The detection of ships on space-borne Synthetic Aperture Radar (SAR) imagery is hardly possible, when the ship’s construction material is non-conductive and in turn the ship’s SAR-signatures are not or badly represented in the SAR images [1
]. Instead of searching for the signatures of ships directly, their presence can be determined indirectly through the ship’s wakes [2
]. Since the automatic detection of ships on SAR has become of interest in earth observation, also the automatic detection of wakes is taken into account [3
]. However, the maturity of automatic ship detection methods is further developed than of automatic wake detection methods, what is also reflected by the diverging amount of publications proposing different methods for the detection approaches [4
A similar context can also be observed in the existence of approaches for modeling the detectability of ship or wake signatures in dependency to parameters influencing their detectability in SAR imagery. In the following these parameters will be called influencing parameters. While different approaches for modeling ship detectability have been published in past years and tuned for various SAR missions [10
], a model for the detectability of wake signatures using real data has only been published recently [14
]. However, theoretical assumptions about the dependency of influencing parameters with the detectability of certain components of wakes using simulated data and physical contemplations exist since decades [15
]. The well-known effects of tilt modulation, hydrodynamic modulation, and velocity bunching are the basis for general theories about the emergence of ocean surface waves and their visibility on SAR imagery [16
SAR signatures of ship wakes are categorized into the four main wake components: turbulent wake, narrow V-wakes, ship-generated internal waves, and the Kelvin wake pattern [19
]. The turbulent wake consists of a rough sea region (white water) up to two ship beams aft the ship induced by the propeller and a calm sea region beginning after it and persisting up to tens of kilometers caused by the attenuation of ambient short surface waves by ascending bubbles and surfactants. The rough sea region is responsible of high radar backscatter due to the strong turbulence and breaking waves while the calm sea region is responsible of low radar backscatter due to the smoothed surface [20
]. By turbulent wake in this study we only refer to the long and smooth region, as the white water region is observable almost independently from the influencing parameters and easily confused with the ship signature itself. The Kelvin wake pattern consists of transverse, divergent, and cusp waves [23
]. The cusp waves lie on the Kelvin wake arms and constitute the dominant backscattering responsible for the detectability of the V-shaped Kelvin envelope [15
]. In this study only high resolution SAR data acquired from the TerraSAR-X satellite at a center frequency of 9.65 GHz (X-band) is used. Therefore, the narrow V-wakes cannot be taken into account as their half angle on X-Band is so small that they are expected being consumed by the turbulent wake [19
]. According to [26
] the visibility of Bragg-based scattering generated by both narrow V-wakes and ship-generated internal waves depends on variety of mechanisms making them also difficult to discriminate. Indeed, Bragg waves can be modulated by ship-generated internal waves on the ocean surface making them also visible on X-Band [27
], but their emergence depends among other things on the water depth and the presence of either surface films or interactions with surface currents [19
]. These kinds of influences can neither be derived from SAR automatically nor be provided by oceanographic models in adequate resolution. The requirement for a large dataset in this study only permits the consideration of influencing parameters which are automatically derivable. This means internal waves cannot be regarded appropriately and the scope of this study is restricted to the detectability of only two main wake components: turbulent wake and Kelvin wake.
Literature is rich in publications describing the dependency of influencing parameters with the detectability of turbulent wake and Kelvin wake. Most of the conclusions are in good agreement with each other. The following paragraphs are dedicated to reviewing previous studies about detectability of ship wakes in dependency to the influencing parameters investigated in this study.
Lyden et al. [19
] state that the whole Kelvin envelope is best detectable when observed in alignment with the azimuth direction, and the individual cusp waves are better visible when traveling into range direction. This statement is also supported by [15
] and [23
], while in [15
] it is pointed out that cusp waves propagating towards the radar-looking direction show an increase in backscatter relative to the surrounding and cusp waves propagating away from the radar-looking direction show a decrease in relative backscatter. Lyden et al. [19
] further suggest that for turbulent wakes the relative-looking direction to the ship track is less influencing, but a relative looking direction perpendicular to the ship track produces the best results.
] the authors pointed out that turbulent wakes and Kelvin wakes are best visible under moderate wind conditions, i.e. wind speed in the value range 2.5–10 m/s [22
]. Hence, the minimum wind speed considered in this study is 2 m/s being also the minimum wind speed retrievable from SAR imagery [29
], and the maximum wind speed is 10 m/s. Hennings et al. [15
] describe that the Kelvin wake arms are better visible with lower wind speeds, as the contrast between cusp waves and background sea surface roughness decreases under the influence of higher wind speeds. Additionally, an outcome of the analysis conducted in [15
] is the low dependency of detectability of Kelvin wake arms to relative wind direction.
] the author suggests that signatures of turbulent wakes are visible also under moderate sea state conditions due the destruction of the ambient wind-generated waves by the wake’s currents, although their extent is larger in low sea state conditions. This is confirmed by Tunaley at al. [24
] at least for large vessels. Additionally, wakes generated by large vessels with slow velocities would further be visible under low sea state conditions and azimuthal wind direction. Reference [24
] further stated that the Kelvin wakes are less visible in high sea state conditions and proposed that velocity bunching produced by transverse waves is responsible for this. The worse detectability of turbulent and Kelvin wakes in high sea state conditions is also confirmed by Zilman et al. [18
Kelvin wakes are expected being better visible in HH-polarized images compared to VV-polarized images [15
]. For the turbulent wakes no definite conclusion about the difference regarding HH and VV polarization was found in the literature, but the SAR imaging of water surfaces smoothed by the turbulent wakes is similar compared to water surfaces smoothed by oceanic surface films. For oceanic surface films, Gade et al. [31
] found that there is no significant difference between detectability on HH- or VV-polarized images. A slightly better total detectability on HH images compared to VV images was also found by [14
]. As the difference in dependency of detectability to influencing parameters is insignificant, HH and VV are not distinguished in this study.
The influence of the radar’s incidence angle on wake detectability is similar for turbulent and Kelvin wakes. While [15
] states that the detectability of Kelvin wake arms decreases, when the incidence angle increases, according to [32
] the detectability of smoothed ocean surfaces, such as turbulent wakes, also decreases with increasing incidence angle.
The model we proposed in [14
] only takes three influencing parameters into account at a time and assumes a linear dependency between the influencing parameters and the detectability of wakes. Especially for influencing parameters with units measured by degree, a linear model basis is assumed insufficient. Further, all influencing parameters must be considered simultaneously in one model in order to obtain comparable probability of detection estimates. This paper presents results achieved using a model with higher complexity and able to take into account all the influencing parameters introduced in [14
] together. Besides these influencing parameters, additional influencing parameters are included and evaluated. Finally, possible applications of the extended wake detectability model are demonstrated.
2. Materials and Methods
The flow-chart in Figure 1
displays the overall procedure divided in three main steps: Extraction of labelled wake samples (Figure 1
A); extraction of the influencing parameters from these samples (Figure 1
B); and building of the detectability model and its visualization (Figure 1
C). The first two steps are fully described in the remainder of this section while the third step deserves a dedicated section which follows-on.
The data used in this study is based on a dataset of 791 high resolution TerraSAR-X scenes acquired between the years 2013 to 2017 in North Sea, Baltic Sea and Mediterranean Sea. The scenes were acquired in Stripmap or Spotlight mode mostly with HH-polarization (in detail: 530 HH-polarized, 81 VV-polarized and 180 dual-co-polarized images). For all images, at least one ship’s self-reporting message via the Automatic Identification System (AIS) was available. AIS provides information about ship properties like speed over ground or vessel location, which were used as influencing parameters as well as to identify possible locations of wake signatures. For the latter, an automatic intersection of AIS with the SAR images was executed to assign AIS messages to image regions. A manual correction of these colocations was performed to let the unreliable AIS data fulfill ground truth requirements, which means colocations have been discarded in case of large amounts of artifacts like ambiguities or marine objects being present. Then on the basis of these two datasets co-located in space and time a manual search for moving vessels was conducted (Figure 1
(A.1)). During the search the background of the moving vessels was checked for unambiguous visibility or non-visibility of wake signatures. By doing so to each wake sample either the class label “detected” or “not detected” was assigned (Figure 1
(A.2)). Detailed information about the manual inspection procedure can be found in [14
The detectability of wake signatures is affected by a number of influencing parameters (Figure 1
(B.3),(B.4),(B.5)). A comparison of Pearson product–moment correlation coefficients was conducted in order to select influencing parameters with distinct physical background. The correlation coefficients are calculated for each influencing parameter between the parameter’s magnitudes of all wake samples and their respective class labels, where “detected” was quantified as 1 and “not detected” as 0. Figure 2
shows a graph with all twelve compared influencing parameters and their absolute correlation scores. From influencing parameters with redundant physical background the respective influencing parameters with lower absolute correlation score were discarded (Figure 1
(B.6)). The discard applies to the following three redundant influencing parameters: WRF-Wind-Direction, which describes the relative wind direction from the Weather Research and Forecasting Model (WRF) towards the radar beam, SAR-Significant-Wave-Direction, which describes the relative wave direction towards the radar beam, and AIS-Width, which defines the width of the ship producing the wake.
A description of the remaining nine influencing parameters can be found in Table 1
. It was decided to not apply any further dimensionality reduction technique as a meaningful, distinct physical background of the influencing parameters is supposed to be more important than expressive or independent parameters. Extreme characteristics of the influencing parameters only rarely occur in reality, e.g., small ships can hardy travel at high wind speeds and sea state conditions, or large ships cannot exceed their hull speed. Thus, the value range of the nine selected influencing parameters was restricted in order to obtain a nine dimensional space non-sparsely filled with wake samples, reducing the risk of curse of dimensionality as well (Figure 1
(B.7)). Additionally, the value range of influencing parameters measured in degrees was projected down from 0°–360° to 0°–90°. The performed projection is displayed in Figure 3
. In this way the complexity of the detectability model is reduced significantly, because only one detectability peak must be modeled, instead of two with reversed direction as in [15
]. After discarding all wake samples with influencing parameters outside the defined value range, a training dataset consisting of 2156 labelled wake samples was concluded (Figure 1
The linear wake detectability model presented in [14
] has been extended by a non-linear basis using a Support Vector Machine classifier with a polynomial kernel of second grade. The model classifies the input data between the classes “detected” and “not detected”, where the probability of class affiliation to the class “detected” is taken as measure for the probability of detection of ship wakes in SAR imagery. Nine influencing parameters, which are affecting the detectability, are considered simultaneously in a single model. Thus, the model can represent not only the dependency of detectability from the influencing parameters, but also depict interdependencies between them. The influencing parameters describe different environmental conditions (i.e., wind speed, wind direction, sea state height, sea state direction and sea state wave length), ship properties (i.e., size, heading, and velocity) and image acquisition settings (i.e., incidence angle, beam looking direction).
Most of the statements about the influencing parameters are theoretically expected, but in this publication they are quantitatively proven using real data. The main outcomes are:
The higher the vessel velocity the higher the detectability
The radar beam looking direction and the ocean waves’ traveling direction should be perpendicular to the angle of Kelvin wake arms for higher detectability
Rough, inhomogeneous ocean surface conditions worsen the detectability
Slow ships are better detectable with lower incidence angles or shorter wavelengths of ocean surface waves and fast ships are better detectable with higher incidence angles and longer wavelengths of ocean surface waves
Beside the statements about the interdependencies of the different influencing parameters, the presented detectability model can also be applied to control an automatic wake detection system. Another possible application of the model is the estimation of minimum vessel velocities, which must be present in order to make the ship produce a detectable wake signature, by inverting the model and setting a fixed level for probability of detection.