# Joint Exploitation of SAR and GNSS for Atmospheric Phase Screens Retrieval Aimed at Numerical Weather Prediction Model Ingestion

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## Abstract

**:**

## 1. Introduction

## 2. Requirements for NWPM Ingestion, SAR Atmospheric Signal Characterization, and Orbit Requirements

#### 2.1. Requirements for NWPM Ingestion

#### 2.2. Atmospheric Contribution in SAR Images

- (1).
- $\mathsf{\Delta}{R}_{0}\left(P\right)$ can be removed easily from the interferometric phase by knowing the acquisition geometry and a Digital Elevation Model (DEM) of the scene.
- (2).
- (3).
- The phase of the target remains stable between the two acquisitions ($\mathsf{\Delta}{\varphi}_{T}\left(P\right)\approx 0)$.

#### 2.3. Orbit Accuracy Requirements

## 3. Target Characterization

## 4. Processing Scheme

#### 4.1. Coregistration and Ionospheric Phase Compensation

#### 4.2. Topographic Phase Compensation

#### 4.3. Phase Estimation via Phase Linking

- (1).
- The phase linking estimator just explained.
- (2).
- The AR(1) estimator that consists in integrating the phases of interferograms formed using consecutive acquisitions:$${\widehat{\psi}}_{i}=\angle {\displaystyle \prod}_{k=1}^{i}\widehat{\mathbf{C}}\left(i,i+1\right)$$

#### 4.4. Phase Linking for APS Estimation

- It reduces the effects of subsidences on the interferometric phase. The model of the interferometric phase in Equation (5) can present another term due to linear displacement in the line of sight direction that is equal to:$${\psi}_{s}\left(P,{t}_{1},{t}_{2}\right)=\frac{4\pi {f}_{0}}{c}v\mathsf{\Delta}t$$
- Following the decorrelation model explained in Section 3, we can say that the stack temporal extent needs to take into consideration the average “life” of a distributed scatterer. With phase linking, we form all the possible interferograms with N images and from them, we estimate N-1 phases, if the coherence of the interferograms with very long temporal baseline is very low, they will bring noise into the final estimate. A solution is then to reduce the maximum temporal baseline by considering the decorrelation model. It is useful to remember that the decorrelation time depends on the wavelength used for the measure: In [18], Rocca made the example of 40 days in C-Band, but the reasoning can be easily extended in L or P Band where the average decorrelation time is much higher and thus a larger dataset can be used.

#### 4.5. Phase Unwrapping

#### 4.6. Orbit Correction: GNSS Processing and Integration

## 5. Case Study

#### 5.1. Dataset

#### 5.2. Processing

#### 5.3. Orbit Correction

#### 5.4. Variograms and Radially Average Spectra

#### 5.5. Comparison with Reference APS Maps from SqueeSAR®

#### 5.6. A Note about GNSS and NWMP Comparison and NWMP Ingestion of SAR-Derived APS

**H**is the design matrix that generates all the differences of absolute phases.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Synthetic Aperture Radar (SAR) acquisition geometry in the zero Doppler plane. The position of the satellite in the master acquisition is defined as M, the slave acquisition is defined as S. The point on ground is defined with the letter P.

**Figure 3.**Variance of the phase estimates in different scenarios. (

**a**) coherence matrix of a Permanent Scatterer. showing coherence equal to 0.6 for all the images. (

**b**) phase variance using different estimators in the PS case.

**Figure 4.**(

**a**) coherence matrix for a distributed scatterer showing an exponential decorrelation with constant equal to 35 days. (

**b**) phase variance using different estimators in the DS case.

**Figure 5.**Standard deviation of the estimated phase versus the number of independent looks used for the estimate. For this processing we used a covariance matrix modelled as in (7), with ${\gamma}_{0}=0.7$, $\rho =0.975$, $T=6$ as suggested in [8].

**Figure 7.**Interferometric phases of a single subswath in the study area. (

**a**) Wrapped interferometric phases. The interferometric phase between image k and image l is on the ${k}^{th}$ row and ${l}^{th}$ column. (

**b**) The reconstructed interferometric phases after phase linking (best rank-1 approximation). (

**c**) The residuals between the two.

**Figure 8.**A comparison between the standard interferogram (top row), the phase linked (middle row) and their residual (bottom row). In the last row the variograms for DInSAR (PS) and Phase Linking (PL) are shown.

**Figure 9.**GNSS (Global Navigation Satellite System) stations (red dots) in the area of interest (blue rectangle).

**Figure 10.**Orbital error parameters estimated in the six interferograms (x-axis). (

**a**) Derivative of the parallel baseline. (

**b**) Error in the normal baseline.

**Figure 12.**(

**a**)Profile of an APS maps before (blue) and after (red) orbit trend correction. (

**b**) Wrapped and geocoded orbital plane corrected in the interferometric phase.

**Figure 13.**(black dashed lines) spatial variograms for all the APS maps derived using the dataset in Table 3. (Blue line) mean of all the previous variograms. (Red dashed line) reference power law with $\mathsf{\rho}=2/3$ and C selected as a best fitting value. (Pink dashed line) reference power law with $\mathsf{\rho}=5/3$.

**Figure 14.**(black dashed lines) radially average power spectrum for all the APS maps derived using the dataset in Table 3. (blue line) mean of all the previous spectra. (red dashed line) theoretical spectrum computed with $\mathsf{\alpha}=5/3$.

**Figure 15.**Comparison between Phase Linking and SqueeSAR® derived APS maps. The SqueeSAR® stack is composed by 46 images, while the PL stack is composed by seven images. The color scale is in millimeters (mm): (

**a**) Phase Linking, (

**b**) SqueeSAR, (

**c**) their residual, and (

**d**) The scatterplot (contour version) of the two measurements.

Requirement for High Res NWPMs | Threshold | Breakthrough | Goal |
---|---|---|---|

Temporal Resolution | 6 h | 60 min | 15 min |

Spatial Resolution | 20 km | 5 km | 0.5 km |

Sensor | Mode | $\mathsf{\lambda}$ | Scene Size | ${\mathit{B}}_{\mathit{\epsilon},\perp}$ | $\frac{\mathit{d}{\mathit{B}}_{\mathit{\epsilon},\parallel}}{\mathit{d}\mathit{t}}$ | Error in Range and Azimuth |
---|---|---|---|---|---|---|

Sentinel-1 | IW | 5.6 cm | 250 km × 170 km | 11 cm | 1.1 mm/s | 28 mm |

Date | Temporal Baseline w.r.t. Master (Days) | Temporal Baseline w.r.t. Previous Image (Days) |
---|---|---|

11 April 2017 | 0 | - |

17 April 2017 | 6 | 6 |

23 April 2017 | 12 | 6 |

29 April 2017 | 18 | 6 |

5 May 2017 | 24 | 6 |

11 May 2017 | 30 | 6 |

23 May 2017 | 42 | 12 |

Date | Temporal Baseline w.r.t. Master (Days) | Temporal Baseline w.r.t. Previous Image (Days) | Standard Deviation (mm) |
---|---|---|---|

11 April 2017 (master) | 0 | - | - |

17 April 2017 | 6 | 6 | 2.25 |

23 April 2017 | 12 | 6 | 2.32 |

29 April 2017 | 18 | 6 | 2.08 |

5 May 2017 | 24 | 6 | 2.35 |

11 May 2017 | 30 | 6 | 2.75 |

23 May 2017 | 42 | 12 | 2.81 |

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**MDPI and ACS Style**

Manzoni, M.; Monti-Guarnieri, A.V.; Realini, E.; Venuti, G.
Joint Exploitation of SAR and GNSS for Atmospheric Phase Screens Retrieval Aimed at Numerical Weather Prediction Model Ingestion. *Remote Sens.* **2020**, *12*, 654.
https://doi.org/10.3390/rs12040654

**AMA Style**

Manzoni M, Monti-Guarnieri AV, Realini E, Venuti G.
Joint Exploitation of SAR and GNSS for Atmospheric Phase Screens Retrieval Aimed at Numerical Weather Prediction Model Ingestion. *Remote Sensing*. 2020; 12(4):654.
https://doi.org/10.3390/rs12040654

**Chicago/Turabian Style**

Manzoni, Marco, Andrea Virgilio Monti-Guarnieri, Eugenio Realini, and Giovanna Venuti.
2020. "Joint Exploitation of SAR and GNSS for Atmospheric Phase Screens Retrieval Aimed at Numerical Weather Prediction Model Ingestion" *Remote Sensing* 12, no. 4: 654.
https://doi.org/10.3390/rs12040654