In the CO2 differential absorption measurement, it is common practice to choose two or more wavelengths (Abshire et al., 2010; Lin et al., 2013; Refaat et al., 2015). One wavelength, referred to as the offline wavelength, is selected far from the center of the absorption line where the CO2 absorption is insignificant, serving as a baseline reference. The other wavelengths, known as the online wavelengths, are chosen on the line where the CO2 absorption is substantial, enabling accurate measurement of CO2 concentrations. The selected online and offline wavelengths are closely positioned, ensuring that the differences in optical depths due to attenuations other than CO2 absorption (mainly scattering optical depths) between these wavelengths are negligibly small. Consequently, the one-way CO2 differential absorption optical depth (DAOD) can then be determined by calculating the ratio of received signals at the online and offline wavelengths (Lin and Liu, 2021): 1ΔτCO2=-12ln⁡Ns,onNs,offC0,offC0,on. Ns,on and Ns,off correspond to the received signal photons within a sample gate Δt at the online and offline wavelengths, respectively. C0,on and C0,off denote the system constant which contains lidar system parameters and other range-independent quantities (refer to Eq. A3), for the online and offline wavelengths, respectively. In practical applications, the ratio of C0,off to C0,on is required to derive ΔτCO2. This ratio can be determined by the ratio of online and offline signals backscattered from a target close to the lidar or a target where the CO2 absorption is effectively zero (Lin et al., 2015; Dobler et al., 2013; Campbell et al., 2020). For the spaceborne DIAL measurement, the CO2 DAOD can be expressed as 2ΔτCO2=∫zTOAαCO2,on(z′)-αCO2,off(z′)nCO2(z′)dz′=ACO2(z)NCO2(z), where αCO2(z) and nCO2(z) are the CO2 absorption cross section and number density at altitude z, respectively. NCO2(z) is the column CO2 molecular number integrated from z to the top of atmosphere (TOA), which refers to the outer boundary of Mars's atmosphere. In the simulation for this study, the upper limit of the integral is set at 60 km, where the pressure is approximately 0.14 % of that at the surface. ACO2(z) is a mean differential absorption cross section from z to TOA weighted by CO2 number density: 3ACO2(z)=∫zTOA[αCO2,on(z′)-αCO2,off(z′)]nCO2(z′)dz′∫zTOAnCO2(z′)dz′. From Eq. (2), we derive 4NCO2(z)=ΔτCO2(z)ACO2(z), and this column molecular number density, NCO2(z)=∫zTOAnCO2(z′)dz′, determines the CO2 partial atmospheric pressure at z: 5PCO2(z)=MCO2gW(z)NCO2(z), where MC02 is the CO2 molecular mass, and 6gW(z)=∫zTOAg(z′)nCO2,model(z′)dz′∫zTOAnCO2,model(z′)dz′ is the mean Martian gravitational acceleration between z and TOA and g(z) the gravitational acceleration at altitude z. The Martian atmospheric pressure is the sum of CO2 pressure and the pressure of all other gases Pother(z): 7P(z)=PCO2(z)+Pothers(z). The Martian atmosphere is predominantly composed of carbon dioxide. The pressure exerted by other gases on Mars, Pothers, is small and remains relatively stable (Trainer et al., 2019) compared to the significant deposition and sublimation activities of CO2. The determination of Pothers can be achieved through climatological analysis, modeling, or other available measurements.

In our previous study (Lin and Liu, 2021), we proposed a DIAL system with a telescope size of 1 m and a laser pulse energy of 5 mJ at the online wavelengths. The system was designed for atmospheric profiling and column measurements of CO2 and pressure. However, in this current study, our focus is on the measurement of the crucial dynamic variable, surface atmospheric pressure. Consequently, we can reduce the telescope size and laser pulse energy to build a more compact lidar system. As illustrated by the simulation results presented in Sect. 3.2, the reduction in telescope size and pulse energy presents challenges for accurately measuring atmospheric CO2 DAOD. However, the surface return signal remains sufficiently strong to enable precise measurement of CO2 DAOD, from which surface pressure can be accurately derived. The surface return signal is consistently available when the airborne dust load is low or moderate.

While the DIAL system considered in this study may not allow for atmospheric vertical profiling of CO2 DAOD due to weaker lidar return signals compared to our previous study (Lin and Liu, 2021, and Sect. 3), it is still possible to derive vertical profiles of atmospheric pressure. This can be accomplished by leveraging DIAL surface pressure measurements and thermal infrared (IR) temperature profile measurements. However, it is important to note that a simultaneous temperature profile measurement is not mandatory in DIAL surface pressure measurements, although it can enhance measurement accuracy. Thermal IR sounders are compact and cost-effective sensors commonly used for satellite temperature measurements (Kalmus et al., 2022; Natraj et al., 2022).

Given the temperature T(z) measured by the sounder at a specific altitude z, the pressure can be determined using the barometric formula: 8P(z)=P0e-∫0zMMarsg(z)RT(z)dz, where P0 represents a reference pressure at the surface or an altitude where a CO2 DAOD is available from a dense dust layer or cloud, MMars=0.04334 kgmol-1 denotes the molar mass of Martian atmosphere (Williams, 2020), and R=8.314 JK-1mol-1 represents the universal gas constant.

To calculate P(z) using Eq. (8), the reference pressure P0 is required. P0 can be obtained from the DIAL CO2 DAOD measurement at the surface. However, to accurately calculate the weighting function ACO2 in Eq. (3) and, subsequently, PCO2 in Eq. (5), some knowledge about the temperature and pressure profiles is necessary. Hence, an iterative procedure is applied. Initially, a climatological or modeled value P0c can be used as an estimate for the surface pressure to calculate the first set of P(z) using Eq. (8). With the initially calculated P(z) and the temperature profile T(z) obtained from the sounder measurements, the weighting function ACO2(z) in Eq. (3) and, consequently, the CO2 pressure at the surface P0,CO2 can be retrieved more accurately from the CO2 DAOD measurement using Eq. (5). As previously mentioned, CO2 comprises the dominant composition of the Martian atmosphere, and the pressure of other gases (Pothers) remains relatively stable. Using P0,CO2, the surface pressure P0 can then be determined from P0,CO2 using Eq. (7). Once P0 is determined from the CO2 DAOD measurement, it can replace the climatological or modeled value P0,c to recalculate P(z) using Eq. (8). This process can be repeated iteratively to improve the retrieval of P0. In cases where very dense dust or cloud layers are present, the surface return may not be available. However, accurate CO2 DAOD measurements may be derived from the lidar return signals from these targets. The pressure P at altitude z0, where the dense dust or cloud layers are located, can be used as the reference P0 in Eq. (8). The aforementioned iterative procedure can then be applied to derive the pressure P at z0, above and below.

Considering the size, weight, and power (SWaP) constraints crucial for space-based systems, particularly for Mars mission lidars, this study utilizes a compact telescope and focuses on the column CO2 and pressure measurement. Furthermore, the online wavelength is selected at the trough region between two adjacent absorption lines. This choice can alleviate sensitivity to laser frequency variability (Korb and Weng, 1983), thereby easing the stringent requirements for laser frequency stability and reducing costs. The wavelengths selected in the 2.05 µm absorption band, specifically line R(32) of the ν′(20013) vibrational band with the line center at 2.050428 µm, in our previous study (Lin and Liu, 2021) are very close to those (line R(30) of the same vibrational band) used in NASA Langley Research Center's (LaRC's) pulsed DIAL systems for CO2 measurement on Earth (Refaat et al., 2015; Yu et al., 2017). However, the differences in line selection reflect the distinct atmospheric environments of Earth and Mars. Compared to Earth's atmosphere with a carbon dioxide (CO2) volume mixing ratio of approximately 400 parts per million (ppm), the Martian atmosphere is predominantly composed of CO2, accounting for about 95.3 % by volume, despite having a much lower total amount or atmospheric pressure. As a result, pressure-induced absorption line broadening is significantly smaller in the Martian atmosphere, and the line shape is much narrower. Consequently, the lidar wavelengths are typically chosen on the wing of an absorption line where the column CO2 DAOD falls within the range of 0.5–2, with an optimal DAOD value of 1.11 (Lin and Liu, 2021).

The criteria for wavelength selection in this study are as follows: (1) the presence of a strong absorption line with a nearby weak absorption line on the wing of the strong line, (2) both the strong and weak lines are from the principal isotope 12C16O2, (3) AOD of the trough region is approximately 1.1, and (4) there is no absorption from other gases. While weak absorption lines from CO2 isotopes other than 12C16O2 could also be selected, the accuracy of current knowledge regarding the abundance of these isotopes on Mars may impact spectroscopic analysis. In this study, the strong absorption line selected is P(10) from the 12C16O2 vibration band (ν′=20011, with a center wavelength of 1.9640146 µm), as shown in Fig. 1. The CO2 absorption is calculated using a typical Martian atmosphere obtained from Viking 1 observations (Seiff and Kirk, 1977), as illustrated in Fig. 2. The online wavelength is set at the trough region near 1.9639572 µm of the selected strong line, along with a weak line centered at 1.9639502 µm from another 12C16O2 vibration band, as shown in Fig. 3. The modeling of the Martian atmosphere in Fig. 3 is based on the Viking 1 observation depicted in Fig. 2. The AOD is calculated using the line-by-line calculation method through the HITRAN Application Programming Interface (HAPI) (Kochanov et al., 2016). All absorption lines of all CO2 isotopes within the wavenumber range of 5063–5128 cm-1, covering the entire absorption band, are taken into account in the HAPI line-by-line calculation. The calculation is performed with a wavelength resolution of 5×10-5 cm-1 (equivalent to ∼ 2×10-5 nm), utilizing the Voigt distribution with a wing length of 10 cm-1. Figure 3b, essentially a derivative of Fig. 3a, illustrates that the sensitivity of AOD to laser frequency variability is significantly smaller in the trough regions compared to the surrounding regions. This is because the derivative or slope at the trough or peak region is close to zero. Thus, in this study, the online wavelength is set in the trough region of the two selected lines. The column CO2 AOD at the trough is approximately 0.885, corresponding to a DAOD of 0.825, which is close to the optimal value of 1.11. The change in online AOD is smaller than 10-4 for a 1 MHz change in laser frequency at the selected trough region (refer to Fig. 3b), and the change in offline AOD is even smaller. These small AOD changes due to laser frequency variations lead to insignificant errors in DAOD calculations and retrievals. Consequently, the requirements for laser frequency stability can be relaxed.

It is worth noting that P(12) of the same 12C16O2 ν′(20011) vibration band could also be considered a good candidate, as it has a few weak absorption lines on its wing. However, in this study, our analysis focuses solely on P(10).

To attain high measurement precision, it is essential to stabilize the laser frequency, as discussed in numerous papers (e.g., Refaat et al., 2015). The NASA LaRC has made significant advancements in laser frequency control and locking techniques over the past decades. Figure 4 illustrates a conceptual diagram depicting the master laser wavelength locking and control system. For this system, two or more continuous-wave single-frequency fiber or semiconductor-distributed feedback lasers can be utilized as master lasers. In this setup, one master laser is locked at the center of the selected line at 1.9640146 µm. The Pound–Drever–Hall frequency stabilization scheme is employed with a CO2 absorption cell to achieve this locking. The other master laser, or possibly two master lasers, can be locked off the line center by 4.44 GHz for the online wavelength or -25.75 GHz for the offline wavelength. The seed lasers employed in the LaRC airborne CO2 DIAL system can be wavelength-locked at the line center or locked up to 35 GHz from the line center, with a long-term frequency jittering of 0.3 MHz (Refaat et al., 2015; Koch et al., 2008). With the laser frequency stability achieved at this level and the online laser wavelength in the trough region, the error in DAOD due to laser frequency variability is smaller than 10-4 for an 80 MHz range, making it insignificant for DIAL DAOD measurements.

The laser transmitter considered in this study is an all-fiber master oscillator power amplifier (MOPA) system. Optical fiber amplifier technology has advanced considerably. Specifically, pulsed laser energy exceeding 1 mJ at kilohertz repetition frequencies has been demonstrated in the 1.97 µm band. These technological breakthroughs enable the development of compact and lightweight laser sources for future Mars missions.

Based on the first-order error propagation theory, the error ε and the relative error due to random noise for all individual quantities in Eqs. (3)–(5) can be estimated (Lin and Liu, 2021) using 9aεΔτCO2(z)=121SNRon(z)2+1SNRoff(z)21/2, 9bεΔτCO2(z)ΔτCO2(z)=12ΔτCO2(z)×1SNRon(z)2+1SNRoff(z)21/2,

10aεNCO2(z)=σΔτCO2(z)ACO2(z)2+NCO2(z)σACO2(z)ACO2(z)2, 10bεNCO2(z)NCO2(z)=εΔτCO2(z)ΔτCO2(z)2+εACO2(z)ACO2(z)2,

11aεPCO2(z)=MCO2gW(z)εNCO2(z), 11aεPCO2(z)PCO2(z)=εNCO2(z)NCO2(z)=εΔτCO2(z)ΔτCO2(z), where εx represents the uncertainty or error for parameter x. Equation (11b) demonstrates that the relative errors in the measured CO2 DAOD are equivalent to the corresponding relative errors in the observations of CO2 amount and atmospheric pressure. As discussed in Sect. 2.3, the vertical profile of atmospheric pressure can be derived using Eq. (8) when the atmospheric temperature profile is measured using an IR sounder. The error and relative error in the retrieval of atmospheric pressure can be estimated using the following equations: 12aεP(z)=e-∫0zMMarsg(z)RT(z)dz⋅εP02+P0e-∫0zMMarsg(z)RT(z)dz∫0zMMarsg(z)RT2(z)dz⋅εT(z)2 12bεP(z)P(z)=εP0(z)P02+∫0zMMarsg(z)RT(z)εT(z)T(z)dz2. The first term in Eqs. (12a) and (12b) represents the contribution of the error in the surface pressure P0, which is used to calculate the atmospheric pressure P using Eq. (8). This term includes the error in the retrieved P0,CO2 from the CO2 DAOD measurement and the error in the pressure of other gases (Pothers). While it is challenging to estimate the exact error in Pothers, it is anticipated to be small. This is because Pothers is relatively stable and constitutes only a small fraction of the total Martian atmospheric pressure (< 5 %) (Williams et al., 2020).

Random errors in the measured temperature T can be partially smoothed out through the integration calculation in Eq. (8). However, it is important to note that any systematic error in T cannot be reduced by integration or signal averaging, and such systematic errors can propagate into the retrieval of atmospheric pressure P using Eq. (8). A study by Natraj et al. (2022) demonstrated that the total error in temperature measurements for the JPL GEO-IR Sounder ranges from 0.3–1 K, with a precision of 0.1–0.3 K. Data fusion techniques that combine measurements from multiple satellite sounders have been shown to reduce bias in near-surface temperature measurements, resulting in mean biases smaller than 0.16 K (Kalmus et al., 2022). Considering these low bias errors, this study conservatively assumes potential temperature bias errors within 2 K.

The error and relative error in atmospheric pressure P (i.e., the second term in Eqs. 12a and 12b) can be estimated as a function of altitude, considering different biases in temperature T of ± 0.5, ± 1.0, and ± 2.0 K. These estimations are presented in Fig. 5. From Fig. 5, it can be observed that the bias in temperature T has a minimal impact on the retrieval of atmospheric pressure near the surface. However, as altitude increases, the influence of the temperature bias on pressure retrieval becomes relatively more significant (Fig. 5a). This is due to the cumulative effect of the temperature bias as altitude increases (via the integration term in Eq. 12). The absolute error in atmospheric pressure P (as shown in Fig. 5b) due to the temperature bias is very small near the surface. It gradually increases with altitude, reaching a maximum around 12 km, and then decreases. This trend is primarily driven by the decreasing trend of atmospheric pressure with increasing altitude.

Systematic errors or biases in temperature can further propagate to the retrieval of CO2 pressure (PCO2) using Eq. (5) through the calculation of the weighting function (ACO2). To assess the impact of T biases on PCO2, errors and relative errors in PCO2 as a function of altitude are simulated using the HAPI software for T biases of ± 0.5, ± 1.0, and ± 2.0 K. The results are presented in Fig. 6. In Fig. 6, the curves represent the systematic errors or relative systematic errors in PCO2 at different altitudes resulting from the T bias. The magnitudes of the relative errors initially decrease with increasing altitude until approximately 1.4 km, after which they start to increase. At z=0 (representing the surface in this study), the magnitudes of the relative errors in PCO2 are smaller than 0.1 % (Fig. 6a), and the absolute errors are smaller than 0.5 Pa (Fig. 6b) when the T bias is smaller than 2 K. The magnitudes of errors reach a maximum around 14 km, remaining below 1.6 Pa when the T bias is smaller than 2 K.

When comparing the CO2 DIAL measurement on Mars to the CALIPSO lidar measurement on Earth (Hunt et al., 2009), several advantages of space lidar measurements on Mars can be observed. These advantages are summarized in Table 1 and quantified by a figure of merit (FOM) in terms of signal-to-noise ratio (SNR) improvement. On Mars, the smaller size and mass of the planet, as well as the greater distance from the Sun, contribute to the advantages of space lidar measurements. A lower orbit height on Mars results in a FOM of 8.05, as the received signal is proportional to the squared range from the lidar to the atmospheric backscatter. Slower ground speed on Mars allows for a longer averaging time for a given horizontal distance, leading to a FOM of 2.17. Moreover, the photon number per unit pulse energy is 3.9 times larger at 1.964 µm compared to the visible region at 0.532 µm. The combined effect of these factors yields a FOM of approximately 67, which is a significant advantage. This allows for the use of lower laser power and/or smaller receiving telescope size, resulting in a more compact lidar system. Furthermore, the solar radiation constant on Mars is 2.3 times smaller than on Earth, and the solar radiation at 1.964 µm is approximately 220 times smaller than in the visible region. As a result, the daytime background noise, which is the dominant noise source in visible lidar measurements on Earth, is significantly reduced in the Mars measurement. This reduction in noise further enhances the performance of the DIAL system.

Considering these advantages, a compact DIAL system for Mars can be developed with relatively small telescope size and laser pulse energy. The specific parameters are listed in Table 2, and they can be achieved using currently available technologies, parts, and devices.

To assess the impact of detection noises and evaluate the performance of the DIAL system, observing system simulation experiments (OSSEs) are conducted. These OSSEs are based on the system parameters listed in Table 2. It should be noted that these parameters are similar to those used in Lin and Liu (2021), with a few differences. In this study, the telescope size is reduced to 0.3 m, which is approximately 3.3 times smaller than in the previous study. Additionally, the laser output energy for both the online and offline wavelengths is set to 1.5 mJ, whereas the previous study assumed values of 5 mJ for the online wavelength and 2 mJ for the offline wavelength. It is worth mentioning that recent advancements in all-fiber MOPA lasers have demonstrated laser output energies close to 2 mJ at the selected wavelengths, supporting the feasibility of the system parameters proposed in this study.

The OSSEs specifically focus on random errors caused by detection noises. The experiments provide valuable insights into the system's sensitivity, accuracy, and overall performance, thereby guiding further improvements and developments in the field of DIAL technology for Mars exploration.

For the detector in the DIAL system, a HgCdTe avalanche photodiode (APD) manufactured by Leonardo DRS Electro-Optical Infrared Systems, referred to as DRS APD hereafter, is assumed, which is currently used for spaceborne lidar applications in the IR region (Lin et al., 2013; Sun et al., 2017). The selection of this detector is based on its suitability for the desired performance and requirements of the lidar system. Furthermore, the optical parameters of the lidar system, including the field of view (FOV), beam expander, and transceiver throughputs, are adapted from the CALIPSO backscatter lidar. CALIPSO is a backscatter lidar that was launched in 2006 (Hunt et al., 2009) and has been nearly continuously operating in space. By utilizing these established optical parameters, the DIAL system can benefit from the experience and success of the CALIPSO mission. These optical parameters, along with the choice of a suitable detector, contribute to the overall design and performance of the DIAL system, enabling accurate and reliable measurements of atmospheric parameters for Mars exploration.

The OSSE results are presented in Fig. 7. Figure 7a shows the modeled dust profile based on the dust vertical distribution observed by the SPICAM occultation measurement on Mars Express (Fedorova et al., 2009). The occultation measurement was conducted above 10 km, and the dust distribution was extrapolated to the surface using an exponential curve. The modeled dust column optical depth from TOA to the surface is 0.373 at 1.964 µm. In the presence of the modeled dust, the online SNR is too small in the atmosphere to accurately profile CO2 DAOD and pressure, as shown in Fig. 7b. However, during nighttime, the offline SNR is greater than 10 below ∼14 km with a horizontal resolution of 10 km and vertical resolution of 1 km. With further averaging, if needed, these measurements can provide dust profiles in the lower atmosphere.

For the daytime simulation, the online and offline SNRs experience a decrease due to the presence of solar background noise. However, the decrease is not significant compared to the nighttime SNRs. This is because the solar background radiation at 1.964 µm is significantly smaller compared to the CALIPSO aerosol measurement at 532 nm (Hunt et al., 2009). It is important to note that the worst-case scenario of a Sun zenith angle (SZA) of 30°, corresponding to the SZA at the equator where the background noise is the strongest, is considered in the daytime simulation. This indicates that the DIAL system can maintain reasonable SNRs even in the presence of solar background noise during daytime operations. These OSSE results provide valuable insights into the performance and limitations of the DIAL system in the presence of dust and under different lighting conditions.

Dust on Mars exhibits significant annual and geophysical variations, leading to fluctuations in dust optical depth (OD) ranging from approximately 0.4 to 1.4 at 880 nm (Chen-Chen et al., 2019). During the Mars year-34 global dust storm, the dust OD was as high as approximately 8 (Guzewich et al., 2019). In cases of heavy dust loading, the DIAL system considered in this study may enable measurements of CO2 DAOD and pressure in the Martian atmosphere. While the SNR in the atmosphere is generally too low to achieve accurate measurements of Martian CO2 DAOD and pressure, the lidar return signal from the surface is several orders of magnitude stronger. This allows for precise retrieval of column CO2 DAOD and surface atmospheric pressure from the lidar surface return. Figure 7c and d present lidar return signals from the surface and surface return SNR, respectively, simulated using Eqs. (A2b) and (A1) for a single laser shot. Due to the strong CO2 absorption for the online wavelength, the return signal is smaller at the online wavelength than at the offline wavelength, resulting in a smaller SNR at the online wavelength than at the offline wavelength. However, the SNR is similar during the day and night due to the dominance of lidar signal noise for both online and offline signals. Figure 7e and f illustrate the relative error and error, respectively, in surface CO2 DAOD (ΔτCO2) and pressure PCO2 simulated for both nighttime and daytime scenarios at a horizontal resolution of 10 km using Eqs. (9) and (11).

Interestingly, the curves for nighttime and daytime measurements closely overlap due to the strong surface return signal, which results in signal shot noise dominating the measurement when a commercial solar blocking filter of 0.8 nm is utilized. The relative error in CO2 DAOD remains below 0.2 % when the dust OD is approximately 1 or lower. Similarly, the error in P0,CO2 stays below 1 Pa when the dust OD is around 0.7 or lower. As the dust OD increases, the error in both measurements rises but remains below 1.6 Pa until the dust OD reaches 1.