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本文中使用WINDCUBE V2 3-D扫描式多普勒激光雷达,发射的激光脉冲波长为1540 nm,扫描径向线上的距离分辨率为50 m,探测盲区为200 m以下,理论探测距离200 m~6000 m,包括距离高度指示器(range height indication, RHI)、平面位置指示器(plane position indication, PPI)。该雷达采用的是外差法的多普勒频移激光探测和测距技术,探测得到的数据参数包括时间、方位角、仰角、距离、径向风速、载噪比(carrier-to-noise ratio, CNR)、谱宽、可信度等, 系统原理如图 1所示。图中,CW(continuous wave)为连续波,ADC(analog-to-digital converter)为模数转换器。
边界层内的气溶胶粒子的分布浓度明显高于边界层之上的“自由大气”部分的气溶胶浓度[21],气溶胶浓度越大,信号越强;反之,信号越弱。基于此原理,本文中使用了RHI扫描模式下的90°朝天顶方向扫描接收到的载噪比数据,载噪比的理论公式可表示为[22-23]:
$ R_{\mathrm{CNR}}=\frac{\eta E \beta \lambda T^2 \pi D^2}{8 \hbar B R^2} $
(1) 式中,η为系统效率,E为激光器发射能量,β为气溶胶后向散射系数,λ为波长, T为传输R处的大气透射率, R为探测距离,D为望远镜孔径, ℏ为普朗克常量, B为探测电路带宽。
作为对比,本文作者还使用了温江站的L波段雷达探空数据。探空数据包括温度、湿度、风速、位温、压强等参数。探测时次(北京时间)为每天3次,分别为02、08和20时刻,采样间隔小于1.5 s。温江站与广汉机场都位于成都平原,直线距离约50 km,边界层高度在一定范围内差距较小,可以用温江站的探空反映广汉机场地区的边界层特征。为了验证及补充探空资料时次少的问题,本文作者还使用了飞机传感器获得的1次/s的高度、温度数据。由于训练飞行高度所限,只能获得1200 m以下的温度廓线信息。
为了了解当天的天气情况,本文作者还使用了广汉机场气象台提供的逐小时的观探测资料,包括自动观测的气温、相对湿度、露点温度和风速,以及人工观测的云量、云底高信息。
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从热力作用角度,边界层高度可以定义为位温或温度梯度变化不连续的高度[6, 24]。本文中依据上述定义,利用位温廓线数据,将位温明显不连续的高度定义为边界层高度。
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利用激光雷达CNR数据反演边界层高度之前,首先对雷达数据进行了质量控制[7],以剔除不可信数据,然后运用梯度法、小波协方差法和标准偏差法计算了边界层高,3种反演方法具体见下。
(a) 梯度法。激光雷达的距离平方校正信号RCNR(Z2)的梯度D(Z)可表示为:
$ D(Z)=\frac{\mathrm{d}\left[R_{\mathrm{CNR}}\left(Z^2\right)\right]}{\mathrm{d} Z} $
(2) 式中, Z表示高度。为了消除气溶胶浓度微小变化造成的梯度值大幅变化的问题,用Savitzjy-Golay方法对每条CNR数据进行了平滑处理后再求取D(Z),最后将D(Z)的负值最小值确定为边界层高度[25]。
(b) 小波协方差法。小波协方差变换是用于检测信号突变的方法,当函数值越大时,表明信号函数与小波函数相似性越高[26]。小波协方差法多使用哈尔小波作为小波基,哈尔小波基由一个复合函数构成:
$ H\left(\frac{Z-b}{a}\right)=\left\{\begin{array}{l} +1, \left(b \leqslant Z \leqslant b+\frac{a}{2}\right) \\ -1, \left(b-\frac{a}{2} \leqslant b+\frac{a}{2}\right) \\ 0, \text { (other) } \end{array}\right. $
(3) 式中,a为空间范围或者计算步长,b为哈尔小波基的函数中心,利用哈尔小波函数定义的协方差如下:
$ W(a, b)=a^{-1} \int_{Z_{\mathrm{b}}}^{Z_{\mathrm{t}}} f(Z) H\left(\frac{Z-b}{a}\right) \mathrm{d} Z $
(4) 式中,f(Z)是后向散射信号,Zt和Zb分别是信号高度的上下限。经整理可得:
$ \begin{gathered} W(a, b)=a^{-1}\left[\int_b^{b+\frac{a}{2}} f(Z) \mathrm{d} Z-\right. \\ \left.a^{-1} \int_{b-\frac{a}{2}}^b f(Z) \mathrm{d} Z\right] \end{gathered} $
(5) 小波协方差变换函数W(a, b)反映的是在高度b±a/2的范围内f(Z)与哈尔函数的相似程度。所以,当W(a, b)越大,表明f(Z)与哈尔函数越相似,即其阶跃变化越明显,由此可将W(a, b)取得最大值的高度作为边界层高度。
(c) 标准偏差法。标准偏差(standard deriation, STD)反映了激光雷达后向散射信号在某高度的离散程度,该值越大, 离散性越强。由于在自由大气与边界层的交界处总是存在强烈的夹卷,信号在边界层顶处会存在剧烈的信号变化,因此可将标准偏差最大值的高度视为边界层高度[27]。标准偏差的公式可表示为:
$ \begin{gathered} D_{\mathrm{STD}}(Z)= \\ \left\{\frac{1}{N} \sum\limits_{i=1}^N\left[R_{\mathrm{CNR}, i}\left(Z^2\right)-\overline{R_{\mathrm{CNR}}\left(Z^2\right)}\right]^2\right\}^{1 / 2} \end{gathered} $
(6) 式中, N表示数据点。本文作者将DSTD(Z)取得最大值的高度定义为边界层高度。
基于多普勒激光雷达的机场边界层高度研究
Research on airport boundary layer height based on Doppler LiDAR
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摘要: 为了探究广汉机场上空边界层高度的变化特征, 利用多普勒激光雷达的载噪比数据, 采用梯度法、小波协方差法和标准方差法, 对机场上空的边界层高度进行了反演, 并与L波段探空和飞机探测数据进行了对比, 利用飞机探测数据和探空仪数据对激光雷达反演的边界层高度进行了验证。结果表明, 在对流边界层顶的识别上, 3种方法都能较好地捕获边界层信息, 且一致性较好, 但在对残余层顶和稳定边界层顶的识别上, 梯度法无论是准确性、连续性还是稳定性上都表现出了明显优势; 反演得到的对流边界层和残余层高度维持在2000 m左右, 稳定边界层高度在100 m~200 m之间; 受边界层内湍流的影响, 物质边界层高度与热力边界层高度在某些时段会出现显著差异。该研究可为飞行训练提供预警信息, 更好地保障飞行安全。Abstract: In order to explore the height variation characteristics of the boundary layer over Guanghan Airport, the carrier noise ratio data of Doppler light detection and ranging (LiDAR) was used to invert the boundary layer height over the airport by gradient method, wavelet covariance method, and standard variance method. The calculated data through these methods was then compared with that of the L-band sounding and aircraft detection data. The results show that boundary layer information can be captured well by these methods, and good consistency in the recognition of convective boundary pause can be observed. However, the gradient method shows obvious advantages in accuracy, continuity and stability in the recognition of residual layer pause and stable boundary top layer. During the observation period, the height of the convective boundary layer and the residual layer is about 2000 m, and the height of the stable boundary layer is between 100 m~200 m. The boundary layer height of LiDAR inversion was verified by aircraft detection data and sonde data. Due to the turbulence in the boundary layer, the material boundary layer and the thermal boundary layer were significantly different at certain times. The study can provide early warning information for flight training and better ensure flight safety.
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