The GNSS reflected signal monitoring system consists of three components: navigation satellites, receiving antennas, and the reflecting surface. Due to the high orbital altitude of GNSS satellites, the transmitted signals can be approximated as plane waves when they reach the Earth’s surface. On an ideal, infinitely large Earth surface, these signals undergo specular reflection, with the GNSS reflected signal dominated by the specular component. The signal received by the antenna is formed by the combined scattering contributions from various reflection elements on the sea surface. Each reflection element corresponds to a unique delay and Doppler shift relative to the specular reflection point. Thus, the observed surface is divided along two dimensions: iso-delay lines and iso-Doppler lines. In the presence of an oil spill on the sea surface, these signal components are altered. By applying Delay-Doppler Map (DDM) techniques, these variations can be accurately measured and extracted, enabling the inversion and detection of the spatial distribution of the oil spill.

According to the GNSS ocean surface scattering Z-V model based on the Kirchhoff approximation theory, the scattered sea surface signals are composed of components with different time delays and Doppler shifts. When an oil spill is present, these signal components change, and this variation can be characterized by the correlation power of the scattered signal at different code delays and Doppler frequencies.

In 2000, Zavortny and Voronovich developed a two-dimensional delay-Doppler correlation power model for GNSS ocean surface scattering signals based on the bistatic radar equation and the Kirchhoff approximation using a geometric optics approach [26]. This Z-V model is now widely applied in various GNSS-R ocean remote sensing applications, such as sea surface wind speed retrieval, sea ice monitoring, and oil spill detection. The model is expressed as follows:

〈 | Y ( Δ τ , Δ f ) | 2 〉 = T i 2 ∬ Z | S ( Δ f ) | 2 σ 0 ( r ) Λ 2 ( Δ τ ) D 2 ( r ) 4 π R R 2 ( r ) R T 2 ( r ) d r 2 (1)

where T i the coherent integration time, D ( r ) is the antenna gain of the receiver, Λ is the autocorrelation function, S is the Doppler filtering function, R T ( r ) and R R ( r ) are the distances of the GNSS satellites and receiver to the scattering points, respectively, Δ f and Δ τ represent the Doppler shifts and time delays of the scattering points on the reflecting surface with respect to the specular reflection points, respectively. Doppler shift and time delay, r is the position vector of the scattering point. The specific equations are expanded as follows.

(1) MSS Model:

According to the MSS (Mean Square Slope) model proposed by Cox & Munk, the presence of oil on the sea surface significantly affects the MSS [27]. For clean seawater, the MSS is a function of the 10-meter wind speed, expressed as:

σ c , c 2 = 0.003 + 1.92 ⋅ 10 − 3 U 10 σ u , c 2 = 3.16 ⋅ 10 − 3 U 10 (2)

When oil is present on the sea surface, it alters the surface roughness and consequently changes the MSS. For oil-covered seas, the relationship becomes:

σ c , s 2 = 0.003 + 0.84 ⋅ 10 − 3 U 10 σ u , s 2 = 0.005 + 0.78 ⋅ 10 − 3 U 10 (3)

where: the first subscript u of the MSS denotes upwind and c denotes crosswind; the second subscript s , c of the MSS denotes oil spill and seawater on the sea surface, respectively; and U₁₀ is the wind speed at a sea surface height of 10 m.

(2) PDF Model

The ECXI (Earth-Centered, X-Z Incidence) coordinate system is used in the study, and assuming that the wind direction is along the X-axis, the expression of the probability distribution function of the sea surface gradient for each scattering point is given by

P p d f ( − q ⊥ q z ) = 1 2 π σ u 2 σ c 2 ⋅ exp [ − 1 2 [ ( − q ⊥ , c / q z ) 2 σ c 2 + ( − q ⊥ , u / q z ) 2 σ u 2 ] ] (4)

where σ c 2 and σ u 2 represent the MSS in the up-wind and cross-wind directions, respectively (based on the ECXI system).

(3) Scattering coefficient σ⁰

σ⁰ refers to the scattering coefficient corresponding to each scattering point within the observation area.

σ 0 ( r ) = π | ℜ | 2 ( | q | q z ) 4 P p d f ( − q ⊥ q z ) (5)

where q is the scattering vector of the transmitter and receiver at a fixed position on the reflecting surface, which can also be considered as a function of the plane coordinate ρ → , ℜ is the Fresnel reflection coefficient, q ⊥ is the horizontal component of the scattering vector, q z is the z-direction component of the scattering vector, and P p d f ( − q ⊥ / q z ) is the probability density function of the sea surface slope.

(4) ∑ function

Before the receiver receives the scattering signal, where the expression for the energy of each scattering point is as follows.

∑ ( Δ τ , Δ f ) = T i 2 D 2 ( r ) σ 0 ( r ) 4 π R R 2 ( r ) R T 2 ( r ) d s (6)

where T i is the coherent integration time, D ( r ) is the antenna gain of the receiver, and r is the position vector of the scattering point.

(5) Convolution of ∑ and x functions

Using the Z-V model based on Kirchhoff’s approximate geometrical optics theory, the time-delay-Doppler two-dimensional correlation power model of the GNSS sea surface scattered signal is constructed as follows

〈 | Y ( Δ τ , Δ f ) | 2 〉 = Σ ( Δ τ , Δ f ) ∗ χ 2 ( Δ τ , Δ f ) (7)

χ 2 ( Δ τ , Δ f ) = Λ 2 ( Δ τ ) ⋅ | S ( Δ f ) | 2 (8)

where ∗ denotes the 2D convolution, χ is the blurring function.

According to the above equation, under specific wind speed and wind direction conditions, the presence of an oil spill on the sea surface alters the local mean square slope (MSS), resulting in significant differences compared to clean seawater. This change in MSS further affects the surface roughness characteristics of each scattering point within the observation area, thereby leading to variations in the corresponding coefficient. The modified scattering coefficient field can then be used as input to the Z-V model, enabling a more accurate representation of scattering characteristics under different sea surface conditions. This, in turn, supports the simulation of the Delay-Doppler Map (DDM) and provides a physical basis for sea surface state identification and oil spill detection.

This study takes the oil spill incident caused by the “Symphony” cargo ship on April 27, 2021, near the coast of Qingdao, China, as the research subject, using it as a representative application scenario for GNSS-R-based sea surface oil spill monitoring. Remote sensing data of the oil spill is used as model input, and the main distribution area of the spill is extracted from Sentinel-1 satellite radar imagery, as shown in Figure 1.

The specific simulation experimental parameters for this experiment are shown in Table 1.

This study conducts a simulation of GNSS-R technology applied to marine oil spill monitoring, using a real oil spill event as the research background. First, wind speed and direction data over the study area are input, and the Cox & Munk model is employed to calculate the mean square slope (MSS) of both clean seawater and oil-covered surfaces, thereby characterizing the roughness under different sea conditions. A probability density function (PDF) model is then used to describe the statistical distribution of sea surface slopes in each region, from which the corresponding sea surface scattering coefficients (σ⁰) are derived. During the scattering coefficient calculation, the directional asymmetry of the sea surface caused by wind is further considered. Based on the actual spatial distribution of wind speed in the study area, the initially estimated σ⁰ values are corrected to obtain scattering coefficients that better reflect real sea surface conditions.

Subsequently, the positions and velocities of the GNSS satellite and receiver are used to accurately locate the specular reflection point and surrounding scattering points within the observation area. Combined with the corrected scattering coefficients and the scattering geometry, the reflected signal power from the sea surface is computed, and a Delay-Doppler Map (DDM) is generated accordingly. By analyzing and interpreting the power distribution patterns in the DDM, the spatial extent and characteristics of the oil spill are extracted and identified. The structural framework of the simulation process is illustrated in Figure 2.

According to the sea surface oil spill distribution shown in Figure 1 and the experimental parameters listed in Table 1, a detailed monitoring simulation scheme was developed. First, the mean square slope (MSS) values of the oil-contaminated area and the clean seawater area were calculated using Equation (2) and Equation (3), respectively, to characterize the differences in surface roughness under varying sea conditions. The obtained MSS values were then substituted into Equation (4) to construct the slope probability density function, which was further combined with Equation (5) to derive the scattering coefficients for each region. The final distribution of the sea surface scattering coefficients is shown in Figure 3.

As illustrated in Figure 3, the scattering coefficients in the oil spill region are significantly higher than those in the clean seawater area. This is because the

presence of an oil film on the sea surface reduces the surface tension of seawater, effectively suppressing the generation of capillary waves and small-scale gravity waves, thereby weakening their scattering contribution to the incident electromagnetic waves. As a result, the forward scattering of GNSS signals is enhanced while the backward scattering is reduced, leading to a distinctive change in the scattering energy distribution in the Delay-Doppler Map (DDM) compared to that of a clean sea surface.

By fully considering the asymmetry of the actual sea surface, and based on the scattering coefficient distribution shown in the experimental scenario in Figure 3, the scattering signal Delay-Doppler Map (DDM) containing oil spill features was extracted in both the delay domain and Doppler frequency domain using the mathematical model established by Equation (1). Figure 4 presents the simulated DDM result, where the horizontal axis represents code delay (in chips), and the vertical axis represents Doppler frequency shift (in Hz). The color intensity indicates the power strength of the GNSS sea surface scattering signal at different positions. From Figure 4, the oil spill region on the sea surface can be clearly distinguished, demonstrating the feasibility and effectiveness of using GNSS-R technology for marine oil spill detection. For comparison, Figure 5 shows the DDM image under clean sea surface conditions.

In addition, in order to elucidate the performance pattern of GNSS-R in detecting

oil spill characteristic parameters under various wind speed conditions, clean and oil-covered sea surface were simulated based on the parameters listed in Table 1 and the SAR images shown in Figure 1. Figure 6 shows the comparison of sea surface MSS for oil-covered and clean sea surface under different wind speed conditions. Figure 6 shows the comparison of scattering coefficients for oil-covered and clean sea surface for different wind speed conditions. These comparisons are critical to understanding how oil spills change sea surface characteristics, which in turn affects the scattering characteristics detected by GNSS-R.

As can be seen in Figure 6 and Figure 7 above, significant differences in MSS and scattering coefficients between the overlying oil and the clean sea surface are observed under different wind speed conditions. Specifically, the differences in MSS and scattering coefficients between oil and seawater are small when the wind speed is less than or equal to 2 m/s. This phenomenon may be due to the limited value of sea surface wave amplitude caused by low wind speed, which is insufficient to show significant differences in the physical properties of oil and seawater. Therefore, the similarity of MSS and scattering coefficients between the oil spill area and the surrounding seawater in a low wind speed environment poses a certain degree of challenge for oil spill detection. When the wind speed exceeds 2 m/s, there are obvious differences in MSS and scattering coefficients between oil and seawater.

The preceding study analyzed the feasibility of using GNSS-R technology to detect marine oil spills from a simulation perspective. To verify the accuracy and reliability of the simulation results and further demonstrate the effectiveness and potential of GNSS-R in real marine environments for oil spill detection, this section conducts an empirical analysis using CYGNSS satellite-borne DDM data related to the Symphony tanker oil spill incident that occurred in 2021.

The incident occurred in the southeastern offshore waters of Zhaolian Island, Qingdao, Shandong Province, China, with the central coordinates located at 35˚43'8"N, 120˚58'5"E. To capture the impact of the oil spill distribution on GNSS-R signal characteristics in this region, CYGNSS constellation data collected between 00:00 and 24:00 on April 30, 2021, were extracted, as shown in Figure 8. Figure 8 displays the remote sensing background image of the affected area along with the spatial distribution of CYGNSS observations during the corresponding

time period. The red dots represent the projected positions of GNSS-R specular reflection points. These reflection points are concentrated around the 35.8˚N latitude line, spanning longitudinally from approximately 120.75˚E to 121.25˚E, with a coverage width of about 0.5˚, effectively encompassing the main area of oil contamination. This spatial-temporal alignment provides a critical data foundation for subsequent DDM analysis and oil spill identification.

This section also utilizes ERA5 sea surface wind data from the European Centre for Medium-Range Weather Forecasts (ECMWF), which correspond spatially and temporally to the CYGNSS satellite observations. ERA5 data offer high temporal and spatial resolution, reaching 1 hour and 0.125˚ × 0.125˚, respectively. To further improve the accuracy of wind field characterization in the study area, bilinear interpolation was applied to enhance the spatial resolution. The resulting sea surface wind distribution in and around the oil spill region is shown in Figure 9.

During the event, wind speeds in the oil spill area remained between 5.9  m/s and 6.2  m/s, with no wave breaking observed, indicating relatively calm sea conditions. Under such environmental conditions, the application of GNSS-R technology for oil spill information extraction and feature analysis is highly feasible. As shown in Figure 10(a), the Delay-Doppler Map (DDM) corresponds to the clean sea surface obtained by CYGNSS-R, while Figure 10(b) presents the DDM image associated with the oil-contaminated area.

As shown in Figure 10(a), the Delay-Doppler Map (DDM) of a clean sea surface acquired by CYGNSS exhibits a structure similar to that of the simulated clean sea surface DDM. Both display typical GNSS-R signal characteristics: the power reaches its maximum at the specular reflection point and forms a distinct

symmetric “horseshoe-shaped” distribution near the zero Doppler frequency line. However, Figure 10(b) illustrates the DDM corresponding to an actual oil spill area, where the power distribution near the specular reflection point shows abnormal variations, significantly differing from the “horseshoe-shaped” structure of the clean sea surface. Specifically, in certain delay-Doppler cells, the power is reduced, exhibiting localized asymmetry and weakened scattering intensity. This variation is primarily caused by the strong suppression of short-wave disturbances by the surface oil film, which diminishes the presence of capillary and small-scale gravity waves, thereby significantly reducing local sea surface roughness and affecting the GNSS signal scattering response.

Overall, the measured DDM is influenced by multiple environmental factors, particularly wind speed and wind direction, which lead to spatial heterogeneity in sea surface roughness and cause asymmetry in the DDM image, with distinct scattering characteristics across different regions. These experimental results not only empirically validate the scientific basis and accuracy of the GNSS-R sea surface oil spill response model proposed in the earlier simulations, but also further emphasize the feasibility and effectiveness of using satellite-borne CYGNSS GNSS-R data for marine oil spill monitoring. With its high temporal resolution, wide spatial coverage, and strong sensitivity to sea surface conditions, CYGNSS is capable of providing stable and reliable observations under complex marine environments. Therefore, it offers critical technical support for rapid identification and dynamic monitoring of marine oil spill events, demonstrating the application potential and development prospects of GNSS-R technology in ocean remote sensing.