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Ocean mixed layer depth estimation using airborne Brillouin scattering lidar: simulation and model

Dapeng Yuan, Peng Chen, Zhihua Mao, Xianliang Zhang, Zhenhua Zhang, Congshuang Xie, Chunyi Zhong, and Zheng Qian

Open Access Open Access

Abstract

The potential of Brillouin scattering lidar for detecting the mixed layer depth (MLD) was studied. We simulated the Brillouin scattering lidar signal in various water environmental parameters and developed an MLD retrieval model for Brillouin scattering lidar data. We first analyzed the theoretical maximum detectable depth for Brillouin scattering lidar in low-latitude sea regions based on the multiple scattering lidar equations. Subsequently, a theoretical method for calculating the Brillouin scattering frequency shift and linewidth was derived based on the international thermodynamic equation of seawater-2010 and the coupled wave equations. Then we used the theoretical method and the temperature-salinity (T-S) profile of the global Argo data in low-latitude regions to simulate the vertical profile distribution of the Brillouin scattering frequency shift and linewidth. Furthermore, we used a maximum angle method to estimate the ocean MLD in low-latitude regions based on the vertical profile distribution of the Brillouin scattering frequency shift and density in seawater. They are well correlated, which indicates that the frequency-shift component of the Brillouin scattering lidar signal for estimating ocean MLD is feasible and reliable. It appears that airborne or spaceborne Brillouin scattering lidar technology provides great potential for high-efficiency, large-area, and long-term monitoring of the global ocean MLD and upper-ocean water bodies.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. INTRODUCTION

The ocean mixed layer is an upper boundary layer of the ocean with a quasi-homogeneous region that is approximately uniformly distributed due to the influence of external forces and physical processes (such as wind stress, heat fluxes, evaporation, rainfall) on the surface and inside the ocean [1]. The dynamic and thermodynamic processes in the mixed layer provide the means for the exchange of mass, momentum, and energy between the atmosphere and the underlying ocean. The spatiotemporal variabilities of the MLD are of primary significance since they contribute to the distribution of net surface heat flux in the upper ocean, the large sea surface temperature annual cycle in the eastern equatorial Pacific, and biological production [2–4]. Thus, estimating the MLD is essential for a wide variety of oceanic investigations. Numerous studies on the estimation of the MLD have been reported in recent decades. de Boyer Montegut et al. proposed an approach that uses threshold values of ${0.03}\;{\rm{kg}}\;{{\rm{m}}^{- 3}}$ for the density and ${{\pm 0.2}}^\circ {\rm C}$ for the temperature from a near-surface value at 10 m to determine the MLD [5]. Subsequently, a maximum angle method to estimate the MLD from sea glider data was constructed by Chu and Fan [6]. Then, Freeland presented a least-squares regression method based on the temperature and salinity in several long-time series [7]. Moreover, existing scientific research is based on the ocean profile data of Argo floats, shipborne conductivity-temperature-depth (CTD) sensors, sea gliders, and autonomous underwater vehicles. These techniques are relatively slow-sampling, low-resolution, and logistically challenging and place high demands on time, material, and labor. In recent years, lidar has shown increasing oceanic applications. Related studies show the great potential of Brillouin scattering lidar for the detection of marine environments [8–11].

From the perspective of the physical mechanism, spontaneous Brillouin scattering from spontaneous density fluctuations moving at the speed of sound produces additional frequency components in the backscattered light that are shifted to the red (Stokes component) and blue (anti-Stokes component) portions of the laser frequency [12]. The density of seawater is related to the function of temperature, salinity, and pressure in seawater. Moreover, the temperature, salinity, and pressure of seawater have direct effects on the Brillouin scattering frequency shift and linewidth [13–17]. Thus, it is possible to estimate ocean MLD based on the Brillouin scattering frequency shift and linewidth. However, few studies have used Brillouin scattering lidar for MLD monitoring, mainly due to the cost and size of the instrument, and few studies have taken into account Brillouin scattering simulations under the conditions of different signal measurement errors during the day and night.

In this paper, the potential of Brillouin scattering lidar for detecting and estimating ocean MLD is described. A theoretical method for calculating the Brillouin scattering intensity, frequency shift, and linewidth is derived from the international thermodynamic equation of seawater-2010 and the coupled wave equations. The effects of temperature, salinity, and pressure in seawater on the Brillouin scattering frequency shift and linewidth are analyzed synthetically. Subsequently, the equatorial and prime meridional vertical profile distributions of the temperature, density, Brillouin scattering frequency shift, and linewidth are compared. Finally, the results of estimating the ocean MLD based on the Brillouin scattering frequency shift and density are described.

 figure: Fig. 1.

Fig. 1. Configuration of the Brillouin scattering oceanic lidar system. M1, beam splitter; M2 and M3, mirrors; PMT, photomultiplier tube; L1 and L2, beam collimation system; S, pinhole filter; ${\rm{F}} \!-\! {\rm{P}}$, Fabry–Perot etalon; ICCD, intensified charge-coupled device; PC, computer; TSC, time schedule controller.

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2. LIDAR SYSTEM AND SIGNAL MODELING

A. Brillouin Scattering Lidar System Configuration

Figure 1 shows the configuration of the Brillouin scattering oceanic lidar system. The laser source utilized was an injection seeded and $Q$-switched Nd:YAG pulse laser operating at 532 nm after passing through an amplifier and a second-harmonic generator (SHG). It emits laser beams with the following parameters: pulse width of 8 ns, repetition frequency of 10 Hz, divergence angle of 0.45 mrad, and linewidth of 90 MHz. The pulse emitted by the laser with vertical polarization penetrates the ocean after passing through the beam splitter and mirror, where photons are scattered by water molecules and suspended particles. The backscattered photons are collected by the telescope. Then, the scattered signals pass through the collimation system and Fabry–Perot etalon and are recorded by an intensified charge-coupled device (ICCD) camera. The fine structure of the spectral concentric rings is obtained by using a collimation system and Fabry–Perot etalon, which can improve the spectral resolution and the accuracy of calculating the Brillouin scattering spectral characteristics.

B. Brillouin Scattering Signal Intensity and Spectral Characteristics

The depth-dependent Brillouin scattering lidar emits a laser pulse into seawater through the air–water interface and receives backscattered light with a telescope. The laser pulse produced multiple forward-scattering and single backscattering during transmission in seawater. Based on an analytical solution of the radiation-transport equation (RTE) in seawater in the small-angle-scattering approximation, the lidar equation can be described as [9,18–21]

$${S_B}(z) = \frac{{{E_0}AO{T_s}^2{T_o}\eta c}}{{2n{{(nH + z)}^2}}}{\beta _B}(z)\exp (- 2\!\int_0^z \!{{K_{\text{lidar}}}} ({z^\prime}){\rm d}{z^\prime})F(z),$$
where ${S_B}$ is the Brillouin scattering lidar signal power, ${E_0}$ is the transmitted laser pulse energy, $A$ is the receiving aperture area of the telescope, $O$ is the overlap factor, ${T_s}$ is the transmission for the laser pulse propagating through the sea surface, ${T_o}$ is the transmission of the Brillouin scattering lidar optical system, $\eta$ is the responsivity of the photodetector, $c$ is the speed of light in a vacuum, $n$ is defined as the refractive index of the seawater, $H$ is the height from the working platform to the sea surface, ${K_{\text{lidar}}}$ is the lidar attenuation coefficient, and ${\beta _B}$ is defined as the Brillouin backscatter coefficient at $\theta = {{180}}$°. The function $F(z)$ accounts for the effect of the receiver field-of-view angle and the Brillouin scattering coefficient on the lidar signal, which can be expressed as [22]
$$\begin{array}{rl}F(z) &= \Psi m\exp (- 2{b_f}z){\int_0^\infty {(x + \sqrt {1 + {x^2}})} ^{2{b_f}z/x}}\\[6pt] &\quad\times \exp \left[{- \frac{{{x^2}{m^2}}}{4}\left({\frac{{R_0^2 + \rho _0^2}}{{{z^2}}} + {\Theta ^2}} \right)} \right]{J_1}(mx\Psi){\rm d}x,\end{array}$$
$$\Psi { = }\frac{{FOV}}{2}\frac{{nH + z}}{{nz}},\Theta = \frac{{div}}{2}\frac{{nH + z}}{{nz}},$$
where the parameters $m$ and ${b_f}$ are defined as the model-scattering-distribution parameter and the forward-scattering index, respectively. The parameter FOV is the receiver field of view, and div is the divergence angle of the laser beam.

Spontaneous Brillouin scattering occurs as a consequence of density or refractive index fluctuations in the optical properties of the medium. For a thermodynamic system with entropy and pressure as the independent variables, the scattered field equation can be obtained by inserting the incremental pressure wave equation into the coupled wave equation, which can be expressed as follows [23]:

$$\begin{split}&{\nabla ^2}{\boldsymbol E} - \frac{{{n^2}}}{{{c^2}}}\frac{{{\partial ^2}{\boldsymbol E}}}{{\partial {t^2}}} \\&\quad= - \frac{{{\gamma _e}{C_s}}}{{{c^2}}}\left[\begin{array}{l}{\left({w - \Omega} \right)^2}{E_0}\Delta {p^*}{e^{i(k - q)\centerdot r - i(w - \Omega)t}} + \\{(w + \Omega)^2}{E_0}\Delta p{e^{i(k + q)\centerdot r - i(w + \Omega)t}} + \text{c.c.}\end{array} \right].\end{split}$$

The first and second terms on the right-hand side of the expression produce an additional frequency that is shifted to the red (Stokes component) and blue (anti-Stokes component) portions of the laser frequency. Thus, the frequency shift of Brillouin scattering is given by

$$\Omega { = }{\nu _B} = \pm \frac{{2n}}{\lambda}{V_S}\sin \frac{\theta}{2}.$$

The principle of the Brillouin backscattering spectrum in seawater is shown in Fig. 2. The backscattering spectrum of suspended particles is nearly idealized for the laser frequency. In addition, the Brillouin scattering components are shifted and broadened by the Brillouin scattering processes. Thus, the full width at half-maximum (FWHM), symbolized as ${{{\Gamma}}_B}$, is also of great significance for Brillouin scattering and can be expressed as

$${\Gamma _B} = \frac{{4{\pi ^2}\nu _B^2(3{\eta _b} + 4{\eta _s})}}{{3\rho V_s^2}},$$
where the parameters ${\boldsymbol \eta _b}$ and ${\boldsymbol \eta _s}$ are related to the bulk and shear viscosity of seawater, respectively.
 figure: Fig. 2.

Fig. 2. Principle of the Brillouin backscattering spectrum in seawater.

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By combining ocean environmental parameters (temperature, salinity, pressure), the international thermodynamic equation of seawater-2010 [24], and Brillouin scattering spectrum characteristics, Eqs. (5) and (6) are thus transformed into the following:

$${\nu _B}\left({{S_A},T,p} \right) = \pm \frac{{2n\left({S,T,\lambda} \right)}}{\lambda}{V_S}\left({{S_A},T,p} \right),$$
$${\Gamma _B}\left({{S_A},T,p} \right) = \frac{{4{\pi ^2}{\nu _B}{{\left({{S_A},T,p} \right)}^2}(3{\eta _b} + 4{\eta _s})}}{{3\rho \left({{S_A},T,p} \right){V_s}{{\left({{S_A},T,p} \right)}^2}}}.$$

C. Signal-to-Noise Ratio

The number of received photons for the Brillouin scattering lidar system can be obtained by taking advantage of Eq. (1):

$${N_S}(z) = \frac{{{S_B}(z)\Delta t}}{{h\nu}},$$
where the parameters $\Delta t$ and $v$ are defined as the pulse width and frequency of the laser, respectively. The Planck constant $h$ is a fundamental physical constant, and its value is ${6.626} \times {{1}}{{{0}}^{- 34}}\;J\;{{\cdot}}\;s$. For the lidar receiving device, the background light radiation is a nonnegligible factor. ${N_{\text{background}}}$ is the received number of photons that is due to diffuse radiation and can be expressed as [25,26]
$${N_{\text{background}}} = {I_{\text{background}}}A\Delta \lambda \Delta t{T_o}\eta \frac{{\pi {\phi ^2}}}{{4h\nu}},$$
where ${I_{\text{background}}}$ is the spectral radiance reflected from the sea surface. We assumed a moonlit cloud condition for nighttime and sunlit cloud condition for daytime. The spectral radiances during daytime and nighttime are 0.58 and ${0.58} \times {{1}}{{{0}}^{- 6}}\;{\rm{W}}\;{{\rm{m}}^{- 2}}\;{\rm{s}}{{\rm{r}}^{- 1\:}}{\rm{n}}{{\rm{m}}^{- 1}}$, respectively [27]. The parameters $\Delta \lambda$ and $\phi$ are defined as the bandwidth of the optical filter and the half-angle field of view of the receiver, respectively. The standard deviation of the detected photon count for a single laser shot can be expressed as
$$\delta N(z) = {\left[{{N_S}(z) + {N_{\text{background}}}{ + }{N_d}} \right]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}},$$
where ${N_d}$ is the number of photons caused by the dark current of the detector. The signal-to-noise ratio (SNR) of the lidar signal is given by
$${\rm SNR}(z) = \frac{{\sqrt M {N_S}(z)}}{{\delta N(z)}},$$
where $M$ is defined as the number of laser shots integrated, and its value is 1. The theoretical maximum detectable depth of the Brillouin scattering lidar is the depth at which ${\rm{SNR}}({{z}}) = {{10/3}}\;{\rm{dB}}$ and the signal-measurement error is 30%. The lidar signal-measurement error is defined in the following equation [28,29]:
$$\delta = \frac{{\delta N(z)}}{{\sqrt M {N_S}(z)}} = \frac{1}{{{\rm SNR}(z)}}.$$

D. Maximum Angle Method

The maximum angle method uses not only the vertically uniform characteristics of the mixed layer but also the sharp gradient feature beneath the mixed layer, and it further establishes two vectors in the mixed layer and beneath the mixed layer. Thus, the maximum angle principle can be used to objectively evaluate the MLD. With the fitting coefficients $G_k^{(1)}$ and $G_k^{(2)}$, $\tan {\theta _k}$ is given by [6]

$$\tan {\theta _k} = \frac{{G_k^{(2)} - G_k^{(1)}}}{{1 + G_k^{(1)}G_k^{(2)}}}.$$

3. RESULTS AND DISCUSSION

A. Brillouin Scattering Lidar Intensity and Spectral Characteristics Simulation

The number of received photons for the Brillouin scattering lidar can be calculated by using the lidar system parameters shown in Table 1. The global Argo temperature and salinity profiles are provided by the China Argo Real-time Data Center [30].

Tables Icon

Table 1. Brillouin Scattering Lidar System Parameters [32,33]

View Table
 figure: Fig. 3.

Fig. 3. (a) Vertical distribution of the temperature and salinity (${115^\circ}E,{18^\circ}N$). (b) Simulated Brillouin scattering lidar SNR versus the ocean depth.

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Figure 3(a) presents the changed behavior of the conservative temperature and absolute salinity with the increase in sea pressure at position (${115^\circ}E,{18^\circ}N$). In detail, the conservative temperature (black curve) drops from 29.9°C to 13.8°C with increasing sea pressure, and the absolute salinity (blue curve) varies from 34.98‰ to 34.87‰ with sea pressure. The corresponding simulated Brillouin scattering lidar SNR varies with depth as shown in Fig. 3(b). The lidar SNR and signal-measurement errors are 1 dB and 100%, respectively, at a depth of approximately 97 m during the day (blue curve). Compared with the low background noise at night, the lidar SNR is equal to 1 dB at a depth of approximately 108 m (red curve). When the lidar SNR is 10/3 dB, the lidar signal-measurement error is 30% (orange line), and the maximum detectable depth during day and night is 89 m and 98 m, respectively. When the lidar signal-measurement error is 10%, the maximum detectable depth during day and night is 82 m and 86 m, respectively. Thus, background spectral radiation has a significant impact on the maximum detection depth of lidar. The low-latitude regions are selected as the study area based on the theoretical maximum detectable depth of the Brillouin scattering lidar and the MLD variability over the global ocean [31].

The vertical profile distribution of the Brillouin scattering frequency shift and linewidth at position (${115^\circ}E,{18^\circ}N$) can be obtained by taking advantage of Eqs. (7) and (8) and the profile data of the temperature and salinity in Fig. 3(a), the results of which are shown in Fig. 4. Figure 4(a) shows the change in the Brillouin scattering frequency shift versus the ocean depth. In detail, the Brillouin scattering frequency shift is almost constant in the range from 0 to 40 m, and it drops from 7.77 to 7.60 GHz in the range from 40 to 200 m. Figure 4(b) shows that the Brillouin scattering linewidth varies with ocean depth. The Brillouin scattering linewidth varies slightly at a depth of 0 to 40 m and decreases from 2.188 to 2.182 GHz when the depth decreases from 40 to 200 m. Furthermore, we can find that the curves of the Brillouin scattering frequency shift and linewidth change slightly within a depth of approximately 40 m because the ocean mixed layer is an upper boundary layer of the ocean with a quasi-homogeneous region that is approximately uniformly distributed due to the influence of external forces and physical processes on the surface and inside the ocean.

 figure: Fig. 4.

Fig. 4. (a) Vertical distribution of the simulated Brillouin scattering frequency shift at position (${115^\circ}E,{18^\circ}N$). (b) Vertical distribution of the simulated Brillouin scattering linewidth at position (${115^\circ}E,{18^\circ}N$).

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B. Effects of Instrument Uncertainty on the Brillouin Scattering Frequency Shift and Linewidth

The Brillouin scattering frequency shift and linewidth can be affected not only by the ocean environmental parameters but also by the uncertainty of the receiving instrument. In this section, the effects of the wavelength fluctuations of the lidar laser source and the uncertainty of the spectral discriminator on the Brillouin scattering frequency shift and linewidth are discussed. The frequency fluctuation of the lidar laser source is $\pm 45\; {\rm MHz}$. Figure 5(a) shows that the amount of variation in the Brillouin scattering frequency shift caused by the frequency fluctuation of the lidar laser source is 0.0017 MHz. As shown in Fig. 5(b), the amount of variation in the Brillouin scattering linewidth caused by the frequency fluctuation of the lidar laser source is 0.0009 MHz. The simulation results indicate that the effects of the lidar laser source with wavelength fluctuations on the Brillouin scattering frequency shift and linewidth are very slight.

 figure: Fig. 5.

Fig. 5. Brillouin scattering (a) frequency shift and (b) linewidth vary with the frequency fluctuations of the lidar laser source.

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The effects of the uncertainty in the free spectral range (FSR) of the F-P etalon on the Brillouin scattering spectral characteristics are shown in Fig. 6. The FSR of the F-P etalon is 19.6 GHz ${ {\pm 1}}\;{\rm{MHz}}$. Figure 6(a) shows that the amount of variation in the Brillouin scattering frequency shift caused by the uncertainty in FSR of the F-P etalon is 0.78 MHz. As shown in Fig. 6(b), the amount of variation in the Brillouin scattering linewidth caused by the uncertainty in the FSR of the F-P etalon is 0.45 MHz. The above simulation results show that the effects of the frequency fluctuations of the lidar laser source and the uncertainty in the FSR of the F-P etalon on the Brillouin scattering spectral characteristics are very small compared to the effect of the ocean environmental parameters. Thus, we consider the effect of only ocean environmental parameters on the Brillouin scattering spectral characteristics in the following simulation.

 figure: Fig. 6.

Fig. 6. Brillouin scattering (a) frequency shift and (b) linewidth vary with the uncertainty in the FSR of the ${\rm{F}} \!-\! {\rm{P}}$ etalon.

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C. Vertical Profile Distribution Simulation for Brillouin Scattering Frequency Shift and Linewidth in Low-Latitude Regions

Based on the above single-point results, we further analyzed the vertical profile distribution of the ocean environmental parameters (temperature, density) and Brillouin scattering spectrum characteristics (frequency shift, linewidth) at the equator. The reason for choosing the temperature and density in the ocean environmental parameters here is that the ocean MLD is obtained by the temperature and density data. Thus, the feasibility of a Brillouin scattering frequency shift and linewidth inversion for the MLD can be found by comparing and analyzing the vertical profile distribution of the temperature, density, Brillouin scattering frequency shift, and linewidth. Fig. 7(a) shows the equatorial profile distribution of the temperature, which drops from 24°C to 10°C at a depth of 0 to 200 m. Figure 7(b) shows the equatorial profile distribution of the density, which increases from ${1.020} \times {{1}}{{{0}}^3}$ to ${1.026} \times {{1}}{{{0}}^3}\;{\rm{kg}}/{{\rm{m}}^3}$ in the range from 0 to 200 m. The equatorial profiles of both the temperature and density produce a distinct vertical layered structure. The white stripes in Fig. 7 and the following are the landmasses.

 figure: Fig. 7.

Fig. 7. (a) Measured vertical profile distribution of the temperature at the equator. (b) Vertical profile distribution of the density at the equator.

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Figure 8(a) shows the vertical profile distribution of the simulated Brillouin scattering frequency shift at the equator, which drops from 7.75 to 7.60 GHz as the depth increases from 0 to 200 m. We can see that the Brillouin scattering frequency shift forms a distinct vertical layered structure as the depth increases. Moreover, the vertical layered structures of the Brillouin scattering frequency shift and temperature are extremely similar based on a comparative analysis of Figs. 7(a) and 8(a) because the effect of the temperature on the Brillouin scattering frequency shift is relatively large compared to that of the salinity and pressure of seawater. Figure 8(b) shows the vertical profile distribution of the simulated Brillouin scattering linewidth at the equator, which decreases from 2.184 to 2.178 GHz in the depth range from 0 to 200 m. However, the gradient of the Brillouin scattering linewidth with depth is not as distinct as the frequency shift. It is concluded that the variations in the frequency shift, sound velocity, and density with depth will counteract each other from the analysis of Eq. (5), thus reducing the variation range of the linewidth with depth.

 figure: Fig. 8.

Fig. 8. (a) Vertical profile distribution of the simulated Brillouin scattering frequency shift at the equator. (b) Vertical profile distribution of the simulated linewidth at the equator.

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 figure: Fig. 9.

Fig. 9. (a) Prime meridional vertical profile distribution of the temperature in low-latitude regions (${30^\circ}N,{30^\circ}S$). (b) Prime meridional vertical profile distribution of the density in low-latitude regions (${30^\circ}N,{30^\circ}S$).

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 figure: Fig. 10.

Fig. 10. (a) Prime meridional vertical profile distribution of the simulated Brillouin scattering frequency shift in low-latitude regions (${30^\circ}N,{30^\circ}S$). (b) Prime meridional vertical profile distribution of the linewidth in low-latitude regions (${30^\circ}N,{30^\circ}S$).

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In addition, the prime meridional vertical profile distribution of the ocean environmental parameters (temperature, density) and Brillouin scattering spectrum characteristics (frequency shift, linewidth) in the low-latitude regions (${30^\circ}N,{30^\circ}S$) is further analyzed as shown in Figs. 9 and 10. Figure 9(a) shows the vertical profile distribution of the temperature at the prime meridian, which drops from 25°C in the surface seawater to 15°C at a depth of 200 m. Figure 9(b) shows the prime meridional vertical profile distribution of the density, which increases from ${1.022} \times {{1}}{{{0}}^3}\;{\rm{kg}}/{{\rm{m}}^3}$ in the surface seawater to ${1.027} \times {{1}}{{{0}}^3}\;{\rm{kg}}/{{\rm{m}}^3}$ at a depth of 200 m. The prime meridional vertical profile distributions of both the temperature and density produce a distinct vertical layered structure. Figure 10(a) shows the prime meridional vertical profile distribution of the Brillouin scattering frequency shift, which decreases from 7.75 GHz in the surface seawater to 7.55 GHz at a depth of 200 m. Figure 10(b) shows the prime meridional vertical profile distribution of the Brillouin scattering linewidth, which drops from 2.184 GHz in the surface seawater to 2.178 GHz at a depth of 200 m. We can see that the prime meridional vertical layered structure of the Brillouin scattering linewidth is not as distinct as that of the frequency shift by comparing Figs. 10(a) and 10(b).

 figure: Fig. 11.

Fig. 11. Three-dimensional vertical layered structures of (a) temperature (°C), (b) salinity (PSU), (c) density (${\rm{kg}}/{{\rm{m}}^3}$), and (d) Brillouin scattering frequency shift (GHz) in low-latitude regions.

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 figure: Fig. 12.

Fig. 12. (a) MLD estimation is based on the vertical profile distribution of the Brillouin scattering frequency shift in seawater. (b) MLD estimation is based on the vertical profile distribution of seawater density.

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D. Estimating the Ocean Mixed Layer Depth Using the Brillouin Scattering Frequency Shift

Based on the analysis results of Section C, we choose the vertical profile distribution of the Brillouin scattering frequency shift with a more distinct layered structure to estimate the ocean MLD. The vertical profile distribution of the Brillouin scattering frequency shift can be obtained by substituting the profile of Argo floats (temperature, salinity, pressure) into Eq. (7). Figures 11(a) and 11(b) show the vertical profile distributions of temperature and salinity, respectively, at depths of 0, 20, 50, 100, and 150 m in low-latitude regions. The temperature drops from 30°C to 10°C as the depth increases from 0 to 150 m and the salinity decreases from 37.5 to 30 PSU in the depth range from 0 to 150 m. Based on the temperature [Fig. 11(a)] and salinity [Fig. 11(b)], the density and Brillouin scattering frequency shift were calculated from the sea surface to 150 m, and the results are shown in Figs. 11(c) and 11(d). The density increases from ${1.018} \times {{1}}{{{0}}^3}$ to ${1.028} \times {{1}}{{{0}}^{3\:}}{\rm{kg}}/{{\rm{m}}^3}$ in the depth range from 0 to 150 m, and the Brillouin scattering frequency shift drops from 7.79 to 7.52 GHz in the depth range from 0 to 150 m.

 figure: Fig. 13.

Fig. 13. Scatter plot of the retrieved MLD from the Brillouin scattering frequency shift [shown in Fig. 12(a)] versus the retrieved MLD from the seawater density [shown in Fig. 12(b)].

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We estimate the ocean MLD from the vertical profile distribution of the Brillouin scattering frequency shift [Fig. 11(d)], the result of which is shown in Fig. 12(a). Furthermore, we estimate the ocean MLD from the vertical profile distribution of the density [Fig. 11(c)] so that it can be compared with the ocean MLD obtained by the Brillouin scattering frequency shift as shown in Fig. 12(b). The method for calculating the ocean MLD is based on the maximum angle method of Eq. (14). We can see that the ocean MLDs in the low-latitude regions of Figs. 12(a) and 12(b) are extremely similar.

To further illustrate the similarity between the two results in Fig. 12, a scatter plot of the MLD obtained from the frequency shift as a function of the MLD obtained from the seawater density for the same inversion method is created, which reveals similar behaviors as shown in Fig. 13. The MLDs of both the frequency shift and density are between 0 and 150 m. The colors in the scatter plot indicate the data density, and the maximum scatter density occurs at a depth of 25 to 35 m. The scatter density is relatively reduced from 35 to 150 m. The values of the correlation coefficient (r) and coefficient of determination (${{\rm{r}}^2}$) are 0.96 and 0.92, respectively, which indicate that the Brillouin scattering frequency shift estimation of the MLD is feasible and reliable.

4. SUMMARY AND CONCLUSION

Fewer studies have taken into account the Brillouin scattering simulation under the conditions of different signal measurement errors during the day and night. In this case, we theoretically analyze the maximum detectable depth of the Brillouin scattering lidar during the day and night under conditions of different signal measurement errors. The low-latitude regions were selected as the study area based on the theoretical maximum detectable depth of the Brillouin scattering lidar and the MLD variability over the global ocean. We employed a theoretical method that can be used to calculate the vertical profile distribution of the Brillouin scattering frequency shift and linewidth. The vertical profile distribution of the Brillouin scattering frequency shift with a more distinct layered structure is found to correspond well to the oceanic upper boundary layer. The MLDs of the frequency shift and density were estimated, and the values of the correlation coefficient (r) and coefficient of determination (${{\rm{r}}^2}$) were 0.96 and 0.92, respectively, which indicates that the frequency-shift component of the Brillouin scattering lidar signal estimation of the MLD is feasible and reliable. These theoretical simulation results are of great significance to the practical application of airborne and spaceborne Brillouin scattering lidar.

Funding

Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) (GML2019ZD0602); National Science and Technology Major Project (05-Y30B01-9001-19/20-2); National Key Research and Development Program of China (2016YFC1400902); Second Institute of Oceanography, State Oceanic Administration (QNYC1803); National Natural Science Foundation of China (61991454, 41901305); Natural Science Foundation of Zhejiang Province (LQ19D060003).

Acknowledgment

The authors thank Prof. Hailong Liu for his helpful discussions regarding ocean mixed layer depth. Additionally, the authors are grateful for all the suggestions of the anonymous reviewers, which helped us significantly improve the quality of the paper.

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (13)
Fig. 1.
Fig. 1. Configuration of the Brillouin scattering oceanic lidar system. M1, beam splitter; M2 and M3, mirrors; PMT, photomultiplier tube; L1 and L2, beam collimation system; S, pinhole filter; ${\rm{F}} \!-\! {\rm{P}}$, Fabry–Perot etalon; ICCD, intensified charge-coupled device; PC, computer; TSC, time schedule controller.

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Fig. 2.
Fig. 2. Principle of the Brillouin backscattering spectrum in seawater.

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Fig. 3.
Fig. 3. (a) Vertical distribution of the temperature and salinity (${115^\circ}E,{18^\circ}N$). (b) Simulated Brillouin scattering lidar SNR versus the ocean depth.

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Fig. 4.
Fig. 4. (a) Vertical distribution of the simulated Brillouin scattering frequency shift at position (${115^\circ}E,{18^\circ}N$). (b) Vertical distribution of the simulated Brillouin scattering linewidth at position (${115^\circ}E,{18^\circ}N$).

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Fig. 5.
Fig. 5. Brillouin scattering (a) frequency shift and (b) linewidth vary with the frequency fluctuations of the lidar laser source.

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Fig. 6.
Fig. 6. Brillouin scattering (a) frequency shift and (b) linewidth vary with the uncertainty in the FSR of the ${\rm{F}} \!-\! {\rm{P}}$ etalon.

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Fig. 7.
Fig. 7. (a) Measured vertical profile distribution of the temperature at the equator. (b) Vertical profile distribution of the density at the equator.

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Fig. 8.
Fig. 8. (a) Vertical profile distribution of the simulated Brillouin scattering frequency shift at the equator. (b) Vertical profile distribution of the simulated linewidth at the equator.

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Fig. 9.
Fig. 9. (a) Prime meridional vertical profile distribution of the temperature in low-latitude regions (${30^\circ}N,{30^\circ}S$). (b) Prime meridional vertical profile distribution of the density in low-latitude regions (${30^\circ}N,{30^\circ}S$).

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Fig. 10.
Fig. 10. (a) Prime meridional vertical profile distribution of the simulated Brillouin scattering frequency shift in low-latitude regions (${30^\circ}N,{30^\circ}S$). (b) Prime meridional vertical profile distribution of the linewidth in low-latitude regions (${30^\circ}N,{30^\circ}S$).

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Fig. 11.
Fig. 11. Three-dimensional vertical layered structures of (a) temperature (°C), (b) salinity (PSU), (c) density (${\rm{kg}}/{{\rm{m}}^3}$), and (d) Brillouin scattering frequency shift (GHz) in low-latitude regions.

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Fig. 12.
Fig. 12. (a) MLD estimation is based on the vertical profile distribution of the Brillouin scattering frequency shift in seawater. (b) MLD estimation is based on the vertical profile distribution of seawater density.

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Fig. 13.
Fig. 13. Scatter plot of the retrieved MLD from the Brillouin scattering frequency shift [shown in Fig. 12(a)] versus the retrieved MLD from the seawater density [shown in Fig. 12(b)].

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Tables (1)

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Table 1. Brillouin Scattering Lidar System Parameters [32,33]

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Equations (14)

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S B ( z ) = E 0 A O T s 2 T o η c 2 n ( n H + z ) 2 β B ( z ) exp ⁡ ( − 2 ∫ 0 z K lidar ( z ′ ) d z ′ ) F ( z ) ,
F ( z ) = Ψ m exp ⁡ ( − 2 b f z ) ∫ 0 ∞ ( x + 1 + x 2 ) 2 b f z / x × exp ⁡ [ − x 2 m 2 4 ( R 0 2 + ρ 0 2 z 2 + Θ 2 ) ] J 1 ( m x Ψ ) d x ,
Ψ = F O V 2 n H + z n z , Θ = d i v 2 n H + z n z ,
∇ 2 E − n 2 c 2 ∂ 2 E ∂ t 2 = − γ e C s c 2 [ ( w − Ω ) 2 E 0 Δ p ∗ e i ( k − q ) ⋅ r − i ( w − Ω ) t + ( w + Ω ) 2 E 0 Δ p e i ( k + q ) ⋅ r − i ( w + Ω ) t + c.c. ] .
Ω = ν B = ± 2 n λ V S sin ⁡ θ 2 .
Γ B = 4 π 2 ν B 2 ( 3 η b + 4 η s ) 3 ρ V s 2 ,
ν B ( S A , T , p ) = ± 2 n ( S , T , λ ) λ V S ( S A , T , p ) ,
Γ B ( S A , T , p ) = 4 π 2 ν B ( S A , T , p ) 2 ( 3 η b + 4 η s ) 3 ρ ( S A , T , p ) V s ( S A , T , p ) 2 .
N S ( z ) = S B ( z ) Δ t h ν ,
N background = I background A Δ λ Δ t T o η π ϕ 2 4 h ν ,
δ N ( z ) = [ N S ( z ) + N background + N d ] 1 / 1 2 2 ,
S N R ( z ) = M N S ( z ) δ N ( z ) ,
δ = δ N ( z ) M N S ( z ) = 1 S N R ( z ) .
tan ⁡ θ k = G k ( 2 ) − G k ( 1 ) 1 + G k ( 1 ) G k ( 2 ) .
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