Wind field retrieval in the coastal zone using X-band radar data at large incidence angles

Full Text

Introduction

The most effective means of monitoring the aquatic environment under any meteorological conditions and at any time of day and night are radar systems. Currently, algorithms have been developed that use satellite radar information to determine wind speed and direction, surface wave characteristics, and to study eddies and frontal partitioning (see, for example, [1, 2] and the literature cited in these works). These data processing techniques are based on developed theoretical models of the formation of the radar signal reflected from the sea surface at incidence angles of 15–60° [3].

However, satellite data cannot be used for continuous monitoring of wind speed fields, currents and surface wave characteristics in ports, coastal waters and areas of heavy shipping. Navigation radar stations (RS) installed on offshore platforms, ships or onshore structures are used for real-time and continuous monitoring of the selected area. In order to analyse RS data, methods to recover velocity and direction of surface currents and determining characteristics of surface waves were developed and tested (see, for example, [4–6] and the literature cited in these works).

Wind speed reconstruction from radar images is mainly based on empirical models that establish the relationship between the radar signal intensity and wind speed vector magnitude U. In [7], it was proposed to use a third-order geophysical model function (GMF). At wind speeds of ~ 4 and 22 m/s, the errors in retrieved wind speeds were ~ 0.8 and ~ 0.1 m/s, respectively. To determine the wind speed direction, the radar signal intensity, depending on sea surface observation azimuth j, is approximated by a harmonic function [8]. The value of the angle at which the maximum radar signal value is observed is taken as wind direction j_U. To determine U, an empirical model function was proposed in [8], in which the radar signal integrated over all azimuth angles was used. Another way to retrieve wind speed vector from marine navigation radar images is to use neural networks [9].

Unfortunately, many papers describing algorithms for wind field retrieval from coastal or ship RS data do not provide information on the linearity of the characteristics of the radar receiving paths and its calibration dependencies. As a result, it is not possible to convert the signal intensity into normalized radar cross-section (NRCS) s₀ and make comparisons with data from other sources and theoretical models. The empirical GMFs listed above are not based on physical ideas about the formation of the radio signal reflected from the sea surface at large sensing angles. Various methods of smoothing and filtering of the initial signal are applied, which makes it difficult to use the proposed techniques for other types of radars.

Onshore or shipboard radars operate generally in horizontal polarised transmission/reception mode at sea surface sensing angles of 75–89°. Under such observational conditions, the main contribution to the NRCS formation is made by wave breaking [1, 3, 10–12]. In current models, s₀ depends on fraction of sea surface q with whitecap coverage. Accordingly, the NRCS changes with wind speed variation should be related to the wind dependency of q. At the same time, q depends on the wave age [13–15], which leads to a change in the level of s₀ for the same wind but different wave ages.

Taking into account the physical state of the sea surface is particularly important for the retrieval of atmospheric parameters in the coastal waters, where the degree of wave development varies widely depending on the wind direction.

The paper aims to develop a semiempirical model of the wind dependency of the sea surface NRCS in the X-band at horizontal polarization of the signal transmission/reception at large incidence angles over a wide range of wave ages.

Experiment location and equipment

The in situ experiment was conducted in August – October 2022–2024 on a stationary oceanographic platform located in Blue Bay near the village of Katsiveli, the Southern Coast of Crimea (Fig. 1, а). With its coordinates 44°23ʹ38ʹʹ N, 33°59ʹ09ʹʹ E, the stationary oceanographic platform is constructed ~ 480 m from the nearest shore point. The depth at the measurement site is about 30 m.

 

Fig. 1. Study area (a) and equipment used. The star indicates the location of the stationary oceanographic platform; the inset shows a radar image of the sea surface; b – MRS-1011 radar station; c – stationary oceanographic platform, the arrows indicate the location of the equipment shown in b, d, e; d – meteorological station; e – string wave recorder

 

An MRS-1011 (produced by Micran JSC, city of Tomsk) short-range vision radar with high range resolution (Dl = 0.79 m) transmitting and receiving horizontally polarized signal. The radar power is not more than 1 W, the width of the radiation pattern in the horizontal plane (Dj) is 1°, in the vertical plane – 30°. In this radar, a continuous linearly modulated signal is generated at an operating frequency of 9430 MHz (wavelength l_r = 3.2 cm) modulated by a periodic sawtooth function with a period of 7 ms. The bandwidth of the sensing signal is 200 MHz relative to the operating frequency. The received reflected signal is subjected to amplification and homodyne processing resulting in a beat signal, the spectrum of which represents the range and radar cross-section s (RCS) of the target.

The radar was mounted on the oceanographic platform at a height of 15 m above sea level (Fig. 1, b, c) and was used during the experiment in the circular view mode with an antenna rotation angular velocity of 2.79 rad/s. Due to the radar specific location on the platform, the sea surface viewing sector ranged from 55° to 315° geographic azimuth.

As an example, the inset of Fig. 1, a shows a radar image of the sea surface, with clearly visible surface waves. The bright area in the upper left part is due to reflections of the radar signal from the shore. The dark area is the result of shading by the platform elements, in this sector the RS transmitter was not activated.

Wind speed and direction, atmospheric pressure, air temperature and humidity were recorded using a Davis Vantage Pro2 6152 meteorological station located 23 m above sea level on the mast of the oceanographic platform (Fig. 1, d). Water temperature was measured at a depth of 3 m.

Wind speed at 10 m horizon for neutral stratification of the atmospheric boundary layer was calculated using meteorological and surface water temperature data with the COARE 3.0 methodology from [16].

Surface wave characteristics were recorded using a string wave recorder (Fig. 1, e). Frequency spectra of sea surface elevations S(f) were obtained as a result of wave data processing. As a rule, during our measurements, in addition to wind waves, ripple waves were also observed. Approach [17] was used to divide the wave frequency spectrum into ripple waves and wind-generated waves. As a result, the values of spectral peak frequency f_p, wave peak frequency f_pw and wave age a = c_pw/U, where c_pw is phase velocity of waves at the wave peak frequency, were determined.

The geometric characteristics of wave breaking were determined from video recordings of the sea surface made with a digital video camera. Additional information on the algorithm and calculation of various breaking parameters is given in [18, 19].

Fig. 2 demonstrates the histograms of values U, j_U and a measured in the experiment. As can be seen from Fig. 2, a, wind speed ranged from 2 to 20 m/s, with the majority of observations being made in the U range of 5 to 15 m/s. During the experiments, winds were predominantly easterly (j_U = 60–120°) and westerly (j_U = 250°) (Fig. 2, b). The wave age distribution shown in Fig. 2, c shows that α varied from 0.1 to 3, with ~96 % of the wave age values ranging within 0.1–1.2.

 

Fig. 2. Histograms of wind and wave measurement conditions: a – wind speed; b – wind direction; c – wave age

 

Cases when the sea was dominated by ripples were excluded from further processing. Strong modulations of the radar signal caused by ripples can affect the mean values of s₀ significantly, but are not studied in the paper.

Data preprocessing

A radar similar in its technical characteristics to the RS in [20], but with increased transmitter power, was used during the experiments.

To convert conventional units of the radar signal into absolute values of NRCS s₀, the RS was calibrated. An inflatable polymer ball (wall thickness ~ 1 mm, diameter D_Ball = 67.5 cm) with added aluminum powder was used as a target. To give conductive properties, the ball was additionally coated with paint with the addition of aluminum powder. Given that l_r << D_Ball /2, the ball RCS is s_Ball = 0.36 m². In calm weather, the target was towed by an inflatable boat up to 1000 m from the platform.

Carrying out calibration works is necessary because the obtained values facilitate data interpretation, since the radar scattering models operate with absolute values of the signal. Note that the calibration constants are different for every device.

As was shown in [20], the receiver characteristics of the RS we use are nonlinear. Accordingly, we should expect that the received signal power from the ball P_R will not be described by the basic radar formula. Fig. 3 shows the dependency of P_R/s_Ball value on the distance to the ball R. Measurement data can be described by the following power function

P_R / s_Ball = C×R^–d, (1)

where coefficients C = 1.1×10¹² and d = 3.4 are obtained by the least squares method.

 

Fig. 3. Dependence of the received signal power normalized to the ball radar cross-section on the distance to the target. The straight line shows approximation by power function (1)

 

The magnitude of the reflected signal scattered by the sea depends on the value of irradiated sea surface area S. To exclude this influence, the signal reflected from the sea surface is described as NRCS s₀ = s / S, where S = 2Dl R tan(Dj/2).

Taking into account the calibration constants, the sea surface NRCS for all points of the radar image was defined as

s₀ = C ¢PR^2.4,

where C ¢ = 1/[2C Dl tan(Dj/2)]; P is power of the received radar signal.

Model of non-Bragg scattering component

A model for the formation of the sea surface radar NRCS is considered in [3]. In general, s₀ can be represented as the sum of Bragg s_0br and non-Bragg s_0nb scattering components

s₀ = s_0br (1 – q) + s_0nb q.

According to [3], s_0nb is formed under conditions of quasi-mirror reflections from very rough parts of the breaking zone, then the whitecap RCS is as follows

${\sigma }_{0nb}(\theta ,\phi )={\sigma }_{0wb}(1+M_{wb}{\overline{\theta }}_{wb}{A}_{wb}(\phi \left)\right),$(2)

s_0nb(q) = (sec⁴(q)/s_wb²) exp(–tan²(q)/s_wb²) + s_wb/s_wb², (3)

where q is incidence angle from nadir; j is observation azimuth of the radar station; M_wb is modulation transfer function; – is whitecap average inclination; A_wb(j) is coefficient determining the angular distribution of non-Bragg scattering and providing the difference between radar signals in “up-wind” and “down-wind” observations; e_wb² is RMS slope of roughness of the breaking zone; e_wb is constant equal to the ratio of the whitecap thickness to its length. At high incidence angles (q > 75°) [21], the main contribution to the horizontally polarized radar signal is made by s_0nb , and the determining role in expression (3) is played by the second summand, hence, taking into account (2), s₀ can be written as

s₀ = (s_wb/s_wb²) (1 + M_wb A_wb(j)) q, (4)

According to expression (4), s₀ should not depend on the sea surface observation angle. For very large angles (q > 88–89°), the NRCS value can be influenced by the effects associated with shading of sea surface areas by long-wave crests. As follows from formula (4), the change in signal power will be determined by the fraction of the sea surface covered by wave breaking.

Traditionally, q is described by power function q = B₀Uⁿ (see, e. g., [19, 22–24]). However, the large scatter in the data [13, 14] indicates that wind speed by itself does not explain all of the observed variability of q. In particular, according to [13–15], coefficient B₀ is wave age function B₀ = f(a). As function f(a) can be nonlinear, let us define it as power function f(a) = a^b. A general form expression for formula (5), which is an analogue of GMF, follows from the above:

s₀(j, q) = B(j, q) a ^{b(j, q)} U ^{n(j, q)}, (5)

where b(j, q), n(j, q) and B(j, q) are constants.

Note that, since our data were obtained under conditions close to neutral stratification of the atmosphere, we will neglect the manifestation of stratification effects on wave breaking.

Analysis of data obtained

Angular dependencies of radar signal

Fig. 4 shows the NRCS dependency on the incidence angle for “up-wind” s₀^up, “perpendicular to the wind” s₀^cr and “down-wind” s₀^dw measurements. The RMS deviation averaged over realisations did not exceed 5 dB. As can be seen from Fig. 4, the sea surface NRCS for incidence angles 83.5 £ q £ 88° is almost unchanged, while at higher values of q, the NRCS decreases due to the influence of shading by long-wave crests. In order to construct the GMF to recover the wind speed vector, we will consider the mean value of s₀ over the range of angles (83.5–88°) and on the descending section of s₀ for values of q equal to 88 and 89°. For our observational conditions, this corresponds to a distance of 130–860 m.

 

Fig. 4. Normalized radar cross-section (NRCS) of the sea surface s a function of the angle of observation for ‘up-wind’ (a), ‘perpendicular to the wind’ (b) and ‘down-wind’ (c) measurements. The blue line is data averaged over the range U = 7.0 ± 1.5 m/s; the red line is 11.0 ± 1.5 m/s; the orange line is 15.0 ± 1.5 m/s. Confidence intervals are given in the bottom left part of the figure

 

Wind dependencies of radar signal

Fig. 5 shows an example of wind dependencies s₀^up, s₀^cr, s₀^dw for the range of angles 83.5 £ q £ 88°, with the colour of symbols corresponding to the wave age colour scale on the right side.

 

Fig. 5. NRCS of the sea surface as a function of wind speed during ‘up-wind’ (a), ‘perpendicular to the wind’ (b) and ‘down-wind’ (c) sensing. The solid lines correspond to dependence (5) with coefficients given in the table for a = 0.1 (lower line) and a = 1.2 (upper line)

 

Coefficients of NRCS wind dependency

q	j = 0°			j = 90°			j = 180°
	107 B	n	b	108 B	n	b	108 B	n	b
83.5–88	4.2	3.3	0.7	2.2	4.2	1.4	0.5	4.4	1.1
88.5	2.9	3.3	0.8	6.4	3.6	1.0	4.9	3.1	0.7
89	0.7	3.5	1.0	17.5	2.9	0.9	–	–	–

 

As follows from Fig. 5, power dependency of s₀ on wind speed is observed. Note that for the same wind speed at the measurement level, the values of s₀ increase with increasing a, i. e., in the process of wave development. This regularity is characteristic of all selected observation azimuths. With a changing from 0.1 to 1.2, the weakest growth of s₀ by ~5 times is observed for s₀^up, and the largest NRCS increase by about 30 times is characteristic for s₀^cr. The obtained dependency of s₀ on wind speed and wave age confirms the appropriateness of describing the sea surface NRCS in form (5).

The values of coefficients B, b, n given in Table for different values of q and azimuths in the interval 0.1 £ a £ 1.2 were determined by the least squares method from experimental arrays of simultaneous measurements of wind speed, wave age and s₀(j, q). In the “up-wind” direction, the values of corresponding powers are almost the same for specified incidence angles q. The decrease in B level at observation angles q ³ 88.5° can be explained by shading conditions.

The obtained values of n fall within the range of wind coefficient estimates known from [14, 25, 26] for the fraction of the sea surface covered by breaking crests.

The NRCS model considered above at large incidence angles (4) indicates that s₀ is determined by the value of q. Hence, wind dependency s₀ should be determined by the dependency of q on U. Note that the first two terms in the right-hand side of expression (4) containing s_wb², M_wb, _wb,, can involve in s₀ = f(U), but we did not determine their values. Let us use the archive data of q and the values of s₀ and q obtained simultaneously during measurements in the experiment.

In Fig. 6, a, squares represent the values of s₀^up at wind speeds from 2.2 to 17.1 m/s, circles represent the values of q obtained at U = 4.7–21.4 m/s. Both wind dependencies almost coincide, but a slight difference is observed at U < 10 m/s; in these cases, a stronger decrease in the value of q is observed with decreasing wind. This can be explained by the fact that during moderate and weak winds, small breaking crests that contribute significantly to the value of q are not identified during video processing [27, 28]. At the same time, such breaking is involved in the formation of the NRCS.

 

Fig. 6. Fractions of the whitecap coverage and NRCS: a – wind dependencies q and s₀; ( – values of s₀^up at U = 2.2¸17.1 m/s,  – values of q at U = 4.7¸21.4 m/s) b – dependency of NRCS on q derived from synchronous measurements

 

It is of interest to compare s₀ and the fraction of the surface covered by the active phase of breaking. Indeed, according to model (4), simple relation s₀ ¥ q should be observed. Fig. 6, b demonstrates the dependency of the NRCS on q obtained from our data as a result of synchronous measurements. As can be seen from Fig. 6, b, the dependency of the NRCS on q is satisfactorily described by the linear function shown by the solid line s₀ = 1.47q. Such a linear dependency confirms model (4) of the NRCS formation at large incidence angles of the radar signal.

Azimuthal dependencies of radar signal

Previous studies [29–31] have shown that for maritime navigation stations operating on a horizontally polarised signal at q > 75°, the maximum value of the radar signal is observed in the “up-wind” direction. To describe the azimuthal dependency of the signal and to find the wind speed and direction, we approximate our data by a standard dependency in the form of a restricted Fourier series (see, e. g., [32])

s(U, j, q) = A₀ + A₁ cos(j – j_w) + A₂ cos[2(j – j_w)], (6)

where j_w is direction of azimuthal dependency maximum; A₀, A₁, A₂ are coefficients, which generally depend on U, a, q and, according to the work ¹⁾, are written as

A₀ = (s₀^up + s₀^cr + s₀^dw)/4, (7)

A₁ = (s₀^up – s₀^dw)/2, (8)

A₂ = (s₀^up – 2s₀^cr + s₀^dw)/4, (9)

In our notations, direction j = j_w corresponds to the “up-wind” measurements, j = j_w + p – to the “down-wind” ones. In formulas (7)–(9), s₀^up, s₀^cr, s₀^dw are described by expression (6), with the values of coefficients B, b, n given in Table. Fig. 7 shows the NRCS azimuthal dependencies for easterly and westerly wind directions. The line is for dependency (6) considering expressions (5) and (7)–(9). The unknowns in formula (6) are U_RL and j_w, which were determined by the least squares method (with U_RL = 10 m/s, j_w = 80° for the line in Fig. 7, a and with U_RL = 14 m/s, j_w = 250° for the line in Fig. 7, b). The wave age in the radar measurements was calculated from the wind wave elevation spectra.

 

Fig. 7. The sea surface NRCS as an azimuth angle function at U = 9 m/s, j_U = 70°, a = 0.8 (a); U = 15 m/s, j_U = 250°, a = 0.2 (b). The dashed lines are for wind direction retrieved from the anemo-meter data

 

At moderate wind speeds (Fig. 7, а), azimuthal dependency s₀(j) has one pronounced maximum when measuring “up-wind”, with the minimum value observed “down-wind”. When the wind speed increases (Fig. 7, b), the azimuthal dependency acquires a bimodal character, a second local maximum appears in the “up-wind” direction. The peculiarities of azimuthal dependencies at large sea surface observation angles are discussed in more detail in [20].

Speeds U_RL and j_w were calculated for the whole data array by the least squares method according to formula (6) using in situ radar measurements. Fig. 8 shows the comparison of wind speed direction and vector magnitude retrieved from radar data with those retrieved from the anemometer.

 

Fig. 8. Wind speed direction (a) and vector magnitude (b) retrieved from the anemometer and radar data. The straight line corresponds to equal values of the two quantities

 

Fig. 8 shows a linear relationship between j_w and j_U as well as between U_RL and U, with standard deviations between these pairs of values being 30° and 1.2 m/s, respectively.

Conclusions

The semiempirical model of the wind dependency of the sea surface NRCS is proposed, which makes it possible to retrieve the driving wind speed for X-band radar sensing of the sea surface at large incidence angles. Radar, meteorological, waveform data and video recordings of the sea surface obtained during 2022-2024 at a stationary oceanographic platform in Blue Bay, the Southern Coast of Crimea, were used for the analysis. Measurements were carried out at wind speeds from 4 to 17 m/s. The observed wave age varied from 0.1 to 3, with 96% of the values of a being in the interval 0.1 £ a £ 1.2.

For radar sensing of the sea at large incidence angles, fraction of the sea surface q covered by breaking crests is the main informative parameter that governs NRCS s₀. Dependency of the fraction of sea surface covered by breaking crests on wind speed and wave age a results in the corresponding dependencies of s₀ on wind speed vector magnitude U and wave age.

The contribution of wave breaking to the sea surface NRCS was confirmed experimentally. The linear dependency of s₀ on the fraction of the sea surface covered by breaking was obtained: s₀ = 1.47q. Presented wind dependencies s₀^up and q obtained in situ, are almost identical. This result confirms experimentally adopted model s₀(U) ¥ q(U) and the essential role of wave breaking in the formation of the radar signal scattered by the sea surface at large incidence angles. It is shown that the degree of wave development affects the NRCS level, which increases five times with increasing wave age from 0.1 to 1.2 for the same “up-wind” direction.

The geophysical model function that takes into account wind speed and wave age a was constructed. Using the results obtained within the geophysical model function, wind speed and wind direction can be retrieved from the radar data. The wind speed vector magnitude and direction calculated from s₀ coincided satisfactorily with the anemometer readings. The RMS errors of retrieved values U_RL and j_w were 1.2 m/s and 30°, respectively.

 

^[1] Ulaby, F.T., Moore, R.K. and Fung, A.K., 1986. Microwave Remote Sensing: Active and Passive. Vol. 3. Dedham, MA, USA: Artech House, 2126 p.

About the authors

Aleksandr E. Korinenko

Marine Hydrophysical Institute of Russian Academy of Sciences

Author for correspondence.
Email: korinenko.alex@yandex.ru
ORCID iD: 0000-0001-7452-8703
Scopus Author ID: 23492523000

Senior Research Associate, PhD (Phys.-Math.)

Russian Federation, Sevastopol

Vladimir V. Malinovsky

Marine Hydrophysical Institute of Russian Academy of Sciences

Email: vladimir.malinovsky@mhi-ras.ru
ORCID iD: 0000-0002-5799-454X
Scopus Author ID: 23012976200
ResearcherId: F-8709-2014

Senior Research Associate, PhD (Phys.-Math.)

Russian Federation, Sevastopol

References

Supplementary files