Sea Ice Detection by an Unsupervised Method Using Ku- and Ka-Band Radar Data at Low Incidence Angles: First Results

Abstract

This paper presents the first results of sea ice detection using the data of Ka- and Ku-band radars at low incidence angles. A classification method based on an unsupervised K-means approach is applied to the arrays of the data for the Arctic and Antarctic regions. Comparison with Advanced Microwave Scanning Radiometer 2 (AMSR-2) data was performed, and the dependence of classification performance was evaluated for incidence angles from 0° to 18.15°. This paper evaluates the classification accuracy of sea ice detection based on Ku-band, Ka-band, and their combination. Preliminary results indicate that the classification based solely on Ku-band data achieves the best performance.

1. Introduction

Variations in sea ice play an important role in global heat balance, atmospheric circulation, ocean water cycle, temperature and salt balance, and the choice of reliable polar waterways [1]. It is necessary to observe the changes in the sea ice cover, as it is a major element of the Earth’s climate system. In addition, taking into account the position of the ice cover is important for numerical simulation of waves in the polar regions [2]. Satellite-based remote sensing serves as a primary source of information regarding sea ice extent, concentration, and type. Passive microwave sensors provide long-term datasets on sea ice concentration (SIC). Several algorithms were reviewed in [3,4], and it was shown that results obtained using these algorithms may differ significantly. However, active remote sensing measurements have demonstrated their applicability for sea ice mapping, and can serve as a complementary source of data to enhance the datasets obtained from radiometers.

Altimeters operate at zero incidence angle, and their data are used to estimate the ice thickness and volume [5,6]. The sea ice type is distinguished by taking into account several waveform features of the reflected pulse [7].

Synthetic aperture radar (SAR) data are applied to obtain high-resolution ice maps using data at several polarizations. The problems of ice–ocean discrimination, sea ice type classification, and ice edge detection are solved by this approach. A review of the most important works can be found in [8]. However, the coverage area for SAR images is predominantly focused on coastal zones.

Sea ice mapping based on scatterometer measurement at moderate incidence angles (20°–60°) deals with sea ice classification, edge detection [9], and measurement of sea ice extent [10]. Algorithms for ice/ocean discrimination have evolved from thresholding techniques to Bayesian methods [11,12].

Interest in sea ice remote sensing using active microwave radars operating at low incidence angles different from zero has risen during recent years. There are two sensors operating at incidence angles from 0° to 18° in orbit at the moment: the Dual-frequency Precipitation Radar (DPR) onboard the Global Precipitation Measurement (GPM) satellite, and the Sea Wave Investigation and Measurement (SWIM) radar onboard the Chinese–French Oceanography Satellite (CFOSAT).

The CFOSAT satellite has an orbit inclination of 97°, allowing for observation of polar areas. The approaches for sea ice mapping in scatterometry and altimetry have been successfully applied for the data at low incidence angles up to 10° in the Ku-band. In [13], the surface type was determined using SWIM radar data. A Bayesian approach was implemented to solve the problem. The models of the scattered signal were incorporated in the algorithm, along with auxiliary information on sea surface temperature. In [14], sea ice type in the Arctic region was determined based on several features of the reflected pulse.

The orbit inclination of the GPM is $65°$. Thus, its satellite tracks do not fully cover the polar areas. However, these data are nonetheless deserving of attention. GPM observes ice cover in the Sea of Okhotsk and Hudson’s Bay in the northern hemisphere, and observes Antarctic ice during the summer season.

This satellite carries onboard Ku- and Ka-band radars, and the exploration of Ka-band data perspectives at low incidence angles for sea ice mapping is a new and interesting problem. In [15], an algorithm was presented to identify the surface type using the data of the Ku-band radar onboard the GPM satellite. The method is based on the difference between ice and water slope statistics. It was shown that the kurtosis coefficient of the probability density function of sea surface slopes can serve as a criterion for surface type classification. In addition, it was demonstrated that a one-directional canny edge detection method may be applied to detect water/ice boundaries.

This paper is devoted to the ice–ocean discrimination problem based on Ku- and Ka-band NRCS data. The performance of the K-means approach widely used for unsupervised classification is evaluated. In previous papers, K-means was applied for sea ice detection using radar altimeter data [16] and SAR measurements [17]. In the present work, this method is applied for the first time to the NRCS data in the Ku- and Ka-bands at low incidence angles different from zero. This paper aims to answer the questions of how classification performance depends on the incidence angle and how it differs when using Ku-band and Ka-band data separately compared to using them together. Validation is performed using the data on SIC from Advanced Microwave Scanning Radiometer 2 (AMSR-2).

The rest of this paper is organized as follows: Section 2 describes the dataset; Section 3 presents the NRCS histograms and describes the algorithm of surface type detection; the performance of the algorithm is discussed in Section 4; and the results are summarized in the conclusion.

2. Dataset

DPR was originally designed to measure the spatial distribution of precipitation in the atmosphere. In the absence of precipitation, its data can be used to investigate the underlying surface. The data of the DPR onboard the GPM satellite on NRCS in the Ku- and Ka-bands (13.6 GHz and 35.5 GHz respectively) were used.

The scheme of scanning is presented in Figure 1. The radars scan across the flight direction, and the angle of scanning changes from $-17°$ to $17°$; thus, the incidence angle changes from $-18.15°$ to $18.15°$. The incidence angle varies with the step $0.77°$. There are 49 beams and 25 different incidence angles.

The antenna footprint size for both the Ku-band and Ka-band radars is 5 km, and their footprints coincide. The Ka-band radar has operated within a wide swath from May 2018 (previously, the maximum incidence angle was 9 degrees). The Ku-band data version V06 were used, while the Ka-band data were from the V06X experimental dataset.

Sea ice concentration (SIC) from AMSR-2 data was used for validation. These data are available on the Bremen university website. SIC is obtained according to ASI algorithm [18]. These data consist of a gridded daily SIC product with 6.25 km resolution.

Example DPR tracks over the SIC map for 3 September 2019 are presented in Figure 2. SIC equal to 1 corresponds to solid ice cover, while 0 indicates open water.

In this study, the data for January 2019 in Arctic region and for September 2019 in the Antarctic region were used. Sea ice concentration values were resampled to the DPR antenna footprint centers. This step was possible because the resolutions of the DPR and SIC products are similar. The data for latitudes higher than $40°$ were considered. The samples with SIC $\ge 0.15$ were labeled as “ice” and those with SIC < 0.15 were labeled as “water”. The value 0.15 was chosen as a typical threshold for ice–ocean discrimination [19]. In total, according to this threshold, the dataset contained $16\times {10}^6$ samples for “water” and $14\times {10}^6$ for “ice” classes in the September dataset and $2\times {10}^6$ samples for “water” and $9\times {10}^6$ for “ice” classes in the January dataset.

3. Method

The two NRCS arrays, labeled as discussed in Section 2 according to AMSR-2 data for the southern and northern hemispheres, were considered. Processing of each dataset included three stages:

1. The histograms of the NRCS for the “water” and “ice” classes are plotted using labeled data. This step is performed in order to illustrate the relative positions of the two classes. This makes it possible to formulate the rule for labeling the classes, which are obtained as a result of unsupervised clustering.

2. Unsupervised clustering of the NRCS data is performed. The classes are labeled according to the rule obtained in the previous step.

3. Validation is performed using the labeled data.

As clustering is unsupervised, the same array is utilized for all three stages.

3.1. NRCS Histograms

For illustration, the data for the southern hemisphere are considered. In Figure 3, the NRCS histograms for “water” and “ice” classes are plotted on the same axes. The red and blue colors correspond to “ice” and “water” samples, respectively.

Each subfigure contains the two-dimensional histogram for both the Ku- and Ka-band channels and the one-dimensional histograms for each channel separately. On the top, the one-dimensional histogram for the Ku-band radar data is presented, while on the right the one-dimensional histogram for the Ka-band radar data is shown.

The figures present the most representative cases among the 25 different incidence angles we considered. The NRCS distributions for the remaining incidence angles fall in between these characteristic cases, representing intermediate scenarios.

In the ocean, there is a wide variety of wave conditions for open water, which strongly influences the backscattered signal at the edge and in the center of the swath. Thus, the histograms of the NRCS data for such incidence angles are wide.

The histograms for “water” in both Ku-band and Ka-band data, whether considered separately or together, depend on the incidence angle. The minimum width of the NRCS histogram is observed between $0°$ and $18.15°$. In [20], it was shown that the maximum negative correlation coefficient between NRCS and wind speed and wave parameters (significant wave height, wave period etc.) is observed at $0°$, the maximum positive correlation coefficient is observed at $18.15°$, and the correlation coefficient is close to zero at about $10°$.

In addition, there are numerous factors that influence NRCS for SIC $\ge 0.15$, including wave conditions, sea ice relief, the temperature of sea ice, etc. These factors explain the extension of “sea ice” histograms.

For nearly all the incidence angles considered, the distributions of NRCS exhibit two distinct peaks corresponding to “ice” and “water” classes. At an incidence angle of $\theta =0.7°$, the peaks corresponding to “ice” and “water” classes overlap, indicating a higher degree of ambiguity in classifying the surface type based on NRCS values alone. These data were used for classification.

From the ground truth labels (see Figure 3), the relations between centroids of the two clusters (${\widetilde{{\sigma }^0}}_{ice}$ and ${\widetilde{{\sigma }^0}}_{water}$) are as follows for both Ku- and Ka-band:

$$\begin{array}{c}\theta <0.7°:{\widetilde{{\sigma }^0}}_{water}<{\widetilde{{\sigma }^0}}_{ice},\\ \theta >0.7°:{\widetilde{{\sigma }^0}}_{water}>{\widetilde{{\sigma }^0}}_{ice}.\end{array}$$

(1)

3.2. Clustering

In the case where the NRCS distributions for two classes are separated, K-means unsupervised clustering was applied. K-means is an iterative algorithm that aims to partition a dataset into non-overlapping subgroups in which each observation belongs to the cluster with the nearest cluster centroid. K-means clustering minimizes the within-cluster variance (squared Euclidean distances).

Three options were considered: (1) one-dimensional clustering using only the Ku-band data; (2) one-dimensional clustering using only the Ka-band data; and (3) two-dimensional clustering using both the Ku- and Ka-band data.

After the data were separated into the two clusters, they were labeled according to the relations (1).

An example of clustering for the September 2019 data at an incidence angle equal to $3.78°$ is presented in Figure 4.

4. Result and Discussion

Classification of NRCS data was performed as described above. Validation was carried out using labeled data according to AMSR-2 measurements.

The components of the confusion matrix were calculated for each incidence angle. The matrix is shown in Figure 5, where true positive (TP) is the number of samples correctly defined as ice, true negative (TN) is the number of samples correctly defined as water, false positive (FP) is the number of samples erroneously defined as ice, and false negative (FN) is the number of samples erroneously defined as water; when saying “correctly” and “erroneously”, we mean that the SIC data are the ground truth.

The classification performance for the Ku- and Ka-band channels separately and for two-dimensional clustering were compared based on the following metrics: false positive rate (FPR), false negative rate (FNR), and F-score (F). It should be noted that the ice and water classes are imbalanced in general; thus, in this case the F-score is preferred over accuracy. The equations for the metrics are as follows:

$$\begin{array}{c}FPR=\frac{FP}{FP+TN}\end{array}$$

(2)

$$\begin{array}{c}FNR=\frac{FN}{FN+TP}\end{array}$$

(3)

$$\begin{array}{c}F=\frac{2TP}{2TP+FP+FN}.\end{array}$$

(4)

In Figure 6 and Figure 7, the FPR and FNR dependencies on the incidence angle are presented, while the F-score is shown in Figure 8.

FPR has a minimum at incidence angle equal to 2–10°, depending on the method of classification. FNR decreases with growth of the incidence angle and grows slightly at the edge of the swath.

The F-score presents the aggregated classification quality metric. It grows with the incidence angle and slightly decreases closer to the edge of the swath. In the part of the swath from 5° to 11°, all three classification methods present similar performance. At the remaining range of incidence angles, clustering using Ku-band data shows the best performance.

In Figure 9, an example of surface type classification using clustering based on Ku-band data is presented for several beams on the map for the first week of September. The same classification for the first week of January is presented in Figure 10. True positive, false positive, and false negative elements are marked with blue, magenta, and yellow respectively. Good agreement between radar and radiometer measurements is observed closer to the edge of the ice cover for zero incidence angle and for ice with high SIC for incidence angles above $1°$. It should be noted that a possible source of mismatch between DPR and radiometer data could be the error in the SIC measurements, which increases with decreasing SIC [18].

The results for the Ku-band at incidence angles within 0°–10° can be compared with those obtained in [13] for SWIM Ku-band data. According to these data, high accuracy is obtained for all the incidence angles. For the Bayesian approach, the performance of classification degrades with the incidence angle growth; in Figure 15 [13], the level of false positive samples is high, while for clustering approach this kind of errors is almost absent (see Figure 9 and Figure 10). Special attention should be paid to this peculiarity, and further comparison of the methods should be performed.

The figures in the present paper were obtained for the case when the dataset for the whole month was used. Another option was considered, when clustering was performed for each day separately, and total performance for the whole month was calculated. The results were similar to the presented results.

5. Conclusions

Preliminary results for ice–ocean discrimination are presented using a simple unsupervised method for Ku- and Ka-band radar data at incidence angles below $18.15°$. For the first time, Ka-band data at low incidence angles were applied for sea ice detection. It was shown that this band is sensitive to the type of underlying surface.

This study investigated the classification performance dependence on the incidence angle, revealing that classification based on Ku-band radar data outperforms two-dimensional clustering and the classification based on Ka-band data. In the part of the swath from 5° to 11°, all three methods present similar performance. According to the F-score metric, the method used in this paper demonstrates good performance for incidence angles in the range of $4°$–$18.15°$, with a maximum at about $12°$. The histograms for ice and water NRCS strongly overlap at lower incidence angles, however, and the accuracy of the clustering method drops.

This method can be applied to new unlabeled datasets. The advantage of unsupervised clustering is the possibility of adapting to various regional and seasonal peculiarities, which may differ for each array under investigation. This simple approach can be used to obtain alternative estimate for sea ice detection performance in the Ka- and Ku-bands at low incidence angles. In future research, a comparison with the Bayesian approach should be performed using the same dataset.