ATMOSPHERIC EFFECTS THIRTY-FIVE DAY ON INSAR

J.M. Leighton, A. Sowter, M. Warren

Institute of Engineering, Surveying and Space Geodesy (IESSG), University of Nottingham, University Park, Nottingham, NG72RD, United Kingdom

Email: isxjl1@nottingham.ac.uk

ABSTRACT Repeat pass InSAR images are subject to variations in the atmosphere, especially from water vapour in the troposphere. This study uses InSAR images with a thirty-five day temporal baseline to demonstrate this link. Interferograms with a thirty-five day temporal baseline are compared with weather satellite imagery, meteorological (met) synoptic measurements and signal delay estimates from continuously operating GPS stations. In some cases a clear relationship is present whilst in others, results are inconclusive. 1 INTRODUCTION Since the radar signals pass through an inhomogeneous atmosphere that varies spatially and temporally, this delays the signal by varying amounts. This means that the signal delay over a 100km x 100km interferogram will vary pixel by pixel and the delay per pixel will be the contribution from both acquisitions which are unlikely to have similar atmospheric conditions, especially with a thirty-five day temporal baseline. Here, differential interferograms corrected for baseline error are examined, noting image characteristics. Knowledge of the atmospheric conditions and, in particular, the presence of water vapour at the time of the acquisitions, is discerned from met data and the two datasets are compared to ascertain correlative effects. The effects discussed here were comprehensively studied by [1] and the link to precipitable water vapour was shown in [2] . This paper represents a small subset of a wider study originally submitted as an MSc dissertation in Sep 05 [3]. InSAR techniques have been used for over fifteen years for use in deformation studies, subsidence and Digital Elevation Model (DEM) creation. 2 ATMOSPHERIC EFFECTS InSAR images tend to exhibit irregular artefacts which according to [1,2] and [6,7], are due to spatial and temporal atmospheric inhomogeneity across the SAR scene. In particular, [2] states that these artefacts result mainly from atmospheric water vapour. Tropospheric variations in pressure and temperature also contribute to the distortions, but these effects are much smaller in magnitude. Antenna to ground ranges (ρ) are determined by multiplying the pulse time (τ) by the speed of light in vacuo (c):

12c! "= (1)

However, since the signal passes through a medium an atmospheric delay term is required which can be thought of as an extra (imaginary) distance !" . This is usually around 2.5-3m in Northern temperate Europe [1] and must be added to the phase measurement to correct it. The modified SAR acquisitions can be stated as:

4 ( )i!

" # #$

= +% (2)

where i! represents the modified path length in cycles for a given acquisition i and ! is the radar instrument wavelength. This leads to a biased interferometric phase:

( ){ }4 'Bcos!" # $ % %&

' = ( +' (' (3)

where !" is the modified interferometric phase, ! is the radar incidence angle and ! is the angle between the baseline and the horizontal plane passing through the acquisition point. Use of an apostrophe denotes values with respect to the second acquisition. If the delay were constant across the whole SAR scene, a biased interferometric phase would result

and the delay for the two acquisitions would not difference due to atmospheric temporal decorrelation. Since most applications are concerned with phase change, this would not be an issue. In reality, the delay across a scene of approximately 100km x 100km size can be expected to vary, especially in Northern temperate latitudes, due to local atmospheric inhomogeneities. If there were localised inhomogeneity at the time of the first acquisition, this would result in a slower propagation velocity or an increase in !" with respect to the reference phase resulting in a positive phase change in the interferogram. A similar effect at the time of the second acquisition would result in a negative phase change in the interferogram. The sign of the phase change is therefore independent of baseline considerations [1]. Also, because of the relative nature of interferometric observations, only variations in the signal delay can be measured, and not absolute atmospheric delay. Note that in areas of significant topography, changes in atmospheric conditions due to height cannot be ignored [7]. 3 THE LONDON SITE & DATA The area covered by the scene includes all or parts of Bedfordshire, Berkshire, Buckinghamshire, Cambridgeshire, Hertfordshire, Kent, Middlesex, Surrey and Sussex. The area is mostly characterised with mildly undulating terrain from sea level to approximately 100m. There is a ridge line in the South running almost the entire length of the scene known as the North Downs which reaches a maximum of 295m on Leith Hill in Surrey in the Southwest of the scene. Any change in atmospheric conditions due to changes in height is considered insignificant here. Fig. 3.1. is a map of the scene area showing the positions of the synoptic met stations and Continuous GPS (CGPS) points with respect to the scene boundary. Note, as definitions do vary, the term ‘large scale’ in terms of interferogram artefacts is taken to mean those effects that cover a large area.

Standard 100km x 100km ERS-1 and -2 SAR SLC-I acquisitions of frame 2565 with a thirty-five day temporal baseline were made available for the study provided by ESA with precise orbits from Delft Institute of Earth Observation and Space Systems (DEOS). Met data was taken from three sources for the study. Firstly, hourly synoptic measurements were collated from twenty-one Met Office stations inside the scene area, including data such as general weather conditions, pressure and cloud cover. Secondly, Zenith Total Delay (ZTD) estimates from three Continuous GPS (CGPS) stations were converted to Zenith Wet Delay (ZWD) values and mapped to the SAR incidence angle. These delay values are hence forward referred to as ‘Wet delay estimates’. Thirdly, Advanced Very High Resolution Radiometer (AVHRR) imagery data have been collated for the acquisition periods concerned from the Dundee Satellite Receiving Station (DSRS). Interferograms were created using the Delft Object-oriented Radar Interferometric Software (DORIS) V3.15 [4]. Differential interferograms were then produced by differencing with the 90m Shuttle Radar Topography Mission (SRTM) [5] Digital Elevation Model (DEM) using MATLAB V6.5 software. The interferograms were then corrected for baseline error fringes, also using MATLAB. The resulting corrected differential interferograms have been re-wrapped for analysis, though there is some discussion of unwrapped interferograms when circumstances warrant it.

Sheerness Barking London Weather Centre

Chenies B Northolt Heathrow Sunbury

Kenley Airfield Redhill

Gatwick

LONDON

Approximate Scale (km) 10 20 30 40 50 0

CGPS Met Stn SLC-I

Scene Shoeburyness London City Airport

Edenbridge Goudhurst

Charing

Southend Aldenham School

High Beach

Silsoe

Luton Rothamstead

Stanstead

Writtle

Rettendon

Fig. 3.1. SAR SLC-I scene overview

London City London City

AirportAirport

Aldenham SchoolAldenham School

High BeachHigh Beach

RothamsteadRothamstead

WrittleWrittle

ShoeburynessShoeburyness

Fig. 4.2 Interferogram 32

Fig 4.1 Interferogram 1

4 ANALYSIS OF RESULTS The wrapped, differential interferograms are initially analysed in general terms with comment on quality and significant features. The met data corresponding to the relevant SAR acquisitions are then interpreted and an outline of the general atmospheric conditions across the scene and specific local features is included. Interferogram and met data are then analysed as a whole to discern whether any link exists between observed phase artefacts and the met data. All interferograms shown are differential interferograms (using the SRTM DEM), corrected for baseline error and rotated 180° about the image’s vertical axis. 4.1 Interferogram 1 4.1.1 Analysis The SAR acquisitions for interferogram 1 occurred on 7 Feb 97 and 14 Mar 97 which resulted in a perpendicular baseline of -250m.

Phase (rad) Fig. 4.1. shows the wrapped differential interferogram 1 corrected for baseline error. Notable signatures in interferogram 32 are cells (red areas) clustered together equally distributed in both the azimuth and range directions. Note that these clusters are phase ‘dips’ rather than ‘hills’. Typically, the clusters measure around 15-20km across and include variations of up to four cycles in the unwrapped interferogram. This may indicate stratiform precipitation in those areas or conversely stratiform precipitation in areas other than the clusters. As the red clusters show a negative phase change, this suggests water vapour in these areas during the second acquisition. Alternatively, clusters may be a complex amalgamation resulting from precipitation during both acquisitions.

The pseudocolour AVHRR weather radar images were scrutinised to check for large scale frontal systems. These images are shown in fig. 4.2. The first acquisition (left) shows wispy high level cold clouds scattered over the scene

Fig. 4.2. Pseudocolour AVHRR weather radar images for interferogram 1

Fig. 4.3. AVHRR channel one images for interferogram 1

Fig. 4.4. Interferogram 36.

GoudhurstGoudhurst

SheernessSheerness BarkingBarking

ShoeburynessShoeburyness SouthenSouthen

dd

StansteadStanstead

WrittlWrit tl

ee

RettendoRettendo

nn

SunburySunbury

CharingCharing

area whilst the second acquisition indicates scattered snow and ice or low level cloud cover. The channel one high resolution images in fig. 4.3. confirm that this is cloud. Synoptic data for the first acquisition shows precipitation reports at Writtle, Aldenham School, Rothamstead, London City Airport and High Beach. Synoptic data for the second acquisition shows rain or showers over Shoeburyness, Writtle, Aldenham School, and Rothamstead. Note that stations marked in italics in fig. 4.1. received precipitation on both acquisition days. No wet delay estimates were available for either SAR acquisition. 4.1.2 Conclusion

As precipitation occurred during both acquisitions, and the spatial density of the met stations is not sufficient to discern the exact precipitation boundaries, untangling these effects is impossible. Water vapour in the second acquisition only would be expected to produce areas of negative phase change therefore Shoeburyness should lie in a low phase areas which bears up to scrutiny. Stations receiving precipitation during the first acquisition only (London City Airport and High Beach) ought to lie in areas of positive phase, which is not the case. The water vapour present in both acquisitions appears to have had a complex effect on the phase values where some areas have cancelled out and others have combined. 4.2 Interferogram 2 4.2.1 Analysis The SAR acquisitions for interferogram 2 occurred on 14 Nov 97 and 19 Dec 97 resulting in a perpendicular baseline of -123m. Interferogram 2 (fig. 4.4.) shows two large phase ridges running from top left towards the centre. The top right corner has complex clusters of artefacts.

Phase (rad)

Fig 4.4 Interferogram 2 Fig.4.5. AVHRR channel one images for interferogram 2

After experimenting with the baseline correction coefficients, it is almost certain that the two phase ridges in the bottom left are baseline error remnants. These could not be removed from the image without introducing errors elsewhere. The area shows no other significant characteristics and would probably be a relatively flat area were it not for the baseline error. The main area for discussion therefore is the right side of the image exhibiting the clusters. These characteristics are expected to be the result of significant spatial variation of water vapour across this part of the scene. The high resolution AVHRR image on the left in fig. 4.5. has thick cloud cover over the scene and entire region with vague banding in the North and West of the scene area. The second high resolution AVHRR image (and the pseudocolour quicklook image) shows a thin swathe of cold cloud across the scene with increasing turbulence towards the top right of the scene area. Synoptic data for the first acquisition reveals mild dry conditions that would not be expected to produce anything of significance in the interferogram. The second acquisition synoptic data splits the scene into two areas with an imaginary line running from the top left to the bottom right. The bottom left area is covered by mist and fog whilst the top right area is characterised by scattered rain and showers. Fig. 4.4. shows the interferogram marked with the synoptic stations that reported precipitation. Wet delay estimates for the first acquisition are all similar in magnitude

whilst during the second acquisition the delay was 13cm higher in Sheerness than Sunbury. There was no wet delay estimate available for Barking. This large variation in wet delay is a further indicator of turbulence in the scene. 4.2.2 Conclusion The phase ridges near the bottom left of the interferogram are remnants of residual baseline error. The clustered area in the top right of the interferogram is clearly related to the reports of precipitation from met stations in that area. This is further corroborated by the increase in wet delay at Sheerness. 4.3 Interferogram 3 4.3.1 Analysis Interferogram 3 acquisition dates were 19 Dec 97 and 23 Jan 98 with a resulting perpendicular baseline of -127m. The interferogram shown in fig. 4.6. shows a diagonal phase trench running the length of the image. This phase pattern and those parallel to it are probably due to residual baseline error which despite repeated attempts could not be entirely removed. This aside, the parallel semi-circular wave like formations in the upper part of the image cannot be due to baseline error. The waves slightly increase in wavelength towards the right side of the image.

The high resolution AVHRR image (Fig. 4.7.) for acquisition one shows an area of turbulence increasing towards the top right of the scene area with a vague curved wave pattern sweeping along the bottom right / top left diagonal. The second AVHRR image indicates thin misty even cloud cover over the whole scene area. The synoptic data available for the both acquisitions is much better than average. The first acquisition synoptic data splits the scene into two areas with an imaginary line running from the top left to the bottom right. The bottom left area is covered by mist and fog whilst the top right area is characterised by scattered rain and showers. Synoptic data for the second acquisition shows a mild North Easterly with no reported precipitation anywhere in the scene and haze reported over the South-western scene area. The wet delay estimates for acquisition one shows twice as much delay in the East for the first acquisition. Delay estimates for the second acquisition are approximately equal. 4.3.2 Conclusion for Interferogram 18 Conclusions for interferogram 3 are very similar to those for interferogram 2. This is because the interferograms share the 19 Dec 97 acquisition and the other acquisitions for the two interferograms are both non-eventful weather days. Interferograms 2 and 3 are good examples of how interferogram artefacts assumed to be due to SAR signal delay can be correlated with atmospheric data when one of the acquisitions has approximately homogeneous conditions and the other shows turbulence. The split described for interferogram 3 is clearly a result of the spatial variation of atmospheric water vapour across the scene. The wave like formations present in the interferogram and first AVHRR acquisition appear to be related as they are of similar scale, position and orientation. 5 SUMMARY

Phase (rad)

Fig. 4.6. Interferogram 3 Fig.4.7. AVHRR channel one images for interferogram 3

The main objective of the project was to ascertain correlative effects between artefacts in differential interferograms and met data. The spatial scales of atmospheric influences varies between hundreds of metres and hundreds of kilometres. The study has been more successful in discerning the smaller effects as many of the larger effects may cover an entire interferogram or are indistinguishable from baseline error. Many of the much larger image characteristics in the interferograms were clearly too regular to be atmospheric artefacts. A more rigorous approach is required for the removal of orbit baseline error, especially when no precise orbit is available. The study has been most successful in correlating interferogram artefacts with areas of precipitation. This is especially true when precipitation is reported during only one of the acquisitions. When precipitation is present in both acquisitions in the same area, the resulting phase delay is a combination of signal delays from both acquisitions. The study was least successful when trying to link large scale cloud formations with atmospheric phase artefacts though there was some success relating cloud and interferogram textures. Although clouds are made up of water vapour, this becomes irrelevant if the entire scene is covered in cloud as was often the case. In addition, water vapour in cloud tends to delay the SAR signal to a much lesser degree than Precipitable Water Vapour (PWV). The data types used in the study were in retrospect a good choice. Unfortunately, significant gaps in the data inhibited the analysis somewhat, especially with regard to synoptic data. A wider use of wet delay estimates would prove invaluable if the spatial density of the stations were to increase, ideally to a level equal or greater than the met station density. Use of weather satellite data proved crucial, though higher resolution data, ideally equal to the interferogram pixel resolution would improve matters considerably. 6 RECOMMENDATIONS FOR FUTURE STUDY As some of the met scales are greater than the size of an interferogram or indistinguishable from baseline error, a similar study covering a larger area, such as a block of four adjacent interferograms could be undertaken. This would also improve analysis of the effect of large cloud formations that might otherwise completely engulf a single interferogram. With sufficient spatial density of CGPS stations, wet delay corrections could be generated. This would require interpolation of the GPS data to provide pixel by pixel corrections. Further study is required to discern details such as the optimal temporal frequency of the wet delay estimates and the best method of interpolation. Further study is then required to test the method. 7. ACKNOWLEDGMENTS The data used is part of Cat-1 project 3108. 8 REFERENCES 1. Hanssen, R.M. (1998). Atmospheric Heterogenities in ERS tandem SAR Interferometry. Delf. Delft University Press. 2. Zebker, H. A., Rosen, P. A., Hensley, S. (1997). Atmospheric effects in interferometric synthetc aperture radar surface deformation and topographic maps.J. Geophys. Res., 102 (B4), 7547-7563. 3. Leighton, J.M. (2005). Atmospheric Effects on Synthetic Apersture Radar. Nottingham University. 4. Kampes, B., Usai, S. (1999). Doris: The Delft Object-oriented Radar Interferometric software. ITC 2nd ORS symposium. (CD Rom). 5. NASA (2003). SRTM Documentation. See: ftp://e0mss21u.ecs.nasa.gov/srtm/SRTM30/SRTM30_Documentation/SRTM_Topo.txt [Aug 17 2005] 6. Delacourt, C./ Briole, P., Achache, J., Fruneau, B. and Carnec, C. (1997). Correction of the tropospheric delay in SAR interferometry and application to 1991-93 eruption of Etna volcano, Italy. AGU Fall Meeting, December 8-12, San Francisco, USA. 7. Massonnet, D., and Feigl, K.L. (1998). Radar Interferometry and its application to the changes in the earth's surface. American Geophysical Union.