## 2 Theory and Experimental Instrument
### Preliminary Configuration and Results  
The preliminary system configuration for the first trial of CO\({}_{2}\) sensing is shown in Figure 1 and the main system parameters are listed in Table 1. The on light was tapped by the splitter, and the 30% portion was used to lock the wavelength at the absorption peak of the CO\({}_{2}\) gas cell, based on the frequency modulation spectroscopy. The off light and 70% of the on light were intensity modulated with CW signals at slightly different frequencies (e.g., 99.7 kHz and 101.8 kHz in Figure 1), in order to distinguish the received on and off radiation. The modulated lights were amplified by an erbium-doped fiber amplifier (EDFA) after being combined with an optical coupler. The polarization state of the on and off radiation is off light output from the single-mode (SM) EDFA was uncertain, so we used a polarization-insensitive SM filter beam splitter, instead of a fused SM fiber beam splitter, to split the output beam of the EDFA into 99% and 1% [18]. The 99% portion was transmitted to a hard-target and the 1% portion was detected by the photodetector for transmission monitoring. The monitored and received signals were analog-to-digital (A/D) converted and their spectrum information was obtained by the fast Fourier transform (FFT). The intensities of two peaks in the spectrum of the received signal were normalized by the monitored signal. The differential absorption optical depth (DAOD) was obtained using the logarithm of the normalized detected intensities ratio of the two wavelengths, as shown in Equation (2). The ranging of the hard-target was possible by utilizing the phase difference between the monitored and the received signal. Because CW signals were used for this ranging, there was folding ambiguity [24]. A priori information on the range--i.e., if the information has the precision of <<_c_/(2f_m), where \(c\) is the speed of light and _f_m is the modulation frequency--solves this problem. This precision can be easily obtained in ground-based measurements if the modulation frequency is lower than or equal to the 100 kHz band [18]. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Transmitter** \\ \hline Seed Laser Type & \multicolumn{2}{c}{DFB Diode Laser Wavelength} \\ Laser linewidth (FWHM) & \(\lambda_{on}\): 1572.335 nm; \(\lambda_{off\_1}\): 1572.205 nm; \(\lambda_{off\_2}\):1572.480 nm \\ Wavelength stability & \multicolumn{2}{c}{\(<\)1 MHz each wavelength} \\ Spectral purity & \multicolumn{2}{c}{\(>\)99.9\%} \\ Modulation type & \multicolumn{2}{c}{IM-CW Modulation frequency} \\ Modulation frequency & \multicolumn{2}{c}{ON: 99.733 KHz; OFF: 101.833 KHz} \\ Optical amplifier & \multicolumn{2}{c}{EYDFA-HP-BA-33C-211B} \\ Power output (max) & \multicolumn{2}{c}{33 dBm} \\ Laser divergence angle & \multicolumn{2}{c}{0.57 mrad (half angle)} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Primary parameters of the 1.57 \(\upmu\)m intensity modulated, continuous-wave (IM-CW) integrated path differential absorption (IPDA) lidar system. Figure 1: The system configuration for the first trial. PMF, polarization maintaining fiber; SMF, single-mode fiber; DDS, direct digital synthesis; PID, proportional-integral-differential control system; AOM, acoustic-optic modulator; EDFA, erbium-doped fiber amplifier. The CO2 concentration measurement results, with a short measurement interval of 30 s during the first CO2 sensing trial with the system configuration shown in Figure 1 on a 1.5 km horizontal path, are shown in Figure 2. The open-path is located in Hongkou District, Shanghai, China, and the measurement date is 14 September 2019. Figure 2a shows the carrier-to-noise ratios (CNRs) of the receiving and monitoring signals for both the on and off wavelengths. The signal-to-noise ratios (SNRs) of the receiving and monitoring signals are equal to the CNRs, if no speckle-related noise appears. By using these CNRs, we calculated that the random error in the CO2 concentration was less than 0.1 ppm.