Development of a Carbon Monoxide Volume Mixing Ratio Retrieval Algorithm Using Passive Open-Path FTIR Spectra

Abstract

Passive open-path Fourier transform infrared (OP-FTIR) spectroscopy enables remote, non-contact characterization of combustion plumes but faces challenges from overlapping emission-absorption features and background variability. To address these limitations, we developed a streamlined retrieval algorithm that simultaneously derives the instrument line shape (ILS) and wavenumber calibration from embedded gas lines and applies a hybrid linear-nonlinear least squares approach for spectral alignment and residual correction. Background variability was mitigated by referencing a low-pass-filtered signal, allowing robust separation of plume contributions from slow radiance fluctuations. Passive OP-FTIR measurements were conducted at an industrial stack in Busan, Korea, and compared against in-stack tele-monitoring system (TMS) data. Time-series analysis revealed consistent agreement between retrieved and measured carbon monoxide (CO) mixing ratios, yielding a correlation coefficient of R≈0.89 and a root-mean-square error (RMSE) of ≈10.0 ppm. The algorithm exhibited robust performance at lower concentrations,while H₂O interference and uncertainties in the optical path length estimation contributed to residual features and overestimation at higher levels. By directly extracting calibration parameters from measured spectra, the method eliminates reliance on radiative transfer modeling or prior background characterization, thereby simplifying operation and enabling near-real-time implementation. This framework is readily extendable to other atmospheric species(e.g., SO₂, NO₂,CH₄) and provides a practical solution for reliable passive OP-FTIR monitoring of industrial emissions.

1. Introduction

Carbon monoxide (CO) is a key indicator of incomplete combustion and plays an important role in tropospheric chemistry, while even low-level exposure has been linked to adverse health effects (Holloway et al., 2000; Chen et al., 2021). Conventional CO monitoring in industrial stacks is most commonly performed with extractive systems, in which flue gas is continuously sampled through heated lines and analyzed using non-dispersive infrared (NDIR) or Fourier transform infrared (FTIR) spectroscopy under standardized protocols (e.g., U.S. EPA Method 10; U.S. EPA Method 320).

These extractive FTIR systems are widely used for stack monitoring but require heated sampling lines and maintenance, limiting their responsiveness to rapidly changing emissions. Open-path FTIR (OP-FTIR) enables non-contact measurements; in active mode, it uses an internal source and retroreflector to achieve high quantitative accuracy (Marshall et al., 1994). However, the need for retroreflector installation restricts its applicability to inaccessible sites such as tall stacks and flare tips (U.S. Environmental Protection Agency, 1999; 2016). Passive OP-FTIR overcomes this limitation by exploiting natural thermal radiation for single-ended measurements.

It has been applied to quantify CO, CO₂, SO₂, and hydrocarbons in stack and flare plumes, supporting combustion-efficiency assessments (Polak et al., 1995; Beil et al., 1998; De Donato et al., 2018). Beyond industrial applications, passive OP-FTIR has also been extended to long open-path measurements of greenhouse gases (Griffith et al., 2018), further demonstrating its versatility for atmospheric monitoring. Nevertheless, major challenges arise from overlapping emission and absorption signals, their dependence on plume temperature and concentration, and variability in background radiation (Harig, 2004; Polak et al., 1995). Previous studies addressed these issues through background correction, radiative transfer modeling, careful microwindow selection, and simultaneous retrieval of interfering species, especially H₂O (Steck and von Clarmann, 2001; Shao et al., 2010), but real-time application remains limited (Smith et al., 2011; U.S. Environmental Protection Agency, 1999).

In this study, we propose a simplified passive OP-FTIR retrieval algorithm for rapid quantification of CO in industrial stack plumes. The method integrates optimized spectral windows, simultaneous CO-H₂O fitting, and filtering to suppress background and noise, using a hybrid least-squares scheme. Its performance was evaluated against in-stack measurements from a tele-monitoring system (TMS).

2. Materials and Methods

2.1. Instrument and Data

LR Tech’s versatile spectro-radiometer (VSR), a passive OP-FTIR system, was used for the measurements. The instrument is equipped with two complementary detectors (InSb and MCT, HgCdTe), which together provide broad coverage across the mid-infrared region. For this study, the spectrometer was operated at its maximum spectral resolution of 1 cm^-1, spanning a measurement range from 500 to 11,111 cm^-1 (≈0.9-20 µm) (Qin et al., 2023).

A critical aspect of passive OP-FTIR analysis is the selection of the spectral fitting window, since it determines the degree of line isolation, potential interferences, and achievable signal-to-noise (Park et al., 2024). Based on these considerations, we adopted a window of 2,100-2,180 cm^-1, which offers pronounced CO fundamental-band lines while minimizing interference from H₂O, thereby ensuring reliable sensitivity. This interval was chosen to balance three key factors: (i) sufficient representation of strong CO lines, (ii) minimal overlap with weak H₂O lines, and (iii) consistency with the thermal emission characteristics of the plume and the spectral sensitivity of the InSb/MCT detectors. Fig. 1 illustrates the CO and H₂O lines within this spectral interval. To maintain radiometric stability throughout the measurements, the optical system employs a Michelson interferometer and includes internal cold and blackbody reference targets for continuous calibration.

Fig.1. CO and H₂O cross-sections in the selected fitting window(2,100-2,180 cm^-1).

The instrument line shape (ILS) was characterized by its full width at half maximum (FWHM), and the wavenumber axis was calibrated using spectral gas lines embedded in the measured spectra. Gas cross-sections for spectral fitting were taken from the HITRAN2020 database and the high-temperature HITEMP database to ensure accurate temperature-dependent line strengths (Gordon et al., 2022; Rothman et al., 2010). This procedure improved both the convolution of the cross-sections and the overall quality of the spectral fits. Fig. 2 shows the instrument and the field installation.

Fig. 2. Passive OP-FTIR instrument (VSR).

2.2. Spectral Fitting Method

The concentration of CO was retrieved using the linear least squares (LLS) method. The ILS was determined from gas lines in the measured spectrum, and wavenumber calibration was performed using the nonlinear LLS (NLLS) method. The spectral model F(i) in Eq. (1) consists of a slowly varying polynomial component and a linear combination of species-specific scale factors. When the nonlinear parameter d is fixed, the scale factors aj and the polynomial terms P_r(i) have a closed-form solution via LLS. When structural residuals or subtle mismatches remain, the Levenberg-Marquardt (LM) algorithm is applied to the cost function to update the wavenumber shift and stretch alignment. This alignment is parameterized by the polynomial coefficients d in fj(i) (Eq. 3), and the reduced cost function (Eq. 2) is minimized iteratively using LM. The overall fitting procedure alternates between LLS and LM until the error function (Eq. 2) converges (Marquardt, 1963; Gavin, 2024).

F(i) = P_r(i) + Σ^m_j=1 a_j × S_j(d_{j, 0}, d_{j, 1}, …)(i)       (1)

X² = Σ_i(J(i) - F(i))²       (2)

f_j(i) = Σ^Pj_k=0 d_{j, k} × (i - i_c)^k       (3)

In Eqs. (1) and (2), J(i) denotes the measured spectrum, and S_j represents the gas cross-section of species j, aligned to the wavenumber grid of J(i) and convolved with the ILS. The retrieved scale factor a_j corresponds to the slant column density (SCD, molecules cm^-2). Multiplying a_j by S_j yields the modeled optical depth contribution of species j. The retrieved SCD was then converted into a path-averaged volume mixing ratio (VMR) using the air number density n_air from the ideal gas law:

\(\begin{align}n_{\text {air }}=\frac{P}{k_{B} T}\end{align}\)       (4)

where P is the pressure, T the absolute temperature, and k_B the Boltzmann constant. With the effective optical path length L, the VMR was then obtained as:

\(\begin{align}V M R=\frac{N}{L \times n_{\text {air }}}\end{align}\)       (5)

L was calculated using the stack width and trigonometric relations based on the measurement geometry. Fig. 3 summarizes the workflow of the proposed spectral-fitting algorithm for passive OP-FTIR spectroscopy. Initially, the ILS and wavenumber shift/stretch are estimated from gas lines in the measured spectrum. Subsequently, the gas temperature is determined by selecting wavenumber points less affected by atmospheric attenuation but with opposite sensitivity to temperature. The ratio of these point pairs is mapped to a pre-established calibration curve to retrieve exhaust gas temperature.

Fig. 3. Spectral fitting algorithm flow chart.

The gas cross-section corresponding to the retrieved temperature is selected from the spectral library. The cross-section is convolved with the ILS, with wavenumber alignment applied. Using the convolved cross-section and the preprocessed spectrum, spectral fitting is carried out to obtain the SCD. In the final step, the retrieved SCD is converted into CO VMR using Eq. (5).

3. Results

3.1. Spectral Characteristics

The accuracy of spectral fitting critically depends on the precise determination of the ILS and the wavenumber calibration. In conventional approaches, the ILS is treated as a single fixed value, typically assuming a Gaussian profile, regardless of potential variations in instrument performance. In this work, the ILS was derived directly from H₂O lines embedded in the measured spectra, allowing it to reflect the actual measurement conditions (Hase, 2012). This procedure effectively minimizes inconsistencies that may arise during spectral fitting. The ILS plays a key role in the convolution of the gas cross-sections during fitting. Fig. 4 compares the directly derived ILS with the conventional assumption of a fixed Gaussian width. The red curve represents the Gaussian function fitted to the measured CO peak, the black solid line shows the measured CO peak, and the blue dashed curve corresponds to the conventional fixed-width Gaussian (FWHM = 1 cm^-1) plotted at the same line center for reference.

Fig. 4. Measured CO peak (black) with Gaussian fit (red; FWHM = 0.542 cm^-1) and conventional fixed-width Gaussian (blue dashed; FWHM = 1 cm^-1).

In addition, accurate wavenumber calibration is essential for aligning measured spectra with gas cross-section data. When a conventional, uncalibrated wavenumber grid is applied, a misalignment occurs between the spectra and the reference cross-sections, leading to errors in concentration retrieval. Fig. 5 presents the results of the wavenumber calibration, while Fig. 6 illustrates the improved alignment compared to the initial misalignment.

Fig. 5. Wavenumber calibration results.

Fig. 6. Improved agreement between spectra and gas cross-sections with calibrated wavenumber information.

3.2. Gas Temperature Determination

Although the retrieval algorithm can estimate path-averaged gas temperature concurrently with the CO mixing ratio, for this field evaluation, we fixed the temperature to the in-stack TMS value to isolate concentration-retrieval accuracy. Even so, we compared the algorithm’s temperature estimates (e.g., from the 2,069.2/2,132.1 cm^-1 line ratio) with TMS and observed a mean bias of -4.8K (OP-FTIR 430.8 K; TMS 435.6 K), indicating close agreement. Thus, in future deployments, the algorithm-derived temperature should be usable directly—without external TMS input—supporting a fully standalone, real-time retrieval pipeline. Fig. 7 shows (a) the temperature-estimation curve for the 2,069.2/2,132.1 cm^-1 pair with OP-FTIR ratios overlaid and (b) a zoom of the data-rich region, highlighting the agreement between the measurements and the fitted curve.

Fig. 7. Temperature retrieval results. (a) Line-ratio fit and temperature estimation, and (b) zoomed-in view of the clustered points and the corresponding fit.

3.3. Comparison of Retrieved CO VMR With TMS Data

To evaluate the field applicability of the CO mixing ratio retrieval algorithm, measurements were conducted at an industrial CO emission source and compared with TMS data. The co-located TMS reports CO as volume mixing ratio (ppm) in 5-min averages. Between 20 December 2024 and 20 January 2025, the OP-FTIR system was deployed at the parking lot of the Myeongji Sports Center in Busan, Korea (35.090125°N, 128.899364°E). The instrument was oriented toward the stack of the Busan Environmental Corporation, with a line-of-sight distance of approximately 134 m and an elevation angle of about 30°.

Fig. 8 shows the fitting results for CO and H₂O using OP-FTIR spectra. The black line denotes the gas optical depth (OD), and the red line represents the residuals. Overall, the gas OD is substantially larger than the residuals, and the spectral features are well reproduced, indicating satisfactory fit quality. In the H₂O fitting results, however, individual peaks are both over- and underestimated, which leaves residual structures in the CO fit and demonstrates that H₂O is a major interfering species with a considerable impact on fit quality.

Fig. 8. Example of spectral fitting results for CO and H₂O.

Fig. 9 presents the time series of CO mixing ratios retrieved from OP-FTIR and measured by TMS. Panel (a) covers 26-27 December 2024, and panel (b) covers 6-7 January 2025. The OP-FTIR retrievals (red) reproduce the temporal variability observed by TMS (blue), capturing high-CO episodes and showing particularly good agreement at lower concentration levels.

Fig. 9. Time series of CO from TMS and OP-FTIR.

Fig. 10 illustrates the correlation between CO mixing ratios retrieved from the spectral fitting algorithm and those measured by TMS. A strong linear relationship is observed, with a correlation coefficient of 0.898, a regression slope of 0.724, and a root mean square error (RMSE) of 10.0 ppm. The relatively high RMSE is primarily attributed to a tendency of the retrieval to overestimate concentrations at higher levels.

Fig. 10. Correlation between CO mixing ratios measured by TMS and retrieved from OP-FTIR.

4. Discussion and Conclusions

We developed a retrieval algorithm for CO mixing ratios from passive OP-FTIR spectra and evaluated its performance in an industrial emission environment. The algorithm enhances spectral fitting accuracy by directly deriving the ILS and wavenumber calibration from gas lines and by employing a hybrid linear-nonlinear least-squares scheme to correct wavenumber alignment and residual structures. Field experiments demonstrated that CO mixing ratios retrieved from OP-FTIR agreed well with TMS measurements (R≈0.89), with particularly robust performance at lower concentrations. At higher concentrations, however, interfering species such as H₂O introduced residual structures that contributed to positive biases.

Unlike previous passive OP-FTIR approaches that relied on complex radiative transfer modeling or prior background measurements, the proposed algorithm extracts ILS and wavenumber information directly from the measured spectra, thereby simplifying operation and enabling near-real-time application. Future work should extend this framework to other key atmospheric species (e.g., SO₂, NO₂, CH₄) and further strengthen its robustness by addressing both interfering species and uncertainties related to effective path length, gas temperature retrieval, and instrument field of view. Such improvements are expected to broaden the applicability of passive OP-FTIR for reliable monitoring across diverse industrial emission environments.

Author Contributions

Conceptualization, Data curation, Formal analysis: Lee GH, Lee HL; Funding acquisition: Kang DI, Kim JH; Investigation, Methodology: Lee GH, Lee HL; Project administration: Lee HL; Software: Lee GH; Supervision: Lee HL; Validation: Lee GH, Lee HL; Writing-original draft: Lee GH, Lee HL; Writing-review & editing: All authors.

Conflicts of Interest

No potential conflict of interest relevant to this article was reported.

Funding

This work was supported by a grant from the National Institute of Environment Research (NIER), funded by the Ministry of Environment of the Republic of Korea (NIER-2025-01-11-002).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.