Incidence angle normalization of Wide Swath SAR data for oceanographic applications

1 Introduction

SAR imagery has proved very effective for observing, measuring and quantifying oceanographic phenomena such as fronts, waves, eddies, winds, storms, oil spills, algae blooms, currents, and boundary layer rolls [1, 2]. The ability of SAR sensors in retrieving data in almost all weather conditions, independently of sunlight surface, is extremely important for oceanographic studies.

The quality of SAR imagery is dependent on the mode of acquisition and raw data processing [3]. Oceanographic phenomena were tracked by spaceborne SAR systems, which cover wide areas, therefore the ScanSAR acquisition mode is mainly used. In the bibliography, the spatial scale of several oceanic processes which mostly lies within tens to hundreds of kilometers has already been described [4]. An example of ScanSAR mode is ENVISAT’s Wide Swath Mode (WSM) with 150 m resolution, a swath width of 405 km and two possible mutually exclusive polarizations (VV or HH). The main issue related to wide swath SAR images is the progressive decrease of backscatter energy from near to far range (Figure 1). The Normalized Radar Cross-Section (NRCS) values derived from SAR images depend on the content of the observed scene as well as the sea and atmospheric conditions at the time of observation [5–7]. Also, NRCS depends on the relative azimuth angle between the radar look direction and wind direction. This means that NRCS at low incidence angles over a certain wind speed and direction is different from that at high incidence angles. Therefore, a normalization is required in order to limit the NRCS variation over the various incidence angles, since:

1. Operators need to visualize the image in a more usable way in order to identify ocean phenomena through visual interpretation. It should be mentioned that the operational service for oil spill detection “CleanSeaNet”, from the European Maritime Safety Agency (EMSA), is primarily based on visual inspection [8].

2. Normalization can be considered as a preprocessing step for semi or fully automatic classification systems. For example, the first crucial step for mesoscale oceanographic phenomena detection and classification (e.g. oil spills, eddies, currents, or fronts) is the identification of dark objects in SAR images [4, 9, 10]. This step is extremely difficult in wide swath images due to backscatter decrease from near to far range. In addition, normalization can be used for inter-comparison of many SAR images or data from the same or different sensor; the transition from one type of data to another will be simpler and more efficient after normalization, as the appearance of dark features will be similar.

Figure 1

An example of ENVISAT ASAR Wide Swath Mode over sea area (Egyptian Coast, acquisition date: 13/03/11) with relatively stable wind speed of 6.5 m/s over 400 km in the range direction. Wind measured directly from the image using the CMOD-5 geophysical model. (a) Amplitude image and its profile and (b) Calibrated image and its profile.

The most widely used incidence angle correction technique is the square cosine correction [11]. The model is based on Lambert’s law for optics and includes two assumptions; the amount of power that is radiated back to the satellite sensor follows a cosine law and the radiation variability as a function of the observed area is also cosine dependent [12]. The backscatter normalized radar crosssection in angle θ(σθ0) is related to the cosine squared of the incidence angle:

where σ00 is the backscatter independent of the incidence angle. Assuming a reference angle θ_ref to which the image will be normalized, equation (1) is applied. Then, after dividing by parts, the radar response to σref0 is given by:

Recent studies updated the square power of equation (2) over particular types of observation. For example in [13] a power index between 1 and 2 was applied characterizing the surface roughness over tropical forest areas. In [12] values varied between 0.2 and 3.4 depending on vegetation type and season, for savanna-dominated areas. In [14] values 10+ over water were applied for the relationship of local incidence angle with σ° values. However, the square cosine correction is valid for surfaces with Lambertian reflectance properties and is not expected to perform in a satisfactory way over the sea. Another method of normalization can be based on backscatter modeling. Backscatter energy over the sea surface is strongly related to the incidence angle and wind speed and presents a broad range of backscatter levels: −40 dB < σ° < +10 dB from far to near range. Ocean backscatter modeling is often described by the Bragg model [15–18], which is appropriate for intermediate incidence angles (approximately 20°–60°) and describes scattering from short gravity–capillary waves at the C-band wavelength. This model is based on physical principles rather than on an empirical relationship and calculates the σ° values based on geometric and hydrodynamic modulation. The Bragg scattering model is widely applied, however, neither the measured σ° values for specific combinations of radar parameters and environmental conditions nor their observed variation can be explained satisfactorily by pure Bragg scattering theory [18]. A more advanced microwave backscatter model is described by [17]. The main advantage of that model is the breaking down of the sea surface into small, intermediate and large scale waves. Scattering from small scale waves is explained by Bragg scattering, from large-scale waves by quasi-specular scattering and from intermediate waves by Kirchhoff scattering [17]. The transition from Bragg to Kirchhoff scattering is dependent on the incidence angle, wind speed and the surface wave spectrum [17, 19]. These models refer to scattering from “pure” roughness. However, ocean roughness described by gravity–capillary and short gravity waves is always influenced by surface, subsurface and atmospheric layer processes. Therefore, the real σ° value derived over a particular sea area cannot be efficiently described by stochastic modeling.

In a recent previous study [1], a theoretical backscattering shape function was introduced for normalizing WSM SAR images over the ocean. In the present work, a quantitative study is presented where the robustness of the proposed method is examined. The aim of this paper is to reveal a simple but consistent scheme for reducing the dynamic range of SAR images by removing the mean incidence angle dependence. The proposed normalization approach aims to normalize the wide swath SAR image to a fixed reference angle. The approach needs to be robust, accurate, easily applicable and transferable for different SAR oceanographic applications. A detailed description of the proposed methods is provided in the next section, followed by data sets and the comparison factors (section 4). In Section 5 the results of the proposed methodologies and further analysis are presented. The discussion of the results and conclusions are given in Section 6.

2 Methodology

The SAR image profile in the range direction shows a squared cosine shape function with respect to the incidence angle θ(cos2 θ) under the same wind conditions. After calibration and quantification in logarithmic scale (dB), the backscattering profile is transformed into a linear shape (Figure 1). This linearity can be questioned whenever a non-stable sea state is present. However, all examined case studies support the linear transformation. For example in Figure 1b the regression analysis revealed a correlation coefficient (R2) of 0.9801 for linear fit, 0.986 for logarithmic fit and 0.9866 for a quadratic polynomial. Since the R2 difference between the different fit lines is on the third decimal number and our scope is to produce a simple and robust normalization method, the linear shape of the backscattering profile was adapted. This linear shape in the range direction is unique for each ASAR image since it is related to the current wind speed and oceanographic phenomena. The proposed normalization approaches use the idea of inverse functions to reverse the extracted profile in slant range. The inverse function of the profile is a hypothetical function describing the increase of backscattering values in the range profile in the symmetrically opposite way to the real decrease. If the inverse function is known, then it can be directly applied for flattening the illumination in slant range. Therefore, the problem is to derive the inverse function with a specific incidence angle for the given SAR images.

The inverse function can be derived using an additive inversion. An additive inversion adds the inverse function to create an identity function (i.e., a function that always returns the same value). Additive normalization averages the basic and the symmetric functions according to:

where σθref0 is the normalized radar cross-section at an incidence angle of reference, θ_ref, σθ0 is a specific linear function describing the relation of σ° values and incidence angle(σ) σθ0−1 is the symmetric function of σθ0. The linear function σθ0 describing the relation of σ° values and incidence angle (θ) for a SAR image over the sea is given by:

with a and b being the linear coefficients. The symmetric function σθ0−1 of equation (4) to angle of reference (θ_ref) is:

Symmetric functions can be calculated for any incidence angle, but usually the mean angle of incident is used. The radiometric normalization function should always be preserved so that the actual σθ0 values can be derived. This is crucial, for example, in wind field retrieval and other oceanographic applications. In the present paper, two correction approaches against the well-known cosine squared were examined: a theoretical backscattering shape function derivation based on instrument incidence angle properties and an empirical range fit of σ° based on image content properties.

3 Data Set

An evaluation of the normalization techniques proposed in this paper was carried out using 30 ASAR Wide Swath Mode (WSM) images from the ENVISAT satellite at VV polarization, operating at C-band. SAR images (apart from normalization) were selected for the study of atmospheric phenomena in sea surface [1]. This was ideal for examining the proposed methods in a complex sea environment because the main challenge was to reveal phenomena not visible before normalization. The ASAR WSM dataset was generated from data collected in the ScanSAR mode. This type of product includes slant range to ground range corrections, and it covers a continuous area along the imaging swath of approximately 400 km. The pixel size of the images was 75 × 75 m. The incidence angle was approximately 15° to 45° and the image cover was approximately 400 km in the slant direction and 1000 km in the azimuth direction [25]. The dataset was obtained for the year 2011.

The Aegean Sea was chosen as the case study area (Figure 2) for its unique characteristics. The Aegean Sea represents the north-eastern part of the eastern Mediterranean Sea and is characterized by a complicated hydrographical and ecological structure due to its geographical position. The study area is connected to the Sea of Marmara through the Dardanelles Straits and contains numerous islands and continuously changing winds. Many types of oceanographic phenomena are observed in this study area and are represented in the acquired dataset.

Figure 2

The selected area of study and dataset coverage.

Before the normalization process, calibration and a land masked operation were carried out on each SAR image. For ENVISAT ASAR WSM, the calibration algorithm is described in [26]. Land masking was performed using the Global Self-Consistent Hierarchical High-Resolution Shoreline (GSHHS) provided by NOAA [27]. Both preprocessing steps were executed within the MATLAB environment.

4 Comparison Factors for SAR Normalization

The comparison of the proposed methods was carried out by developing and applying six comparison factors based on the mean and variance values of specific sea areas of SAR imagery. The calculation of the comparison factors was made in σ° [dB] after land masking. Comparison factors were calculated for the original images, before any normalization and after the theoretical and empirical normalizations. The first two comparison factors calculated on whole image statistic parameters. These parameters are biased by the main sea clutter contained in the area covered. For that reason the rest of the four comparison factors calculated for selected regions of interest (ROIs) parameters. Although the sea surface roughness is not constant throughout a SAR image, much effort is given to select ROIs with same sea characteristics. The comparison ROIs was chosen as objectively as possible; with the same size and wind speed, and under exactly the same pixel distance from close and far range edges. To identify the best performing normalization, the sum of the comparison factors was calculated after being log-transformed. Their values are included in the final results for highlighting the performance of the normalization methods. In the next paragraphs, these six factors are described.

5 Results – analysis

In this section, the results produced are presented and analyzed corresponding to the six comparison factors. An example of the normalized images and their scatter plots is illustrated in Figures 3 and 4, respectively.

Figure 3

Image example of normalization: (a) L1B ASAR WSM product, (b) Squared cosine normalization, (c) Theoretical normalization, (d) Linear empirical normalization.

Figure 4

Range profile plots from Figure 3 images: (a) L1B ASAR WSM product, (b) Squared cosine normalization, (c) Theoretical normalization, (d) Linear empirical normalization.

The difference in the coefficient of variation was found very low (maximum 0.4 dB) for all three examined methods, i.e., squared cosine, additive theoretical and linear empirical fit. The latter confirms the initial claim that σ° values’ variability should remain relatively constant before and after normalization. However, the coefficients of variation for the three normalization methods were similar in implying that there is no significant difference among the examined methods. This result illustrates that σ° values do remain relatively constant after normalization, and the actual differences of the normalization methods should be highlighted by the other comparison factors.

The absolute mean column difference (Figure 5) among the original and the normalized methods presented a relatively higher difference between the squared cosine and the other two methods. Squared cosine correction produced the worst column difference of 18 dB, while the mean column difference for the original imagery was 15 dB. This was an awkward result, since the cosine normalization produced results inferior to the original imagery. The latter can be explained by comparing the original imagery and the produced results, not only for the measured columns but for the whole image. Indeed, the cosine normalization was valid for the central part of the image but did not function correctly on the image sides (especially in the close range); therefore, cosine correction is not good enough for the edges in the range direction. On the contrary, linear and theoretical normalizations had a significant reduction (5 dB − 15 dB) in their mean column difference. Linear normalization is the one with the most significant reduction. For all the 30 images examined, linear normalization presented a mean column difference of less than 5 dB. A similar performance was given by the theoretical normalization, with only 7 images having a column difference larger than 5 dB and in all cases smaller than 8 dB.

Figure 5

Results of mean column difference.

Concerning the difference, the variation of σ° due to the existence of several oceanographic phenomena cannot be avoided. On the contrary, the next three comparison factors (i.e. mean window, radiometric error and signalto-noise ratio differences) were based on image windows in the near and far range, selected by the criterion of representing the same sea condition as far as possible. The absolute differences in the mean window were quite similar to the mean column difference. The linear and theoretical corrections presented small differences, mostly lower than 5 dB. In the case of linear normalization, only four images presented a higher difference than 5 dB, with the maximum being 6.18 dB. In the case of the theoretical normalization, three images exceeded the 5 dB difference, but their values ranged from 7.5 to 8.6 dB. Noteworthy were the minimum values of theoretical normalization compared to those of linear normalization. For the former, eight out of thirty examined cases were less than 1 dB, while for the latter only four. The opposite behavior was observed for the squared cosine normalization. The differences for most of the cases were lower than the original image. The same explanation can be given for column difference. While the cosine normalization works to a relatively satisfactory level for the middle part of the image, the normalization does not perform correctly for the edges in the range direction.

The results of the radiometric error difference (Figure 6) were similar to the previous two comparison factors. The linear and theoretical normalizations had differences of less than 0.05 dB, while squared cosine normalization presented values that were mostly larger than 0.1 dB. Both the linear and theoretical normalizations performed very efficiently regarding their normalization ability. Only six images presented values larger than 0.05 dB, and these can be treated as outliers or areas with very different roughness conditions in the near and far range. In addition, squared cosine normalization did not improve the image performance at all.

Figure 6

Results of radiometric error difference.

The results of the signal-to-noise ratio difference had the highest differences among the comparison factors. Theoretical and linear normalization presented values less than 5 dB for the most part, while the original image and cosine correction had higher differences. The lowest differences were recorded for theoretical and linear normalization with values of almost 0.30 dB. Nevertheless, the highest differences of 18 dB were similar for all methods. The signal-to-noise ratio mean values were found important for the comparison. The theoretical normalization with a mean signal-to-noise ratio of 4.81 dB predominated among the remaining methods. The next best result was for the linear normalization with 6.39 dB and the worst for the cosine normalization with 10.09 dB (worse than the original image of 9.25 dB).

The results for the constant describing the mean transect angle clearly showed the difference of cosine normalization from the theoretical and the linear methods. The constant of the mean angle of the cosine correction was between 0.8 and 1.1 dB, while for the other two methods it was almost stable at 0.1 dB. The calculation of the mean transect angles clearly showed the successful normalization of ASAR images for the theoretical and linear methods and their similarities in the produced results.

The six comparison factors showed significant differences. The absolute difference of the coefficient of variation had values in the range 0.1–0.6 dB, while the mean box difference from 0.0 to 30.00 dB. Therefore, the simple sum of the produced results would lead to biased results. The quantitative factor for successful normalization was represented by the sum of the log-transformed measurement results and is shown in Figure 7. The points represent the performance for each image and the line used to highlight the trend of the normalizations although no data exist between them. The best performing normalization is the one with the minimum sum value. Squared cosine correction is clearly not adequate for normalization above the sea. Its performance was unexpected since it did not show any difference from the original image measurements. The opposite happens for the theoretical and linear empirical fit functions, which differ by 2 to 7 dB from the original image; they have similar performance in several cases. Indeed, the performance follows a similar pattern for both normalizations, although the theoretical performance is always below the linear one. Upon a closer look, the theoretical normalization functions were much better than the linear one. From the 30 images examined, 19 (63%) had a significant difference in performance (i.e., larger than 0.5 dB) for the theoretical normalization against the linear one, and 11 images (37%) showed similar performance. Concerning those with a significant difference, the higher value was 2.8 dB and the lowest 0.55 dB, with the majority around 0.8 dB. The sum of the log transform indicated the better performance of theoretical normalization.

Figure 7

Results of comparison factors after summarization and log-transformation.

6 Conclusions – Discussion

The present paper examined different normalization functions for correcting the progressive brightness reduction of SAR WSM images in the range direction over the ocean. The problem is due to the large incidence angle variation from near to far range in WSM images which clearly affects dark spot detection for oil spill classification. Two methods were proposed for correcting the brightness reduction: the theoretical shape function derivation and the empirical range fit. Their efficiency was examined against the squared cosine correction which is based on Lambert’s law for optics. The former methodology exploits a theoretical backscattering profile in the range direction formed by the image geometry (i.e., its incidence angle θ and the theoretical σ° value at a specified wind speed). It can be universally applied to all SAR sensors in ScanSAR mode since it is independent of the image content. However, its limitation is the dependence on a specific wind speed for all images. On the other hand, the empirical range fit calculates the backscattering profile by averaging the pixel values of each image column. It depends on the image content and therefore on any mesoscale oceanographic phenomena present in the image. No additional data is required either for the sea clutter distribution or for the theoretical/modeled backscatter values of the sea surface. It is image-dependent, meaning that every image has its own shape function.

The effectiveness of the normalization functions was examined in 30 wide-swath ASAR images after image calibration over the Aegean Sea. Normalization was made in the middle plane of the 30° incidence angle using six newly developed and introduced comparison factors: one refers to the image as a whole (i.e., the image coefficient of variation), one to the difference in specific columns at near and far range, i.e., column difference, one to the slope of image transects (i.e., lines slope) and three to specific windows in the near and far range (i.e., mean window difference, radiometric error difference and signal-to-noise ratio difference).

Figure 8

Image example of normalization: (a) L1B ASAR WSM product, (b) Theoretical normalization.

From the present study, three main conclusions are derived. Firstly, the cosine squared normalization has the lowest efficiency and in many cases adversely affects the NRCS values in an awkward way. In general, cosine normalization works relatively well for the middle part of the ASAR image but does not perform correctly at the edges in the range direction. This can be seen from the absolute difference of the coefficient of variation, where it presents similar results to the other two normalization methods, i.e., approximately 0.1 dB. On the contrary, in the following three comparison factors cosine normalization presents worse results than the original image. Therefore, it is suggested that cosine correction cannot be used for successful normalization in wide swath SAR data.

Secondly, the theoretical and the empirical normalization functions show similar behavior and present comparable results for each comparison factor. For the image coefficient variation, both methods present high stability and a negligible difference of 0.1 dB was recorded between them. Similarly, the mean column difference highlights the high performance for both methods, with most of the images having differences of less than 5 dB between the near and far range. The mean difference between the two methods is less than 0.05 dB. Therefore, the two methods present equal effectiveness. The same behavior with negligible differences (less than 0.05 dB) was detected for the radiometric error differences and for mean transects angle measurements. Close but comparable results were presented in the mean window and signal-tonoise ratio differences. The theoretical method has better mean window difference value (2.35 dB) than the empirical one (2.45 dB). Finally, the largest difference was recorded for the radiometric error difference, where the theoretical method proved superior to the empirical one by 1.57 dB.

Therefore, taking into account the six comparison factors, it can be concluded that both the theoretical and the empirical methods perform in a reliable and robust way. Nevertheless, after the above measurements are logtransformed and summed, it is clearly shown that theoretical normalization performs better than the empirical. From the 30 SAR images used, 19 presented a better performance for the theoretical normalization than for the empirical one. The remaining 11 images showed similar performance for both normalizations. In conclusion, theoretical normalization can be chosen as the most appropriate normalization method, since it performs better, does not need any information on the image content and requires less computational time.

The outcome of the theoretical normalization function is a new image with stable NRCS values in the range direction. It can be seen as an image of the “sea roughness” directly related with the local wind stress or presence of oceanographic phenomena and can be broadly used for detecting oceanographic phenomena in Wide ScanSAR images.

However, the proposed methods present specific limitations which should be mentioned. Empirical normalization i.e. normalization derived from the image itself is biased by the oceanographic phenomena and might show an opposite tendency. This is intense when large phenomena are present in the images e.g. large low wind areas. In these cases, even image degradation is expected after normalization. On the contrary, theoretical normalization is independent of any present phenomenon. However the method and its parameters are based on limited experimental measurements which were derived in specific polarimetry and wind conditions. While the polarimetric issue can be bypassed using the same polarimetric mode, wind speed is most likely to alter in a 400 km swath. This always happens in complicated sea environments as in the examined Aegean Sea with its numerous islands and bays. Moreover, in the experiment, the measurements which define the parameters in the theoretical normalization did not include the small differences on NRCS due to upwind or downwind sea waves direction in relation to SAR geometry acquisition.

The six comparison factors were carefully developed to represent the performance of the normalization methods, and each one examines the normalization from a different perspective. The overall performance was calculated by log transformed values of comparison factors and the summation of their values. Log transformation was chosen due to unstable scale differences in comparison factors, and summation was performed because all factors were assumed to have the same importance. The selected accuracy performance scheme was simple and effective. In a future study, a more sophisticated statistical accuracy assessment could be examined under a multi-variance logic weighting the comparison factors. In addition, in future work Wide ScanSAR images could be normalized to arbitrary values of NRCS, e.g., not necessarily to the 30° reference incidence angle, and normalization could be examined for wind speeds other than 3 m/s.

The proposed methodology can be applied in new SAR sensors such as Sentinel-1 for the ScanSAR mode.