# A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products

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## Abstract

**:**

## 1. Introduction

## 2. Experiment Description and Data Retrieval

#### 2.1. Data Description

#### 2.2. Retrieval of ZHD, ZWD, and Tm Using GRAPES_MESO and Radiosonde Data

#### 2.3. Interpolating GRAPES Products to Any Location

## 3. Biases in ZWD and Tm

## 4. Bias Correction

#### 4.1. Correcting Systematic Biases between GRAPES-Based and Radiosonde-Based ZWD(Tm)

#### 4.2. Interpolating $a$ and $b$ Using a Spherical Cap Harmonic (SCH) Model

## 5. Results

#### 5.1. Validation with Radiosonde Data

#### 5.1.1. Overall Performance

#### 5.1.2. Spatial Variations of Accuracy

#### 5.1.3. Temporal Variations of Accuracy

#### 5.2. Validate the CTropGrid Products with IGS ZTD

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Daily biases from GRAPES water vapor pressure (

**a**) and temperature (

**b**) in 2017. The dashed red lines indicate the values 0. The dashed green lines represent the mean bias. The reference values are from radiosonde data.

**Figure A2.**The $p$ values of statistical significance from the estimated $a$ and $b$ for GRAPES-radiosonde ZWD (

**a**,

**b**) and Tm (

**c**,

**d**). The statistical significance is tested using t-Test with 95% confidence level.

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**Figure 1.**Flowchart of the main steps of generating ZHD, ZWD, and Tm in China and its surrounding areas using GRAPES_MESO forecasting products.

**Figure 3.**The radiosonde ZHD (

**a**), ZWD (

**b**), and Tm (

**c**) profile and the interpolated ZHD (

**a**), ZWD (

**b**), and Tm (

**c**) from GRAPES product.

**Figure 4.**Daily biases from GRAPES ZWD (

**a**) and Tm (

**b**) in 2017. The dashed red lines indicate the values 0. The dashed green lines represent the mean bias.

**Figure 6.**ZWD (

**a**,

**c**,

**e**,

**g**) and Tm (

**b**,

**d**,

**f**,

**h**) time series from GRAPES, radiosonde, and calibrated GRAPES at BAGUIO, WENJIANG, LUCKNOW, and KASHI stations in 2017.

**Figure 7.**The variation of the RMS of fitting $a$ (

**a**) and $b$ (

**b**) for the GRAPES ZWD at each degree.

**Figure 8.**$a$ (

**a**,

**c**) and $b$ (

**b**,

**d**) fields represented by the SCH models with different degrees for the GRAPES ZWD. Circles mark the radiosonde stations. Red ellipses mark the distortions.

**Figure 10.**The distribution of $a$ (

**a**,

**c**,

**e**,

**g**) and $b$ (

**b**,

**d**,

**f**,

**h**) for the GRAPES Tm expanded by the SCH models with different degrees. Circles mark the radiosonde stations. Red ellipses mark the distortions.

**Figure 11.**Bias, STD, and RMS of CTropGrid ZHD (

**a**–

**c**), ZWD (

**d**–

**f**), and Tm (

**g**–

**i**) at radiosonde stations.

**Figure 12.**Percentage RMS reductions of the CTropGrid ZHD (

**a**), ZWD (

**b**), and Tm (

**c**) in comparison with the GPT2w model.

**Figure 13.**Time series of the accuracy from ZHD (

**a**,

**b**), ZWD (

**c**,

**d**), and Tm (

**e**,

**f**) derived by the CTropGrid products and the GPT2w model.

**Figure 14.**Power spectrums of bias and RMS for ZHD (

**a**,

**b**), ZWD (

**c**,

**d**), and Tm (

**e**,

**f**) derived by the CTropGrid products and the GPT2w model.

**Figure 15.**Time series of twice-daily bias (

**a**) and RMS (

**b**) of the CTropGrid and the GPT2w ZTD tested by IGS ZTD data in 2017.

**Table 1.**Statistics of the mean bias, STD, and RMS for ZHD, ZWD, and Tm derived from the CTropGrid and the GPT2w model at radiosonde stations in the year 2017. The numbers in the square brackets indicate the range of bias, STD, or RMS.

Method | ZHD (mm) | ZWD (mm) | Tm (K) | ||||||
---|---|---|---|---|---|---|---|---|---|

Bias | STD | RMS | Bias | STD | RMS | Bias | STD | RMS | |

CTropGrid | 1.5 | 5.2 | 8.9 | −0.7 | 19.0 | 20.2 | −0.1 | 1.5 | 1.5 |

[−15.8, 35.8] | [0.7, 7.3] | [3.0, 35.9] | [−24.1, 26.2] | [7.9, 38.3] | [10.2, 38.7] | [−2.2, 1.3] | [0.7, 2.5] | [0.7, 2.6] | |

GPT2w | 0.6 | 9.3 | 10.1 | −7.0 | 43.8 | 45.5 | −0.7 | 3.5 | 3.8 |

[−4.0, 45.4] | [4.0, 21.0] | [4.4, 45.8] | [−61.8, 20.5] | [13.8, 78.1] | [13.8, 79.0] | [−7.1, 3.8] | [1.4, 5.7] | [1.4, 7.7] |

**Table 2.**Statistics of bias, STD, and RMS for ZTD from the CTropGrid product and the GPT2w model at IGS stations in the year 2017.

Model | Bias (mm) | STD (mm) | RMS (mm) |
---|---|---|---|

GPT2w | 1.0 [−13.9, 21.8] | 45.2 [17.5, 67.0] | 46.3 [20.9, 67.2] |

CTropGrid | −0.7 [−16.8, 23.6] | 34.1 [22.7, 49.6] | 35.8 [24.7, 49.8] |

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## Share and Cite

**MDPI and ACS Style**

Cao, L.; Zhang, B.; Li, J.; Yao, Y.; Liu, L.; Ran, Q.; Xiong, Z.
A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products. *Remote Sens.* **2021**, *13*, 2644.
https://doi.org/10.3390/rs13132644

**AMA Style**

Cao L, Zhang B, Li J, Yao Y, Liu L, Ran Q, Xiong Z.
A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products. *Remote Sensing*. 2021; 13(13):2644.
https://doi.org/10.3390/rs13132644

**Chicago/Turabian Style**

Cao, Liying, Bao Zhang, Junyu Li, Yibin Yao, Lilong Liu, Qishun Ran, and Zhaohui Xiong.
2021. "A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products" *Remote Sensing* 13, no. 13: 2644.
https://doi.org/10.3390/rs13132644