CORRECTING INSAR DATA FOR TROPOSPHERIC PATH EFFECTS OVER VOLCANOESUSING DYNAMIC ATMOSPHERIC MODELS

G. Wadge(1), P.W. Webley(2) and N.F. Stevens(3)

(1)Environmental Systems Science CentreHarry Pitt Building

3 Earley Gate, University of ReadingReading RG6 6AL, UK

Email:gw@mail.nerc-essc.ac.uk

(2) Department of Geography,Kings College London,

The Strand, London WC2R 2LS, UK

Email:peter.webley@kcl.ac.uk

(3) Institute of Geological and Nuclear SciencesGracefield Research Centre

Gracefield Road,Lower Hutt, New Zealand

Email:n.f.stevens@cri.gns.nz

ABSTRACT

The benefits of applying independent models of atmospheric path effects over volcanoes on differential InSAR-measuredground motion are potentially considerable. The technique that has been developed consists of running a three dimensionalmesoscale atmospheric model at high resolution over the volcano to simulate the state of the atmosphere at the time of radarimage acquisition. The amounts of water vapou and the resultant wave delays can be calculated along the radar lines ofsight. Differencing two models gives the correction field to apply to the interferogram. We illustrate this approach bysimulating the delay fields associated with a tandem ERS pair from 5/6 September 1995. The availability of goodinitialisation data for the models is vital and the quality of the archived data for this purpose is less than ideal. However, thelatest generation of operational mesoscale models promises major improvements in the ability to ingest timely data and torepresent water phase transitions correctly.

1 INTRODUCTION

Radio wave delays caused by temporal and spatial variability of tropospheric water vapour can add considerable noisewithin the technique of repeat-pass radar interferometry (InSAR) [1]. The amount and location of water vapour at lowelevations (first few kilometres above sea level) can change significantly in a matter of hours. A radar interferogram seesthis as a relative change of phase, which without correction can be interpreted as a relative motion of the ground. There arenumerous ways to mitigate the problem, but none of them work well in all circumstances. Table 1 groups the maintechniques into two groups: those dependent on manipulating the SAR data themselves and independent, calibratorytechniques.

Our concern is with the delay effects over mountains, specifically volcanoes that have substantial relief. This environmenthas two characteristics that make a dynamic atmospheric modelling approach particularly relevant. Firstly, there are manyhigh relief volcanoes in the humid tropics where delay effects are strong [2], are poorly monitored (e.g. no cGPS) and have

____________________________________________________________

Proc. of FRINGE 2003 Workshop, Frascati, Italy,1 – 5 December 2003 (ESA SP-550, June 2004) 18_wadge

very small archives of SAR data. Secondly, prevailing winds can produce quasi-permanent spatial asymmetries in watervapour distribution around mountains that would be difficult to distinguish from a ground motion signal in InSAR timeseries data.

Table 1. Characteristics of some techniques to mitigate the effects of tropospheric water vapour on InSAR

SAR-Data Techniques CharacteristicsSignal/noise Ignore problem if signal is large enoughLogical Pairwise combinations discriminates the "problem" image. SubjectiveStacking (1/√no. of interferograms) noise reduction if water vapour noise non-stationary in spaceTime series analysis Can invert for water vapour delay field, assumes spatial non-stationarityIndependent TechniquesRadiometers Doesn’t work at night or through cloudscGPS Good temporal but uneven global spatial coverageAtmospheric modelling: static Applicable to mountains, assumes a static layered atmosphere, meteo. station dataAtmospheric modelling: dynamic Accounts for horizontal gradients. Needs radiosonde or NWP data

2 DYNAMIC ATMOSPHERIC MODEL METHOD

This method calculates the water vapour field over the volcano at the time of radar imaging using forward models of thedynamic flow of the atmosphere over the topography. The model is three dimensional and has a digital representation of thetopography at its base. The intention is to simulate the local flow of the troposphere over and around this topography until astable state is reached and then to calculate the 3D water distribution at that time. The steps in the method can besummarised thus:

1 . Initialise the model using observations (e.g. radiosonde), or other numerical weather prediction model data, oftemperature, wind speeds and specific humidity at the time of the radar imaging.

2. Simulate the dynamic flow until stable.3. Calculate the 3D water vapour field of the stable state.4. Extract the radar line of sight (LOS) radio wave delay field from 3.5. Repeat for the second image, difference the LOS delay fields and apply the correction to the interferogram.

If appropriate initialisation data can be acquired then this technique can be used anywhere and at anytime. The use ofnumerical weather prediction data opens up the potential for an operational application. The main drawbacks are that themodelling is compute intensive, it can be difficult to initialise correctly and also difficult to simulate local convection.

3 APPLICATION OF NH3D TO ETNA

We have performed a number of numerical experiments of the above method applied to the Etna volcano in Sicily using asimulation program called NH3D [3]. Etna is an excellent place to test this approach because it has over 3 km of relief risingfrom sea level. In 2000 we set up a temporary network of 14 continuous GPS receivers over Etna and monitored their watervapour delay estimates for comparison with the a ERS interferograms and NH3D simulations [4], [5] and [6].The NH3D program is a non hydrostatic and non linear representation of the atmosphere and the computational space is anf-plane, three dimensional model. The characteristics of our use of NH3D are shown in Table 2. NH3D treats water vapouras a passive tracer. So the thermo-dynamic effects of phase transitions from vapour to water or ice are not treated explicitly.This is a limitation to the accuracy of the simulations. Another known limitation of our method using NH3D is the use ofinitialisation conditions that may not be appropriate [6].

Table 2. Typical features of the NH3D models used in the Etna study

Model Feature Use in the Etna NH3D modelsSpatial dimensions 110 x 110 x 30Model height (km) 10Horizontal cell size (km) 1.7Co-ordinate system Sigma (terrain-following / normalised pressure), verticalLateral boundary condition Radiative, to minimise wave reflectionsUpper boundary Several "sponge" layers above 10 kmLower boundary GTOPO30 DEM grown into the model space to minimise spurious accelerationsTime stepping (s) 4Simulated flow time (hr) 8Computation time (hr) ~8 (SPARC workstation)

3.1 Initialisation of NH3D

At the start of a model run the cells are populated with one dimensional (vertical) state variable values of temperature, (east-west and north-south) wind vectors and specific humidity. These intitialisation data should come from the upwind directionat the time to be simulated. For Etna we had access to two sources of these initialisation data:

(i) Radiosonde data from Trapani. The prevailing wind direction at Etna is from the west and Trapani is about 250 kmwest of Etna. At average wind velocities the Trapani atmosphere is advected into the location of the Etna modelspace in 2-3 hours. Radiosondes are released every six hours and the data are available from 1990.

(ii) Numerical Weather Prediction (NWP) model data. Since 1990 the operational analysis data fields from theEuropean Centre for Medium Range Weather Forecasting (ECMWF) have been available at six hourly intervals at250 km grid spacing and since 1998 at 120 km grid spacing. Since 1999 the UK Meteorological Office UnifiedModel data have been available every three hours and at 60 km resolution.

If the prevailing wind is not from the west then the use of NWP data is to be preferred. Depending on the situation we haveused azimuthal averages of such data to initialise the models [6]. The other important issue is timing. The "frozenadvection" assumption of the Trapani radiosonde and the coarser NWP model initialisations admits considerable possibleerror. This is particularly critical when a frontal atmospheric system is close [6]. Examination of geostationary weathersatellite imagery and synoptic weather charts helps to identify this problem.

3.2 Example Simulation: 5/6 September 1995

The tandem ERS-1, -2 acquisitions over Etna provide a good indication of the nature of the water-vapour induced delayscreated by day-to-day changes in water vapour content, assuming no ground motion signal over 24 hours (see Plate 11 [7]).Here we simulate the water vapour induced delay difference between the times (about 21:16 UTC) of the two tandem ERSascending pass images acquired on 5 and 6 September 1995. Meteosat images indicate no cloud cover over Sicily on eitherday. The nearest available initialisation data is at 18:00 UTC either from the Trapani radiosonde or the 250 km resolutionECMWF model. Because the wind was from the west on both days we chose the Trapani radiosonde data (Fig.1) toinitialise the models.

The data in Fig.1 are quite similar. The main differences relevant to the NH3D simulations are the slightly higher values ofspecific humidity on the 5th at the lowest altitudes and the divergence with altitude of the N-S wind components on the twodays such that the winds come from the southwest on the fifth yet slightly from the northwest on the next day. Based on ourexperience with other NH3D models and Etna interferograms [5],[6], we would expect the 5th (master) - 6th (slave)

interferogram to have an overall positive phase delay due to the atmosphere and for any spatial variability of the delay fieldto exist mainly over the eastern flanks of the volcano in the lee of the prevailing winds.

Fig.1 Radiosonde data for the lowest 10 km of the troposphere from Trapani in western Sicily at 18:00 UTC on 5 and 6September 1995. The upper left panel is temperature versus height and the lower left is specific humidity. The upper rightpanel is the E-W wind vector (west to east positive) and the lower right panel is the north-south wind vector (south to northpositive).The blue diamond data are from 5 September and the pink square data are from 6 September.

This is largely what we see in the unwrapped interferogram of this tandem pair (21660 - 01987) (Fig.2a). There are positivedelays on most of the lower slopes of the volcano up to a peak to the east and southeast of the summit. There is a negativearea around the summit elongated N-S and a larger negative feature to the northeast . The NH3D delay difference field(Fig.2b) is broadly similar to the interferogram : there is a large positive feature above the eastern / southeastern slopesmatched by a north-south oriented negative feature over the summit. The other main negative feature is also to thenortheast. However there are some obvious differences between the interferogram and the model. The negative/neutral areaof the interferogram around Catania, inland from the southernmost coast, is positive in the model, and the upwind gradienton the western side of Etna is more positive in the interferogram. In addition, the overall range of values in the model isgreater than that seen in the interferogram by a factor of about 1.5. This may be caused by the lack of explicit treatment ofthe water phase transitions. The subtraction of the two fields leaves significant residuals and this is not shown here.

In terms of the likely range of wave vapour delay effects on Etna this illustrative interferogram is in the lower half of thedistribution. In fact when treated as a static atmospheric problem measured by a profile from Catania to the summit [8] thisinterferogram ranks as one of the least affected by water vapour.

4 FUTURE DEVELOPMENTS

If this method of mitigating the tropospheric water vapour effects on volcano InSAR is to be accepted by the widercommunity then both more testing and improvements to the method are needed. We see one obvious further development.To become "operational" the method must be coupled with the global NWP modelling effort. This will, potentially,

Fig.2 (a) The unwrapped ascending pass tandem interferogram (21660- 01987) of Etna from 5th and 6th September 1995,(b) the equivalent NH3D model of delay differences using Trapani radiosonde data for initialisation. Both are orientednorth-south. The irregular boundary on the right is the coast of the Ionian Sea and the summit of Etna lies immediately tothe right of the kidney-shaped black area which is the area of incoherent layover on the western summit slopes of thevolcano. The colour cycle is from +75mm (red) to -45mm (blue) with zero at the pale green-pale blue boundary. Eachimage represents 45 km in width.

provide a consistent source of initialisation data for anywhere in the world. If the NWP modelling effort itself can beemployed to perform the local modelling, via nesting techniques, then this will make the models fully consistent. The latestNWP models can also improve both the timeliness of the local model and the treatment of water phase transitions directlywithin their code.

5 CONCLUSIONS

The Etna volcano, and other high relief volcanoes, are susceptible to large water vapour induced path delays affectingdifferential interferometry. Numerical experiments with the NH3D code shown here and published elsewhere show howsimulation of the dynamic atmospheric flow at volcanoes can be used to simulate the water vapour fields at the times ofERS radar imaging. The simulations replicate the typical asymmetry of the path delay field, with highest variance on theeastern, lee side of the volcano, resulting from the prevailing westerly winds. The data available for model initialisationfrom the 1990s was relatively coarse in space and time. The quality of the NWP model data now available is significantlybetter and should enable much more accurate simulations to be achieved and an improved method of InSAR correction to bebased on that.

6 ACKNOWLEDGEMENTS

Professor Ian James and Dr Peter Clarke provided help and guidance. This work was supported by NERC through grantGR/M86156, and studentship GR4/99/222. Stevens was partly supported by ESSC on a visiting scientist programme. TheERS data were supplied by ESA under the ERS AO1.

a b

7 REFERENCES

1. Hanssen, R.F., Radar Interferometry. Data interpretation and analysis. Dordrecht, Kluwer, 2001.2. Stevens, N.F. and Wadge, G., Towards operational repeat-pass SAR interferometry at active volcanoes. Natural

Hazards, (in press), 2004.3 . Miranda, P.M.A. and James, I.N., Non-linear three-dimensional effects on gravity wave drag: splitting flow and

breaking waves. Q. J.R. Meteorol. Soc., Vol. 118, 1057-1081, 1992.4. Webley, P.W., Bingley, R.W., Dodson, A.H., Wadge, G., Waugh, S.J. and James, I.N., Atmospheric water vapour

correction to InSAR surface motion measurements on mountains: results from a dense GPS network on Mount Etna.Phys. Chem. Earth, Vol. 27, 363-370, 2002.

5. Wadge, G., Webley, P.W. et al.., Atmospheric models, GPS and InSAR measurements of the tropospheric water vapourfield over Mount Etna. Geophys. Res. Lett., Vol. 29, 10.1029/2002GL015159, 2002.

6. Webley, P.W., Wadge, G. and James, I.N., Determining radio wave delay by non-hydrostatic atmospheric modelling ofwater vapour over mountains. Phys. Chem. Earth (in press), 2004.

7. Massonnet, D. and Feigl, K., Radar interferometry and its application to changes in the Earth s surface. Rev. Geophys.,Vol.36, 441-500, 1998.

8. Beauducel, F., Briole, P. and Froger, J-L., Volcano-wide fringes in ERS synthetic aperture radar interferograms of Etna(1992-1998): deformation or tropospheric effect? J. Geophys. Res., Vol. 105, 16391-16402, 2000.