# Study on Icing Environment Judgment Based on Radar Data

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data

#### 2.2. Icing Index

_{C}’:

_{C}is 0–100. The larger the value, the stronger the ice accretion [35].

#### 2.3. Methods

#### 2.4. Feasibility Analysis

## 3. Contributions of Radar Data to Icing Index

^{−}

^{15}, suggesting that each variable does not contain overlapping information.

_{1}, which had the largest variance contribution, had very little correlation with the ice accumulation index, which may indicate that X

_{1}mainly represents a large amount of noise contained in radar data. In general, all new variables with a cumulative contribution rate of 85% are selected after principal component analysis. Therefore, the expressions of X

_{1}, X

_{2}, X

_{3}and X

_{4}are given below:

- (1)
- It is significant to use principal component analysis to process data in this study;
- (2)
- Although the variable X
_{1}contains a lot of information, introducing X_{1}into the linear regression will reduce the correction determination coefficient and linear significance of the equation, and increase the error variance, so it is reasonable not to introduce X_{1}, which also confirms that X_{1}mainly represents the noise in the radar data; and - (3)
- Although the correlation coefficient of X
_{2}and X_{3}is small, and the opposite value of their correlation is similar, it will cause the loss of a lot of the main information in the sample if they are removed.

## 4. Qualitative Classifications of Radar Data

## 5. Quantitative Judgment of Icing Index

## 6. Discussions

#### 6.1. The Correspondence between Radar Data and Sounding Data

#### 6.2. Cause Analysis of Test Results

## 7. Conclusions

- (1)
- Combined with the data of Lidar and millimeter-wave radar, the principal component analysis method was used to improve the correction determination coefficient to 0.7240, and the noise in the data was effectively eliminated.
- (2)
- Clustering analysis can increase the proportion of ice accumulation samples from 18.81% to 33.03%. If the classification number continues to increase, there will be overfitting, so it is difficult to further improve this proportion. However, the samples that significantly deviate from the central value can be considered as impossible for ice accumulation and excluded.
- (3)
- Two kinds of neural networks are constructed, which have similar performance on the judgment results of the test set, and can reach more than a 50% accuracy rate. The error is mainly shown as a false report, and the omission rate is very low, but it is difficult to calculate the ice accumulation index quantitatively.
- (4)
- Possible reasons for inaccurate quantitative judgment include inconsistency between the location of the radar station and the sounding station, a great difference between the samples of the training set and the test set, and the ice accumulation index cannot fully represent the ice accumulation environment, etc.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Location of Chilbotton Station and sounding stations. The figure shows the location and number of multiple sites around Chilbotton, with Herstmonceux being the closest.

**Figure 2.**Radar data clustering analysis. From (

**a**–

**f**), the number of clusters increases from two to seven, respectively. In (

**a**), red is category A and green is category B. After the number of categories is increased, the color and category number remain unchanged, and the newly added color is a new category (category C to category G).

**Figure 3.**Calculation of icing index based on neural network. Structure 1 takes the Zh, v, and w as input to judge whether there is icing. For points with icing, another network is used to calculate the icing index, and for points without icing, it is directly output no-icing. Structure 2 takes the Zh, v, and w as input, takes temperature and relative humidity as output, and calculates the icing index according to Equation (1). (

**a**) Neural Network Structure 1; (

**b**) Neural Network Structure 2.

**Figure 5.**Comparison of millimeter-wave radar data and radiosonde Data in November 2003. (

**a**) Galileo Radar; (

**b**) Sounding.

**Figure 6.**Profiles of average temperature and relative humidity in November 2003 and November 2008. (

**a**) Monthly average temperature profile; (

**b**) Monthly average RH profile. Considering the definition of Icing Index, vertical dash lines are added to illustrate the range of possible icing.

Data Type | Sample Size | Sample Proportion |
---|---|---|

Class 0 (Lack of Radar Data, no Risk of Icing) | 5379 | 73.48% |

Class 1 (Lack of Radar Data, Risk of Icing) | 431 | 5.888% |

Class 2 (with Radar Data, Risk of Icing) | 284 | 3.880% |

Class 3 (with Radar Data, no Risk of Icing) | 1226 | 16.75% |

${\mathbf{I}}_{\mathbf{C}}$ | $\mathbf{Z}{\mathbf{h}}^{*}$ | ${\mathbf{v}}^{*}$ | ${\mathbf{w}}^{*}$ | ${\mathbf{\sigma}}^{*}$ | ${\mathsf{\beta}}^{*}$ | |
---|---|---|---|---|---|---|

${\mathrm{I}}_{\mathrm{C}}$ | 1 | 0.4429 | 0.1959 | 0.5262 | 0.0834 | −0.1005 |

${\mathrm{Zh}}^{*}$ | 0.4429 | 1 | −0.3858 | −0.0933 | −0.5473 | −0.2310 |

${\mathrm{v}}^{*}$ | 0.1959 | −0.3868 | 1 | 0.0163 | 0.5585 | 0.1874 |

${\mathrm{w}}^{*}$ | 0.5262 | −0.0933 | 0.0163 | 1 | 0.4268 | 0.3043 |

${\mathsf{\sigma}}^{*}$ | 0.0834 | −0.5473 | 0.5585 | 0.4268 | 1 | 0.6059 |

${\mathsf{\beta}}^{*}$ | −0.1005 | −0.2310 | 0.1874 | 0.3043 | 0.6059 | 1 |

Variable | ${\mathbf{X}}_{1}$ | ${\mathbf{X}}_{2}$ | ${\mathbf{X}}_{3}$ | ${\mathbf{X}}_{4}$ | ${\mathbf{X}}_{5}$ |
---|---|---|---|---|---|

Contribution | 48.7108% | 22.1684% | 13.1940% | 12.1635% | 3.7633% |

Coefficient | 0.0358 | 0.3731 | −0.3005 | 0.7156 | 0.0203 |

${\mathbf{R}}^{2}$ | $\overline{{\mathbf{R}}^{2}}$ | F | p | ${\mathbf{s}}^{2}$ | |
---|---|---|---|---|---|

Equation (3) | 0.7433 | 0.7127 | 24.3171 | $2.06\times {10}^{-11}$ | 159.6470 |

Equation (8) | 0.7428 | 0.7189 | 31.0531 | $3.54\times {10}^{-12}$ | 156.1843 |

Equation (9) | 0.7416 | 0.7240 | 42.0839 | $5.51\times {10}^{-13}$ | 153.3960 |

Equation (10) | 0.5120 | 0.5014 | 48.2668 | $1.09\times {10}^{-8}$ | 277.0431 |

Class Number | Clustering Centroid Coordinates | ||
---|---|---|---|

2 | A: −0.0641, 0.1995, −0.2051 | B: 0.8320, −2.5901, 2.6630 | |

3 | A: −0.9357, 0.5370, −0.4123 | B: 0.8336, −2.6728, 2.6869 | C: 0.6812, −0.0907, −0.0173 |

4 | A: −0.9288, 0.5410, −0.4338 | B: 0.3101, −0.0073, 1.8097 | C: 0.7175, −0.1236, −0.2475 |

D: 1.0626, −3.3536, 2.4532 | |||

5 | A: −0.9272, 0.5579, −0.4562 | B: 1.0696, −0.7167, 6.1073 | C: 0.7279, −0.1161, −0.2576 |

D: 1.0190, −3.3857, 2.2587 | E: 0.1607, −0.0542, 1.4754 | ||

6 | A: −0.9137, 0.5984, −0.4645 | B: 1.0696, −0.7167, 6.1073 | C: 0.7347, −0.0896, −0.2614 |

D: 1.0795, −3.4246, 2.3176 | E: −0.5444, −0.9664, 1.0476 | F: 0.9914, 0.8563, 1.7943 | |

7 | A: −0.9137, 0.5984, −0.4645 | B: 0.9658, 0.0421, 5.9582 | C: 0.7347, −0.0896, −0.2614 |

D: 1.0688, −3.4310, 2.2907 | E: −0.5444, −0.9664, 1.0476 | F: 0.9914, 0.8563, 1.7943 | |

G: 1.4486, −2.6048, 5.9101 |

Class Number | Ratio of Icing Risk (Number of Samples with Icing Risk/Total Number of Samples in This Category) | ||||||
---|---|---|---|---|---|---|---|

Class A | Class B | Class C | Class D | Class E | Class F | Class G | |

2 | 284/1402 | 0/108 | |||||

3 | 65/646 | 0/104 | 219/760 | ||||

4 | 67/641 | 1/136 | 216/654 | 0/79 | |||

5 | 67/629 | 0/10 | 215/646 | 0/77 | 2/148 | ||

6 | 61/617 | 0/10 | 215/641 | 0/74 | 8/107 | 0/61 | |

7 | 61/617 | 0/7 | 215/641 | 0/73 | 8/107 | 0/61 | 0/4 |

Neural Network Structure 1 | Neural Network Structure 2 | |
---|---|---|

COR | 49.80% | 76.52% |

WRO | 50.20% | 23.48% |

FOH | 37.06% | 56.88% |

FAR | 62.94% | 43.12% |

DFR | 0% | 7.97% |

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**MDPI and ACS Style**

Wang, J.; Xie, B.; Cai, J.; Wang, Y.; Chen, J.
Study on Icing Environment Judgment Based on Radar Data. *Atmosphere* **2021**, *12*, 1534.
https://doi.org/10.3390/atmos12111534

**AMA Style**

Wang J, Xie B, Cai J, Wang Y, Chen J.
Study on Icing Environment Judgment Based on Radar Data. *Atmosphere*. 2021; 12(11):1534.
https://doi.org/10.3390/atmos12111534

**Chicago/Turabian Style**

Wang, Jinhu, Binze Xie, Jiahan Cai, Yuhao Wang, and Jiang Chen.
2021. "Study on Icing Environment Judgment Based on Radar Data" *Atmosphere* 12, no. 11: 1534.
https://doi.org/10.3390/atmos12111534