海洋科学  2020, Vol. 44 Issue (5): 34-41 PDF
http://dx.doi.org/10.11759/hykx20190726001

#### 文章信息

ZHANG Yuan-yuan, PANG Hua-ji, LIU Zhao, SONG Lin, DENG Meng. 2020.

Propagation characteristics of the lightning electromagnetic fields along rough sea surface and the effects on the accuracy of ToA-based lightning location

Marina Sciences, 44(5): 34-41.
http://dx.doi.org/10.11759/hykx20190726001

### 文章历史

1. 青岛市气象灾害防御技术中心, 山东 青岛 266003;
2. 青岛市气象灾害防御工程技术研究中心, 山东 青岛 266003;
3. 山东省气象局气象灾害防御技术中心, 山东 济南 250000

Propagation characteristics of the lightning electromagnetic fields along rough sea surface and the effects on the accuracy of ToA-based lightning location
ZHANG Yuan-yuan1,2, PANG Hua-ji1,2, LIU Zhao1,2, SONG Lin1,2, DENG Meng3
1. Qingdao Engineering Technology Research Center for Meteorological Disaster Prevention, Qingdao 266003, China;
2. Qingdao Technology Research Center for Meteorological Disaster Prevention, Qingdao 266003, China;
3. Shandong Engineering Technology Research Center for Meteorological Disaster Prevention, Jinan 250000, China
Abstract: An improved two-dimensional fractal model was used to describe the rough sea surface, and based on Barrick's formulations and Wait's formulations, this paper selected a lightning stroke to analyze the lightning electromagnetic field along the rough sea surface. Furthermore, the effects of the sea surface fluctuation on the time-of-arrival (ToA)-based lightning location systems (LLS) were discussed. The results revealed that the sea surface fluctuation had a significant effect on the wave shape and time delay of the electromagnetic fields propagating along the rough sea surface, but had little effect on the magnitude of the electromagnetic fields. The rise time of the wave shape became longer with an increase in the wave height. When the observation distance increased, the rise times of the lightning vertical electric fields and magnetic fields became longer. The observed time delay caused by the electromagnetic field propagation along the rough sea surface might impact the location accuracy of ToA-based LLS. Affected by the sea surface, different lightning stroke points lead to different lightning location errors, and the location error reached several to ten kilometers.
Key words: an improved two-dimensional fractal sea surface model    lightning return stroke    lightning vertical electric field    lightning magnetic field

1 起伏海面的雷电垂直电场近似算法 1.1 计算起伏海面的雷电垂直电场

 $\begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{E_{v, \infty }}(0, r, t) = \\ \frac{1}{{2\pi {\varepsilon _0}}}\int_{\;0}^{\;L'(t)} {\frac{{2 - 3{{\sin }^2}\theta (z')}}{{{R^3}(z')}}} \int_{\;{t_b}(z')}^{\;t} {i\left[ {z', t - R(z')/{\rm{c}}} \right]\;} {\rm{d}}t{\rm{d}}z'\\ + \frac{1}{{2\pi {\varepsilon _0}}}\int_{\;0}^{\;L'(t)} {\frac{{2 - 3{{\sin }^2}\theta (z')}}{{{\rm{c}}{R^2}(z')}}} i\left[ {z', t - R(z')/{\rm{c}}} \right]{\rm{d}}z'\\ - \frac{1}{{2\pi {\varepsilon _0}}}\int_{\;0}^{\;L'(t)} {\frac{{{{\sin }^2}\theta (z')}}{{{{\rm{c}}^2}R(z')}}} \frac{{\partial i\left[ {z', t - R(z')/{\rm{c}}} \right]}}{{\partial t}}{\rm{d}}z', \end{array}$ (1)

 图 1 雷电回击过程示意图 Fig. 1 Geometry of lightning return stroke

 ${E_{\nu , \sigma }}(0, r, t) = \int_0^t {{E_{v, \infty }}(0, r, t - \tau )w(0, r, \tau ){\rm{d}}\tau , }$ (2)

 $W(0, r, j\omega ) = 1 - j\sqrt {\pi q} \exp ( - q){\rm{erfc}}(j\sqrt q ),$ (3)
 $q = - \frac{{{\rm{j \mathsf{ ω} r}}}}{{{\rm{2c}}}}\Delta _{{\rm{eff}}}^2,$ (4)

 ${\Delta _{{\rm{eff}}}} = \Delta + \Delta \prime .$ (5)

 $\Delta = \frac{{{k_0}}}{k}{\left( {1 - \frac{{k_0^2}}{{{k^2}}}} \right)^{1/2}},$ (6)
 $k = {k_0}{({\varepsilon _r} - j60\sigma {\lambda _0})^{1/2}},$ (7)
 ${k_0} = \omega {({\mu _0}{\varepsilon _0})^{1/2}},$ (8)
 ${\lambda _0} = {\mathop{\rm c}\nolimits} /(\omega /2\pi ),$ (9)
 $\Delta ' = \frac{1}{4}\int_{ - \infty }^{ + \infty } {{\rm{d}}\gamma } \int_{ - \infty }^{ + \infty } {G(\gamma , \eta )V(\gamma , \eta ){\rm{d}}\eta } ,$ (10)
 $\begin{array}{l} G(\gamma , \eta ) = \frac{{{\gamma ^2} + b \cdot \Delta \cdot ({\gamma ^2} + {\eta ^2} - \omega \gamma /{\rm{c}})}}{{b + \Delta \cdot ({b^2} + 1)}} + \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\frac{{\Delta \cdot ({\gamma ^2} - {\eta ^2})}}{2} + \Delta \cdot \omega \cdot \gamma /{\rm{c}}, \end{array}$ (11)
 $b = \frac{{\rm{c}}}{\omega }{\left[ {{{\left( {\frac{\omega }{{\rm{c}}}} \right)}^2} - {{\left( {{\gamma ^2} + \frac{\omega }{{\rm{c}}}} \right)}^2} - {\gamma ^2}} \right]^{1/2}},$ (12)

1.2 模拟起伏海面的模型

 $V(\gamma , \eta ) = S(\gamma , \eta )D(\gamma , \eta , \phi ),$ (13)

 $S(\gamma , \eta ) = \left\{ \begin{array}{l} - \frac{{{\tau ^2}{\chi ^2}}}{{2\ln a}}k_0^{2(d - \xi )}{\left( {\sqrt {{\gamma ^2} + {\eta ^2}} } \right)^{[ - 2(d - \xi ) - 1]}}, \sqrt {{\gamma ^2} + {\eta ^2}} < {k_0}\\ \frac{{{\tau ^2}{\chi ^2}}}{{2\ln b}}k_0^{2(d - 3)}{\left( {\sqrt {{\gamma ^2} + {\eta ^2}} } \right)^{[ - 2(d - 3) - 1]}}, \sqrt {{\gamma ^2} + {\eta ^2}} \ge {k_0} \end{array} \right.,$ (14)
 $D(\gamma , \eta , \phi ) = 1 + \frac{{4\pi }}{{\sqrt {{\gamma ^2} + {\eta ^2}} }}\sum\limits_{l = 1}^\infty {U(\sqrt {{\gamma ^2} + {\eta ^2}} , 2l)\cos [2l(\phi - {\beta _0})]} ,$ (15)

 $U(\sqrt {{\gamma ^2} + {\eta ^2}} , 2l) = \frac{1}{{4{\rm{ \mathsf{ π} }}}}\int_{ - {\rm{ \mathsf{ π} }}}^{\rm{ \mathsf{ π} }} {{\alpha _0}\sec {h^2}({\alpha _0}\varphi )\exp ( - j2l\varphi ){\rm{d}}\varphi } ,$ (16)
 $\left\{ \begin{array}{l} {\alpha _0}{\rm{ = }}2.61{({{\sqrt {{\gamma ^2} + {\eta ^2}} } \mathord{\left/ {\vphantom {{\sqrt {{\gamma ^2} + {\eta ^2}} } {{k_0}}}} \right. } {{k_0}}})^{1.3}}, 0.65 \le {{\sqrt {{\gamma ^2} + {\eta ^2}} } \mathord{\left/ {\vphantom {{\sqrt {{\gamma ^2} + {\eta ^2}} } {{k_0}}}} \right. } {{k_0}}} \le 0.95\\ {\alpha _0}{\rm{ = }}2.61{({{\sqrt {{\gamma ^2} + {\eta ^2}} } \mathord{\left/ {\vphantom {{\sqrt {{\gamma ^2} + {\eta ^2}} } {{k_0}}}} \right. } {{k_0}}})^{ - 1.3}}, 0.956 {{\sqrt {{\gamma ^2} + {\eta ^2}} } \mathord{\left/ {\vphantom {{\sqrt {{\gamma ^2} + {\eta ^2}} } {{k_0}}}} \right. } {{k_0}}} < 1.6\\ {\alpha _0}{\rm{ = }}1.24, 其他 \end{array} \right..$ (17)
2 个例分析 2.1 长门岩浮标站风速数据的应用

 图 2 2015年4月2日雷暴天气过程时的十分风速 Fig. 2 Ten minute-mean wind speed data of Qingdao buoy station on April 2, 2015
2.2 雷电回击通道基电流的选取

 $i(0, t) = \frac{{{I_{01}}}}{{{\eta _1}}}\frac{{{{(t/{\tau _{11}})}^{{n_1}}}}}{{\left[ {{{(t/{\tau _{11}})}^{{n_1}}} + 1)} \right]}}{{\rm{e}}^{ - t/{\tau _{12}}}} + \frac{{{I_{02}}}}{{{\eta _2}}}\frac{{{{(t/{\tau _{21}})}^{{n_2}}}}}{{\left[ {{{(t/{\tau _{21}})}^{{n_2}}} + 1)} \right]}}{{\rm{e}}^{ - t/{\tau _{22}}}},$ (18)
 ${\eta _1} = \exp \left[ { - \frac{{{\tau _{11}}}}{{{\tau _{12}}}} \cdot {{\left( {{n_1}\frac{{{\tau _{12}}}}{{{\tau _{11}}}}} \right)}^{1/{n_1}}}} \right],$ (19)
 ${\eta _2} = \exp \left[ { - \frac{{{\tau _{21}}}}{{{\tau _{22}}}} \cdot {{\left( {{n_2}\frac{{{\tau _{22}}}}{{{\tau _{21}}}}} \right)}^{1/{n_2}}}} \right],$ (20)

 继后回击参数 I01/kA τ11/μs τ21/μs I02/kA τ12/μs τ22/μs 继后回击参数取值 10.7 0.25 2.5 6.5 2 230

 图 3 闪电通道底部采用的基电流波形 Fig. 3 Channel-based current waveform corresponding to a typical subsequent return stroke

 $i\left( {z',t - {{z'} \mathord{\left/ {\vphantom {{z'} v}} \right. } v}} \right) = i\left( {0,t} \right)\left( {1 - {{z'} \mathord{\left/ {\vphantom {{z'} H}} \right. } H}} \right),$ (21)

2.3 海浪对雷电电磁场传播的影响

 图 4 起伏海面对时域垂直电场的影响 Fig. 4 Propagation effect of sea surface on the lightning vertical electric field in the time domain at distances of 1 km (a, b), 30 km (c, d), 100 km (e, f), and 200 km (g, h) from the lightning channel 注:黑色虚线表示电导率无限大的理想海面, 彩色实曲线分别表示风速为2.5、5.2、8.7和13.4 m/s的起伏海面。观测点距闪电通道的距离为: a: 1 km; b: 30 km; c: 100 km; d: 200 km

 图 5 起伏海面对垂直电场频谱的影响 Fig. 5 Propagation characteristics of sea surface on the lightning vertical electric field in the frequency domain at distances of 1 km (a, b), 30 km (c, d), 100 km (e, f), and 200 km (g, h) from the lightning channel 注:观测点距闪电通道的距离为a: 1 km; b: 30 km; c: 100 km; d: 200 km

2.4 海浪对闪电定位精度的影响

2.4.1 山东省闪电定位系统介绍

 图 6 山东省LD-II闪电定位系统探测效率图 Fig. 6 Detection efficiency of LLS in Shandong Province
2.4.2 计算结果及分析

 观测点距闪电通道的距离d 风速v 0 m/s 2.5 m/s 5.2 m/s 8.7 m/s 13.4 m/s 1 km 1.45 1.45 1.45 1.45 1.475 30 km 0.45 0.455 0.46 0.47 0.49 100 km 0.44 0.45 0.46 0.49 0.53 200 km 0.44 0.45 0.48 0.52 0.575

 观测点距闪电通道的距离d 风速v 2.5 m/s 5.2 m/s 8.7 m/s 13.4 m/s 1 km 0 0 0 0.025 30 km 0.005 0.01 0.02 0.04 100 km 0.01 0.02 0.05 0.09 200 km 0.01 0.03 0.08 0.135

 观测点距闪电通道的距离d 风速v 0 m/s 2.5 m/s 5.2 m/s 8.7 m/s 13.4 m/s 1 km 0.25 0.26 0.27 0.27 0.27 30 km 0.185 0.205 0.205 0.23 0.245 100 km 0.185 0.215 0.23 0.24 0.315 200 km 0.185 0.22 0.24 0.265 0.35

 观测点距闪电通道的距离d 风速v 2.5 m/s 5.2 m/s 8.7 m/s 13.4 m/s 1 km 0.01 0.02 0.02 0.02 30 km 0.02 0.02 0.045 0.06 100 km 0.03 0.045 0.055 0.13 200 km 0.035 0.055 0.08 0.165

 图 7 海面起伏对闪电定位的影响 Fig. 7 Effect of rough sea surface on lightning location 注: “+”为闪电定位系统探测的闪击点位置, “○”为起伏海面模型修订后闪击点位置。右侧一组为第一次闪击的位置, 左侧一组为第二次闪击的位置

 闪电定位系统探测的闪击点位置 风速, v/(km/s) 闪击点距各测站间的延迟时间/μs 起伏海面模型修订后闪击点位置 定位误差/m 即墨站 龙口站 日照站 荣成站 35.79°N, 120.683°E 13.4 0.04 0.061 0.087 0.049 35.78°N, 120.84°E 12 662 35.7°N, 120.32°E 11 0.08 0.08 0.08 0.15 35.67°N, 120.344°E 3 944
3 结论