The Canadian Forces Meteorology and Oceanography Center produces a near-daily ocean feature analysis, based on sea surface temperature (SST) images collected by spaceborne radiometers, to keep the fleet informed of the location of tactically important ocean features. Ubiquitous cloud cover hampers these data. In this paper, a methodology for the identification of SST front signatures in cloud-independent synthetic aperture radar (SAR) images is described. Accurate identification of ocean features in SAR images, although attainable to an experienced analyst, is a difficult process to automate. As a first attempt, the authors aimed to discriminate between signatures of SST fronts and those caused by all other processes. Candidate SST front signatures were identified in Radarsat-2 images using a Canny edge detector. A feature vector of textural and contextual measures was constructed for each candidate edge, and edges were validated by comparison with coincident SST images. Each candidate was classified as being an SST front signature or the signature of another process using logistic regression. The resulting probability that a candidate was correctly classified as an SST front signature was between 0.50 and 0.70. The authors concluded that improvement in classification accuracy requires a set of measures that can differentiate between signatures of SST fronts and those of certain atmospheric phenomena and that a search for such measures should include a wider range of computational methods than was considered. As such, this work represents a step toward the goal of a general ocean feature classification algorithm.
To provide near-daily manual assessments of the location of sea surface temperature (SST) fronts, such as the Gulf Stream North Wall (GSNW), the Canadian Forces Meteorology and Oceanography Center (MetOc) in Halifax, Nova Scotia, currently produces operational ocean feature analyses (OFAs) for its fleet. OFAs are based on SST images from the Moderate Resolution Imaging Spectroradiometer (MODIS; King et al. 1992) and the Advanced Very High Resolution Radiometer (AVHRR; Hastings and Emery 1992). A mean annual cloud cover of more than 70% heavily contaminates these data in the region of the Gulf Stream, according to the International Satellite Cloud Climatology Project (http://isccp.giss.nasa.gov). Synthetic aperture radar (SAR) images of the ocean surface are independent of cloud cover, have long been known to exhibit signatures of SST fronts (Vesecky and Stewart 1982), and therefore represent a potential source of additional information. As such, the Spaceborne Ocean Intelligence Network (SOIN) has been tasked to develop and implement techniques that exploit SAR images from the Radarsat-2 satellite to complement SST images in the production of OFAs.
SAR images of the ocean’s surface capture spatial patterns in the amplitude of Bragg waves that are signatures of wind-induced surface roughness modulated by co-occurring atmospheric and oceanographic processes (Vesecky and Stewart 1982). Synoptic-scale atmospheric fronts (Young et al. 2005), convection cells and roll vortices in the marine atmospheric boundary layer (MABL) (Sikora and Ufermann 2004), and the entrainment of surfactant in ocean eddies (Ivanov and Ginzburg 2002) are but a few of the many processes that produce identifiable signatures in SAR images. Others include surface current shear, ocean upwelling, heavy precipitation, phytoplankton blooms, and internal waves (Holt 2004).
With such a large number of possibilities, manually assigning a cause to a given signature or feature can be a considerable challenge to analysts not familiar with SAR images. It was therefore deemed necessary to facilitate manual analysis with objective information provided by an automated procedure. Feature identification and classification in over-ocean SAR images is widely acknowledged to be a difficult process to automate. As a first step, we set out to develop an algorithm that can discriminate SST front signatures from those of all other processes using a method similar to that of Borghys et al. (2006). Therein, the classification of features in overland SAR images begins with binomial classification using logistic regression. Features are classified as being either 1) forests or hedges or 2) other. A multinomial classifier is subsequently applied to features that fall into the second of these classes. In a similar way, we aimed to classify features in over-ocean SAR images as being either 1) SST front signatures or 2) other.
The subjects of our analysis are candidate SST front signatures consisting of edge-like features in SAR images. Changes in the MABL forced by a positive ocean–atmosphere buoyancy flux on the warm side of a mesoscale SST front include a reduction in near-surface stability, the convective transport of momentum from the upper MABL toward the surface, and the formation of horizontal pressure gradients (Small et al. 2008). These processes combine, in various degrees, to enhance near-surface horizontal winds on the warm side of the SST front, which force an intensification of surface roughness compared to the cold side of the front. This results in a gradient in the backscatter that sometimes resembles the gradient in SST, including a sharp boundary or edge between regions of large and small backscatter (e.g., Beal et al. 1997). Signatures resembling bright or dark filaments that may be produced by current shear or surfactant entrainment (Johannessen et al. 1996; Ivanov and Ginzburg 2002) are commonly collocated with SAR images of the GSNW and therefore can also inform its location.
In this paper, we describe a three-step classification procedure. Candidate SST front signatures are first identified using an edge detector. Although sophisticated methods have been devised to automatically identify SST fronts in various types of satellite images (e.g., Cayula and Cornillon 1992; Wu and Liu 2003), most were not designed to detect thin filaments. We therefore chose to use a simple detection algorithm, the Canny edge detector (Canny 1986), which is inclusive of edges of all types. Once an edge is identified, logistic regression is applied to a feature vector, consisting of a set of associated textural and contextual measures, to estimate the probability that it is an SST front signature. A decision rule then assigns a classification. It will be shown that our procedure leaves room for improvement, and as such we discuss modifications to the algorithm that may result in better performance and speculate as to how a more general procedure of classification may be constructed for over-ocean SAR images.
2. Data and methods
a. Gulf Stream North Wall search region
The North Atlantic subtropical gyre (Ebbesmeyer et al. 2011) is a current system driven by differential solar heating, persistent winds, and the Coriolis effect. Its western component is the Gulf Stream, a jet of warm water that emerges from the Florida Straits; flows northward along the eastern coast of North America as far as Cape Hatteras; and then turns eastward, eventually bifurcating near 50°W into the North Atlantic Current and the Azores Current. The location of the Gulf Stream was expected to be relatively easy to identify in SAR images, especially along its northern edge, where SST gradients are usually large. For this reason, we decided to aim in particular to identify signatures of the GSNW in SAR images.
We first set out to construct an envelope inside which the GSNW is expected to exist, using data from the Hybrid Coordinate Ocean Model (HYCOM) consortium, a multi-institutional project supported by the National Ocean Partnership Program (NOPP) (Thacker et al. 2004). Daily model-assimilated images at 12-km resolution from 2003 to the present are freely available online (http://www.hycom.org). Daily HYCOM SST and sea surface height (SSH) anomaly images for June 2003–July 2008 were collected, constituting approximately 1800 images. SST data were first analyzed, but the results were difficult to interpret. We could not clearly delineate the location of the GSNW by automated edge detection in many of the SST images because of apparent horizontal mixing in the surface layer sometimes resulting in small SST gradients across the GSNW. We therefore turned to the SSH data, with the assumption that the boundary between positive and negative SSH anomalies can be used as a proxy for the location of the GSNW.
The edge between regions of positive and negative anomalies in each SSH image was determined using a simplified version of the front detection algorithm developed by Cayula and Cornillon (1992), in which histogram analysis was applied to the entire image without window or local analysis and without application of the cohesion algorithm. This produced accurate boundaries along the contour of mean elevation (i.e., zero anomaly) due to the simple structure of the SSH data, which was dominated by a well-defined gradient directed toward the center of the North Atlantic subtropical gyre. SSH images were converted into binary maps with ones and zeros indicating the shoreward and seaward sides of the detected edge. The node of the first eigenvector of the set of all binary images was taken to be the southern boundary of the GSNW. A two-dimensional histogram of the location of the edges was constructed from which a northern boundary was determined. We defined the region between the southern and northern boundaries to be the GSNW search region (GSNWSR) (Fig. 1).
As the Gulf Stream moves north from the Florida Straits, the amplitude of horizontal oscillations or meanders in its flow are constrained by bathymetry (Savidge 2004). A numerical study indicated that barotropic and baroclinic instabilities in the Gulf Stream, forced by a combination of large curvature in the isobaths and the topographic elevation of the Charleston Bump (see Fig. 1), initiate meanders with wavelengths of 100–250 km that propagate at a rate of 30–40 km day−1 (Xie et al. 2007). These meanders typically decline in amplitude as they approach Cape Hatteras (Savidge 2004). A relaxation in the bathymetry constraint beyond Cape Hatteras results in quasi-stationary meanders driven by baroclinic instabilities with typical wavelengths of 180–460 km. Past 68°W, these instabilities can lead to the calving of cold- and warm-core eddies (Savidge 2004). The GSNWSR in Fig. 1 widens slightly just past the Charleston Bump and gradually narrows as it approaches Cape Hatteras. It then widens again as it extends past Cape Hatteras, becoming markedly wider at about 68°W. The GSNWSR (and the HYCOM SSH data from which it was derived) therefore captures realistic variability in the trajectory of the Gulf Stream.
b. Data collection and image processing
Radarsat-2 is a commercial SAR satellite designed and built by MacDonald Dettwiler and Associates Ltd. (MDA) in partnership with the Canadian Space Agency (CSA) (http://www.radarsat2.info). Launched in December 2007, the satellite can measure C-band (5.405 GHz), quad-polarization (VV, HH, VH, HV) backscatter using one of several transmit pulse bandwidths (11.6, 17.3, 30, 50, and 100 MHz), on a 24-day repeating, near-polar, sun-synchronous orbit. Images are distributed via a global network of ground receiving stations. The ScanSAR Narrow A (SCNA) beam mode on Radarsat-2, providing images covering a 300 km by 300 km area with incident angles from 20° to 39°, is suited for identifying large-scale features such as SST front signatures. This mode is available in single polarization (one of VV, HH, HV, or VH) or dual polarization (VV+VH or HH+HV). For our study, dual polarization (VV+VH) was selected, with all analysis being conducted on VV images, chosen because scattering by Bragg waves is strongest in VV polarization in the C band (Holt 2004). The VH images were used for other components of the SOIN project.
An average of 80 VV+VH SCNA frames, with a pixel spacing of 25 m and a nominal resolution of 50 m, are being collected each month starting in September 2008. SST images, consisting of composite MODIS and AVHRR images produced by taking the maximum SST value at each pixel, with a nominal resolution of approximately 1 km, were also collected. Although MODIS data are available at significantly higher resolution, we decided that 1 km would be sufficient for an operator to identify signatures of the GSNW in the SAR images by visual comparison with SST. Radarsat-2 images were each paired with a concurrent composite SST image, when available, with concurrence defined as acquisition within ±3 days. This fairly large range was necessary because of the paucity of data, where cloud cover renders unusable between 70% and 90% of the SST images. Image processing was implemented using Image Analyst Pro (IA Pro), a software package developed by Defense Research and Development Canada (DRDC), (Secker and Vachon 2007). The SAR Ocean Feature Detection Tool (SOFDT) in IA Pro subjects a Radarsat-2 image to a land mask; then to a special median filter to remove ship signatures; and then to block averaging, which increases pixel spacing from 25 m (12 000 by 12 000 pixels) to 300 m (1000 by 1000 pixels). The reduction in image size saves on computation time and also removes some of the high-frequency variability (i.e., noise) from the image. The SAR image is then subjected to one processing stream to prepare it for ocean feature detection and another to estimate SAR-derived wind speed (SDW).
To prepare an image for edge detection, it is first radiometrically flattened. Large changes in look angle required to obtain a scene size of 300 km by 300 km results in systematic variation in backscatter in the range direction. This is caused by the increase in attenuation of the return signal with distance, as well as changes in the amplitude of Bragg scattering as a function of incident angle. Radiometric correction removes this apparent variation in backscatter. Using IA Pro, resolution-reduced images were radiometrically flattened by fitting and subtracting a two-dimensional third-degree polynomial.
IA Pro’s SOFDT uses a Canny edge detector (Canny 1986; for a discussion of other methods of edge detection, see Kirbas and Quek 2004) to identify edges, which requires noise-free images. High-frequency variation in backscatter, known as speckle, is an inherent property of SAR images caused by wave interference in the return signal. Speckle has the effect of introducing multiplicative noise to a SAR image and constitutes a large proportion of the total variance in over-ocean SAR images. Although resolution reduction by block averaging mentioned previously removes some speckle, a significant amount remains. IA Pro’s SOFDT applies a Gaussian-smoothing kernel to the radiometrically flattened image to further reduce the remaining speckle prior to edge detection. This leads to some loss of information due to Gaussian blur, but the loss is confined mainly to finescale detail. For the purpose of detecting signatures of large-scale SST fronts, a Gaussian-smoothing kernel is appropriate. Methods of speckle reduction that avoid Gaussian blur include the use of wavelets (Pizurica et al. 2001; Wu and Liu 2003) as well as patched-based approaches (Deledalle et al. 2009).
An empirical C-band geophysical model (CMOD) is used in IA Pro’s SOFDT to produce SDW. In our analysis, CMODifr2K (Vachon and Dobson 2000) was selected from a range of choices in IA Pro. Although the inherent pattern in the amplitude of Bragg waves on the ocean’s surface is driven primarily by near-surface winds, the apparent pattern in normalized radar cross section depends upon radar incident angle, wavelength, polarization, and the orientation of the crests of the Bragg waves with respect to the radar (e.g., Young et al. 2008). The CMOD takes these factors into account to estimate wind speed. Because the wind directions cannot be resolved in a SAR image in a way similar to traditional scatterometers, the CMOD requires independently acquired wind directions, which in IA Pro can be provided by a variety of sources. For our study, we used Quick Scatterometer (QuikSCAT) (Liu 2002) level-3 data obtained from the National Aeronautics and Space Administration (NASA) Physical Oceanography Distributed Active Archive Center (PO.DAAC) website (http://podaac.jpl.nasa.gov/).
c. Candidate SST front signatures
The Canny edge detector was applied in IA Pro’s SOFDT to radiometrically corrected, speckle-reduced SAR images to produce candidate SST front signatures. The edge detector was also applied to corresponding SDW images. To justify concatenating textural measures from both SAR and SDW images into a feature vector, a one-to-one correspondence between Canny edges detected in a SAR image and those found in the corresponding SDW image was assumed (i.e., the same Canny edge appears in both images), although anomalous edges in the SDW do sometimes occur (Beal et al. 2005; Young et al. 2007). Only Canny edges greater than 21 km (70 pixels) in length were included in the analysis, for no other purpose than to reduce the number of SST front candidates to a manageable level for manual validation by comparison with SST data. Also, edges that occurred in regions where the SDW was greater than 10 m s−1 or where the backscatter was close to the noise floor were excluded from the analysis.
d. Feature vector components and validation
A statistical classification algorithm generally consists of a set of measures or feature vectors and a rule that partitions feature space into regions, one for each class. In land applications, classification algorithms have been constructed based upon measures of entropy (H) and angle (α), which are both obtained from polarimetric decomposition of quad-polarization images in the form of the complex vector (SHH+SVV, SHH−SVV, and 2SVH), in which SVH represents horizontally polarized backscatter from a vertically polarized transmitted pulse, with SVV and SHH being similarly defined. Computed using values contained in a small window around each image pixel, α ranges from 0° to 90° and is associated with the type of scattering (surface, volume, or multiple scattering), whereas entropy ranges from 0 to 1, with lower values occurring when a single scattering mechanism is dominant. Higher values of entropy are associated with backscatter from a collection of highly anisotropic scattering elements, such as a forest canopy. The location of a feature vector in the (H, α) plane can be used as an unsupervised classifier (Cloude and Pottier 1997; Lee et al. 1999; Neumann et al. 2009).
Radar reflectance from the ocean surface is mainly due to Bragg or resonance scattering, which is a low entropy scattering mechanism. Furthermore, Radarsat-2 quad-polarization data are only available to a maximum nominal scene size of 25 km by 25 km, which we judged to be too small to routinely capture potentially large-scale features, such as signatures of the GSNW. Radarsat-2 quad-polarization data also has a pixel spacing of less than 10 m, which is too fine for meaningful comparison with SST images resolved to 1 km. Classification based upon the (H, α) plane was therefore considered to be inappropriate for our study, and we turned to the use of textural and contextual information to construct feature vectors.
A key assumption in our analysis was the existence of a set of feature vector components that can discriminate between SST front signatures and those of other atmospheric and oceanographic processes. To maximize the probability of meeting this assumption, we aimed to extract a fairly large number of measures, using the reduced resolution and radiometrically flattened SAR images, SDW images, Gaussian-smoothed SDW (GSDW), and Gaussian-smoothed SDW-squared (GSDW2) images.
For example, atmospheric processes forced by SST have been observed to produce modulations in the divergence and curl of the wind stress vector field that are linearly related to the downwind and crosswind components of the SST gradient, respectively (Chelton et al. 2001; O’Neill et al. 2010; Xie et al. 2010). To take this into account, textural measures were obtained from the curl and divergence of the SDW, GSDW, and GSDW2 images.
As with the smoothing kernel applied prior to Canny edge detection, IA Pro allows the user to specify the window size and standard deviation of the kernels that produce GSDW and GSDW2. For our study, a window size of 13 pixels by 13 pixels and a standard deviation of 5 pixels were selected for all smoothing kernels, which were chosen by trial and error to produce Canny edges that accurately captured edges visible by eye.
A feature vector for each candidate SST front signature, composed of a total of 35 contextual and textural measures, was constructed using IA Pro’s target analysis tool. Each row in Tables 1a,b describes one feature vector component. The first column in each table indicates the source image of the feature component. The second column indicates the pixels used, where “edge” means pixels on the Canny edge, “center” means the pixel midway along the edge, and “polygon” means pixels within a polygonal region around the edge. The third column gives a description of the feature vector component. The last three columns will be described in a subsequent section. Each feature vector was assigned a label (1 = SST front signature; 0 = other) by manual comparison with concurrent SST images using IA Pro’s autoblend feature, which allows the user to dynamically adjust the visual blending of two images. A total of 1441 labeled feature vectors were collected from 58 Radarsat-2–SST image pairs, and it this dataset that we used to train our classification algorithm.
3. The classification algorithm
The capture probability (Pcap) is the probability that a feature vector manually labeled as an SST front signature is automatically classified as such. The efficacy (Peff) is the probability that a feature vector automatically classified as an SST front signature is manually labeled as such. Generally, efficacy is increased when greater evidence is required before a feature vector is classified as an SST front signature, but this may be accompanied by a decrease in capture probability, depending upon how well separated the labeled feature vectors are in feature space. In constructing a classification algorithm, the objective is to identify a subset of feature vector components and a set of model parameters that maximize the efficacy while maintaining an acceptably high capture probability. Note that some sources designate capture probability as producer’s accuracy and efficacy as user’s accuracy (Tso and Mather 2009). In the context of meteorological forecasting, capture probability and efficacy are congruent to hit rate and one minus the false-alarm rate, respectively (Mason 1982).
Logistic regression (Hilbe 2009) was used to estimate the probability that a labeled feature vector x = (x1, … , xk) is an SST front signature, as given by
where Z is a linear combination of the feature vector components, each with its own units, standard deviation (σi) and coefficient (ai). In order for Z to be meaningful, feature vector components must be normalized to make them dimensionless. This was accomplished by dividing each component by its standard deviation computed from all available data. A hard classification was generated for each labeled feature vector by comparing its assigned probability to a specified decision bound 0 < Pb < 1. A labeled feature vector was classified as being an SST front signature when the probability in Eq. (1) was greater than the decision bound. By this means, the k-dimensional feature space was partitioned into two half spaces by the hyperplane defined by
The hyperplane in Eq. (2) is oriented perpendicular to the mean probability gradient of the labeled feature vectors in feature space. The plane is moved along the gradient by changing the decision bound. Moving the decision bound closer to zero results in a greater capture probability but also falsely classifies more labeled feature vectors as SST front signatures, thus reducing efficacy. Moving the decision bound closer to one increases efficacy but, by demanding stronger evidence that a labeled feature vector is an SST front signature, falsely rejects more vectors with SST front signature labels, thus reducing the capture probability. The performance of the classification algorithm therefore depends upon the location and slope of the hyperplane specified by parameters μ, a1–ak, and Pb.
a. Preliminary study
Initially, a study was conducted in which each feature vector component from Table 1 was tested individually. Tests were conducted by fitting each component to Eq. (1) using all 1441 labeled feature vectors, where 294 of which were labeled as SST front signatures. We performed the initial study using a decision bound of Pb = 0.20, reasoning that information content must be significant whenever the probability assigned by Eq. (1) was greater than the a priori probability that a randomly selected feature vector was manually labeled as being an SST front signature.
The fourth column of Table 1 gives the p value for each feature vector component provided by the function glmfit1 in Matlab (Mathworks) for the null hypothesis that the feature vector component contains no classification information (i.e., that the probability of correct classification is not significantly greater than the a priori probability 0.20). The p value is the probability of incorrectly rejecting this hypothesis; small p values provide evidence that the null hypothesis is false. The fifth and sixth columns of Table 1 give the efficacy and capture probability for each feature vector component. Efficacy can be interpreted by considering the fact that, if class were determined by the toss of a coin, the efficacy would be equal to the a priori probability of 0.20. Small p values therefore occur when efficacy is significantly greater than 0.20. This initial study demonstrated that only 11 feature vector components contain classification information, identified by p values less than 0.01 (indicated by boldface in Table 1). These included seven contextual measures obtained from SAR Canny edges and four textural measures obtained from SDW and its smoothed variants.
b. Variable selection
Feature vector components were subjected to a stepwise forward selection procedure (Guyon and Elisseeff 2003) to obtain an optimal model. At each step in this procedure, 1009 (70%) of the labeled feature vectors were selected randomly without replacement to comprise a set of training data. The function glmfit, set for binomial data with the logit link function, was applied to the training data to estimate model parameters μ and a1–ak. The resulting parameters were then used in Eq. (1) to calculate probabilities for each labeled feature vector in the set of test data, composed of the remaining unselected 432 (30%) labeled feature vectors. The test-data capture probability and efficacy were then computed using Pb = 0.50. This process was repeated 2500 times at each step so that the standard deviation of the mean test-data capture probability and efficacy would be at most 0.01.
Feature vector components were entered into the model one at a time, starting with the component that provided the greatest test-data efficacy. At each step, all feature vector components not already in the model and not strongly correlated with components already in the model (|ρ| < 0.75) were tested. The component that resulted in the greatest increase in mean test-data efficacy was accepted into the model. In cases where more than one component resulted in the same increase in test-data efficacy, the one that resulted in the smallest decrease in test-data capture probability was chosen. This process was continued until the incremental increase in test-data efficacy dropped below 0.01.
The result of the forward selection procedure was a model containing only three of the 35 feature vector components: x1, the distance between the endpoints of a Canny edge on the SAR image; x2, the length of the Canny edge on the SAR image; and x3, the mean Canny edge strength on the SDW image. The model that resulted, with coefficients averaged over 2500 replicates, is
The p value for the null hypothesis that the component does not contain classification information was 0.0000, 0.0025, and 0.0031 for x1, x2, and x3, respectively.
As previously mentioned, our study was limited to Canny edges greater than 21 km (70 pixels) in length. To examine the effect of this constraint on the model, Eq. (3) was used to compute the probability for an edge of x2 = 21 km in length, with a distance between endpoints of x1 = 15 km (the mean distance between endpoints for a Canny edge of length 21 km as determined by regressing x1 onto x2) and a mean Canny edge strength from SDW (x3) equal to the mean observed value. Using values for σ1, σ2, and σ3 computed from all data, Eq. (3) gave Prob(SST signature) = 0.10. This low probability suggests that the decision to exclude Canny edges less than 21 km in length, undertaken for practical reasons, did not artificially bias the model to assign larger probabilities to longer edges, as the model predicts that the excluded edges would not have been expected to be classified as SST front signatures.
c. Model evaluation
The mean efficacy and capture probability was computed from 2500 runs, with splits of training and test data [labeled feature vectors x = (x1, x2, x3)], using decision bounds 0.40, 0.50, and 0.60. The results are shown in Table 2. Efficacy ranged from just above 0.50, when the capture probability was 0.26, up to 0.70, which would be acceptable except that it came at the cost of the very low capture probability of 0.11. This result tells us that the labeled feature vectors x = (x1, x2, x3) often do not contain sufficient information to distinguish between a Canny edge that is the signature of an SST front and a Canny edge that is the signature of some other process.
Geometrically, this means that the labeled feature vectors x = (x1, x2, x3) are not well separated in feature space, as shown in Fig. 2, where red circles indicate the feature vectors that were labeled as SST front signatures, and blue circles indicate those that were labeled as signatures of some other process. The translucent gray plane is the decision bound of Eq. (2) when Pb = 0.50. All of the circles above the plane were classified as SST front signatures, although only 57% of them are red (Peff = 0.57). This includes 16% of all of the red circles (Pcap = 0.16); the remaining 84% of the red circles are below the plane and were therefore misclassified.
d. Case study: A meander in the Gulf Stream
A Radarsat-2 SCNA VV image acquired at approximately 2230 UTC 7 March 2009, with geographical extent indicated by the box in Fig. 1, is shown in Fig. 3a. This SAR image contains signatures of atmospheric and oceanographic processes via their effect on surface roughness, and was chosen to test the ability of the classification algorithm to discriminate between the two. Collocated maximum pixel composite MODIS SST data acquired between 1333 and 1851 UTC 7 March 2009 (i.e., between 3 and 9 h earlier) is shown in the box in Fig. 4, where small gaps have been filled using bilinear interpolation. The SST image validated the identification of features in the SAR image, which included (i) a band of reduced backscatter caused by the stabilizing effect on the MABL of a cold-water intrusion from the north, where the western boundary of which is marked by a thin bright line indicating convergence in Bragg waves likely forced by current shear; (ii) bright and dark filaments to the immediate north of the meander that resemble signatures produced by current shear and surfactant entrainment in eddies (cf. Ivanov and Ginzburg 2002); and (iii) dark patches indicating surfactant concentrations in cold water accumulated in the lee of the meander. From our experience, these are common features in SAR images of meanders in the Gulf Stream, and they correspond to features evident in Fig. 4: (i) cold-water intrusions along the eastern edge of each meander; (ii) patches of warm water sheared by horizontal mixing processes from the northernmost portion of each meander; and (iii) pockets of cooler water where biogenic surfactants generated by the spring phytoplankton bloom may be concentrated, although concurrent satellite-derived estimates of phytoplankton biomass were not available to confirm this. An additional common feature is the chain of Kelvin–Helmholtz shear eddies (Ivanov and Ginzburg 2002) that can be seen near 40°N in Fig. 4, along the interface where cold and relatively freshwater from the slope current flowing southwest along the shelf break meets the warm and more saline water of the Gulf Stream.
Meteorological data (not shown) indicated a high pressure system centered to the southeast of the SAR image with a synoptic-scale front in the vicinity (see the National Oceanic and Atmospheric Administration Surface Analysis for 0000 UTC 8 March 2009 at http://www.hpc.ncep.noaa.gov/html/sfc_archive.shtml). Evident within Fig. 3a are several east–west oriented lines, which are due to bands of horizontal wind shear (labels d). The features in the vicinity of label e are akin to previous reports of the SAR signature of precipitating convection (Alpers and Melsheimer 2004). The dashed line in Fig. 3a indicates a boundary that inside of which is a region where surface roughness was apparently reduced, corresponding to slightly cooler water in the meander’s interior. Also notable in Fig. 3a and shown in detail in Fig. 3b are signatures of roll vortices (Sikora and Ufermann 2004) aligned with winds flowing toward the northeast.
We examined Terra MODIS data from 1525 UTC 7 March 2009 (http://rapidfire.sci.gsfc.nasa.gov/realtime/). Notwithstanding the nearly 7-h difference in overpass time, the Terra data suggest that some of the textures in Fig. 3a correspond to areas where moist (cloudy) convective processes, often associated with warmer SST (e.g., Sikora et al. 1995), occurred in the MABL. The roll vortex signatures in Fig. 3b, for example, are greatly enhanced on the warm (west) side of the SST front. In contrast, the mesoscale edges near the labels d in Fig. 3a are associated with the bands of horizontal wind shear and are apparently independent of variations in SST. We therefore suggest that these edges be described as signatures of pure atmospheric processes, to emphasize that they are independent (or at least mostly so) of the location of SST fronts and to distinguish them from edges associated with SST fronts alone (e.g., those found within Fig. 3b and discussed below in the context of Fig. 5a).
Canny edges computed using IA Pro’s SOFDT are shown in Fig. 5a. The SST data, bilinearly interpolated onto the SAR grid, are shown in Fig. 5b for comparison. The number next to each edge is the probability that it is an SST front signature, expressed as a percent computed from Eq. (3). Only edges with Prob(SST | x1, x2, x3) > 0.6 were included in the plot, and all of the edges shown were classified as being SST front signatures. The blue edges in Fig. 5a were determined to be signatures of pure atmospheric processes, as described above. These eight edges are all long and relatively linear and were consequently assigned high probabilities by Eq. (3). Of the remaining edges, only two located to the northeast and one to the southeast, drawn in yellow, were confirmed to be SST front signatures by comparison with Fig. 5b. The remaining six edges consist of signatures of current shear, marked in green, and surfactant entrainment, also marked in yellow, because, although not SST front signatures per se, they are well aligned with the GSNW as seen in Fig. 5b. Thus, for this case study, the efficacy of our algorithm was only .
a. Contextual measures
With the exception of x3, the mean Canny edge strength from SDW, none of the textural measures listed in Table 1b were found to contribute to the model. Furthermore, x3 only provides a very minor improvement in efficacy above a model that only includes x1, the distance between the endpoints of a Canny edge on the SAR image, and x2, the length of the edge on the SAR image. We conclude that, of the measures that we devised, it is only the contextual measures that give the model any power to discriminate between feature vectors labeled SST front signatures and those labeled other.
Figure 6 demonstrates the relationships between three contextual measures and the probability that a given Canny edge was manually labeled as an SST front signature. Based on all 1441 Canny edges, the probability that an edge was labeled as an SST front signature was fully 10% higher inside the GSNWSR (probability = 0.29) than it was outside (probability = 0.19). This difference is statistically significant, although the variable selection procedure did not identify location with respect to the GSNWSR as being a significant contributor to the classification model. We took the median length of all Canny edges (30 km) to be the boundary between short and long features. In combination with the two shape classes linear and curved, as defined in Table 1a, the general trend was for long, relatively straight edges to have a higher probability of having been labeled as SST front signatures than short, relatively curved edges. This is quantified by the probabilities in the corners of the two boxes in Fig. 6. These relationships are statistically significant but are not useful because all of the probabilities are well below 0.50.
b. A general ocean feature classification scheme
The case study showed that Canny edges associated with the signatures of pure atmospheric processes such as horizontal wind shear may be long and gently curved and therefore appear, at least to our classification algorithm, to be SST front signatures. Furthermore, we expect other pure atmospheric processes, such as synoptic-scale fronts, to produce similar signatures within SAR images (Young et al. 2005). Our SST–other dichotomous approach may therefore be insufficient, and a classification scheme that can distinguish between pure atmospheric edges and SST front edges in SAR and SDW images may be necessary in order to improve classification accuracy. Indeed, discriminating between SST front edges and pure atmospheric edges that are similar in appearance may be the crux of the ocean feature classification problem.
It is helpful to visualize the problem as is shown in Fig. 7, which is analogous to Fig. 1 in Cloude and Pottier (1997). The dashed box indicates the forcing atmospheric and oceanographic processes that conflate to produce a modulated field of small-scale waves on the ocean’s surface. This inherent field of Bragg waves interacts with components of the satellite’s configuration, such as transmit frequency, transmitted and received polarization, and the geometric orientation of the transmitted beam with respect to the orientation of the Bragg waves, to produce an apparent SAR image. A detailed forward model can be devised to quantify the flow of information from the forcing processes to the SAR image (e.g., Johannessen et al. 2005). The inverse of this forward model is required to solve the classification problem. In principle, given sufficient information, it is possible to precisely reverse the forward model to obtain, from SAR images, the field of modulated Bragg waves. A CMOD, for example, comes close to this, and all that remains is to convert wind speed or stress into a set of parameters that describe the Bragg waves: that is, wavelength, amplitude, and orientation. Deconflating the forcing processes, however, is almost certainly unattainable, and it is for this reason that a statistical approximation is necessary.
It is convenient to partition the forcing atmospheric and oceanographic processes that can produce edges or filaments in SAR images into three categories:
pure atmospheric processes:
atmospheric processes that produce signatures in SAR images that are apparently independent of SST fronts, as defined above;
pure oceanographic processes:
horizontal and vertical modes of oscillation in the water column that impact the ocean’s surface, including internal waves, current shear, Kelvin–Helmholtz instability waves, meanders and eddies, and oscillations in phytoplankton biomass, and the entrainment of surfactants by currents; and
surface roughness variability forced by air–sea interaction in the vicinity of an SST front.
Note that anthropogenic processes, such as ships, ship wakes, and anthropogenic surfactant, are ignored, as they are seldom apparent in SCNA images. As is apparent from the case study, a statistical approximation of the inverse model should aim to distinguish between processes from all three categories in what might be called a general ocean feature classification scheme. This may yet require the identification of discriminating textural measures.
The textural differences on the two sides of the SST front signature in Fig. 3b and also noted in SAR images of other SST fronts (e.g., Sikora et al. 1995) argue for the existence of a discriminating textural measure. The formulation of a general ocean feature classification scheme therefore likely requires the identification of a set of textural measure that is more informative than the measures listed in Table 1b. One untried approach would be to contrast textural information extracted from the two sides of a Canny edge. The mean value over the polygonal region surrounding a Canny edge may contain less information than the difference between the mean computed on either side of the edge, for example. Also, the signatures of convective processes that often appear on the warmer side of an SST front may be distinguishable from the smoother, cooler side of the front by a textural measure constructed from a high-pass filtered version of the SAR image. An alternative to our edge-based approach is to extract textural measures from small windows around each image pixel, as has been done in the context of the classification of sea ice (Barber and LeDrew 1991) and meteorological phenomena (Young et al. 2008). Pixel-based textures include measures computed from the gray level co-occurrence matrix (Haralick et al. 1973) measures such as local entropy, standard deviation and median used by Young et al. (2008), and the spectral histograms of Liu and Wang (2003). A pixel-based approach might involve the classification of regions of similar texture and of the boundaries between them based on comparisons with a library of textures and boundaries associated with known processes. All of these possibilities will be investigated as our study continues.
Accurate identification of ocean features in over-ocean SAR and SDW images, although attainable to an experienced analyst, is widely acknowledged to be a difficult process to automate. The objective of our study was to automate the identification of only one type of ocean feature, the signatures of SST fronts in the vicinity of the Gulf Stream North Wall, which was expected to be relatively easy. We based our classification scheme on logistic regression, aiming to partition ocean features identified in Radarsat-2 images by a Canny edge detector into the classes 1) SST front signature and 2) other. IA Pro’s SOFDT provided Canny edges and feature vectors consisting of 35 contextual and textural measures. Each feature vector was validated by comparison with SST data (MODIS and AVHRR). Our results indicate that, in addition to the mean Canny edge strength from SDW, the size and shape of the Canny edge on the SAR image were all that determined the probability a given edge was an SST front signature. Based on 1441 labeled feature vectors, 294 of which were labeled as SST front signatures, our model results were quite poor, with efficacy (cf. user’s accuracy and hit rate) between about 0.50 and 0.70 and capture probability (cf. producer’s accuracy and one minus the false-alarm rate) of less than 0.30. Our case study suggested that this poor performance was due to the lack of discrimination between signatures of SST fronts and those of certain pure atmospheric processes. We concluded that improvement in classification accuracy requires a set of measures that can differentiate between signatures of SST fronts and certain atmospheric processes and that a search for such measures should consider a wider range of computational methods than was considered in our study thus far. As such, this work represents a small step toward the goal of a general ocean feature classification algorithm.
The authors thank the Canadian Space Agency (CSA), who funded this study via its Government Related Initiatives Program (GRIP). Dr. Sikora was partially supported by ONR Grant N00014-10-1-0569. We would also like to thank Brendan DeTracey at MetOc Halifax for his work in organizing and processing data files. Finally, the authors thank Igor Belkin, and the two anonymous reviewers for their very helpful comments.
This function fits data to a generalized linear model or GLM. A GLM relates a response variable, such as the binomial class in our study, to a linear predictor via a specified link function. This allows inferences to be made using least squares regression when random errors are non-Gaussian but follow a probability distribution that is a member of the exponential family.