# Probabilistic River Water Mapping from Landsat-8 Using the Support Vector Machine Method

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

#### 2.2. Data

## 3. Methods

#### 3.1. FMask Algorithm

#### 3.2. Feature Set Construction

#### 3.3. Posterior Probability Support Vector Machine (SVM)

_{xy}= [(Green

_{1}, Red

_{1}, NIR

_{1}, SWIR1

_{1}, SWIR2

_{1}, HAND

_{1}), (Green

_{2}, Red

_{2}, NIR

_{2}, SWIR1

_{2}, SWIR2

_{2}, HAND

_{2}), …, (Green

_{n}, Red

_{n}, NIR

_{n}, SWIR1

_{n}, SWIR2

_{n}, HAND

_{n})] as the training sample set with n samples. x

_{i}represents the ith vector of the training set. yi ∊ [1, 2, 3, 4, 5, 6] represents the six features in each vector.

_{i}is the Lagrange multiplier, K(x,x

_{i}) is the kernel function, and b is the classification threshold. An SVM with different kernel functions can generate different algorithms [24]. The general verdict output of SVM is:

_{Y|x}(Y = water|f,θ) represents the probability value of the given pixel x belonging to the water class. The parameter vector θ = [A, B]

^{T}may be obtained by the maximum likelihood estimation based on the training set as in Equation (4).

#### 3.4. Water Mapping Using Traditional Water Index Methods

#### 3.5. Accuracy Assessment

#### 3.5.1. Accuracy Assessment on Posterior Probability Images

_{wrms}) between the posterior probability image and the reference classification map. Specific steps are as follows [15]:

_{i}, the number of pixels (A

_{i}) that were observed as river water in the binary map from Sentinel-2 images was calculated, and T

_{i}is the total number of pixels in U

_{i}. Then, the fraction (F

_{i}) of the actual river water pixels in U

_{i}could be calculated by dividing A

_{i}by T

_{i}.

_{i}) in each interval, E

_{wrms}was calculated using Equation (8):

_{wrms}represents the proximity of the posterior probability distribution to the reference water pixel distribution. An E

_{wrms}value closer to 0 represented higher accuracy in the posterior probability image.

#### 3.5.2. Accuracy Assessment on Binary Water Maps

_{0}is overall accuracy, and P

_{1}was calculated as Equation (13). Here, N is the total number of the pixels, T

_{water}and T

_{land}is the number of water and land pixels in the reference map, R

_{water}and R

_{land}is the number of water and land pixels in the resultant map.

## 4. Result and Discussion

#### 4.1. Posterior Probability Results

_{wrms}) between the posterior probability image and the referencing classification map. The value of E

_{wrms}was 0.067, indicating that the posterior probability results in the Zhengyixia reach were reasonable.

_{wrms}of this study area is 0.057, smaller than that of the Zhengyixia reach, indicating an even higher accuracy.

_{wrms}value for the Yingluoxia reach is 0.031, representing accuracy.

#### 4.2. Histogram-Based Thresholding

#### 4.3. Binary Water Maps

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Three study areas (

**a**) Zhengyixia reach of the Heihe River, (

**b**) Shuangtabu reach of the Shule River, (

**c**) Yingluoxia reach of the Heihe River, and nine demonstration zones (in red rectangles).

**Figure 3.**Distribution of the surface reflectance ranges of pure water and land samples on Landsat-8 OLI bands.

**Figure 4.**(

**a**) The posterior probability map in the Zhengyixia reach of the Heihe River, and (

**b**) the referencing water map derived from visually interpreting the Sentinel-2 image.

**Figure 5.**(

**a**) The posterior probability map in the Shuangtabu reach of the Shule River, and (

**b**) the referencing water map derived by visually interpreting the Sentinel-2 image.

**Figure 6.**(

**a**) The posterior probability map in the Yingluoxia reach of the Heihe River and (

**b**) the referencing water map derived by visually interpreting Sentinel-2 images.

**Figure 7.**The boxplots of probability values obtained by posterior probability support vector machine (PPSVM) in the referencing water areas.

**Figure 8.**Histograms of posterior probability, modified Normalized Difference Water Index (mNDWI), and NDWI for the Zhengyixia, Shuangtabu, and Yingluoxia reaches.

**Figure 9.**The Kappa coefficient values when using different thresholding values for (

**a**) posterior probability images, (

**b**) mNDWI images, and (

**c**) NDWI images at three river reaches. Optimal threshold values were highlighted with dots on each line.

**Figure 10.**Binary water maps derived from posterior probability, mNDWI, NDWI, and Sentinel-2 visual interpretation of three demonstration zones in the Zhengyixia reach.

**Figure 11.**Binary water maps derived from posterior probability, mNDWI, NDWI, and Sentinel-2 visual interpretation for the three demonstration zones in the Shuangtabu reach.

**Figure 12.**Binary water maps derived from posterior probability, mNDWI, NDWI, and Sentinel-2 visual interpreted for three demonstration zones in the Yingluoxia reach.

**Figure 13.**Boxplots of posterior probability, mNDWI, and NDWI values of hill shade pixels in the Yingluoxia reach (blue dots represent the optimal thresholds).

Site | Path/Row of Landsat-8 Image | Date of Landsat-8 Image | Date of Sentinel-2 Image |
---|---|---|---|

Zhengyixia | 134/32 | 2019-3-23 | 2019-3-22 |

Shuangtabu | 136/32 | 2019-3-21 | 2019-3-18 |

Yingluoxia | 134/33 | 2019-3-23 | 2019-3-22 |

Name | Wavelength (μm) | Description |
---|---|---|

U-BLUE | 0.435–0.451 | Band 1 (ultra blue) surface reflectance |

BLUE | 0.452–0.512 | Band 2 (blue) surface reflectance |

GREEN | 0.533–0.590 | Band 3 (green) surface reflectance |

RED | 0.636–0.673 | Band 4 (red) surface reflectance |

NIR | 0.851–0.879 | Band 5 (near infrared) surface reflectance |

SWIR1 | 1.566–1.651 | Band 6 (shortwave infrared 1) surface reflectance |

SWIR2 | 2.107–2.294 | Band 7 (shortwave infrared 2) surface reflectance |

**Table 3.**Accuracy indices of three water maps derived from different methods for The Zhengyixia Reach.

Method | Overall Accuracy | Commission Error | Omission Error | Kappa | Critical Success Index (CSI) |
---|---|---|---|---|---|

PPSVM | 98.3% | 0.9% | 0.6% | 0.877 | 0.795 |

mNDWI | 98.2% | 1.0% | 0.7% | 0.868 | 0.781 |

NDWI | 97.7% | 1.1% | 1.2% | 0.824 | 0.723 |

**Table 4.**Accuracy indices of three water maps derived from different methods for the Shuangtabu Reach.

Method | Overall Accuracy | Commission Error | Omission Error | Kappa | Critical Success Index (CSI) |
---|---|---|---|---|---|

PPSVM | 98.9% | 0.6% | 0.5% | 0.719 | 0.574 |

mNDWI | 99.1% | 0.5% | 0.3% | 0.784 | 0.650 |

NDWI | 97.6% | 1.5% | 0.9% | 0.465 | 0.321 |

**Table 5.**Accuracy indices of three water maps derived from different methods for the Yingluoxia Reach.

Method | Overall Accuracy | Commission Error | Omission Error | Kappa | Critical Success Index (CSI) |
---|---|---|---|---|---|

PPSVM | 98.8% | 0.6% | 0.6% | 0.822 | 0.707 |

mNDWI | 98.6% | 0.7% | 0.7% | 0.804 | 0.682 |

NDWI | 98.9% | 0.5% | 0.6% | 0.839 | 0.730 |

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**MDPI and ACS Style**

Liu, Q.; Huang, C.; Shi, Z.; Zhang, S.
Probabilistic River Water Mapping from Landsat-8 Using the Support Vector Machine Method. *Remote Sens.* **2020**, *12*, 1374.
https://doi.org/10.3390/rs12091374

**AMA Style**

Liu Q, Huang C, Shi Z, Zhang S.
Probabilistic River Water Mapping from Landsat-8 Using the Support Vector Machine Method. *Remote Sensing*. 2020; 12(9):1374.
https://doi.org/10.3390/rs12091374

**Chicago/Turabian Style**

Liu, Qihang, Chang Huang, Zhuolin Shi, and Shiqiang Zhang.
2020. "Probabilistic River Water Mapping from Landsat-8 Using the Support Vector Machine Method" *Remote Sensing* 12, no. 9: 1374.
https://doi.org/10.3390/rs12091374