相干差分吸收二氧化碳激光雷达仿真与误差分析

阐述了相干差分吸收激光雷达（CDIAL）探测大气二氧化碳（CO₂）的原理，设计了1.57 μm波段微脉冲相干探测系统，并对系统的回波信号进行了仿真。通过仿真计算分别探究了温度、压力、波长等因素对差分光学厚度计算及CO₂体积分数的反演精度的影响。仿真结果显示：当波长漂移为0.5 pm、温度不确定度为1 K、压强不确定度为1 hPa、水汽体积分数测量不确定度为10%时，这些参数引起的总体误差为0.45%；在大气中CO₂的体积分数为4×10^-4时，微脉冲相干激光雷达探测CO₂体积分数的测量误差约为1.8×10^-6。

Abstract

Objective

Since the middle of the 20th century, due to the greenhouse effect, the global average surface temperature has increased by 0.85 ℃ between 1880 and 2012, and larger scale temperature increases have been investigated in some regions. Atmospheric carbon dioxide, as one of the important gases causing the greenhouse effect, plays an important role in global climate change. Due to the characteristics of large emissions and easy accumulation, carbon dioxide is often used as the main indicator of energy conservation and emission reduction. Understanding the spatiotemporal distribution pattern of atmospheric CO₂ concentration in different regions can help to grasp the footprint of the“source”and“sink”of CO₂ gas, which is conducive to achieving emission reduction control in China and accelerating the high-quality development of green and low carbon. The traditional methods of observing CO₂ concentration use various meteorological satellites equipped with passive remote sensing observation instruments to observe the global large-scale CO₂ concentration. However, passive remote sensing is limited by its observation characteristics, and there are problems such as difficult measurement at night, poor detection performance in high latitude regions, vulnerability to clouds and aerosols, and insufficient near-surface CO₂ observation accuracy. As one of the active remote sensing technologies, coherent differential absorption lidar technology can work all day and detect with high accuracy. Compared to ground-based or airborne CO₂ column concentration observation methods, it can provide CO₂ concentration profile observation results with higher resolution. This observation method combines two technical systems, i.e., optical heterodyne and differential absorption, and can achieve high sensitivity, high integration, and diversified detection of atmospheric parameters. Coherent differential absorption lidar can obtain information about the vertical profile of carbon dioxide concentration and has the ability to detect point sources, cities, and key areas with high accuracy. However, its system structure is complex, and its development is difficult in the case of limited detection energy, with relatively little research. To assist in the parameter design of the lidar hardware system and explore the detection performance of the system, we explore the impact of atmospheric and optical parameter changes on the differential optical thickness calculation and theoretically analyze the error of the system in retrieving CO₂ concentration.

Methods

Differential absorption optical thickness refers to the difference in the ratio of backscatter signals at two wavelengths in the carbon dioxide differential absorption lidar detection system. It represents the difference in the two laser backscatter signals caused by the absorption of carbon dioxide molecules and the absorption effect of carbon dioxide molecules on a specific emitted laser on the detection path. Using typical optical parameters of the lidar system and the atmospheric parameters, we simulate the backscatter signals at different detection altitudes within the range of 0-3 km and calculate the differential optical thickness for different distances. By setting a certain amount of deviation for the parameter model used, we explore the impact of these parameter changes on the accuracy of differential optical thickness calculation. In the pre-research stage of a micro pulse coherent differential absorption lidar system, the results of the error estimation are of great significance for the design of hardware system parameters and the evaluation of system performance. For the inversion of carbon dioxide concentration from monopulse backscatter signals, based on the differential absorption principle, it can be approximated that the aerosol backscattering and atmospheric extinction in the atmospheric environment remain constant. As a result, the instability of differential optical thickness caused by the hardware system acquisition can be ignored. We evaluate the detection performance of the system by exploring the relative system error caused by the uncertainty of relevant parameters in the carbon dioxide concentration inversion method.

Results and Discussions

Through the simulation, we find that at different altitudes, the variation trend of differential optical thickness with the increase in wavelength offset is consistent, showing a trend of increasing first and then decreasing. This indicates that the absorption of probe laser energy at different altitudes increases first and then decreases with the increase in wavelength offset. In the altitude range of nearly 3.5 km, when the wavelength offset is less than 0.5 pm, the relative system error is less than 0.015%. As the wavelength offset increases, the relative system error of differential optical thickness at different heights also increases. At different altitudes, with the increase in temperature offset, the differential optical thickness also shows a downward trend. When the temperature deviation is less than 1 K, the relative system error of differential optical thickness for each altitude layer is less than 0.34%. The pressure measurement deviation does not have a specific impact on calculation results of differential optical thickness. Within the entire simulation range, the pressure offset has a small impact on the calculation of differential optical thickness, with an overall relative error of less than 0.008%. Aiming at the key parameters in the CO₂ concentration inversion method for the coherent differential absorption lidar system, we investigate the error in CO₂ concentration inversion caused by their uncertainty. The results show that the total error caused by each parameter for the system is 0.45%. If the average CO₂ concentration in a certain distance is 4×10^-4, the overall absolute error of the system is 1.8×10^-6.

Conclusions

We introduce the simulation calculation and error analysis of micropulse coherent differential absorption lidar. For the typical system optical parameters and the atmospheric parameters, we conduct a simulation to obtain the backscatter signal detected by the lidar system and calculate differential optical thickness at different heights. By setting different offsets for the parameter model, we explore their impact on the accuracy of optical thickness calculation. In addition, we theoretically analyze the uncertainty errors of atmospheric parameters (atmospheric temperature, atmospheric pressure, and water vapor concentration) and the errors introduced by the wavelength drift of the lidar system for a certain altitude and distance database. In addition, the absolute errors of CO₂ concentration inversion caused by these error sources are evaluated. These works are important in the pre-research stage of lidar systems, and the results of simulation calculations and error analysis are of great significance for hardware system parameter design and system performance evaluation.

1　引言

自20世纪中叶以来，受温室效应的影响，全球平均地表温度在1880年到2012年间上升了0.85 ℃^［1］，并且部分地区出现更大程度的变暖。大气二氧化碳（CO₂）作为引起温室效应的主要气体之一，在全球气候变化中扮演重要作用。了解不同区域的大气CO₂体积分数的时空分布格局，有助于掌握CO₂气体“源”与“汇”的足迹，便于实现国内减排控制，加快推进我国绿色低碳的高质量发展。

高时空分辨率、高精度的CO₂体积分数数据是进行气候研究的基础。传统的观测手段是利用卫星搭载被动遥感观测设备，以进行全球大尺度的CO₂体积分数观测，包括欧洲航天局的ENVISAT^［2］和极轨气象卫星METOP-A^［3］，美国NASA的EOS/Aqua^［4］和OCO-2^［5］卫星，日本的温室气体监测卫星GOSAT^［6］，以及我国CO₂监测科学实验卫星TanSat^［7］等。但被动遥感受限于自身观测特性，存在着夜间难测量、高纬度区域探测性能差、易受云和气溶胶影响，以及近地面CO₂观测精度不足等问题。

激光雷达主动遥感技术能够很大程度上弥补以上问题。相干差分吸收激光雷达（CDIAL）技术作为主动遥感技术之一，具有对点源、城市和重点区域进行全天时、高精度探测的能力。2004年，Koch等^［8-9］研究了一种测量大气CO₂体积分数的高脉冲能量地基CDIAL，其利用相干探测技术获得足够高的信噪比（SNR），用于测量大气边界层中CO₂的体积分数，并具有通过相干多普勒测风技术进行风廓线测量的附加功能。Gibert等^［10-11］研制了一种2.0 μm CDIAL系统，用于高精度监测大气边界层中CO₂体积混合比，并在2015年展示了其连续时间段内CO₂浓度垂直廓线的监测结果^［12］，该团队^［13］在2021年尝试用2.05 μm的全光纤脉冲激光源借助相干技术进行CO₂体积分数和风速的测量。

国内陶小红等^［14-15］在2008年对大气CO₂相干探测激光雷达系统进行了仿真计算，通过估算信噪比，对系统性能及探测精度进行了分析。此外，刘豪等^［16-19］对大气CO₂柱浓度观测进行了研究，我国研制的全球首颗探测大气CO₂体积分数的星载IPDA系统ACDL已于2022年4月成功升空，该系统可全天时获得卫星轨迹方向全球大气CO₂柱浓度分布信息。2015年，韩舸等^［20］研制了一台地基直接能量探测的CO₂差分吸收激光雷达（DIAL），以获取时间上连续的CO₂浓度垂直廓线观测结果。2021年，余赛芬^［21］提出了一种基于激光雷达的光子计数分布式自由空间光谱技术，结合频率梳扫描激光源和超导纳米线单光子探测器，对大气中CO₂和HDO的体积分数进行观测。

但目前对于微脉冲相干差分吸收CO₂激光雷达来说，其系统结构复杂，且在探测能量有限的情况下研制难度大，因此其相关研究较少。为了能够辅助雷达硬件系统的参数指标设计，探究系统的探测性能，研究了相干激光雷达方程中参数变化对于差分光学厚度（DAOD）计算产生的影响，并对系统测量CO₂体积分数的误差进行了理论分析。

2　CDIAL原理

DIAL通过发射两束对CO₂气体敏感程度不同的激光脉冲，借助大气分子及气溶胶的后向散射作用，使用望远镜接收两波长的回波信号并进行处理，通过两者吸收衰减程度的不同，计算待测气体体积分数^［22-23］。DIAL发射的两束激光波长相近，但CO₂气体对两束激光的吸收程度相差很大，且该波段激光受其他干扰气体的影响小。因为发射间隔极短，可认为大气状况以及激光雷达系统条件等并未发生改变，故可以通过信号处理反演CO₂体积分数。

结合相干探测技术，望远镜接收到的回波信号与出射激光分离出的本振光信号在光纤耦合器处混合，混合光在平衡探测器PIN管光敏面混频^［24］，完成光电信号转换，最终得到光电流信号，即相干信号；然后，利用采集板将信号数字化，并把接收到的电信号划分为等间隔距离门，使系统具备距离分辨的观测能力；最后，对各门频谱最大值附近的功率谱分量进行求和，其积分值表示实际大气后向散射谱功率^［25］：

〈P (r)〉 = \frac{1}{N} {(2 \frac{η_{q} e λ}{h c} R_{i n} G)}^{2} η_{L O} P_{L O} η_{h} (r, λ) P_{s d} (r, λ)

，（1）

式中： $N = 512$ 为每个距离门中的数字量； $η_{q}$ 为探测器的量子效率； $e$ 为单位电子的电荷量； $h$ 为普朗克常数； $λ$ 为出射激光波长； $c$ 为光速； $R_{i n}$ 为采集卡的输入阻抗； $G$ 为接收链增益； $η_{L O}$ 和 $η_{h} (r, λ)$ 分别为本振光的截断效率和系统的外差效率； $P_{L O}$ 和 $P_{s d} (r, λ)$ 分别为本振光功率和大气后向散射功率； $P_{s d} (r, λ)$ 为望远镜接收到的大气回波信号的功率，其表达式为

P_{s d} (r, λ) = k_{i n} E_{0} \frac{A}{r^{2}} \frac{c}{2} β (r, λ) e x p \{- 2 \int_{0}^{r} [α_{0} (r, λ) + N_{C O_{2}} (r) σ_{C O_{2}} (r, λ)] d r\}

，（2）

式中： $k_{i n}$ 为激光雷达系统常数； $E_{0}$ 为激光发射能量； $A$ 为接收望远镜的面积； $r$ 为探测距离； $β (r, λ)$ 为气溶胶后向散射系数； $α_{0} (r, λ)$ 为除CO₂气体之外大气总的消光系数； $N_{C O_{2}} (r)$ 和 $σ_{C O_{2}} (r, λ)$ 分别为CO₂分子数密度和分子吸收截面。CDIAL利用分子具有不同的吸收特征这一事实，提供了对大气中气体体积分数的测量方法。采用1572 nm波段中的两束相近波长：其中一个波长选在靠近CO₂吸收峰的位置，记为 $λ_{o n}$ ；另一个波长选在吸收波谷位置，记为 $λ_{o f f}$ ，从而形成较大的吸收差异。这样，在相近的激光波长以及极短的发射间隔情况下，大气后向散射系数、消光系数等大气参数以及系统光学参数可被抵消。因此，在只考虑干洁大气的条件下，结合理想气体状态方程，最终得到的CO₂体积分数的反演公式为

N_{C O_{2}} (r) = \frac{1}{2 Δ r [σ_{C O_{2}} (λ_{o n}, r) - σ_{C O_{2}} (λ_{o f f}, r)]} l n \frac{P (λ_{o f f}, r_{t o p}) P (λ_{o n}, r_{b o t t o m})}{P (λ_{o n}, r_{t o p}) P (λ_{o f f}, r_{b o t t o m})}

，（3）

X_{C O_{2}} (r) = \frac{N_{C O_{2}} (r)}{N_{a i r} (r)} = \frac{R T (r)}{2 Δ σ_{_{C O_{2}}} (r) Δ r P (r) N_{A}} l n \frac{P (λ_{o f f}, r_{t o p}) P (λ_{o n}, r_{b o t t o m})}{P (λ_{o n}, r_{t o p}) P (λ_{o f f}, r_{b o t t o m})}

，（4）

式中： $r_{t o p}$ 和 $r_{b o t t o m}$ 分别为 $Δ r$ 距离库的上、下高度边界，即 $Δ r = r_{t o p} - r_{b o t t o m}$ ； $R$ 为理想气体常数； $N_{A}$ 为阿伏伽德罗常数； $T (r)$ 为温度； $P (r)$ 为压力； $Δ σ_{_{C O_{2}}} (r) = σ_{C O_{2}} (λ_{o n}, r) - σ_{C O_{2}} (λ_{o f f}, r)$ 为CO₂分子吸收截面差。

3　CDIAL系统仿真

3.1　CDIAL系统设计

为了实现大气CO₂体积分数高分辨率、高精度探测，对CDIAL系统进行了设计。设计主要包括三大单元模块：种子激光单元模块、激光收发器单元模块、数据采集和处理单元模块。图1为CDIAL系统结构设计图。