*3.2. Gas Analyzer Performance*

To evaluate the performance of numerical analysis of derivative absorption spectroscopy, we prepared a series of reference gas mixtures of CO2 and H2O with different concentrations and made measurements at atmospheric pressure. The subsequent second derivative absorption signals were calculated by using the Savitzy–Golay filter method, as shown in Figure 4a for CO2 and Figure 4c for H2O. As expected, a linear correlation between the signal peak magnitude of the second derivative spectra and the CO2 and H2O concentrations were confirmed. The results presented in Figure 4b,d show a good linear dependence (adj. R2 = 0.995 for CO2 and adj. R2 = 0.999 for H2O), and demonstrate that the algorithm is valid for trace gas measurements. The slope of the fitted straight-line also serves as a conversion coefficient between the experimental measurements and the resulting gas concentrations.

The detection limit of the developed laser gas analyzer is evaluated by using Allan variance plots [35]. Figure 5 shows the results of Allan deviations for CO2 and H2O concentration measurements with a sample containing 500 ppmv CO2 and 2% H2O, plotted in a log–log scale. The measurement noise at 100 Hz data rate (i.e., 0.01 s averaging time) is about 0.40 ppmv for CO2, and 8.17 ppmv for H2O, respectively. As the averaging time increases, the minimum reaches about 0.026 ppmv for CO2 at 6 s integration time, and 3.12 ppmv for H2O at 0.13 s integration time. Table 1 summarizes the performance comparison between the laser gas analyzer we developed, and the commercial instrument LI-7500-CO2/H2O based on non-dispersive infrared technology [36]. The TDLAS gas analyzer we developed performs slightly better for H2O than the LI-7500 instrument, but was slightly worse for CO2. The major advancement of our device is its fast maximum measurement data rate of 100 Hz, corresponding to a time resolution of 10 ms, which would enable observation of fast turbulent motions for eddy covariance.

**Figure 4.** Numerically processed second derivative spectra of measurements at different gas concentrations of (**a**) CO2 and (**c**) H2O. The corresponding straight-line fits of the spectral peak magnitudes to the gas concentrations are displayed in (**b**,**d**).

**Figure 5.** Allan deviation analyses of CO2 and H2O detection limits as a function of averaging time.


**Table 1.** Performance comparison between our laser gas analyzer and a commercial instrument.
