A first quantitative evaluation of atmospheric effects on SAR interferometry
Since the state-of-the-art in SAR interferometry is strongly progressing
towards a more quantitative and localized approach, the influence of error
budgets is becoming more important. The influence of atmospheric inhomogeneities
on SAR interferometry has been studied by several authors (see e.g. (Tarayre
and Massonnet, 1994/1996), (Goldstein, 1995) and (Zebker and Rosen, 1996)).
In this study, special attention is paid to the influence of tropospheric
inhomogeneities for small baseline tandem interferograms of an area with
no significant variation in elevation. The purpose of these interferograms
is to estimate the feasibility of the detection of very slow subsidence
rates over a long time span. Although the main problem for this type of
measurements seems to be the temporal decorrelation, atmospheric effects
can be easily misinterpreted as subsidence. Therefore, it is tried to estimate
what the magnitude of the phase shifts due to atmospheric effects can be,
and to suggest some possibilities to tackle these problems. The area of
interest, Groningen, is situated in the North-East of the Netherlands and
is slowly subsiding due to the extraction of natural gas.
For two-pass, short baseline interferometry, the influence of elevation
on the interferometric phase is small due to the large height ambiguity.
Therefore,assuming sufficiently correlated imagery, an interferometric
phase change can only be due to surface deformations and inhomogeneities
in the propagating medium. Whereas SAR interferometry for the estimation
of Digital Elevation Models (DEM's) is strongly dependent on the length
of the baseline, its use for deformation studies is not. The phase shift
due to atmospheric inhomogeneities is equal for both DEM applications and
deformation studies. However, the magnitude of these errors in the final
products, DEM's and deformation maps, is different. For DEM's, the magnitude
of the error is directly proportional to the height ambiguity, and therefore
inversely proportional to the baseline. For deformation maps, the magnitude
of the error is not related to the baseline.
The phase shift of a radio signal that propagates two-way in a medium with a refractive index equal to 1 (free space) can be expressed as:
where rho is the one-way propagation path length. For a signal propagating in a medium with a refractive index unequal to 1, an incremental path length will be observed due to the signal delay in the medium, hence
If we compare the phases of two SAR images, to calculate the interferometric phase, we obtain
Assuming that we are dealing with a very short baseline (< 50 m) and a flat, horizontal area with no deformations, the only coherent phase fluctuations will be caused by the difference in incremental path length:
From the latter equation we see that we cannot differ between the tropospheric
states of the two acquisitions.
The Saastamoinen model
in which P is the total atmospheric pressure in HPa, t is the temperature in degrees Celcius, theta is the inclination angle and e is the partial water vapour pressure. The latter can be derived from the relative humidity rh[%] using:
The important consequence of this model is that an estimation of the
phase delay can be determined without having to know all the parameters
The Saastamoinen model can be used to perform a first quantitative evaluation
of the sensibility of phase changes due to the three major parameters;
relative humidity ,temperature and pressure. What
we assume here, is that the atmosphere is divided spatially into columns
with a certain average value of the three variables. In the horizontal
direction, differences can occur between the columns, resulting in a relative
phase shift in the interferogram.
Figure 1 shows the influence of pressure changes (HPa) on the interferometric phase. We can see that e.g. a difference of 5 HPa represents a corresponding phase shift of 0.4 phase cycle. Note that the pressure is not correlated with temperature or relative humidity. Pressure changes of 5 HPa over 50 kilometers are possible to occur in a meteorological front zone, and will be visible as a linear trend in the interferogram.
In figure 2 the connection between temperature and relative phase change
is shown for three values of the relative humidity and a fixed pressure
of 1010 HPa. Here we see that a (horizontal) temperature gradient of 5
degrees can have considerable influence on the corresponding phase shift,
depending on the absolute temperature and the relative humidity. If we
keep in mind that in a standard atmosphere the temperature drops with 6.5
degrees every kilometer, the influence of the lower layers will be significantly
more important than higher layers.
In the horizontal direction the first 40 meters above ground level can have strong variations in temperature, depending on the nature of the surface. Above this layer, at fixed altitudes, the horizontal differences in temperature will be limited to large scale trends. Due to the limited extend of this lower layer, it can be doubted if it will have enough influence to alter the interferometric phase.
Finally, figure 3 shows the influence of the relative humidity on the
relative phase change, for three different temperatures. These temperatures
can be coupled directly to altitude, and due to the decrease in temperature
with height, the influence of a humidity change at low temperatures becomes
significantly more important than at higher temperatures. For a temperature
of 0 degrees Celsius, a 20% change in relative humidity horizontally would
count for a half cycle phase difference in the interferogram.
Strong variations in relative humidity are to be expected e.g. near cumulus clouds, where dry and warm air is moving upwards, cools down, and condensates (increase in relative humidity). The consequence of this movement is a downward movement at some distance from the upward one. In this downward movement, cold and humid air is warmed up, hereby decreasing in humidity. As a consequence we might expect changes in relative humidity of tens of percents, even on a kilometer scale.
In the Groningen Interferometric SAR Experiment (GISARE), an interferogram
was obtained using the ERS images of february 26 and 27, 1996 at 10:29
UTC (see figure 4). The elevation differences in this area do not exceed
5 meters, which corresponds to a phase cycle of 0.02 for this baseline.
Therefore, topography can be neglected as a source of phase changes in
The remaining phase differences are not influenced by the baseline, so only phase delay or surface deformation will be visible in the interferogram. However, large scale deformations are unlikely within a time period of one day. Over the land areas we see changes in interferometric phase of about 0.4 phase cycle, corresponding with approximately 1 cm excess path length in the direction of the satellite. Furthermore, there appear to be patterns in these disturbances in North-East South-West direction. The inclination of the image for this descending orbit is approximately 13 degrees.
Three minutes before the ERS image acquisitions, Meteosat observations
of the area were made. At that time, the visual channel (VIS) was operating
in a double resolution mode of 2.5 by 5 kilometers for this latitude. NOAA-AVHRR
(Advanced Very High Resolution Radiometer) images were acquired 115 minutes
later. All four images show approximately the same area. In the NOAA images,
the contours of the Netherlands overlay the data. The Groningen area, shown
in the interferogram, is located in the North-Eastern part of the area.
We can see patterns in these images, especially on february 27, which correlate
in direction with the interferometric patterns.
|Figure 5. Meteosat, 26 february, 10:26, Double VIS||Figure 6. Meteosat, 27 february, 10:26, Double VIS|
|Figure 7. NOAA-AVHRR, 26 february, 12:14, channel 2||Figure 8. NOAA-AVHRR, 27 february, 12:02, channel 2|
From the Meteosat and NOAA-AVHRR imagery it can be clearly seen that a frontal zone passed the Groningen area during the SAR acquisitions. In the frontal zone relative humidity is high from the ground up till several kilometers. Behind the frontal zone the atmosphere dries out. This can be clearly seen from the radiosonde profiles of relative humidity. Such a frontal zone could due to the high spatial variability of the relative humidity perpendicular to the frontal zone,and influence the results from the SAR interferometer. To test this hypothesis, vertical radio probe profiles of temperature, pressure and relative humidity were analysed from ground level to a height of 12 kilometers. The total path delay was calculated using formula 5. It resulted in a constant increase in path delay of 1.5 cm during the 24 hours in which the frontal zone passed. These calculated path delays from actual atmospheric profiles clearly support our hypothesis.
Meteorological ground observations at Groningen airport were acquired at the moment of the SAR data acquisitions. The airport is located in the imaged area. The data are presented in table 1 and 2. Evaluation of the results show that they can be used to get a first estimation for the parameters in the Saastamoinen model.
|Rel Hum||100 %|
|Wind speed||11 m/s|
|Wind direction||180 degrees|
|Precipitation||Very light drizzle|
A smoothed version of the interferogram is shown in figure 9. We applied a bicubic low pass filtering to obtain an image with a pixel size of 200 by 200 m. The colours represent the phase changes in the interferogram, using a colourbar from 0 to 255, which corresponds with one phase cycle (2.8 cm). Note that by this procedure water surfaces will get an average value which we should not falsely interpret as an area with constant phase!
In this smoothed image, a profile was taken from one corner to the other, perpendicular to the main disturbances. This profile is plotted in figure 10. We see diferences in interferometric phase in the order of 0.2 phase cycle. Using the Saastamoinen model, assuming a mean temperature of -10 degrees Celsius and a ground pressure of 1010 HPa, we can calculate how large relative humidity changes have to be in order to explain the phase variation. For a phase variation of 0.2 phase cycles, the corresponing change in relative humidity is 20%.
For detecting subsidence rates over more than a year time span in areas with much agricultural use, the biggest problem is formed by the temporal decorrelation, which will obscure most of the data for further interpretation. The only regions that were found to be coherent are e.g. urban areas, roads and public works. However, for these parts of the area, atmospheric disturbances will play an important role, since we cannot actually see the spatial structures in the mostly decorrelated interferogram. Here we will give some preliminary ideas for suppressing the influence of the disturbances.
Time series seem to be a possible approach for eliminating or suppressing atmosferic artifacts. If a significantly long time series of coregistered interferograms is analysed, it can be expected that atmospheric phase shifts will behave like noise with a wavelength of less than 30 km. Therefore, by low-pass filtering of the images, using appropriate statistical assumptions, the effects might be suppresed.
Another possibility, which is only possible for a time series of correlated interferograms, is to estimate the atmosphere's influence on one particular image. This can be based on the comparison of three SAR images in two interferograms. Since the effects of the atmosphere will be unique for every image, the two interferograms must convey the identical features of the image which is used twice. In flat areas, as which we are discussing here, we only have to distinguish between deformations and atmospheric effects, were it should be noted that the time scale of the subsidence deformations is likely to be much larger than that of the atmosphere.
Different types of other techniques can give useful information on the possible disturbance of the atmosphere. GPS is able to estimate accurate zenith delays which can be mapped to the incidence angle of the SAR sensor. Although these measurements yield point wise information, information on the variablibity of the atmosphere can be extracted from time series of measurements. Satellite systems as Meteosat or NOAA-AVHRR deliver images which could be used, e.g. if watervapour content is measured. Unfortunately the resolution of these instruments for the latitude of the Netherlands is in the order of kilometers, and they seem more appropriate for a qualitative than a quantitative analysis. An important restriction to all these additional measurements is that they should be made simultaneously with the two SAR images, due to the high temporal variation of the atmospherical conditions.
A last, and very straightforward, possibility is the selection of those interferograms which are not contaminated by atmospheric effects. As long as sufficient SAR images have been observed, it is possible to use only those which are likely not to be too much disturbed by weather conditions. Unfortunately, for a lot of regions in the world undisturbed images are quite unlikely.
The influence of the atmosphere on interferometric SAR images is strongly
determined by its high temporal and spatial variability. Atmospherical
models are mostly too generalized to explain the artifacts that can occur
within one interferogram. With respect to the spatial variability, SAR
images are influenced by artifacts of the size of single clouds.
The phase value of every SAR image is always influenced by the atmosphere. Problems arise when the spatial variability of e.g. the three main tropospheric parameters pressure, temperature and relative humidity is such that the horizontal path delay differences are significant with respect to the wavelength of the radar signal. Using the Saastamoinen model, these differences can be related to changes in the average integrated value of these three parameters over a column of air. It seems that especially relative humidity is an important parameter causing local path delays.
For a qualitative evaluation of observed effects, meteorological satellites can be used. A more quantitative analysis is always strongly influenced by the models that were used. However, when atmospheric effects can be detected and positively identified, possibilities arise for their elimination. Further studies need to be performed on how this detection and elimination can be improved.
This work has been performed in close cooperation with the Physics and Electronics Laboratory of TNO in the Netherlands. We like to thank ESA for the generous provision of the required ERS images.
Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry