Green algae monitoring via ground-based GNSS-R observations

Outbreaks of harmful algal blooms (HABs) exhibit high frequency, large range and damage aggravation characteristics, but existing monitoring methods, such as artificial and optical near-infrared remote sensing, cannot accommodate these characteristics. We propose a new method for monitoring green algae using Global Navigation Satellite System Reflectometry (GNSS-R) observations. The basic principle states that changes in the seawater dielectric constant and sea surface roughness due to the emergence of green algae lead to an increase in brightness temperature, which can be inverted based on the reflection time delay waveform. Shipboard reflection waveform data collected during an Enteromorpha prolifera outbreak in the Qingdao sea area were used for model development and validation of the detection and estimation performance. The results indicated that the root mean square error of GNSS-R-based inversion of the green algae density was 6.74%, indicating the potential of GNSS-R technology for rapid preliminary monitoring of green algae. Moreover, the advantages of a low cost, short return time and no climatic limitations support GNSS-R technology as a new and efficient means of green algae monitoring.


Introduction
Over the past few decades, the Global Navigation Satellite System (GNSS) has been rapidly developed, especially considering its L-band signal, which has facilitated its application in microwave remote sensing. Martin-Neira (1993) first verified the feasibility of GNSS reflected signals and proposed the concept of passive reflection and interferometry systems for ocean altimetry. Subsequently, the notable potential of GNSS Reflectometry (GNSS-R) applications has been increasingly explored and applied, and great progress has also been made in remote sensing of the earth's surface, including land and ocean remote sensing.
The GNSS-R has been applied to retrieve earth land parameters, such as the snow depth (Larson et al. 2009;Yu et al. 2015), soil moisture (Chew et al. 2014;Zavorotny et al. 2010) and vegetation index (Camps et al. 2016). The most effective GNSS-R applications have occurred in marine remote sensing. Garrision and Katzberg (1997) first detected the GPS scattering signal from the ocean surface through the airborne receiver. Subsequently, Zavorotny and Voronovich (2000) developed a theoretical scattering power model, which is a function of geometric and environmental parameters. At present, the GNSS-R has been widely applied to estimate ocean surface characteristics, such as the sea surface height (SSH) (Yu et al. 2014), sea surface salinity (SSS) (Camps et al. 2006), wind speed and wind direction (Komjathy et al. 2000;Park et al. 2017) and sea state (Riur et al. 2002).
With the continuous performance improvement in reflection signal receivers, including the availability of multifrequency delay-Doppler map (DDM) observations, the scope of GNSS-R marine applications has been greatly expanded. The eddy experiment emphasizes the utilization of the entire DDM to more precisely infer ocean roughness parameters (Germain et al. 2004). An airborne field campaign conducted by Voo et al. was also intended to estimate the ocean surface roughness. The result indicated that the ocean surface roughness exhibits a strong correlation with the brightness temperature (Voo et al. 2010). Then, many studies revealed a strong correlation between GNSS-R observations and the brightness temperature (Carreno-Luengo et al. 2018;Marchan-Hernandez et al. 2008;Valencia et al. 2009;Wang et al. 2017). In addition, Kim et al. (2004) proposed an approach for red tide monitoring at microwave frequencies, and the experimental results revealed that red tides could be distinguished from clean seawater conditions based on variations in the brightness temperature, which further verified the feasibility of L-band signals, i.e., GNSS signals were also included, in the monitoring of harmful algal blooms (HABs).
Blooms of algae can cause damage to aquatic environments by blocking sunlight and depleting oxygen. Certain species of algae, including green algae and various types of cyanobacteria, can produce potent toxins with adverse health effects on wildlife and humans, which are referred to as HABs (Hennon and Dyhrman 2020). In recent years, scientists have observed an increase in the frequency, severity and geographic distribution of HABs worldwide (Hallegraeff 2019). Therefore, effective and continuous monitoring of HABs has become particularly important.
At present, there are two main HAB monitoring methods. One method entails manual or buoy-based water quality monitoring, which is slow, inefficient and limited in range (Ishizaka 2003). The other method involves optical or near-infrared remote sensing (Gower 1994;Qiu et al. 2007), which realizes indirect HAB detection through the normalized difference vegetation index (NDVI), sea surface temperature (SST) (Huang and Lou 2003) and chlorophyll, denoted as (Kahru et al. 2004;Su et al. 2016). It has been found that the SST is the observation parameter with the highest timeliness and practicability. The mechanism of SST change caused by green algae is that a given seawater body exhibits different colors, such as green and red, and the water body absorbs solar heat, resulting in an increase in surface water temperature.
The GNSS-R cannot directly obtain the SST but can invert the sea surface brightness temperature . Meanwhile, the brightness temperature of the sea surface covered by green algae differs from that of clean seawater. Therefore, brightness temperature inversion based on L-band signal observations can be used to monitor green algae. As an intermediate parameter, the brightness temperature relates GNSS-R observations to the presence of green algae, which can eventually be used to indirectly monitor green algae based on GNSS-R observations. Although red tide or phytoplankton detection based on spaceborne GNSS-R observations, such as TDS-1, CYGNSS has been proposed (Rodriguez-Alvarez et al. 2021;Ban et al. 2022) recently, these methods only analyze the correlation between the observations and the red tide. At the same time, different from red tide, green algae are easy to gather, and the spaceborne resolution is low, so it may not be the best way for green algae monitoring. More importantly, the research method we proposed is also applicable to satellites, which is a good verification for GNSS-R red tide monitoring.
In the following section, we investigate the possibility of green algae detection based on GNSS-R observations with the sea surface brightness temperature as an intermediate parameter. Then, we present details on simulated GNSS-R observations and a green algae density model and validate the performance of the proposed green algae inversion method via simulated and experimental data. Finally, conclusions are outlined.

Theory of green algae detection based on GNSS-R observations
The outbreak of green algae can cause changes in dielectric constant, SST and sea surface state, which directly affect the brightness temperature of sea surface. Therefore, if changes in sea surface brightness temperature can be detected using GNSS-R observations, GNSS-R can be used to monitor the outbreak of green algae. This section describes and verifies this relationship in detail.

Relationship between green algae and the brightness temperature
The sea surface brightness temperature can be determined as follows Font et al. 2004): where θ is the signal incidence angle, f is the electromagnetic frequency of the GNSS signal, p is the surface roughness defining the sea state, and SSS is the sea surface salinity. T B,f lat is the brightness temperature of the flat sea surface, and ΔT B,state is the change in brightness temperature related to the sea surface state or roughness. T B,flat can be written as : where e( ) is the emissivity of the sea surface with respect to L-band radio waves and can be expressed as: where ℜ( ) is the sea surface Fresnel reflectivity.
According to (1) and (2), the brightness temperature depends on the SSS, SST, sea surface reflectivity and roughness, which can vary with the outbreak of green algae, especially the sea surface reflectivity and roughness (Zhang Green algae float on the sea surface and produce much foam or bubbles (Fig. 1), so the reflecting surface is a mixture of foam, seawater and green algae, leading to a change in the dielectric constant or reflectivity of seawater.
The effective dielectric constant of a mixture is determined by the combination of the volume ratio of the mixture components, dielectric constant, shape of the mixture, and directional relationship between each dependent variable and the electric field (Polder et al. 1946). According to the dielectric constant model of heterogeneous mixtures proposed by Looyenga (1965), the dielectric constant of seawater containing green algae and foam can be written as: where v i denotes the volume proportion of the ith component, m and i denote the permittivity values of the primary and secondary components of mixtures, respectively, * denotes the apparent permittivity of the mixture, m ≤ * ≤ ef f , A j is the depolarization factor along the direction of the ellipsoid principal axis, and n is the number of secondary mixtures contained within the mixture. In addition, the selection of A j is related to the green algae species. Because green algae are acicular or strip-shaped organisms, their factors can be selected as (1/2,1/2,0) (Looyenga 1965).
Equation (4) indicates that the dielectric constants of seawater w , foam and green algae must be known to obtain the equivalent permittivity of the mixture. The dielectric constant of seawater can be calculated with the Debye equation (Klein and Swift 1977). The dielectric constant of a foam-water mixture wf can be obtained with the Maxwell garnet equation (Guo et al. 2001), as follows: where v f is the fractional volume occupied by foam.
Considering the composition of green algae, we used the dual dispersion model proposed by , which can be expressed as: where s is the nondispersive residual part of the plant water content ( M g ) ( s = 1.7 − 0.74M g + 6.16M 2 g ) ; v fw andv b denote the volume components of free water and bound mixture in plants, respectively; sw and b are the dielectric constants of seawater and the bound mixture, respectively. v fw andv b are a function of the plant water content, which can be obtained with the following equation: Moreover sw can be obtained with (1), while b can be obtained as: where f b0 is the relaxation frequency.
The dielectric constant of the mixture can be obtained according to (4). The Fresnel reflectivity for vertical polarization ( ℜ vv ) and that for horizontal polarization ( ℜ hh ) are functions of the seawater dielectric constant (ε) and incidence angle ( γ = π − θ ), given as follows: where n is the complex refractivity of seawater and can be expressed as n = √ and n ′ is the real part of n.
In the case of circular polarization, such as GNSS reflected signals, which involves a transition from RHCP to LHCP, the Fresnel reflectivity ( ℜ ) in (3) can be written as (Ban et al. 2018): Fig. 1 Top view of green algae with foam (bubble) (http:// www. quanj ing. com) By substituting (10) into (3), the emissivity of the sea surface can be obtained. Figure 2 shows the sea surface emissivity under different satellite elevation angles, while the volume ratio of foam is 10%, which is also consistent with the experimental results obtained by Liu (2020). We can observe that the emissivity of seawater covered with green algae is higher than that of clean water. ΔT B,state depends on the wind-driven sea surface roughness or significant wave height (SWH).  established a correlation model between the SWH and brightness temperature change based on Wind and Salinity Experiment (WISE) data, where is the incidence angle. Red tide coverage leads to an increase in sea surface tension and a reduction in the influence of sea wind on the sea surface. However, blooms of green algae are mainly caused by the aggregation of algae and plants at the sea surface, which covers clean sea surfaces and increases roughness. We analyzed mean square slope (MSS) data observed by the CYGNSS in the presence (or absence) of an outbreak of Enteromorpha prolifera. The results indicated that the MSS in the area with a clean sea surface is lower than that in the green algae area under the same wind speed, so the occurrence of green algae also affects ΔT B,state through the SWH, which suggests that (11) is also suitable for green algae surfaces. In addition, ΔT B,state under horizontal polarization is inversely proportional to the SWH, which is consistent with GNSS observations, as verified by Valencia et al. (2011). Therefore, ΔT B,state under horizontal polarization was selected as the brightness temperature change attributed to the roughness. Table 1 provides simulated sea surface brightness temperatures under different sea surface conditions at an incident angle of 30°. Wind speed and SWH data were obtained from the National Marine Environment Prediction Center of China (NMEFC-CN). v ga is the green algae volume ratio of the mixture. The SST was derived from actual data observed during an outbreak of Enteromorpha prolifera in the Qingdao sea area. Figure 3 shows the relationship between the green algae density and brightness temperature variation.   . 3 Relationship between the brightness temperature and green algae volume ratio According to Table 1 and Fig. 3, the change in brightness temperature is directly related to the volume ratio of green algae on the sea surface. With increasing green algae density, the difference between the brightness temperature in the presence of green algae on the sea surface and that of clean water increases, which indicates that green algae accumulation can increase the brightness temperature of the sea surface. The corresponding linear and second-order fitting models are given in (12) and (13), respectively.
where BT is the brightness temperature. The fitting error in terms of the RMSE was 1.782 and 0.258 for the above linear and polynomial models, respectively. The second-order polynomial model was preferable for the typical range of the green algae volume ratio due to the much smaller fitting error. This was also verified by the obtained squared correlation coefficients of 0.9852-0.9997, respectively, for these two models, and only the second-order model was thus used in the following section. In addition, the actual observations indicated that the temperature variation due to green algae remained within 3 degrees, as listed in Table 2. Moreover, according to (2), the change in the sea surface brightness temperature caused by temperature change was even smaller than the model error. Therefore, the brightness temperature variation is only related to the volume ratio of green algae and the sea surface state.

Relationship between the brightness temperature and GNSS-R observations
According to the Z-V model proposed by Zavorotny and Voronovich (2000), the reflected signal can be described as follows: where P t is the power of the transmitted signal, G t and G r are the antenna gains of the transmitter and receiver, respectively, � ⃗ is the distance vector from the specular point to any point on the scattering surface, s is the reflection field, and q is the magnitude of vector � ⃗ q (often denoted as the scattering vector bisecting the incident and reflection vectors), which can be defined as � ⃗ q = 2 � ⃗ n − �� ⃗ m , where � ⃗ n and �� ⃗ m are the unit vectors of the incident and scattered waves, respectively. The direction of � ⃗ q is exactly perpendicular to the scattering surface at the scattering point.
According to the Z-V model, the power of the scattering signal at the receiver can be written as: is the Woodward ambiguity function (WAF) of pseudorandom sequences (Barton et al. 1988;Lewis et al. 1986) and 0 is the scattering cross section, which can reflect the sea surface state and can be written as: where q x and q y are the components of q, q z defines its normal, and P can be defined as an isotropic Gaussian probability density function. Equations (15) and (16) indicate that the GNSS-R observations depend on the sea surface state and sea surface reflectivity. Additionally, outbreaks of green algae, as mentioned in the previous section, affect the sea surface brightness temperature by altering the reflection coefficient of seawater and roughness of the sea surface. Therefore, the change in sea surface brightness temperature can be monitored using GNSS-R observations, such as DDM and waveform data, which in turn facilitates the monitoring of green algae on the sea surface.

Simulation modeling
Since the numerical calculation of the DDM volume and area requires an infinite domain delay and Doppler integration (Marchan-Hernandez et al. 2008), we chose to use a normalized two-dimensional waveform to retrieve the brightness temperature due to green algae. GNSS-R waveforms were simulated with the same data listed in Table 1. Figure 4 shows the simulated waveform results. The waveforms were normalized to eliminate the effects of distance variations between the satellite and receiver, variations in system parameters and propagation environment. Notable, the waveform peak was set to 1, and the waveform values in the other pixel were accordingly adjusted. According to Fig. 4 and Table 1, the time delay waveform could clearly distinguish the green algae volume ratio under different sea surface brightness temperatures, which indicates that these waveforms could be used to determine whether green algae occur. Once the waveforms of pure seawater surface and those under different green algae densities were obtained, the position of other waveforms relative to the given waveform could be used to quickly and approximately determine whether green algae occurred.
Based on the relationship between the waveform and green algae density, as shown in Fig. 4, the green algae density could be estimated using the length of the waveform's tail defined as the time from peak decay to that value divided by the delay of e (Valencia et al., 2011) or the slope of the trailing edge of the waveform used in the wind speed inversion method of Zavorotny and Voronovich (2000), which in turn could enable the detection and inversion of the green algae density. However, due to the slowly decreasing trailing edge of the waveform under high green algae densities, the delay of the Valencia method could not be calculated, so only the minimum trailing edge slope, which is related to power dispersion of the waveform attributable to the sea surface roughness determining the brightness temperature, was employed for modeling. Figure 5 shows the relationship between the green algae volume ratio, brightness temperature and minimum trailing edge slope. The second-order fitting model between the green algae volume ratio and minimum trailing edge slope is given as: where k is the minimum trailing edge slope of the waveforms. The fitting error in terms of the RMSE and squared correlation coefficient was 2.658 and 0.9763, respectively. Similarly, the second-order fitting model between the brightness temperature and minimum trailing edge slope can be given as: The fitting error in terms of the RMSE and squared correlation coefficient were 1.45 and 0.989, respectively.
It should be noted that Model (13) was theoretically derived, and the effect of SST variation was smaller than that of the simulation variance, which universally applies. In contrast, establishing (17) and (18)   According to Figs. 4 and 5, GNSS-R observations (waveforms) can be used to determine the volume ratio of green algae via inversion. In the case that the green algae volume ratio in some areas is known, we can establish a relationship model similar to (17) and directly invert the green algae volume ratio in other areas based on corresponding waveform data. However, in most cases, no green algae volume ratio data or density data are available, while low-resolution sea surface brightness temperature data can be obtained from models or brightness temperature products, such as SMOS L1C or Chinese Fengyun data. Due to the large distribution area of green algae, the distribution of green algae under the given brightness temperature resolution can be treated as uniform. Based on a small number of brightness temperature and waveform pairs, high-resolution brightness temperature data can be derived by building a model similar to (18), and the volume ratio of sea surface green algae can be inverted according to (13). Eventually, green algae monitoring can be indirectly achieved via the brightness temperature.
There are several notable model application-related points. Changes in the relative positions of the satellite and receiver could lead to a change in the elevation angle, which could also lead to a change in the waveform slope. Figure 6 shows the influence of the elevation angle on the waveform. There exists a high correlation between the waveform slope and elevation angle change between 30° and 60°, which could result in errors in the inversion model. Nevertheless, the waveform slope is insensitive to the change rate of the elevation angle. Therefore, to avoid any effect of the satellite elevation angle, a given inversion model should select data with satellite elevation angles lower than 30° or higher than 60° and angular variations within 5° as much as possible.
Finally, it should be noted that there also exists a notable relationship between the waveform delay and sea surface wind speed. Therefore, this model is only applicable in cases where the wind speed remains consistent in the observation area and the wind speed slightly changes throughout the observation period.

Empirical modeling and experimental results
Reflection waveform data of typical harmful algae Enteromorpha prolifera were collected on July 7 and 8, 2021, to validate the proposed method. A GNSS-R receiver was installed on a ship, and the antenna was fixed 3.5 m above the water surface. The temporal resolution of the GNSS-R receiver is 0.25 chips, and two antennas could receive direct and reflected signals. The waveform data were sampled every two minutes and recorded for 1 min each time. Moreover, the coverage density of green algae and SST were simultaneously recorded with the waveform data. The ship exhibited a fixed position, but green algae at the sea surface floated due to the sea wind, and the green algae density continuously changed, as shown in Fig. 7. Figure 8 shows a comparison of the simulated waveforms (six dashed lines) and measured reflectance waveforms under different Enteromorpha prolifera coverage densities. The dotted lines in the figure indicate the waveforms based on the observed data under 0-100% Enteromorpha prolifera coverage levels. A satellite elevation angle of 30° and a wind speed of 3 m/s were applied to the simulated waveforms, while the satellite elevation angle of the selected measured data varied between 20° and 50° and the wind speed remained within 5 m/s due to the limitations of the data volume and observation conditions. The simulated and observed data were in good agreement.
There are several noteworthy points. First, the slope of the simulated waveforms was lower than that of the measured waveforms for the sea surface without Enteromorpha prolifera (density of 0%), which is mainly attributed to the influence of the satellite elevation angle. The simulated satellite elevation angle was 30°, whereas the two satellite elevation angles of the model without Enteromorpha prolifera were 24°-23°. This is consistent with the conclusion based on Fig. 7 that the higher the satellite elevation angle is, the lower the corresponding slope. Second, when the measured Enteromorpha prolifera area coverage density reached 100%, the corresponding Enteromorpha prolifera volume ratio was lower than 20%, which occurred because Enteromorpha prolifera floated and accumulated on the sea surface, and the volume submerged in water resulted in complete sea surface coverage by Enteromorpha prolifera above an area coverage density of 20%. In addition, the difference between the volume ratio used to represent the density of the simulated Enteromorpha prolifera and the coverage density used to represent the measured density could explain this problem. Finally, the trailing edge of the simulated waveform rapidly became horizontal, which was mainly caused by the proximity of the receiver to the sea surface.
We built inversion models using partial waveform trailing edge slope of satellite datasets considering various satellite elevation angles at 5° intervals based on the above analysis. Figure 9 shows five representative waveforms when the elevation angle was varied by 5° for modeling under different sea surface Enteromorpha prolifera coverage densities. Due to sea wind and waves, green algae rapidly drifted with the wind and waves. There was a complete process in which green algae belts rapidly floated past the observation point. Limited by the resolution of the GNSS-R receiver, the slope of the line between 0.25-0.5 chips (the range shown in the dotted box in Fig. 8) was used as the slope of the trailing edge of the waveform. An inversion model was developed using the waveform trailing edge slope and Enteromorpha prolifera density as follows: where Dep is the coverage density and k is the slope of the waveform trailing edge. The fitting error in terms of the RMSE is 9.764%, and the squared correlation coefficient value is 0.968.
After establishing an inversion model at 5° satellite elevation angle intervals, the remaining dataset was thereafter used to evaluate the green algae density inversion performance. The inversion results and inversion errors are shown in Fig. 10. The mean absolute error (MAE) reached 5.74%, and the RMSE was 6.74%.
The inversion results indicated that, due to the secondorder polynomial fitting model used in the simulations, the inverted density value could be negative when the density of Enteromorpha prolifera was very low or when there occurred no Enteromorpha prolifera, which is inconsistent with the actual conditions. Therefore, all negative inversion results were recorded as zero.
The MAE and RMSE values of the retrieved Enteromorpha prolifera density for different elevation angle ranges are given in Table 2. Consistent with the results shown in Fig. 6, the inversion results of the measured data verified that the inversion accuracy of the Enteromorpha prolifera cover density was closely related to the satellite elevation angle. The accuracy of the inversion of Enteromorpha prolifera at both ends of the satellite elevation angle range was high, while the accuracy at the middle was low, especially within the (19) Dep = 17.74 * k 2 + 258.6 * k + 299.6 range of 40-50°. However, there was no difference in inversion performance between the satellite ascent and descent data. In addition, limited by the experimental condition, the Enteromorpha prolifera distribution data we used in the simulation modeling part and empirical modeling part are different, which are volume ratio V ga and coverage density Dep, respectively. However, since the inversion model we present was simulated based on actual observation data and related parameters of this experiment, models in (13) and (18) are also applicable to the experiment data, which mean that the minimum trailing edge slope of waveform k can be used to calculate the volume ratio of Enteromorpha prolifera, and the feasibility and reliability and of the model can be verified according to the distribution characteristics of Enteromorpha prolifera shown in Fig. 8. The volume ratios of Enteromorpha prolifera can be obtained by using the same slope k used in Fig. 10 and (18) and (13). The relationship between the recorded green algae coverage and retrieved green algae volume ratio is shown in Fig. 11. From Fig. 11, we can see that the coverage of green algae increases with increasing volume ratio, and when the volume ratio of green algae is higher than 20%, green algae completely cover the sea surface. This is because at the initial stage, the volume of Enteromorpha prolifera increased with the increase in biomass per unit area, but the growth rate gradually decreased and finally tended to saturation, that is, the volume ratio continues to increase, and the area has been fully covered. This has been confirmed by previous relevant studies (Wan et al. 2022;Xiao et al. 2017). In addition, this phenomenon is consistent with the previous results that are shown in Fig. 8. The above contents can verify the feasibility of the method proposed.

Conclusion
We proposed a new method to monitor the density of green algae using GNSS-R observations. The method used the relationship between the seawater dielectric constant and sea surface state change due to green algae, which involves consistent changes in brightness temperature and waveform, and detection of the sea surface green algae density by GNSS-R technology was achieved through changes in the sea surface brightness temperature. In addition, the feasibility of the GNSS-R for green algae monitoring was verified by directly  Relationship between the green algae ratio and coverage density establishing the relationship between the reflected waveform and green algae density from measured data. The results indicated that the reflection waveform can be used as an auxiliary tool for green algae detection and green algae density inversion, and the coverage density inversion accuracy is higher than 10%. This method solves the problems whereby existing optical remote sensing of green algae is severely affected by weather conditions and long revisit times. The method is a low-cost and time-efficient technique and is important for future seawater environmental monitoring and green algae prediction.
The established model only represents a preliminary result, and multiple models should be established in parts. In the future, we will attempt to introduce the satellite elevation angle as a parameter to establish a unified inversion model. Data availability All data included in this research are available upon request by contacting the corresponding author.
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