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 **Section 1**
 **Persistent Scatterers Study of Deformation Leading up to the 2004 Eruption of Mount St Helens**
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 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.
+**Investigation of the Effects of Atmospheric Variability on StaMPS InSAR at Mount St Helens**
+**Introduction**
+The contribution of changes in the properties of the atmosphere, specifically the troposphere, to Interferometric phase is a substantial obstacle to InSAR studies in many places around the world. The effect of atmospheric phase delay is manifested over a large range of spatial wavelengths and can produce signal of up to tens of centimeters in interferograms (Jolivet et al. 2011). Studying volcanoes with InSAR can be particularly challenging, as both atmospheric effects and surface deformation often correlate with topography and act over similar length scales. In light of these relationships, stacking and the persistent scatterer method StaMPS attempt to remove the contribution of the atmosphere based on the assumption that its changes are not correlated with time, either through temporal averaging or filtering. This assumption may not be sound however, because it has been shown that large portions of the atmosphere are temporally correlated and have distinct seasonal trends (Jung et al. 2014).
+In order to more confidently interpret the results of StaMPS processing at Mount St Helens and differentiate between potential deformation and atmospheric effects, I have begun to evaluate the effectiveness of the algorithm for removing atmospheric effects. This has been accomplished by calculating maps of atmospheric phase delay from remote sensing data. I have also started to investigate the spatial and temporal trends in atmospheric phase lag in both a quantitative and qualitative sense.
+**Dataset Description**
+The remote sensing atmospheric data used in this study comes from the Moderate Resolution Imaging Spectroradiometer instrument carried by NASA’s Terra and Aqua satellites. A set of 13 MODIS acquisitions spread over the year 2013 were selected to maximize the data coverage and resolution over Mount St Helens. Profiles of various atmospheric properties, including pressure, temperature, and water vapor mixing ratio are collected at roughly five kilometer spacing in a grid-like fashion.  Vertical profiles are sampled at between ten and twenty pressure levels within the atmosphere. 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).
+**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 ##. 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 ##.
+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.
+**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. 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).
+**Discussion and Conclusions**
+While this study looks at only a single StaMPS like result, derived from 13 MODIS scenes spanning one year,  it seems to be a weak  assumption that the effects of the atmosphere are temporally uncorrelated and can be removed by temporal filtering of a time series. For StaMPS studies containing a number of scenes comparable to the 13 in this work, it is likely that an effective low-pass filter in time will find some sort of trend which is manifested as a velocity in a time series. It is also possible that the temporal filter could amplify any apparent average velocity signal by removing the high frequency noise.
+With so few atmospheric acquisition dates, it is difficult at this time to make conclusions about spatial and temporal patterns of atmosphere around Mount St Helens. At a minimum, it can be concluded that due to the magnitude of phase shifts caused by atmospheric variations, care should be taken when interpreting the results of single interferograms and even StaMPS results. Additionally, with a low number of SAR scenes, the effectiveness of temporally filtering time-series to remove the atmospheric noise may be insufficient.
+**Future Work**
+In the future, much more MODIS data should be analyzed in order to look for seasonal and spatial patterns in phase lag near Mount St Helens. Additional StaMPS-like runs on atmospheric data spanning shorter or longer time intervals than one year, or containing fewer or many more acquisitions could be performed to quantify the ranges of time intervals and number of scenes over which atmospheric changes are handled effectively.

mark/main.txt · Last modified: 2014/12/10 13:05 by mdw12

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