# Assessment of Mitigation Strategies for Tropospheric Phase Contributions to InSAR Time-Series Datasets over Two Nicaraguan Volcanoes

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. InSAR Time-Series Analysis

_{N}and U

_{E}are the north-south and east-west horizontal components, and U

_{Z,}the vertical component of the ground displacement field, respectively. $\varnothing $ is the azimuth of the satellite heading vector (positive clockwise from North), and $\theta $ is the incidence angle of the satellite.

#### 2.2. Linear Stratified Correction

#### 2.3. Global Weather Models (GWMs)

^{2}s

^{−2}) defined at 29 pressure levels (1000–100 hPa).

_{0}) and at reference height (z

_{ref}), T is the temperature, ${P}_{{H}_{2}O}$ is the partial pressure of water vapor, and g

_{0}is the gravitational acceleration at ground level. ${k}_{1},{k}_{2},{k}_{3}$ represent laboratory-derived atmospheric refractivity constants (see Table 2) [73]. A reference height of 15 km was chosen for both ERA5 and NARR as the changes in water vapor above this height are assumed to be negligible [12,21]. Constants ${R}_{d}$ and R

_{v}are the specific gas constants for dry air and water vapor respectively (see Table 2). A TanDEM-X digital elevation model with a resolution of 12 m was used to horizontally interpolate the slant total delay vertical profiles from the original spatial resolutions as given in Table 1. This procedure allows the final delay maps to extract the vertically integrated atmospheric properties for each pixel elevation at the spatial resolution of the digital elevation model [29]. Each slant total delay map was then downsampled to 90 m and re-referenced to the same location as the uncorrected interferogram datasets. The resulting 2D tropospheric total delay map is in centimeters and corresponds to each satellite acquisition date.

#### 2.4. Statistical Assessments

^{2}) greater than 0.1 (equivalent to a correlation coefficient of ~0.3) suggests that there are stratified tropospheric components present within the scene [33,34,45]. Overlaying the phase-elevation for the tropospheric total delay maps against its respective uncorrected interferogram gives an indication of whether or not the total delay map is capturing LOS phase due to tropospheric phase delays within an uncorrected interferogram [33]. We computed R

^{2}for each uncorrected interferogram and associated total phase delay maps for each tropospheric phase delay method. In addition, we also visually assessed the phase-elevation relationships of the full CSK scenes between the uncorrected interferograms and the total delay maps for each tropospheric phase delay method for all case study interferograms in terms of the trend in the plot (i.e., the slope) and the spread in the LOS phase.

## 3. Case Studies

#### 3.1. Telica Volcano

#### 3.1.1. Background

#### 3.1.2. Telica InSAR Dataset

#### 3.1.3. Tropospheric Phase Delay Correction Results

#### Phase-Elevation Plots

^{2}$\ge $ 0.1, and 165 interferograms with R

^{2}< 0.1, suggesting that turbulence is playing a dominate role in the tropospheric phase delays within the interferograms. Comparing the phase-elevation plots for all 199 interferograms visually, none of the linear phase delay maps capture the same range in LOS phase as the uncorrected interferograms; however, they demonstrate a similar phase-elevation trend in ~67% of the interferograms. For the trends in the GWM phase-elevation plots for all 199 interferograms, we noted the ranges in elevation for which the GWM phase-elevation plots diverged from that of the uncorrected phase-elevation plots. An example of this concept can be seen in Figure 2m, where the GACOS phase-elevation plot diverges from the uncorrected dataset around 350–400 m elevation. Divergences were observed for 37%, 55% and 90% of the phase-elevation plots for ERA5, NARR and GACOS respectively. The majority of the divergences for the ERA5 and NARR plots appeared to fall between 1100–1500 m elevation. While 20% of the diverging GACOS phase-elevation plots also occurred between 1200–1500 m elevation, the majority of the divergences were observed between 500–1000 m. Overall, all of the GWM phase-elevation plots have good agreement (same trend and range in LOS phase) with each other and the uncorrected interferograms in about 18% of the interferograms, and all GWMs had poor agreement (opposite trend and/or poor range in LOS phase) in about 7% of the interferograms (Figure S8a). About 30% of the interferograms show a good correlation between ERA5 and NARR total delay maps with each other and the uncorrected interferograms. ERA5 has the highest overall correlation with the uncorrected interferograms compared to the other GWMs in 15% of the interferograms, followed by NARR only and GACOS only in 6% and 4% of the interferograms respectively.

#### Variance and Variance Reduction

#### Correcting for Stratified and Turbulent Components

^{2}values the linear method reduces the variance (Figure 3b). For the GWMs, correlation is less apparent. The majority of the GWM corrected interferograms (~75%) are centered over the zero-variance reduction line and within the 100% variance increase/reduction bounds. The interferograms outside of these bounds are associated with ERA5 and GACOS corrected interferograms and R

^{2}values less than 0.2, with the exception of two GACOS corrected interferograms.

#### 3.1.4. Time-Series Analysis

^{2}area) (Figure 4a). We first focus on the corrected and uncorrected InSAR time-series results, followed by a comparison with the GPS data from the station TECF.

^{2}to 1.71 cm

^{2}. All remaining tropospheric correction methods increase the variance in the time-series: NARR corrected (2.46 cm

^{2}), linear corrected (2.75 cm

^{2}) and the largest scatter for GACOS corrected (6.20 cm

^{2}).

#### 3.2. Masaya Volcano

#### 3.2.1. Background

_{2}/SO

_{2}ratio ~2 weeks prior to the lava lake appearance, and was interpreted as a pulse of gas-rich magma from depth into the magma plumbing system [94]. Observations of the SO

_{2}flux spanning a 3-year period indicate that the appearance of the lava lake has increased the SO

_{2}degassing flux to >1500 t/d [95]. During the period of interest, only one GPS station within the caldera was operating and taking continuous measurements, beginning in November 2015.

#### 3.2.2. Masaya InSAR Dataset

#### 3.2.3. Tropospheric Phase Delay Correction Results

#### Phase-Elevation Plots

^{2}$\ge $ 0.1, and 201 with R

^{2}$<$ 0.1 (Figure 8b). This suggests that the majority of the CSK scenes used contain turbulent phase delays. Unlike the Telica phase-elevation plots, the Masaya scenes are slightly more complicated in terms of the spread in LOS phase. In some cases, the uncorrected phase-elevation plots appear to have two lobes of LOS phase between 0–300 m elevation (Figure S5). Examination of the associated unwrapped uncorrected interferograms to account for these lobes suggests an apparent ramp in the data, which was only captured in 43%, 19% and 35% of the ERA5, NARR and GACOS phase-elevation plots, respectively. Visual examination of the phase-elevation plots for all 281 corrected interferograms suggest that the GWMs all have good agreement with the uncorrected interferograms for about 27% of the interferograms, and about 17% where all of the GWMs have poor agreement (Figure S8). The linear phase-elevation plots have poor agreement in terms of range in LOS phase compared to the uncorrected interferograms; however, they capture a similar phase-elevation trend in ~70% of the interferograms. Approximately 7% of the phase-elevation plots demonstrate a good agreement of ERA5 and NARR total delay maps with the uncorrected interferograms, and 13% for ERA5 and GACOS total delay maps. GACOS total delay maps appear to have the highest correlation with the uncorrected interferograms compared to ERA5 and NARR in about 16% of the interferograms (Figure S8).

#### Variance and Variance Reduction

^{2}).

#### Correcting for Stratified and Turbulent Components

^{2}< 0.1 (Figure 8b). Plotting these results against the variance reduction after the different tropospheric corrections have been applied, the linear correction shows a clear correlation of increasing variance reduction with increasing R

^{2}values. For the GWM corrected interferograms, there does not appear to be as clear of a trend.

#### 3.2.4. Time-Series Analysis

^{2}area) was selected in Masaya town as the reference region (Figure 9a). For the preferred model time-series location, we averaged an area of 5-by-5 pixels (450-by-450 m

^{2}) centered over the preferred model location. A single coherent pixel closest to the location of MAVC GPS station was selected for the second time-series location.

## 4. Discussion

#### 4.1. Statistical Assessments Results

^{2}values, turbulent phase delays appear to be the dominant atmospheric features within the CSK scenes at both case study regions. From the semivariogram analyses (Figure S7), we observe that at ~10 km lag distance the average variance ranges between 1.5–1.75 cm for both case study sites. Our results are double that observed in theoretical estimates of atmospheric noise over the Mojave desert in California, in which ~0.8 cm variance was observed at 10 km lag distance [96]. Besides the fact that the two case study volcanoes are located in a tropical region with highly spatiotemporal variability in water vapor concentrations, this degree of turbulent noise versus stratified noise is expected, particularly because the full CSK scenes at Telica consists of mainly topographic lows and low gradient changes in elevation at Masaya (Figure 12c,d). In conjunction with the observation that Telica is located near the boundary between a two different tropical climate regions, the local acquisition time of the CSK datasets are also important to keep in mind (17:30 over Telica and 05:30 over Masaya). Acquisitions in the early evening are expected to contain more turbulent phase delays compared to early morning acquisitions due to solar heating of the atmosphere [54], which could potentially explain the difficulty that the tropospheric corrections had in capturing tropospheric phase delays at Telica.

#### 4.2. Time-Series Results (InSAR and GPS)

#### 4.2.1. Telica GPS Results

#### 4.2.2. Masaya GPS Results

#### 4.3. Comparison of Tropospheric Phase Delay Corrections

^{2}values and range in elevation (Figure 3b, Figure 12c and Figure S3), the Telica region contains fairly localized topographic highs, and thus stratified tropospheric phase delay are only captured over a small percentage of our interferograms. While the Masaya region contains more broad phase-elevation gradients (Figure 12d and Figure S3), the linear correction only slightly outperformed at Masaya compared to Telica (Table 3).

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

^{®}Recipes for Earth Sciences” (2015, 4 ed) by Martin H. Trauth. GMT6 was used to produce one figure [98]. Finally, this work was also conducted as part of the “Optimizing satellite resources for the global assessment and mitigation of volcanic hazards” Working Group supported by the John Wesley Powell Center for Analysis and Synthesis, funded by the U.S. Geological Survey. Authors would like to thank Romain Jolivet, Angélique Benoit, Kenneth Davis, Travis Tasker, Chuck Ammon, Raphäel Grandin, Francisco Delgado, Juliet Biggs, Fabien Albino, and Rowena Lohman for their helpful discussions and insight into weather models, time-series analysis and statistical assessment techniques, and Judit Gonzales-Santana and Sam Poppe for proof-reading later drafts of the manuscript. The authors would also like to thank five anonymous reviewers and the editor for their comments and suggestions which have helped to greatly improve this manuscript.

## Conflicts of Interest

## Abbreviations

CAVA | Central American Volcanic Arc |

CSK | COSMO-SkyMed |

ECMWF | European Center for Medium-Range Weather Forecasts |

ERA-I | ERA-Interim |

GACOS | Generic Atmospheric Corrections Online Service for InSAR |

GPS | Global Positioning System |

GWM | Global Weather Model |

HRES ECMWF | High-RESolution European Center for Medium-Range Weather Forecasts |

INETER | Instituto Nicaragüense de Estudios Territoriales |

InSAR | Interferometric Synthetic Aperture Radar |

LOS | Line-Of-Sight |

MERRA | Modern-Era Retrospective Analysis for Research and Applications |

MODIS | Moderate Resolution Imaging Spectroradiometer |

NARR | North American Regional Reanalysis |

NCEP-NCAR | National Centers for Environmental Prediction- National Center for Atmospheric Research |

SAR | Synthetic Aperture Radar |

SBAS | Small BAseline Subset |

UTC | Coordinated Universal Time |

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**Figure 1.**Hillshade topography image obtained using the TanDEM-X digital elevation model of Telica volcano. Orange triangles indicate Holocene volcanoes [82] and nearby towns with populations greater than 10,000 are indicated with green circles [83]. The Pacific coastline is indicated by the blue dashed line. Inset image indicates the location of the descending CSK scene in Nicaragua.

**Figure 2.**Comparison of the different tropospheric phase delay correction methods for Telica unwrapped interferogram 20150217–20150516. (

**a**) Uncorrected interferogram, (

**b**–

**e**) Total tropospheric delay map for each correction method, (

**f**–

**i**) Corrected interferograms using the tropospheric total delay maps in the first row, and (

**j**–

**m**) Phase-elevation plots of the uncorrected interferogram (black dots) versus the total delay map (colored dots). The geographic extent and colorbar scale for all the interferograms and delay maps are the same, as indicated by the original uncorrected interferogram. The colorbar scale for the GACOS resultsis indicated on the GACOS total delay map. The black triangles in the interferograms and maps indicate the location of Telica volcano in the CSK scene, which is masked out for the phase-elevation plots.

**Figure 3.**Variance reduction and R

^{2}results for the 199 Telica descending CSK uncorrected and corrected interferograms. (

**a**) Variance reduction box plots, and (

**b**) R

^{2}derived from uncorrected interferograms phase-elevation plots versus the associated variance reduction results shown in (

**a**).

**Figure 4.**InSAR uncorrected and corrected time-series results for Telica CSK centered over GPS station TECF (199 interferograms made from 50 CSK acquisition dates). (

**a**) Hillshade topography image showing the location of TECF GPS station (red hexagon), the reference region used in the time-series analysis (blue rectangle), and the summit of Telica volcano (orange triangle). (

**b**) InSAR time-series results centered over GPS station TECF. The grey shaded regions in the time-series plots indicate the three phases of explosive activity as defined by Roman et al. [81]. Error bars were not computed for InSAR data as the time-series is plotted for a single pixel.

**Figure 5.**LOS displacement time-series plots of GPS station TECF against (

**a**) InSAR uncorrected, and (

**b**) InSAR uncorrected and corrected time-series at the same location (199 interferograms made from 50 CSK acquisition dates). The three components from the GPS data were converted into the LOS of CSK descending path over Telica volcano (red dots). The InSAR symbols are the same as those used in Figure 4b. Error bars were not computed for InSAR data as the time-series is plotted for a single pixel. The grey shaded regions indicate the three phases of explosive activity observed in 2015 [81]. The blue arrows in (

**a**) indicate visually identified outlier dates in the InSAR uncorrected time-series. The labelled GACOS time-series outlier in (

**b**) as A is discussed further in Section 4.2.

**Figure 6.**Hillshade topography image obtained using the TanDEM-X digital elevation model of CSK ascending scene covering Masaya caldera. Orange triangles indicate Holocene volcanoes [82] and nearby towns with populations greater than 10,000 are indicated with green circles [83]. Bodies of water are indicated in blue writing and dashed lines. Inset image indicates the location of the CSK scene in Nicaragua.

**Figure 7.**Comparison of the different tropospheric phase delay correction methods for Masaya unwrapped interferogram 20160617–20160711. (

**a**) Uncorrected interferogram, (

**b**–

**e**) Total tropospheric delay map for each correction method, (

**f**–

**i**) Corrected interferograms using the tropospheric delay maps from the first row, and (

**j**–

**m**) Phase-elevation plots of the uncorrected interferogram (black dots) versus the total delay map (colored dots). The geographic extent and colorbar scale for all the interferograms and delay maps are the same, as indicated by the original uncorrected interferogram. The black triangles in the interferograms and maps indicate the location of the summit of Masaya in the CSK scene, and the outline of Masaya caldera.

**Figure 8.**Variance reduction and R

^{2}results for the 281 Masaya ascending CSK uncorrected and corrected interferograms. (

**a**) Variance reduction box plots, and (

**b**) R

^{2}derived from uncorrected interferograms phase-elevation plots versus the associated variance reduction results shown in (

**a**).

**Figure 9.**InSAR time-series results for Masaya CSK (281 interferograms made from 60 CSK acquisition dates). (

**a**) Hillshade topography image showing the area selected for the time-series centered over the preferred model spherical source location from Stephens & Wauthier [5] (orange star), the reference region for time-series analysis within Masaya town (blue rectangle), and the location of GPS station MAVC (red hexagon). (

**b**) Time-series plot for the uncorrected and corrected InSAR datasets centered over the preferred model source location. The orange shaded region in the time-series plot indicates the presence of the lava lake in Santiago pit crater. Plotted error bars represent the standard deviation of the selected time-series region.

**Figure 10.**LOS displacement time-series plots of GPS station MAVC against (

**a**) InSAR uncorrected, and (

**b**) InSAR uncorrected and corrected time-series at the same location (281 interferograms made from 60 CSK acquisition dates). The three components from the GPS data were converted into the LOS of CSK ascending path over Masaya caldera (red dots). The InSAR symbols are the same as those used in Figure 11b. Error bars were not computed for InSAR data as the time-series is plotted for a single pixel. The orange shaded region in the time-series plots indicates the presence of the lava lake in Santiago pit crater.

**Figure 11.**Venn diagrams displaying the increase in variance results for the GWM datasets only at Telica (

**a**) and Masaya (

**b**). Within the circles, each number represents the percentage of interferograms for which the GWM increased the variance in the corrected interferogram. The numbers outside the circles represent the percentage of interferograms for which all GWMs demonstrated a reduction in the variance for a single interferogram. The converse of these Venn diagrams (variance reduction) are given in Figure S9.

**Figure 12.**Vertical pressure levels resolution of GWMs in relation to elevation within the CSK scenes over both Telica and Masaya. (

**a**) GWMs vertical pressure levels in kilometers altitude and associated temporal resolutions, the black dashed box indicates the zoomed in area in panel (

**b**), (

**b**) zoomed area of panel (

**a**) that encompasses the maximum elevation of both CSK scenes, with the shaded regions indicating the elevation range specifically over Telica (orange) and Masaya (blue). The symbols indicate the elevation of GPS station TECF (green hexagon), MAVC station (red hexagon), and the preferred model center of displacement at Masaya (orange star). (

**c**) Histogram plot of the range of pixel elevations within the Telica CSK full scene (black) and scene cropped to Telica edifice (orange), with the elevation of TECF station indicated (green hexagon). (

**d**) Histogram plot of the range of pixel elevations within the Masaya CSK full scene (black) and scene cropped to Masaya caldera (blue), with the elevation of MAVC station (green hexagon) and preferred model center of displacement (orange star) indicated. The blue vertical lines in the histogram plots indicate the ERA5 and NARR coinciding vertical pressure levels as seen in panel (

**b**).

GWMs | Spatial Resolution | Temporal Resolution | Vertical Resolution |
---|---|---|---|

NARR | 0.3° × 0.3° (32 km) | 3 h (00, 03, 06, 09, 12, 15, 18, 21) | 29 levels (1000–100 hPa) |

ERA5 | 0.281° × 0.281° (30 km) | Hourly | 37 levels (1000–1 hPa) |

HRES ECMWF (GACOS) | 0.125° × 0.125° (14 km) | 6 h (00, 06, 12, 18) | 137 levels (1000–0.01 hPa) |

Variable | Values |
---|---|

k_{1} | 0.776 K.Pa^{−1} |

k_{2} | 0.716 K.Pa^{−1} |

k_{3} | 3750 K^{2}.Pa^{−1} |

R_{d} | 287.05 J.kg^{−1}.K^{−1} |

R_{v} | 461.495 J.kg^{−1}.K^{−1} |

**Table 3.**Statistical analyses of uncorrected and corrected interferograms for both Telica and Masaya CSK datasets. For each volcano, the average variance (in cm

^{2}) and variance reduction (%) for all interferograms are indicated in bold. The values given in brackets indicate the minimum and maximum range for the variance and variance reduction. The range in variance reduction values are also shown in Figure 3 and Figure 8.

Correction Method | Telica | Masaya | ||
---|---|---|---|---|

Var (cm^{2}) | Var Red (%) | Var (cm^{2}) | Var Red (%) | |

Uncorrected | 5.44(0.60, 43.94) | – | 5.69(0.71, 47.55) | – |

Linear | 5.23(0.55, 43.51) | 5.97(–0.33, 65.40) | 5.43(0.49, 47.44) | 6.65(–3.21, 42.47) |

ERA5 | 5.55(0.65, 44.21) | –17.58(–353.73, 64.19) | 6.36(4.46, 64.40) | –20.94(–675.48, 70.12) |

NARR | 5.54(0.79, 46.32) | −11.63(–197.08, 51.80) | 6.68(0.56, 62.82) | –24.56(–364.80, 58.07) |

GACOS | 6.58(0.74, 54.89) | –53.61(–863.31, 78.30) | 5.92(0.64, 50.90) | –20.37(–286.53, 83.32) |

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## Share and Cite

**MDPI and ACS Style**

Stephens, K.J.; Wauthier, C.; Bussard, R.C.; Higgins, M.; LaFemina, P.C.
Assessment of Mitigation Strategies for Tropospheric Phase Contributions to InSAR Time-Series Datasets over Two Nicaraguan Volcanoes. *Remote Sens.* **2020**, *12*, 782.
https://doi.org/10.3390/rs12050782

**AMA Style**

Stephens KJ, Wauthier C, Bussard RC, Higgins M, LaFemina PC.
Assessment of Mitigation Strategies for Tropospheric Phase Contributions to InSAR Time-Series Datasets over Two Nicaraguan Volcanoes. *Remote Sensing*. 2020; 12(5):782.
https://doi.org/10.3390/rs12050782

**Chicago/Turabian Style**

Stephens, Kirsten J., Christelle Wauthier, Rebecca C. Bussard, Machel Higgins, and Peter C. LaFemina.
2020. "Assessment of Mitigation Strategies for Tropospheric Phase Contributions to InSAR Time-Series Datasets over Two Nicaraguan Volcanoes" *Remote Sensing* 12, no. 5: 782.
https://doi.org/10.3390/rs12050782