Interactive comment on “ Accurate measurements of carbon monoxide in humid air using the cavity ring-down spectroscopy ( CRDS ) technique ”

The manuscript ‘Accurate measurements of carbon monoxide in humid air using the cavity ring-down spectroscopy (CRDS) technique’ by H. Chen et al. investigates the interferences of water vapor and CO2 on carbon monoxides measurements made with Picarro CRDS instruments. The methodology of obtaining appropriate correction functions is described in detail and will help users of these instruments to improve their measurements.

Published by Copernicus Publications on behalf of the European Geosciences Union. Comprehensive comparisons of measurements made using these techniques are given by Zellweger et al. (2009 and. Because variations of water vapor in the atmosphere modify the mole fractions of CO (known as the dilution effect), sample air has always been dried in previous techniques to obtain dry air mole fractions. A major advantage of some recently available techniques (QCL/ICOS/CRDS) is that water vapor mole fractions can be simultaneously measured. This makes measurements of CO in humid air feasible as the H 2 O values can be used to correct for dilution and potential spectroscopic effects. Zellweger et al. (2012) have derived water corrections for the QCL and ICOS analyzers, but not for the CRDS analyzer due to the fact that the more complicated nature of the spectral interference requires more complicated interference testing and analysis procedures. Carbon monoxide is detected by QCL or ICOS in the mid-infrared region where the CO absorption is well separated from other absorption features; in contrast, the CRDS technique measures CO in the near-infrared region (∼ 1.57 µm) where there are significant interferences from adjacent absorption lines of CO 2 and H 2 O at ambient mole fractions of CO, CO 2 , and H 2 O. An example of the spectral absorptions for typical ambient mole fractions of CO (238 ppb), CO 2 (386.2 ppm), and H 2 O (0.578 %) is given in Fig. 1a. In the scanned spectral region of the CO absorption line, there are four CO 2 absorption lines and three H 2 O absorption lines. The ratios of the largest line for each species in the scanned spectral region are 1 : 23 : 22 for CO : CO 2 : H 2 O. For each raw spectrum (collected every few seconds), the absorption lines of CO, CO 2 , and H 2 O are fit using a Levenberg-Marquardt optimization algorithm with a Galatry profile for CO (Varghese and Hanson, 1984) and a composite, empirically derived spectral profile for CO 2 and H 2 O. The mole fraction of CO is determined from the peak height of the CO spectral component (see Fig. 1b). Although it is challenging to get precise measurements of CO in the near-infrared region using the CRDS technique, a big advantage is that this technique employs reliable, cheap, and stable infrared lasers rather than expensive quantum cascade lasers, and the same apparatus can also be employed to measure both CO 2 and CH 4 precisely. In fact, CRDS analyzers that measure CO 2 /CH 4 /CO/H 2 O or CO 2 /CO/H 2 O (Picarro, Inc., Santa Clara, CA, USA, the G2401 or G2302 series) in one unit are commercially available. Extensive efforts have been carried out to make accurate measurements of CO 2 and CH 4 possible without drying the sample air Winderlich et al., 2010;Nara et al., 2012;Rella et al., 2013). It is therefore beneficial to be able to accurately measure CO in humid air with the same analyzer as well.
In this paper, we derive water correction functions for the CO measurements made by the Picarro CRDS technique to account for the dilution and spectroscopic effects. In Sect. 2, we present the results from a series of laboratory experiments that are then used to derive the water correction functions. The comparison of water correction functions for CO from different CRDS analyzers is given in Sect. 3. The field comparison between in situ and flask measurements on board an aircraft is shown in Sect. 4. In the final section, we present the discussion and conclusion.

Water correction functions for CO measurements
Mole fractions of CO and other trace gases are influenced significantly by variations of water vapor in the atmosphere. For this reason, atmospheric CO measurements need to be reported as mole fractions in dry air. In principle, there is a simple linear relationship between the CO mole fraction in wet air (CO wet ) and in dry air (CO dry ) if only the water vapor dilution effect is considered: where H 2 O is the water vapor mole fraction.
In the case of CO measurements by the CRDS technique, there are a number of factors that complicate the correlation between CO wet and CO dry : (1) the linear term in Eq. (1) is not equal to −1 if water vapor is not accurately determined; (2) a nonlinear term exists as a result of pressure broadening (the mole fraction of CO is determined from the peak height of the absorption profile instead of the integrated spectral absorption area); (3) residual line interference remains due to imperfect quantifications of adjacent absorption lines of CO 2 and H 2 O. These effects can be compensated for by the following equation: where CO wet is the mole fraction of CO in humid air. For compatibility between different analyzers of the same type, we consistently calculate CO wet in ppb from the reported raw analyzer signal "peak84 raw" or "P84 RAW" as "peak84 raw" × 0.427 × 1000 or "P84 RAW" × 0.427 × 1000 (0.427 is the default factory calibration factor). CO dry is the mole fraction of CO in dry air; CO is the line interference adjustment to account for the residuals in the line fits of adjacent absorption lines of CO 2 and H 2 O, and is a function of CO 2 and H 2 O mole fractions, not of CO mole fraction; a and b are coefficients in the quadratic function to correct for the dilution and pressure-broadening effects and are given in % −1 ; H 2 O pct is one of the water vapor mole fraction measurements reported by the Picarro instrument (with the variable name "H 2 O pct"), and is determined from the detection of the absorption lines of H 2 O that are adjacent to the absorption line of CO, and is given in %. Since H 2 O pct directly affects the CO absorption line, it is appropriate to use measurements of these water vapor lines to correct all water vapor effects for CO measurements.
The CRDS analyzers mentioned above use the same spectroscopic fitting algorithms to derive the mole fractions of CO and CO 2 , and therefore the dilution and pressurebroadening effects for CO are expected to be similar to those for CO 2 . The corrections for these effects are a function of water vapor mole fractions, and are proportional to the mole fractions of CO. On the other hand, the line interferences caused by the residuals in the quantifications of adjacent CO 2 and H 2 O absorption lines are independent of the mole fractions of CO as they only affect the baseline of the CO absorption. Since the parameters associated with dilution and pressure broadening (a and b ) and line interference ( CO) in Eq. (2) cannot be directly fit using measurements of CO wet and known CO dry , we solve for these two effects separately based on water test data from laboratory experiments.
The water test data presented in this paper were obtained based on two different methods described in Rella et al. (2013). Method #1 employs a dew point generator (LI-COR model 610) or a micromodule (http://www.liqui-cel. com/product-information/micromodule.cfm) to humidify a gas stream from a cylinder. The advantage of this method is that mole fractions of CO in humidified gas are determined when the system has reached some equilibrium state at each humidity level. Method #2 can be described as a water droplet test. In this method, a small amount (0.2-0.8 mL) of distilled (or deionized) water is injected into the inlet of the CRDS analyzer to humidify air from a cylinder. The water droplet added to the inlet line is held at the hydrophobic particulate filter of the analyzer, through which water can only pass in the form of water vapor. This method is easy to perform and provides water vapor ranging from 0 to 6 %, but the vapor amount changes rapidly. To obtain slowly changing water vapor mole fraction, a small amount of silica gel soaked with deionized or acidified water and housed inside a small flow through chamber has been used at NOAA/ESRL to humidify the gas stream. Water test data from a list of experiments are summarized in Table 1. The two methods have been employed at different times by different groups. We have performed water droplet tests to demonstrate that the CO mole fractions are not affected by silica gel or acidified water, where the humidified air was passed through a chemical dryer (magnesium perchlorate) and the dry mole fractions of CO were then determined by a second CRDS analyzer. No significant variations/drifts in the dry mole fractions of CO were found (less than 1 ppb CO on 30 s averaged data).

Corrections for dilution and pressure-broadening effects
At typical CO mole fractions found in the atmosphere (50-500 ppb), the effects of dilution and pressure broadening are of the same order of magnitude as the line interferences. Therefore, these two types of effects cannot be differentiated in one experiment with ambient levels of CO. To minimize the effect of line interferences from CO 2 and H 2 O, a water test was performed at Picarro Inc. in August 2010 on a CO 2 /CO/H 2 O analyzer (S/N: CKADS017) using cylinder air with a very high mole fraction of CO (∼ 10 6 ppb) and no CO 2 . The experiment was carried out under a fume hood, using the simple water droplet test (method #2, with a heated filter) and water vapor mole fractions ranging from 0 to 6 %. In this case, the line interferences are negligible when compared to the influences by dilution and pressure broadening. The experimental data and analysis results are shown in Fig. 2. Both dilution and pressurebroadening effects can be accounted for using the quadratic function in Eq.
(2) ( CO ≈ 0), and the derived coefficients a = −1.24 × 10 −2 % −1 and b = −6.0 × 10 −4 % −2 . These two coefficients are very close to those for CO 2 : a = −1.20 × 10 −2 % −1 and b = −2.67 × 10 −4 % −2 . The residuals of the quadratic fit applied to 200 ppb dry mole fraction of CO are much smaller than the WMO-recommended compatibility of ±2 ppb for atmospheric CO measurements, with a standard deviation of 0.06 ppb (Fig. 2d). Here we scale the CO residuals from the quadratic fit for the 1000 ppm CO test proportionally to the equivalent residuals for a CO mole fraction of 200 ppb. The dilution effect is proportional to the mole fractions of CO, and the pressure-broadening effect is assumed to be proportional to the mole fractions of CO based on the fact that the coefficients a and b are close to those for CO 2 . Transferring the water correction coefficients for CO 2 from one CRDS analyzer to another causes uncertainty on the order of 0.1 ppm out of 400 ppm for CO 2 Rella et al., 2013), which is at least one order of magnitude more accurate than needed for the transferability of CO water corrections for dilution and pressure broadening among different analyzers (with the WMO-recommended inter-laboratory compatibility goal of 2 ppb for CO). Furthermore, the total water vapor dilution and pressure-broadening effects for CO are relatively small (∼ 5 ppb for 2 % water vapor at a level of 200 ppb CO) when compared to the line interference effect (up to ∼ 20 ppb for the range of 0-2 % water vapor). Therefore, these coefficients can be assumed to be transferable to all CO measurements made by the same type of CRDS analyzer to account for dilution and pressure-broadening effects with insignificant transferability errors.

Corrections for line interferences
An additional correction to the derivation of CO dry involves the line interferences caused by the residuals in the quantification of adjacent absorption lines of CO 2 and H 2 O; these are functions of CO 2 and H 2 O mole fractions. To simplify the problem, we develop a function to correct for the line interferences caused by the residuals in the quantification of adjacent absorption lines of H 2 O only, and only estimate the influences from variations of CO 2 mole fractions. For operation over a wider range of CO 2 mole fractions, a more complete analysis is required. Five water tests have been performed on one CO 2 /CH 4 /CO/H 2 O analyzer (S/N CFKBDS2007) at the laboratory of NOAA/ESRL (see Table 1): one was done in February 2011 using a micromodule (method #1), and four were completed in March 2012 using water droplets with different mole fractions of CO 2 and CO (silica gel soaked with deionized water, method #2).
We fit a fourth-order polynomial function (Eq. 3) to the data from three droplet tests with 360-390 ppm CO 2 in air using a weighted least squares method using the R software (one droplet test was rejected due to a significant difference between the dry mole fraction measurements of CO before and after the test, probably due to a leak), and the weights in the curve fit were calculated based on the density of the measurements in the water vapor domain so that equal water vapor range contributed equally to the curve fit: A, B, C, and D are coefficients of the polynomial fit, and CO is calculated as CO wet − CO dry × (1 + a × H 2 O + b × H 2 O 2 ), with a = −1.24 × 10 −2 % −1 , and b = −6.0 × 10 −4 % −2 from Sect. 2.1.
The fourth-order function was empirically chosen. We tried to fit these data with a series of polynomial functions from the second order to the fifth order, and found the residuals of those fits below the fourth order exhibited a clear dependence on water vapor (not shown). Besides this, the standard deviations of the residuals were 3.3, 2.3, 1.1, and 1.1 ppb for the 2nd-5th order fits. It is important to note that the coefficients A-D represent the water vapor bias in the CO measurement after the basic spectral model for water vapor has been removed from the raw spectral data. In other words, if the spectral model describing this spectral region were perfect, then these coefficients would be zero. The experimentally derived CO and the fourth-order polynomial fit are given in Fig. 3. The February 2011 test was not fit due to the lack of data below 1 % H 2 O.
The derived coefficients of the weighted fourth-order polynomial fit are A = 16.628 % −1 , B = 12.460 % −2 , C = −10.692 % −3 , and D = 1.275 % −4 . The CO values from the experiment performed in February 2011 are plotted in the same figure. The 0.5 % bin averaged residuals are mostly within ±2 ppb, except for two points that are slightly greater than 2 ppb for the four tests with CO 2 ranging from 360-390 ppm. The lowest water vapor interval exhibits a bias of ∼ −2 ppb, which is caused by the inaccurate determination of dry CO values of the gases used in the experiments. Because we force the curve through zero, this would not lead to a systematic error in reported CO mole fractions at very low water vapor mole fractions. The noise of the CRDS CO measurements is mostly random, which has been shown in the Allan deviation plot by Zellweger The tests cover CO mole fractions ranging from 131 to 303 ppb, CO 2 mole fractions ranging from 360 to 390 ppm, and H 2 O mole fractions ranging from 0 to 4 %. The fact that all these data can be fit to one single function with small residuals demonstrates that this correction is independent of CO mole fractions for the range of CO 2 from 360 to 390 ppm. An extensive characterization of the dependence of CO water corrections on CO 2 abundance requires determination of a linear term in CO 2 and a term that is linear in the product of CO 2 and H 2 O. We do not have enough test data to quantify these two terms from the water tests. However, we performed a water test using 550 ppm CO 2 for a different CRDS analyzer and did not observe significant differences in the CO water corrections from what is determined from a water test using 380 ppm CO 2 (see Sect. 2.3, Fig. 4). The dependence of CO measurements in dry air on CO 2 is presented in Sect. 2.4. Note that the sizes of the third-and fourth-order terms are large at high water concentrations, and the correction factors can only be used for the tested water vapor range of 0-4 %. Extrapolating the polynomial curve to higher water vapor values will cause a large uncertainty.

Corrections for line interferences for analyzers with a new fitting algorithm
Since the beginning of 2012, a new line fitting algorithm has been applied by Picarro Inc. to the CO analyzers, which reduces the line interferences from water vapor on the CO measurements. We performed two water droplet tests (method #2, 380 and 550 ppm CO 2 ) at NOAA/ESRL on a CO 2 /CH 4 /CO/H 2 O analyzer (CFKBDS2059) that uses the new fitting algorithm. Note that the corrections for water vapor dilution and pressure-broadening effects for CO have not been changed with the new fitting algorithm, and the coefficients obtained in Sect. 2.1 apply for instruments with the new fitting algorithm as well. The same fourth-order polynomial function was used to fit the data from the water test (see Fig. 4), and the derived coefficients are A = 2.032 % −1 , B = 1.821 % −2 , C = −0.671 % −3 , and D = 0.048 % −4 . Compared to the corrections shown in Fig. 3, the magnitude of the correction has been significantly reduced, especially in the higher order terms. Note that no significant differences have been observed for the test data using 550 ppm CO 2 .

Dependence of CO measurements on CO 2 mole fractions
A dependence of CO measurements on CO 2 mole fractions is expected due to line interferences. To characterize the dependence, one experiment was performed on one CO 2 /CH 4 /CO/H 2 O analyzer (S/N CFKBDS2007) at Picarro Inc. in January 2011, and the apparatus is shown in Fig. 5.
To start with, air from a low CO 2 cylinder was provided to the CRDS analyzer after passing through a CO scrubber (Sofnocat 514), and then switched to air from a high CO 2 cylinder. The Sofnocat responds very slowly to changes in CO 2 (it was adsorbed on the Sofnocat substrate) so that a slow change in CO 2 was obtained (Fig. 6a). The water level was about 0.4 %, and was stable throughout the measurement (Fig. 6b). The reading of raw CO was not close to zero due to the presence of water vapor (Fig. 6c). Water corrections were then applied based on Eq. (5) and the coefficients in Sects. 2.1 and 2.2 to derive dry CO, which was indeed around zero (Fig. 6d). From a linear fit of dry CO to CO 2 , we derive a dependence of CO measurements of −0.3 ppb CO/100 ppm CO 2 , and the 100 ppm bin averaged residuals of the linear fit are smaller than ±1 ppb ( Fig. 6e and f). . Tech., 6, 1031-1040, 2013 www.atmos-meas-tech.net/6/1031/2013/ Fig. 5. Schematics of the CO 2 dependence test.

Atmos. Meas
Alternatively, the CO 2 dependence can be derived from measurements of a series of CO standards with different CO 2 mole fractions by fitting the following equation: Here CO cylinder is the known CO mole fraction, CO raw the measured mole fraction by a CRDS analyzer ("peak84 raw × 0.427 ×1000), and CO 2 the CO 2 mole fraction. To be able to determine the parameters A , B , and C accurately, a large span of CO 2 is required (our calibration data are not shown due to a narrow span of CO 2 ).

Application of corrections for CO measurements
Combining the corrections for dilution and pressure broadening and for line interferences, Eqs.
(2)-(3), the corrected CO values can be expressed as The coefficients a = −1.24 × 10 −2 % −1 and b = −6.0 × 10 −4 % −2 can be used for different analyzers, whereas coefficients A, B, C, and D need to be determined from instrument-specific water tests (see Sect. 3). Note that we do not include any CO 2 dependence in the correction function because it is determined to be small for CO 2 mole fractions ranging from 360-390 ppm. The standard deviations of the CO measurements made by the CRDS analyzers at the reported frequency (∼ 0.5 Hz) are in the range of 4-17 ppb. For H 2 O pct the standard deviations increase with water vapor levels, and are smaller than 100 ppm for up to 3.6 % water vapor. The uncertainty of the CO water corrections due to the precision of H 2 O pct at the reported frequency is calculated based on Eq. (5) and is less than 0.5 ppb for up to 3.6 % water vapor, which is a smaller effect when compared to the uncertainty in the determined water vapor corrections for CO.

Transferability of water corrections across different analyzers
When using the water corrections given in Eq. (4), it is important to understand how consistent they are from one instrument to the other. In total, water tests have been performed on five analyzers with the old fitting algorithm in groups from NOAA/ESRL (CFKBDS2008 and CK-ADS2027), MPI-Jena (CFKBDS2003 and CKADS2004), and MPI-Mainz (CKADS018) using method #1 and/or method #2 (see Table 1). The differences between the corrected CO values based on the coefficients derived in Sect. 2.2 and the measured dry mole fraction of CO for each test and analyzer are shown in Fig. 7. Note that several test results may have been averaged for each individual analyzer. The results clearly show that each analyzer requires instrument-specific water corrections (i.e., coefficients A, B, C, and D) to meet the WMO-recommended compatibility of ±2 ppb. The variations in the CO correction function between analyzers capture the small differences in the spectrograms delivered by each instrument, due to tiny differences between the reported wavelengths, absorbances, temperature, or pressure.

Field validation
The CRDS analyzer tested in Sect. 2 (CFKBDS2007) was flown without a drying system on board an aircraft in Alaska from April to November 2011, and from April 2012 until the present. A detailed description of the field deployment is given by Karion et al. (2013). A total of 12 flights were performed in 2011, and each flight took ∼ 8 h, during which 24 flasks were sampled. In-flight calibrations were made by providing air from three cylinders to the CRDS analyzer every 30 min. The flasks were analyzed at NOAA/ESRL, with an uncertainty of 2 ppb (Novelli et al., 2003). The in situ CO measurements were integrated using weighting functions that accounted for observed atmospheric variability during the flask sampling period (Chen et al., 2012). To accurately represent the weighting functions, knowing the times when the pressurizing process started and ended is critical. Since only the times when the pressurizing process ended were recorded, the times when the pressurizing process started were estimated based on the ambient pressure and the time it takes to fill a flask on the ground. The comparison of integrated in situ measurements with flask measurements of CO during all flights shows a mean bias of −0.6 ppb and a standard deviation of the differences of 2.8 ppb, which is better than the WMO-recommended inter-laboratory compatibility of ±2 ppb. Further, no significant linear trend of the differences between in situ and flask measurements on any of the variables (day, H 2 O pct , CO 2 , CO, CH 4 , and ambient pressure) has been found (the calculated linear coefficients are not statistically different from 0), partially due to the relatively large scatter in the differences between in situ and flask measurements (Fig. 8).  For measurements of CO aboard aircraft or at a background observational site, the dependence seems to be rather small, since variations of CO 2 larger than 100 ppm CO 2 are rarely seen (corresponding to a bias of CO ±0.3 ppb). For the cases when significant CO 2 variations are possible (e.g., exhaust measurements and soil chamber experiments), the dependence of CO measurements on mole fractions of CO 2 needs to be better characterized.
Unlike the good transferability of the water correction coefficients for CO 2 and CH 4 among different CRDS analyzers (Rella et al., 2013), comparisons of water correction functions for CO from five different analyzers of the same type show significant differences, making it necessary to perform instrument-specific water tests for each individual analyzer. The magnitude of the water corrections has been significantly reduced by employing a new fitting algorithm (in Picarro CRDS CO analyzers newer than early 2012). Further tests need to be done to determine if the transferability of the water corrections for analyzers using the new fitting algorithm has been improved. From our limited experience, significant drift has not been observed in the water corrections for one CRDS analyzer (CFKBDS2007) over a period of one year. Based on these laboratory studies showing the sensitivity of the water correction to CO 2 mole fraction and the analyzer to analyzer variability, it is recommended that fits be made to each analyzer periodically with standard gas concentrations that closely resemble both the span of CO 2 and CO that will be observed. This study applies to the CRDS instruments manufactured by Picarro Inc. that determine the CO mole fractions of air sample in a pressure-(∼ 186 mbar) and temperature-(∼ 45 • C) controlled cavity based on light absorption in the near-infrared region (∼ 1.57 µm). CRDS instruments operated under different conditions or based on absorption at a different wavelength would need to be independently tested to see if the same or similar conclusions apply.
The CRDS analyzer was flown on an aircraft in Alaska from April to October in 2011, and the accuracy of the CO measurements by the CRDS analyzer has been validated against discrete NOAA/ESRL flask sample measurements made on board the same aircraft, with a mean difference between integrated in situ and flask measurements of −0.6 ppb and a standard deviation of 2.8 ppb. No significant linear trend of the differences between in situ and flask measurements could be detected, partly because the noise in the differences is relatively large. Direct comparisons of in situ measurements of CO by two or more side-by-side analyzers, as already investigated by Zellweger et al. (2012), could potentially discover or exclude issues that influence the accuracy of the CO measurements by the CRDS technique.
Although the precision of the CO measurements by the CRDS technique on a short-time period is not as high as other available techniques, such as QCL and ICOS, it is possible to make accurate measurements of CO using this technique without drying the air if measurements over a sufficiently long period can be integrated and calibrated against standards. The CRDS analyzer does not need frequent calibration Karion et al., 2013;Richardson et al., 2012) or a drying system, and could be an accurate and low-maintenance instrument useful for monitoring the atmospheric mole fractions of CO.