51 |

22/03/2015 | 19.19 | |

09/05/2015 | 6.69 |

EVI | −3000~−2000 | −2000~−1000 | −1000~0 | 0~1000 | 1000~2000 | 2000~3000 | 3000~4000 | 4000~5000 | 5000~6000 | 6000~7000 | 7000~8000 | 8000~9000 | 9000~10000 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

CII | ||||||||||||||

0–0.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 27.6 | 67.3 | 5.1 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

0.1–0.2 | 0.0 | 0.0 | 0.0 | 0.0 | 8.3 | 80.5 | 11.2 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

0.2–0.3 | 0.0 | 0.0 | 0.0 | 0.0 | 15.0 | 83.1 | 1.9 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

0.3–0.4 | 0.0 | 0.0 | 0.0 | 0.8 | 82.0 | 17.2 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

0.4–0.5 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 14.9 | 53.9 | 24.9 | 4.2 | 1.0 | 1.0 | 0.0 | |

0.5–0.6 | 0.0 | 0.0 | 0.0 | 0.0 | 8.3 | 42.0 | 34.7 | 12.9 | 2.1 | 0.0 | 0.0 | 0.0 | 0.0 | |

0.6–0.7 | 0.0 | 0.0 | 34.1 | 42.0 | 18.6 | 1.3 | 3.9 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

0.7–0.8 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 26.1 | 47.6 | 23.2 | 2.5 | 0.6 | 0.0 | 0.0 | 0.0 | |

0.8–0.9 | 0.0 | 0.0 | 0.0 | 0.0 | 65.5 | 34.5 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | |

0.9–1.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 7.6 | 46.6 | 44.1 | 1.7 | 0.0 | 0.0 | 0.0 | 0.0 |

Relative Error (%) | Logarithmic Loss | Quadratic Loss | Spherical Payoff | |
---|---|---|---|---|

BN | 47.75 | 0.46 | 0.51 | 0.72 |

BNPK | 27.68 | 0.17 | 0.22 | 0.93 |

**Table 4.**Coefficient of determination R

^{2}, intercept

**a**and slope

**b**of the simple linear regression for test samples at the pixel level.

BN | BNPK | |||||||
---|---|---|---|---|---|---|---|---|

R^{2} | RMSE | a | b | R^{2} | RMSE | a | b | |

SP1 | 0.424 | 0.081 | 0.280 | 0.405 | 0.501 | 0.094 | 0.144 | 0.553 |

SP2 | 0.269 | 0.131 | 0.300 | 0.455 | 0.484 | 0.136 | 0.180 | 0.589 |

NCP | 0.440 | 0.148 | 0.159 | 0.495 | 0.541 | 0.154 | 0.168 | 0.623 |

HRV | 0.679 | 0.147 | 0.139 | 0.655 | 0.836 | 0.117 | 0.089 | 0.810 |

YRV | 0.450 | 0.151 | 0.137 | 0.506 | 0.620 | 0.138 | 0.152 | 0.670 |

**Table 5.**Coefficient of determination R

^{2}, RMSE, intercept a and slope b, p-value of the simple linear regression between the referenced, and the modeled CII at the 95% confidence level at the block level.

R^{2} | RMSE | a | b | p-Value | |
---|---|---|---|---|---|

SP1 | 0.87 | 0.044 | 0.029 | 0.941 | 0 |

SP2 | 0.823 | 0.049 | 0.051 | 0.973 | 0.04 |

NCP | 0.82 | 0.082 | −0.074 | 1.08 | 0 |

HRV | 0.97 | 0.046 | 0.030 | 0.945 | 0 |

YRV | 0.89 | 0.067 | −0.034 | 1.036 | 0 |

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## Share and Cite

**MDPI and ACS Style**

Tao, J.; Wu, W.; Xu, M.
Using the Bayesian Network to Map Large-Scale Cropping Intensity by Fusing Multi-Source Data. *Remote Sens.* **2019**, *11*, 168.
https://doi.org/10.3390/rs11020168

**AMA Style**

Tao J, Wu W, Xu M.
Using the Bayesian Network to Map Large-Scale Cropping Intensity by Fusing Multi-Source Data. *Remote Sensing*. 2019; 11(2):168.
https://doi.org/10.3390/rs11020168

**Chicago/Turabian Style**

Tao, Jianbin, Wenbin Wu, and Meng Xu.
2019. "Using the Bayesian Network to Map Large-Scale Cropping Intensity by Fusing Multi-Source Data" *Remote Sensing* 11, no. 2: 168.
https://doi.org/10.3390/rs11020168