Analysis of ERS-SAR Tandem Time-Series Using Coherence and Backscattering Coefficient
Keywords - InSAR DEM, SAR data calibration, backscattering coefficient, coherence estimation, time-series
For a qualitative and quantitative analysis of SAR time-series data, the backscattering coefficient and coherence need to be properly normalized to correct for biases introduced by topography, baseline, and processing. For a test site in an area surrounding Bern, Switzerland, we present examples showing why such normalization is necessary, followed by presentation and interpretation of the time-series.
2. Data Sets
Our ERS Tandem time-series consists of eight complete tandem acquisitions, dating from June 1995 to April 1996. Two pairs are incomplete due to satellite dropouts in September 1995 and February 1996. The perpendicular components of all tandem baselines are below 210 meters. Precise orbits were used during the interferometric data processing.
The acquired data cover an entire vegetation cycle, including a variety of ground cover types, such as agricultural fields, forests, lakes, and urban areas. The data set was collected over varying terrain, ranging from flat to mountainous. Meteorological conditions during the acquisition were measured hourly by the Swiss Meteorological Office. Ground truth samples were taken at different sites within the scene.
3. Estimation of Backscattering Coefficient
From the radar equation for distributed targets it is known that the received power is modulated with the 2-way-antenna gain and with the reciprocal value of , where is the local incidence angle. For each pixel these quantities are therefore dependent on the radar look angle , the depression angle of the antenna, the sensor position and attitude, the position of the backscatter element, as well as on the processed pixel spacing in range and azimuth, (Holecz F. et al., 1994), (Holecz F. et al., 1995).
Since SAR processing does not include topographic information, these radiometric corrections are omitted during the processing step, and need to be considered in a postprocessing step. Additionally, for ERS SLC products two further factors have to be taken into account, namely the calibration constant (dependent on sensor and processing facility) and the R3 correction.
4. Estimation of Coherence
Coherence is defined (Foster M.R. and Guinzy J., 1967) as the magnitude of the correlation coefficient of the complex signal data; it is directly related to the phase noise that is present in a SAR interferogram. This information can be used to estimate the achievable elevation accuracy during DEM generation, to investigate temporal changes of an observed area or to optimize the processing of the data.
The estimation is carried out on a window basis; it has been shown that this is the Maximum Likelihood Estimator (MLE) (Touzi R. et al., 1996). The statistical confidence of the estimated coherence is a function of the number of independent samples (degrees of freedom n, (Prati C. et al., 1994)) and the true coherence . The estimator is biased for all values of coherences, especially for areas with low coherence; estimates in these areas show a high variance.
Other sources of coherence mis-estimation are introduced by `baseline decorrelation', processing effects and topographic modulation of the interferometric phase. Therefore, to compare coherence estimates within a time-series, a careful design of the processing has to be carried out, i.e. including spectral shift filtering (Gatelli F. et al., 1994); removal of topography must be performed before the coherence estimation, and in a final step the coherence bias is corrected.
Consideration of the local slope improves the estimation of the coherence. Figure 4 shows coherence histograms for the October 1995 pair. The interferograms were flattened with (a) an ellipsoid model, (b) InSAR derived slopes and (c) with a high resolution digital elevation model provided by the Swiss Federal Office of Topography (DHM25) (Small D. et al., 1995).
Improvement of the coherence distribution is obtained when the influence of the topography is removed before coherence calculation. The use of pre-existing DEMs (when available) allows an accurate modelling of the topography. With this information, an accurate coherence estimation is possible also in low coherence areas, where the InSAR derived slopes are poor. InSAR-derived slopes can also provide better bias removal - for example, in areas where the independent DEM is no longer current (gravel pits) or where the heights references differ (ground vs. tree height) (Small D. et al., 1995).
The last step, correction of the estimation bias, is strictly related to the number of degrees of freedom n used in the estimation. This value is equal to the number of independent samples contained in the moving window (of dimension m) used for the estimation. For several reasons, n and m are different (Joughin I. R. and Winebrenner D. P., 1994): the system resolution and the sampling of the SLC data in general do not correspond, a spectral weighting is present in the data, and defocusing effects can affect the images.
In general it is not easy to obtain an analytical value of n: in the present work it has been estimated in an area with known homogeneous coherence (e.g. large water areas, where is assumed to be zero).
Next, the a posteriori density function for all measured coherences and a given n is computed (Foster M.R. and Guinzy J., 1967). Now the relation between measured and true coherence is known. An example with a given degree of freedom is shown in figure 5. The correction for all ERS Tandem pairs was performed based on this relation.
Figure 5: Top: A posteriori density functions for measured coherences (0.01-0.99). Middle: Plot of maxima of a posteriori density functions. Bottom: Relation between measured and true coherence (degrees of freedom: 32.4, estimated from a large water area, dotted lines: 10% significance level).
5. Time-Series Analysis
Coherence was estimated for five thematic classes: agricultural land, forest, meadow, urban area and water (lake). Figure 8 shows corrected coherence values.
Agriculture: In summer there is a lot of agricultural activity, some fields are coherent, while others show no coherence (high variance). In Winter fields are bare and coherence is generally very high (see figures 6 and 7).
With a given estimator of coherence, we conclude that correction of the coherence estimation bias is significant only in low coherence areas. For higher coherences, there is little difference between corrected and uncorrected values (see figures 5 and 8).
Figure 9 illustrates backscattering coefficients and their deviations for several ground cover types. For these two particular acquisition dates (November 26th and 27th) it is evident that backscatter-based discrimination between the selected ground cover types is not possible. Coherence provides a much better discriminator between different ground cover types. However, the class separability depends on the season (i.e. 13./14.8.95, figure 8) as well as terrain types and weather conditions (i.e. 31.12.95/1.1.96, figures 8 and 10).
Figure 10: Meteorological data provided by the Swiss Meteorological Office for the BernLiebefeld station. Note the heavy snow- and rainfall between December 31st, 1995 January 1st, 1996 causing the loss of coherence seen in Figure 8. Acquisitions were at approximately 11:20 local time.
We show in figure 11 for one example within the time-series a combination of backscatter and coherence information. The correction of backscattering intensity and coherence estimation presented in this paper significantly enhances the value of these types of products.
Figure 11: ERS Tandem InSAR signatures (26./27.11.95) for the test site `Büren'. Red: interferometric correlation (raw coherence), green: backscatter intensity of first acquisition, blue: backscatter intensity change.
3. After these calibration and estimation steps, one is able to compare backscatter and coherence values within the time-series (i.e. different coherence products). These processing steps are a fundamental prerequisite for further analysis such as classification based on these values.
ERS SAR data and precise orbit ephemeris information were provided courtesy of ESA/ESRIN. The DHM25 elevation model used within some calculations shown here was provided courtesy of the Swiss Federal Office of Topography. Meteorological data was provided courtesy of the Swiss Meteorological Office (SMA).
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
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