Weighting function modified differential optical absorption spectroscopy is mainly employed to retrieve the total concentration of CO, CH₄, CO₂, H₂O and N₂O in the near-infrared (NIR) for SCIAMACHY.^[14–16] Subsequently, WFM-DOAS was succeeded by global ozone monitoring experiment (GOME) data inversion to obtain the total ozone column.^[21] At the same time, the water vapor column density near 700 nm was obtained from SCIAMACHY satellite and GOME satellite spectral retrieval.^[22] The basic principle of WFM-DOAS is least squares fitting, as shown in the equation given below this paragraph, where the summation of the logarithm of the reference spectrum and the first derivative of the interfering component are taken, a second-order polynomial is subtracted from the logarithm of the value of the measured spectrum, and least squares fitting on this difference is performed to obtain the best solution. In the equation given below, subscript i refers to each detector pixel of the central wavelength λ_i, and refer to the normalized measurement spectrum and reference spectrum, respectively, represents the true vertical column, represents the vertical column model simulation, represents the retrieved vertical columns (the subscript j stands for CO₂, H₂O, or temperature (Temp)), and P_i(a_m) represents the effect of broadband structures, such as aerosol and ground reflectance, on the retrieval results. In this study, the 1590–1620 nm band is selected as the retrieval band. The main interference factors are H₂O, Temp, and CH₄.

A schematic diagram of the CO₂ IR remote sensing system is shown in Fig. 1. It contains two parts: one part is the spectral acquisition system, including IR spectrometer, InGaAs detector, telescope (both tube and inner wall are black in order to avoid transmitted and reflected light), 5-m-long optical fiber, and automatic position adjuster, and the other part is the data collection and processing system, i.e., the laptop. The IR spectrometer (Andor SR303i) is a high-performance grating spectrometer for weak light absorption. It can choose different coupling methods or combine with different types of detectors according to different needs. It adopts triple raster wheel design, and is not required to change other raster and redo optical calibration. In addition, the experimental operation is simple. The detector is an Andor iDus depth-cooled InGaAs 1024 array detector with a compact design, dedicated vacuum seal and dedicated deep thermoelectric (TE) cooling, which can acquire a minimum temperature of − 70 °C. It is stable and easy to use, with a photon efficiency of 80% ± 5% in the 900–1650 nm band. The basic parameters of the system are tabulated in Table 1.

Fig. 1.

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	Fig. 1. Schematic diagram of the CO2 IR remote sensing system.

Table 1.

Table 1.

Table 1. The parameters of the CO2 NIR remote sensing system. . Measurement band/nm 900–1700 Spectral range/nm 1590–1620 Focal length f/mm 303 Aperture/mm f/4 Grating 600/mm Spectral resolution/nm 0.4 Photon efficiency/% 80% ± 5% Instantaneous field of view (IFOV)/(°) 1.12 Filter band range/nm 1500–1700 Filter transmittance 90% Detector liquid nitrogen (LN) cooled (−90 °C) 1024 pixel InGaAs CCD

Table 1. The parameters of the CO2 NIR remote sensing system. .

Fitting residue is an important manifestation of the retrieval quality. As is known, residuals are mainly determined by measurement noise and system noise. The measurement noise originates from spectral calibration, spectral structure of the light source, the instrument measurement limitation, and so on. The system noise comes from the spectrometer and the type of connection between the telescope and spectrometer. In order to reduce the fitting residuals and improve retrieval accuracy, the basic performance testing of the spectrometer and IR remote sensing system is carried out at the beginning, including the measurement of the relationship between the temperature, dark current, and offset and integration time of the spectrometer; the whole system spectral calibration is performed and sample gas measurement is undertaken in the laboratory.

The relationship between spectrometer temperature, dark current, and offset and integration time are depicted in Fig. 2. The spectrometer cools down slowly from 0 °C to − 60 °C, and the dark current drops rapidly at − 10 °C followed by a gradual drop until it is stabilized at 160 counts when the charge-coupled device (CCD) maintains a temperature below − 50 °C. The temperature is maintained at − 50 °C, while the integration time increases continuously from 0 to 2000 ms. With the increase of the integration time, the dark current exhibits a linear relationship with the integration time, i.e., y = 0.17798x + 16.17 (R² = 0.99978). Taking the minimum integration time of the spectrometer (1.4 μs) as the unit, the number of integrals increases continuously. The result shows that the average offset of different integral times is independent of the number of integrals and is a constant value of about 1260 counts/scan. In order to ensure the minimum noise signal during the acquisition of the spectra, firstly, the CCD temperature is stabilized at − 50 °C to − 70 °C; secondly, a certain integration time is achieved for a light intensity of at least 20000 counts; and thirdly, the signal to noise ratio is kept as high as possible while collecting the spectra, thereby reducing the system noise error.

Fig. 2.

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	Fig. 2. Basic performance of the spectrometer: the relationship between temperature, dark current, and offset and integral time/integral number.

The 1590–1620 nm band is selected as the measurement band, and there are 1024 pixels corresponding to 104.07 nm. Taking 1600 nm as the center, the measurable waveband is 1547.87–1651.94 nm. The Kr lamp is used as the linear-infrared light source for calibration (the Kr lamp spectrum is shown in Fig. 3(a)). The Kr lamp is fixed on the bracket of the optical rail (the optical rail is perpendicular to the telescope) and moved to the position of the strongest signal and the best peak shape; the integration time is adjusted until the Kr lamp peak intensity is the strongest with the premise of being unsaturated, and the signal is acquired. Five peaks, namely 1568.1, 1582.009, 1589.0068, 1592.578 and 1631.5258, are selected as the reference values to calibrate, and the relationship between the pixel and wavelength y = 1547.871 + 0.10166x (R² = 0.9994) is obtained, as shown in Fig. 3(b).

Fig. 3.

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	Fig. 3. (a) Standard Kr spectrum. (b) System calibration.

In order to measure reference light spectra, the device is set up as shown in Fig. 4. A Xenon (Xe) lamp, which is a continuous light source in the 1550–1650 nm waveband with the advantages of large power and cost-effectiveness, is used as the light source. The sample cell is 100 cm long with a diameter of 3 cm, and the measurement temperature is 25 °C. First, N₂ is pumped into the sample cell to remove the air, and the process lasts for about 5 minutes. Then the N₂ intake rate is decreased down to 0.1 L/min. After one minute, 10 spectra of N₂ are collected as the reference spectra. Samples of CO₂ with the measurements 0.1, 0.2, 0.3, 0.5, 0.6, 0.7 and 1.0 million ppmv are poured into the cell to obtain a series of sample gas spectra. All measurement absorption spectra are divided by the reference spectra, and the data are converted into optical density values by taking the logarithm of the quotients thus obtained. The sample gas spectrum retrievals are performed using CO₂ absorption cross-sections at 25 °C acquired from a database to obtain the CO₂ column density. Since for the lamp spectra it is assumed that there is no CO₂ absorption, the fitting coefficients obtained from spectral retrieval are gas column densities. By dividing the gas column densities by the optical path, a mixing ratio is obtained, which is calculated based on the actual pressure and temperature of the sample gas. By comparing with the standard sample gas values, the retrieval error and retrieval accuracy are obtained, and the details are shown in Table 2. The sample gas spectrum of 7 × 10⁵ ppmv fitting result is taken as an example, which is shown in Fig. 5.

Fig. 4.

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	Fig. 4. Sample gas measurement device in the laboratory.

Fig. 5.

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	Fig. 5. Example of 7 × 105 ppmv. (a) The sample gas measurement spectrum along with reference and background spectra, where OD indicates optical density; (b) retrieval results.

Table 2.

Table 2.

Table 2. CO2 measurement and relative errors. . CO2 density/million ppm Number of measurements 1 2 3 4 5 Average/million ppm 0.1 measurement 0.1046 0.1018 0.097 0.097 0.099 0.099 relative error/% 4.6 1.82 3 3 1 1 0.2 measurement 0.198 0.199 0.197 0.206 0.204 0.2008 relative error/% 1 0.5 1.5 3 2 0.4 0.3 measurement 0.294 0.289 0.299 0.298 0.298 0.2956 relative error/% 2 3.7 0.4 0.7 0.7 1.5 0.5 measurement 0.498 0.499 0.475 0.501 0.502 0.495 relative error/% 0.4 0.1 5 0.2 0.4 1 0.6 measurement 0.599 0.598 0.602 0.61 0.596 0.501 relative error/% 0.2 0.4 0.3 1.6 0.7 1.6 0.7 measurement 0.698 0.701 0.72 0.709 0.698 0.705 relative error/% 0.3 0.1 2.8 1.28 0.3 0.7 1.0 measurement 0.988 0.987 0.98 0.982 0.97 0.98 relative error/% 1.2 1.3 2 1.8 3 2

Table 2. CO2 measurement and relative errors. .

In Fig. 5, red and black lines represent the reference and measured values, respectively. Through retrieval, we obtain the sample gas column concentration, which is 1.827 × 10²¹ ± 8.98 × 10¹⁹ molecules·cm⁻², when the theoretical value is 1.876 × 10²¹ molecules·cm⁻²; the retrieval residue is 0.13%, and retrieval accuracy is 3.6%. As shown in Fig. 6, when the CO₂ concentration is less than 7 × 10⁵ ppmv, the theoretical value is close to the measured value. With the increase of the sample gas concentration, the measured CO₂ column density no longer increases linearly. When the CO₂ concentration is less than 3 × 10⁵ ppmv, the detector cannot measure the spectral absorption, that is, the detection limit of the system is 8.5 × 10²⁰ molecules·cm⁻². Converting the limited column density into the atmosphere CO₂ column without emission sources, we can conclude that the effective optical length of the spectral absorption is at least 1 km when we assume that X_CO2 (volume mixing ratio of CO₂) is 400 ppmv in the atmosphere.

Fig. 6.

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	Fig. 6. Linear relationship between the measured and theoretical values of different concentrations of sample gas.

A sketch of the experimental site and the viewing method is shown in Fig. 7. Observations were carried out at a distance of about 1000 m and 1200 m away from the power plant chimneys at 11:00 am on May 26, 2018, measuring the solar radiation that is backscattered by the plume or atmosphere to the entrance objective. There was no other pollution source nearby. Two chimneys, 140 m high, with respective widths of 12 m and 18 m, were spaced about 138 m apart. The weather was clear with a wind speed of about 1.5 m/s.

Fig. 7.

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	Fig. 7. Experimental site at the Feng-tai power plant.

The power plant emission measurements presented in this study were carried out with the IR differential optical absorption spectroscopy remote sensing system instrument (refer to Section 2), which measures in multiple azimuthal and elevation viewing directions, pointing directly towards the plume while different viewing azimuth angles and elevation angles cover a large part of the region. We select the zenith light as the reference spectra. The data retrieval results are shown in Fig. 8 and the retrieval error in Fig. 9. During the measurement, the retrieved differential slant column densities (dSCDs) of CO₂ are around 2 × 10²¹ molecules·cm⁻² for the areas which are similarly unpolluted as the rural reference region, and 5.5 × 10²¹ molecules·cm⁻² for locations most strongly affected by local CO₂ emissions. In addition, most of the retrieval errors are lower than 2 × 10²⁰ molecules·cm⁻²; retrieval precision is better than 4%. All spectra in this section are obtained in 0.7 s exposure time.

Fig. 8.

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	Fig. 8. CO2 dSCD at different elevation and azimuthal angles.

Fig. 9.

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	Fig. 9. CO2 dSCD retrieval errors at different elevation and azimuthal angles.

The locations of the two maximum values are marked in Fig. 8 by two black dots. Our observation site is about 1000 meters away from the chimney; hence, we can calculate the height of the two maximum values which is about 140.5 m, matching the chimney height of 140 m. During the observation, our instrument was located at a point with an azimuthal angle of 40°. Through geometric calculation, we calculate that the distance between the two chimneys is about 131.8 meters, which agrees well with the chimney distance of 138 m. It is obvious that the first maximum is in good agreement with the mouth of the chimney. There are two reasons for this: one is that the observation angle is exactly at the top of the chimney; and the other is that the chimney has not been improved for efficiency. Therefore, the first chimney emits more CO₂, which can explain the two high values marked by a red dot on the right of the first chimney. Another maximum value appears on the left of the second chimney owing to the plume accumulated there. One part of the plume is blown by the wind from the first chimney, and the other part comes from the plume spread of the second chimney.

Referring to the measurements in different azimuthal and vertical viewing directions, the movement direction of the plume can be easily distinguished, as shown in Fig. 8. During the observation, the wind speed is about 1.5 m/s stably at the height of 140 m, and the direction is east to north 45°, as shown in Fig. 8, so v_|| = v_⊥ = 1.06 m/s. In the azimuthal direction, the plume spreads from 46.5° to 52°, which represents about 107.45 m. We can calculate the spread time, which is about 100 s, because v_|| can be supposed to be fixed. In the vertical direction, the plume spreads from 7° to 18°, which represents about 202.12 m. The plume is approximately 100 meters high from the chimney, because the plume speed from the chimney is nearly 10 m/s; though the speed decreases as the height increases, the spread distance is still longer than the azimuthal direction.