# Modify the Accuracy of MODIS PWV in China: A Performance Comparison Using Random Forest, Generalized Regression Neural Network and Back-Propagation Neural Network

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Area and PWV data

#### 2.1. Research Area

#### 2.2. PWV Data

## 3. Methodology

#### 3.1. BPNN

**W**

_{2,1}and

**W**

_{3,2}are weight matrices and

**b**

_{1}and

**b**

_{2}are bias matrices; these four matrices store the coefficients of the BPNN and should be optimized via back-propagation algorithm [32],

**X**and

**Y**are respectively the input and output variables.

#### 3.2. RF

**X**indicates the input variables,

**Y**is the final output of the RF,

**T**

_{b}denotes the output of each regression tree, and B is the number of trees.

#### 3.3. GRNN

#### 3.4. 10-Fold Cross-Validation

#### 3.5. Multiple Linear Regression for Comparison

_{0}is the intercept; α

_{1}–α

_{5}are the regression coefficients for the input variables, derived using least-squares method, and every model is tested by 10-fold cross-validation method.

## 4. Model Construction and Performance

#### 4.1. Formation of PWV Data Pairs

#### 4.2. Determine Hyperparameters

#### 4.3. Model Performance at Annual Timescale

Accuracy | Hyperparameter | Bias (mm) | STD (mm) | RMS (mm) | R | |
---|---|---|---|---|---|---|

Original | - | −2.4 | 5.3 | 5.8 | 0.95 | |

GRNN | Modified | 0.05 | 0.1 | 3.9 | 3.9 | 0.97 |

Fitting | 0.05 | −0.1 | 3.6 | 3.6 | 0.98 | |

RF | Modified | 70 | 0.0 | 3.3 | 3.3 | 0.98 |

Fitting | 70 | 0.0 | 2.3 | 2.3 | 0.99 | |

BPNN | Modified | 256 | 0.0 | 4.1 | 4.1 | 0.97 |

Fitting | 256 | 0.0 | 4.1 | 4.1 | 0.97 | |

MLR | Modified | − | 0.0 | 5.0 | 5.0 | 0.96 |

#### 4.4. Model Performance at Monthly Timescale

Month | Original Accuracy | Methods | Modified Accuracy | Fitting Accuracy | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Hyperparameter | Bias | STD | RMS | R | Bias | STD | RMS | R | ||||

201901 | Bias | −1.8 | GRNN | 0.05 | 0.0 | 1.7 | 1.7 | 0.98 | 0.0 | 1.1 | 1.1 | 0.99 |

STD | 4.0 | BPNN | 128 | 0.0 | 1.8 | 1.8 | 0.98 | 0.0 | 1.5 | 1.5 | 0.99 | |

RMS | 4.4 | RF | 40 | 0.0 | 2.0 | 2.0 | 0.98 | 0.0 | 1.3 | 1.3 | 0.99 | |

R | 0.91 | MLR | - | 0.0 | 3.5 | 3.5 | 0.92 | - | - | - | - | |

201902 | Bias | −1.4 | GRNN | 0.06 | 0.0 | 1.7 | 1.7 | 0.98 | 0.0 | 1.2 | 1.2 | 0.99 |

STD | 4.2 | BPNN | 128 | 0.0 | 1.9 | 1.9 | 0.98 | 0.0 | 1.5 | 1.5 | 0.99 | |

RMS | 4.4 | RF | 60 | 0.0 | 1.9 | 1.9 | 0.98 | 0.0 | 1.3 | 1.3 | 0.99 | |

R | 0.9 | MLR | - | 0.0 | 3.5 | 3.5 | 0.92 | - | - | - | - | |

201903 | Bias | −1.0 | GRNN | 0.05 | 0.0 | 2.2 | 2.2 | 0.98 | 0.0 | 1.3 | 1.3 | 0.99 |

STD | 4.0 | BPNN | 128 | 0.0 | 2.4 | 2.4 | 0.97 | 0.0 | 2.1 | 2.1 | 0.98 | |

RMS | 4.2 | RF | 85 | 0.0 | 2.4 | 2.4 | 0.97 | 0.0 | 1.6 | 1.6 | 0.99 | |

R | 0.93 | MLR | - | 0.0 | 3.8 | 3.8 | 0.93 | - | - | - | - | |

201904 | Bias | −1.5 | GRNN | 0.06 | 0.0 | 2.9 | 2.9 | 0.97 | 0.0 | 1.8 | 1.8 | 0.99 |

STD | 4.9 | BPNN | 128 | 0.0 | 3.1 | 3.1 | 0.97 | 0.0 | 2.6 | 2.6 | 0.98 | |

RMS | 5.1 | RF | 50 | 0.0 | 3.0 | 3.0 | 0.97 | 0.0 | 2.1 | 2.1 | 0.99 | |

R | 0.93 | MLR | - | 0.0 | 4.6 | 4.6 | 0.93 | - | - | - | - | |

201905 | Bias | −1.6 | GRNN | 0.07 | 0.1 | 3.0 | 3.0 | 0.98 | 0.0 | 2.0 | 2.0 | 0.99 |

STD | 4.7 | BPNN | 128 | 0.0 | 3.1 | 3.1 | 0.97 | 0.0 | 2.5 | 2.5 | 0.98 | |

RMS | 5.0 | RF | 65 | 0.0 | 3.2 | 3.2 | 0.97 | 0.0 | 2.2 | 2.2 | 0.99 | |

R | 0.94 | MLR | - | 0.0 | 4.4 | 4.4 | 0.94 | - | - | - | - | |

201906 | Bias | −2.6 | GRNN | 0.06 | 0.0 | 3.4 | 3.4 | 0.98 | 0.0 | 2.4 | 2.4 | 1.00 |

STD | 5.8 | BPNN | 128 | 0.0 | 3.7 | 3.7 | 0.97 | 0.0 | 3.3 | 3.3 | 0.98 | |

RMS | 6.4 | RF | 50 | 0.0 | 3.7 | 3.7 | 0.97 | 0.0 | 2.5 | 2.5 | 0.99 | |

R | 0.93 | MLR | - | 0.0 | 5.7 | 5.7 | 0.94 | - | - | - | - | |

201907 | Bias | −4.2 | GRNN | 0.06 | 0.0 | 3.5 | 3.5 | 0.97 | 0.0 | 2.7 | 2.7 | 0.99 |

STD | 6.8 | BPNN | 128 | 0.0 | 4.0 | 4.0 | 0.97 | 0.0 | 3.6 | 3.6 | 0.97 | |

RMS | 8.0 | RF | 80 | 0.0 | 3.8 | 3.8 | 0.97 | 0.0 | 2.6 | 2.6 | 0.99 | |

R | 0.91 | MLR | - | 0.0 | 6.1 | 6.1 | 0.92 | - | - | - | - | |

201908 | Bias | −3.8 | GRNN | 0.06 | 0.0 | 3.6 | 3.6 | 0.97 | 0.0 | 2.8 | 2.8 | 0.99 |

STD | 6.6 | BPNN | 128 | 0.0 | 4.2 | 4.2 | 0.96 | 0.0 | 3.8 | 3.8 | 0.97 | |

RMS | 7.6 | RF | 95 | 0.0 | 3.9 | 3.9 | 0.97 | 0.0 | 2.6 | 2.6 | 0.99 | |

R | 0.91 | MLR | - | 0.0 | 6.4 | 6.4 | 0.91 | - | - | - | - | |

201909 | Bias | −3.4 | GRNN | 0.05 | 0.0 | 2.8 | 2.8 | 0.98 | 0.0 | 1.9 | 1.9 | 0.99 |

STD | 5.6 | BPNN | 128 | 0.0 | 3.3 | 3.3 | 0.97 | 0.0 | 3.0 | 3.0 | 0.98 | |

RMS | 6.5 | RF | 90 | 0.0 | 3.2 | 3.2 | 0.97 | 0.0 | 2.1 | 2.1 | 0.99 | |

R | 0.93 | MLR | - | 0.0 | 5.2 | 5.2 | 0.93 | - | - | - | - | |

201910 | Bias | −2.2 | GRNN | 0.05 | 0.0 | 2.3 | 2.3 | 0.98 | 0.0 | 1.6 | 1.6 | 1.00 |

STD | 5.3 | BPNN | 128 | 0.0 | 2.8 | 2.8 | 0.98 | 0.0 | 2.5 | 2.5 | 0.98 | |

RMS | 5.7 | RF | 75 | 0.0 | 2.6 | 2.6 | 0.98 | 0.0 | 1.8 | 1.8 | 0.99 | |

R | 0.93 | MLR | - | 0.0 | 4.8 | 4.8 | 0.93 | - | - | - | - | |

201911 | Bias | −2.1 | GRNN | 0.05 | 0.0 | 1.8 | 1.8 | 0.98 | 0.0 | 1.2 | 1.2 | 0.99 |

STD | 4.2 | BPNN | 128 | 0.0 | 2.1 | 2.1 | 0.97 | 0.0 | 1.8 | 1.8 | 0.98 | |

RMS | 4.7 | RF | 55 | 0.0 | 2.0 | 2.0 | 0.97 | 0.0 | 1.4 | 1.4 | 0.99 | |

R | 0.91 | MLR | - | 0.0 | 3.5 | 3.5 | 0.92 | - | - | - | - | |

201912 | Bias | −1.4 | GRNN | 0.05 | 0.0 | 1.6 | 1.6 | 0.98 | 0.0 | 1.2 | 1.2 | 0.99 |

STD | 3.4 | BPNN | 128 | 0.0 | 1.8 | 1.8 | 0.97 | 0.0 | 1.6 | 1.6 | 0.98 | |

RMS | 3.7 | RF | 55 | 0.0 | 1.7 | 1.7 | 0.98 | 0.0 | 1.2 | 1.2 | 0.99 | |

R | 0.92 | MLR | − | 0.0 | 3.0 | 3.0 | 0.92 | − | − | − | − |

## 5. Accuracy Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Radiosonde PWV Calculation Method

_{2}= 3.7310

^{−3}K

^{2}/Pa, h the layer height in m.

_{s}is the saturated water vapor pressure which is related to the temperature and can be calculated by the Wexler formula [37,38].

_{2}to that at a GNSS station at height h

_{1}. All height belongs to the orthometric height system.

_{h1}and PWV

_{h2}are the PWV values corresponding to the heights of h

_{1}and h

_{2}, respectively.

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**Figure 5.**Scatter plots of Modified MODIS PWV (annual model) against observed (GNSS) PWV from all samples.

**Figure 6.**Scatter plots of Modified MODIS PWV (monthly model) against observed (GNSS) PWV from all samples in 2019. (

**a**) the results of BPNN, (

**b**) the results of GRNN, (

**c**) the results of RF, (

**d**) the results of MLR.

Unit: mm | Bias | STD | RMS | Bias in Percentage |
---|---|---|---|---|

PPP-derived PWV | 0.9 | 1.7 | 1.9 | 4.1% |

CMA PWV | −0.3 | 1.4 | 1.4 | 1.3% |

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**MDPI and ACS Style**

Xiong, Z.; Sun, X.; Sang, J.; Wei, X.
Modify the Accuracy of MODIS PWV in China: A Performance Comparison Using Random Forest, Generalized Regression Neural Network and Back-Propagation Neural Network. *Remote Sens.* **2021**, *13*, 2215.
https://doi.org/10.3390/rs13112215

**AMA Style**

Xiong Z, Sun X, Sang J, Wei X.
Modify the Accuracy of MODIS PWV in China: A Performance Comparison Using Random Forest, Generalized Regression Neural Network and Back-Propagation Neural Network. *Remote Sensing*. 2021; 13(11):2215.
https://doi.org/10.3390/rs13112215

**Chicago/Turabian Style**

Xiong, Zhaohui, Xiaogong Sun, Jizhang Sang, and Xiaomin Wei.
2021. "Modify the Accuracy of MODIS PWV in China: A Performance Comparison Using Random Forest, Generalized Regression Neural Network and Back-Propagation Neural Network" *Remote Sensing* 13, no. 11: 2215.
https://doi.org/10.3390/rs13112215