1 Introduction*

Polar mesosphere summer echoes (PMSE) are extremely strong radar echoes in the polar summer mesopause region,and have been detected in many radar observations during the past decades. Several theories have been put forward to explain PMSE since they were first detected by the Poker Flat 50-MHz radar in 1979 (Hoppe et al., 1988; Röttger et al., 1988; Ecklund et al., 1981). Although charged ice particles in the mesosphere likely play a crucial role in creating PMSE, the actual mechanism is not well understood. The reviews by Cho et al. (1997) and Rapp and Lübken (2004) provide detailed information about the characteristics of PMSE, and their relation to other mesosphere phenomena.

Very high frequency (VHF) radar echoes from the mesosphere can originate from either a turbulent or a non-turbulent medium, whose physics are quite different,but can produce echoes of comparable power. Most investigations of PMSE have applied the theory of scattering from turbulent irregularities to explain the echoes.Indeed, some properties of PMSE can been explained by turbulence scattering theory (La Hoz et al., 2006; Kelley et al., 1990; Ulwick et al., 1988), but some of the echoes are of a non-turbulent type (Belova et al., 2008; Lübken et al.,2002; Blix et al., 1996). A better distinction between these two types of echoes is the consideration of the aspect sensitivity, which describes the relationship between the scattered power and incident angle, and can provide information about the potential scattering processes, as well as the nature of the scatterers. In general, a signal dependence on the tilting angle is usually not attributable to scattering from isotropic turbulence structures. However, a strong signal decreases when increasing the tilting angle,implying that the observed scatterers operate under an anisotropic scattering mechanism, such as Fresnel reflection or Fresnel scatter. An important feature of PMSE is the aspect sensitivity, which measurements by Czechowsky et al. (1988) first showed is significant in the lower part of PMSE layers. Czechowsky et al. (1997) also reported that,in 90% of their observations, PMSE appeared to have a narrow spectral width and strong aspect sensitivity, whereas in 10% of their measurements, they found turbulence characterized by an extremely broad spectral width in the upper part of the PMSE region. Similar features were later also confirmed by several independent investigators(Smirnova et al., 2012; Zecha et al., 2001; Hoppe et al.,1990). Although there are many experiments concerning the aspect sensitivity of PMSE, no rational theoretical model conforming to observations has yet to be put forward, while the potential scattering processes, as well as the actual scatter structure, are not yet clear.

The European Incoherent Scatter Scientific Association(EISCAT) 224-MHz Radar (peak power: 2 × 1.5 MW,average power: 2 × 0.19 MW, pulse width: 1 µs–2.0 ms,beam width: 0.6ºEW and 1.7ºNS) can be manipulated to collect information about the aspect sensitivity of PMSE by traversing the antenna. However, to our knowledge, no experimental reports of the aspect sensitivity of PMSE from this radar have been published. Additionally, there does not seem to be any experimental measurements of the aspect sensitivity at such a high frequency. Therefore, we report new experiments carried out with the EISCAT 224-MHz Radar during the period from 13–15 July 2010. We then discuss the relationship between the received power and the tilt angle of the radar beam, with the focus on developing a theoretical model to explain the experimental observations. Finally, we summarize the main conclusions, and offer some suggestions for future work.

2 Data presentation

Often used to study PMSE (Röttger et al., 1990, 1988), the EISCAT 224-MHz Radar located in northern Norway(69.6ºN, 19.2ºE) is used here to compare the echo powers between the vertical and oblique beams for examination of the aspect sensitivity of PMSE. Experiments were performed from 13–15 July 2010 for about 3 h each day,during which we traversed the antenna beam from 90º to 84º off the zenith on 13 July, and 90º to 78º on the following two days. Each antenna traversal from the zenith to the respective angle took approximately 6 min, which is a smaller time period than any irregularity variations in time(15 min; Rapp et al., 2004).

C层：听说测试成绩<11分，英语基础薄弱，无学习兴趣，有不同程度的畏难和厌学情绪，严重者有放弃学英语的念头，共有10人，占总人数24%。

Two mechanisms have the potential to explain the aspect sensitivity of PMSE: reflections from a sharp gradient in the refractive index (Alcala et al., 2001), and turbulence anisotropic scattering (Dovika et al., 1984). If the radar echoes were to result from turbulence irregularities, some physical mechanism must exist to cause these anisotropic irregularities, since isotropic irregularities cannot explain the dependence of echo power on the radar zenith angle.Were such anisotropic irregularities to somehow be created,a preferable direction at which the maximum echoes occur would be detected, as evident in the experimental results in Figure 1. However, as turbulence irregularities often exhibit isotropic structures at such small scales, and magnetic field effects can be ignored because of the high collision frequency with neutral particles at this altitude range(PMSE range, 80–90 km), turbulence anisotropic scattering is unlikely the cause of the aspect sensitivity. Therefore, as our experimental results contradict the characteristics of scattering resulting from the turbulence, these features suggest that the strong radar echoes appear to be, at least partially, caused by the reflection from sharp gradients in the refractive index.

where the parameters assumed in this simulation are made as consistent with the experimental measurements as possible. Here, σ = 2.5 km is the half-width of the pre-existing layers, and the reference height h0= 86 km. As a typical horizontal wavelength is around 100–1000 km,while the vertical wavelength is about 3–7 km in the mesopause region, for the reference case, values of the horizontal and vertical wavelengths are chosen to be 200 km and 4 km, respectively. The other gravity-wave parameters in the model are found by solving the relation for gravity-wave dispersion. Further model assumptions are a neutral atmosphere number density n0=1× 10 20 m3, a particle radius rd= 20nm , and the mass ratio of ice to neutral particles md / mn ≈ 105.

3 Analysis and discussion

To illustrate the credibility and complexity of the observations, Figure 1 shows the mean backscatter power relative to the received power in the vertical beam as a function of the elevation angle for the three different observational periods, where, for example, the average received power by the oblique beams is often larger than the vertical beam. Specifically, according to the data from 13 July, with the increase in elevation, the average intensity of echoes gradually becomes stronger, reaching a peak at 86º,before trending downward, similar to that observed on 15 July. In contrast, the data from 14 July have a smaller relative power for radar-beam traversals from 88º to 82º,since the maximum average echo power actually occurs at 78º. The phenomenon of smaller relative power in the range 82°–88° may be caused by the measurement error of the radar, or some other echo mechanism. We note that identical results were also observed in similar experiments with other VHF radars (Chen et al., 2004; Chilson et al., 2002).

这一惊人的数据，足以引起各界对海洋生态环境及塑料微珠是否通过食物链进一步对人体健康造成影响的担忧。因此，对塑料微珠限制使用更是到了刻不容缓的阶段。

In fact, many rocket soundings and radar data have confirmed the existence of electron density depletion layers in this region, with the strong radar echoes often corresponding to the altitudes of these layers (Havens et al.,2001; Havens et al., 1996; Ulwick et al., 1988), which often have very sharp vertical gradients because of the presence of thin ice-particle layers resulting from the scavenging of electrons. Also named a dusty plasma layer, this layer consists of electrons, ions and charged ice particles. In addition, based on the theory of Fresnel reflection, the echo power is largely dependent on the gradients in the refractive index, so the maximum echo power should be in a direction perpendicular to the reflected layers, which, if they are tilted, it is possible for the oblique beams to receive a stronger echo than the vertical beam, as sketched in Figure 2. Moreover, Alcala et al. (2001) have calculated the reflection coefficient of the radar echoes by using rocket data and radar measurements to obtain similar results to that observed here.

Figure 1 The mean echo power relative to that received in the vertical beam as a function of the elevation angle.

Figure 2 Sketch describing the radar backscatter from the dusty plasma layers.

Although rocket soundings have confirmed the relationship between the dusty plasma layers and PMSE,individual rocket flights have not provided any information about the fully two-dimensional nature of the structure of dusty plasma layers in the mesopause region, and whether their orientation as depicted in Figure 2 is accurate. Were the layers to have a tilt angle, the question would arise as to which mechanism does the tilting, and which factor would control the tilt angles leading to a maximum intensity in the echoes found at angles of 86º or 78º. Therefore, in the next section, we address our understanding of this feature in detail by using a theoretical model.

一方面，管理者特质和内部控制机制形成协同作用共同维护企业发展的目标和运营基础。另一方面，企业管理者结合内外环境对企业发展战略内控结构进行综合优化，维护内外信息资源的时效性，并且保证企业研发水平、经营水平以及人力资本管理效率都能顺应时代发展趋势，真正意义生提高企业的市场价值，为企业可持续发展奠定基础。

4 Model description

4.1 Model equation

To quantitatively assess whether the motion associated with gravity waves leads to tilting of the dusty plasma layers,density variations of ice particles resulting from gravity-wave activity are described by the continuity equation,

In an earlier work (Hui et al., 2010), we proposed that the wind-speed variation caused by gravity waves, which can significantly influence the transport of heavy ice particles through collision coupling between the neutral atmosphere and ice particles, ultimately results in their convergence into thin and dense multiple layers. Here, we are particularly interested in studying the effects of gravity waves on the tilting of these layers using a theoretical two-dimensional model to explain the aspect sensitivity of PMSE.

where nd and ud are the iceparticle density and velocity components, respectively.Strictly speaking, the forces acting on the ice particles include the drag force, atmospheric pressure and gravity in the mesopause region. The velocity of the ice-particle is given by the momentum equation as

where md is the ice-particle mass, υdn is the effective collision frequency, p d =nd kTd is the partial pressure,and g is the acceleration due to gravity. The effective collision frequency υdn for ice particles is represented by(Lie-svendsen et al., 2003)

where nn, mn and rd are the neutral density, mass and particle radius, respectively. The term un=v(u,w) in equation (2) is the velocity of the neutral particles, which is assumed to represent the gravity-wave perturbation velocity,where u and w are its components in the horizontal and vertical directions, respectively. According to linear gravitywave theory, the horizontal velocity component u and the vertical velocity component w are related to the neutral density n/n0by Hines et al. (1960).

respectively, where H0 is the scale height, γ is the ratio of the specific heats, and kx and kz are the horizontal and vertical wave numbers, respectively. Finally, the wavedensity perturbation n/n0 is written in terms of the amplitude and phase as

舒尔曼并对应当如何从事“案例研究”进行了具体分析：“一个被恰当理解的案例，绝非仅仅是对事实或一个偶发事件的报道．把某种东西称作案例是提出了一个理论主张——认为那是一个‘某事的案例’”；“尽管案例本身是对某些事件或一系列事件的报道，然而是它们所表征的知识使它们成为案例．案例可以是实践的具体实例——对一个教学事件发生进行的细致描述，并伴随着特定的情境、思想和感受．另一方面，它们可以是原理的范例，例证一个较为抽象的命题或理论的主张．”[5]

The set of equations (1–5) describes the ice-particle,dynamic transport process coupling with gravity waves. The numerical methods used to solve these equations are presented in the next section.

4.2 Model results

To address with our theoretical model to what extent gravity waves affect the tilting of dusty plasma layers, we first assume the ice-particle size and their initial number density distribution with height in this region, and then study the density variation of charged ice-particles relative to gravity-wave perturbations. To simplify the calculation procedure, we assume that the ice particles in the PMSE region have an initially fixed horizontal distribution, and are uniform in size, and that by imposing gravity-wave perturbations on this region, any changes in the height distribution may be attributed to gravity waves. According to measurements of the temperature structure as observed by multiple sounding rockets, the initial vertical density distribution can be simply regarded as Gaussian,

从表4中可以发现，两种版本在例题的表征方式上都比较注重多元化．苏教版的例题不仅有实物图，还有几何模型图．康轩版例题之间的衔接坡度小，表征方式主要是文字和几何模型图，纯文字的例题也占了30%多．在引导学生思考方面，两个版本教材都非常注重导引语的设计，尤其是起始内容的例题，既有方法的启发和提示，还有思考过程的呈现．康轩版除此以外在每个重要的内容和活动的下面设有“亲师沟通站”及配套习题提示，“亲师沟通站”主要是对学习内容的具体解释和说明，既是对教师教学重点提示，也是对学生学习时难点的启发．

Equations (1) and (2) are solved by using the full-implicit-continuous-Eulerian (FICE) scheme with a difference grid technique as described in detail in Hu et al.(1984). In general, as the numerical solutions of the continuity equation (1) are dependent upon the boundary conditions, we used periodic boundary conditions in the horizontal direction, so that any material advected out of one side of the grid is advected into the opposite side. To avoid vertical boundary reflections at the upper and lower boundary conditions, the first-order spatial derivative is set to zero∂nd /∂ z= 0. The calculation domain in the horizontal direction is one wavelength, and the vertical domain extends from 78 km to 92 km.

Figure 3 illustrates the evolution of the ice-particle layer under the influence of gravity-wave perturbations according to the numerical results, with the layers displayed as a function of the horizontal distance and height. As evident from the simulation results, 2 h into the simulation(Figure 3b), the waves have already distorted the pre-existing layers (Figure 3a) by modulating the ice-particle concentration, which gradually transforms a single, thick ice layer into distinct, thin double layers. Most importantly, the reflection layers are not strictly horizontal,but have been tilted with respect to the horizontal by the gravity-wave perturbation. However, it should be noted that the ice-layer structures are transient, continuously varying with the cyclical activity of the gravity waves. In addition,because the diffusion of the ice particles is very slow, ice layers with a sharp gradient can be maintained for a long period after the disappearance of the gravity waves. These results are not only consistent with observations, but also confirm our contention that, on many occasions, the reflection layers are tilted.

Figure 3 Ice-particle-layer evolution resulting from gravity-wave perturbations as functions of the horizontal distance and height.

5 Conclusions

We have presented data from the EISCAT VHF radar to investigate the aspect sensitivity of PMSE during the period 13–15 July 2010 by traversing the antenna beam in the zenith direction, and comparing the corresponding received power. Based on these data, we find a complex angular dependence of the PMSE, which cannot be explained by the pure isotropic structure of turbulence. Instead, these experimental results are consistent with, at least qualitatively, with the idea that partial reflections from the gradients of the refractive index of dusty plasma layers at the altitudes of PMSE contribute significantly to the received echo power of the VHF band. Additionally, the experimental results demonstrate that the echo intensity received by the oblique beam is larger than the vertical beam, the cause of which we propose is the presence of tilted reflection layers. To confirm this idea and describe the physical process, we have developed a theoretical model to demonstrate the formation process of tilted reflection layers by using numerical simulations.

As mentioned above, because the individual rocket flights give us no information about the full two-dimensional scattering structure in the mesopause region, our model results not only attempt to make up for this shortcoming, but also explain why ice particles near the summer polar mesopause are frequently seen to be confined to multiple layers. Furthermore, for the reference case, the model contains a large number of assumed parameters, such as the ice size distribution, number density and other particle microphysics, which may affect the model results,but were not given a detailed consideration here, and thus need further investigation. The gravity wavelength is also a crucial parameter, since it determines the tilt angle of the layers, which depends on the ratio of the horizontal to the vertical gravity wavelength in our model. This dependence may be used to explain why the maximum echo power can occur at different angles in our experimental data.

It should be noted that while we have primarily considered a possible theory to explain the aspect sensitivity of PMSE, the quantitative relationship between the dusty plasma layers and the strong radar echoes has not been addressed. We have only shown that the presence of dusty plasma layers with sharp gradients may contribute significantly to the received echo power, which should be further confirmed with the help of more in situ and ground-based observations. Further studies of the characteristics of the radar signals are also needed for a better quantitative understanding of the overall reflection and scattering processes, using, for example, multifrequency observations, the frequency dependence of the echo power on the turbulence scattering, the degree of partial reflection, as well as techniques, such as the variation in the pulse length and the examination of the power spectrum of the received signal. These methods are proposed to be implemented simultaneously in future investigations.

Acknowledgments The authors thank the staff of the EISCAT for their collaboration in running the experiments and giving useful advice. The EISCAT Scientific Association is supported by CRIRP (China), NIPR(Japan), NFR (Sweden), PPARC (UK), RCN (Norway) and SA (Finland).The authors would like to thank Dr. Xu Bin for his help during the experimentation.

由于自然条件和资金等因素的影响，公路建设项目需要根据地形地貌条件进行开挖和高填，开挖和高填方施工对土石特性有特殊要求，从而导致土石方量不平衡。在建造过程中产生了大量的弃土弃渣。研究表明，公路工程产生的废弃土石主要包括临时开挖路基、路堑、隧道等。如果这些废石处理不当，会造成严重的水土流失，破坏周围生态环境。

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