# Statistical Assessments of InSAR Tropospheric Corrections: Applicability and Limitations of Weather Model Products and Spatiotemporal Filtering

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## Abstract

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## 1. Introduction

## 2. Materials

#### 2.1. Study Area

#### 2.2. Data

#### 2.2.1. Sentinel-1 SAR Imagery

#### 2.2.2. Digital Elevation Model (DEM)

#### 2.2.3. Weather Model Products

## 3. Methods

#### 3.1. Evaluation Metrics for InSAR Tropospheric Correction

#### 3.1.1. Tropospheric Noise Estimated by Time Series Decomposition

#### 3.1.2. Semi-Variograms with Model Fitted Range and Sill

#### 3.1.3. Spearman’s Rank Correlation between Phase and Elevation

#### 3.2. Analysis of Primary and Secondary Images’ Contribution in Tropospheric Corrections

## 4. Experiments and Results

#### 4.1. Experimental Settings

#### 4.2. Elimination of Overall Tropospheric Noise

#### 4.3. Mitigation of Distance-Dependent Signals

#### 4.4. Reduction of Phase-Elevation Dependence

#### 4.5. The Roles of Primary and Secondary TOE in Tropospheric Corrections

#### 4.6. Local Subsidence Maps Derived after Tropospheric Correction

## 5. Discussion

#### 5.1. The Applicability and Limitations of Different InSAR Tropospheric Correction Methods

#### 5.2. Comparison of ERA-I, ERA5, and GACOS for the Tropospheric Correction in Coastal Areas

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Topography map of the study area. The blue frame indicates the coverage of Sentinel-1 data, and the red boxes denote the hilly areas involved in the analysis of phase-elevation dependence in Section 4.4.

**Figure 2.**Analysis of the different roles taken by primary and secondary tropospheric and orbit error (TOE) on InSAR tropospheric corrections.

**Figure 3.**The stable region (marked by the blue polygon) that serves as the spatial reference for resolving the phase time series.

**Figure 4.**Location of selected points marked by the green star in all sub-figures. (

**a**) “P1” in the Qianhai sub-area on a typical ocean reclaimed land; (

**b**) “P2” in Hong Kong International Airport (HKIA), an airport built on an ocean reclaimed area; (

**c**) “P3” in Wutong Mountain at an altitude over 600 m; (

**d**) “P4” in the Liantang sub-area affected by tunneling works of metro construction.

**Figure 5.**PS time series decomposition results of representative PS points after tropospheric correction using ERA5 and spatiotemporal filtering. (

**a**) “P1” in the Qianhai sub-area; (

**b**) “P2” in the HKIA sub-area; (

**c**) “P3” in the Wutong Mountain sub-area; (

**d**) “P4” in the Liantang sub-area. The blue line shows the original PS time series measurements. The red line plots the sum of the fitted first term and second term in Equation (1) by time series decomposition. The green line displays only the periodic component. The black dots represent the unmodeled noise as defined in Equation (1).

**Figure 6.**The histograms of the unmodeled noise derived for “P1”, “P2”, “P3”, and “P4” using the time series decomposition method. (

**a**) PI in Qianhai sub-area, (

**b**) P2 in HKIA sub-area, (

**c**) P3 in Wutong Mountain sub-area, (

**d**) P3 in Liantang sub-area.

**Figure 7.**Time series RMS estimated in the Qianhai sub-area after correction using ERA5 and StaMPS spatiotemporal filtering. (

**a**) Derived based on the none-deformation assumption; (

**b**) derived with bias mitigated using the proposed time series decomposition method.

**Figure 8.**Percentile plots of the time series RMS of the tropospheric noise derived over the whole study area. (

**a**) No correction, GACOS, ERA-I, or ERA5 derived corrections. (

**b**) Corrections using StaMPS spatiotemporal or its integration with GACOS, ERA-I, or ERA5. The entries “*” in the legend represent the corrections with the primary TOE retained in interferograms.

**Figure 9.**Semi-variograms of the 20170312–20170815 interferogram before and after tropospheric corrections. (

**a**) No correction, GACOS, ERA-I, ERA5 correction, or combined approaches with the primary TOE retained. (

**b**) Corrections using spatiotemporal filtering or the combined approaches, after removing the primary TOE. The symbol “*” denote the corrections with primary TOE retained in the interferograms.

**Figure 10.**Example scatter plots of phase vs. elevation with least-squares reference lines. Outliers have been marked with black circles or ellipses. The phase values have been converted to millimeters. (

**a**) Interferogram 20170312-20150615 with a 30 km window size, after tropospheric correction using ERA5 and spatiotemporal filtering; (

**b**) interferogram 20170312-20160516 with a 30 km window size, after tropospheric correction using the GACOS product.

**Figure 11.**Phase-elevation rank correlation coefficient before and after tropospheric corrections, using the interferograms referenced to the acquisition date of 12 March 2017. (

**a**) Results with the primary TOE retained. (

**b**) Results after subtracting the primary TOE in the spatiotemporal filtering and the combined approaches.

**Figure 12.**Phase-elevation rank correlation coefficient before and after tropospheric corrections, using the interferograms referenced to the acquisition date of 4 February 2017. (

**a**) Results with the primary TOE retained. (

**b**) Results after subtracting the primary TOE in the spatiotemporal filtering and the combined approaches.

**Figure 13.**Line-of-Sight (LOS) deformation rates derived after tropospheric correction using ERA5 and spatiotemporal filtering, and superimposed on Google Earth high resolution images. Sub-areas exhibiting significant subsidence are highlighted by black circles. (

**a**) Annual deformation rate derived in the ocean-reclaimed land in the Qianhai area, Shenzhen; (

**b**) annual deformation rate derived in the ocean-reclaimed land in HKIA; an original rocky island Chek Lap Kok is outlined with white lines and labeled as “A”, and the other original rocky island Lam Chau is drawn with white lines and labeled as “B”; (

**c**) annual deformation rate derived in a residential area nearby metro tunneling works at Liantang station, Shenzhen.

Sentinel-1 IW SLC Data | |
---|---|

Timespan | 15 June 2015~7 March 2018 |

Revisit cycle (days) | 12 |

Polarization | VV |

Incidence angle (°) | 41.69~46.11 |

Wavelength (cm) | 5.5 |

Slant range spacing (m) | 2.33 |

Azimuth spacing (m) | 13.92 |

|r|_{s} | Correlation Strength |
---|---|

0.00~0.19 | Very weak |

0.20~0.39 | Weak |

0.40~0.69 | Moderate |

0.70~0.89 | Strong |

0.90~1.00 | Very strong |

Latitude | Longitude | Altitude | Topography | |
---|---|---|---|---|

P1 | N 22.523119° | E 113.889458° | −3.6 m | Low altitude, flat terrain, ocean-reclaimed area |

P2 | N 22.313656° | E 113.917023° | −1.1 m | Low altitude, flat terrain, ocean-reclaimed area |

P3 | N 22.571257° | E 114.188890° | 639 m | High altitude, hilly area |

P4 | N 22.568163° | E 114.171921° | 39.4 m | Low altitude, flat terrain, metro tunneling area |

**Table 4.**The model-fitted mean decorrelation range and sill of semi-variograms before and after tropospheric corrections. Entries denoted by ‘*’ preserve the primary TOE in the interferograms.

Weighted Mean Range (km) | Weighted Mean Sill (mm) | ||
---|---|---|---|

Original | No correction | 53.20 | 761.39 |

Group 1 | GACOS | 48.19 | 561.66 |

ERA-I | 50.57 | 489.88 | |

ERA5 | 51.50 | 563.68 | |

Group 2 | Spatiotemporal filtering * | 63.57 | 223.61 |

GACOS and filtering * | 76.61 | 71.92 | |

ERA-I and filtering * | 61.41 | 63.82 | |

ERA5 and filtering * | 63.57 | 134.54 | |

Group 3 | Spatiotemporal filtering | 15.97 | 2.79 |

GACOS and filtering | 16.75 | 3.34 | |

ERA-I and filtering | 13.72 | 2.86 | |

ERA5 and filtering | 13.78 | 3.50 |

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## Share and Cite

**MDPI and ACS Style**

Sun, L.; Chen, J.; Li, H.; Guo, S.; Han, Y.
Statistical Assessments of InSAR Tropospheric Corrections: Applicability and Limitations of Weather Model Products and Spatiotemporal Filtering. *Remote Sens.* **2023**, *15*, 1905.
https://doi.org/10.3390/rs15071905

**AMA Style**

Sun L, Chen J, Li H, Guo S, Han Y.
Statistical Assessments of InSAR Tropospheric Corrections: Applicability and Limitations of Weather Model Products and Spatiotemporal Filtering. *Remote Sensing*. 2023; 15(7):1905.
https://doi.org/10.3390/rs15071905

**Chicago/Turabian Style**

Sun, Luyi, Jinsong Chen, Hongzhong Li, Shanxin Guo, and Yu Han.
2023. "Statistical Assessments of InSAR Tropospheric Corrections: Applicability and Limitations of Weather Model Products and Spatiotemporal Filtering" *Remote Sensing* 15, no. 7: 1905.
https://doi.org/10.3390/rs15071905