J. Foster, 1 B. Brooks, 1 T. Cherubini, 1 C. Shacat, 1 S. Businger, 1 and C. L. Werner Introduction

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1 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 33,, doi: /2006gl026781, 2006 Mitigating atmospheric noise for InSAR using a high resolution weather model J. Foster, 1 B. Brooks, 1 T. Cherubini, 1 C. Shacat, 1 S. Businger, 1 and C. L. Werner 2 Received 3 May 2006; revised 10 July 2006; accepted 12 July 2006; published 17 August [1] A high resolution weather model is used to predict atmospheric delays for the acquisition times of synthetic aperture radar images over Hawaii. Refraction of the radar by water vapor in the atmosphere in Hawaii leads to apparent ground-motions with wavelengths and magnitudes similar to the actual ground motions generated by tectonic and volcanic processes. We examine the potential for a weather model to help characterize the atmospheric component in InSAR scenes and find that in the best cases it models the observed delays well, reducing the variance at wavelengths of 30 km and greater by 60%, while even in the worst cases it provides an independent means of quantifying the expected variance in the image due to the atmosphere. Citation: Foster, J., B. Brooks, T. Cherubini, C. Shacat, S. Businger, and C. Werner (2006), Mitigating atmospheric noise for InSAR using a high resolution weather model, Geophys. Res. Lett., 33,, doi: / 2006GL Introduction [2] The biggest source of noise for the interferometric synthetic aperture radar (InSAR) technique is the differential delay caused by changes in the distribution of water vapor in the atmosphere [e.g., Hanssen, 1998]. The radar signal is refracted by the atmosphere, and an increase in the amount of atmospheric water vapor between the acquisition times appears as an apparent increase in the distance to the ground surface, indistinguishable from real ground motion. Atmospheric effects can range over all wavelengths, with amplitudes of up to several centimeters or even greater, leading to inevitable difficulties in identifying and interpreting deformation events captured with InSAR. The problem is particularly acute for the Island of Hawaii, with its moist, heterogeneous tropical atmosphere, and a strong, highly variable interaction between winds and the huge (4000 m high) volcanoes that form the island. As a consequence, although the two active volcanoes, Kilauea and Mauna Loa, are rich sources of deformation signals from the interplay of volcanic and tectonic forces, these signals are typically difficult to isolate in single InSAR differential pairs [Rosen et al., 1996]. The moisture gradient is illustrated in Figure 1 where the color pattern roughly follows the contours of the topography of Mauna Loa, and to a lesser extent, of Mauna Kea and Hualalai. The correlation of the signal with the topography and the absence of any measurable deformation with GPS for Mauna Kea and the distal regions of Mauna Loa [Miklius et al., 2005] confirm that the pattern is an atmospheric artifact that makes it difficult to resolve the ground motion signal due to inflation under Mauna Loa s summit. [3] Traditional efforts to mitigate atmospheric effects have used a large number of SAR scenes to generate an averaged image [e.g., Sandwell and Price, 1998; Sandwell and Sichoix, 2000]. If the atmospheric components are roughly random in time then they will be reduced, while persistent deformation will be retained. Alternatively, the persistent scatterers technique (PSInSAR) [Ferretti et al., 2001, 2004; Werner et al., 2003a, 2003b; Hooper et al., 2004] estimates the atmospheric component of the phase delay through a series of images based on the residuals after low-pass time-domain filtering. Although both these approaches have demonstrated their practical utility, they require larger data sets (>10 20 scenes) that may not be available for a given geographic region and time of interest. An atmospheric mitigation technique that could be applied on a scene-to-scene basis would be highly desirable. [4] Attempts have been made to model the atmosphere in InSAR images based on concurrent observations [e.g., Webley et al., 2002], however in general any ground-based network of instruments will offer poor spatial resolution, and space based instruments [e.g., Li et al., 2005] are typically limited to daylight hours or by sparse repeat times. To increase the signal to noise ratio for InSAR over short time spans and wavelengths so that events can be more accurately modeled and interpreted it is necessary to adopt a more sophisticated approach to deal with the atmospheric component. In support of the astronomical facility on Mauna Kea, the Mauna Kea Weather Center runs a highresolution weather model, the MM5 [Grell et al., 1995], that allows us to get very high (3 km) resolution estimates of the atmospheric delays for the acquisition time for each scene of an InSAR pair [Wadge et al., 2002; Webley et al., 2004]. The ideal approach would use a weather model to perform a meteorological analysis of the atmosphere for the exact time of the SAR acquisitions [e.g., Barnes, 1964; McGinley, 1989]. Here we take a step in that direction by using the short-term predictions of the MM5 to calculate the predicted atmospheric delay. The predicted delays can be used to generate a synthetic interferogram that can be compared with the observed interferogram and subtracted from it, reducing the atmospheric noise and improving our ability to identify and resolve the geodetic signals. 1 School of Ocean and Earth Science and Technology, University of Hawaii at Manoa, Honolulu, Hawaii, USA. 2 GAMMA Remote Sensing AG, Gümligen, Switzerland. Copyright 2006 by the American Geophysical Union /06/2006GL026781$ Data and Processing 2.1. MM5 Weather Model [5] The MM5 (NCAR-Penn State Mesoscale Model Version 5) [Grell et al., 1995] is run twice daily for the 1of5

2 island of Hawaii by the Mauna Kea Weather Center [Businger et al., 2001; Cherubini et al., 2006, mkwc.ifa.hawaii.edu] in support of Mauna Kea s astronomical observatories. The MM5 process has a 60-hour forecast window and the forecast fields are output in 1-hour increments. A high-resolution analysis [McGinley, 1989; McGinley et al., 1991] that incorporates operational weather observations and satellite data from the University of Wisconsin, provides the initial conditions for MM5 [Cherubini et al., 2006]. In turn, MM5 produces predictions of thermodynamic properties of the atmosphere, including temperature, pressure, and moisture fields at a 3 km horizontal resolution. The vertical resolution is density weighted with the greatest vertical resolution (10s of meters) near the surface. For any radar image acquisition there is a high-resolution 3D simulation of refractivity valid within 0.5 hours of the acquisition time and predicted forward no more than 12 hours from the initial observations. The pressure, temperature and water vapor fields are used to predict the refractive delay of the radar [e.g., Bevis et al., 1992]. The incidence angle is small (23 ) relative to the 3 km grid, so rather than tracing ray paths through the 3D model the delay is vertically integrated and mapped to the incidence angle with a cos 1 a function InSAR [6] Differential interferograms were formed from Envisat ASAR acquisitions using the USGS 1 arc second SRTM data as a prior DEM, precise orbits from ESA and a generally standard processing approach with the GAMMA software [Werner et al., 2000]. We note specifically, however, that because baseline errors may cause phase anomalies with wavelengths similar to those from atmospheric effects, we refine baselines by minimizing, in a least squares sense, the residuals between the observed phases and a model that is linearly dependent on distance. A total of 44 interferograms were formed from 10 acquisition dates for which MM5 predictions were available. All scenes are from the descending path. The perpendicular baselines for these pairs range between 10 and 880 meters. Finally, to compare the InSAR directly with the relatively coarse predictions from the MM5, we filtered and sub-sampled the 20 m posting InSAR data down to a 3 km spacing. Figure 1. Differential interferogram for 27 Jan 2003 to 12 Jan 2004 from Envisat ASAR. Radar look direction is indicated by white arrow and has a 23 incidence angle. Color represents the line of sight differential range change. ML, Mauna Loa; MK, Mauna Kea; HU, Hualalai; KI, Kilauea; SWRZ; Mauna Loa South West Rift Zone. Current GPS sites are shown as white dots. 3. Results [7] In Figure 2 we present 3 interferograms for pairs of dates between 2003 and 2005, selected both to illustrate the variety of features commonly observed in InSAR data for Hawaii, and as representative of the performance of the MM5. The interferogram formed from acquisitions on 29 Sep 2003 and 03 Nov 2003 (Figure 2a) provides a typical example of the impact of the island orography on the atmosphere. The short period between the acquisitions precludes significant deformation for Mauna Loa, so the signal can be reasonably interpreted as purely due to the atmosphere. The primary visible features are the phase residuals located over, or near, the summits of the two highest volcanoes, Mauna Kea and Mauna Loa. These relative highs correspond very well with the anomalies predicted by the MM5 (Figure 2b), both in location as well as in many of the details of the contour shapes; the straight contours on the north-east flank of Mauna Loa and the bifurcation along its middle south-west rift zone match well. Similarly the shape of the high predicted over Mauna Kea matches the observed anomaly. These residual highs over the summits are probably caused by a drop in the height of the inversion layer, which caps the surface layer of moist warm air. Other features that can be matched between the InSAR image and the MM5 are the ridge of relatively high differential delays located over Hualalai and the low located to the north of this. The MM5 predicts a more pronounced high, and the low is located slightly south of the corresponding feature in the InSAR however the degree of correspondence is encouraging. The MM5 corrected interferogram (Figure 2c) reflects this correspondence, with the highs associated with the peaks almost entirely eliminated. Most of the lows in the InSAR have also been corrected, though the effect of the slight southerly mislocation of the MM5 predicted low to the north of Hualalai can be seen as a residual high. The MM5 has also slightly overpredicted the amplitude of the low in the saddle between Kilauea and Mauna Loa producing a band of high relative delay. [8] A second pair for 27 Jan 2003 and 12 Jan 2004 (Figures 2d 2f) spans almost exactly one year and deformation of the summit area of Mauna Loa is now significant, with vertical motions of up to 2 cm/yr and horizontal opening of 5 cm/yr across the summit measured by GPS [Miklius et al., 2005]. The atmospheric influence for these acquisitions is lower amplitude, but shows a similar pattern to Figure 2a, although in this case the summits appear as relative lows suggesting a relative increase in high altitude 2of5

3 FOSTER ET AL.: WEATHER MODEL FOR INSAR Figure 2. 3 km subsampled interferogram, MM5 predicted atmospheric delays and MM5 corrected interferogram for 3 date-pairs: (a c) 29 Sep 2003 to 03 Nov 2003, (d f) 27 Jan 2003 to 12 Jan Arrow in Figure 2f indicates signal due to inflation. (g i) 21 Jul 2003 to 26 Apr Color scale is identical for all panels and is shown in units of mm in Figure 2c. Box in Figure 2e is area of focus for Figure 4. Principal surface features are shown in black, and 500 m topographic contours in gray. water vapor for the second date. Once again the patterns of the anomalies over and around the summits show good correspondence between the InSAR image and the model (Figure 2e). The signal associated with Mauna Loa s summit is likely related to recent re-inflation detected with GPS [Miklius and Cervelli, 2003]. In order, however, to relate unambiguously this signal to some geophysical model of magmatic process such as deeper dike opening [i.e., Yun et al., 2005], the atmospheric component needs to be removed. The prominent positive anomaly visible along the southeastern coast is probably predominantly atmospheric in nature and illustrates clearly the difficulty of separating atmospheric artifacts from actual ground motion in Hawaii. Although the south flank of Kilauea does move rapidly seaward [Miklius et al., 2005], the pattern of observed motions does not match the feature in the interferogram. The MM5, however, is unable to reproduce this feature, perhaps due to a mismodeling of the time of the event, or because the physics and parameterization of the MM5 reduce its ability to accurately model the atmosphere in areas with steep slopes such as this location. [9] A more complicated atmospheric contribution is illustrated in Figures 2g 2i for 21 Jul 2003 and 26 Apr Although there are still anomalies associated with the major peaks, these are no longer so dominant, and are not so closely correlated with the topography. An arcuate front between Mauna Kea and Mauna Loa is striking in the InSAR image but is not reproduced by the MM5. Once again the MM5 predicts the shapes of the anomalies over the summits well, and the lows that extend along the southeast flank of Mauna Loa and over Kilauea are also closely matched as are the highs extending to the north-west from the summit of Mauna Loa, and the high along the west coast. The western and eastern most portions of the area are poorly matched however, introducing large amplitude artifacts and a gradient into the differenced image. It appears that the MM5 is predicting a relatively moist atmosphere on the windward (east) side of the island and dry on the leeward side for the 26 Apr 2004 acquisition, probably due to a subtropical low that was present to the northeast of the island. The weather was particularly unstable due to this 3 of 5

4 Figure 3. Spectra of variances for InSAR and MM5 data for the 3 date-pairs in Figure 2. InSAR = solid black, MM5 = solid gray. MM5 corrected InSAR = dashed gray. (a) 29 Sep 2003 to 03 Nov 2003, (b) 27 Jan 2003 to 12 Jan 2004, (c) 21 Jul 2003 to 26 Apr low, making prediction, particularly the timing of events, difficult. [10] To more quantitatively examine the effect of subtracting the MM5 predictions from the InSAR we plot in Figure 3 the variance spectra for each of the 3 pairs examined above. We use the discrete cosine transform [Denis et al., 2002] as it avoids some of the problems with periodicity and trends suffered by the traditional Fourier transform. The MM5 shows similar variances at all wavelengths as the InSAR, except perhaps at the longest wavelength. This is probably specific to the dates shown here, where the MM5 is clearly predicting a much larger gradient in delays from east to west across the island (Figures 2e and 2h) than the InSAR observes. Discrepancies for long wavelengths may be at least partly a consequence of the baseline adjustment procedure in the InSAR processing. Note that, as the MM5 output is on a 3 km grid, wavelengths shorter than 6 km cannot be modeled. The good correspondence visually between the MM5 and InSAR for the 29 Sep 2003 and 03 Nov 2003 pair (Figures 2a 2c) is confirmed (Figure 3a) by a significant reduction in variance at most wavelengths: for wavelengths of 30 km and greater the variance is reduced on average by 60%. The variance for the second pair shows a small improvement at most wavelengths, while the result for the final pair is more ambivalent, with no obvious reduction in variance and a significant increase for the longest wavelength. The variance for the longer wavelengths in the InSAR is notably lower for this final pair than the previous two. This suggests that for this scene the differential delays are less dominated by the interplay between the island topography and a simple (but changing) vertical layering. The finer scale meteorology illustrated here is far more difficult to predict accurately, both temporally and spatially, as small changes in the initial conditions will have large impacts on the timing, location and amplitude of these kinds of features. Nevertheless, although simply removing the predicted delays does not lead to a quantitative improvement in this case, the variance spectra of the predicted delays is very similar to the InSAR variance spectra, suggesting that useful statistical constraints could be derived from the MM5 predictions and applied as a weighting factor, for example, with a stacking approach or simply as an aid in assessing the likely magnitudes and scales of atmospheric artifacts in a given differential scene. [11] Focusing more directly on Mauna Loa, which is an area of great current interest as recent its inflation suggests it is building toward an eruption, Figure 4 shows the variance spectrum for all the MM5-corrected interferograms for the Mauna Loa area. This suggests that the MM5 predictions are significantly reducing the power in longer (30 km and greater) wavelengths, or alternatively that it is reducing the power related to height differences. Power at the shorter wavelengths is not generally reduced, and it is clear that the MM5 is not predicting sufficient variation at these wavelengths. However, accounting for a large proportion of the longer wavelength, elevation dependent component of the Figure 4. Spectrum of variances for InSAR and MM5 data for all (44) date-pairs with both SAR and MM5 data for Mauna Loa only (box location indicated in Figure 2). Details as Figure 3. 4of5

5 InSAR signal should help significantly in the separation of the local inflation signal from the regional field. 4. Conclusions [12] Synthetic interferograms generated from MM5 models show promise as an independent means of predicting the atmospheric component in InSAR images and assisting in identifying the component due to actual ground motion. The association, but only loose correlation, of atmospheric anomalies predicted by the MM5 synthetic interferograms with the summits of the volcanoes illustrates the difficulties in unambiguously resolving volcanic deformation in InSAR data from Hawaii, and this is likely to be the case for other volcanoes or areas with strong topographic relief around the world, particularly those in moist, tropical and subtropical latitudes. [13] Even in those cases where the MM5 predicted delays do not significantly reduce the variance of the InSAR image, it may be possible to utilize the MM5 to quantify the expected variances and use this as a weighting function during stacking. The delays could also be used to constrain or assess the accuracy of the atmospheric phase screens estimated during PSInSAR analysis. [14] The performance of any weather model is naturally dependent on the initial conditions, the choice of model physics and model resolution etc. The next generation Weather Research and Forecasting model is expected to offer improved predictions over MM5. Including extra data sources, such as additional satellite borne atmosphere measuring instruments, or ground-based instruments like GPS sites to help define the initial state of the atmosphere would also help improve the short-term predictions. A final iteration is envisioned which would use short-term predicted fields as the background for a weather analysis package such as LAPS [Albers, 1995]. All available atmospheric measurements and estimates for the instant of SAR acquisition (e.g., the MERIS instrument on Envisat [Santer et al., 1999]) would then be ingested and used to generate a full 3-D weather analysis for that time rather than a prediction. [15] Acknowledgments. We thank Ramon Hanssen and another reviewer for their valuable comments. This work was supported by the Geophysics and Geochemistry programs of the US National Science Foundation. References Albers, S. (1995), The LAPS wind analysis, Weather Forecasting, 10, Barnes, S. L. (1964), A technique for maximizing details in numerical weather map analysis, J. Appl. Meteorol., 3, Bevis, M., S. Businger, T. A. Herring, C. Rocken, R. A. Anthes, and R. H. Ware (1992), GPS meteorology: Remote sensing of atmospheric water vapor using the Global Positioning System, J. 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Wiesmann (2003a), Interferometric point target analysis for deformation mapping, paper presented at International Geoscience and Remote Sensing Symposium, Inst. of Electr. and Electron. Eng., Toulouse, France. Werner, C., U. Wegmüller, A. Wiesmann, and T. Strozzi (2003b), Interferometric point target analysis with JERS-1 L-band SAR data, paper presented at International Geoscience and Remote Sensing Symposium, Inst. of Electr. and Electron. Eng., Toulouse, France. Yun, S., F. Amelung, A. Miklius, T. Walter, and P. Segall (2005), Magma chamber geometry at Mauna Loa Volcano from InSAR and GPS , Eos Trans AGU, 86(52), Fall Meet. Suppl., Abstract G52A-07. B. Brooks, S. Businger, T. Cherubini, J. Foster, and C. Shacat, School of Ocean and Earth Science and Technology, 1680 East West Road, University of Hawaii at Manoa, Honolulu, HI 96822, USA. (jfoster@soest.hawaii.edu) C. Werner, GAMMA Remote Sensing AG, Gümligen CH-3073, Switzerland. 5of5