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Abstract
Obtaining turbulence parameters in the marine atmospheric boundary layer (MABL) is limited by the observation environment and cost. Therefore, estimating based on the weather forecast model or combining the model output with limited observations is a more flexible choice. We conducted cruise observation experiments in the Bohai Sea, China, from May 17 to June 4, 2021. On the basis of the wind profile observed by the coherent Doppler lidar and the temperature, as well as pressure profiles output by the Weather Research and Forecasting (WRF) model, we implemented the Tatarskii turbulence model to estimate the refractive index structure constant $C_{n}^{2}$ in the atmospheric boundary layer of the Bohai Sea under clear sky. The temporal and spatial variations of turbulence in the Bohai Sea atmospheric boundary layer are studied by combining the vertical velocity variance $\sigma _{w}^{2}$, skewness Ske and kurtosis Kur. The performance of simulated $C_{n}^{2}$ and meteorological parameters in the WRF in the atmospheric boundary layer at the Bohai Sea is evaluated through the experimental measurements of UAV-borne (unmanned aerial vehicle) radiosonde and lidar. Finally, we give the model of the $C_{n}^{2}$ variation with height in the atmospheric boundary layer at the Bohai Sea. The results show that WRF can better simulate $C_{n}^{2}$ in most cases. The bias between the measured and simulated $C_{n}^{2}$ is within one order of magnitude, and the root mean square error ( RMSE ) is within two orders of magnitude. Due to the potential uncertainty of the WRF, the RMSE between the measured and simulated wind speed is 4 ms−1 to 6 ms−1, which is almost two times of the result in previous studies on the underlying land surface. The overall changes of $C_{n}^{2}$ and $\sigma _{w}^{2}$ are similar when the turbulence is well mixed and developed, which shows the consistency in both of optical and dynamics turbulence. But this consistency is not absolute. The temperature difference between the sea surface and the atmosphere leads to the widespread existence of an inversion layer from the sea surface to hundreds of meters in the Bohai Sea. The suppression of the inversion layer weakens the near sea surface turbulence. There is an enhancement of turbulence intensity below the inversion layer and a decrease from the upper inversion layer to top of the boundary layer among the entire boundary layer, also, the position of the inflection point is determined by the height of top of the inversion layer. The main results of this study are the reference significance for further understanding the development and change characteristics of turbulence in the MABL.
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1. Introduction
The nonuniform refractive index caused by atmospheric turbulence will affect the propagation of an electromagnetic wave in the atmosphere, which will seriously reduce the signal quality of the photoelectric system. Wind speed fluctuation and the temperature difference between the ground and the atmosphere directly affect the change of atmospheric refractive index. The refractive index structure constant $C_{n}^{2}$ is a statistical index to describe the intensity of atmospheric optical turbulence [1,2]. It is necessary to obtain accurate $C_{n}^{2}$ vertical profile to evaluate the impact of atmospheric turbulence on the performance of a photoelectric system.
The $C_{n}^{2}$ measurement work has been carried out by a plenty of researchers, mainly using scintillation detection and rangefinder (SCIDAR) and radiosonde to obtain $C_{n}^{2}$ vertical distribution information [3–6]. Due to the differences in the atmospheric environment and experimental conditions, conducting similar measurements in different regions is uneasy. In recent years, the $C_{n}^{2}$ is estimated by some very effective work using the mesoscale model that is a more flexible choice. Masciadri et al. [7,8] simulated the three-dimensional distribution of $C_{n}^{2}$ over Paranal based on the Meso-Nh (mesoscale, non-hydrostatic) model and compared it with the SCIDAR measurement. The results show that the Meso-Nh model can accurately reproduce the spatial distribution of $C_{n}^{2}$. A set of $C_{n}^{2}$ simulation results of the Meso-Nh model in the Canary Islands show that the horizontal distribution of optical turbulence is not necessarily uniform, especially in the first 10km on the ground [9]. They proposed new optical turbulence parameterized calibration scheme to improve the system error of the model simulation in Paranal and Canary Islands [10]. The simulation results in the San Pedro Mártir Observatory show that the improved parametric calibration scheme can better qualitatively and quantitatively estimate the $C_{n}^{2}$ profile [11,12]. In addition, the ability of the Meso-NH model to reproduce optical turbulence and distinguish different types of turbulence was verified over Dome C, Dome A, and the South Pole [13,14]. The Mt Graham simulation results were calibrated and quantified utilizing generalized SCIDAR profiles measured over 41 nights to evaluate the performance of the model in different seasons. It shows that the model has good ability to reconstruct the vertical distribution of $C_{n}^{2}$ and seeing $\varepsilon$, isoplanatic angle $\theta _{0}$ and wavefront coherence time $\tau _{0}$ [15,16]. Observations and simulations in Paranal and Armazones show that the Meso-Nh model has a very satisfactory performance in reconstructing atmospheric parameters at a distance of 20km from the ground and can be used in astronomical observations [17]. Cherubini et al. [18,19] used the turbulence energy information provided by Fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) to invert optical turbulence data and verified the preliminary results of the algorithm in the field monitoring experiment of Mauna Kea, which has been implemented in MM5 of Mauna Kea Meteorological Center. Cheinet proposed a method to calculate the near surface optical turbulence using the European Centre for Medium-Range Weather Forecasts (ECMWF) model product. The method was evaluated based on the scintillation measurement results under different locations and climatic conditions in Western Europe, and the results showed that the model can predict near surface $C_{n}^{2}$ [20].
As one of the widely used mesoscale weather forecast models, WRF can predict atmospheric turbulence parameters in many practical works. Giordano used WRF to simulate the atmospheric turbulence parameters on the Roque de Los Muchachos site for more than 4,500 hours. There is good agreement between the simulated results and the in-situ measurements, and the simulated results can be improved by increasing the grid resolution [21]. Qing et al. used WRF and the bulk model in Monin-Obukhov similarity theory (MOST) to calculate the $C_{n}^{2}$ at the near sea surface. The correlation coefficient between simulated and the measured results was 77.57%, which showed that using the WRF to predict $C_{n}^{2}$ was a feasible and meaningful method of offshore regions [22]. The method is also applied to estimate near surface $C_{n}^{2}$ in Southwest China and Antarctica. The statistical data results show that the simulated and measured have good consistency in both of and magnitude, and there is a better performance of the WRF to estimate $C_{n}^{2}$ on the underlying land surface in Southwest China and Antarctica than the near sea surface [23–25]. Qing et al. [26] used the WRF to output the $C_{n}^{2}$ vertical profile over the Lhasa radiosonde station on the Qinghai-Tibet Plateau and compared it with the measured results of radiosonde. The results show that the performance of WRF output of turbulence parameters is generally convinced, but there is still uncertainty. Qian et al. evaluated the performance of WRF in simulating optical turbulence in the Ngari area of Qinghai-Tibet Plateau with the $C_{n}^{2}$ measured by the radiosonde, and the simulated and measured value showed a great consistency [27]. In conclusion, the performance of the WRF to simulate optical turbulence is reliable, and it is reasonable to combine WRF output results with restricted in-situ measurements to estimate turbulence parameters.
As an emerging active remote sensing method, lidar has higher temporal and spatial resolution than traditional turbulence observation equipment and is almost undisturbed by terrain and atmospheric environment. It can obtain a vertical profile of the daily variation of turbulence parameters with high temporal and spatial resolution, which is useful to the in-depth understanding of the structural characteristics and temporal as well as spatial changes of atmospheric turbulence. In this study, we use coherent Doppler wind lidar and WRF to estimate the turbulence parameters of the atmospheric boundary layer in the Bohai Sea, China, and evaluate the performance of WRF to simulate $C_{n}^{2}$ in this region. Section 2. introduces the observation of shipborne coherent Doppler wind lidar and the configuration of WRF. Section 3. describes the method of using Tatarskii turbulence statistics theory [28] to estimate the optical turbulence parameters and the vertical wind speed observed by lidar to calculate the dynamics turbulence parameters vertical velocity variance $\sigma _{w}^{2}$, skewness $S_{\mathrm {ke}}$ and kurtosis $K_{\mathrm {ur}}$, and the method of fitting $C_{n}^{2}$ profile model based on Hufnagel$-$Valley model (H$-$V model) [29]. In section 4, the performance of WRF in simulating $C_{n}^{2}$ in the atmospheric boundary layer of the Bohai Sea is evaluated by statistical parameters. Then the $C_{n}^{2}$ is estimated by combining the lidar measurement and the model. At the same time, the characteristics of atmospheric turbulence in the atmospheric boundary layer at the Bohai Sea are analyzed using dynamics turbulence parameters. In addition, the causes of the near sea surface inversion layer at the Bohai Sea and the influence of the inversion layer on turbulence are analyzed. Finally, the variation model of the average $C_{n}^{2}$ profile with height in the atmospheric boundary layer of the Bohai Sea is given based on the H-V model.
2. Measurement and WRF configuration
2.1 Lidar measurement
The Bohai Sea (117$^{\circ }{35}'$E-121$^{\circ }{10}'$E, 37$^{\circ }{7}'$N-41$^{\circ }$N) is a semi-enclosed continental shelf sea in northern China, off the North West Pacific Ocean. Bohai Bay is located at the west of the Bohai Sea and is surrounded by the Bohai Economic Ring (BER), which is the economic center of northern China, including the metropolitans of Beijing and Tianjin [30]. The atmospheric environment in this area has attracted extensive attention. We conducted a navigational observation experiment in the Bohai Sea from May 17 to June 5, 2021. The High Detectability Lidar (HDL) 10K coherent Doppler wind lidar is installed on the foredeck of the scientific research ship to carry out wind field observation. It was developed by the Ocean University of China and Qingdao Leice Transient Technology Co., Ltd. on the basis of Wind3D 10K. The Doppler Beam Swing (DBS) is used to obtain the wind profile during observation [31,32]. The lidar picture and experimental route are shown in Fig. 1, and the lidar technical performance are shown in Table 1. In this study, we reprocess data with a signal-to-noise ratio (SNR) of less than 8 dB to ensure the reliability of the data, and the data rejection rate was about 6%. In order to deal with the influence of the undulation of the scientific research ship on the wind profile measurement, an inertial navigation system is installed on the lidar to record the attitude information of the ship in real time and obtain the real wind field information through the real-time correction algorithm [31]. We use the iMex-XQ2 radiosonde mounted on the UAV to obtain temperature and pressure profiles when the weather condition is permitted. The maximum flying height of the UAV is 500m.
Fig. 1. Installation location and picture of lidar system(top); Route map from May 17 to June 4, 2021(bottom, UTC+8).
Table 1. Technical parameters of HDL 10K coherent Doppler wind lidar
2.2 WRF model configuration
WRF is a unified mesoscale weather forecast model developed by the National Center for Environmental Prediction (NCEP), the National Center for Atmospheric Research (NCAR), and other US scientific research institutions. The system has the characteristics of portability, easy maintenance, scalability, and high efficiency [33]. This study used the Final Operational Global Analysis (FNL) data initialization model, and the data horizontal resolution was $\rm {1^{\circ }\times 1^{\circ }}$ [34]. The grid nesting mode adopts two-way nesting. The vertical grid is 35 layers and the top layer is 50hPa. Table 2 shows the configuration of the WRF nested grid. Table 3 shows the main physical parameter configuration schemes. We use WRF to output meteorological parameters such as wind speed, wind direction, temperature, humidity, and pressure. The time resolution of the output data is 30min (after interpolation is 5s) and the vertical resolution after interpolation is 20m.
Table 2. WRF grid-nested configuration scheme
Table 3. Main physical parameter configuration scheme of WRF
3. Methodology
3.1 Refractive index structure constant
$C_{n}^{2}$ is usually used to describe the intensity of atmospheric optical turbulence. The temperature, pressure, and wind speed combined with the turbulence statistical model can obtain $C_{n}^{2}$. The Tatarskii turbulence statistical model expresses $C_{n}^{2}$ as [28,38]
where $M$ is the potential refractive index gradient, $L_{0}$ is the outer scale, where [1] and where $T$ is the absolute atmospheric temperature in K, $P$ is the atmospheric pressure in hPa, $h$ is the altitude, $\theta$ is the potential temperature. Since the difference between the unsaturated wet air potential temperature $\theta$ and the dry clean air potential temperature $\theta _d$ is generally less than 0.1K, the unsaturated wet air potential temperature is generally expressed as the dry clean air potential temperature as [39] In this study, the HMNSP99 outer-scale model is adopted, which introduces the vertical shear of horizontal wind $S$ and temperature gradient $\frac {{\rm {d}}T}{{\rm {d}}h}$ that have an important influence on the change of $C_{n}^{2}$ [40].3.2 Vertical velocity variance, skewness and kurtosis
The vertical velocity variance $\sigma _{w}^{2}$ mainly reflects the intensity of atmospheric dynamics turbulence and the degree of mixing. It can provide accurate mixing layer height in most cases [41], which is
where $w$ is the vertical speed. $\overline {w}$ is the average vertical speed over a period of time, in this study is 30min. ${w}'$ is the vertical wind speed fluctuation. Skewness and kurtosis are the third and fourth moments of vertical velocity, defined as follows The symbol of $S_{\rm ke}$ indicates the source of turbulence driving force. When $S_{\rm ke}$ tends to be positive, it means that the atmospheric boundary layer is driven by land surface heating [41]. Kurtosis quantifies the frequency of extreme values in the relative normal distribution. When $K_{\rm ur}-\rm {3}$ is greater than 0, it indicates that the distribution produces more extreme outliers than the normal distribution. Therefore, kurtosis can be used to study the intermittency of turbulence. The larger kurtosis means the more pronounced intermittency.3.3 Hufnagel-Valley model
Through long-term experimental measurement and statistical analysis of different experimental locations, researchers have proposed different $C_{n}^{2}$ profile models. Hufnagel-Valley model is a widely used $C_{n}^{2}$ profile estimation model [29]. The commonly used H-V models are as follows
4. Results
4.1 Performance evaluation of WRF output $C_{n}^{2}$
We estimated $C_{n}^{2}$ using the temperature and pressure profile measured by the radiosonde during the experiment and the wind profile measured by the lidar. The measured results were compared with the output results of WRF. The performance of WRF in simulating atmospheric boundary layer meteorological parameters and $C_{n}^{2}$ in the Bohai Sea area was evaluated. In order to remove the influence of the lidar near-field effect, we selected the profile between 70 to 500m height for comparison. Figure 2 shows the measured and simulated parameter profiles at different times (8:50, 9:15, May 24; 6:54, 14:26, 18:13, May 30). The value of $C_{n}^{2}$ is concentrated between $10^{-19}$ to $10^{-15}\rm {m^{-2/3}}$, the variation trend and magnitude of measurement and simulation are the same in most cases. The difference between the simulated outputs and measurements is usually within two orders of magnitude. In a few cases, the difference of measured and simulated results is big. For example, the profile at 8:50 on May 24 varies greatly between 400m and 500m. The measured $C_{n}^{2}$ increases with the height above 400m, while the simulated $C_{n}^{2}$ decreases, with a difference of three orders of magnitude at 500m. The measured profile shows more detailed changes than the simulated profile in most cases. Such as 6:54 on May 30, there is increased trend below 200m, but the decreased trend is above this height. There is an detailed obvious difference between measured and simulated profile the range of 150m to 300m, while the trend and magnitude are similar at other heights. From the corresponding wind speed profile, it can be seen that there is a large wind shear between 150m and 300m, which causes a sudden increase in turbulence intensity. Obviously, the modeling results cannot fully express the detailed variations of turbulence.
Fig. 2. Measured and simulated $C_{n}^{2}$ (top), temperature (middle), and wind speed (bottom) at different moments (mmdd-hh:MM, UTC+8).
The difference between the measured temperature and the simulated temperature is usually around 2K, and in some cases it can exceed 4K, which is similar to the results of literature [26] on the underlying land surface. Since the MABL has more stable temperature changes than the terrestrial atmospheric boundary layer, we believe that the performance of WRF simulated temperature in the Bohai Sea region is equivalent to that of the underlying land surface. The difference between the measured wind speed and the simulated wind speed is usually more than $\rm {5 ms^{-1}}$, sometimes even more than $\rm {10 ms^{-1}}$. In the research of the underlying land surface, the difference between the measured and the simulated wind speed in the atmospheric boundary layer is usually within $\rm {5 ms^{-1}}$ [26]. Obviously, the performance of WRF simulated wind speed in the Bohai Sea area is worse than that of the underlying land surface. This excessive difference may be related to the influence of small-scale weather processes and the underlying surface. In order to quantitatively describe the performance of outputting parameters of WRF, we evaluated the accuracy of WRF using bias and RMSE. The bias characterizes the difference between the measurements and the simulated results. On the one hand, the RMSE represents the difference between the measured and the simulated values. On the other hand, it reflects the stability of these parameters simulated by WRF, as follows:
where $Y_{i}$ is the measured value, $X_{i}$ is the simulated value corresponding to $Y_{i}$, and $N$ is the total number of samples. We use a total of 306 points of 18 measured profiles to compare with the corresponding simulated profiles to obtain the mean bias and RMSE profiles, as shown in Fig. 3. The bias of $C_{n}^{2}$ is within one order of magnitude, and the RMSE is not exceeding two orders of magnitude, which shows that WRF can simulate $C_{n}^{2}$ in the Bohai Sea region effectively. The temperature bias is within 2K, the RMSE of the temperature is between 2 to 3K, and with the increasing of height the stability of simulated temperature by WRF becomes more accurate. The bias of wind speed is within $\rm {2ms^{-1}}$. Because the bias has positive and negative signs, the average result underestimates the difference between the simulated and the measured wind speed, but RMSE can better reflect the difference. The RMSE of wind speed is between $\rm {4 }$ to $\rm {6 ms^{-1}}$, which is almost more than twice the result of the literature [26]. This shows that the accuracy and stability of WRF simulation of wind speed in the Bohai Sea are far lower than that of the underlying land surface.Fig. 3. Statistical results of measured and simulated $C_{n}^{2}$ (left), temperature (middle) and wind speed (right).
To sum up, WRF can simulate $C_{n}^{2}$ and temperature in the Bohai Sea, and its performance in simulating $C_{n}^{2}$ and temperature is equivalent to that in the study of the underlying land surface. But the performance of simulating wind speed is significantly worse than the underlying land surface. There are sometimes huge differences in trend and magnitude between simulated and measured $C_{n}^{2}$. The main factor causing this difference is that the spatial-temporal resolution of measured and simulated data cannot be strictly corresponding [21,22]. At the same time, the small-scale weather process at sea, underlying surface factors, mode configuration scheme and interpolation method will also have an impact. Improving the temporal and spatial resolution of the model and strict time correspondence can effectively reduce this huge difference.
4.2 Turbulence parameters
Figure 4 shows the vertical profile of the daily variation of turbulence parameters in the atmospheric boundary layer on June 4, 2021, where $C_{n}^{2}$ is estimated from the wind speed measured by the lidar and the temperature output by the WRF. The weather and sea conditions were good on June 4, and 24-hour cruise observations were carried out. The height of the atmospheric boundary layer can be roughly determined by the lidar echo SNR, which in this study is set to 8dB. It means the lidar echo SNR in the atmospheric boundary layer is greater than 8dB.
Fig. 4. Vertical profile of turbulence parameters on June 4 (a) refractive index structure constant $C_{n}^{2}$; (b) vertical velocity variance $\sigma _{w}^{2}$; (c) skewness $S_{\mathrm {ke}}$; (d) kurtosis $K_{\mathrm {ur}}-\rm {3}$.
On the whole, there is a weak turbulence layer from the near surface to 300m. Except from 8:00 to 16:00, the turbulence above the weak turbulence layer gradually weakens with the increase of height, and the turbulence is almost below 1km. The main reason for the weak turbulence layer is related to the inversion layer that generally exists in the near sea surface of the Bohai Sea. The existence of the layer can be seen from the temperature profile in Fig. 2. At around 8:00, the height of strong turbulence increase to the top of the atmospheric boundary layer continuously and till about 16:00. Driven by the thermal radiation on the surface, the turbulence at the top of the boundary layer has been continuously mixed and developed during this period, and the intermittent is very weak. After 13:00, near sea surface turbulence starts to weaken and the degree of turbulent mixing decreases with time. The weak turbulence takes the lead. The reason for this phenomenon may be related to the change of cruise route (Fig. 1(b)). At about 8:00, the turbulence was driven by the thermal radiation of the land warming and began to mix and develop, also the height of turbulence developing gradually rose to the atmospheric boundary layer top. This induces turbulence near the sea surface weakening progressively. The strong turbulence (as showed in Fig. 4(a), the light green part) of high-altitude continued from 13:00 to 16:00 due to the uplift effect. When the turbulence is fully mixed and developed from 8:00 to 16:00, the $C_{n}^{2}$ characterizing the optical turbulence intensity can correspond well to the dynamics turbulence parameters. It is not always the cases, the optical turbulence is weak below 200m from 2:00 to 4:00, but the dynamics turbulence is stronger. Optical turbulence is weaker due to the suppression of temperature inversion and the low-altitude wind shear at night drives the mixing development of dynamics turbulence.
Figure 5 shows the daily average profiles of $C_{n}^{2}$ and temperature gradients on May 24, May 30, and June 4 respectively, with the 1% data elimination of maximum and minimum values when calculating the error bars. $C_{n}^{2}$ is calculated from the wind profile observed by lidar and the temperature as well as pressure profile simulated by WRF, while the temperature gradient profile is calculated from the temperature profile simulated by WRF. There is a weak turbulence layer from the near sea surface to 300m at different times. The top height of the weak turbulence layer corresponds to the top height of the inversion layer approximately, which indicates that the weak turbulence is caused by the inversion layer. Since the inversion layer is relatively stable, it has an inhibitory effect on the development of turbulent mixing. This temperature inversion often exists in the Bohai Sea which is related to its geographical environment. From Fig. 1(b), it can be seen that the Bohai Sea is only connected to the Pacific in the southeast direction, and all other directions are surrounded by land. Figure 6 shows the temperature and flow field results at different heights in the Bohai Rim area simulated by WRF at 18:00 on May 24. It can be seen that the land temperature in the Bohai Rim is almost higher than the sea surface. The relatively warm air masses are transported to the Bohai Sea continuously where source from the southeast direction. The temperature difference between the sea surface and the atmosphere caused to decrease of the atmospheric temperature near sea surface, and formed the inversion layer from the sea surface to about 200m height. The influence of this difference decreases with height. In fact, due to the influence of the surrounding terrain, the wind is mainly from southwest and northeast directions in the Bohai Sea. Almost all these wind directions will bring the relatively warm air from land to the sea, and the temperature difference between the sea surface and the atmosphere forms an inversion layer.
Fig. 5. Daily average vertical profile of $C_{n}^{2}$ and temperature gradient on different dates (left: May 24; middle: May 30; right: June 4).
Fig. 6. Temperature and flow field distribution at different height simulated by WRF at 18:00 on May 24 (UTC+8).
4.3 $C_{n}^{2}$ model in the Bohai Sea region
In practical applications, we hope to use a simple model to describe the change of $C_{n}^{2}$ with height. Based on the H-V model and the $C_{n}^{2}$ average profile during the experiment, the $C_{n}^{2}$ variation model in the Bohai Sea area is fitted. Since the height of $C_{n}^{2}$ in this study is limited to the atmospheric boundary layer, we only considered the second term of Eq. (10) to describe the atmospheric boundary layer turbulence. Based on this term, an exponential term is added to describe the inversion layer, as shown in Eq. (13).
The research results of this paper, $d$ , $e$ , and $f$ are respectively 1.4, 0.84 and $\rm {0.97\times10^{-16.03}}$. $d$ and $f$ jointly control the turbulence intensity, and $d$ also determines the rate at which the turbulence intensity in the atmospheric boundary layer decreases with height. $e$ adjusts the height of the inversion layer top. The turbulence intensity increases with height in the inversion layer and decreases above the inversion layer top. Figure 7 shows the fitted $C_{n}^{2}$ model in red line, which conforms to the magnitude and trend characteristics during the experiment. The correlation coefficient between the model result and average $C_{n}^{2}$ reaches 0.86. The model results depend on the atmospheric and meteorological conditions, and the spatial and temporal differences of these factors should be noted when using them. Due to the limitation of data set, this model only reflects the overall trend of atmospheric turbulence variations while it cannot reflect the details of turbulence variations. Therefore, obtaining the more accurate atmospheric turbulence profile in practical application is necessary.5. Conclusions and discussions
In summary, we evaluated the performance of WRF in simulating $C_{n}^{2}$ and meteorological parameters in the MABL in the Bohai Sea, China. The wind profiles from coherent Doppler lidar and the temperature simulated by WRF are combined to obtain the $C_{n}^{2}$ and dynamics turbulence parameter profiles with high temporal and spatial resolution. In addition, we analyzed the spatial and temporal characteristics of atmospheric turbulence in this region. Finally, the average profile model of $C_{n}^{2}$ in the atmospheric boundary layer of the Bohai Sea is given. We got the following conclusions:
- 1. In most cases, WRF can simulate $C_{n}^{2}$ and temperature in the Bohai Sea. Its performance in simulating $C_{n}^{2}$ and temperature is equivalent to that in the study of the underlying land surface. However, the performance of simulating wind speed is significantly lower than that of the underlying land surface. At the same time, the simulated $C_{n}^{2}$ cannot fully reflect the details of turbulence variations. These problems may be caused by the potential uncertainty of the model, such as the limited temporal and spatial resolution of model data and the inability of the physical scheme to fully reflect the weather processes of various scales in the region.
- 2. When the turbulence is fully mixed and developed, the $C_{n}^{2}$ characterizing the optical turbulence intensity is similar to the dynamics turbulence parameters in overall variation. This phenomenon reflects the consistency of optical and dynamics turbulence, but this consistency is not always the case.
- 3. The relatively warm air from the land around the Bohai Sea continues to be imported to the MABL. The sea-atmosphere temperature difference has led to a widespread inversion layer on the near sea surface to a height of several hundred meters. The suppression of the turbulence by the inversion layer makes the turbulence near the sea surface weaker. The turbulence intensity in the entire boundary layer has the characteristics of first increasing and then decreasing with height. The height of the inversion layer top determines the position of the inflection point.
Because of the limitation of observation conditions and cost in the offshore environment, it is a reasonable and reliable way to combine measurement data with model simulation to study the characteristics of atmospheric turbulence. So far, the number of research results at sea is far lower than that on land. In order to study the characteristics of turbulence in the MABL deeper, it is necessary to combine the lidar’s all-weather, high temporal resolution profile detection capabilities with other detection methods to carry out long-term observations. On the other hand, a large amount of observation data is needed to improve the simulation performance of the model and reduce the influence of potential uncertainty. The main results of this paper can deepen the understanding of the turbulence characteristics of MABL.
Funding
National Key Research and Development Program of China (2018YFC0213101); National Natural Science Foundation of China (No.61775200).
Acknowledgments
The authors gratefully acknowledge NCEP/NCAR for the provision of the Weather Research and Forecasting (WRF) Model and acknowledge the Meteorological Observation Center of China Meteorological Administration for visiting support.
Disclosures
The authors declare no conflict 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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