Carbon dioxide (CO₂) and water vapor (H₂O) play crucial roles in global climate change through the carbon?water cycle. Semi-heavy water, as a stable isotope of water vapor, helps deepen our understanding of the water cycle process. A large number of active and passive remote sensing technologies based on absorption spectroscopy have been applied to the detection of atmospheric CO₂ and H₂¹⁶O. However, passive remote sensing, which relies on sunlight, cannot provide continuous day-and-night monitoring, while active remote sensing based on differential absorption LiDAR (DIAL) can effectively compensate for this limitation. Research has shown that H₂¹⁶O is the primary interfering gas in CO₂ detection that causes measurement errors. Since dual-wavelength DIAL can only measure one type of gas, the interference effect of H₂¹⁶O on CO₂ is minimized by selecting an appropriate absorption line, where the absorptions of H₂¹⁶O at the on-line and off-line wavelengths are almost equal. However, HD¹⁶O, a stable isotope of H₂¹⁶O, also affects the detection accuracy of CO₂, though this is rarely addressed. In addition, in terms of vertical height, especially within the troposphere, H₂O and atmospheric parameters can vary significantly. To date, no DIAL system can simultaneously provide vertical profile measurements for CO₂ and HD¹⁶O, and there has been limited theoretical analysis and feasibility verification of this. In the present study, we report the sensitivity analysis of simultaneous remote sensing of atmospheric CO₂ and HD¹⁶O profiles using LiDAR. This analysis is based on the MODTRAN atmospheric model. This sensitivity analysis aids in improving the inversion algorithm for the concentration profiles of CO₂ and HD¹⁶O, which is significant for enhancing the detection capability and inversion accuracy of both ground-based and airborne DIAL systems. It also provides a theoretical framework for accurate remote sensing of greenhouse gases and a deeper understanding of climate change in the context of carbon neutrality.

The sensitivity analysis of simultaneous remote sensing of atmospheric CO₂ and HD¹⁶O profiles using LiDAR, based on the MODTRAN atmospheric model, is conducted. First, the mixed spectral lines of CO₂ and HD¹⁶O under different atmospheric models are calculated using HITRAN spectroscopy parameters, and the feasibility of simultaneous measurement of these two gases by LiDAR is verified by selecting appropriate absorption lines. Next, considering the variation of atmospheric parameters with vertical height, the column and range-resolved concentration inversion errors of CO₂ and HD¹⁶O are evaluated based on the optimization of weight functions and spectral line shapes. Further investigation is conducted on atmospheric factors, the frequency stability of LiDAR laser emissions, the overlapping effects of CO₂ and HD¹⁶O, and the influence of altitude changes on concentration inversion errors.

In response to potential sources of error in the inversion of column and range-resolved concentrations of CO₂ and HD¹⁶O, we comprehensively consider atmospheric factors, laser frequency stability, the overlap effect of the two gases, and altitude-induced changes in concentration inversion. When the temperature variation is ±1 K, the column concentrations of CO₂ and HD¹⁶O reach their maximum temperature sensitivity of 0.18% and 0.09% at altitudes of 12.6 km and 23.4 km, respectively. The range-resolved concentrations of the two gases show maximum sensitivity of 0.21% and 0.38% near the tropopause. At a pressure variation of ±0.5 hPa, the sensitivity of both column and range-resolved concentrations of CO₂ and HD¹⁶O gradually increases with altitude. The column concentration errors for CO₂ and HD¹⁶O reach 0.33% and 0.03% at the top of the stratosphere, while the range-resolved concentration errors reach 0.54% and 0.83% at 20 km. The frequency sensitivity for CO₂ column and range-resolved concentrations is generally higher than that of HD¹⁶O, and the frequency sensitivity at the center of both gas absorption lines is close to zero at any altitude. When the H₂O mixing ratio variation is 5%, errors in CO₂ column and range-resolved concentrations due to overlapping effects decrease with increasing altitude, reaching 0.15% and 0.01% at sea level in tropical and sub-arctic winter models, respectively. For altitudes greater than 5 km, the range-resolved concentration error of CO₂ at the line centers for all atmospheric models is less than 0.001%, and the error caused by the overlapping effect can be ignored. When the tropic model and the 1976 U.S. standard atmospheric model are used, without considering the absorption of HD¹⁶O, the errors for the range-resolved CO₂ concentrations at sea level are 1.87% and 0.60%, respectively. Even under the sub-arctic winter model, the column concentration error at the center line reaches 0.17%, which confirms the non-negligible role of HD¹⁶O in CO₂ inversion. In addition, with an 80 dB signal-to-noise ratio at the LiDAR origin in mid-latitude regions, the altitude sensitivity of CO₂ and HD¹⁶O column concentrations at the top of the troposphere is 0.10% and 0.18%, respectively, while the sensitivity of range-resolved concentrations is 1.1% and 6.3%, respectively.

To meet precise greenhouse gas monitoring requirements, we conduct a theoretical analysis on the simultaneous remote sensing of atmospheric CO₂ and HD¹⁶O using LiDAR. Based on the MODTRAN atmospheric model, independent and mixed optical depth spectra of CO₂, H₂¹⁶O, and HD¹⁶O are derived under different models. The absorption lines suitable for detecting CO₂ and HD¹⁶O are identified by analyzing the relative absorption intensities and spectral parameters of each gas. The spectral broadening of CO₂ and HD¹⁶O caused by collision and Doppler effects is calculated based on temperature and pressure profiles from the 1976 U.S. standard atmospheric model. The two spectra exhibit Voigt line shapes in the altitude ranges of 9.4?34.5 km and 8.3?33.8 km, and their absorption lines are optimized for different altitudes. The systematic errors in range-resolved and column concentrations of CO₂ and HD¹⁶O, considering factors like atmospheric conditions, laser frequency stability, and the overlapping effect of the two gases, are analyzed. Our findings confirm that HD¹⁶O plays a critical role in CO₂ inversion at the R16 line. Considering the errors introduced by these factors, inversion accuracy for CO₂ and HD¹⁶O column concentrations of better than 1% and 2%, respectively, and range-resolved concentrations of 2% and 8%, respectively, can be achieved in the troposphere of mid-latitudes.