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  • View in gallery

    (a) Comparison of Tυ from RASS (dashed line; °C) and the radiosonde (solid line). The profiles of (b) Nb2, (c) ε2/3, (d) logCn2 calculated from the WPR-RASS at 1915 LT 17 Oct 2014.

  • View in gallery

    Comparison of (a) the atmospheric refractivity gradient and (b) M from WPR-RASS (dashed line) and the radiosonde (solid line) at 1915 LT 17 Oct 2014.

  • View in gallery

    (a) Comparison of Tυ from RASS (dashed line; °C) and the radiosonde (solid line). The profiles of (b) Nb2, (c) ε2/3, (d) logCn2 calculated from the WPR-RASS at 1910 LT 1 Jun 2015.

  • View in gallery

    Comparison of (a) the atmospheric refractivity gradient and (b) M from WPR-RASS (dashed line) and the radiosonde (solid line) at 1910 LT 1 Jun 2015.

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Atmospheric Duct Detection Using Wind Profiler Radar and RASS

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  • 1 Dalian Naval Academy, Dalian, China
  • 2 Navy Marine Hydrometeorological Center, Beijing, China
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Abstract

A method of detecting atmospheric ducts using a wind profiler radar (WPR) and a radio acoustic sounding system (RASS) is proposed. The method uses the RASS to measure the virtual temperature profile and calculate the Brunt–Väisälä frequency; it also uses the WPR to measure the spectral width of the atmosphere and the atmospheric refractive index structure constant. Then the profile of the atmospheric refractive index gradient and modified refractivity are calculated using virtual temperature, spectral width, and the atmospheric refractive index structure constant. Finally, the height and intensity of the atmospheric duct are calculated to achieve continuous monitoring of the atmospheric duct. To verify the height and intensity of the atmospheric duct, comparison experiments between WPR-RASS and radiosondes were carried out from June 2014 to June 2015 in Dalian, Liaoning Province, China. The results show that the profile of modified refractivity by WPR-RASS has exactly the same trend as the radiosondes, the two methods have a good consistency, and the atmospheric duct value from WPR-RASS is in good agreement with that from radiosondes.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Hua Wang, dlwhua@sina.com

Abstract

A method of detecting atmospheric ducts using a wind profiler radar (WPR) and a radio acoustic sounding system (RASS) is proposed. The method uses the RASS to measure the virtual temperature profile and calculate the Brunt–Väisälä frequency; it also uses the WPR to measure the spectral width of the atmosphere and the atmospheric refractive index structure constant. Then the profile of the atmospheric refractive index gradient and modified refractivity are calculated using virtual temperature, spectral width, and the atmospheric refractive index structure constant. Finally, the height and intensity of the atmospheric duct are calculated to achieve continuous monitoring of the atmospheric duct. To verify the height and intensity of the atmospheric duct, comparison experiments between WPR-RASS and radiosondes were carried out from June 2014 to June 2015 in Dalian, Liaoning Province, China. The results show that the profile of modified refractivity by WPR-RASS has exactly the same trend as the radiosondes, the two methods have a good consistency, and the atmospheric duct value from WPR-RASS is in good agreement with that from radiosondes.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Dr. Hua Wang, dlwhua@sina.com

1. Introduction

Atmospheric radio wave ducting, which has a significant influence on electromagnetic wave propagation (Dockery 1988), is a common phenomenon in some areas (Abdul-Jauwad et al. 1991; Babin 1996); the probability of its occurrence is mainly related to the geographical position, season, and weather systems of the area. An atmospheric duct has significant influence on electronic equipment such as radars and communication equipment. It causes surveillance radar, navigation radar, and other radars over-the-horizon detection, increases radar clutter, and causes the appearance of such phenomena as over-the-horizon communication in VHF communication equipment. In particular, a surface duct has a greater impact on shipboard or ground-based electronic equipment. A surface duct is a grounded atmospheric duct (Babin and Rowland 1992; Babin 1996; Brooks et al. 1999); during the advection of a warm and dry air mass to the cold and wet sea surface, an atmospheric layer of inverse temperature and sharply declining humidity is formed, thus forming a surface duct.

The detection of atmospheric ducts is very important for research of the formation mechanism and characteristics of atmospheric ducts. Radiosondes are often used to detect atmospheric ducts (Patterson 1982; Babin 1996; Mentes and Kaymaz 2007). In recent years, the vertical resolution of radiosonde data can reach the meter level. Hayton and Craig (1997) used WMO radiosonde data to analyze the distribution of atmospheric ducts worldwide. However, radiosondes are unable to measure atmospheric ducts continuously. In addition, the sounding balloons drift downwind; thus, the values measured are not at the same position. The use of aircraft measurements is another effective method of atmospheric duct detection, including the use of helicopters to measure atmospheric temperature, humidity, and pressure to calculate the modified refractivity (Babin and Rowland 1992; Babin 1996), and the use of aircraft to take zigzag routes to measure atmospheric ducts (Brooks et al. 1999). Using aircraft to measure atmospheric ducts has similar shortcomings as radiosondes. A low-altitude rocket is a convenient atmospheric duct measurement device used on board. In addition, there is also a method for measuring the atmospheric duct by a tethered sounding balloon, but the measurement height by this method is limited to the boundary layer. All these methods have inevitable shortcomings: 1) unable to be observed continuously; 2) the equipment is complicated to use and inconvenient; 3) some measurement methods are lossy or less economical, such as the use of radiosondes and sounding rockets. Therefore, it is desirable to find a new remote sensing method to monitor atmospheric ducts, which can continuously observe atmospheric ducts without using sounding equipment.

Wind profiler radar (WPR) can measure the wind field, spectral width and volume refractivity (Tatarski 1961), atmospheric refractive index structural constant (VanZandt et al. 1978; Ruan et al. 2008), etc. The virtual temperature of the atmosphere could be measured if equipped with a radio acoustic sounding system (RASS) (Matuura et al. 1986; May et al. 1989; Tsuda et al. 1994). In this paper, WPR with RASS is used to measure the profile of atmospheric virtual temperature, spectral width, and the atmospheric refractive index structure constant; the Brunt–Väisälä frequency, the turbulence dissipation rate, and the atmospheric refractive index gradient profile are calculated, and then the profile of atmospheric modified refractivity is calculated to get the atmospheric duct value. To verify the height and intensity of the atmospheric duct, comparison experiments between WPR-RASS and radiosondes were carried out from June 2014 to June 2015 in Dalian, Liaoning Province, China. The difference of the atmospheric refractivity gradient and the atmospheric modified refractivity between the two methods is analyzed.

2. Method

a. Virtual temperature

Virtual temperature is measured by RASS; RASS has been used for 30 years for the purpose of getting high-resolution profiles of tropospheric virtual temperature Tυ (Matuura et al. 1986; May et al. 1989; Tsuda et al. 1994). The sound source of the RASS is located near the antenna of the WPR; the sound emitted by the sound source changes the atmospheric refractivity of the surrounding air. When the electromagnetic waves emitted by the WPR measure these areas, backscattering occurs; thus, the WPR measures this part of the energy. When these refractivity disturbances propagate upward at the local sound speed, WPR can measure the sound speed at different heights. The Tυ is calculated according to the relationship between sound speed and temperature and is corrected according to the relation between vertical wind speed and virtual temperature (Angevine et al. 1994; Alexander and Tsuda 2008); Tυ is determined in each profiler gate by sound speed ca and vertical wind speed w:
Tυ=(caw)220.0462.

The w is measured by WPR; upward the sign is negative, and downward the sign is positive. Because the sound source is spreading out, the sign of ca is negative.

b. Brunt–Väisälä frequency

Brunt–Väisälä frequency Nb is a parameter related to atmospheric static stability; the larger Nb is, the greater the stability of the atmosphere, which is calculated by (Alexander and Tsuda 2008) as
Nb(i)2=glnθυz=glim(zizi1)0lnθυ(i)lnθυ(i1)zizi1glnθυ(i)lnθυ(i1)zizi1.
Here θυ is virtual potential temperature, z is height, g is gravitational acceleration, and θυ is calculated by Tυ (Sheng et al. 2013):
θυ=Tυ(P0P)0.286.
Here P0 is 1000 hPa, and P is the atmospheric pressure at the height of the Tυ and is calculated by the barometric height formula (Sheng et al. 2013):
lnP=lnP1g(hh1)287Tυ.

Here, h1 is the height of the radar antenna above sea level, P1 is the pressure at h1, g is 9.8 m s−2, h is the height of each level, P is the pressure at h, and Tυ is the virtual temperature at h.

c. Turbulence dissipation rate

Turbulence dissipation rate ε is an important parameter characterizing the turbulent environment; Hocking (1985) pointed out the relationship between turbulent dissipation rate ε and spectral width σ2:
ε=bNbσ2.

Here Nb is Brunt–Väisälä frequency and b, a dimensionless constant, is 0.6 (Carol and Lakshmi 2008). Spectral width σ2 is measured by the WPR.

d. Refractive index structure constant

In theory, in the local uniform, isotropic turbulence inertial subregion, the ability of the turbulent motion of clear air to cause backscattering of electromagnetic waves is expressed by the refractive index structure constant Cn2 (m−2/3); Cn2 is exponentially distributed from the bottom to the top within the range of 10−13–10−17 in the troposphere. The trend of Cn2 is decreasing as the height increases; Cn2 is related to the volume reflectivity η (Tatarski 1961):
η=0.38Cn2λ1/3.
Here λ is the wavelength of electromagnetic wave; the unit of η is per meter (m−1). The scattering of electromagnetic waves by atmospheric turbulence is similar to the scattering of electromagnetic waves by clouds; it is a dispersion target. The relation between the backscatter power of a radar and η is (Cohn 1995)
Pr=PtGL2λ2θ2hη1024π2(ln2)R2.
Here pt is the radar transmitted power, pt the radar received power, R the range to the target, G the antenna gain, L the radar system loss, λ the radar wavelength, θ the radar beamwidth, and h the transmitted pulse length. Place Eq. (6) into Eq. (7) to derive the wind profiler radar received power method for estimating the refractive index structure constant Cn2:
Cn2=PrR21.085×104λ5/3Pt(h/2)GL2θ2.
According to the relationship between Pr and the signal-to-noise ratio SNR0 (Ding and Geng 2004), the above equation is written as
Cn2=SNR0kTsysB0R21.085×104λ5/3Pt(h/2)GL2θ2.
Here k=1.38×1023 is the Boltzmann constant, Tsys is the system noise temperature, and B0 is the receiver’s bandwidth. The estimation equation of the refractive index structure constant is converted to
Cn2=CSNR0R2.
The C is related to the parameters of the radar:
C=kTsysB01.085×104λ5/3Pt(h/2)GL2θ2.

e. Refractive index gradient

The propagation of electromagnetic waves in the atmosphere is usually described by atmospheric refractive index n. The refractive index gradient can represent the propagation path of the electromagnetic wave in the atmosphere; WPR-RASS is used to calculate the refractive index gradient. Tusda et al. (2001) studied the WPR to measure atmospheric turbulence; the relationship between the refractive index gradient dn/dz and the refractive index structure constant Cn2, the Brunt–Väisälä frequency Nb, and the turbulent dissipation rate ε is
(dndz)2=aCn2Nb2ε2/3.
Here a is a constant determined by radar parameters. The sign of dn/dz directly influences the change tendency of refractive index; Tusda et al. (2001) pointed out the sign is determined by Nb2 threshold methods. Based on the statistical analysis of this type of WPR-RASS measurement data, the empirical threshold is 1.0×105rad2s2. If Nb2 is less than this value, it is positive; otherwise, it is negative. The above equation can be converted to
dndz={a1/2(Cn2)1/2Nbε1/3,Nb2<1.0×105,a1/2(Cn2)1/2Nbε1/3,Nb21.0×105.
The relationship between the refractivity gradient and the refractive index gradient is
dNdz=dndz×106.
The atmospheric refractivity gradient is calculated using the above method, and its accuracy is verified by radiosonde measurements. The equation for calculating atmospheric refractivity using radiosonde measurements is (Bean and Dutton1968)
N(z)=77.6P(z)T(z)5.6e(z)T(z)+3.75×105e(z)T2(z).

Here P is air pressure, T is absolute temperature, e is partial pressure of water vapor, and then the atmospheric refractivity gradient is calculated based on N.

f. Atmospheric ducts

Atmospheric ducts in the atmosphere are determined by the modified refractivity gradient method. The relationship between modified refractivity M (M units) and refractivity N is the following (Bean and Dutton 1968):
M=N+za×106=N+0.157z.
The a is the radius of Earth; here the value is 6371 km, the curvature of Earth is 1/a=0.157×103 km−1, and z (m) is height above sea level. The relationship between the modified refractivity gradient dM/dz and refractivity gradient dN/dz is
dMdz=dNdz+0.157.

When dM/dz<0(dN/dz<0.157), trapped refraction appears (Turton et al. 1988); the layer of dM/dz<0 is the trapped layer, which means the emergence of the atmospheric duct. The intensity of the atmospheric duct is expressed by ΔM; it represents the ability of the atmosphere to trap electromagnetic waves. The ΔM=M2M1; here M2 is the modified refractivity of the top of the trapped layer, M1 is the modified refractivity of the bottom of the trapped layer, and the height of M2 is the height of the top of the atmospheric duct. Make a line perpendicular to the ground at M2 in the profile of modified refractivity and intersect the line at a point of the profile of modified refractivity; the height of the intersection is the height of the bottom of the duct.

3. WPR-RASS detection atmospheric duct experiment

To verify the height and intensity of the atmospheric duct, comparison experiments between WPR-RASS and radiosondes were carried out from June 2014 to June 2015 in Dalian. During the period of observation, 16 experiments were carried out; 2 of them were under conditions of atmospheric ducts. The intensity of these two ducts was weak. The two times were 1915 LT 17 October 2014 and 1910 LT 1 June 2015.

The GTS1 Digital Radiosonde produced by Shanghai Changwang Meteotech Co., Ltd., was used in these experiments. The radiosonde launch site was 3 km away from the WPR-RASS; the WPR-RASS site was near the beach. The terrain elevation between the two sites was about 60 m. The observations of radiosondes and WPR-RASS were carried out at the same time.

Radiosondes took approximately 20 min to ascend to 5.7 km. To compare the WPR-RASS and radiosonde data, WPR-RASS data were extracted from the time of each launch until 20 min after. During this time, wind velocity is measured first, and the virtual temperature is measured about four minutes later. The WPR-RASS altitude above sea level was 70.8 m; the parameters of WPR-RASS are listed in Tables 1 and 2. In low-detection mode, the range of detection height for the WPR was from 150 to 3225 m, the range gate was 75 m, the number of fast Fourier transforms was 256, and the WPR had five beams: one vertical beam and four tilted beams with a zenith angle of 14.2°. The Tυ was measured by RASS, the height range of the Tυ was from 150 to 3300 m, and the range gate of Tυ is 75 m from 150 to 1050 m and 150 m from 1350 to 3300 m. To align the height of Tυ with the height of the WPR measurement data, these Tυ need to be interpolated to the height corresponding to the measurement data of the WPR.

Table 1.

The parameters of CFL-16 WPR.

Table 1.
Table 2.

The parameters of RASS.

Table 2.

The Tυ profile calculated from the radiosonde is shown as a solid line in Fig. 1a at 1915 LT 17 October 2014. The Tυ profile from the WPR-RASS is shown as a dashed line in the figure. The Tυ from WPR-RASS is in good agreement with that from the radiosonde. Since the range gate of RASS is 75 m, and the vertical interval of the measured data of the radiosonde is about 10 m, even though the data measured from the WPR-RASS and the radiosonde are exactly the same, the profiles of the two will be different. Figure 2b shows the profile of modified refractivity calculated from the radiosonde (solid line). The figure shows two elevated ducts. The top height of the first elevated duct is 285 m, and the duct intensity ΔM=1.4; the top height of the second elevated duct is 491 m, and the duct intensity ΔM=1.0.

Fig. 1.
Fig. 1.

(a) Comparison of Tυ from RASS (dashed line; °C) and the radiosonde (solid line). The profiles of (b) Nb2, (c) ε2/3, (d) logCn2 calculated from the WPR-RASS at 1915 LT 17 Oct 2014.

Citation: Journal of Atmospheric and Oceanic Technology 36, 4; 10.1175/JTECH-D-18-0009.1

Fig. 2.
Fig. 2.

Comparison of (a) the atmospheric refractivity gradient and (b) M from WPR-RASS (dashed line) and the radiosonde (solid line) at 1915 LT 17 Oct 2014.

Citation: Journal of Atmospheric and Oceanic Technology 36, 4; 10.1175/JTECH-D-18-0009.1

The profile of Brunt–Väisälä frequency squared Nb2, turbulence dissipation rate ε, and the atmospheric refractive index structure constant Cn2 calculated from the WPR-RASS are also shown in Fig. 1. Figure 1b is the profile of Nb2. This value shows the gradient of virtual potential temperature; the greater the gradient of virtual potential temperature is, the greater Nb2. At that moment, there were four large-value areas at heights of 500, 750, 1050, and 1750 m, respectively. Figure 1c shows ε as a function of altitude, and there are two large-value zones near heights of 220 and 1870 m. Figure 1d is the profile of Cn2. The general trend is to decrease with height, and Cn2 reaches its maximum near 500 m.

According to Eq. (12), (dn/dz)2 is determined by the product of Nb2, Cn2, and ε2/3. The Nb2 varies the most with height, followed by ε2/3, so the change of (dn/dz)2 is mainly determined by Nb2. The profile of dN/dz from WPR-RASS is shown by the dashed line in Fig. 2a. The refractivity gradient dN/dz<0.157 at the height of 445.8 and 520.8 m indicates the emergence of the atmospheric duct, according to the atmospheric duct determination method. The line dN/dz0.157 is shown by a long dashed line in the figure.

When the modified refractivity profile is calculated from WPR-RASS data, the first layer of modified refractivity is calculated approximately by Eqs. (15) and (16), the humidity of the first layer is calculated from WPR-RASS data by the method of Tsuda et al. (2001), and the air pressure of the first layer is calculated by ground pressure, which was measured at the WPR-RASS site and the height of first layer. The profile of modified refractivity is calculated from the refractivity gradient profile as shown by the dashed line in Fig. 2b, the top height of the duct is 595.8 m in the figure, and duct intensity ΔM=11.8. The profile of modified refractivity from the radiosonde is also shown by the solid line in the figure. There is a good consistency between the two profiles; both these methods have detected the atmospheric duct. The height of the duct is similar, except that the duct intensity from WPR-RASS is stronger. In addition, the profile of modified refractivity from WPR-RASS does not show a duct at 285 m. This is mainly caused by the accuracy of RASS near ground due to the presence of the ground clutter which affects the accuracy of the Tυ. It can also be seen from Fig. 2b that the modified refractivity from WPR-RASS is generally small; this is mainly determined by the empirical threshold of Nb2.

Another atmospheric duct was detected in summer. The Tυ profile calculated from the radiosonde is shown as a solid line in Fig. 3a at 1910 LT 1 June 2015. The Tυ profile from the WPR-RASS is shown as a dashed line in the figure. Both of the Tυ profiles have inversion layers, and their trends are exactly the same. The Tυ profile from WPR-RASS increased from 23.7°C at 220.8 m to 26.2°C at 520.8 m, and the intensity of the inversion temperature is 0.83°C hm−1. The Tυ profile from the radiosonde increased from 22.2°C at 197 m to 25.9°C at 497 m, and the intensity of the inversion temperature is 1.2°C hm−1. Both of them are in good agreement in the vicinity of the inversion layer, and the Tυ above the inversion layer is also in good agreement. Figure 4b shows the profile of modified refractivity calculated from the radiosonde (solid line). The figure shows an elevated duct, the top height of the duct is 389 m, and the duct intensity ΔM=1.4.

Fig. 3.
Fig. 3.

(a) Comparison of Tυ from RASS (dashed line; °C) and the radiosonde (solid line). The profiles of (b) Nb2, (c) ε2/3, (d) logCn2 calculated from the WPR-RASS at 1910 LT 1 Jun 2015.

Citation: Journal of Atmospheric and Oceanic Technology 36, 4; 10.1175/JTECH-D-18-0009.1

Fig. 4.
Fig. 4.

Comparison of (a) the atmospheric refractivity gradient and (b) M from WPR-RASS (dashed line) and the radiosonde (solid line) at 1910 LT 1 Jun 2015.

Citation: Journal of Atmospheric and Oceanic Technology 36, 4; 10.1175/JTECH-D-18-0009.1

The profile of Nb2, ε, and the Cn2 calculated from the WPR-RASS are shown in Fig. 3. Figure 3b is the profile of Nb2. At that moment, there are two large-value areas at the height of 220.8–445.8 and 1046 m, respectively. Figure 3c shows the ε2/3 as a function of altitude, and there is a large-value zone near the height of 595 m. Figure 3d is a profile of Cn2. The general trend is also decreasing with height. The reduction rate is weaker than the calculated value on 14 October 2014. At the height of 370.8 m, the Cn2 has a large value.

The profile of dN/dz from WPR-RASS is shown by the dashed line in Fig. 4a. At the heights of 370.8 and 445.8 m, dN/dz is −0.164 and −0.162, respectively. Both of these are less than −0.157, indicating the presence of the atmospheric duct. The profile of modified refractivity calculated from the refractivity gradient profile is shown by the dashed line in Fig. 4b. The top height of the duct is 520.8 m, and the duct intensity ΔM=1.0. The profile of modified refractivity from the radiosonde is shown by the solid line in the figure. It can be seen that the trends of the modified refractivity calculated by the two methods are exactly the same and have good consistency. The modified refractivity from WPR-RASS is slightly less than that from the radiosonde, the duct height from WPR-RASS is slightly higher than the height from radiosonde, and the duct intensity is slightly weaker than the result from radiosonde.

4. Discussion and conclusions

WPR-RASS is used to detect atmospheric ducts. Two examples from different seasons show that the profile of modified refractivity and the atmospheric duct value by this method is consistent with the method by radiosondes. The validity of this method has been proved preliminarily, and the main conclusions are summarized below:

  1. The method of detecting atmospheric ducts using WPR-RASS is to measure the profile of Tυ by the RASS and the profile of σ2 and SNR0 by WPR; calculate Nb2, ε, Cn2, and atmospheric refractive index gradient dn/dz; and then calculate the profile of modified refractivity according to the atmospheric refractive index gradient. Finally, the atmospheric duct is determined according to the decision method of the atmospheric refractivity gradient, and the height and intensity of the atmospheric duct is calculated according to the profile of modified refractivity.
  2. The accuracy of atmospheric duct detection is mainly determined by the accuracy of the refractive index gradient. The value of the refractive index gradient is determined by Nb2, ε, and Cn2. Among them, the Nb2 plays a major role, so the accuracy of Tυ is very important for atmospheric duct detection.
  3. The method of detecting an atmospheric duct by WPR-RASS sometimes leads to missing ducts. This mainly occurs at times when the Tυ deviation is larger or the measurement value is missing. There are three main conditions: 1) the wind speed is higher (>10 m s−1 for CFL-16); 2) humidity changes with height are rather significant; 3) close to the ground, there is influence of noise affecting the signal-to-noise ratio, which affects the Tυ measurement; it is particularly obvious at the Tυ of the bottom two layers. In addition, the CFL-16 WPR has a slightly larger spectral width than other WPRs. This leads to larger ε and smaller absolute values of the atmospheric refractive index gradient, thus leading to the duct being missed. In addition, because the measurement of sound speed and wind velocity is not completely simultaneous in the experiment, there are still vertical wind errors.
  4. The vertical resolution of WPR-RASS data is 75 m in the low mode of CFL-16.The low vertical resolution of data has led to deviations of the measured atmospheric data from the reality, leading to errors in detecting atmospheric duct, or even missing the duct.

Continuous automatic detection of the atmospheric duct is of great significance for the study of the phenomenon and the mechanism of the atmospheric duct. It is also important to study the application of atmospheric ducts. To improve this method, the following research will be carried out: 1) studying how to improve the accuracy of Tυ measured by RASS and reduce the absence of measurement data; 2) studying methods to reduce clutter; 3) acquiring and accumulating Nb2 and atmospheric refractive index gradient data in different seasons, adding data samples, and analyzing the relationship between the two, in order to determine the impact of different seasons and different weather conditions on the Nb2 threshold; 4) improving the calculation accuracy of the turbulent dissipation rate by WPR; 5) improving the vertical resolution of WPR-RASS data so that the vertical resolution of data is no more than 50 m; and 6) measuring sound speed and wind velocity simultaneously to modify wind error.

Acknowledgments

This research is supported by the National Natural Science Foundation of China under Grant 41276019. We deeply thank Dalian Meteorological Bureau for providing us with radiosonde data during the WPR-RASS experiments.

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