# Kriging Interpolation in Modelling Tropospheric Wet Delay

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## Abstract

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## 1. Introduction

## 2. Kriging Interpolation in Modelling Tropospheric Wet Delay

## 3. Experiments in Sparse and Dense Network

## 4. Conclusions and Discussions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sparse global navigation satellite system (GNSS) network with 8 reference stations and 15 user stations.

**Figure 5.**RMSEs of the prediction errors for the user stations inside the (

**a**) sparse network and (

**b**) dense network.

**Figure 6.**Values of the predicted zenith wet delays at particular locations (the smaller circle) in the local area by using the sparse and dense network (the bigger circle) on 1 February 2019. The unit is m.

**Figure 7.**Values of the predicted zenith wet delays at particular locations (the smaller circle) in the local area by using the sparse and dense network (the bigger circle) on 1 August 2019. The unit is m.

**Figure 8.**RMSEs of the prediction errors for the user stations on the edge of the (

**a**) sparse network and (

**b**) dense network.

**Figure 10.**RMSEs of the prediction errors for the user stations outside the (

**a**) sparse network and (

**b**) dense network.

**Figure 11.**Average RMSE of the user stations in (

**a**) the sparse and (

**b**) the dense network. Stations from the left to the right are sequential 5 inside the network, 5 on the edge of the network and 5 outside the network.

**Figure 12.**Violin plot of the RMSEs of each user station in (

**a**) the sparse network and (

**b**) the dense network. Stations from the left to the right are sequential 5 inside the network, 5 on the edge of the network and 5 outside the network.

Parameter | Strategy and Value |
---|---|

Positioning mode | Static |

Constellation | GPS |

Frequency | L1 and L2 |

Satellite orbit and clock corrections | IGS |

Interval | $60\text{}\mathrm{s}$ |

Kalman filter | Forward and backward |

STD of phase/code observable | $0.005\text{}\mathrm{m}$/$0.5\text{}\mathrm{m}$ |

Weighting strategy | Elevation dependent |

Zenith hydrostatic delay | Saastamoinen model |

Zenith wet delay | Spectral density $0.02{\text{}\mathrm{m}}^{2}/\mathrm{h}$ |

Troposphere gradients | Spectral density $0.001{\text{}\mathrm{m}}^{2}/\mathrm{h}$ |

Ambiguity | Float |

Region | User Station | RMSE of Sparse Network | Average | RMSE of Dense Network | Average |
---|---|---|---|---|---|

Inside | LITH | 0.83 | 0.74 | 0.77 | 0.69 |

LELY | 0.74 | 0.75 | |||

LWRD | 0.74 | 0.67 | |||

HOOG | 0.70 | 0.66 | |||

ADR2 | 0.67 | 0.61 | |||

On the edge | WARM | 2.26 | 1.12 | 1.90 | 0.98 |

TERS | 1.31 | 1.22 | |||

DZYL | 0.96 | 0.80 | |||

OLDE | 0.54 | 0.51 | |||

HHOL | 0.53 | 0.48 | |||

Outside | KERK | 1.35 | 1.17 | 1.21 | 1.09 |

MSTR | 1.28 | 1.14 | |||

SASG | 1.13 | 1.13 | |||

VLIS | 1.12 | 1.12 | |||

RIL2 | 0.99 | 0.85 |

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**MDPI and ACS Style**

Ma, H.; Zhao, Q.; Verhagen, S.; Psychas, D.; Dun, H.
Kriging Interpolation in Modelling Tropospheric Wet Delay. *Atmosphere* **2020**, *11*, 1125.
https://doi.org/10.3390/atmos11101125

**AMA Style**

Ma H, Zhao Q, Verhagen S, Psychas D, Dun H.
Kriging Interpolation in Modelling Tropospheric Wet Delay. *Atmosphere*. 2020; 11(10):1125.
https://doi.org/10.3390/atmos11101125

**Chicago/Turabian Style**

Ma, Hongyang, Qile Zhao, Sandra Verhagen, Dimitrios Psychas, and Han Dun.
2020. "Kriging Interpolation in Modelling Tropospheric Wet Delay" *Atmosphere* 11, no. 10: 1125.
https://doi.org/10.3390/atmos11101125