Sea Ice Concentration Manifestation in Radar Signal at Low Incidence Angles Depending on Wind Speed

Abstract

In previous studies, the possibilities of Ku-band radar measurements at low incidence angles were investigated for the task of sea ice detection. In this paper, the sensitivity of normalized radar cross-section to sea ice concentration is investigated at various wind conditions. The data of Ku-band radar onboard GPM satellite are used, and the sea ice concentration product from Bremen University website is implemented as reference data and the information on wind speed from reanalysis was applied. Simple analytical parameterization was obtained for the normalized radar cross-section depending on sea ice concentration and wind speed for various incidence angles using the regression method. The threshold behavior of the normalized radar cross-section with increase in wind speed was revealed and preferable wind conditions for sea ice concentration detection were identified.

1. Introduction

Investigations of sea ice properties are critically important for understanding polar ice dynamics and climate variability. The information on various sea ice properties such as sea ice concentration, sea ice type, and thickness can be evaluated using active and passive microwave data.

Microwave radiometers is a powerful source of information on ice properties. Sea ice concentration (SIC) is the fraction of an ocean area covered by sea ice. The information on SIC is globally obtained using microwave radiometer data on a regular basis, and various algorithms to obtain this parameter exist [1,2,3]. In [4,5], it was shown that the brightness temperature measured by radiometers is sensitive to sea ice thickness. In [6], the method to detect the ice type is suggested. Passive instruments are sensitive to a variety of conditions in the atmosphere; therefore, the results obtained from their data can differ significantly.

Active radars are less sensitive to atmospheric conditions, and the value of the reflected signal is also applied to retrieve sea ice properties. Scatterometer data at moderate incidence angles were utilized to evaluate the type of sea ice: one-year or multi-year [7,8]. Sea ice altimetry is an effective method to obtain sea ice thickness [9,10] from the information on the ice freeboard. In recent work, high-resolution altimeter data were implemented to obtain a “linear" analog of sea ice concentration [11]. Except for these studies, no papers were found where sea ice concentration manifestations are studied using the normalized radar cross-section (NRCS) at low incidence angles.

Another phenomena in polar regions, which can manifest itself in the form of a radar signal, is wave propagation in marginal ice zone. Remote sensing techniques were applied to evaluate the parameters of waves propagating in a marginal ice zone [12]. A range of works were devoted to study the effect of sea wave attenuation in the marginal ice zone, and the coefficients of wave attenuation was obtained depending on the distance from the ice edge using in situ measurements, for example, [13], and satellite data [14].

Microwave radars operating at low incidence angles different from nadir are able to observe polar areas. These radars are Dual-Frequency Precipitation Radar (DPR) onboard Global Precipitation Measurement (GPM) satellite and Surface Waves Investigation and Monitoring instrument (SWIM) onboard the Chinese–French Oceanic Satellite (CFOSAT). The signal at low incidence angles is sensitive not only to surface dielectric properties, but also to large-scale wave manifestations.

In previous studies, the possibilities of Ku-band radar scanning at low incidence angles were discussed to detect two classes: open water and sea ice. Two algorithms were developed. The first is based on the value of NRCS [15], the second one implements the dependence of NRCS on the incidence angle to distinguish between the two kinds of surface [16]. It was shown that both algorithms allow us to classify water and sea ice with high accuracy (F-score above 0.9).

For the case of open water in the absence of sea ice, the data of Ku-band radars operating at low incidence angles was used to investigate the dependence of NRCS on wave parameters and wind speed [17,18]. The dependencies for NRCS on wind speed at incidence angles ranging from 0 to 18 degrees were obtained.

The present work is aimed to study the manifestations of various SICs in radar signal depending on the wind conditions in Antarctica.

The data of the Ku-band radar onboard the GPM satellite are used. From these data, the normalized radar cross-section (NRCS) at incidence angles from 0 to 18 degrees is available. Along with the data on sea ice concentration, the information on wind speed from reanalysis is included. It was found that SIC manifestations in a radar backscattered signal depend on the wind conditions. The effect of the threshold behavior of NRCS depending on wind speed was observed. As a result, the parameterization for NRCS depending on SIC and wind speed was obtained.

The paper is organized as follows. In Section 2, the dataset is described. In Section 3, the parameterization for NRCS depending on sea ice concentration and wind speed is obtained, and in Section 4, the accuracy of the model is evaluated.

2. Data

The GPM satellite, launched in February 2014, carries five instruments, including the DPR and the GPM Microwave Imager (GMI). The satellite’s ground track is limited to between 65°S and 65°N. The DPR is a Ku- and Ka-band pulsed radar with horizontal polarization. The DPR antenna scans perpendicular to the flight direction. The scanning angle ranges from −17° to +17°, with 49 beam positions spaced 0.71°. The local incidence angle depends on the Earth’s shape, with the maximum local incidence angle of approximately 18° and a spatial resolution of around 5 km. The GPM data include a land mask and rain flag for each resolution element. Data containing precipitation, as well as scans over land, were excluded from the analysis. Additionally, auxiliary data on near-surface wind speed at 10 m height ($U_{10}$), resampled to the DPR resolution elements, were used. These are the Japanese Global Analysis Model data (GANAL), which provide atmospheric environmental conditions. The comparison of the GANAL reanalysis wind speed with ECMWF model and scatterometer data is given, for example, in [19]. The data are resampled and distributed by the DPR team as a complementary dataset and stored in the GPM/DPR ENV product.

In this study, Ku-band radar data on normalized radar cross-section (NRCS) for July 2019 over Antarctica, specifically for latitudes south of 50°S, were collocated with wind speed data from GANAL reanalysis and sea ice concentration information from the Bremen University website. The SIC product is derived from AMSR-2 data using the ASI algorithm [2]. In this work, SIC = 1 corresponds to the fully consolidated ice and SIC = 0 to open water.

In the present study, the parameterization of NRCS for ice-covered surface is discussed, and thus, only the data with SIC > 0.15 were left. The data for wind speed below 20 m/s were considered. The data contained gridded daily SIC products with 6.25 km resolution. The values of SIC were resampled to DPR resolution elements using the nearest neighbor method.

In Figure 1, the histograms for wind speeds and SIC for the array under consideration is presented.

The entire array contains the data for the incidence angles ranging from 0° to 18.1° with the step 0.71°. In the present study, data are selected only at the incidence angles above 4° and below 11°.

In [15], it was shown that the NRCS histograms for ice and water surface are strongly overlapped at incidence angles below 4°. For the present study, only the data where the NRCS over ice surface strongly differs from that of the water surface was selected, i.e., for incidence angles above 4°.

In the present dataset, the information on the angle between the scanning direction and wind direction is absent. In [20], it was shown that, for a water surface at incidence angles lower than ≈11°, the modulation of the signal due to the azimuth angle is not strong, and the same is expected for the surface where SIC > 0. At higher incidence angles, the azimuth dependence of the signal becomes more pronounced and should be taken into account. Thus, at this stage of the study, we do not consider incidence angles above 11°.

In Figure 2, the NRCS at 4–11° for the tracks for 30 July 2019 are shown over the SIC map.

3. Parameterization of NRCS Depending on Sea Ice Concentration and Wind Speed

3.1. Binning Procedure

The data of NRCS were grouped by incidence angle, and for each incidence angle, the binning procedure was applied to the data. The bins of wind speed with the step of 2 m/s and bin size is 2 m/s were considered. The bins for sea ice concentration were selected with the step of 0.1, and the bin size is equal to 0.04 for SIC from 0.2 to 1. The less populated bins correspond to low SIC and high wind speeds, according to Figure 1. Even for these bins, the amount of samples in the bin is not lower than ${10}^2$.

The values of NRCS corresponding to a particular two-dimensional wind speed/SIC bin were obtained as follows. Firstly, the probability density function (pdf) for NRCS in each bin was evaluated. Secondly, the value of NRCS corresponding to the peak of the pdf was selected. We have chosen to select the most probable value of the signal instead of the mean value. The example of the NRCS histogram for the incidence angle 10.65°, and bins with their centers at SIC = 0.2, $U_{10}$ = 10 m/s (left) and SIC = 0.8, $U_{10}$ = 10 m/s is shown in Figure 3.

Using the averaged value in the bin is suitable when the measurable amount contains random noise, and its values are normally distributed around the true value. However, in the present case, the NRCS measured over sea ice is not only the subject of random noise, but it depends on many factors, besides SIC and $U_{10}$, which are not taken into account at the moment. Moreover, the distribution of NRCS in the bin is not normal. Thus, the parameterization is further obtained using the values of the most probable NRCS in the bin. For brevity, these values are designated by the symbol $\widehat{{\sigma }^0}$.

3.2. NRCS Dependence on Wind Speed and SIC

Firstly, let us consider the dependence of $\widehat{{\sigma }^0}$ on wind speed at fixed values of SIC. In Figure 4, the dependencies for SIC = 0.2 and SIC = 0.4 at incidence angles of 4°, 6°, 8°, and 10° are shown. At the other incidence angles intermediate results are obtained. Blue dots represent the experimental data $\widehat{{\sigma }^0}$, and the shaded area represents the scatter of NRCS around $\widehat{{\sigma }^0}$. The behavior of $\widehat{{\sigma }^0}\left(U_{10}\right)$ can be described by the sigmoid function. The following parameterization of this dependence is suggested

$${\widehat{\sigma }}^0={\sigma }_b^0+{\displaystyle \frac{\Delta {\sigma }^0}{1+exp(U_{10}^{th}-U_{10})}}.$$

(1)

The red lines in Figure 4 visualize the parameterization function in Equation (1). The function reveals the threshold behavior, and the black asterisk in each subfigure shows the position of this threshold wind speed $U_{10}^{th}$. Below the threshold, NRCS is not sensitive to wind speed growth. When reaching a threshold value of $U_{10}$, the signal starts to increase rapidly. A further increase in the wind speed leads to the saturation of the NRCS value. This threshold value is higher for a higher incidence angle. Comparing the plots for SIC = 0.2 and SIC = 0.4, one can observe that, for all incidence angles the threshold values of the wind speed are higher for the ice cover with a higher concentration.

The remaining parameters in Equation (1) have the following physical meaning: ${\sigma }_b^0$ is the basic value of NRCS in the absence of wind, and $\Delta {\sigma }^0$ describes the diapason of ${\sigma }^0$ variations when wind speed grows. It can be noticed from Figure 4 for two different SICs that all three parameters $U_{10}^{th}$, ${\sigma }_b^0$, and $\Delta {\sigma }^0$ depend on SIC.

Furthermore, the nonlinear fit for all incidence angles at several SIC was performed and the coefficients in Equation (1) were obtained and the dependencies of the three parameters $U_{10}^{th}$, ${\sigma }_b^0$, and $\Delta {\sigma }^0$ on SIC are considered. In Figure 5, the dependence of $U_{10}^{th}\left(SIC\right)$ is shown. Points represent the experimental data and lines are the linear regression dependencies for $U_{10}^{th}\left(SIC\right)$.

In Figure 5, the dependence of $U_{10}^{th}\left(SIC\right)$ is shown. Points represent the experimental data and lines are the linear regression dependencies for $U_{10}^{th}\left(SIC\right)$.

As it was previously discussed, $U_{10}^{th}$ grows with the increase in SIC for all incidence angles. To obtain these dependencies, the data for SIC < 0.7 were used and the linear function was suggested

$$U_{10}^{th}=a·SIC+b.$$

(2)

At a higher SIC, the difference between the NRCS at low and high wind speeds is small, and the values of $U_{10}^{th}$ are unstable. Thus, the dependence was extrapolated to a higher SIC assuming that $U_{10}^{th}$ maintains growth.

In Figure 6, the dependence ${\sigma }_b^0\left(SIC\right)$ is shown. Points represent the experimental data and lines are the regression dependencies

$${\sigma }_b^0=c·tanh\left(d(1-SIC)\right)+e.$$

(3)

One can clearly observe the growth in NRCS with the decrease in the incidence angle for the entire range of SIC. Also, it follows from the figure that ${\sigma }_b^0$ is insensitive to SIC up to 0.7–0.8, while in the range of SIC 0.8 –1, ${\sigma }_b^0$ rapidly decreases.

In Figure 7, the dependence of $\Delta {\sigma }^0$ on SIC is shown for the data and the following parameterization is suggested

$$\Delta {\sigma }^0=f·{(1-SIC)}^g.$$

(4)

This parameter, $\Delta {\sigma }^0$, characterizes the diapason of NRCS variations with wind speed. The value of $\Delta {\sigma }^0$ grows with increase in incidence angle. At SIC = 1, this value equals to zero and grows with the increase in open water fraction of the surface. A possible reason of the small discrepancy between the model and data at SIC > 0.8 indicates that $\Delta {\sigma }^0$ may be explained by $\Delta {\sigma }^0$, approaching zero at SIC values slightly less than 1.

To summarize, the dependence of NRCS on wind speed and SIC takes the following form

$${\widehat{\sigma }}^0=c·tanh\left(d(1-SIC)\right)+{\displaystyle \frac{f·{(1-SIC)}^g}{1+exp(-U_{10}+a·SIC+b)}}+e,$$

(5)

where the coefficients $a,b,c,d,e,f,g$ are obtained for each incidence angle separately and their values are given in

Table A1. The coefficients in the Equation (5).

Incidence Angle	a	b	c	d	e	f	g
4.62°	7.42	2.89	5.71	4.60	0.33	5.52	0.49
5.37°	8.48	2.74	4.99	5.07	−0.60	7.46	0.66
6.13°	7.55	3.40	4.50	6.82	−1.47	8.38	0.67
7.63°	5.58	5.66	4.03	5.33	−2.53	8.61	0.55
6.88°	6.80	4.57	3.96	6.51	−2.04	9.15	0.67
8.39°	6.10	5.94	3.67	6.14	−3.21	9.48	0.67
9.14°	5.06	5.65	3.52	5.82	−3.65	9.67	0.71
9.89°	8.60	5.34	3.44	4.18	−3.93	9.67	0.78
10.65°	8.52	5.64	3.25	6.34	−4.57	9.74	0.74

.

The physical meaning of several coefficients can be explained when limiting cases of SIC = 0 or 1 are considered: the coefficient b corresponds to the threshold wind speed for an open water surface; e equals to the NRCS for ice surface with SIC = 1; f equals to the diapason of NRCS between $U_{10}=0$ m/s and high wind speeds for open water.

The function ${\widehat{\sigma }}^0(SIC,U_{10})$ is plotted in Figure 8 for two incidence angles: 4.6° and 10.6°. It is monotonous with respect to both variables. Isolines of NRCS in the plot indicate that the same value of the signal can be obtained for a wide variety of ice and wind conditions.

The phenomenon of the thresholding behavior of NRCS can be explained as follows. Within the frameworks of quasispecular approximation, NRCS is proportional to the probability density function of sea surface slopes. The radar signal depends on the quantity of surface facets, oriented perpendicularly to the incidence radiation. When waves grow, the contribution to the signal from the facets oriented at incidence angles of 4–10° increases, which results in the growth of NRCS. The threshold behavior of NRCS at a particular incidence angle demonstrates how a high wind speed is required to generate the waves steep enough, so that the contribution of the corresponding facets to the signal is significant. The higher the incidence angle, the steeper waves should be that are generated to observe the increase in the signal. Therefore, the threshold value of the wind speed grows with the incidence angle.

When the sea ice concentration grows, the value of the wind speed threshold is shifted towards higher values for each incidence angle. Intuitively, it is evident that the higher the mass of floating ice is per unit area, the higher the wind force should be that is applied to generate waves. Therefore, the value of NRCS indirectly contains information on the degree of surface waves development.

Two zones of the parameters in Figure 8 can be identified. At a low wind speed, the radar signal is insensitive to variation of SIC up to SIC values 0.7–0.8. When the wind speed increases, waves emerge on the surface and this allows the variations in SIC to manifest in the radar signal. There is a transition zone for wind speed values between these two regimes around the threshold value of $U_{10}$, the position of which depends on SIC and the incidence angle. At higher incidence angles, this transition happens at higher wind speeds.

It is interesting to note that, even at low wind speeds, the transition from partially consolidated ice to fully consolidated ice (at SIC from 0.8 to 1) is clearly manifested in a fast decrease in the signal for all the considered incidence angles.

These plots for ${\widehat{\sigma }}^0(SIC,U_{10})$ allow us to evaluate the possibilities of SIC retrieval from the radar signal. According to the figures, the most favorable conditions, when the gradient of ${\sigma }^0\left(SIC\right)$ is high enough for the entire range of SIC, are at high wind speeds. In this area of parameters, the isolines of NRCS are almost parallel to the $U_{10}$ axis. For example, at θ = 4.6°, this regime starts at $U_{10}>11$ m/s, and at θ = 10.6°, it exists at $U_{10}>14$ m/s.

4. Results and Discussion

The parameterization was obtained for the values of the maximum probability density function of NRCS in each bin. Now, let us evaluate the efficiency of the obtained model for the entire dataset. The model values were calculated using Equation (5) for all incidence angles and SIC and wind conditions. In Figure 9, the comparison between the model values and real data is presented. According to the metrics, very good agreement was obtained: bias equals to −0.96 dB, correlation coefficient equals to 0.75, and standard deviation is 2.87 dB.

In fact, the dependence of NRCS on three parameters was obtained: there is a functional dependence of NRCS on SIC and wind speed and the tabulated dependence on incidence angle (in the experimental data discrete values of incidence angles are given). Possible reasons of scattering the data around the bisector are given below:

• The errors of mismatch of SIC and radar data: within one antenna footprint, various sea ice concentrations can be present;
• The sea ice concentration product is obtained from radiometer data, and the influence of the atmosphere may cause errors in defining this parameter;
• Wind speed is obtained from the reanalysis dataset, and these values may differ from real measurements; however, at this moment, reanalysis is the only source of information about wind speed over sea ice cover: remote sensing methods tuned for a water surface do not work there;
• Numerous factors regarding ice properties are not taken into account: the temperature of water and ice, the presence and conditions of snow cover, sea ice types, the size of sea ice floes [21], the relief of ice cover, ice thickness and salinity, etc.

In spite of this, the proposed parameterization is sufficiently good to explain the behavior of Ku-band NRCS over sea ice, taking into account wind speed value.

It should be noted that the obtained parameterization should not be generalized. It was inferred for Antarctic ice in July. In the seasons of sea ice cover formation or melting, NRCS may vary significantly. In [22], strong variations of Ku-band altimeter signal depending on the wetness of the surface are reported. In the Arctic region, where the conditions of ice formation, water temperature, and salinity differ, the model should also be adjusted separately.

Sea ice concentration from the radiometer data depends on the algorithm applied to obtain the product [23]. Therefore, the model parameters derived from the other SIC product as a reference will differ. Also, using alternative reanalysis data will probably yield different parameters for the model.

The existence of the threshold for wind wave generation is known for clean water [24]. This threshold depends on the viscosity of the water, which itself varies with temperature and salinity.

A review of the literature identified no prior studies regarding the thresholding behavior or the radar signal depending on wind speed in natural ice floe. However, in the experimental wave tank with artificial ice floes, the threshold behavior of significant wave height depending on wind speed was found [25]. The authors revealed that waves start to be generated after wind speed exceeds the threshold value, and this value grows with the increase in the density of artificial ice floes. Conclusions from [25] are consistent with our results. The difference is that, in the laboratory setup, at wind speeds above the threshold, significant wave height maintains continuous growing, while according to the radar data, the signal undergoes saturation at wind speeds above the threshold.

The further development of the parameterization, taking into account numerous factors affecting the signal, may imply the use of artificial neural networks. In the recently published paper on bistatic measurements [26], the inverse problem of SIC determination from the Delay–Doppler map is discussed. The authors implement similar idea to involve the information on wind speed from the reanalysis dataset. This approach revealed the improvement of accuracy in SIC evaluation; however, the physical meaning of the retrieval function cannot be deduced from this method. In order to take advantage of the approach based on neural networks, the following approach can be used. Having a basic semi-empirical model, the extended model can be obtained, taking into account more parameters such as the azimuth angle between radar look and wind speed, as well as surface temperature. For this purpose, the multilayer perceptron can be used where the loss function will be tuned in order to preserve the known behavior of the original semi-empirical function.

5. Conclusions

The parameterization for NRCS at Ku-band over the ice-covered sea surface was performed. The simple analytical function was inferred using a nonlinear fit for incidence angles of 4–11°. At the first step, the dependence of NRCS on wind speed at a constant SIC was obtained, and the parameters of the model were evaluated. At the second step, the regression of these parameters on SIC was performed. This approach allows us to explain the physical meaning of the parameters included in the model, which is difficult for the approach based on neural networks.

The threshold behavior of NRCS depending on wind speed was revealed. It was shown that there exist two wind regimes: when NRCS is almost insensitive to SIC, at low wind speeds, and another regime, at high wind speeds, when the variations of SIC are evidently manifested in the radar signal. Therefore, in general, the retrieval of SIC having only data on NRCS yields poor accuracy. However, at high wind speed, (above 10–14 m/s, depending on the incidence angle), when waves are developed, the task to retrieve SIC from the radar signal can be considered.

To our knowledge, no geophysical model functions exist for NRCS at low incidence angles, taking into account wind and ice conditions. The present work represents the first steps to solve this problem. Furthermore, our results can be used for the numerical simulation of the radar signal of the SWIM radar and DPR radar in polar areas. This model, in the future, can be applied to improve the SIC estimates and wind speed retrieval in polar areas from radar data. The information on the threshold behavior of wave generation depending on wind speed may bring new insights in the field of numerical models for the simulation of sea waves in presence of ice.