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仿真模拟初始输入的水体参数可以是水体光学参数(水体和颗粒物的吸收光谱和散射光谱、散射相函数),也可以输入水体的叶绿素a浓度剖面,通过叶绿素a浓度与水体光学参数的经验关系计算得出各种水体光学参数,包括水体吸收系数 a与散射系数 b,由此计算激光雷达测量信号中的消光系数 α与激光雷达后向散射系数 β( π)(即180°体积散射函数),结合设定的雷达系统参数,代入激光雷达方程计算回波光子数,并求得单光子探测深度。
文中假定大洋海水中的吸收和散射主要为浮游植物的贡献。由叶绿素a浓度剖面计算浮游植物吸收系数 a ph的计算方法为1998年Lee等给出的经验关系 [ 10] :
$$ {a}_{{\rm{ph}}}\left(\lambda \right)=\left[{a}_{0}\right(\lambda )+{a}_{1}(\lambda \left){\rm ln} ({a}_{{\rm{ph}}}\right(440\left)\right)\left]{a}_{{\rm{ph}}}\right(440) $$ (1) 式中:
$ {a}_{{\rm{ph}}}\left(\lambda \right) $ 为浮游植物吸收系数; a 0、 a 1是与波长相关的经验系数(如 图3所示 [ 11] );$ {a}_{{\rm{ph}}}\left(440\right) $ 为固定波长440 nm处的浮游植物吸收系数,可由1998年Bricaud等人提出的方法 [ 12] 计算,如公式(2)所示,式中< chl>为叶绿素a浓度(mg/m 3):$$ {a}_{{\rm{ph}}}\left(440\right)=0.037\;8<chl{>}^{0.627} $$ (2) 纯水吸收系数 a w为1997年Pope和Fry利用积分球测量的不同波长下的结果,表现为蓝绿光波段吸收系数较低,红光波段较高,如 图4所示 [ 11] 。
由叶绿素a浓度剖面计算颗粒物散射系数 b p的方法采用1983年Gordon与Morel提出的经验关系 [ 13] ,如公式(3)所示:
$$ {b}_{\rm p}\left(\lambda \right)=0.3<chl{>}^{0.62}\left(\dfrac{550}{\lambda }\right) $$ (3) 颗粒物相函数采用1972年Petzold给出的测量结果 [ 14] ,如 图5所示。
纯水的散射系数为1977年Morel提出的散射系数模型 [ 15] ,如 图6所示。
纯水相函数为 [ 16] :
$$ {\tilde {\beta }}_{\rm w}\left(\phi \right)=0.062\;25(1+0.835{{\rm cos}}^{2}\phi ) $$ (4) 水体的180°体积散射系数 β( π)可由散射系数 b与散射相函数的乘积计算。
激光雷达消光系数
$ \mathrm{\alpha } $ 可由1972年Kattawar基于蒙特卡罗模拟给出的经验关系式计算 [ 17] :$$ \alpha ={K}_{\rm d}+\left(c-{K}_{\rm d}\right){\rm exp}(-0.85cD) $$ (5) 式中: c为海水衰减系数; D为海面接收光斑直径; K d为海水的漫射衰减系数,可由2005年Lee给出的关系计算 [ 18] 。
$${K_d} = a + 4.18{b_{\rm b}}\left[ {1 - 0.52{\rm{exp}}\left( { - 10.8a} \right)} \right]$$ (6) 将上述计算结果代入激光雷达方程即可求得星载海洋激光雷达接收的回波光子数 [ 19] :
$$N\left( {\textit{z}} \right) = \dfrac{{{E_0}}}{{h\nu }}\dfrac{{{A_{rec}}}}{{{{(nH + {\textit{z}})}^2}}}T_{\rm atm}^2T_{\rm sur}^2\eta \varDelta {\textit{z}}\beta \left( {\textit{π}} \right){\rm exp} [ - 2\mathop \int \nolimits_0^{\textit{z}} \alpha \left( {{\textit{z}}'} \right){\rm d}{\textit{z}}']$$ (7) 式中:
$ N\left({\textit{z}}\right) $ 为探测器接收的深度 z处的回波光子数;$ {E}_{0} $ 为发射的激光能量;$ h $ 为普朗克常数;$ \nu $ 为激光频率;$\dfrac{{E}_{0}}{h\nu }$ 即为发射光子数,${A}_{\rm rec}$ 为望远镜接收面积;$ H $ 为激光雷达所在高度;$ n $ 为海水折射率;$\dfrac{{A}_{\rm rec}}{(nH+{\textit{z}}{)}^{2}}$ 即为接收立体角;${T}_{\rm atm}$ 为大气透过率;${T}_{\rm sur}$ 为海气界面透过率;$ \eta $ 为光学系统的光学效率;$ \varDelta {\textit{z}} $ 为垂直分辨率。利用此节描述的方法,可以使用输入的叶绿素a浓度剖面模拟计算不同激光雷达参数情况下的星载海洋激光雷达海洋水体剖面回波信号,用于激光雷达探测能力的评估和探测精度的分析。
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文中选择443 nm、486.1 nm与532 nm三个典型激光波长对激光雷达回波信号进行对比分析。三个典型波长中,443 nm是水色遥感的常用典型波长,在最清洁的大洋水中穿透力较好;486.1 nm波长在大洋水中具有较好的穿透能力,而且该波长对应一条太阳夫朗和费暗线,可以有效降低太阳背景光对激光雷达探测性能的影响;532 nm是激光技术最成熟的蓝绿波长,在沿岸海水比蓝光有更好的穿透能力。
使用2009~2019年的Argo全球海域叶绿素a剖面数据,将数据进行质量控制与经纬度1°×1°的空间网格化处理,得到全球海域1 m垂直分辨率的叶绿素a浓度剖面。虽然Argo叶绿素a数据不足以覆盖全部海域,但仍可以选择典型海域进行统计分析。根据连续10年的全球Argo叶绿素a浓度剖面数据得到的地中海(4°W~42°E, 32°N~46°N,共8 824个剖面)、印度洋(65°E~110°E, 30°S~10°N,共3 417个剖面)、南大洋(180°W~180°E, 80°S~40°S,共15 838个剖面)与太平洋(170°E~120°W, 30°S~40°N,共2 000个剖面)四个海区的平均叶绿素a浓度剖面如 图7所示。可以看出:南大洋海域平均叶绿素a峰值浓度较高、峰值深度较浅,太平洋峰值深度最深、峰值浓度较小。
根据 表1所列的激光雷达系统参数以及所需的大气光学参数(1976年美国标准大气模型)、水体光学参数(由叶绿素a剖面计算得到)等,通过公式(7)所示的激光雷达方程计算得到无背景光情况下的1 s累加回波光子数,以1个回波光子作为阈值确定单光子探测深度, 图8为地中海(a)、印度洋(b)、南大洋(c)、太平洋(d)四个海区在三个典型波长下的激光雷达回波光子数剖面,横向虚线为各个波长的单光子探测深度,0 m处尖峰为模拟的海面强反射信号。
表 1 星载海洋激光雷达仿真模拟参数
Table 1. Parameters for simulation of spaceborne oceanographic lidar
Input parameters Value Laser wavelength/nm 443, 486.1, 532 Repetition rates/Hz 20 Pulse energy/mJ 200 Pulse width/ns 10 Laser linewidth/nm 0.1 Laser divergence/mrad 0.2 Telescope diameter/m 1.2 Field of view/mrad 0.3 Receiving spectrum width/nm 0.2 Optical efficiency 0.6 Orbital height/km 550 Solar spectral irradiance/W·m −2·um −1 205 Sea surface wind speed/m·s −1 5 Solar altitude angle/(°) 60 Range resolution/m 1 图 8 四个海区不同波长下的激光雷达回波光子数(横向的虚线为单光子回波对应的探测深度)
Figure 8. Photon number of lidar echo at different wavelengths in four sea areas (the transverse dotted line is the detection depth corresponding to single photon echo)
由于太平洋海域水体最清澈,叶绿素a浓度较小且峰值深度较深,回波信号衰减较慢,探测深度最深,486.1 nm与443 nm探测深度约为120 m,532 nm探测深度较浅,约为80 m;地中海和印度洋叶绿素a浓度高于太平洋且峰值深度较浅,两海域探测深度结果类似,486.1 nm与443 nm探测深度约为100 m,532 nm探测深度约为75 m;南大洋叶绿素a浓度较大且峰值深度较浅,回波信号衰减较快,各个波长的探测能力都相对较弱,探测深度约为65 m,同时也能看出在较为浑浊的海域,532 nm的信号与其他两个波长更加接近,486.1 nm比443 nm衰减的更慢,探测深度最深。图中0 m处尖峰为模拟的海面强反射信号。
在上述回波光子数曲线中加入背景光子数,模拟经采集后得到的光子计数值,并计算信噪比。以太平洋海域为例的光子计数值剖面与信噪比剖面如 图9所示。
图 9 太平洋海域的激光雷达光子计数值剖面(a)和信噪比剖面(b)
Figure 9. Lidar profiles of photon counts (a) and signal-to-noise (b) in Pacific ocean
从 图9中可以看出532 nm波长采集光子计数值、信噪比都低于486.1 nm、443 nm波长。若以SNR = 2作为最大探测深度判据,486.1 nm、443 nm约能达到90~100 m深度,532 nm只能探测到60 m。
Estimation of chlorophyll profile detection capability of spaceborne oceanographic lidar
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摘要: 为了评估和分析星载海洋激光雷达探测全球海洋光学参数的性能,依据激光雷达方程和蒙特卡罗模型结果模拟计算激光传输信号,开发了星载海洋激光雷达仿真模拟系统。仿真模拟系统由正向模拟、数据反演与误差分析三部分组成,能够模拟激光发射、传输和探测的全过程。根据给定的激光雷达参数,模拟了443 nm、486.1 nm和532 nm波长在地中海、印度洋、南大洋与太平洋四个典型海区的探测信号。研究结果表明,443 nm和486 nm波长的探测深度在各个海区均比较接近,并且均比532 nm更深。在给定的激光雷达参数情况下,486.1 nm波长在太平洋和南大洋的探测深度分别为120 m和70 m,在地中海和印度洋的探测深度均为约100 m。叶绿素a浓度在以上海区的探测深度分别约为80 m、50 m和70 m。Abstract: In order to evaluate and analyze performance of spaceborne oceanographic lidar for global ocean optical properties detection, a simulation system for spaceborne oceanographic lidar was developed based on lidar equation and the results of Monte Carlo simulation model. The lidar simulation system consisted of three modules, forward simulation, data inversion and error analysis, which could simulate the whole process of laser emission, transmission and detection. According to the given lidar parameters, the detection signals of 443 nm, 486.1 nm and 532 nm in four typical areas, Mediterranean Sea, Indian Ocean, Southern Ocean and Pacific Ocean, were simulated. The results show that the detection depths of 443 nm and 486 nm are approximately the same and deeper than that of 532 nm. For the given lidar parameters, the detection depths of 486.1 nm wavelength in the Pacific Ocean and the Southern Ocean are 120 m and 70 m, respectively, and the detection depth in the Mediterranean Sea and the Indian Ocean is about 100 m. The detection depths of chlorophyll-a concentration in the above sea areas are about 80 m, 50 m and 70 m, respectively.
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Key words:
- spaceborne oceanographic lidar /
- simulation system /
- Chl-a /
- detection depth
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表 1 星载海洋激光雷达仿真模拟参数
Table 1. Parameters for simulation of spaceborne oceanographic lidar
Input parameters Value Laser wavelength/nm 443, 486.1, 532 Repetition rates/Hz 20 Pulse energy/mJ 200 Pulse width/ns 10 Laser linewidth/nm 0.1 Laser divergence/mrad 0.2 Telescope diameter/m 1.2 Field of view/mrad 0.3 Receiving spectrum width/nm 0.2 Optical efficiency 0.6 Orbital height/km 550 Solar spectral irradiance/W·m −2·um −1 205 Sea surface wind speed/m·s −1 5 Solar altitude angle/(°) 60 Range resolution/m 1 -
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