# Establishment and Evaluation of a New Meteorological Observation-Based Grid Model for Estimating Zenith Wet Delay in Ground-Based Global Navigation Satellite System (GNSS)

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## Abstract

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## 1. Introduction

## 2. Data and Methods

#### 2.1. Radiosonde Data

#### 2.2. European Centre for Medium-Range Weather Forecasts (ECWMF) Data

#### 2.3. ZWD Calculation Using Meteorological Data

#### 2.4. Saastamoinen-ZWD Model

#### 2.5. Hopfield-ZWD Model

#### 2.6. GPT2w Model

## 3. Establishment of the Model

#### 3.1. Correlation between ZWD and Water Vapor Pressure

#### 3.2. Expression of the Formula and Determination of the Coefficients

## 4. Evaluation Results

#### 4.1. Evaluation with the ECMWF Data

#### 4.2. Evaluation with the Radiosonde Data

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Time series of zenith wet delay (ZWD) and e for a 3-year period (2013–2015) and the linear correlation between them at the radiosonde station 71964 (60.73°N, 135.09°W, altitude: 707 m, in Whitehorse, Canada). (

**a**) 3-year time series of ZWD. (

**b**) 3-year time series of e. (

**c**) Linear correlation of ZWD and e. The linear regression line and the correlation coefficient are also depicted.

**Figure 4.**The global distributions of the model coefficients calculated using the European Centre for Medium-Range Weather Forecasts (ECWMF) data for 3 years (2013–2015). (

**a**) The global distribution of the proportionality coefficients. (

**b**) The global distribution of the mean values of the ZWD residuals.

**Figure 5.**The global distributions of the mean relative biases (MRBs) (first column) and relative root of mean square errors (RRMSs) (second column) of each model evaluated with the ECMWF data. (

**a**) The global distribution of the MRBs of the Saastamoinen model. (

**b**) The global distribution of the RRMSs of the Saastamoinen model. (

**c**) The global distribution of the MRBs of the Hopfield model. (

**d**) The global distribution of the RRMSs of the Hopfield model. (

**e**) The global distribution of the MRBs of the GPT2w model. (

**f**) The global distribution of the RRMSs of the GPT2w model. (

**g**) The global distribution of the MRBs of the GridZWD model. (

**h**) The global distribution of the RRMSs of the GridZWD model.

**Figure 6.**The statistical comparisons of the radiosonde-derived ZWDs and the model-estimated ZWDs. (

**a**) The Biases, RMSs, MRBs and RRMSs of each model in each latitude band. (

**b**) The Biases, RMSs, MRBs and RRMSs of each model in the 12 months of the 2016 year for the northern hemisphere. (

**c**) The Biases, RMSs, MRBs and RRMSs of each model in the 12 months of the 2016 year for the southern hemisphere.

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**MDPI and ACS Style**

Yao, Y.; Sun, Z.; Xu, C.
Establishment and Evaluation of a New Meteorological Observation-Based Grid Model for Estimating Zenith Wet Delay in Ground-Based Global Navigation Satellite System (GNSS). *Remote Sens.* **2018**, *10*, 1718.
https://doi.org/10.3390/rs10111718

**AMA Style**

Yao Y, Sun Z, Xu C.
Establishment and Evaluation of a New Meteorological Observation-Based Grid Model for Estimating Zenith Wet Delay in Ground-Based Global Navigation Satellite System (GNSS). *Remote Sensing*. 2018; 10(11):1718.
https://doi.org/10.3390/rs10111718

**Chicago/Turabian Style**

Yao, Yibin, Zhangyu Sun, and Chaoqian Xu.
2018. "Establishment and Evaluation of a New Meteorological Observation-Based Grid Model for Estimating Zenith Wet Delay in Ground-Based Global Navigation Satellite System (GNSS)" *Remote Sensing* 10, no. 11: 1718.
https://doi.org/10.3390/rs10111718