# A Global Conversion Factor Model for Mapping Zenith Total Delay onto Precipitable Water

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method of Establishing the GΠ Model

^{3}). ${T}_{m}$ represents the weighted average atmospheric temperature (unit: K). A linear relationship between the weighted average temperature and ground temperature was proposed by Bevis et al. [7,22,23] using radiosonde data over many years:

#### 2.1. Methods of Obtaining the Conversion Factor

#### 2.2. Analysis of the Conversion Factor

- Relationship between the conversion factor and the annual change.

- 2.
- Relationship between the conversion factor and the semiannual change.

- 3.
- Relationship between the conversion factor and the elevation.

- 4.
- Analysis of the modelling grid division.

#### 2.3. Expression of the Conversion Factor Model

## 3. Result

#### 3.1. Internal Accuracy Testing

^{−3}. It also can be seen from Figure 7 that the RMS and MAE range from 0 to 0.0317 and from 0 to 0.026 on the global scale, which indicates a good accuracy in the G$\mathsf{\Pi}$ model; however, some abnormal values appeared near the equator, which may have been affected by the El Niño event at that time [31].

#### 3.2. External Accuracy Testing

#### 3.3. Case Study

## 4. Discussion

## 5. Conclusions

^{−3}, which accounts for only 1.5–2% of the conversion factor value. To validate the applicability of the established G$\mathsf{\Pi}$ model, a case study was assessed that involved two sites in different regions with large PWV values for the whole year over different time periods. The statistical results from both sites revealed that the RMS error of the PWV calculated based on the established G$\mathsf{\Pi}$ model was about 3 mm; in addition, the model coefficient could be easily obtained at a specific grid point and the conversion factor was directly obtained, which was of significance for the calculation of the PWV, especially when faced with the unavailability of meteorological parametric data.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Changes of the conversion factors with time over the period from 2006 to 2013 at the four selected locations of (

**a**) N30° E120°, (

**b**) N30° W120°, (

**c**) S30° E120° and (

**d**) S30° W120°, globally.

**Figure 2.**Relationship between the conversion factor and the semiannual change at the four selected locations of (

**a**) N30° E120°, (

**b**) N30° W120°, (

**c**) S30° E120° and (

**d**) S30° W120° using the data from the year 2013.

**Figure 3.**Relationship between the conversion factor and the elevation globally using the data from the year 2013.

**Figure 4.**Relationship between the conversion factor and the longitude using the data of grid points globally from the year 2013.

**Figure 5.**Relationship between the conversion factor and the latitude using the data of grid points globally from the year 2013.

**Figure 6.**Coefficients distribution of the established global conversion factors globally estimated using the least squares method, where (

**a**–

**d**) represent the distribution of coefficients a2, a3, a4, and a5, respectively.

**Figure 7.**Distribution of the (

**a**) MAE and (

**b**) RMS: internal accuracy testing of the GΠ model when compared with that from the GGOS data of 2012.

**Figure 8.**Distribution of the (

**a)**MAE and (

**b**) RMS: external accuracy testing of the GΠ model when compared with that from the GGOS data of 2014.

**Figure 9.**Histogram of the average RMS of external accuracy testing for the GΠ model when compared with that from the GGOS data of 2014.

**Figure 10.**Distribution of the MAE and RMS with respect to height, latitude, and longitude in 2004, where (

**a**,

**b**) refer to the MAE and RMS with height, (

**c**,

**d)**are the MAE and RMS with the latitude while the (

**e**,

**f**) represent the MAE and RMS with longitude, respectively.

**Figure 11.**Comparison of the met-derived and model-derived PWV for the two selected stations, where (

**a**) is the PWV comparison of ANJI station with the data from 1 May to 20 July 2015 while (

**b**) is the PWV comparison of HKSC station with the data for the whole year of 2014.

Model | MAE | RMS | ||||
---|---|---|---|---|---|---|

Mean | Max | Min | Mean | Max | Min | |

GΠ | 0.0026 | 0.026 | 0.0005 | 0.0031 | 0.0317 | 0.0006 |

Model | MAE | RMS | ||||
---|---|---|---|---|---|---|

Mean | Max | Min | Mean | Max | Min | |

GΠ | 0.0026 | 0.0244 | 0.0005 | 0.0030 | 0.0304 | 0.0006 |

Height Range (m) | MAE | RMS | ||||
---|---|---|---|---|---|---|

Mean (10 ^{−3}) | Max (10 ^{−3}) | Min (10 ^{−3}) | Mean (10 ^{−3}) | Max (10 ^{−3}) | Min (10 ^{−3}) | |

<500 | 2.5 | 24.4 | 0.5 | 2.9 | 30.4 | 0.6 |

500~1000 | 2.9 | 19.5 | 0.6 | 3.4 | 22.1 | 0.7 |

1000~2000 | 3 | 7.7 | 0.5 | 3.5 | 8.9 | 0.7 |

>2000 | 3 | 7.9 | 0.7 | 3.6 | 9.1 | 0.9 |

**Table 4.**Statistical results: MAE and RMS for the GΠ model across different latitude ranges in 2014.

Longitude Range | MAE | RMS | ||||
---|---|---|---|---|---|---|

Mean (10 ^{−3}) | Max (10 ^{−3}) | Min (10 ^{−3}) | Mean (10 ^{−3}) | Max (10 ^{−3}) | Min (10 ^{−3}) | |

0°~30° | 2 | 24.4 | 0.5 | 2.3 | 30.4 | 0.6 |

30°~60° | 2.4 | 10.2 | 0.6 | 2.9 | 11.6 | 0.8 |

60°~90° | 2.7 | 22.5 | 0.5 | 3.2 | 30.4 | 0.6 |

90°~120° | 2.8 | 11.5 | 0.5 | 3.4 | 13 | 0.6 |

120°~150° | 2.7 | 21.8 | 0.5 | 3.2 | 24.8 | 0.6 |

150°~180° | 2.4 | 6.3 | 0.6 | 2.8 | 7.5 | 0.8 |

**Table 5.**Statistical results: MAE and RMS for the GΠ model across different longitude ranges in 2014.

Latitude Range | MAE | RMS | ||||
---|---|---|---|---|---|---|

Mean (10 ^{−3}) | Max (10 ^{−3}) | Min (10 ^{−3}) | Mean (10 ^{−3}) | Max (10 ^{−3}) | Min (10 ^{−3}) | |

0°~30° | 1.4 | 24.4 | 0.5 | 1.7 | 30.4 | 0.6 |

30°~60° | 2.8 | 7.8 | 1.1 | 3.3 | 9.1 | 1.4 |

60°~90° | 3.7 | 8.1 | 1.3 | 4.3 | 9.4 | 1.6 |

Station | HKSC | ANJI | ||||
---|---|---|---|---|---|---|

Lat. (°) | Lon. (°) | Height (m) | Lat. (°) | Lon. (°) | Height (m) | |

Value | 22.32 | 114.13 | 20.15 | 30.37 | 119.41 | 35.40 |

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**MDPI and ACS Style**

Zhao, Q.; Liu, K.; Zhang, T.; He, L.; Shen, Z.; Xiong, S.; Shi, Y.; Chen, L.; Liao, W.
A Global Conversion Factor Model for Mapping Zenith Total Delay onto Precipitable Water. *Remote Sens.* **2022**, *14*, 1086.
https://doi.org/10.3390/rs14051086

**AMA Style**

Zhao Q, Liu K, Zhang T, He L, Shen Z, Xiong S, Shi Y, Chen L, Liao W.
A Global Conversion Factor Model for Mapping Zenith Total Delay onto Precipitable Water. *Remote Sensing*. 2022; 14(5):1086.
https://doi.org/10.3390/rs14051086

**Chicago/Turabian Style**

Zhao, Qingzhi, Kang Liu, Tengxu Zhang, Lin He, Ziyu Shen, Si Xiong, Yun Shi, Lichuan Chen, and Weiming Liao.
2022. "A Global Conversion Factor Model for Mapping Zenith Total Delay onto Precipitable Water" *Remote Sensing* 14, no. 5: 1086.
https://doi.org/10.3390/rs14051086