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| **Figure 1.** A stack of interferograms made by Poland and Lu (2008) reveals no apparent deformation.\\ Coherence on the edifice and within the crater is limited due to the presence and disturbance caused by snow. | **Figure 1.** A stack of interferograms made by Poland and Lu (2008) reveals no apparent deformation.\\ Coherence on the edifice and within the crater is limited due to the presence and disturbance caused by snow. | ||
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| Because of the wide spatial and temporal spacing, and to a lesser extent, the levels of noise, in data collected by trilateration and GPS, no conclusions could be made about any potential surface deformation that may have occurred locally on the edifice or within the crater of Helens. The ability to produce spatially continuous maps of surface displacements gives InSAR the ability to resolve the question of whether localized deformation may have occurred at Mt St Helens prior to its 2004 eruption. A study conducted by Poland and Lu in 2008 attempted to image both pre and post eruptive deformation at Mount St Helens using interferogram stacking. Because of decorrelation caused by the presence of snow and dense vegetation, even stacks of interferograms were unable to obtain signal within the crater or on the edifice prior to the eruption (Fig 1). While the results prior to the 2004 eruption were inconclusive, post eruptive results successfully imaged subsidence around and on parts of the edifice. | Because of the wide spatial and temporal spacing, and to a lesser extent, the levels of noise, in data collected by trilateration and GPS, no conclusions could be made about any potential surface deformation that may have occurred locally on the edifice or within the crater of Helens. The ability to produce spatially continuous maps of surface displacements gives InSAR the ability to resolve the question of whether localized deformation may have occurred at Mt St Helens prior to its 2004 eruption. A study conducted by Poland and Lu in 2008 attempted to image both pre and post eruptive deformation at Mount St Helens using interferogram stacking. Because of decorrelation caused by the presence of snow and dense vegetation, even stacks of interferograms were unable to obtain signal within the crater or on the edifice prior to the eruption (Fig 1). While the results prior to the 2004 eruption were inconclusive, post eruptive results successfully imaged subsidence around and on parts of the edifice. | ||
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| **Figures 2(a,b)** The map of Washington state on the left shows the location of the SAR scene track 156, frame 2673. StaMPS processing was carried out on a small ~200 square kilometer patch within the frame centered on Mount St. Helens. The table to the right lists the dates of each SAR scene used in StaMPS processing and its perpendicular baseline relative to the master scene. | **Figures 2(a,b)** The map of Washington state on the left shows the location of the SAR scene track 156, frame 2673. StaMPS processing was carried out on a small ~200 square kilometer patch within the frame centered on Mount St. Helens. The table to the right lists the dates of each SAR scene used in StaMPS processing and its perpendicular baseline relative to the master scene. | ||
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| StaMPS processing was run successfully on the pre-eruptive ERS-2 data, yielding a decent density of stable pixels both on the edifice and within the crater. Refined interferograms were created alongside maps of average velocity over the timespan of 1996-2002. An example interferogram and average velocity map overlain on Google Earth imagery are shown below (Figs 3, 4). | StaMPS processing was run successfully on the pre-eruptive ERS-2 data, yielding a decent density of stable pixels both on the edifice and within the crater. Refined interferograms were created alongside maps of average velocity over the timespan of 1996-2002. An example interferogram and average velocity map overlain on Google Earth imagery are shown below (Figs 3, 4). | ||
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| {{:mark:ex_int.jpg}} | {{:mark:ex_int.jpg}} | ||
| - | **Figure 3.** An example interferogram from StaMPS processing, spanning nearly one year from September 1997 to August 1998.\\ A clear relationship between phase or range change and elevation can be seen in this interferogram indicating contribution from\\ the atmosphere. Velocities are in the Line Of Sight with red (positive) moving towards the satellite and blue (negative) moving away from the satellite. | + | **Figure 3.** An example interferogram from StaMPS processing, spanning nearly one year from September 1997 to August 1998.\\ A clear relationship between phase or range change and elevation can be seen in this interferogram indicating contribution from\\ the atmosphere. Displacements are in the Line Of Sight with red (positive) moving towards the satellite and blue (negative) moving\\ away from the satellite. |
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| {{:mark:stamps.jpg}} | {{:mark:stamps.jpg}} | ||
| - | However, there is still much uncertainty about what physical features on the edifice the persistent scatterers correspond to. While it may appear that there is a distinct signal of uplift just off-center of the volcano, there is good reason to believe that the presented results are heavily influenced by atmospheric effects. In several of the interferograms created through StaMPS processing, a strong correlation between phase and elevation was present (Figure ##), indicating influence from atmospheric changes. | + | **Figure 4.** Final StaMPS result showing average velocities over the time period of 1996-2002. Apparent uplift signal just\\ west of the crater is likely an artifact of the atmosphere removal process. Velocities are in the Line Of Sight with red \\ (positive) moving towards the satellite and blue (negative) moving away from the satellite. |
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| + | However, there is still much uncertainty about what physical features on the edifice the persistent scatterers correspond to. While it may appear that there is a distinct signal of uplift just off-center of the volcano, there is good reason to believe that the presented results are heavily influenced by atmospheric effects. In several of the interferograms created through StaMPS processing, a strong correlation between phase and elevation was present (Figure 5), indicating influence from atmospheric changes. | ||
| {{:mark:ph_v_elev.jpg}} | {{:mark:ph_v_elev.jpg}} | ||
| - | In generating the velocity map shown in Figure ##, a tool within StaMPS was used to try and estimate the atmospheric contribution to phase. This tool takes advantage of the fact that the atmospheric contribution to Interferometric phase, is often correlated with terrain elevation. Plots of phase versus elevation are displayed for each interferogram, and the user decides whether and how to fit a line to the data (Figure ##). The linear fit to the data is used to create an atmospheric phase mask which is subtracted from the interferogram after unwrapping phase. In some interferograms, however, the relationship between phase and elevation is less clear (Figure ##), and deciding how or whether to fit a line at all can be subjective, difficult, and substantially impact the final results. | + | **Figures 5 (left) and 6 (right).** On the left is an example plot of unwrapped phase vs elevation for an interferogram heavily influenced by the atmosphere. The red line fit to the data is used to create and remove an atmospheric phase screen. On the right is an example of when fitting a line to the phase-elevation data may be subjective or not fully representative of the atmosphere in the interferogram. |
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| + | In generating the velocity map shown in Figure 4, a tool within StaMPS was used to try and estimate the atmospheric contribution to phase. This tool takes advantage of the fact that the atmospheric contribution to Interferometric phase, is often correlated with terrain elevation. Plots of phase versus elevation are displayed for each interferogram, and the user decides whether and how to fit a line to the data (Figure 5). The linear fit to the data is used to create an atmospheric phase mask which is subtracted from the interferogram after unwrapping phase. In some interferograms, however, the relationship between phase and elevation is less clear (Figure 6), and deciding how or whether to fit a line at all can be subjective, difficult, and substantially impact the final results. | ||
| StaMPS processing of SAR data over Mount St Helens identifies pixels with low phase noise on the edifice and within the crater. This indicates that there is promise for Persistent Scatterers processing techniques like StaMPS to overcome decorrelation due to snow and trees and potentially image pre-2004 eruptive deformation. However, because of the possibility that StaMPS results are heavily influenced by atmospheric changes which are difficult to remove using the phase - elevation correlation alone, more work must be done before real signal can be differentiated from artifacts of the atmosphere removal process. It is this fact which motivates the second part of this study: an investigation of the effects of atmosphere on StaMPS processing at Mount St Helens. | StaMPS processing of SAR data over Mount St Helens identifies pixels with low phase noise on the edifice and within the crater. This indicates that there is promise for Persistent Scatterers processing techniques like StaMPS to overcome decorrelation due to snow and trees and potentially image pre-2004 eruptive deformation. However, because of the possibility that StaMPS results are heavily influenced by atmospheric changes which are difficult to remove using the phase - elevation correlation alone, more work must be done before real signal can be differentiated from artifacts of the atmosphere removal process. It is this fact which motivates the second part of this study: an investigation of the effects of atmosphere on StaMPS processing at Mount St Helens. | ||
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| **Section 2** | **Section 2** | ||
| - | **Investigation of the Effects of Atmospheric Variability on StaMPS InSAR at Mount St Helens** | + | ====== Investigation of the Effects of Atmospheric Variability on StaMPS InSAR at Mount St Helens ====== |
| **Introduction** | **Introduction** | ||
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| {{:mark:profs.jpg}} | {{:mark:profs.jpg}} | ||
| - | The altitude of each pressure level is estimated for each climate data point. Example profiles are shown in figure ##. The Digital Elevation Model (DEM) used is from the NASA’s Shuttle Radar Topography Mission (SRTM). | + | **Figure 7.** Example MODIS profiles of Pressure, Temperature, Water Vapor Pressure, and Refractivity with respect to Altitude are shown.\\ The refractivity is integrated from the DEM height to the top of the profile in the calculation of phase delay. |
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| + | The altitude of each pressure level is estimated for each climate data point. Example profiles are shown in figure 7. The Digital Elevation Model (DEM) used is from the NASA’s Shuttle Radar Topography Mission (SRTM). | ||
| **Methods** | **Methods** | ||
| - | Maps of phase lag for each MODIS acquisition time can be calculated from altitude profiles of pressure, temperature, and water partial pressure (calculated from pressure and water vapor mixing ratio). To calculate phase lag, first a profile of refractivity (N) with respect to height is calculated using Equation ##. | + | Maps of phase lag for each MODIS acquisition time can be calculated from altitude profiles of pressure, temperature, and water partial pressure (calculated from pressure and water vapor mixing ratio). To calculate phase lag, first a profile of refractivity (N) with respect to height is calculated using Equation 1. |
| {{:mark:eqns.jpg}} | {{:mark:eqns.jpg}} | ||
| - | The resulting refractivity profiles are then interpolated to the spacing of the DEM using a distance weighted spatial average. Finally, equation ## is applied to the refractivity profiles, integrating from the DEM height up to an arbitrarily high point, above which there is little atmospheric contribution to phase lag (Jung et al. 2014). An example map of phase lag over Mount St Helens is shown in Figure ##. | + | **Equations 1 and 2.** |
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| + | The resulting refractivity profiles are then interpolated to the spacing of the DEM using a distance weighted spatial average. Finally, equation 2 is applied to the refractivity profiles, integrating from the DEM height up to an arbitrarily high point, above which there is little atmospheric contribution to phase lag (Jung et al. 2014). An example map of phase lag over Mount St Helens is shown in Figure 8. | ||
| {{:mark:lag.jpg}} | {{:mark:lag.jpg}} | ||
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| + | **Figure 8.** Example map of atmospheric phase delay calculated on a DEM grid covering the Mount St Helens Region. Black Dots spaced at 5km show the locations of the MODIS data points. Mount St Helens is seen as a Blue crescent in the middle of the scene. Red portions of the map experience more delay because they are at lower elevations and the radar will have more atmosphere to pass through. | ||
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| Atmospheric Phase Screens (APS) depict the difference in phase lag from one time to another and represent the atmospheric component that would be seen in an interferogram. It is important to note that the magnitude of the phase screen at each pixel is relative like phase in interferograms, and that atmospheric phase screens can be simply calculated by subtracting one phase lag scene from another. In this study, the APS calculated from the MODIS data are treated as interferograms containing no deformation or other source of error. A close approximation to the StaMPS processing chain, is applied to APS calculated from the 13 MODIS scenes spanning 2013 to investigate the algorithm’s effectiveness at mitigating atmospheric effects over Mount St Helens. | Atmospheric Phase Screens (APS) depict the difference in phase lag from one time to another and represent the atmospheric component that would be seen in an interferogram. It is important to note that the magnitude of the phase screen at each pixel is relative like phase in interferograms, and that atmospheric phase screens can be simply calculated by subtracting one phase lag scene from another. In this study, the APS calculated from the MODIS data are treated as interferograms containing no deformation or other source of error. A close approximation to the StaMPS processing chain, is applied to APS calculated from the 13 MODIS scenes spanning 2013 to investigate the algorithm’s effectiveness at mitigating atmospheric effects over Mount St Helens. | ||
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| **Results** | **Results** | ||
| - | Maps of atmospheric phase lag like the one shown in Figure ## are all tightly correlated with topography due to its control of the lower bound of integration in Equation ## and their magnitudes which are on the order of two meters can vary amounts up 20 cm. | + | Maps of atmospheric phase lag like the one shown in Figure 8 are all tightly correlated with topography due to its control of the lower bound of integration in Equation 2 and their magnitudes which are on the order of two meters can vary amounts up 20 cm. |
| {{:mark:aps.jpg}} | {{:mark:aps.jpg}} | ||
| - | This effect can be clearly seen in an example of APS (Figure ##), where differences in delay of up to 12cm can exist across a scene, arising from differential changes in the water vapor content of the air. Figure ## shows the map of average apparent velocities that would result from the application of a StaMPS-like algorithm to a series of 12 APS made from 13 maps of atmospheric delay. Differences in velocity on the order of 2 cm/yr are seen over short length scales (~5km), smaller than the StaMPS scene over St Helens (Pictured). | + | **Figure 9.** Example of an atmospheric phase screen calculated by subtracting the phase screen for May 1 from Jan 1. In this example, there is a positive (red) delay sitting over Mount St Helens, indicating that more water vapor was likely in the air over Helens on Jan 1 than May 1. Black Dots spaced at 5km show the locations of the MODIS data points. Mount St Helens is centered in the scene. |
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| + | This effect can be clearly seen in an example of APS (Figure 9), where differences in delay of up to 12cm can exist across a scene, arising from differential changes in the water vapor content of the air. Figure 10 shows the map of average apparent velocities that would result from the application of a StaMPS-like algorithm to a series of 12 APS made from 13 maps of atmospheric delay. Differences in velocity on the order of 2 cm/yr are seen over short length scales (~5km), smaller than the StaMPS scene over St Helens (Pictured). | ||
| {{:mark:av_vel.jpg}} | {{:mark:av_vel.jpg}} | ||
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| + | **Figure 10.** The end result of a StaMPS like algorithm applied to a series of atmospheric phase screens. Gradients in velocity vary across the scene, but are on the order of 2 cm/yr over a 5km distance at Mount St Helens (Red Circle). It is clear from this figure that the applied temporal filtering does not remove all of the atmospheric signal. | ||
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| **Discussion and Conclusions** | **Discussion and Conclusions** | ||
