<table><caption>**Table 3**
The VP and SDV line-shape parametrization and their notation in HITRANonline and HAPI<sup>a</sup>.</caption><thead><tr><th>VP parameters<sup>b</sup></th><th>Common notation</th><th>Symbol (units)</th><th>Database notation</th></tr></thead><tbody><tr><td rowspan="2">Half-widths</td><td>γ<sub>air</sub></td><td>γ<sub>air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma-air</td></tr><tr><td>γ<sub>self</sub></td><td>γ<sub>self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma-self</td></tr><tr><td rowspan="2">Temp. dep. half-widths</td><td>n<sub>air</sub></td><td>n<sub>air</sub> (unitless)</td><td>n-air</td></tr><tr><td>n<sub>self</sub></td><td>n<sub>self</sub> (unitless)</td><td>n-self</td></tr><tr><td rowspan="2">Line shifts</td><td>δ<sub>air</sub></td><td>δ<sub>air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta-air</td></tr><tr><td>δ<sub>self</sub></td><td>δ<sub>self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta-self</td></tr><tr><td rowspan="2">First-order line-mixing</td><td>Y<sub>air</sub></td><td>Y<sub>air</sub> (cm<sup>-1</sup>)</td><td>Y-air</td></tr><tr><td>Y<sub>self</sub></td><td>Y<sub>self</sub> (cm<sup>-1</sup>)</td><td>Y-self</td></tr><tr><th>SDV parameters<sup>b</sup></th><th>Common notation</th><th>Symbol (units)</th><th>Database notation</th></tr><tr><td rowspan="2">Half-widths</td><td>γ<sub>0</sub>-air(SDV)</td><td>γ<sub>SDV_0-air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_0-air_296</td></tr><tr><td>γ<sub>0</sub>-self(SDV)</td><td>γ<sub>SDV_0-self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_0-self_296</td></tr><tr><td rowspan="2">Temp. dep. half-widths</td><td>n<sub>γ<sub>0</sub></sub>-air(SDV)</td><td>n<sub>SDV_0-air</sub> (unitless)</td><td>n_SDV_0-air_296</td></tr><tr><td>n<sub>γ<sub>0</sub></sub>-self(SDV)</td><td>n<sub>SDV_0-air</sub> (unitless)</td><td>n_SDV_0-air_296</td></tr><tr><td rowspan="2">Speed dep. half-widths</td><td>γ<sub>2</sub>-air(SDV)</td><td>γ<sub>SDV_2-air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_2-air_296</td></tr><tr><td>γ<sub>2</sub>-self(SDV)</td><td>γ<sub>SDV_2-self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_2-self_296</td></tr><tr><td rowspan="2">Temp. dep. speed dep.</td><td>n<sub>γ<sub>2</sub></sub>-air(SDV)</td><td>n<sub>γ<sub>2</sub></sub>SDV_2-air (unitless)</td><td>n_gamma_SDV_2-air_296</td></tr><tr><td>n<sub>γ<sub>2</sub></sub>-self(SDV)</td><td>n<sub>γ<sub>2</sub></sub>SDV_2-self (unitless)</td><td>n_gamma_SDV_2-self_296</td></tr><tr><td rowspan="2">Line shifts</td><td>δ<sub>0</sub>-air(SDV)</td><td>δ<sub>SDV_0-air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta_SDV_0-air_296</td></tr><tr><td>δ<sub>0</sub>-self(SDV)</td><td>δ<sub>SDV_0-self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta_SDV_0-self_296</td></tr><tr><td rowspan="2">First-order line-mixing</td><td>Y<sub>air</sub>(SDV)</td><td>Y<sub>SDV_0-air</sub> (cm<sup>-1</sup>)</td><td>Y_SDV_0-air_296</td></tr><tr><td>Y<sub>self</sub>(SDV)</td><td>Y<sub>SDV_0-self</sub> (cm<sup>-1</sup>)</td><td>Y_SDV_0-self_296</td></tr><tr><td>Temp. dep. first-order line-mixing</td><td>n<sub>γ</sub>-air(SDV)</td><td>n<sub>γ</sub>SDV_0-air (unitless)</td><td>n_Y_SDV_0-air_296</td></tr><tr><td></td><td>n<sub>γ</sub>-self(SDV)</td><td>n<sub>γ</sub>SDV_0-self (unitless)</td><td>n_Y_SDV_0-self_296</td></tr></tbody></table>

<sup>a</sup> The notations presented here are common notations often encountered in this paper (although sometimes they slightly differ, for instance (SDV) is dropped if there is a dedicated SDV section where parameter is presented), symbols/notation that users can select on HITRANonline, and “database notation” (referring to actual names of the parameters in the SQL structure). The latter are used by HAPI for instance to download a particular parameter.

<sup>b</sup> The speed dependence and the temperature dependence of the line shift parameters are not presented in this table because of the lack of accurate measurements for these parameters.

broadening and shift parameters together with their temperature dependences. The air-broadening parameters of CO₂ were determined from requantized classical molecular dynamics simulations (rCMDS) [174] using the SDV profile as presented in Table 1 of the supplemental files from Ref. [161] with adequate coverage of the rotational transitions and an extensive set of the required SDV parameters. The results were extrapolated using the Padé approximants and applied to all the bands of CO₂ for the air-broadening, air-speed dependence of width (γ₂-air), and their temperature dependences. Isotopic dependence of the broadening parameters was ignored and therefore the same approach was used for all 12 isotopologues. Comparison of the temperature dependence of the half-widths and the temperature dependence of the speed-dependent parameter in Ref. [161] revealed that the temperature exponents for γ₀ and γ₂ parameters were not the same. Using HAPI, the SDV parameters were checked by modeling the laboratory spectra, and the corresponding residuals (experiment-calculations) confirmed the validity of the parameters [161]. It is noteworthy that for verifying the parameters, we have also examined the measurements which were issued after the release of the Ref. [161] data and in general very good agreement was found between HITRAN2020 and these measurements. See for example Ref. [175].

For updating the self-broadening half-widths (γ₀-self) of CO₂ and the self speed dependence (γ₂-self) of CO₂ using the SDV profile originally, the measured self-broadening by Predoi-Cross et al. [176] and the self speed-dependence measured by Daneshvar et al. [177] were used in Ref. [161]. However, for the HITRAN2020 edition, the very recent high-accuracy measurements for several bands in the 1.6 µm region by Birk et al. [153] were used. These data potentially allow for assessing the vibrational dependence of the self-half-width parameters. Fig. 6 presents the self-broadening parameters as a function of *m* for different bands. The agreement between the measured self-broadening in Ref. [176] and the measured data by Birk et al. [153] for the 30013–00001 band is apparent. The measured self-broadening of Ref. [177] for the 21102–00001 band is also comparable with those of 30013–00001 band values.

<figure><img src="image_10.png" /><figcaption>**Fig. 6.** The self-broadening parameters for CO₂ transitions at 296 K using the SDV profile. The values by Predoi-Cross et al. [176] are compared with the measurement of Ref. [177]. The Birk et al. [153] values are also presented for different bands.</figcaption></figure>

Among the various bands measured in Ref. [153], for the 30011–00001, 30012–00001, 30013–00001, and 30014–00001 bands the vibrational dependence is principally smaller than 1%. However, several data fall outside of the regular pattern for the lines with *J* > 30 of the 00031–00001 band. An appreciable difference of about 10% for the self-broadening parameters, when comparing the 00031–00001 and 30013–00001 band lines, indicates the vibrational dependence of the self-widths. Therefore for HITRAN2020, the 3ν₃ band was treated separately, and for all other
<table><caption>**Table 3**
The VP and SDV line-shape parametrization and their notation in HITRANonline and HAPI<sup>a</sup>.</caption><thead><tr><th>VP parameters<sup>b</sup></th><th>Common notation</th><th>Symbol (units)</th><th>Database notation</th></tr></thead><tbody><tr><td rowspan="2">Half-widths</td><td>γ<sub>air</sub></td><td>γ<sub>air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma-air</td></tr><tr><td>γ<sub>self</sub></td><td>γ<sub>self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma-self</td></tr><tr><td rowspan="2">Temp. dep. half-widths</td><td>n<sub>air</sub></td><td>n<sub>air</sub> (unitless)</td><td>n-air</td></tr><tr><td>n<sub>self</sub></td><td>n<sub>self</sub> (unitless)</td><td>n-self</td></tr><tr><td rowspan="2">Line shifts</td><td>δ<sub>air</sub></td><td>δ<sub>air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta-air</td></tr><tr><td>δ<sub>self</sub></td><td>δ<sub>self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta-self</td></tr><tr><td rowspan="2">First-order line-mixing</td><td>Y<sub>air</sub></td><td>Y<sub>air</sub> (cm<sup>-1</sup>)</td><td>Y-air</td></tr><tr><td>Y<sub>self</sub></td><td>Y<sub>self</sub> (cm<sup>-1</sup>)</td><td>Y-self</td></tr><tr><th>SDV parameters<sup>b</sup></th><th>Common notation</th><th>Symbol (units)</th><th>Database notation</th></tr><tr><td rowspan="2">Half-widths</td><td>γ<sub>0</sub>-air(SDV)</td><td>γ<sub>SDV_0-air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_0-air_296</td></tr><tr><td>γ<sub>0</sub>-self(SDV)</td><td>γ<sub>SDV_0-self</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_0-public_296</td></tr><tr><td rowspan="2">Temp. dep. half-widths</td><td>n<sub>γ<sub>0</sub></sub>-air(SDV)</td><td>n<sub>SDV_0-air</sub> (unitless)</td><td>n_SDV_0-air_296</td></tr><tr><td>n<sub>γ<sub>0</sub></sub>-self(SDV)</td><td>n<sub>SDV_0-self</sub> (unitless)</td><td>n_SDV-public_296</td></tr><tr><td rowspan="2">Speed dep. half-widths</td><td>γ<sub>2</sub>-air(SDV)</td><td>γ<sub>SDV_2-air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_2-air_296</td></tr><tr><td>γ<sub>2</sub>-self(SDV)</td><td>γ<sub>SDV_2-public</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>gamma_SDV_2-public_296</td></tr><tr><td rowspan="2">Temp. dep. speed dep.</td><td>n<sub>γ<sub>2</sub></sub>-air(SDV)</td><td>n<sub>γ<sub>2</sub></sub>SDV_2-air (unitless)</td><td>ngamma_SDV_2-air_296</td></tr><tr><td>n<sub>γ<sub>2</sub></sub>-self(SDV)</td><td>n<sub>γ<sub>2</sub></sub>SDV_2-public (unitless)</td><td>ngamma_SDV_2-public_296</td></tr><tr><td rowspan="2">Line shifts</td><td>δ<sub>0</sub>-air(SDV)</td><td>δ<sub>SDV_0-air</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta_SDV_0-air_296</td></tr><tr><td>δ<sub>0</sub>-self(SDV)</td><td>δ<sub>SDV_0-public</sub> (cm<sup>-1</sup>atm<sup>-1</sup>)</td><td>delta_SDV_0-public_296</td></tr><tr><td rowspan="2">First-order line-mixing</td><td>Y<sub>air</sub>(SDV)</td><td>Y<sub>SDV_0-air</sub> (cm<sup>-1</sup>)</td><td>Y_SDV_0-air_296</td></tr><tr><td>Y<sub>self</sub>(SDV)</td><td>Y<sub>SDV_0-public</sub> (cm<sup>-1</sup>)</td><td>Y_SDV-public_296</td></tr><tr><td>Temp. dep. first-order line-mixing</td><td>n<sub>γ</sub>-air(SDV)</td><td>n<sub>γ</sub>SDV_0-air (unitless)</td><td>n<sub>γ</sub>SDV_0-air_296</td></tr><tr><td></td><td>n<sub>γ</sub>-self(SDV)</td><td>n<sub>γ</sub>SDV_0-public (unitless)</td><td>n<sub>γ</sub>SDV-public_296</td></tr></tbody></table>

<sup>a</sup> The notations presented here are common notations often encountered in this paper (although sometimes they slightly differ, for instance (SDV) is dropped if there is a dedicated SDV section where parameter is presented), symbols/notation that users can select on HITRANonline, and “database notation” (referring to actual names of the parameters in the SQL structure). The latter are used by HAPI for instance to download a particular parameter.

<sup>b</sup> The speed dependence and the temperature dependence of the line shift parameters are not presented in this table because of the lack of accurate measurements for these parameters.

broadening and shift parameters together with their temperature dependences. The air-broadening parameters of CO₂ were determined from requantized classical molecular dynamics simulations (rCMDS) [174] using the SDV profile as presented in Table 1 of the supplemental files from Ref. [161] with adequate coverage of the rotational transitions and an extensive set of the required SDV parameters. The results were extrapolated using the Padé approximants and applied to all the bands of CO₂ for the air-broadening, air-speed dependence of width (γ₂-air), and their temperature dependences. Isotopic dependence of the broadening parameters was ignored and therefore the same approach was used for all 12 isotopologues. Comparison of the temperature dependence of the half-widths and the temperature dependence of the speed-dependent parameter in Ref. [161] revealed that the temperature exponents for γ₀ and γ₂ parameters were not the same. Using HAPI, the SDV parameters were checked by modeling the laboratory spectra, and the corresponding residuals (experiment-calculations) confirmed the validity of the parameters [161]. It is noteworthy that for verifying the parameters, we have also examined the measurements which were issued after the release of the Ref. [161] data and in general very good agreement was found between HITRAN2020 and these measurements. See for example Ref. [175].

For updating the self-broadening half-widths (γ₀-self) of CO₂ and the self speed dependence (γ₂-self) of CO₂ using the SDV profile originally, the measured self-broadening by Predoi-Cross et al. [176] and the self speed-dependence measured by Daneshvar et al. [177] were used in Ref. [161]. However, for the HITRAN2020 edition, the very recent high-accuracy measurements for several bands in the 1.6 µm region by Birk et al. [153] were used. These data potentially allow for assessing the vibrational dependence of the self-half-width parameters. Fig. 6 presents the self-broadening parameters as a function of *m* for different bands. The agreement between the measured self-broadening in Ref. [176] and the measured

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** The self-broadening parameters for CO₂ transitions at 296 K using the SDV profile. The values by Predoi-Cross et al. [176] are compared with the measurement of Ref. [177]. The Birk et al. [153] values are also presented for different bands.</figcaption></figure>

data by Birk et al. [153] for the 30013–00001 band is apparent. The measured self-broadening of Ref. [177] for the 21102–00001 band is also comparable with those of 30013–00001 band values.

Among the various bands measured in Ref. [153], for the 30011–00001, 30012–00001, 30013–00001, and 30014–00001 bands the vibrational dependence is principally smaller than 1%. However, several data fall outside of the regular pattern for the lines with *J* > 30 of the 00031–00001 band. An appreciable difference of about 10% for the self-broadening parameters, when comparing the 00031–00001 and 30013–00001 band lines, indicates the vibrational dependence of the self-widths. Therefore for HITRAN2020, the 3ν₃ band was treated separately, and for all other
<figure><img src="image_11.png" /><figcaption>**Fig. 7.** The self speed-dependence of width parameters for CO₂ transitions at 296 K using the SDV profile. The measured values for different bands by Birk et al. [153] and Daneshvar et al. [177] are compared.</figcaption></figure>

bands no vibrational dependence has been assumed at the moment and the 30013–00001 band results were used. The measured self-shifts of Ref. [153] were used to update the self-shifts for the measured bands and were also used to improve the prediction algorithm for the bands that were not measured.

Similarly, for updating the self speed-dependence of widths, the measured data of Ref. [153] were used to avoid mixing the data from different sources. Fig. 7 displays the γ₂-self parameters for different bands and, as can be seen after *m* > 35, the values deviate from each other. The Padé approximants (Eq. (1)) were used for extrapolating the 30013–00001 band results from Ref. [153] to all the bands except for the 00031–00001 band. After more high-quality experiments become available in various bands, it would be worth attempting to determine the vibrational dependence of the self-broadened half-widths, their temperature, and speed-dependencies.

### 2.2.9. Updating the CO₂ line-mixing package

The FORTRAN code by Lamouroux et al. [166] is used for predicting the line-mixing effect in all the bands of CO₂ either accounting for the full line-mixing (using the VP) or the first-order approximation (using the VP and SDV profiles). The update to the CO₂ line-mixing package is specified in Ref. [161] and the modifications to the line positions, intensities [134] and the relevant line-shape parameters [161] for the HITRAN2020 edition were addressed to update the package. Also, the partition functions were calculated employing TIPS2017 [178]. Moreover, the first-order line-mixing and its temperature dependence were implemented in HAPI to be taken into account with different line-shape profiles [52]. Based on the analyses performed using the measured laboratory spectra in Ref. [161], similar residuals were obtained when the transmission spectra were generated using i) the VP accounting for full line-mixing, and ii) the SDV modeled with first-order line-mixing. For instance, for the examined regions when only the P- and R-branch lines were present, the difference was on the order of 0.1% at 296K. Compared to HITRAN2016, an improvement of about 0.5% in the calculated residuals was achieved when using the new spectroscopic parameters and including line-mixing (implied by Fig. 13, 16, 18, and 19 of Ref. [161]).

For the purpose of atmospheric validation, the CO₂ line-mixing package was used to calculate the absorption coefficients (ABSCO-formatted tables) in the 4700–5100 cm⁻¹ region corresponding to the so-called “strong band” in the OCO-2 mission. The ABSCO tables are produced using both Voigt profile accounting for the first-order and full line-mixing, and the speed-dependent Voigt including

the first-order line-mixing which are available at Zenodo [179]. The preliminary ABSCO-formatted tables were tested by the OCO-2 science team through comparison of modeled spectra to TCCON measurements of atmospheric transmission and the results showed substantial improvement over those generated with HITRAN2016 as discussed in Ref. [180].

All of the verification investigations [161] confirmed that including the first-order line-mixing parameters is a quick method for calculating the cross-sections with a reasonable improvement in the residuals. Nevertheless, wherever the Q-branch lines are present, the first-order approximation fails to correctly model the spectra, and ultimately, it creates negative absorption coefficients. Therefore, for the more compact spectral regions, the application of full line-mixing is recommended. The current form of the line-mixing code does not support the formulation of the SDV profile accounting for the full line-mixing effect because of the complexity of the calculation. This issue will be studied for the forthcoming releases of the database. Furthermore, for future editions, we plan to add the HT profile [74] parameters to the database of carbon dioxide parameters, which will be valuable in enhancing the retrieval accuracy if the proper functional forms are adopted in the radiative transfer codes.

### 2.2.10. Introducing water-vapor broadening parameters

The predominant importance of water vapor in the terrestrial atmosphere, and its key role in the Earth's climate system, mean the water spectrum has been the subject of numerous studies. At the same time the collisional broadening effects introduced by water vapor on other molecules are required in order to accurately characterize and model spectra of the atmospheres with significant amounts of water vapor. Furthermore, the collisional broadening of spectral lines by water vapor is much larger than that by nitrogen and oxygen. Therefore, we introduced the pressure-broadening parameters including the temperature-dependent exponents due to water vapor in the HITRAN database through semi-empirical models based on the third- to fourth-order Padé approximants (Eq. (1)). The first part of this work was reported for the lines of CO₂, N₂O, CO, CH₄, O₂, NH₃, and H₂S [49].

The water-vapor broadening parameters (γH₂O) and their temperature dependence exponents (nH₂O) for CO₂ transitions were determined using a semi-empirical approach by fitting accurate parameters to a Padé approximant. The collected data sets included early theoretical calculations from Rosenmann et al. [181,182] and the more recent experimental results from Sung et al. [183–185]. The fitted half-widths of water-vapor broadening are valid up to *J* ≤ 121. The new Padé function approach is advantageous over extend the standard polynomial functions as it overcomes the convergence issues for high rotational *J* transitions, which can become significant at high temperatures. Meanwhile, the temperature-dependent exponents for water vapor broadening of CO₂ are also included in the updating water-vapor broadening parameter data sets.

## 2.3. O₃: ozone (molecule 3)

Ozone plays a crucial role in the chemistry of the terrestrial atmosphere. Its concentrations and vertical distribution are among key factors that drive the quality of human life on Earth, a protector from harmful UV radiation but also a pollutant. Not surprisingly, it is actively monitored by satellite [19,21,22,186], balloon [187,188], and ground-based spectrometers [189] operating from the MW to UV parts of the spectrum.

Although ozone was one of the first gases introduced into HITRAN, and there is no lack of laboratory measurements (see, for instance, the review by Barbe et al. [190]) or theoretical calculations, it remains one of the most challenging line lists in the database. In
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** The self speed-dependence of width parameters for CO₂ transitions at 296 K using the SDV profile. The measured values for different bands by Birk et al. [153] and Daneshvar et al. [177] are compared.</figcaption></figure>

bands no vibrational dependence has been assumed at the moment and the 30013–00001 band results were used. The measured self-shifts of Ref. [153] were used to update the self-shifts for the measured bands and were also used to improve the prediction algorithm for the bands that were not measured.

Similarly, for updating the self speed-dependence of widths, the measured data of Ref. [153] were used to avoid mixing the data from different sources. Fig. 7 displays the γ₂-self parameters for different bands and, as can be seen after *m* > 35, the values deviate from each other. The Padé approximants (Eq. (1)) were used for extrapolating the 30013–00001 band results from Ref. [153] to all the bands except for the 00031–00001 band. After more high-quality experiments become available in various bands, it would be worth attempting to determine the vibrational dependence of the self-broadened half-widths, their temperature, and speed-dependencies.

### 2.2.9. Updating the CO₂ line-mixing package

The FORTRAN code by Lamouroux et al. [166] is used for predicting the line-mixing effect in all the bands of CO₂ either accounting for the full line-mixing (using the VP) or the first-order approximation (using the VP and SDV profiles). The update to the CO₂ line-mixing package is specified in Ref. [161] and the modifications to the line positions, intensities [134] and the relevant line-shape parameters [161] for the HITRAN2020 edition were addressed to update the package. Also, the partition functions were calculated employing TIPS2017 [178]. Moreover, the first-order line-mixing and its temperature dependence were implemented in HAPI to be taken into account with different line-shape profiles [52]. Based on the analyses performed using the measured laboratory spectra in Ref. [161], similar residuals were obtained when the transmission spectra were generated using i) the VP accounting for full line-mixing, and ii) the SDV modeled with first-order line-mixing. For instance, for the examined regions when only the P- and R-branch lines were present, the difference was on the order of 0.1% at 296K. Compared to HITRAN2016, an improvement of about 0.5% in the calculated residuals was achieved when using the new spectroscopic parameters and including line-mixing (implied by Fig. 13, 16, 18, and 19 of Ref. [161]).

For the purpose of atmospheric validation, the CO₂ line-mixing package was used to calculate the absorption coefficients (ABSCO-formatted tables) in the 4700–5100 cm⁻¹ region corresponding to the so-called “strong band” in the OCO-2 mission. The ABSCO tables are produced using both Voigt profile accounting for the first-order and full line-mixing, and the speed-dependent Voigt including

the first-order line-mixing which are available at Zenodo [179]. The preliminary ABSCO-formatted tables were tested by the OCO-2 science team through comparison of modeled spectra to TCCON measurements of atmospheric transmission and the results showed substantial improvement over those generated with HITRAN2016 as discussed in Ref. [180].

All of the verification investigations [161] confirmed that including the first-order line-mixing parameters is a quick method for calculating the cross-sections with a reasonable improvement in the residuals. Nevertheless, wherever the Q-branch lines are present, the first-order approximation fails to correctly model the spectra, and ultimately, it creates negative absorption coefficients. Therefore, for the more compact spectral regions, the application of full line-mixing is recommended. The current form of the line-mixing code does not support the formulation of the SDV profile accounting for the full line-mixing effect because of the complexity of the calculation. This issue will be studied for the forthcoming releases of the database. Furthermore, for future editions, we plan to add the HT profile [74] parameters to the database of carbon dioxide parameters, which will be valuable in enhancing the retrieval accuracy if the proper functional forms are adopted in the radiative transfer codes.

### 2.2.10. Introducing water-vapor broadening parameters

The predominant importance of water vapor in the terrestrial atmosphere, and its key role in the Earth's climate system, mean the water spectrum has been the subject of numerous studies. At the same time the collisional broadening effects introduced by water vapor on other molecules are required in order to accurately characterize and model spectra of the atmospheres with significant amounts of water vapor. Furthermore, the collisional broadening of spectral lines by water vapor is much larger than that by nitrogen and oxygen. Therefore, we introduced the pressure-broadening parameters including the temperature-dependent exponents due to water vapor in the HITRAN database through semi-empirical models based on the third- to fourth-order Padé approximants (Eq. (1)). The first part of this work was reported for the lines of CO₂, N₂O, CO, CH₄, O₂, NH₃, and H₂S [49].

The water-vapor broadening parameters (γH₂O) and their temperature dependence exponents (nH₂O) for CO₂ transitions were determined using a semi-empirical approach by fitting accurate parameters to a Padé approximant. The collected data sets included early theoretical calculations from Rosenmann et al. [181,182] and the more recent experimental results from Sung et al. [183–185]. The fitted half-widths of water-vapor broadening are valid up to *J* ≤ 121. The new Padé function approach is advantageous over extend the standard polynomial functions as it overcomes the convergence issues for high rotational *J* transitions, which can become significant at high temperatures. Meanwhile, the temperature-dependent exponents for water vapor broadening of CO₂ are also included in the updating water-vapor broadening parameter data sets.

## 2.3. O₃: ozone (molecule 3)

Ozone plays a crucial role in the chemistry of the terrestrial atmosphere. Its concentrations and vertical distribution are among key factors that drive the quality of human life on Earth, a protector from harmful UV radiation but also a pollutant. Not surprisingly, it is actively monitored by satellite [19,21,22,186], balloon [187,188], and ground-based spectrometers [189] operating from the MW to UV parts of the spectrum.

Although ozone was one of the first gases introduced into HITRAN, and there is no lack of laboratory measurements (see, for instance, the review by Barbe et al. [190]) or theoretical calculations, it remains one of the most challenging line lists in the database. In
particular, a major challenge is related to obtaining self-consistency
in band intensities of ozone in various spectral intervals. This is
mandatory to avoid discrepancies in the atmospheric ozone re-
trieval using different spectral windows. In this context, the pre-
viously available line-by-line compilations were not fully satisfac-
tory, as shown by laboratory and atmospheric validations (see for
instance, [191,192]).

The IR measurements of line intensities of ozone are very chal-
lenging. Usually, relative uncertainties in line intensities obtained
via fits of observed spectra with effective spectroscopic models
could be significantly smaller than the absolute uncertainties. This
is because the dynamic range in line intensities is very large,
making it necessary to use spectra obtained at different pres-
sure/path length conditions in the fit. As ozone is an unstable
species, the partial pressure conditions are difficult to control pre-
cisely, which is one of the main factors contributing to inconsis-
tencies between absolute band intensities in different spectral in-
tervals. Related issues for laboratory measurements have been dis-
cussed in Refs. [193–198] and references therein. Therefore simul-
taneous measurements in the MW or UV regions are usually car-
ried out, because the intensities of low-J MW lines can be directly
linked to the permanent dipole moment of the molecule, which
is known very precisely. The UV standards were considered to be
well-calibrated. Also, due to relatively small rotational constants,
the IR spectra of ozone are quite congested. Consequently, only
a restricted number of the non-blended lines could be accurately
measured. Complete line lists for a given band system are typically
produced by calculations using empirically-fitted parameters of the
effective Hamiltonian (EH) and effective dipole transition moment
(EDTM) parameters [190,199]. This implies the increase of uncer-
tainties for extrapolated/interpolated ranges.

As described in the previous section devoted to carbon dioxide,
modern *ab initio* calculations allow the determination of precise
intensity values for many molecules, except for so-called "sensi-
tive" bands or lines that for molecules like carbon dioxide are not
very frequent. Unfortunately, for ozone, it is not always the case,
and although a great many calculated intensities are of very good
quality, the amount of lines where intensities can not be calculated
reliably from first principles is quite large due to severe resonance
perturbations, many of which are caused by the "dark" states [190].
Nevertheless, as will be shown below, *ab initio* calculations can be
employed for many transitions or serve as a validation tool.

Ozone data in HITRAN2016 [16] were a substantial improvement compared to previous editions in many spectral regions [76]. Following the release of HITRAN2016, Ref. [195] measured the MW and IR bands at 10 µm simultaneously and found an excellent consistency (better than 1%) between these bands when using HITRAN2016. Assuming that the intensities of the strongest lines in the pure rotational band should be known at a sub-percent level, Ref. [195] concluded that the intensities in the 10- µm band in HITRAN2016 are therefore also of excellent quality. However, Birk et al. [200] have shown that the MW intensities in HITRAN were too weak by ~3.8%, which in the context of the conclusions of Ref. [195] implies that the same scaling should apply to the 10-µm band. These findings have paved the way to an extensive international campaign for remeasuring and recalculating spectral parameters of ozone in all spectral regions from the MW to UV. Although not all of these works have been published, the new data have gone through intensive evaluation procedures, including comparisons with laboratory, ground-based, satellite, and balloon measurements. It was concluded that a combination of data from new laboratory and theoretical sources yield much better consistency of the intensities of ozone bands and also increase the quality of all parameters of individual lines. This is undoubtedly one of the highlights of HITRAN2020. Below we describe three sets of experimental and theoretical data in the IR region and how they were com-

bined, based on the validations, to form the HITRAN2020 ozone
line list. UV data are still only available in cross-sections, and that
new dataset is described in Section 3.2.1.

2.3.1. New "S&MPO_2020d" line list

In December 2020, a new update for the S&MPO Reims-
Tomsk line list (http://smpo.iao.ru, http://smpo.univ-reims.fr)
[194] was made, featuring substantial changes in line intensities
[201,202] and line positions [203] not only for the principal but
also for minor isotopologues [204,205]. The line positions and
lower-state energies in S&MPO are based on empirical Hamil-
tonian models, while the intensities are mostly empirical or
semi-empirical, which in the new edition often includes correc-
tions based on *ab initio* calculations.

2.3.1.1. <sup>16</sup>O<sup>16</sup>O<sup>16</sup>O: *ab initio* intensity corrections and empirical line positions. *Ab initio* calculations of ozone have significantly advanced over the years, which enables one to improve the modeling of collisional processes [206,207] and of vibrational dynamics [208,209] using the PES [210] obtained at a high level of electronic structure theory. Recently, it was shown [201] that line intensity calculations by variational method from the *ab initio* dipole moment surfaces (DMS) of Tyuterev et al. [211] can help to resolve controversies among previously reported <sup>16</sup>O<sup>16</sup>O<sup>16</sup>O data sets in the MW, 5- and 10-µm ranges.

A comparison of results from Ref. [211] with very accurate FTS
intensity measurements of Barbe et al. (GSMA, Reims) and prelim-
inary data from Refs. [196,197] in the 5- and 10-µm ranges and
with Stark-effect data in the MW [212] have shown an average
agreement within 0.3–1.0% for strong lines between *ab initio* the-
ory and these experiments. The tight scatter in these results made
it evident that the HITRAN2016 intensities must be increased by
2.5% to 4.5% in the corresponding regions. This was also consis-
tent with the results reported in Refs. [195,198,200]. For the 2020
update of the S&MPO line list (and ultimately HITRAN2020 in se-
lected spectral regions), we have extended *ab initio* intensity cor-
rections for 31 bands including 14 cold and 17 hot bands in the
range from 0 to 4300 cm⁻¹ using the DMS from Ref. [211]. The
corresponding details of calculations are described in the dedicated
publication by Tyuterev et al. [202] in this special issue. The sum-
mary of changes in line intensities between S&MPO_2020d and HI-
TRAN2016 is shown in Fig. 8.

The target accuracy of line intensities for unstable species like
ozone is currently considered as being within 1% for strong and

<figure><img src="image_12.png" /><figcaption>**Fig. 8.** Summary for the line intensity deviations. $dS = [S(\text{S\&MPO}_{20\text{d}}) - S(\text{HITRAN2016})]/S(\text{HITRAN2016})$ in % for the ozone $^{16}\text{O}_3$ transitions in the 0–5791 cm$^{-1}$ range. Most of changes with $dS > 2\%$ correspond to the *ab initio* intensity correction as described in Ref. [202]. Shaded areas correspond to the spectral regions where S\&MPO\_20\_d was not used for the HITRAN2020 ozone database.</figcaption></figure>
particular, a major challenge is related to obtaining self-consistency in band intensities of ozone in various spectral intervals. This is mandatory to avoid discrepancies in the atmospheric ozone retrieval using different spectral windows. In this context, the previously available line-by-line compilations were not fully satisfactory, as shown by laboratory and atmospheric validations (see for instance, [191,192]).

The IR measurements of line intensities of ozone are very challenging. Usually, relative uncertainties in line intensities obtained via fits of observed spectra with effective spectroscopic models could be significantly smaller than the absolute uncertainties. This is because the dynamic range in line intensities is very large, making it necessary to use spectra obtained at different pressure/path length conditions in the fit. As ozone is an unstable species, the partial pressure conditions are difficult to control precisely, which is one of the main factors contributing to inconsistencies between absolute band intensities in different spectral intervals. Related issues for laboratory measurements have been discussed in Refs. [193–198] and references therein. Therefore simultaneous measurements in the MW or UV regions are usually carried out, because the intensities of low-J MW lines can be directly linked to the permanent dipole moment of the molecule, which is known very precisely. The UV standards were considered to be well-calibrated. Also, due to relatively small rotational constants, the IR spectra of ozone are quite congested. Consequently, only a restricted number of the non-blended lines could be accurately measured. Complete line lists for a given band system are typically produced by calculations using empirically-fitted parameters of the effective Hamiltonian (EH) and effective dipole transition moment (EDTM) parameters [190,199]. This implies the increase of uncertainties for extrapolated/interpolated ranges.

As described in the previous section devoted to carbon dioxide, modern *ab initio* calculations allow the determination of precise intensity values for many molecules, except for so-called “sensitive” bands or lines that for molecules like carbon dioxide are not very frequent. Unfortunately, for ozone, it is not always the case, and although a great many calculated intensities are of very good quality, the amount of lines where intensities can not be calculated reliably from first principles is quite large due to severe resonance perturbations, many of which are caused by the “dark” states [190]. Nevertheless, as will be shown below, *ab initio* calculations can be employed for many transitions or serve as a validation tool.

Ozone data in HITRAN2016 [16] were a substantial improvement compared to previous editions in many spectral regions [76]. Following the release of HITRAN2016, Ref. [195] measured the MW and IR bands at 10 µm simultaneously and found an excellent consistency (better than 1%) between these bands when using HITRAN2016. Assuming that the intensities of the strongest lines in the pure rotational band should be known at a sub-percent level, Ref. [195] concluded that the intensities in the 10-µm band in HITRAN2016 are therefore also of excellent quality. However, Birk et al. [200] have shown that the MW intensities in HITRAN were too weak by ~3.8%, which in the context of the conclusions of Ref. [195] implies that the same scaling should apply to the 10-µm band. These findings have paved the way to an extensive international campaign for remeasuring and recalculating spectral parameters of ozone in all spectral regions from the MW to UV. Although not all of these works have been published, the new data have gone through intensive evaluation procedures, including comparisons with laboratory, ground-based, satellite, and balloon measurements. It was concluded that a combination of data from new laboratory and theoretical sources yield much better consistency of the intensities of ozone bands and also increase the quality of all parameters of individual lines. This is undoubtedly one of the highlights of HITRAN2020. Below we describe three sets of experimental and theoretical data in the IR region and how they were com-

bined, based on the validations, to form the HITRAN2020 ozone line list. UV data are still only available in cross-sections, and that new dataset is described in Section 3.2.1.

### 2.3.1. New "S&MPO_2020d" line list

In December 2020, a new update for the S&MPO Reims-Tomsk line list (http://smpo.iao.ru, http://smpo.univ-reims.fr) [194] was made, featuring substantial changes in line intensities [201,202] and line positions [203] not only for the principal but also for minor isotopologues [204,205]. The line positions and lower-state energies in S&MPO are based on empirical Hamiltonian models, while the intensities are mostly empirical or semi-empirical, which in the new edition often includes corrections based on *ab initio* calculations.

#### 2.3.1.1. $^{16}\text{O}^{16}\text{O}^{16}\text{O}$: *ab initio* intensity corrections and empirical line positions.
*Ab initio* calculations of ozone have significantly advanced over the years, which enables one to improve the modeling of collisional processes [206,207] and of vibrational dynamics [208,209] using the PES [210] obtained at a high level of electronic structure theory. Recently, it was shown [201] that line intensity calculations by variational method from the *ab initio* dipole moment surfaces (DMS) of Tyuterev et al. [211] can help to resolve controversies among previously reported $^{16}\text{O}^{16}\text{O}^{16}\text{O}$ data sets in the MW, 5- and 10-µm ranges.

A comparison of results from Ref. [211] with very accurate FTS intensity measurements of Barbe et al. (GSMA, Reims) and preliminary data from Refs. [196,197] in the 5- and 10-µm ranges and with Stark-effect data in the MW [212] have shown an average agreement within 0.3–1.0% for strong lines between *ab initio* theory and these experiments. The tight scatter in these results made it evident that the HITRAN2016 intensities must be increased by 2.5% to 4.5% in the corresponding regions. This was also consistent with the results reported in Refs. [195,198,200]. For the 2020 update of the S&MPO line list (and ultimately HITRAN2020 in selected spectral regions), we have extended *ab initio* intensity corrections for 31 bands including 14 cold and 17 hot bands in the range from 0 to 4300 cm⁻¹ using the DMS from Ref. [211]. The corresponding details of calculations are described in the dedicated publication by Tyuterev et al. [202] in this special issue. The summary of changes in line intensities between S&MPO_2020d and HITRAN2016 is shown in Fig. 8.

The target accuracy of line intensities for unstable species like ozone is currently considered as being within 1% for strong and

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** Summary for the line intensity deviations. $dS = [S(\text{S\&MPO}_{20\text{d}}) - S(\text{HITRAN2016})]/S(\text{HITRAN2016})$ in % for the ozone $^{16}\text{O}_3$ transitions in the 0–5791 cm⁻¹ range. Most of changes with $dS > 2\%$ correspond to the *ab initio* intensity correction as described in Ref. [202]. Shaded areas correspond to the spectral regions where S\&MPO\_20\_d was not used for the HITRAN2020 ozone database.</figcaption></figure>
<caption>**Table 4**</caption>

New (with respect to HITRAN2016) bands added to HITRAN2020 adapted from S&MPO_20d for the principle isotopologue of ozone in "natural" abundance. Minimum and maximum wavenumbers $v_{min}$ and $v_{max}$, number of lines N and sum of line intensities within individual bands $S_v$.

<table><thead><tr><th>$v'$</th><th>$v''$</th><th>$v_{min}$, cm<sup>-1</sup></th><th>$v_{max}$, cm<sup>-1</sup></th><th>N</th><th>$S_v$, cm/mol</th></tr></thead><tbody><tr><td>22 0</td><td>02 1</td><td>1139.984</td><td>1187.006</td><td>164</td><td>4.218E-24</td></tr><tr><td>30 0</td><td>00 2</td><td>1155.052</td><td>1208.551</td><td>12</td><td>2.628E-25</td></tr><tr><td>22 0</td><td>11 0</td><td>1761.375</td><td>1817.097</td><td>92</td><td>3.032E-24</td></tr><tr><td>20 2</td><td>00 2</td><td>1994.841</td><td>2105.185</td><td>82</td><td>2.899E-24</td></tr><tr><td>20 2</td><td>03 0</td><td>2011.499</td><td>2043.890</td><td>2</td><td>4.439E-26</td></tr><tr><td>23 0</td><td>20 0</td><td>2015.029</td><td>2062.849</td><td>5</td><td>1.524E-25</td></tr><tr><td>05 0</td><td>02 0</td><td>2020.866</td><td>2073.526</td><td>4</td><td>6.219E-25</td></tr><tr><td>30 1</td><td>10 1</td><td>2154.827</td><td>2159.443</td><td>6</td><td>1.271E-25</td></tr><tr><td>02 2</td><td>00 1</td><td>2320.650</td><td>2365.711</td><td>191</td><td>2.514E-24</td></tr><tr><td>12 1</td><td>00 1</td><td>2423.376</td><td>2435.536</td><td>29</td><td>4.182E-25</td></tr><tr><td>22 0</td><td>10 0</td><td>2476.903</td><td>2484.720</td><td>15</td><td>1.717E-25</td></tr><tr><td>05 0</td><td>01 0</td><td>2718.726</td><td>2771.609</td><td>4</td><td>6.880E-25</td></tr><tr><td>22 0</td><td>01 0</td><td>2794.977</td><td>2922.083</td><td>488</td><td>2.933E-23</td></tr><tr><td>05 0</td><td>00 0</td><td>3419.165</td><td>3472.267</td><td>4</td><td>2.591E-25</td></tr><tr><td>30 2</td><td>00 1</td><td>4069.803</td><td>4143.464</td><td>905</td><td>5.364E-23</td></tr><tr><td>30 2</td><td>10 0</td><td>4109.876</td><td>4143.008</td><td>3</td><td>3.816E-26</td></tr></tbody></table>

about 3 or 5% for weak transitions. At this level of accuracy, the best *ab initio* calculations can be competitive with precise experimental measurements [201]. However, it is well known that *ab initio* calculations for multi-electron molecules are not able to achieve experimental high-resolution accuracy in line positions (0.001–0.0001 cm⁻¹) because this corresponds to relative precision requirements in wavenumbers of 10⁻⁷ or 10⁻⁸. In a previous release of the S&MPO database [194], the line positions were computed from empirically-fitted EH parameters except for the cases where effective models do not provide experimental accuracy because of the large number of strongly coupled bands and “dark states” perturbations [190]. Empirical corrections to line positions and energy levels must then be accounted for. Detailed explanations on the improvements in the line positions are provided in Ref. [203] and only brief summary is provided here. Part of these changes corresponded to a simple update of old EH parameters from the previous S&MPO releases by more recent ones: this concerns MW and $v_2$ ranges, as well as the 4000 cm⁻¹ range [213].

Furthermore, a new list including both line positions and intensities was generated for the strongest $v_1/v_3$ bands using EH and EDTM parameters [203] obtained from the analyses of GSMA/Reims spectra at 10 µm. In particular, the line positions with large ($K_a > 20$) rotational quantum numbers were improved for the $v_3$ band. The third type of change concerns empirical corrections of line positions near 2700 cm⁻¹ and in the 2900–5500 cm⁻¹ range. Following the recent analysis of Ref. [213], the most significant corrections concern the complex band system (103)/(004)/(310)–(000) near 4000 cm⁻¹ and in the corresponding hot bands. Some other corrections concern “exotic” accidental resonance perturbations like those involving the (040) and (050) states. Note that a line position correction in one range resulted in many more “induced” corrections in other ranges via the shifts in energy levels. Finally, a limited number of line intensities were empirically adjusted, particularly in the ranges near 3000 cm⁻¹ and 5000 cm⁻¹ [203]. Overall, in the spectral range of 0–5791 cm⁻¹, the S&MPO_20d list contains 312,669 lines. There are 25 newly generated weak hot bands in that list, 16 of which (above 1180 cm⁻¹) were adapted to HITRAN2020. A summary of these 16 bands is presented in Table 4. A global Table including band statistics for all the bands versus HITRAN2016 is given in the Supplementary Materials.

A summary of line position corrections and new lines is given in Fig. 9. A detailed description will be presented in a dedicated publication in this special issue [203].

<figure><img src="image_13.png" /><figcaption>**Fig. 9.** Summary for newly added (with respect to HITRAN2016) hot bands (in green) and line position corrections [203] for HITRAN2020. The transitions for the ¹⁶O₃ ozone in the 0–5791 cm⁻¹ range corrected by more than $d\nu = \nu(S&MPO_20d) - \nu(HITRAN2016) > 0.0003$ cm⁻¹ are indicated in magenta. Shaded areas correspond to the spectral regions where S&MPO_20d was not used for the HITRAN2020 ozone database.</figcaption></figure>

An example of an improvement for the transmittance calculation near 4000 cm⁻¹ using the S&MPO_20d (and hence HITRAN2020 in this region) list including recent results of analysis [213] with the subsequent *ab initio* corrections for intensities [202] is given in Fig. 10.

It is instructive to compare the S&MPO_20d line list with other recent data based on accurate laboratory intensity measurements. Tables 5 and 6 show an excellent agreement for RMS and mean deviations in line-by-line intensities with the DLR list described in Section 2.3.2 in the 10-µm range. On the full sample of the common lines of these lists, the sum of intensities $S_v$ gives very close values with a deviation of only 0.07% for the strongest ozone band $v_3$ and of 0.25% for $v_1$ (see Table 5). A systematic offset is almost negligible – between 0.1% and 0.2% for the mean intensity values. For the strong and medium lines, the RMS deviation is significantly smaller for the dominant band $v_3$ within about 0.25% (Fig. 11). The deviation increases to an RMS of 0.5% when extending to medium lines including the sample of 1000 transitions (see Table 6). As expected, the scatter increases for weak lines, though many of these weak lines have not been experimentally measured and rely on extrapolations.

Another accurate set of intensities in the 5- and 10-µm ranges have been recently obtained in Refs. [196,197]. Preliminary comparison between the *ab initio* and empirical list fitted to LERMA spec-

<caption>**Table 5**</caption>

Comparison of integrated intensities for the cold bands in the 10 µm range between S&MPO_20d and DLR line lists for the principle isotopologue, for the common sample of transitions.

<table><caption>**Table 6**</caption><thead><tr><th>Band</th><th>N</th><th>$v_{min}$</th><th>$v_{max}$</th><th>S&MPO $S_v$</th><th>DLR $S_v$</th><th>$\Delta(S_v)$</th></tr></thead><tbody><tr><td>$v_3$</td><td>6212</td><td>980.042</td><td>1219.990</td><td>1.398E-17</td><td>1.397E-17</td><td>0.07%</td></tr><tr><td>$v_1$</td><td>5991</td><td>980.126</td><td>1219.838</td><td>5.287E-19</td><td>5.274E-19</td><td>0.25%</td></tr></tbody></table>

Comparison of RMS and mean intensity deviations between S&MPO_20d and DLR ¹⁶O₃ line lists for strong lines of the $v_1$ and $v_3$ bands

<table><thead><tr><th>Band</th><th>N</th><th>S<sub>min</sub></th><th>S<sub>max</sub></th><th>RMS(S), %</th><th>Mean(S), %</th></tr></thead><tbody><tr><td>$v_3$</td><td>500</td><td>9.4E-21</td><td>4.2E-20</td><td>0.24</td><td>0.08</td></tr><tr><td></td><td>1000</td><td>2.0E-21</td><td>4.2E-20</td><td>0.50</td><td>0.15</td></tr><tr><td>$v_1$</td><td>500</td><td>3.0E-22</td><td>3.4E-21</td><td>0.60</td><td>0.23</td></tr><tr><td></td><td>1000</td><td>1.6E-22</td><td>3.4E-21</td><td>0.88</td><td>0.13</td></tr></tbody></table>
<caption>**Table 4**</caption>

New (with respect to HITRAN2016) bands added to HITRAN2020 adapted from S&MPO_20d for the principle isotopologue of ozone in "natural" abundance. Minimum and maximum wavenumbers $v_{min}$ and $v_{max}$, number of lines N and sum of line intensities within individual bands $S_v$.

<table><thead><tr><th>v'</th><th>v''</th><th>v<sub>min</sub>, cm<sup>-1</sup></th><th>v<sub>max</sub>, cm<sup>-1</sup></th><th>N</th><th>S<sub>v</sub>, cm/mol</th></tr></thead><tbody><tr><td>22 0</td><td>02 1</td><td>1139.984</td><td>1187.006</td><td>164</td><td>4.218E-24</td></tr><tr><td>30 0</td><td>00 2</td><td>1155.052</td><td>1208.551</td><td>12</td><td>2.628E-25</td></tr><tr><td>22 0</td><td>11 0</td><td>1761.375</td><td>1817.097</td><td>92</td><td>3.032E-24</td></tr><tr><td>20 2</td><td>00 2</td><td>1994.841</td><td>2105.185</td><td>82</td><td>2.899E-24</td></tr><tr><td>20 2</td><td>03 0</td><td>2011.499</td><td>2043.890</td><td>2</td><td>4.439E-26</td></tr><tr><td>23 0</td><td>20 0</td><td>2015.029</td><td>2062.849</td><td>5</td><td>1.524E-25</td></tr><tr><td>05 0</td><td>02 0</td><td>2020.866</td><td>2073.526</td><td>4</td><td>6.219E-25</td></tr><tr><td>30 1</td><td>10 1</td><td>2154.827</td><td>2159.443</td><td>6</td><td>1.271E-25</td></tr><tr><td>02 2</td><td>00 1</td><td>2320.650</td><td>2365.711</td><td>191</td><td>2.514E-24</td></tr><tr><td>12 1</td><td>00 1</td><td>2423.376</td><td>2435.536</td><td>29</td><td>4.182E-25</td></tr><tr><td>22 0</td><td>10 0</td><td>2476.903</td><td>2484.720</td><td>15</td><td>1.717E-25</td></tr><tr><td>05 0</td><td>01 0</td><td>2718.726</td><td>2771.609</td><td>4</td><td>6.880E-25</td></tr><tr><td>22 0</td><td>01 0</td><td>2794.977</td><td>2922.083</td><td>488</td><td>2.933E-23</td></tr><tr><td>05 0</td><td>00 0</td><td>3419.165</td><td>3472.267</td><td>4</td><td>2.591E-25</td></tr><tr><td>30 2</td><td>00 1</td><td>4069.803</td><td>4143.464</td><td>905</td><td>5.364E-23</td></tr><tr><td>30 2</td><td>10 0</td><td>4109.876</td><td>4143.008</td><td>3</td><td>3.816E-26</td></tr></tbody></table>

about 3 or 5% for weak transitions. At this level of accuracy, the best *ab initio* calculations can be competitive with precise experimental measurements [201]. However, it is well known that *ab initio* calculations for multi-electron molecules are not able to achieve experimental high-resolution accuracy in line positions (0.001–0.0001 cm⁻¹) because this corresponds to relative precision requirements in wavenumbers of 10⁻⁷ or 10⁻⁸. In a previous release of the S&MPO database [194], the line positions were computed from empirically-fitted EH parameters except for the cases where effective models do not provide experimental accuracy because of the large number of strongly coupled bands and “dark states” perturbations [190]. Empirical corrections to line positions and energy levels must then be accounted for. Detailed explanations on the improvements in the line positions are provided in Ref. [203] and only brief summary is provided here. Part of these changes corresponded to a simple update of old EH parameters from the previous S&MPO releases by more recent ones: this concerns MW and $v_2$ ranges, as well as the 4000 cm⁻¹ range [213].

Furthermore, a new list including both line positions and intensities was generated for the strongest $v_1/v_3$ bands using EH and EDTM parameters [203] obtained from the analyses of GSMA/Reims spectra at 10 µm. In particular, the line positions with large ($K_a > 20$) rotational quantum numbers were improved for the $v_3$ band. The third type of change concerns empirical corrections of line positions near 2700 cm⁻¹ and in the 2900–5500 cm⁻¹ range. Following the recent analysis of Ref. [213], the most significant corrections concern the complex band system (103)/(004)/(310)–(000) near 4000 cm⁻¹ and in the corresponding hot bands. Some other corrections concern “exotic” accidental resonance perturbations like those involving the (040) and (050) states. Note that a line position correction in one range resulted in many more “induced” corrections in other ranges via the shifts in energy levels. Finally, a limited number of line intensities were empirically adjusted, particularly in the ranges near 3000 cm⁻¹ and 5000 cm⁻¹ [203]. Overall, in the spectral range of 0–5791 cm⁻¹, the S&MPO_20d list contains 312,669 lines. There are 25 newly generated weak hot bands in that list, 16 of which (above 1180 cm⁻¹) were adapted to HITRAN2020. A summary of these 16 bands is presented in Table 4. A global Table including band statistics for all the bands versus HITRAN2016 is given in the Supplementary Materials.

A summary of line position corrections and new lines is given in Fig. 9. A detailed description will be presented in a dedicated publication in this special issue [203].

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Summary for newly added (with respect to HITRAN2016) hot bands (in green) and line position corrections [203] for HITRAN2020. The transitions for the ¹⁶O₃ ozone in the 0–5791 cm⁻¹ range corrected by more than $d\nu = \nu(S\&MPO_20d) - \nu(HITRAN2016) > 0.0003$ cm⁻¹ are indicated in magenta. Shaded areas correspond to the spectral regions where S&MPO_20d was not used for the HITRAN2020 ozone database.</figcaption></figure>

An example of an improvement for the transmittance calculation near 4000 cm⁻¹ using the S&MPO_20d (and hence HITRAN2020 in this region) list including recent results of analysis [213] with the subsequent *ab initio* corrections for intensities [202] is given in Fig. 10.

It is instructive to compare the S&MPO_20d line list with other recent data based on accurate laboratory intensity measurements. Tables 5 and 6 show an excellent agreement for RMS and mean deviations in line-by-line intensities with the DLR list described in Section 2.3.2 in the 10-µm range. On the full sample of the common lines of these lists, the sum of intensities $S_v$ gives very close values with a deviation of only 0.07% for the strongest ozone band $v_3$ and of 0.25% for $v_1$ (see Table 5). A systematic offset is almost negligible – between 0.1% and 0.2% for the mean intensity values. For the strong and medium lines, the RMS deviation is significantly smaller for the dominant band $v_3$ within about 0.25% (Fig. 11). The deviation increases to an RMS of 0.5% when extending to medium lines including the sample of 1000 transitions (see Table 6). As expected, the scatter increases for weak lines, though many of these weak lines have not been experimentally measured and rely on extrapolations.

Another accurate set of intensities in the 5- and 10-µm ranges have been recently obtained in Refs. [196,197]. Preliminary comparison between the *ab initio* and empirical list fitted to LERMA spec-

<caption>**Table 5**</caption>

Comparison of integrated intensities for the cold bands in the 10 µm range between S&MPO_20d and DLR line lists for the principle isotopologue, for the common sample of transitions.

<table><caption>**Table 6**</caption><thead><tr><th>Band</th><th>N</th><th>v<sub>min</sub></th><th>v<sub>max</sub></th><th>S&MPO S<sub>v</sub></th><th>DLR S<sub>v</sub></th><th>Δ(S<sub>v</sub>)</th></tr></thead><tbody><tr><td>v<sub>3</sub></td><td>6212</td><td>980.042</td><td>1219.990</td><td>1.398E-17</td><td>1.397E-17</td><td>0.07%</td></tr><tr><td>v<sub>1</sub></td><td>5991</td><td>980.126</td><td>1219.838</td><td>5.287E-19</td><td>5.274E-19</td><td>0.25%</td></tr></tbody></table>

Comparison of RMS and mean intensity deviations between S&MPO_20d and DLR ¹⁶O₃ line lists for strong lines of the $v_1$ and $v_3$ bands

<table><thead><tr><th>Band</th><th>N</th><th>S<sub>min</sub></th><th>S<sub>max</sub></th><th>RMS(S), %</th><th>Mean(S), %</th></tr></thead><tbody><tr><td>v<sub>3</sub></td><td>500</td><td>9.4E-21</td><td>4.2E-20</td><td>0.24</td><td>0.08</td></tr><tr><td></td><td>1000</td><td>2.0E-21</td><td>4.2E-20</td><td>0.50</td><td>0.15</td></tr><tr><td>v<sub>1</sub></td><td>500</td><td>3.0E-22</td><td>3.4E-21</td><td>0.60</td><td>0.23</td></tr><tr><td></td><td>1000</td><td>1.6E-22</td><td>3.4E-21</td><td>0.88</td><td>0.13</td></tr></tbody></table>
<figure><img src="image_14.png" /><figcaption>**Fig. 10.** Example of an improvement of the line list of ozone when compared to the experimental FTS laboratory spectra. It is clear that S&MPO_20d (hence HITRAN2020 in this region) line list in the range of the 4ν₃ band is superior to that from HITRAN2016.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**Fig. 11.** Ratio of intensities S(DLR)/S(S&MPO_20d) for the strongest lines in the 10-μm range. Note that the DLR data are used in HITRAN2020 in this spectral region.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>**Fig. 12.** Ratio of intensities S(S&MPO_20d) / S(LERMAobs) for the strongest lines in the 5-μm range. Note that the S&MPO data are used in HITRAN2020 in this spectral region.</figcaption></figure>

tra [197] was reported in Ref. [201] where only 50 of the strongest transitions were included. Table 7 summarizes the results of an extended statistical comparison with a complete set of experimental lines determined by Jacquemart et al. [197] from LERMA spectra using a speed-dependent line profile. The comparison for individual strong lines is shown in Fig. 12. Excellent agreement is obvious from these comparisons.

Interestingly, on the common sample of measured lines, the LERMA(obs) gives almost exactly the same ratio S<sub>v</sub>(10 μm)/S<sub>v</sub>(5 μm) as the S&MPO_20d line list testifying to a perfect intensity consistency of the two data sets between these spectral ranges, which are of primary importance for atmospheric applications.

<caption>**Table 7**</caption>

Comparison of RMS, mean and integrated deviations for line intensities between the S&MPO_20d list and experimental values from LERMA [197] in the 10- and 5- μm ranges for (<sup>16</sup>O<sub>3</sub>)

<table><thead><tr><th>Range</th><th>Bands</th><th>N</th><th>Δ(S<sub>v</sub>)<sup>a</sup></th><th>RMS(S)</th><th>Mean (S)</th></tr></thead><tbody><tr><td>10 μm</td><td>ν<sub>3</sub>, ν<sub>1</sub>, ν<sub>2</sub> + ν<sub>3</sub> - ν<sub>2</sub></td><td>497</td><td>0.28 %</td><td>0.78%</td><td>0.26%</td></tr><tr><td>5 μm</td><td>ν<sub>1</sub> + ν<sub>3</sub>, 2ν<sub>3</sub></td><td>319</td><td>-0.04%</td><td>0.37%</td><td>-0.02%</td></tr></tbody></table>

2.3.1.2. <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O isotopologue. About thirty ozone spectra enriched with <sup>18</sup>O were recorded with the GSMA FTS spectrometer using different cell lengths, <sup>18</sup>O/<sup>16</sup>O oxygen isotopic mixtures, and different pressures varying from 4 to 20 Torr. The analyses of the spectra in the range between 900 and 3850 cm<sup>-1</sup> allowed Ref. [205] to extend substantially the information about ro-vibrational transitions and energy levels of the <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O isotopologue, belonging to the C<sub>5</sub> point group. The assignment and modeling have been carried out using EH and EDTM operators with the help of theoretical predictions of the band centers, rotational constants and some coupling parameters. The latter ones have been derived from an *ab initio* potential energy surface (PES) [210] using the MOL_CT code [214] in the standard format of the EH [194,215] of the S&MPO system. We fixed the coupling term values to the predicted ones for the complete polyads of observed bands below 2500 cm<sup>-1</sup> to characterize the intensity transfer among the observed bands. Above 2500 cm<sup>-1</sup>, our effective models include only those coupling terms, which correspond to the observed perturbations. In total, 9976 ro-vibrational transitions belonging to the 15 bands of <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O were assigned and modeled with average accuracy of the order of 10<sup>-3</sup> cm<sup>-1</sup>. The set of 7030 corresponding upper-state ro-vibrational energy levels were determined. Overall a line list of 49,148 transitions is provided for the HITRAN2020 database for 13 observed bands of <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O

<footnote><sup>a</sup>relative deviations of sums of all line intensities for the range</footnote>
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** Example of an improvement of the line list of ozone when compared to the experimental FTS laboratory spectra. It is clear that S&MPO_20d (hence HITRAN2020 in this region) line list in the range of the 4ν₃ band is superior to that from HITRAN2016.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Ratio of intensities S(DLR)/S(S&MPO_20d) for the strongest lines in the 10-μm range. Note that the DLR data are used in HITRAN2020 in this spectral region.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Ratio of intensities S(S&MPO_20d) / S(LERMAobs) for the strongest lines in the 5-μm range. Note that the S&MPO data are used in HITRAN2020 in this spectral region.</figcaption></figure>

tra [197] was reported in Ref. [201] where only 50 of the strongest transitions were included. Table 7 summarizes the results of an extended statistical comparison with a complete set of experimental lines determined by Jacquemart et al. [197] from LERMA spectra using a speed-dependent line profile. The comparison for individual strong lines is shown in Fig. 12. Excellent agreement is obvious from these comparisons.

Interestingly, on the common sample of measured lines, the LERMA(obs) gives almost exactly the same ratio S<sub>v</sub>(10 μm)/S<sub>v</sub>(5 μm) as the S&MPO_20d line list testifying to a perfect intensity consistency of the two data sets between these spectral ranges, which are of primary importance for atmospheric applications.

**Table 7**

Comparison of RMS, mean and integrated deviations for line intensities between the S&MPO_20d list and experimental values from LERMA [197] in the 10- and 5- μm ranges for (<sup>16</sup>O<sub>3</sub>)

<table><thead><tr><th>Range</th><th>Bands</th><th>N</th><th>Δ(S<sub>v</sub>)<sup>a</sup></th><th>RMS(S)</th><th>Mean (S)</th></tr></thead><tbody><tr><td>10 μm</td><td>ν<sub>3</sub>, ν<sub>1</sub>, ν<sub>2</sub> + ν<sub>3</sub> - ν<sub>2</sub></td><td>497</td><td>0.28 %</td><td>0.78%</td><td>0.26%</td></tr><tr><td>5 μm</td><td>ν<sub>1</sub> + ν<sub>3</sub>, 2ν<sub>3</sub></td><td>319</td><td>-0.04%</td><td>0.37%</td><td>-0.02%</td></tr></tbody></table>

2.3.1.2. <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O isotopologue. About thirty ozone spectra enriched with <sup>18</sup>O were recorded with the GSMA FTS spectrometer using different cell lengths, <sup>18</sup>O/<sup>16</sup>O oxygen isotopic mixtures, and different pressures varying from 4 to 20 Torr. The analyses of the spectra in the range between 900 and 3850 cm<sup>-1</sup> allowed Ref. [205] to extend substantially the information about ro-vibrational transitions and energy levels of the <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O isotopologue, belonging to the C<sub>5</sub> point group. The assignment and modeling have been carried out using EH and EDTM operators with the help of theoretical predictions of the band centers, rotational constants and some coupling parameters. The latter ones have been derived from an *ab initio* potential energy surface (PES) [210] using the MOL_CT code [214] in the standard format of the EH [194,215] of the S&MPO system. We fixed the coupling term values to the predicted ones for the complete polyads of observed bands below 2500 cm<sup>-1</sup> to characterize the intensity transfer among the observed bands. Above 2500 cm<sup>-1</sup>, our effective models include only those coupling terms, which correspond to the observed perturbations. In total, 9976 ro-vibrational transitions belonging to the 15 bands of <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O were assigned and modeled with average accuracy of the order of 10<sup>-3</sup> cm<sup>-1</sup>. The set of 7030 corresponding upper-state ro-vibrational energy levels were determined. Overall a line list of 49,148 transitions is provided for the HITRAN2020 database for 13 observed bands of <sup>16</sup>O<sup>16</sup>O<sup>18</sup>O

<footnote><sup>a</sup>relative deviations of sums of all line intensities for the range</footnote>
<table><caption>**Table 8**
HITRAN2020 ozone update summary: isotopologues ¹⁶O¹⁶O¹⁸O, ¹⁶O¹⁶O¹⁷O and ¹⁶O¹⁷O¹⁶O</caption><thead><tr><th>Isotopologue</th><th>Band</th><th>N</th><th>Region, cm<sup>-1</sup></th><th>S<sub>ν</sub>, cm·mol<sup>-1</sup></th></tr></thead><tbody><tr><td rowspan="10">¹⁶O¹⁶O¹⁸O</td><td>001-000</td><td>3694</td><td>961.88-1117.65</td><td>5.122E-20</td></tr><tr><td>100-000</td><td>7216</td><td>973.69-1187.47</td><td>4.017E-21</td></tr><tr><td>020-000</td><td>505</td><td>1342.89-1398.80</td><td>7.706E-25</td></tr><tr><td>011-000</td><td>2474</td><td>1644.36-1720.54</td><td>2.033E-22</td></tr><tr><td>110-000</td><td>4188</td><td>1663.38-1894.67</td><td>6.376E-23</td></tr><tr><td>002-000</td><td>8149</td><td>1897.41-2113.39</td><td>6.941E-22</td></tr><tr><td>101-000</td><td>3468</td><td>2017.37-2113.59</td><td>3.889E-21</td></tr><tr><td>200-000</td><td>8635</td><td>2063.76-2274.12</td><td>2.354E-22</td></tr><tr><td>111-000</td><td>1910</td><td>2701.72-2767.50</td><td>9.528E-23</td></tr><tr><td>111-010</td><td>2166</td><td>2015.15-2084.74</td><td>3.835E-27</td></tr><tr><td rowspan="5">¹⁶O¹⁶O¹⁷O</td><td>003-000</td><td>1562</td><td>2930.52-3011.53</td><td>4.316E-22</td></tr><tr><td>102-000</td><td>3241</td><td>2965.77-3123.18</td><td>1.221E-22</td></tr><tr><td>201-000</td><td>1940</td><td>3103.03-3164.88</td><td>3.782E-23</td></tr><tr><td>Total</td><td>49148</td><td>961.88-3164.88</td><td>6.101E-20</td></tr><tr><td>101-000</td><td>2135</td><td>2045.82-2121.62</td><td>6.078E-22</td></tr><tr><td rowspan="4">¹⁶O¹⁷O¹⁶O</td><td>001-000</td><td>1157</td><td>968.30-1054.70</td><td>4.857E-21</td></tr><tr><td>100-000</td><td>107</td><td>1082.60-1124.24</td><td>3.571E-23</td></tr><tr><td>101-000</td><td>820</td><td>2029.66-2101.31</td><td>2.674E-22</td></tr><tr><td>Total</td><td>2084</td><td>968.30-2101.31</td><td>5.160E-21</td></tr></tbody></table>

up to $\Delta\nu = 3$. The corresponding information is summarized in Table 8.

### 2.3.1.3. ¹⁶O¹⁶O¹⁷O and ¹⁶O¹⁷O¹⁶O isotopologues.
The 5- and 10-μm ranges of the ¹⁷O-substituted ozone isotopologue were reinvestigated using GSMA Fourier spectra. The line positions for 15 transitions in the $\nu_3$ band in HITRAN2016 data for the ¹⁶O¹⁷O¹⁶O isotopomer were shifted by an order of $10^{-3}$ cm$^{-1}$ with respect to the experimental spectrum. The spectral line parameters for this isotopic species have been available in the HITRAN database for almost two decades: the $\nu_1$ and $\nu_3$ bands from Ref. [216] and $\nu_1 + \nu_3$ from Ref. [217]. In these calculations, different parameters for the ground state have been used. In Ref. [204], the $\nu_1$, $\nu_3$ and $\nu_1 + \nu_3$ bands of the ¹⁶O¹⁷O¹⁶O isotopomer were modeled simultaneously to improve the parameters of the ground state energy level. The analysis of the $\nu_1 + \nu_3$ bands of ¹⁶O¹⁶O¹⁷O was also extended. The parameters allowed for the generation of new line lists in the corresponding spectral ranges (see Table 8).

### 2.3.2. O₃ DLR database

New mid-infrared ozone measurements in the range 600–1200 cm$^{-1}$ were carried out within the framework of the ESA project SEOM-IAS, ESA/AO/1-7566/13/I-BG. A detailed publication is in preparation [198]. The goal of this task was to resolve discrepancies in retrieved atmospheric ozone amount between observations in the mid-infrared (MIR) and ultraviolet (UV). An important output of this effort is the new data described in this section and in the section on UV absorption cross-sections for O₃ (see Section 3.2.1).

The new FTS transmittance measurements were carried out with a Bruker IFS 125 HR high resolution spectrometer in combination with a coolable four-window single-pass cell [218] of path-length 22.15 cm which was also used for the UV measurements utilizing a different window pair. The same four-window cell was used under reproducible conditions for both the UV and MIR measurements, and absorption spectra were recorded under sealed-off conditions. Ozone was prepared from O₂ in a silent discharge and purified and handled using procedures similar to those given in Ref. [219]. Because decomposition of ozone was negligible at the low temperatures considered, the sample number densities could be derived from absolute pressure and temperature measurements. The new measurements were recorded with high-column amounts and different temperatures (23 mbar at 293 K, 11 mbar at 234 K).

These measurements were combined with four previously published ambient temperature measurements [219] with lower column amount, which were complementary to the new measurements. The availability of a new multi-spectrum fitting tool (see Ref. [66] and reference cited therein) motivated re-analysis of the previous measurements and yielded improved results, especially when combined with the new measurements.

Four N₂-broadened and three O₂-broadened ozone measurements at ambient temperature from Ref. [219] were re-analyzed with the multi-spectrum fitting tool, also yielding air-broadening and shift parameters.

#### 2.3.2.1. Self-broadened spectra.
The primary goal of the line fitting was new line positions and intensities of the main isotopologue. The analysis has shown that for this purpose self-broadening and self speed-dependence have to be considered. All self-broadened spectra were analyzed simultaneously using multi-spectrum fitting. The initial guess was HITRAN2016. The measurements were individually frequency-calibrated against HITRAN2012 ozone line positions. Lines were fitted in the intensity range $1.0 \times 10^{-23}$ to $4.0 \times 10^{-20}$ cm/molecule with statistical line intensity uncertainties <10% for the weakest lines. The weaker lines are especially important for limb-sounding space instruments measuring ozone. An EH approach was applied to fit line positions and intensities of the fundamentals $\nu_1$ and $\nu_3$ simultaneously. Hot bands in the $\nu_3$ region were also considered in the intensity analysis. Using the parameters from this analysis, the line positions and intensities were calculated, avoiding extrapolation. The calculated data were used to replace the HITRAN2016 values. In the case of $\nu_2$, a scalar (1.014) was fitted to match HITRAN2016 intensities to the experimental ones. All $\nu_2$ intensities were replaced by scaled HITRAN2016 values. Experimental line positions for hot bands in the $\nu_3$ region were used in the database for isolated lines when the line intensity statistical error was less than 10% and the difference to the HITRAN2016 line position was less than $0.02 \text{ cm}^{-1}$. In the case of the most abundant isotopologue, and lines in the $\nu_3/\nu_1$ region where no predictions from the EH were available, the intensities were scaled by $(1.023+1.017)/2$. The two values were obtained by weighted fitting of the experimental line intensities against HITRAN for the $\nu_1$ and $\nu_3$ bands.

Data are given for three different regions: 700–800 cm$^{-1}$ ($\nu_2$), 980–1070 cm$^{-1}$ (mainly $\nu_3$), 1070–1180 cm$^{-1}$ (mainly $\nu_1$). Line positions and intensities of ozone isotopologues were fitted but not used for the final database. The isotopologue abundance differs from the natural abundance by more than 10% due to the kinetics in the ozone production in the silent discharge. Therefore, no reliable line intensities were available from the line fitting.

Previous sections already implied an excellent agreement of both DLR and Janssen et al. [196,197] with S&MPO data, and there is naturally an excellent agreement between these two experimental datasets. It should be noted that the DLR experimental data contain lines up to 100 times weaker than those of Janssen et al.

The measurement and line parameter databases can be downloaded from Ref. [220].

#### 2.3.2.2. N₂- and O₂-broadened spectra.
Ambient temperature N₂- and O₂-broadened spectra were presented and analyzed in Ref. [219]. The air-broadened values were taken from polynomial representations and the resulting air-broadening parameters are given in the editions HITRAN2004 (and with some corrections in HITRAN2008) through HITRAN2016. These measurements had considerable self-broadening contributions. The new measurements at high ozone pressure together with the old pure ozone measurements allowed for the determination of the self-broadening parameters to be more accurate than in the old analysis. The multi-spectrum fitting was thus applied for the N₂- and O₂-broadened
<table><caption>**Table 8**
HITRAN2020 ozone update summary: isotopologues ¹⁶O¹⁶O¹⁸O, ¹⁶O¹⁶O¹⁷O and ¹⁶O¹⁷O¹⁶O</caption><thead><tr><th>Isotopologue</th><th>Band</th><th>N</th><th>Region, cm<sup>-1</sup></th><th>S<sub>ν</sub>, cm·mol<sup>-1</sup></th></tr></thead><tbody><tr><td rowspan="10">¹⁶O¹⁶O¹⁸O</td><td>001-000</td><td>3694</td><td>961.88-1117.65</td><td>5.122E-20</td></tr><tr><td>100-000</td><td>7216</td><td>973.69-1187.47</td><td>4.017E-21</td></tr><tr><td>020-000</td><td>505</td><td>1342.89-1398.80</td><td>7.706E-25</td></tr><tr><td>011-000</td><td>2474</td><td>1644.36-1720.54</td><td>2.033E-22</td></tr><tr><td>110-000</td><td>4188</td><td>1663.38-1894.67</td><td>6.376E-23</td></tr><tr><td>002-000</td><td>8149</td><td>1897.41-2113.39</td><td>6.941E-22</td></tr><tr><td>101-000</td><td>3468</td><td>2017.37-2113.59</td><td>3.889E-21</td></tr><tr><td>200-000</td><td>8635</td><td>2063.76-2274.12</td><td>2.354E-22</td></tr><tr><td>111-000</td><td>1910</td><td>2701.72-2767.50</td><td>9.528E-23</td></tr><tr><td>111-010</td><td>2166</td><td>2015.15-2084.74</td><td>3.835E-27</td></tr><tr><td rowspan="5">¹⁶O¹⁶O¹⁷O</td><td>003-000</td><td>1562</td><td>2930.52-3011.53</td><td>4.316E-22</td></tr><tr><td>102-000</td><td>3241</td><td>2965.77-3123.18</td><td>1.221E-22</td></tr><tr><td>201-000</td><td>1940</td><td>3103.03-3164.88</td><td>3.782E-23</td></tr><tr><td>Total</td><td>49148</td><td>961.88-3164.88</td><td>6.101E-20</td></tr><tr><td>101-000</td><td>2135</td><td>2045.82-2121.62</td><td>6.078E-22</td></tr><tr><td rowspan="4">¹⁶O¹⁷O¹⁶O</td><td>001-000</td><td>1157</td><td>968.30-1054.70</td><td>4.857E-21</td></tr><tr><td>100-000</td><td>107</td><td>1082.60-1124.24</td><td>3.571E-23</td></tr><tr><td>101-000</td><td>820</td><td>2029.66-2101.31</td><td>2.674E-22</td></tr><tr><td>Total</td><td>2084</td><td>968.30-2101.31</td><td>5.160E-21</td></tr></tbody></table>

up to $\Delta\nu = 3$. The corresponding information is summarized in Table 8.

### 2.3.1.3. ¹⁶O¹⁶O¹⁷O and ¹⁶O¹⁷O¹⁶O isotopologues.
The 5- and 10-μm ranges of the ¹⁷O-substituted ozone isotopologue were reinvestigated using GSMA Fourier spectra. The line positions for 15 transitions in the $\nu_3$ band in HITRAN2016 data for the ¹⁶O¹⁷O¹⁶O isotopomer were shifted by an order of $10^{-3}$ cm$^{-1}$ with respect to the experimental spectrum. The spectral line parameters for this isotopic species have been available in the HITRAN database for almost two decades: the $\nu_1$ and $\nu_3$ bands from Ref. [216] and $\nu_1 + \nu_3$ from Ref. [217]. In these calculations, different parameters for the ground state have been used. In Ref. [204], the $\nu_1$, $\nu_3$ and $\nu_1 + \nu_3$ bands of the ¹⁶O¹⁷O¹⁶O isotopomer were modeled simultaneously to improve the parameters of the ground state energy level. The analysis of the $\nu_1 + \nu_3$ bands of ¹⁶O¹⁶O¹⁷O was also extended. The parameters allowed for the generation of new line lists in the corresponding spectral ranges (see Table 8).

### 2.3.2. O₃ DLR database

New mid-infrared ozone measurements in the range 600–1200 cm$^{-1}$ were carried out within the framework of the ESA project SEOM-IAS, ESA/AO/1-7566/13/I-BG. A detailed publication is in preparation [198]. The goal of this task was to resolve discrepancies in retrieved atmospheric ozone amount between observations in the mid-infrared (MIR) and ultraviolet (UV). An important output of this effort is the new data described in this section and in the section on UV absorption cross-sections for O$_3$ (see Section 3.2.1).

The new FTS transmittance measurements were carried out with a Bruker IFS 125 HR high resolution spectrometer in combination with a coolable four-window single-pass cell [218] of path-length 22.15 cm which was also used for the UV measurements utilizing a different window pair. The same four-window cell was used under reproducible conditions for both the UV and MIR measurements, and absorption spectra were recorded under sealed-off conditions. Ozone was prepared from O$_2$ in a silent discharge and purified and handled using procedures similar to those given in Ref. [219]. Because decomposition of ozone was negligible at the low temperatures considered, the sample number densities could be derived from absolute pressure and temperature measurements. The new measurements were recorded with high-column amounts and different temperatures (23 mbar at 293 K, 11 mbar at 234 K).

These measurements were combined with four previously published ambient temperature measurements [219] with lower column amount, which were complementary to the new measurements. The availability of a new multi-spectrum fitting tool (see Ref. [66] and reference cited therein) motivated re-analysis of the previous measurements and yielded improved results, especially when combined with the new measurements.

Four N$_2$-broadened and three O$_2$-broadened ozone measurements at ambient temperature from Ref. [219] were re-analyzed with the multi-spectrum fitting tool, also yielding air-broadening and shift parameters.

#### 2.3.2.1. Self-broadened spectra.
The primary goal of the line fitting was new line positions and intensities of the main isotopologue. The analysis has shown that for this purpose self-broadening and self speed-dependence have to be considered. All self-broadened spectra were analyzed simultaneously using multi-spectrum fitting. The initial guess was HITRAN2016. The measurements were individually frequency-calibrated against HITRAN2012 ozone line positions. Lines were fitted in the intensity range $1.0 \times 10^{-23}$ to $4.0 \times 10^{-20}$ cm/molecule with statistical line intensity uncertainties <10% for the weakest lines. The weaker lines are especially important for limb-sounding space instruments measuring ozone. An EH approach was applied to fit line positions and intensities of the fundamentals $\nu_1$ and $\nu_3$ simultaneously. Hot bands in the $\nu_3$ region were also considered in the intensity analysis. Using the parameters from this analysis, the line positions and intensities were calculated, avoiding extrapolation. The calculated data were used to replace the HITRAN2016 values. In the case of $\nu_2$, a scalar (1.014) was fitted to match HITRAN2016 intensities to the experimental ones. All $\nu_2$ intensities were replaced by scaled HITRAN2016 values. Experimental line positions for hot bands in the $\nu_3$ region were used in the database for isolated lines when the line intensity statistical error was less than 10% and the difference to the HITRAN2016 line position was less than $0.02 \text{ cm}^{-1}$. In the case of the most abundant isotopologue, and lines in the $\nu_3/\nu_1$ region where no predictions from the EH were available, the intensities were scaled by $(1.023+1.017)/2$. The two values were obtained by weighted fitting of the experimental line intensities against HITRAN for the $\nu_1$ and $\nu_3$ bands.

Data are given for three different regions: 700–800 cm$^{-1}$ ($\nu_2$), 980–1070 cm$^{-1}$ (mainly $\nu_3$), 1070–1180 cm$^{-1}$ (mainly $\nu_1$). Line positions and intensities of ozone isotopologues were fitted but not used for the final database. The isotopologue abundance differs from the natural abundance by more than 10% due to the kinetics in the ozone production in the silent discharge. Therefore, no reliable line intensities were available from the line fitting.

Previous sections already implied an excellent agreement of both DLR and Janssen et al. [196,197] with S&MPO data, and there is naturally an excellent agreement between these two experimental datasets. It should be noted that the DLR experimental data contain lines up to 100 times weaker than those of Janssen et al.

The measurement and line parameter databases can be downloaded from Ref. [220].

#### 2.3.2.2. N$_2$- and O$_2$-broadened spectra.
Ambient temperature N$_2$- and O$_2$-broadened spectra were presented and analyzed in Ref. [219]. The air-broadened values were taken from polynomial representations and the resulting air-broadening parameters are given in the editions HITRAN2004 (and with some corrections in HITRAN2008) through HITRAN2016. These measurements had considerable self-broadening contributions. The new measurements at high ozone pressure together with the old pure ozone measurements allowed for the determination of the self-broadening parameters to be more accurate than in the old analysis. The multi-spectrum fitting was thus applied for the N$_2$- and O$_2$-broadened
measurements using the new self-broadening data to determine N₂- and O₂-broadening parameters on an individual line basis. In case of the weaker v₁ and v₂ bands, the data were too noisy but still confirmed the validity of the polynomials mentioned above. For the stronger v₃ band, more accurate values are available. As in Ref. [219], a simple Voigt profile was used, neglecting speed dependence. Air-broadening parameters were calculated for the strong lines in the v₃ region when the statistical uncertainty for the N₂- and O₂-broadening parameter was better than 4% and 8%, respectively.

N₂- and O₂-pressure shifts were obtained for several lines in the v₃ region. Since absolute frequencies were not available, the shifts were calibrated with the accurate shifts of two lines determined by Minissale et al. [221]. Among the eight lines where Minissale et al. determined air-pressure shifts, two were also available in the DLR data set with sufficient precision. The calibration is accurate to 0.00024 cm⁻¹/ atm. A second-order polynomial in γ₀,air was found to be a reasonable representation of the shifts. In the case where the N₂- and O₂-pressure shifts both had smaller statistical uncertainties than 0.001 cm⁻¹/ atm, their resulting air shift was added into the database. For all other transitions in the v₃ fundamental, the value calculated from the polynomial was entered.

### 2.3.2.3. Error considerations.
Line position accuracy is the same as for HITRAN2012 through HITRAN2016 given for most lines (10⁻⁴–10⁻³ cm⁻¹). For line intensity, several error sources have to be considered: number density, absorption path, temperature, instrumental line shape, line model, EH approach. The excellent agreement with Janssen et al. data validates overall accuracy <1% for at least the stronger lines. Definitely, the integrated band intensities have accuracies <1% too. From comparison of experimental and predicted line intensities, it was assumed that for lines with intensities >3×10⁻²³ the error was <1%. Since the v₂ band has no Coriolis perturbation in contrast to the v₁/v₃ pair, the relative intensities in the v₂ band in HITRAN2016 should be better than 1% for lines >3×10⁻²³. All new EH approach predictions in the v₁/v₃ band <3×10⁻²³, and the v₂ HITRAN2016 intensities <3,×10⁻²³ were assigned 1–2% errors. For all other lines in the v₁/v₃ region, which are scaled HITRAN2016, the error was set to 2–5%.

The error for γ₀,air in HITRAN2016 for lines based on the polynomial representation of Ref. [219] was 2–5%. The same error was given for the new data. It should be noted that this error bar is quite conservative and includes statistical and systematic uncertainties. Due to ignoring speed dependence, the broadening could be systematically too small by ~2%.

For all lines in the v₃ band, where the air shift was updated, an error of 10⁻⁴ to 10⁻³ cm⁻¹/ atm was estimated.

### 2.3.3. O₃ UCL line intensities

A synthetic line list calculated at University College London (UCL) for the principle isotopologue of ozone has been recently presented in Ref. [222]. Variational calculation using a semi-empirical PES [223] and ab initio DMS [211] produced very accurate values for the line intensities for the intense cold bands v₁ and v₁ + v₃ as compared to recent measurements performed in LERMA [196,197], respectively, at 10 and 5 µm. However, variational line positions are far away from their experimental values and complete assignment of rotational and vibrational quantum numbers are missing from the variationally calculated line list. Corrections for intensities distorted by resonances in the variational calculation with ab initio DMS due to the artificial intensitystealing has been developed and applied [222]. When resonances occur between levels, the distribution of the line intensities between the transitions involving the resonant levels is often incorrectly represented in variational calculations [115], but the sum of intensities is correct. As a consequence, based on the sum of variation-

ally calculated intensities, the distribution has been corrected using the intensity distribution from HITRAN2016 for the transitions involved.

In the work of Ref. [222], the complementary nature of EH models used in HITRAN2016 [16] (with full vibrational and rotational assignment and accurate line positions) and variational calculated intensities has been used to generate a line list between 0 and 4930 cm⁻¹ for the main isotopologue. Only transitions with an intensity cutoff of 10⁻²⁴ cm/molecule at 296 K and with J values below 60 have been generated. Note that for 5% of the transitions generated for the line list (77,819 total transitions), the variationally-calculated intensities were corrected using the intensity distribution from HITRAN2016.

As already noted, the variationally-calculated line intensities have been found to be in very good agreement with recent measurements [196,197] at 10 and 5 µm: sub-percent average discrepancies (as well as sub-percent standard deviation associated with the averages values) are reached for the v₁ and v₁ + v₃ bands for 476 and 316 common transitions respectively. The whole comparison file is available as supplemental data to Ref. [222]. An interesting case has been noticed concerning the 2v₁–v₃ band in the 10-µm region. Indeed for this band, the average deviation between variational and HITRAN2016 intensities reaches 28% whereas recent measurements from Birk et al. [220] leads to intensities in better agreement with the variational calculation (average deviation 5.2%). In this region HITRAN2016 is based on the EH model from Flaud et al. [224] constructed when no measurements were available for this band. When accounting for the recent measurements by Birk et al. [220] in an EH model, the average discrepancy between the variationally calculated intensities and the EH calculated intensities from Flaud [225] (that were ultimately employed in HITRAN2020) is 3.3% (with a standard deviation of 2.1%). The 2v₁–v₃ band provides another example that variationally-calculated intensities could provide a better alternative for the bands where no reliable experimental or semi-empirical information exists.

In order to be tested against atmospheric validations, a HITRAN2016 type line list has been generated where HITRAN2016 line intensities were replaced by the variationally calculated ones (eventually corrected as discussed in Ref. [222]) for transitions presented in Ref. [222].

### 2.3.4. O₃ atmospheric validations and choices for HITRAN2020

The three line lists presented above were rigorously validated against laboratory, TCCON, and balloon spectra by Toon [226]. The quality was assessed based on minimal RMS in selected spectral windows and consistency of the amount of ozone from window to window. It is important to stress again that not only intensities are different in the new line lists. With respect to HITRAN2016, the S&MPO line list contains new bands, updated line positions and intensities for four isotopologues, including the principal isotopologue; however line-shape parameters are the same as in HITRAN2016. It is the most complete list and yields the most consistent retrieved amount of ozone over all spectral windows. It is therefore used as a base line list for HITRAN2020, with parts of it being replaced, where appropriate, with other line lists based on the atmospheric validations. The DLR line list contains new line positions, intensities and line-shape parameters; however the isotopologue information is that from HITRAN2016. The UCL line list contains only new intensity information. It was found that in overlapping spectral ranges in most cases all three line lists supersede the HITRAN2016 line list in quality. An exception is only the region of the v₂ fundamental, where the intensities in the S&MPO and UCL line lists seem to be inferior to those in HITRAN2016 and especially the DLR line list. Based on the validations presented in Ref. [226] and findings in Ref. [200], the following wavenumber-
measurements using the new self-broadening data to determine N₂- and O₂-broadening parameters on an individual line basis. In case of the weaker v₁ and v₂ bands, the data were too noisy but still confirmed the validity of the polynomials mentioned above. For the stronger v₃ band, more accurate values are available. As in Ref. [219], a simple Voigt profile was used, neglecting speed dependence. Air-broadening parameters were calculated for the strong lines in the v₃ region when the statistical uncertainty for the N₂- and O₂-broadening parameter was better than 4% and 8%, respectively.

N₂- and O₂-pressure shifts were obtained for several lines in the v₃ region. Since absolute frequencies were not available, the shifts were calibrated with the accurate shifts of two lines determined by Minissale et al. [221]. Among the eight lines where Minissale et al. determined air-pressure shifts, two were also available in the DLR data set with sufficient precision. The calibration is accurate to 0.00024 cm⁻¹/ atm. A second-order polynomial in γ₀,air was found to be a reasonable representation of the shifts. In the case where the N₂- and O₂-pressure shifts both had smaller statistical uncertainties than 0.001 cm⁻¹/ atm, their resulting air shift was added into the database. For all other transitions in the v₃ fundamental, the value calculated from the polynomial was entered.

#### 2.3.2.3. Error considerations.
Line position accuracy is the same as for HITRAN2012 through HITRAN2016 given for most lines (10⁻⁴–10⁻³ cm⁻¹). For line intensity, several error sources have to be considered: number density, absorption path, temperature, instrumental line shape, line model, EH approach. The excellent agreement with Janssen et al. data validates overall accuracy <1% for at least the stronger lines. Definitely, the integrated band intensities have accuracies <1% too. From comparison of experimental and predicted line intensities, it was assumed that for lines with intensities >3×10⁻²³ the error was <1%. Since the v₂ band has no Coriolis perturbation in contrast to the v₁/v₃ pair, the relative intensities in the v₂ band in HITRAN2016 should be better than 1% for lines >3×10⁻²³. All new EH approach predictions in the v₁/v₃ band <3×10⁻²³, and the v₂ HITRAN2016 intensities <3,×10⁻²³ were assigned 1–2% errors. For all other lines in the v₁/v₃ region, which are scaled HITRAN2016, the error was set to 2–5%.

The error for γ₀,air in HITRAN2016 for lines based on the polynomial representation of Ref. [219] was 2–5%. The same error was given for the new data. It should be noted that this error bar is quite conservative and includes statistical and systematic uncertainties. Due to ignoring speed dependence, the broadening could be systematically too small by ~2%.

For all lines in the v₃ band, where the air shift was updated, an error of 10⁻⁴ to 10⁻³ cm⁻¹/ atm was estimated.

### 2.3.3. O₃ UCL line intensities

A synthetic line list calculated at University College London (UCL) for the principle isotopologue of ozone has been recently presented in Ref. [222]. Variational calculation using a semi-empirical PES [223] and ab initio DMS [211] produced very accurate values for the line intensities for the intense cold bands v₁ and v₁ + v₃ as compared to recent measurements performed in LERMA [196,197], respectively, at 10 and 5 µm. However, variational line positions are far away from their experimental values and complete assignment of rotational and vibrational quantum numbers are missing from the variationally calculated line list. Corrections for intensities distorted by resonances in the variational calculation with ab initio DMS due to the artificial intensitystealing has been developed and applied [222]. When resonances occur between levels, the distribution of the line intensities between the transitions involving the resonant levels is often incorrectly represented in variational calculations [115], but the sum of intensities is correct. As a consequence, based on the sum of variation-

ally calculated intensities, the distribution has been corrected using the intensity distribution from HITRAN2016 for the transitions involved.

In the work of Ref. [222], the complementary nature of EH models used in HITRAN2016 [16] (with full vibrational and rotational assignment and accurate line positions) and variational calculated intensities has been used to generate a line list between 0 and 4930 cm⁻¹ for the main isotopologue. Only transitions with an intensity cutoff of 10⁻²⁴ cm/molecule at 296 K and with J values below 60 have been generated. Note that for 5% of the transitions generated for the line list (77,819 total transitions), the variationally-calculated intensities were corrected using the intensity distribution from HITRAN2016.

As already noted, the variationally-calculated line intensities have been found to be in very good agreement with recent measurements [196,197] at 10 and 5 µm: sub-percent average discrepancies (as well as sub-percent standard deviation associated with the averages values) are reached for the v₁ and v₁ + v₃ bands for 476 and 316 common transitions respectively. The whole comparison file is available as supplemental data to Ref. [222]. An interesting case has been noticed concerning the 2v₁–v₃ band in the 10-µm region. Indeed for this band, the average deviation between variational and HITRAN2016 intensities reaches 28% whereas recent measurements from Birk et al. [220] leads to intensities in better agreement with the variational calculation (average deviation 5.2%). In this region HITRAN2016 is based on the EH model from Flaud et al. [224] constructed when no measurements were available for this band. When accounting for the recent measurements by Birk et al. [220] in an EH model, the average discrepancy between the variationally calculated intensities and the EH calculated intensities from Flaud [225] (that were ultimately employed in HITRAN2020) is 3.3% (with a standard deviation of 2.1%). The 2v₁–v₃ band provides another example that variationally-calculated intensities could provide a better alternative for the bands where no reliable experimental or semi-empirical information exists.

In order to be tested against atmospheric validations, a HITRAN2016 type line list has been generated where HITRAN2016 line intensities were replaced by the variationally calculated ones (eventually corrected as discussed in Ref. [222]) for transitions presented in Ref. [222].

### 2.3.4. O₃ atmospheric validations and choices for HITRAN2020

The three line lists presented above were rigorously validated against laboratory, TCCON, and balloon spectra by Toon [226]. The quality was assessed based on minimal RMS in selected spectral windows and consistency of the amount of ozone from window to window. It is important to stress again that not only intensities are different in the new line lists. With respect to HITRAN2016, the S&MPO line list contains new bands, updated line positions and intensities for four isotopologues, including the principal isotopologue; however line-shape parameters are the same as in HITRAN2016. It is the most complete list and yields the most consistent retrieved amount of ozone over all spectral windows. It is therefore used as a base line list for HITRAN2020, with parts of it being replaced, where appropriate, with other line lists based on the atmospheric validations. The DLR line list contains new line positions, intensities and line-shape parameters; however the isotopologue information is that from HITRAN2016. The UCL line list contains only new intensity information. It was found that in overlapping spectral ranges in most cases all three line lists supersede the HITRAN2016 line list in quality. An exception is only the region of the v₂ fundamental, where the intensities in the S&MPO and UCL line lists seem to be inferior to those in HITRAN2016 and especially the DLR line list. Based on the validations presented in Ref. [226] and findings in Ref. [200], the following wavenumber-
<figure><img src="image_17.png" /><figcaption>**Fig. 13.** Volume mixing ratio scaling factors (VSF) obtained in different IR spectral windows from the analyses of the FTS spectra from Kitt Peak laboratory. The absolute values are not definitive as it is hard to control the partial pressure of ozone in the cell. Note the much improved consistency of the retrieved amount of ozone in 5 and 10 µm regions.</figcaption></figure>

dependent selections have been made for the MW-IR transitions of ozone:

1. In the region of pure rotational transitions of all HITRAN isotopologues of ozone, the values from the JPL catalogue [227] were chosen. To take advantage of increased precision of MW transitions, it should be noted that the wavenumber format for ozone in the traditional “.par” format has been updated to F12.9 for transitions below 1.0 cm⁻¹, F12.8 for transitions 1.0–10.0 cm⁻¹, and F12.7 for transitions 10.0–100.0 cm⁻¹ (as previously implemented for HNO₃, PH₃, O₂ and NO⁺).

2. Between 280 and 600 cm⁻¹ the HITRAN2016 line list is retained for HITRAN2020.

3. Between 600 and 1180 cm⁻¹ the DLR line list is used.

4. Above 1180 cm⁻¹ and up to 5791 cm⁻¹ the new S&MPO line list is used except for the 2975–3205 cm⁻¹ region, where the RMS of the UCL line list are the lowest. Therefore in that window the UCL line list is used. However, one should be aware that the retrieved amount of ozone with the latter list is noticeably lower compared to other regions.

5. Above 5791 cm⁻¹ the HITRAN2016 line list is retained for HITRAN2020.

Fig. 13 demonstrates the improved consistency in the ozone amounts retrieved from the Kitt Peak laboratory spectra in the 5- and 10-µm regions.

## 2.4. N₂O: nitrous oxide (molecule 4)

Due to its prominent presence in the terrestrial atmosphere, nitrous oxide (N₂O) has been the subject of many spectroscopic studies in different spectral ranges, enabling the remote-sensing measurements of N₂O concentrations. In HITRAN2020, intensities of the NIR bands have been updated, while a complete overhaul of the line-shape parameters has been carried out.

### 2.4.1. N₂O intensities in NIR

An update to the near-infrared N₂O line intensities has been performed based upon recent frequency-agile, rapid-scanning cavity ring-down spectroscopy measurements of the 4200–0000 and 5000–0000 bands near 1.6 µm [228]. A band-wide fit of these measurements has allowed for the range of |*m*| included for these bands to be increased from |*m*| ≤ 46 to |*m*| ≤ 85. Furthermore, these measurements led to combined standard uncertainties near

1%, which is roughly a factor of five lower than the values found in HITRAN2016 [16], which were based on measurements from Toth [229]. We note that these new measurements (and hence HITRAN2020 intensity values for these bands) are roughly 5% greater than the values found in HITRAN2016 [16]. With that being said, good agreement was observed with the Fourier-transform spectroscopy measurements of Daumont et al. [230].

### 2.4.2. N₂O line shapes

In the description of the atmospheric retrievals by ACE-FTS (Atmospheric Chemistry Experiment–Fourier transform spectrometer), Boone et al. [231] have stressed the need for a revision of line-shape parameters for certain bands in HITRAN and the importance of including the non-Voigt parameters. This issue has been attended in the 2020 edition of the database, where we updated the N₂O-air and N₂O-N₂O line-shape parameters using the Voigt and speed-dependent Voigt parameters, including the first-order line-mixing parameters [232] as presented in Table 3 of Section 2.2.

In updating the line-shape parameters of N₂O, we used the approach similar to the one used for updating the line-shape parameters of CO₂. This approach enabled providing both Voigt and the speed-dependent Voigt parameters (including first order line-mixing) for each transition (see Ref. [233] for more details).

The air- and self-broadening parameters (using VP), their temperature dependence, and the pressure shifts of N₂O in the HITRAN2016 database were based on the earlier studies from Refs. [234–237]. The vibrational dependence of the line widths was assumed negligible. The parameters were revised based on the recent high-quality experimental data from Adkins et al. [228]. The new NIST spectroscopic parameters were measured in the near-IR region for the 4200–0000 and 5000–0000 bands obtained using their Multi-spectrum Analysis Tool for Spectroscopy (MATS) [238] using the line-shape functions defined in HAPI. The non-measured transitions were given an approximated value, estimated from the results reported in Ref. [233], where the Padé approximant functions (Eq. (1)) were applied as a smoothing function over the measured transitions and extrapolated to the higher *J* lines in all the bands. The reported error codes for the measured lines correspond to the combined error type A (statistical) and B (systematic) error in the measurement. The temperature exponents of the air-broadening parameters were also updated using the Padé approximants fit to the data from Ref. [236]. For the self-broadening (VP) parameters, there were not many measurements of N₂O available in the literature. In HITRAN2016, these values were produced from the study by Toth [235]. For HITRAN2020, a fit of the recent measurement of γ₀-self half-widths by Werwein et al. [239] for the 0002–0000 band was used to extrapolate the results for all the transitions in all the bands [233].

The speed-dependent parameters were not provided in HITRAN2016 except for the ν₃ band of N₂O-air [240], which were obtained from a multi-spectrum fit of FTS measurements. Note that these parameters were present under the HT profile parametrization in the HITRAN2016 edition. We used the air-broadened parameters measured by NIST [228] for the 5000–0000 band and expanded them for all the bands except for the ν₃ band, where the data from Ref. [240] were used for updating the air-broadening, air speed-dependence of width, air-shift, and the first-order line-mixing parameter for the measured transitions. Based on the uncertainties of the parameters reported by NIST, in smoothing the collisional air-broadening (for the SDV) and air-speed-dependence, only data with |*m*| ≤ 40 were included in the fit. For the temperature dependence of the air-broadening, we used Ref. [233] data to produce the temperature exponent for the SDV line widths. Also, in the absence of the measurement of the temperature exponent of γ₂ (i.e., nγ₂), the predicted ones for the half-width parameters were used.
<figure><img src="image_15.png" /><figcaption>**Fig. 13.** Volume mixing ratio scaling factors (VSF) obtained in different IR spectral windows from the analyses of the FTS spectra from Kitt Peak laboratory. The absolute values are not definitive as it is hard to control the partial pressure of ozone in the cell. Note the much improved consistency of the retrieved amount of ozone in 5 and 10 µm regions.</figcaption></figure>

dependent selections have been made for the MW-IR transitions of ozone:

1. In the region of pure rotational transitions of all HITRAN isotopologues of ozone, the values from the JPL catalogue [227] were chosen. To take advantage of increased precision of MW transitions, it should be noted that the wavenumber format for ozone in the traditional “.par” format has been updated to F12.9 for transitions below 1.0 cm⁻¹, F12.8 for transitions 1.0–10.0 cm⁻¹, and F12.7 for transitions 10.0–100.0 cm⁻¹ (as previously implemented for HNO₃, PH₃, O₂ and NO⁺).

2. Between 280 and 600 cm⁻¹ the HITRAN2016 line list is retained for HITRAN2020.

3. Between 600 and 1180 cm⁻¹ the DLR line list is used.

4. Above 1180 cm⁻¹ and up to 5791 cm⁻¹ the new S&MPO line list is used except for the 2975–3205 cm⁻¹ region, where the RMS of the UCL line list are the lowest. Therefore in that window the UCL line list is used. However, one should be aware that the retrieved amount of ozone with the latter list is noticeably lower compared to other regions.

5. Above 5791 cm⁻¹ the HITRAN2016 line list is retained for HITRAN2020.

Fig. 13 demonstrates the improved consistency in the ozone amounts retrieved from the Kitt Peak laboratory spectra in the 5- and 10-µm regions.

## 2.4. N₂O: nitrous oxide (molecule 4)

Due to its prominent presence in the terrestrial atmosphere, nitrous oxide (N₂O) has been the subject of many spectroscopic studies in different spectral ranges, enabling the remote-sensing measurements of N₂O concentrations. In HITRAN2020, intensities of the NIR bands have been updated, while a complete overhaul of the line-shape parameters has been carried out.

### 2.4.1. N₂O intensities in NIR

An update to the near-infrared N₂O line intensities has been performed based upon recent frequency-agile, rapid-scanning cavity ring-down spectroscopy measurements of the 4200–0000 and 5000–0000 bands near 1.6 µm [228]. A band-wide fit of these measurements has allowed for the range of |*m*| included for these bands to be increased from |*m*| ≤ 46 to |*m*| ≤ 85. Furthermore, these measurements led to combined standard uncertainties near

1%, which is roughly a factor of five lower than the values found in HITRAN2016 [16], which were based on measurements from Toth [229]. We note that these new measurements (and hence HITRAN2020 intensity values for these bands) are roughly 5% greater than the values found in HITRAN2016 [16]. With that being said, good agreement was observed with the Fourier-transform spectroscopy measurements of Daumont et al. [230].

### 2.4.2. N₂O line shapes

In the description of the atmospheric retrievals by ACE-FTS (Atmospheric Chemistry Experiment–Fourier transform spectrometer), Boone et al. [231] have stressed the need for a revision of line-shape parameters for certain bands in HITRAN and the importance of including the non-Voigt parameters. This issue has been attended in the 2020 edition of the database, where we updated the N₂O-air and N₂O-N₂O line-shape parameters using the Voigt and speed-dependent Voigt parameters, including the first-order line-mixing parameters [232] as presented in Table 3 of Section 2.2.

In updating the line-shape parameters of N₂O, we used the approach similar to the one used for updating the line-shape parameters of CO₂. This approach enabled providing both Voigt and the speed-dependent Voigt parameters (including first order line-mixing) for each transition (see Ref. [233] for more details).

The air- and self-broadening parameters (using VP), their temperature dependence, and the pressure shifts of N₂O in the HITRAN2016 database were based on the earlier studies from Refs. [234–237]. The vibrational dependence of the line widths was assumed negligible. The parameters were revised based on the recent high-quality experimental data from Adkins et al. [228]. The new NIST spectroscopic parameters were measured in the near-IR region for the 4200–0000 and 5000–0000 bands obtained using their Multi-spectrum Analysis Tool for Spectroscopy (MATS) [238] using the line-shape functions defined in HAPI. The non-measured transitions were given an approximated value, estimated from the results reported in Ref. [233], where the Padé approximant functions (Eq. (1)) were applied as a smoothing function over the measured transitions and extrapolated to the higher *J* lines in all the bands. The reported error codes for the measured lines correspond to the combined error type A (statistical) and B (systematic) error in the measurement. The temperature exponents of the air-broadening parameters were also updated using the Padé approximants fit to the data from Ref. [236]. For the self-broadening (VP) parameters, there were not many measurements of N₂O available in the literature. In HITRAN2016, these values were produced from the study by Toth [235]. For HITRAN2020, a fit of the recent measurement of γ₀-self half-widths by Werwein et al. [239] for the 0002–0000 band was used to extrapolate the results for all the transitions in all the bands [233].

The speed-dependent parameters were not provided in HITRAN2016 except for the ν₃ band of N₂O-air [240], which were obtained from a multi-spectrum fit of FTS measurements. Note that these parameters were present under the HT profile parametrization in the HITRAN2016 edition. We used the air-broadened parameters measured by NIST [228] for the 5000–0000 band and expanded them for all the bands except for the ν₃ band, where the data from Ref. [240] were used for updating the air-broadening, air speed-dependence of width, air-shift, and the first-order line-mixing parameter for the measured transitions. Based on the uncertainties of the parameters reported by NIST, in smoothing the collisional air-broadening (for the SDV) and air-speed-dependence, only data with |*m*| ≤ 40 were included in the fit. For the temperature dependence of the air-broadening, we used Ref. [233] data to produce the temperature exponent for the SDV line widths. Also, in the absence of the measurement of the temperature exponent of γ₂ (i.e., nγ₂), the predicted ones for the half-width parameters were used.
With a similar fitting approach, we produced the results for the γ₀-self and γ₂-self (for the SDV profile) parameters based on the high-accuracy measured self-broadening using a diode laser spectrometer in Ref. [241] for eight transitions in the 3ν₁ + 2ν₂ band, acquired at room-temperature. In Ref. [233], it is described how the γ₀-self and γ₂-self were generated for the lines where these parameters were not measured.

We used the method proposed by Hartmann [173], which was successfully tested for the CO₂-air and CO₂-CO₂ systems [161], to calculate the pressure shifts of the transitions of air- and self-broadened N₂O bands. Because there were not many measurements available for educating the model with the SDV and VP shifts for different bands, we used the same air- and self-shifts for the VP and SDV profiles to populate the database. The fitting coefficients were presented in Ref. [233]. >

The first-order line-mixing parameters of the N₂O lines were calculated using the Exponential Power Gap law (EPG) approximation [242] explained in Ref. [233] and provided for every transition in HITRAN separately for the VP and SDV profiles for N₂O broadened by air and N₂O [233]. It should be noted that the line-shape parameters were not updated for the ¹⁴N₃¹⁸O isotopologue in the HITRAN2020 line list because of the ambiguities in assignments for some of the NIR bands discussed in the HITRAN2016 paper.

HAPI was used to validate the results against the laboratory spectra. By taking into account the line-mixing effect, the absorption coefficient for the mixture of N₂O-air at specific temperature *T* and pressure *P* was obtained. Using the new NIST parameters led to improvements in calculating the spectra both for the VP and SDV profiles as shown in Ref. [233].

Finally, every transition of N₂O now has γH₂O and nH₂O parameters as described in Ref. [49].

### 2.4.3. N₂O in HITEMP

The addition of N₂O to HITEMP is described in Ref. [55]. This N₂O line list was based on the Nitrous Oxide Spectroscopic Data Bank at 1000 K (NOSD-1000) [243]. Comparisons to PNNL spectra [244] in the region of the 1000–0110 band of ¹⁴N₂O required a correction to the effective dipole moment used to calculate intensities for NOSD-1000 (see Fig. 1 of Ref. [55]). To create the line list for HITEMP, a recalculated version of the NOSD line list was then merged with the N₂O data in HITRAN2016 [16].

The N₂O line list was added to HITEMP prior to the updates for HITRAN2020 described in Sections 2.4.1 and 2.4.2. To maintain consistency, updates to HITRAN will be incorporated into HITEMP in due course. Readers should refer to Ref. [55] for a full description of the HITEMP line list for N₂O.

### 2.4.4. *Forthcoming updates*

In its present status, the HITRAN line list for N₂O has room for improvement above 8000 cm⁻¹. Data relative to the main isotopologue are limited to FTS data below 7796 cm⁻¹, mostly from the Toth database [229,245] and correspond to an intensity cutoff of 2×10⁻²⁵ cm/molecule at 296 K. The inclusion in the HITRAN dataset of the calculated line list of the ¹⁴N₃¹⁸O isotopologue from Ref. [246] with an intensity cutoff of 1×10⁻²⁹ cm/molecule leads to a somewhat unusual situation. In spite of it being only forth in abundance, ¹⁴N₂¹⁸O has the largest amount of transitions in the HITRAN N₂O list, extending up to 10,363 cm⁻¹, while many NIR bands of the principal isotopologue are missing. This situation was illustrated in a recent CRDS study in the 8325–8622 cm⁻¹ region where the HITRAN line list includes only ¹⁴N₃¹⁸O transitions (see Fig. 7 in Ref. [247]). In addition, there are no ¹⁴N¹⁵N¹⁶O and ¹⁵N¹⁴N¹⁶O transitions in the HITRAN and HITEMP lists (in the considered region) while the 4ν₃ band of the ¹⁴N¹⁵N¹⁶O isotopologue is dominant in the 8500–8550 cm⁻¹ interval. Fortunately, many of

these bands have been accurately measured in the recent literature, in particular by CRDS [245,248–256]. Spectroscopic data available in the literature will be gathered and critically evaluated in order to significantly extend and improve the N₂O lists of the first four isotopologues in the next editions of the HITRAN and HITEMP databases.

## 2.5. CO: carbon monoxide (molecule 5)

The HITRAN2016 [16] line list for carbon monoxide was based on the semi-empirical line list from Li et al. [257]. For the purpose of inclusion into HITRAN2016, the line list was truncated, and the line positions were replaced with updated calculation or state-of-the-art experimental data (see HITRAN2016 paper [16] for details). For the HITRAN2020 edition, the line positions have not been changed, but the intensity and line-shape data have been updated.

### 2.5.1. CO intensities

Intensities in Li et al. [257] were calculated using the piece-wise dipole moment function fitted to existing experimental and *ab initio* data. Therefore, it is not surprising that the values of the intensities are primarily driven by the quality of the experimental data used as input. Recent state-of-the-art experiments have either confirmed the quality of CO intensities in HITRAN or have issued recommendations for improvements.

Despite the fundamental band being by far the strongest band of CO, experimental and theoretical data for its intensities in the literature do not agree well. Devi et al. [258] found that the intensities of the principal isotopologue of CO in HITRAN differ by about two percent when compared to their measurements. For the HITRAN2020 edition, the intensities of the Δν = 1 transitions of all isotopologues of CO in HITRAN were reduced by 2% following the recommendation of Ref. [258]. In the meantime, it is highly desirable that more experiments are carried out in this band.

Intensities of the second overtone in Li et al. [257] were primarily driven by the experimental values reported in Ref. [259] with sub-percent uncertainty. Recently the authors of Ref. [259] revised their experimental procedure, and their new measurements [260] suggest that HITRAN2016 intensities in this band are underestimated by about 2.6%. This assessment was corroborated by independent FTS measurements by Borkov et al. [261]. Therefore, in the HITRAN2020 edition, the intensities of the Δν = 3 transitions of all isotopologues of CO in HITRAN were increased by 2.6%.

Another recent paper by Borkov et al. [262] is devoted to the third overtone of CO. There the authors find that although HITRAN intensities are within respective error bars, they may be systematically off by about 2%. However, an independent CRDS study by Bordet et al. [263] has confirmed HITRAN values for this band to be better than 1%. Therefore, the intensities in this band remain unchanged.

In the future, a better way to address the intensities in the fundamental and second overtone bands would be to refit the dipole moment function from Li et al. [257] with new experimental data and recalculate intensities. Ref. [257] notes that although their procedure should yield the same quality of results for all isotopologues (assuming no Born-Oppenheimer breakdown), comparisons with different experimental values yield different deviations for each of the six isotopologues. New experiments reported in Refs. [259,261–263] do not resolve this issue. One possible explanation is that none of the experiments had a way of measuring the relative abundance of isotopologues in the sample. Experiments with controlled abundance are highly desirable to resolve this issue.

### 2.5.2. CO line shapes

The line broadening and the pressure-shift parameters of transitions of CO perturbed by air and by CO itself have been re-
With a similar fitting approach, we produced the results for the γ₀-self and γ₂-self (for the SDV profile) parameters based on the high-accuracy measured self-broadening using a diode laser spectrometer in Ref. [241] for eight transitions in the 3ν₁ + 2ν₂ band, acquired at room-temperature. In Ref. [233], it is described how the γ₀-self and γ₂-self were generated for the lines where these parameters were not measured.

We used the method proposed by Hartmann [173], which was successfully tested for the CO₂-air and CO₂-CO₂ systems [161], to calculate the pressure shifts of the transitions of air- and self-broadened N₂O bands. Because there were not many measurements available for educating the model with the SDV and VP shifts for different bands, we used the same air- and self-shifts for the VP and SDV profiles to populate the database. The fitting coefficients were presented in Ref. [233]. >

The first-order line-mixing parameters of the N₂O lines were calculated using the Exponential Power Gap law (EPG) approximation [242] explained in Ref. [233] and provided for every transition in HITRAN separately for the VP and SDV profiles for N₂O broadened by air and N₂O [233]. It should be noted that the line-shape parameters were not updated for the ¹⁴N₃¹⁸O isotopologue in the HITRAN2020 line list because of the ambiguities in assignments for some of the NIR bands discussed in the HITRAN2016 paper.

HAPI was used to validate the results against the laboratory spectra. By taking into account the line-mixing effect, the absorption coefficient for the mixture of N₂O-air at specific temperature *T* and pressure *P* was obtained. Using the new NIST parameters led to improvements in calculating the spectra both for the VP and SDV profiles as shown in Ref. [233].

Finally, every transition of N₂O now has γH₂O and nH₂O parameters as described in Ref. [49].

### 2.4.3. N₂O in HITEMP

The addition of N₂O to HITEMP is described in Ref. [55]. This N₂O line list was based on the Nitrous Oxide Spectroscopic Data Bank at 1000 K (NOSD-1000) [243]. Comparisons to PNNL spectra [244] in the region of the 1000–0110 band of ¹⁴N₂O required a correction to the effective dipole moment used to calculate intensities for NOSD-1000 (see Fig. 1 of Ref. [55]). To create the line list for HITEMP, a recalculated version of the NOSD line list was then merged with the N₂O data in HITRAN2016 [16].

The N₂O line list was added to HITEMP prior to the updates for HITRAN2020 described in Sections 2.4.1 and 2.4.2. To maintain consistency, updates to HITRAN will be incorporated into HITEMP in due course. Readers should refer to Ref. [55] for a full description of the HITEMP line list for N₂O.

### 2.4.4. *Forthcoming updates*

In its present status, the HITRAN line list for N₂O has room for improvement above 8000 cm⁻¹. Data relative to the main isotopologue are limited to FTS data below 7796 cm⁻¹, mostly from the Toth database [229,245] and correspond to an intensity cutoff of 2×10⁻²⁵ cm/molecule at 296 K. The inclusion in the HITRAN dataset of the calculated line list of the ¹⁴N₃¹⁸O isotopologue from Ref. [246] with an intensity cutoff of 1×10⁻²⁹ cm/molecule leads to a somewhat unusual situation. In spite of it being only forth in abundance, ¹⁴N₂¹⁸O has the largest amount of transitions in the HITRAN N₂O list, extending up to 10,363 cm⁻¹, while many NIR bands of the principal isotopologue are missing. This situation was illustrated in a recent CRDS study in the 8325–8622 cm⁻¹ region where the HITRAN line list includes only ¹⁴N₃¹⁸O transitions (see Fig. 7 in Ref. [247]). In addition, there are no ¹⁴N¹⁵N¹⁶O and ¹⁵N¹⁴N¹⁶O transitions in the HITRAN and HITEMP lists (in the considered region) while the 4ν₃ band of the ¹⁴N¹⁵N¹⁶O isotopologue is dominant in the 8500–8550 cm⁻¹ interval. Fortunately, many of

these bands have been accurately measured in the recent literature, in particular by CRDS [245,248–256]. Spectroscopic data available in the literature will be gathered and critically evaluated in order to significantly extend and improve the N₂O lists of the first four isotopologues in the next editions of the HITRAN and HITEMP databases.

## 2.5. CO: carbon monoxide (molecule 5)

The HITRAN2016 [16] line list for carbon monoxide was based on the semi-empirical line list from Li et al. [257]. For the purpose of inclusion into HITRAN2016, the line list was truncated, and the line positions were replaced with updated calculation or state-of-the-art experimental data (see HITRAN2016 paper [16] for details). For the HITRAN2020 edition, the line positions have not been changed, but the intensity and line-shape data have been updated.

### 2.5.1. CO intensities

Intensities in Li et al. [257] were calculated using the piece-wise dipole moment function fitted to existing experimental and *ab initio* data. Therefore, it is not surprising that the values of the intensities are primarily driven by the quality of the experimental data used as input. Recent state-of-the-art experiments have either confirmed the quality of CO intensities in HITRAN or have issued recommendations for improvements.

Despite the fundamental band being by far the strongest band of CO, experimental and theoretical data for its intensities in the literature do not agree well. Devi et al. [258] found that the intensities of the principal isotopologue of CO in HITRAN differ by about two percent when compared to their measurements. For the HITRAN2020 edition, the intensities of the Δν = 1 transitions of all isotopologues of CO in HITRAN were reduced by 2% following the recommendation of Ref. [258]. In the meantime, it is highly desirable that more experiments are carried out in this band.

Intensities of the second overtone in Li et al. [257] were primarily driven by the experimental values reported in Ref. [259] with sub-percent uncertainty. Recently the authors of Ref. [259] revised their experimental procedure, and their new measurements [260] suggest that HITRAN2016 intensities in this band are underestimated by about 2.6%. This assessment was corroborated by independent FTS measurements by Borkov et al. [261]. Therefore, in the HITRAN2020 edition, the intensities of the Δν = 3 transitions of all isotopologues of CO in HITRAN were increased by 2.6%.

Another recent paper by Borkov et al. [262] is devoted to the third overtone of CO. There the authors find that although HITRAN intensities are within respective error bars, they may be systematically off by about 2%. However, an independent CRDS study by Bordet et al. [263] has confirmed HITRAN values for this band to be better than 1%. Therefore, the intensities in this band remain unchanged.

In the future, a better way to address the intensities in the fundamental and second overtone bands would be to refit the dipole moment function from Li et al. [257] with new experimental data and recalculate intensities. Ref. [257] notes that although their procedure should yield the same quality of results for all isotopologues (assuming no Born-Oppenheimer breakdown), comparisons with different experimental values yield different deviations for each of the six isotopologues. New experiments reported in Refs. [259,261–263] do not resolve this issue. One possible explanation is that none of the experiments had a way of measuring the relative abundance of isotopologues in the sample. Experiments with controlled abundance are highly desirable to resolve this issue.

### 2.5.2. CO line shapes

The line broadening and the pressure-shift parameters of transitions of CO perturbed by air and by CO itself have been re-
vised mainly based on a review performed in Ref. [233] on a variety of measurements. Compared to the HITRAN2016 line list, which included the speed-dependent parameters for only transitions of the 2–0 band (up to $J_{max}$ = 29), in the 2020 edition of the CO line list, every line includes the speed-dependent Voigt and the Rozenkranz line-mixing parameters [232] for both air- and self-broadened lines. The importance of including non-Voigt line shapes in atmospheric retrievals of CO has been highlighted by Hochstafff et al. [264,265]. Furthermore, the CO line-shape parameters for the important planetary broadeners such as CO-H₂, CO-He, and CO-CO₂ were revised [266], while parameters associated with broadening by H₂O were introduced for the first time as described in Ref. [49]. A summary of these modifications for the HITRAN2020 edition is given below:

### 1. The CO-air broadened parameters:

(a) For the air half-widths (the VP parameters), to evaluate the effect of vibration, the relative difference of the broadening parameters for various measured bands were calculated and the average difference was well below 1% for different band values. Therefore, the broadening parameters were considered to be vibrationally independent. Then, the Padé approximants model (Eq. (1)) was employed to fit all the measured air-broadening data for several bands, including Ref. [267] for the 1–0 band, Ref. [268] for the 2–0 band, and Ref. [269] for the 3–0 band simultaneously [233]. The fit coefficients are provided in Ref. [233] and the resulting broadening parameters were expanded to all the transitions of CO perturbed by air.

(b) The update of the speed-dependent Voigt line-shape parameters heavily relies on the semi-empirical Padé approximant fits to the experimental data of Ref. [270]. For the air broadening (the SDV parameters), and the temperature dependence of the air-broadening parameters, the 2–0 band data measured by Devi et al. [270] were used in the fit, and the approximated values from the model were expanded for lines of every band. The air speed dependence of line widths were fitted as well using the same data source, and the corresponding γ₂-air parameters were estimated and attributed to each transition. Wherever the measured SDV parameters were available, the original experimental results were used in populating the database. For instance, the Ref. [258] data were used for the lines of the 1–0 band and the measured parameters of Ref. [271] were used for updating the 2–0 band lines for different isotopologues of CO.

### 2. The CO-CO broadened parameters:

(a) To find the values for the self-broadened half-widths (using the VP) for the high-J transitions, the measurements for different bands were used (i.e., 1–0 band [272], 2–0 band [273–275], 3–0 band [276]). All these data were fitted simultaneously to estimate the self-broadening parameters for the lines that were not measured for all the bands except for the measured transitions in the 2–0 band, where the data from Ref. [273] were used for the update.

(b) The self-broadening parameters, their temperature exponents, and the speed-dependence of the broadening (the SDV profile parameters) were approximated using the measured line widths of Ref. [270] fitted to the Padé approximants model, and we imported the experimental values for different isotopologues reported in Refs. [258,271] for the 1–0 and 2–0 bands, respectively.

### 3. The CO-air and CO-CO pressure shifts:

The air and self shifts (for both VP and SDV) were calculated by employing the sophisticated vibrational-dependent approach of Hartmann [173] for all the transitions. The quality of the calculated shifts were validated by comparison of the shifts in dif-

ferent bands [233]. The measured air shifts for the transitions in the 1–0, 2–0, and 3–0 bands remained unchanged as they were reported in HITRAN2016. Also it should be emphasized that measured pressure self shifts of CO for the 1–0 [272], 2–0 [270], 3–0 [269] and 4–0 [263] bands were written into the database directly for the measured lines.

### 4. The CO-air and CO-CO first-order line-mixing:

The first-order line-mixing parameters were calculated based on the EPG formalism [242] using both the VP and SDV broadening parameters and provided for every transition. For the 2–0 band of the main isotopologue, the CO-air and CO-CO line-mixing were taken from the measurement of Ref. [270].

### 5. Planetary perturbers:

Broadening parameters due to pressure of “planetary” (H₂, CO₂, He) gases were first introduced in HITRAN in 2016, based on the procedure described by Li et al. [257]. In this edition we updated these parameters. For the update of the CO-H₂ broadening parameters and their temperature dependence, the data from Refs. [273,277] were taken into the semi-empirical fitting models [266] and the results were extrapolated for every CO line. The line-shape parameters of CO perturbed by helium were also modified, based on Refs. [278–282], and the CO₂ pressure broadening and the temperature dependence of the broadening parameters of CO were generated from extrapolating the data from Ref. [283]. Finally, the pressure shift parameters for all three broadeners of CO were obtained based on the Hartmann semi-classical routine [173] and the values agree well with the available experimental data [266].

## 2.6. CH₄: methane (molecule 6)

HITRAN2016 provided substantial improvements in methane spectroscopy (with respect to previous editions) in many spectral regions (see, for instance, the validation of the ACE-FTS experiment [76]). In general, the line positions and intensities were considerably improved, and the spectral coverage increased. Nevertheless, the spectroscopy of methane is still far from perfect. In this edition, several spectral regions have been improved. However, one of the largest issues that remain is the quality of the line shape parameters. In particular, the tetradecad region targeted by GOSAT and MethaneSat requires revision (as indicated, for instance, in Ref. [284]). A major global revision of the methane line shape parameters is currently underway for Voigt and speed-dependent Voigt parametrizations, as well as the inclusion of line-mixing parameters. At present, this work is still ongoing and will not form part of the current update for methane. The improvements for HITRAN2020 concern updating line-shapes of individual transitions where major issues have been identified. Nevertheless, several spectral regions have received significant updates and are described below.

### 2.6.1. 3760–4100 cm⁻¹

A new line list from Rodina et al. [285] was used to completely replace HITRAN data for the principal isotopologue in this spectral region. This line list is based on the analyses of the FTS experimental spectra recorded in Reims under different thermodynamic conditions. This line list improves the quality of spectroscopic parameters in this spectral region and contains assignments for all lines, enabling easier conversion between temperatures.

### 2.6.2. 4190–4315 cm⁻¹

This spectral region is important in remote sensing as it is used by TROPOMI and by TCCON to monitor both methane and carbon monoxide. Lorente et al. [286] evaluated HITRAN2008, HITRAN2016, and SEOM-IAS [103] databases against retrievals from TROPOMI. The sensitivity tests did not indicate an improved data
vised mainly based on a review performed in Ref. [233] on a variety of measurements. Compared to the HITRAN2016 line list, which included the speed-dependent parameters for only transitions of the 2–0 band (up to $J_{max}$ = 29), in the 2020 edition of the CO line list, every line includes the speed-dependent Voigt and the Rozenkranz line-mixing parameters [232] for both air- and self-broadened lines. The importance of including non-Voigt line shapes in atmospheric retrievals of CO has been highlighted by Hochstafff et al. [264,265]. Furthermore, the CO line-shape parameters for the important planetary broadeners such as CO-H₂, CO-He, and CO-CO₂ were revised [266], while parameters associated with broadening by H₂O were introduced for the first time as described in Ref. [49]. A summary of these modifications for the HITRAN2020 edition is given below:

### 1. The CO-air broadened parameters:

(a) For the air half-widths (the VP parameters), to evaluate the effect of vibration, the relative difference of the broadening parameters for various measured bands were calculated and the average difference was well below 1% for different band values. Therefore, the broadening parameters were considered to be vibrationally independent. Then, the Padé approximants model (Eq. (1)) was employed to fit all the measured air-broadening data for several bands, including Ref. [267] for the 1–0 band, Ref. [268] for the 2–0 band, and Ref. [269] for the 3–0 band simultaneously [233]. The fit coefficients are provided in Ref. [233] and the resulting broadening parameters were expanded to all the transitions of CO perturbed by air.

(b) The update of the speed-dependent Voigt line-shape parameters heavily relies on the semi-empirical Padé approximant fits to the experimental data of Ref. [270]. For the air broadening (the SDV parameters), and the temperature dependence of the air-broadening parameters, the 2–0 band data measured by Devi et al. [270] were used in the fit, and the approximated values from the model were expanded for lines of every band. The air speed dependence of line widths were fitted as well using the same data source, and the corresponding γ₂-air parameters were estimated and attributed to each transition. Wherever the measured SDV parameters were available, the original experimental results were used in populating the database. For instance, the Ref. [258] data were used for the lines of the 1–0 band and the measured parameters of Ref. [271] were used for updating the 2–0 band lines for different isotopologues of CO.

### 2. The CO-CO broadened parameters:

(a) To find the values for the self-broadened half-widths (using the VP) for the high-J transitions, the measurements for different bands were used (i.e., 1–0 band [272], 2–0 band [273–275], 3–0 band [276]). All these data were fitted simultaneously to estimate the self-broadening parameters for the lines that were not measured for all the bands except for the measured transitions in the 2–0 band, where the data from Ref. [273] were used for the update.

(b) The self-broadening parameters, their temperature exponents, and the speed-dependence of the broadening (the SDV profile parameters) were approximated using the measured line widths of Ref. [270] fitted to the Padé approximants model, and we imported the experimental values for different isotopologues reported in Refs. [258,271] for the 1–0 and 2–0 bands, respectively.

### 3. The CO-air and CO-CO pressure shifts:

The air and self shifts (for both VP and SDV) were calculated by employing the sophisticated vibrational-dependent approach of Hartmann [173] for all the transitions. The quality of the calculated shifts were validated by comparison of the shifts in dif-

ferent bands [233]. The measured air shifts for the transitions in the 1–0, 2–0, and 3–0 bands remained unchanged as they were reported in HITRAN2016. Also it should be emphasized that measured pressure self shifts of CO for the 1–0 [272], 2–0 [270], 3–0 [269] and 4–0 [263] bands were written into the database directly for the measured lines.

### 4. The CO-air and CO-CO first-order line-mixing:

The first-order line-mixing parameters were calculated based on the EPG formalism [242] using both the VP and SDV broadening parameters and provided for every transition. For the 2–0 band of the main isotopologue, the CO-air and CO-CO line-mixing were taken from the measurement of Ref. [270].

### 5. Planetary perturbers:

Broadening parameters due to pressure of “planetary” (H₂, CO₂, He) gases were first introduced in HITRAN in 2016, based on the procedure described by Li et al. [257]. In this edition we updated these parameters. For the update of the CO-H₂ broadening parameters and their temperature dependence, the data from Refs. [273,277] were taken into the semi-empirical fitting models [266] and the results were extrapolated for every CO line. The line-shape parameters of CO perturbed by helium were also modified, based on Refs. [278–282], and the CO₂ pressure broadening and the temperature dependence of the broadening parameters of CO were generated from extrapolating the data from Ref. [283]. Finally, the pressure shift parameters for all three broadeners of CO were obtained based on the Hartmann semi-classical routine [173] and the values agree well with the available experimental data [266].

## 2.6. CH₄: methane (molecule 6)

HITRAN2016 provided substantial improvements in methane spectroscopy (with respect to previous editions) in many spectral regions (see, for instance, the validation of the ACE-FTS experiment [76]). In general, the line positions and intensities were considerably improved, and the spectral coverage increased. Nevertheless, the spectroscopy of methane is still far from perfect. In this edition, several spectral regions have been improved. However, one of the largest issues that remain is the quality of the line shape parameters. In particular, the tetradecad region targeted by GOSAT and MethaneSat requires revision (as indicated, for instance, in Ref. [284]). A major global revision of the methane line shape parameters is currently underway for Voigt and speed-dependent Voigt parametrizations, as well as the inclusion of line-mixing parameters. At present, this work is still ongoing and will not form part of the current update for methane. The improvements for HITRAN2020 concern updating line-shapes of individual transitions where major issues have been identified. Nevertheless, several spectral regions have received significant updates and are described below.

### 2.6.1. 3760–4100 cm⁻¹

A new line list from Rodina et al. [285] was used to completely replace HITRAN data for the principal isotopologue in this spectral region. This line list is based on the analyses of the FTS experimental spectra recorded in Reims under different thermodynamic conditions. This line list improves the quality of spectroscopic parameters in this spectral region and contains assignments for all lines, enabling easier conversion between temperatures.

### 2.6.2. 4190–4315 cm⁻¹

This spectral region is important in remote sensing as it is used by TROPOMI and by TCCON to monitor both methane and carbon monoxide. Lorente et al. [286] evaluated HITRAN2008, HITRAN2016, and SEOM-IAS [103] databases against retrievals from TROPOMI. The sensitivity tests did not indicate an improved data
<figure><img src="image_18.png" /><figcaption>**Fig. 14.** The FTS transmission spectrum at *P* = 232.81 Torr, *T* = 296 K, and volume mixing ratio *X*<sub>CH<sub>4</sub></sub> = 0.00249 (for a CH<sub>4</sub>-air mixture) in the octad region measured at DLR. Transmission spectra calculated using HAPI for four different line lists are also presented. In the lower panel, the residuals (experiment-calculation) are shown for: i) HITRAN2016 line list, ii) the Ref. [287] line list, iii) the Ref. [287] line list when using the line broadening from Ref. [289], and iv) the HITRAN2020 line list.</figcaption></figure>

quality when either of the spectroscopic databases was used. How-
ever, the RMS and χ² values were much improved with HI-
TRAN2016 over HITRAN2008, with the SEOM-IAS data giving the
best results. Indeed the SEOM-IAS [103] database is a very ac-
curate line list, which, apart from accurate line positions and in-
tensities, provides advanced line-shape parameters including line-
mixing. However, it is not completely assigned, and some of the
existing assignments contradict the assignments in HITRAN and
variational line lists. In addition, the line-mixing formalism used
in that work is not yet adapted in HITRAN. This is the reason
why only 122 lines from Ref. [103] were adapted for HITRAN2016.
For HITRAN2020 substantially more lines from Ref. [103] were as-
signed and incorporated into HITRAN using the recent HITEMP line
list [56]. This, however, has both advantages and disadvantages. On
the one hand, assignments allow one to use correct lower-state en-
ergies, which provides better applicability of the line list at differ-
ent temperatures. On the other hand, parameters determined in a
multi-spectrum fit of experimental data in Ref. [103] are somewhat
correlated; therefore, the changes in lower-state energies could
now conflict with other parameters determined in that study. In
general, the specifics of the data proposed in Ref. [103] requires a
dedicated software or precalculated cross-sections to be used suc-
cessfully in radiative-transfer codes. The authors of the SEOM-IAS
database are working on this approach.

2.6.3. 4315–4600 cm⁻¹

The recent line list from Nikitin et al. [287] was examined to
update the methane line list in this spectral region. This line list
was based on FTS measurements in Reims and the SOLEIL Syn-
chrotron in France for different pressures and temperatures. To
verify the quality of this line list, HAPI was used to calculate
transmission spectra to compare with the laboratory measurments.
For the air-broadening and shift parameters, the suggested val-
ues from Ref. [287] were used. Fig. 14 presents the experimen-
tal transmission spectra measured at DLR [132,288], compared to
those calculated based on the new line list from Nikitin et al.
[287], the HITRAN2016 line list, and the Nikitin et al. [287] line
list supplemented with the broadening half-widths from Predoi-
Cross et al. [289]. The last set is the HITRAN2020 line list, which
is, in principle, the same as the HITRAN2016 line list with the
broadening half-widths substituted with the measured values from
Predoi-Cross et al. [289], and a few spectral intervals that have

been updated using the line positions and intensities from the Ref.
[287] line list for the weaker spectral lines.

As can be seen, the Nikitin et al. [287] line list itself did not
improve the quality of spectroscopic parameters compared to the
HITRAN2016 list in this region for most of the lines. However,
using the broadening values from Ref. [289] reduced the residu-
als slightly. The lowest residuals were achieved when utilizing the
proposed line list for the HITRAN2020.

Another validation analysis was performed using the FTS spec-
tra measured at the Jet Propulsion Laboratory (JPL). Fig. 15 shows
the transmission spectra and residuals for similar calculations be-
ing described in Fig. 14, in a slightly extended spectral range but
at lower temperature. This also allows evaluation of the tempera-
ture dependence of the widths and reliability of spectroscopic as-
signments, i.e., lower-state energies. These validation examinations
also confirm the effectiveness of the procedure for constructing the
HITRAN2020 methane line list in this region.

2.6.4. 8850-9180 cm⁻¹

A new line list from Nikitin et al. [290] was used to update HI-
TRAN for the principal isotopologue of methane in this spectral re-
gion. This line list is based on the analyses of FTS spectra that were
recorded in Tomsk with a cell path length of 2.2 m under differ-
ent thermodynamic conditions. This line list improves the quality
of spectroscopic parameters in this spectral region and provides
substantially more quantum assignment information than the HI-
TRAN2016 list in this region, making conversions between temper-
ature more reliable.

2.6.5. Line-shape parameters

As was already mentioned, a major revision of methane line-
shape parameters is underway and will feature as an update to
HITRAN2020. At the moment, only individual parameters from se-
lected lines (that were deemed to be definite outliers) have been
updated. Moreover, in the tetradecad region, the air-broadening
half-widths were updated using the measured parameters of Refs.
[291,292] averaged with the line-broadening values in the so-
called "HITRAN2016 Beta" list, which are based on the GOSAT2014
[293] line list for methane. Validation against laboratory spectra
showed improved residuals (with a smaller RMS value) when cal-
culating the transmission using the HITRAN2016 line list when in-
troducing the newly averaged line widths (see Fig. 16).
<figure><img src="image_16.png" /><figcaption>**Fig. 14.** The FTS transmission spectrum at *P* = 232.81 Torr, *T* = 296 K, and volume mixing ratio *X*<sub>CH<sub>4</sub></sub> = 0.00249 (for a CH<sub>4</sub>-air mixture) in the octad region measured at DLR. Transmission spectra calculated using HAPI for four different line lists are also presented. In the lower panel, the residuals (experiment-calculation) are shown for: i) HITRAN2016 line list, ii) the Ref. [287] line list, iii) the Ref. [287] line list when using the line broadening from Ref. [289], and iv) the HITRAN2020 line list.</figcaption></figure>

quality when either of the spectroscopic databases was used. How-
ever, the RMS and χ² values were much improved with HI-
TRAN2016 over HITRAN2008, with the SEOM-IAS data giving the
best results. Indeed the SEOM-IAS [103] database is a very ac-
curate line list, which, apart from accurate line positions and in-
tensities, provides advanced line-shape parameters including line-
mixing. However, it is not completely assigned, and some of the
existing assignments contradict the assignments in HITRAN and
variational line lists. In addition, the line-mixing formalism used
in that work is not yet adapted in HITRAN. This is the reason
why only 122 lines from Ref. [103] were adapted for HITRAN2016.
For HITRAN2020 substantially more lines from Ref. [103] were as-
signed and incorporated into HITRAN using the recent HITEMP line
list [56]. This, however, has both advantages and disadvantages. On
the one hand, assignments allow one to use correct lower-state en-
ergies, which provides better applicability of the line list at differ-
ent temperatures. On the other hand, parameters determined in a
multi-spectrum fit of experimental data in Ref. [103] are somewhat
correlated; therefore, the changes in lower-state energies could
now conflict with other parameters determined in that study. In
general, the specifics of the data proposed in Ref. [103] requires a
dedicated software or precalculated cross-sections to be used suc-
cessfully in radiative-transfer codes. The authors of the SEOM-IAS
database are working on this approach.

2.6.3. 4315–4600 cm⁻¹

The recent line list from Nikitin et al. [287] was examined to
update the methane line list in this spectral region. This line list
was based on FTS measurements in Reims and the SOLEIL Syn-
chrotron in France for different pressures and temperatures. To
verify the quality of this line list, HAPI was used to calculate
transmission spectra to compare with the laboratory measurments.
For the air-broadening and shift parameters, the suggested val-
ues from Ref. [287] were used. Fig. 14 presents the experimen-
tal transmission spectra measured at DLR [132,288], compared to
those calculated based on the new line list from Nikitin et al.
[287], the HITRAN2016 line list, and the Nikitin et al. [287] line
list supplemented with the broadening half-widths from Predoi-
Cross et al. [289]. The last set is the HITRAN2020 line list, which
is, in principle, the same as the HITRAN2016 line list with the
broadening half-widths substituted with the measured values from
Predoi-Cross et al. [289], and a few spectral intervals that have

been updated using the line positions and intensities from the Ref.
[287] line list for the weaker spectral lines.

As can be seen, the Nikitin et al. [287] line list itself did not
improve the quality of spectroscopic parameters compared to the
HITRAN2016 list in this region for most of the lines. However,
using the broadening values from Ref. [289] reduced the residu-
als slightly. The lowest residuals were achieved when utilizing the
proposed line list for the HITRAN2020.

Another validation analysis was performed using the FTS spec-
tra measured at the Jet Propulsion Laboratory (JPL). Fig. 15 shows
the transmission spectra and residuals for similar calculations be-
ing described in Fig. 14, in a slightly extended spectral range but
at lower temperature. This also allows evaluation of the tempera-
ture dependence of the widths and reliability of spectroscopic as-
signments, i.e., lower-state energies. These validation examinations
also confirm the effectiveness of the procedure for constructing the
HITRAN2020 methane line list in this region.

2.6.4. 8850-9180 cm⁻¹

A new line list from Nikitin et al. [290] was used to update HI-
TRAN for the principal isotopologue of methane in this spectral re-
gion. This line list is based on the analyses of FTS spectra that were
recorded in Tomsk with a cell path length of 2.2 m under differ-
ent thermodynamic conditions. This line list improves the quality
of spectroscopic parameters in this spectral region and provides
substantially more quantum assignment information than the HI-
TRAN2016 list in this region, making conversions between temper-
ature more reliable.

2.6.5. Line-shape parameters

As was already mentioned, a major revision of methane line-
shape parameters is underway and will feature as an update to
HITRAN2020. At the moment, only individual parameters from se-
lected lines (that were deemed to be definite outliers) have been
updated. Moreover, in the tetradecad region, the air-broadening
half-widths were updated using the measured parameters of Refs.
[291,292] averaged with the line-broadening values in the so-
called "HITRAN2016 Beta" list, which are based on the GOSAT2014
[293] line list for methane. Validation against laboratory spectra
showed improved residuals (with a smaller RMS value) when cal-
culating the transmission using the HITRAN2016 line list when in-
troducing the newly averaged line widths (see Fig. 16).
<figure><img src="image_19.png" /><figcaption>**Fig. 15.** The FTS transmission spectrum for CH₄ in the octad region at *P* = 254 Torr, *T* = 250 K, and *X*<sub>CH₄</sub> = 0.0572 (for a CH₄-air mixture) measured at JPL. The description for the lower panel is the same as in Fig. 14.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Fig. 16.** The FTS transmission spectrum of CH₄ in the tetradecad region at *P* = 0.525 atm, *T* = 297.9 K, and *X*<sub>CH₄</sub> = 0.01 (for a CH₄-air mixture) measured at Kitt Peak National Solar Observatory (NSO). The top panel also shows calculated transmission spectra employing HAPI and the following data: i) the "HITRAN2016 Beta" line list, ii) the HITRAN2016 line list, iii) the HITRAN2016 line list with the broadening values collected from the "HITRAN2016 Beta" list, iv) the HITRAN2016 line list with the broadening parameters collected from Refs. [291,292], and v) the HITRAN2016 line list with the average broadening values obtained from Refs. [291,292]. The latter line list was eventually used for the HITRAN2020 update. The lower panel shows the differences between the experimental spectra and calculated transmission spectra using these line lists.</figcaption></figure>

Note that for every line of methane, HITRAN2020 features the inclusion of the half-widths (and their temperature dependencies) due to the ambient pressure of water as explained by Tan et al. [49].

### 2.6.6. Future work

Many other new experimental works on spectroscopy of different isotopologues of the methane molecule exist, which could benefit the HITRAN database, including (but not limited to) Refs. [294–306]. A very extensive effort is underway to evaluate new data against current HITRAN data and experimental and atmospheric spectra. Methane is a very complex molecule from the spectroscopic standpoint and it is not straightforward to make choices for individual parameters of individual lines. One interesting example is a pure rotational spectrum of CH₃D. In the HITRAN2016 paper an argument was made regarding updating the intensity of these lines with results from Bray et al. [307]. Since then, the authors of this work have revised these values [308] but these data still disagree

with *ab initio* calculations and other theoretical works, which are not in agreement between themselves either. More work is needed to understand these discrepancies.

The high-temperature theoretical line list for ¹²CH₄ produced by Rey et al. [309] (and available online as part of the Theo-ReTS project [310]) has been used to create a line list suitable for HITEMP [53]. The approach involved merging Ref. [309] with the HITRAN2016 ¹²CH₄ data [16]. A method was devised to compress the weak underlying *ab initio* transitions into “effective lines” so that the complete HITEMP line list can be used directly in radiative transfer calculations. For a full description of the HITEMP line list of ¹²CH₄, including validation against experimental works, readers are referred to Ref. [56], which describes the addition to HITEMP. Users should be mindful that this HITEMP update was carried out before the ¹²CH₄ updates described above for HITRAN2020. To maintain consistency, these updates will be incorporated into HITEMP in due course.
<figure><img src="image_17.png" /><figcaption>**Fig. 15.** The FTS transmission spectrum for CH₄ in the octad region at *P* = 254 Torr, *T* = 250 K, and *X*<sub>CH₄</sub> = 0.0572 (for a CH₄-air mixture) measured at JPL. The description for the lower panel is the same as in Fig. 14.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Fig. 16.** The FTS transmission spectrum of CH₄ in the tetradecad region at *P* = 0.525 atm, *T* = 297.9 K, and *X*<sub>CH₄</sub> = 0.01 (for a CH₄-air mixture) measured at Kitt Peak National Solar Observatory (NSO). The top panel also shows calculated transmission spectra employing HAPI and the following data: i) the "HITRAN2016 Beta" line list, ii) the HITRAN2016 line list, iii) the HITRAN2016 line list with the broadening values collected from the "HITRAN2016 Beta" list, iv) the HITRAN2016 line list with the broadening parameters collected from Refs. [291,292], and v) the HITRAN2016 line list with the average broadening values obtained from Refs. [291,292]. The latter line list was eventually used for the HITRAN2020 update. The lower panel shows the differences between the experimental spectra and calculated transmission spectra using these line lists.</figcaption></figure>

Note that for every line of methane, HITRAN2020 features the inclusion of the half-widths (and their temperature dependencies) due to the ambient pressure of water as explained by Tan et al. [49].

### 2.6.6. Future work

Many other new experimental works on spectroscopy of different isotopologues of the methane molecule exist, which could benefit the HITRAN database, including (but not limited to) Refs. [294–306]. A very extensive effort is underway to evaluate new data against current HITRAN data and experimental and atmospheric spectra. Methane is a very complex molecule from the spectroscopic standpoint and it is not straightforward to make choices for individual parameters of individual lines. One interesting example is a pure rotational spectrum of CH₃D. In the HITRAN2016 paper an argument was made regarding updating the intensity of these lines with results from Bray et al. [307]. Since then, the authors of this work have revised these values [308] but these data still disagree

with *ab initio* calculations and other theoretical works, which are not in agreement between themselves either. More work is needed to understand these discrepancies.

The high-temperature theoretical line list for ¹²CH₄ produced by Rey et al. [309] (and available online as part of the Theo-ReTS project [310]) has been used to create a line list suitable for HITEMP [53]. The approach involved merging Ref. [309] with the HITRAN2016 ¹²CH₄ data [16]. A method was devised to compress the weak underlying *ab initio* transitions into “effective lines” so that the complete HITEMP line list can be used directly in radiative transfer calculations. For a full description of the HITEMP line list of ¹²CH₄, including validation against experimental works, readers are referred to Ref. [56], which describes the addition to HITEMP. Users should be mindful that this HITEMP update was carried out before the ¹²CH₄ updates described above for HITRAN2020. To maintain consistency, these updates will be incorporated into HITEMP in due course.
## 2.7. O₂: molecular oxygen (molecule 7)

Due to the dominant presence and uniform mixing of oxygen in the terrestrial atmosphere, its spectral lines are often used as a benchmark for intensity calibration of atmospheric spectra taken by satellite and ground-based instruments. Although there is over a century of measurements and calculations of spectral parameters of oxygen, their quality and extent was still not able to achieve the sub-percent goal (in retrieved oxygen amount) in many important spectral bands. In this edition, major revisions of the oxygen line lists have been carried out.

### 2.7.1. 1.27 µm region

Spectroscopy of the $a^1\Delta_g - X^3\Sigma_g^-$ band at 1.27 µm is more complex [311] than that of the A-band at 0.76 µm. It has more branches, a denser spectrum with overlapping lines, stronger underlying collision-induced absorption, and interfering emission features (air-glow) at the top of the terrestrial atmosphere due to the production of oxygen in the $a^1\Delta_g$ state through photo-dissociation of ozone. Nevertheless, it is located closer (on the spectral scale) to the bands of CO₂ and CH₄ that are targeted by the remote-sensing missions and therefore has better benchmarking characteristics to remove systematic errors. In fact, the Total Carbon Cycle Observing Network (TCCON) [312], which is less sensitive to the emission contamination from the top of the atmosphere, already employs this band. Sun et al. [313] have demonstrated that emission features could also be modeled accurately, and therefore, if one knows the spectroscopic parameters to the necessary degree of accuracy, this band can be used in remote sensing and is intended to be used by upcoming satellite missions, including MicroCarb [314] and MethaneSAT [26].

A major overhaul of the spectroscopic parameters for the $a^1\Delta_g - X^3\Sigma_g^-$ band of the ¹⁶O₂ and ¹⁶O¹⁸O isotopologues was carried out for this edition. The details for the calculations of line positions and intensities will be provided in a separate paper [315], but a general overview is provided below.

The $a^1\Delta_g - X^3\Sigma_g^-$ band consists of nine magnetic dipole (M1) branches (with $\Delta J = 0, \pm 1$) and 15 electric quadrupole (E2) branches (with $\Delta J = 0, \pm 1, \pm 2$, nine of these branches overlap with M1 ones). Typically E2 transitions are about six orders of magnitude weaker than M1 transitions. However, as explained in Gordon et al. [311], intensities of the E2 lines in this particular band are enhanced due to mixing of the different spin-components of the $X^3\Sigma_g^-$ state with the $b^1\Sigma_g^+$ state at around 13,000 cm⁻¹ and to a lesser extent with much higher-lying $^1\Pi$ states. These contributions affect each branch differently, and it is very hard to model these overlapping transitions. Therefore, in HITRAN2012 [15] and HITRAN2016 [16] only those E2 transitions with $\Delta J = \pm 2$ were included based on measurements reported in Ref. [311] and a model proposed by Mishra et al. [316]. The E2 lines overlapping with M1 lines were not included, therefore creating difficulty in modeling absorption due to M1+E2 lines on a sub-percent level as E2 contribution to the total intensity should be considered almost negligible for some of the bands, but up to 1.5% for others.

Gordon et al. [315] make use of an extensive campaign of new measurements carried out in Grenoble and NIST. These measurements are a continuation of published works [317–319] that take advantage of the extremely sensitive CRDS setup equipped with frequency combs. Intensities with the lowest uncertainties were used in the fit to the model [316] for E2 transitions and the modified model [320] for M1 transitions. Modifications are connected to the Herman-Wallis-like rovibronic deviations that were modeled by introducing polynomials as a function of rotational quanta to the groups of transitions that are connected to the same spin component in the ground state.

<figure><img src="image_21.png" /><figcaption>**Fig. 17.** Comparison between measured transmissions from Park Falls FTS and simulations using different versions of the database.</figcaption></figure>

Frequency comb-calibrated line positions from the new Grenoble and NIST experiments were also used to refit all the ¹⁶O₂ and ¹⁶O¹⁸O data involving the $a^1\Delta_g$ and $X^3\Sigma_g^-$ states simultaneously. Effectively, a systematic change by about $2 \times 10^{-4}$ cm⁻¹ (slightly larger at $J'' \ge 29$) was introduced with respect to the HITRAN2016 values that were based on Ref. [321].

The Voigt line shapes were taken from the analyses of the Grenoble data carried out in Ref. [318], while advanced line-shape parameters, including first-order line-mixing, are from the new study in NIST that updates data from Mendonca et al. [319]. No new studies have been carried out for the temperature dependencies of the width, but in order to satisfy TCCON retrievals, the previous values in HITRAN were multiplied by a factor of 0.93.

Fig. 17 demonstrates how spectroscopic parameters in HITRAN affect the residuals of the TCCON spectra in Park Falls, WI (USA). The use of the HITRAN2020 line list clearly reduces the residuals to a sub-percent level.

### 2.7.2. A-band region

Updates to O₂ in the A-band region reflect ongoing efforts to improve the balance between line-mixing and collision-induced absorption that have been shown to bias surface pressure retrievals [322,323]. The effort [323] which drives this update does not improve the precision of line positions which may be correlated with self-shift parameters [324]. Therefore this HITRAN update retains the positions produced from the updated global model of Yu et al. [321] and additional uncertainty is recommended for the self-shift parameters. Line intensities are changed up to 5% at higher *J* values due to a re-assessment of the high-*J* data [325] used to determine Herman-Wallis terms utilized in the last two HITRAN editions [326]. Intensities in the present update, see Fig. 18, reflect a median value found in the FTS and CRDS datasets analyzed for production of ABSorption COefficient (ABSCO) tables used for the OCO missions [323]. The present adjustment appears larger with respect to HITRAN2016 than in comparison to HITRAN2012. Direct measurements of intensities have been performed subsequently by NIST after mitigating biases associated with the CRDS signal digitization, and found the ABSCO table intensities to be consistent to approximately better than 1%. The intensity changes are largest for the weakest features, such that the total band intensity is less variant, changing 0.92% from ABSCO 5.0 [327] (HITRAN2016) to ABSCO 5.1 [323] (HITRAN2020).

Changes in the air-broadened half-width and its temperature-dependence parameter (both Voigt and speed-dependent Voigt) are subtle, the latter showing increases of a few percent at low *m* and decreases of a few percent at high *m*, whereas the for-
## 2.7. O₂: molecular oxygen (molecule 7)

Due to the dominant presence and uniform mixing of oxygen in the terrestrial atmosphere, its spectral lines are often used as a benchmark for intensity calibration of atmospheric spectra taken by satellite and ground-based instruments. Although there is over a century of measurements and calculations of spectral parameters of oxygen, their quality and extent was still not able to achieve the sub-percent goal (in retrieved oxygen amount) in many important spectral bands. In this edition, major revisions of the oxygen line lists have been carried out.

### 2.7.1. 1.27 µm region

Spectroscopy of the $a^1\Delta_g - X^3\Sigma_g^-$ band at 1.27 µm is more complex [311] than that of the A-band at 0.76 µm. It has more branches, a denser spectrum with overlapping lines, stronger underlying collision-induced absorption, and interfering emission features (air-glow) at the top of the terrestrial atmosphere due to the production of oxygen in the $a^1\Delta_g$ state through photo-dissociation of ozone. Nevertheless, it is located closer (on the spectral scale) to the bands of CO₂ and CH₄ that are targeted by the remote-sensing missions and therefore has better benchmarking characteristics to remove systematic errors. In fact, the Total Carbon Cycle Observing Network (TCCON) [312], which is less sensitive to the emission contamination from the top of the atmosphere, already employs this band. Sun et al. [313] have demonstrated that emission features could also be modeled accurately, and therefore, if one knows the spectroscopic parameters to the necessary degree of accuracy, this band can be used in remote sensing and is intended to be used by upcoming satellite missions, including MicroCarb [314] and MethaneSAT [26].

A major overhaul of the spectroscopic parameters for the $a^1\Delta_g - X^3\Sigma_g^-$ band of the ¹⁶O₂ and ¹⁶O¹⁸O isotopologues was carried out for this edition. The details for the calculations of line positions and intensities will be provided in a separate paper [315], but a general overview is provided below.

The $a^1\Delta_g - X^3\Sigma_g^-$ band consists of nine magnetic dipole (M1) branches (with $\Delta J = 0, \pm 1$) and 15 electric quadrupole (E2) branches (with $\Delta J = 0, \pm 1, \pm 2$, nine of these branches overlap with M1 ones). Typically E2 transitions are about six orders of magnitude weaker than M1 transitions. However, as explained in Gordon et al. [311], intensities of the E2 lines in this particular band are enhanced due to mixing of the different spin-components of the $X^3\Sigma_g^-$ state with the $b^1\Sigma_g^+$ state at around 13,000 cm⁻¹ and to a lesser extent with much higher-lying $^1\Pi$ states. These contributions affect each branch differently, and it is very hard to model these overlapping transitions. Therefore, in HITRAN2012 [15] and HITRAN2016 [16] only those E2 transitions with $\Delta J = \pm 2$ were included based on measurements reported in Ref. [311] and a model proposed by Mishra et al. [316]. The E2 lines overlapping with M1 lines were not included, therefore creating difficulty in modeling absorption due to M1+E2 lines on a sub-percent level as E2 contribution to the total intensity should be considered almost negligible for some of the bands, but up to 1.5% for others.

Gordon et al. [315] make use of an extensive campaign of new measurements carried out in Grenoble and NIST. These measurements are a continuation of published works [317–319] that take advantage of the extremely sensitive CRDS setup equipped with frequency combs. Intensities with the lowest uncertainties were used in the fit to the model [316] for E2 transitions and the modified model [320] for M1 transitions. Modifications are connected to the Herman-Wallis-like rovibronic deviations that were modeled by introducing polynomials as a function of rotational quanta to the groups of transitions that are connected to the same spin component in the ground state.

<figure><img src="image_19.png" /><figcaption>**Fig. 17.** Comparison between measured transmissions from Park Falls FTS and simulations using different versions of the database.</figcaption></figure>

Frequency comb-calibrated line positions from the new Grenoble and NIST experiments were also used to refit all the ¹⁶O₂ and ¹⁶O¹⁸O data involving the $a^1\Delta_g$ and $X^3\Sigma_g^-$ states simultaneously. Effectively, a systematic change by about $2 \times 10^{-4}$ cm⁻¹ (slightly larger at $J'' \ge 29$) was introduced with respect to the HITRAN2016 values that were based on Ref. [321].

The Voigt line shapes were taken from the analyses of the Grenoble data carried out in Ref. [318], while advanced line-shape parameters, including first-order line-mixing, are from the new study in NIST that updates data from Mendonca et al. [319]. No new studies have been carried out for the temperature dependencies of the width, but in order to satisfy TCCON retrievals, the previous values in HITRAN were multiplied by a factor of 0.93.

Fig. 17 demonstrates how spectroscopic parameters in HITRAN affect the residuals of the TCCON spectra in Park Falls, WI (USA). The use of the HITRAN2020 line list clearly reduces the residuals to a sub-percent level.

### 2.7.2. A-band region

Updates to O₂ in the A-band region reflect ongoing efforts to improve the balance between line-mixing and collision-induced absorption that have been shown to bias surface pressure retrievals [322,323]. The effort [323] which drives this update does not improve the precision of line positions which may be correlated with self-shift parameters [324]. Therefore this HITRAN update retains the positions produced from the updated global model of Yu et al. [321] and additional uncertainty is recommended for the self-shift parameters. Line intensities are changed up to 5% at higher *J* values due to a re-assessment of the high-*J* data [325] used to determine Herman-Wallis terms utilized in the last two HITRAN editions [326]. Intensities in the present update, see Fig. 18, reflect a median value found in the FTS and CRDS datasets analyzed for production of ABSorption COefficient (ABSCO) tables used for the OCO missions [323]. The present adjustment appears larger with respect to HITRAN2016 than in comparison to HITRAN2012. Direct measurements of intensities have been performed subsequently by NIST after mitigating biases associated with the CRDS signal digitization, and found the ABSCO table intensities to be consistent to approximately better than 1%. The intensity changes are largest for the weakest features, such that the total band intensity is less variant, changing 0.92% from ABSCO 5.0 [327] (HITRAN2016) to ABSCO 5.1 [323] (HITRAN2020).

Changes in the air-broadened half-width and its temperature-dependence parameter (both Voigt and speed-dependent Voigt) are subtle, the latter showing increases of a few percent at low *m* and decreases of a few percent at high *m*, whereas the for-
<figure><img src="image_22.png" /><figcaption>**Fig. 18.** Ratios of intensities from HITRAN2020 (ABSCO 5.1) [328] compared with HITRAN2016 and HITRAN2012. The HITRAN2016 update, which utilized a prior ABSCO release (5.0), [327], kept the Herman-Wallis factors from HITRAN2012 fixed. The changes are due to band scaling and the application of new Herman-Wallis factors.</figcaption></figure>

mer generally increases and exhibits more variability. Changes in air-induced pressure shifts follow the same trends as the air-broadened half-width, but with a clearer monotonic structure now presented in the P-branch. All of these air-induced line-shape parameters show significant deviations from monotonic behavior near the band head of the R-branch, where there are strong interactions with line-mixing model parameters. It is likely that the subtle *J*-dependent changes in widths and shifts are also attributable to the modified line-mixing model which re-proportioned the odd and even elements of the relaxation matrix. The allocation of a small weight (instead of zero weight) to the odd elements produces a notable zigzag effect in the first-order Rosenkranz parameters provided with the HITRAN2020 database. The median of these elements closely traces prior Rosenkranz parameters except for a stronger slope in the R-branch vs. *m*.

### 2.7.3. Corrections to the line-broadening parameters for the O₂ B-band

The speed-dependent Voigt line-broadening parameters of the O₂ B-band adopted in the HITRAN2016 database from Domysławska et al. [329,330] were treated as half-widths (while apparently the full-widths were reported in the original papers). This discrepancy was discovered by Sung et al. [331] and the speed-dependent Voigt parameters have now been corrected for this band.

### 2.7.4. Water-vapor broadening parameters

A variety of experimental methods have been applied to study the water-vapor broadening of O₂ lines including early O₂ Q-branch Raman spectroscopic studies for a wide temperature range (460–990 K) [332]. The pure rotational and A-band transitions have been studied using laser-based photoacoustic spectroscopy [333], frequency-multiplier spectrometers with a Zeeman-modulated absorption cell [334], radio-acoustic detection spectrometers [335], as well as Fourier transform (FT) spectroscopy [336]. A complete analysis for all collected experimental data were presented in Ref. [49]. The Padé approximant (Eq. (1)) was applied to fit the collected data for transitions $N'' \le 35$. There is an exception with $N'' = 1$ which is treated separately due to the large spin splitting in the lowest rotational level.

### 2.7.5. Future improvements in the 60 GHz band

The band of oxygen at 60 GHz represents the manifold of transitions between spin components within the same rotational levels.

It is an important band from an atmospheric perspective, and although line-positions, intensities, and to a lesser extent Voigt parameters in HITRAN are of very high quality, the close proximity of transitions requires advanced line-shape parameterizations that include line-mixing. The recent study by Koshelev et al. [337] is considered to potentially introduce advanced line-shape parameters for these “fine-structure” transitions.

## 2.8. NO: nitric oxide (molecule 8)

Nitric oxide (NO) plays a key role in tropospheric chemistry [338] and contributes significantly to air pollution [339]. Spectroscopic NO emissions from the upper-atmosphere require the consideration of high rotational transitions in radiative-transfer models due to non-local thermodynamic equilibrium conditions [340].

Hargreaves et al. [55] provide a detailed description of the NO update for HITRAN2020 and HITEMP [53], therefore only a summary is provided here. In HITRAN2016 [16], the ¹⁴N¹⁶O line list contained transitions within the electronic ground state X²Π<sub>Ω'</sub>-X²Π<sub>Ω''</sub> (with Ω = 1/2 and 3/2) for vibrational bands up to Δν = 5 (with ν'' = 5). For ¹⁵N¹⁶O and ¹⁴N¹⁸O, only 699 and 679 lines of the 1–0 band were provided, respectively.

The comprehensive semi-empirical “NOname” line list [341], part of the ExoMol project [342], contains six isotopologues of NO (¹⁴N¹⁶O, ¹⁵N¹⁶O, ¹⁴N¹⁸O, ¹⁴N¹⁷O, ¹⁵N¹⁷O, ¹⁵N¹⁸O). For ¹⁴N¹⁶O, the NOname line list was created using an effective Hamiltonian by fitting to available experimental energies (with *J* < 99.5, *ν* < 28) and combined with *ab initio* intensities. To allow extension to higher rotational levels and vibrational bands, a second variational model was also built by fitting to experimentally-obtained energy levels and positions using the *Duo* program for diatomic molecules [343].

The HITRAN and HITEMP update for ¹⁴N¹⁶O was built around the NOname line list, but some adjustments were necessary. Discontinuities at the stitching point of the two methods used to create the NOname line lists, and intensity issues observed for Δν = 0 (see Fig. 6 of Ref. [55]), required the effective Hamiltonian to be extended to higher rotational levels for the Δν = 0 and Δν = 1 bands [55]. Furthermore, comparisons to experimental observations required the NOname intensities for the Δν = 4, Δν = 5 and Δν = 7 bands to be scaled by a factor of 1.35, 1.30 and 0.55, respectively.

For the 0–0 and 1–1 bands, positions and intensities from the Cologne Database for Molecular Spectroscopy (CDMS) [344] replace the corresponding lines in the adjusted NOname line list. Any lines of the 0–0, 1–1, 1–0, 2–1, 2–0, and 3–1 bands with hyperfine splitting from HITRAN2016 (that were not replaced by CDMS data) have been retained. Further details for transitions with *J* ≥ 99.5 are given by Hargreaves et al. [55]. In addition, magnetic dipole transitions (identified by “m” in the local upper-state quanta in the HITRAN line-transition format) for the 0–0 band remain unchanged.

For HITRAN2020, an intensity threshold for nitric oxide has been applied. Lines that remain less than 1.0 × 10⁻⁹⁹ cm/molecule, or do not exceed 1.0 × 10⁻³¹ cm/molecule (at 100, 296, 500, 1000 or 2000 K) have been omitted from the HITRAN2020 line list. However, readers should be aware that the full ¹⁴N¹⁶O line list is available via HITEMP [55]. Fig. 19 provides an overview of the update for ¹⁴N¹⁶O, which highlights the expanded spectral range (up to 23,727 cm⁻¹) and the increase in vibrational band coverage (up to Δν ≤ 14, ν' ≤ 26), when compared to HITRAN2016. To take advantage of the increased precision of MW transitions, it should be noted that the wavenumber format for NO has been updated to F12.9 for transitions below 1.0 cm⁻¹, F12.8 for transitions 1.0 to 10.0 cm⁻¹, and F12.7 for transitions 10.0 to 100.0 cm⁻¹ (as previously implemented for HNO₃, PH₃, O₂ and NO⁺).

Air- and self-broadening parameters of NO in HITRAN and HITEMP have been refit to available measurements, and are described in detail by Hargreaves et al. [55]. The air-broadening
<figure><img src="image_20.png" /><figcaption>**Fig. 18.** Ratios of intensities from HITRAN2020 (ABSCO 5.1) [328] compared with HITRAN2016 and HITRAN2012. The HITRAN2016 update, which utilized a prior ABSCO release (5.0), [327], kept the Herman-Wallis factors from HITRAN2012 fixed. The changes are due to band scaling and the application of new Herman-Wallis factors.</figcaption></figure>

mer generally increases and exhibits more variability. Changes in air-induced pressure shifts follow the same trends as the air-broadened half-width, but with a clearer monotonic structure now presented in the P-branch. All of these air-induced line-shape parameters show significant deviations from monotonic behavior near the band head of the R-branch, where there are strong interactions with line-mixing model parameters. It is likely that the subtle *J*-dependent changes in widths and shifts are also attributable to the modified line-mixing model which re-proportioned the odd and even elements of the relaxation matrix. The allocation of a small weight (instead of zero weight) to the odd elements produces a notable zigzag effect in the first-order Rosenkranz parameters provided with the HITRAN2020 database. The median of these elements closely traces prior Rosenkranz parameters except for a stronger slope in the R-branch vs. *m*.

### 2.7.3. Corrections to the line-broadening parameters for the O₂ B-band

The speed-dependent Voigt line-broadening parameters of the O₂ B-band adopted in the HITRAN2016 database from Domyslawska et al. [329,330] were treated as half-widths (while apparently the full-widths were reported in the original papers). This discrepancy was discovered by Sung et al. [331] and the speed-dependent Voigt parameters have now been corrected for this band.

### 2.7.4. Water-vapor broadening parameters

A variety of experimental methods have been applied to study the water-vapor broadening of O₂ lines including early O₂ Q-branch Raman spectroscopic studies for a wide temperature range (460–990 K) [332]. The pure rotational and A-band transitions have been studied using laser-based photoacoustic spectroscopy [333], frequency-multiplier spectrometers with a Zeeman-modulated absorption cell [334], radio-acoustic detection spectrometers [335], as well as Fourier transform (FT) spectroscopy [336]. A complete analysis for all collected experimental data were presented in Ref. [49]. The Padé approximant (Eq. (1)) was applied to fit the collected data for transitions $N'' \le 35$. There is an exception with $N'' = 1$ which is treated separately due to the large spin splitting in the lowest rotational level.

### 2.7.5. Future improvements in the 60 GHz band

The band of oxygen at 60 GHz represents the manifold of transitions between spin components within the same rotational levels.

It is an important band from an atmospheric perspective, and although line-positions, intensities, and to a lesser extent Voigt parameters in HITRAN are of very high quality, the close proximity of transitions requires advanced line-shape parameterizations that include line-mixing. The recent study by Koshelev et al. [337] is considered to potentially introduce advanced line-shape parameters for these “fine-structure” transitions.

## 2.8. NO: nitric oxide (molecule 8)

Nitric oxide (NO) plays a key role in tropospheric chemistry [338] and contributes significantly to air pollution [339]. Spectroscopic NO emissions from the upper-atmosphere require the consideration of high rotational transitions in radiative-transfer models due to non-local thermodynamic equilibrium conditions [340].

Hargreaves et al. [55] provide a detailed description of the NO update for HITRAN2020 and HITEMP [53], therefore only a summary is provided here. In HITRAN2016 [16], the ¹⁴N¹⁶O line list contained transitions within the electronic ground state X²Π<sub>Ω'</sub>–X²Π<sub>Ω''</sub> (with Ω = 1/2 and 3/2) for vibrational bands up to Δν = 5 (with ν'' = 5). For ¹⁵N¹⁶O and ¹⁴N¹⁸O, only 699 and 679 lines of the 1–0 band were provided, respectively.

The comprehensive semi-empirical “NOname” line list [341], part of the ExoMol project [342], contains six isotopologues of NO (¹⁴N¹⁶O, ¹⁵N¹⁶O, ¹⁴N¹⁸O, ¹⁴N¹⁷O, ¹⁵N¹⁷O, ¹⁵N¹⁸O). For ¹⁴N¹⁶O, the NOname line list was created using an effective Hamiltonian by fitting to available experimental energies (with *J* < 99.5, *ν* < 28) and combined with *ab initio* intensities. To allow extension to higher rotational levels and vibrational bands, a second variational model was also built by fitting to experimentally-obtained energy levels and positions using the *Duo* program for diatomic molecules [343].

The HITRAN and HITEMP update for ¹⁴N¹⁶O was built around the NOname line list, but some adjustments were necessary. Discontinuities at the stitching point of the two methods used to create the NOname line lists, and intensity issues observed for Δν = 0 (see Fig. 6 of Ref. [55]), required the effective Hamiltonian to be extended to higher rotational levels for the Δν = 0 and Δν = 1 bands [55]. Furthermore, comparisons to experimental observations required the NOname intensities for the Δν = 4, Δν = 5 and Δν = 7 bands to be scaled by a factor of 1.35, 1.30 and 0.55, respectively.

For the 0–0 and 1–1 bands, positions and intensities from the Cologne Database for Molecular Spectroscopy (CDMS) [344] replace the corresponding lines in the adjusted NOname line list. Any lines of the 0–0, 1–1, 1–0, 2–1, 2–0, and 3–1 bands with hyperfine splitting from HITRAN2016 (that were not replaced by CDMS data) have been retained. Further details for transitions with *J* ≥ 99.5 are given by Hargreaves et al. [55]. In addition, magnetic dipole transitions (identified by “m” in the local upper-state quanta in the HITRAN line-transition format) for the 0–0 band remain unchanged.

For HITRAN2020, an intensity threshold for nitric oxide has been applied. Lines that remain less than 1.0 × 10⁻⁹⁹ cm/molecule, or do not exceed 1.0 × 10⁻³¹ cm/molecule (at 100, 296, 500, 1000 or 2000 K) have been omitted from the HITRAN2020 line list. However, readers should be aware that the full ¹⁴N¹⁶O line list is available via HITEMP [55]. Fig. 19 provides an overview of the update for ¹⁴N¹⁶O, which highlights the expanded spectral range (up to 23,727 cm⁻¹) and the increase in vibrational band coverage (up to Δν ≤ 14, *ν'* ≤ 26), when compared to HITRAN2016. To take advantage of the increased precision of MW transitions, it should be noted that the wavenumber format for NO has been updated to F12.9 for transitions below 1.0 cm⁻¹, F12.8 for transitions 1.0 to 10.0 cm⁻¹, and F12.7 for transitions 10.0 to 100.0 cm⁻¹ (as previously implemented for HNO₃, PH₃, O₂ and NO⁺).

Air- and self-broadening parameters of NO in HITRAN and HITEMP have been refit to available measurements, and are described in detail by Hargreaves et al. [55]. The air-broadening
<figure><img src="image_23.png" /><figcaption>**Fig. 19.** Overview of the <sup>14</sup>N<sup>16</sup>O (top), <sup>15</sup>N<sup>16</sup>O (middle) and <sup>14</sup>N<sup>18</sup>O (bottom) line lists in HITRAN2020, when compared to HITRAN2016 (indicated by black points).</figcaption></figure>

(where $\gamma_{air} = 0.79\gamma_{N_2} + 0.21\gamma_{O_2}$) is calculated from rotationally-dependant $N_2$ and $O_2$ half-widths provided by separate Padé functions (Eq. (1)) for the $\Omega = 1/2$ and $3/2$ components. The HITEMP update includes transitions with maximum $J = 184.5$, so care was taken to ensure good performance at high-J. The self-broadening half-widths were also revised as part of the HITRAN and HITEMP updates and were fit to the same functional form. The coefficients of Eq. (1) for $N_2$, $O_2$- and self-broadening of the $\Omega = 1/2$ and $3/2$ components of NO are given in Table 3 of Ref. [55].

In addition, the pressure-induced line shifts for air ($\delta_{air}$) that are measured for the fundamental vibrational band [345] have been extended to additional vibrational bands (up to $\Delta\nu = 6$) using the method outlined by Hartmann and Boulet [346]. This same method was previously applied to CO [257] for HITRAN2016.

The HITRAN2020 update for NO also includes the NOname line lists of <sup>15</sup>N<sup>16</sup>O and <sup>14</sup>N<sup>18</sup>O, with the same intensity thresholds as <sup>14</sup>N<sup>16</sup>O applied. The extended coverage when compared to HITRAN2016 is also shown in Fig. 19. Isotopologue analysis of human breath [347] highlighted issues for the intensities of <sup>15</sup>N<sup>16</sup>O in HITRAN2016. The present update contains intensities from NOname for each isotopologue and is therefore expected to address this issue. The NOname line lists for the minor isotopologues <sup>14</sup>N<sup>17</sup>O, <sup>15</sup>N<sup>18</sup>O and <sup>15</sup>N<sup>17</sup>O (with abundances of $3.7 \times 10^{-4}$, $7.3 \times 10^{-6}$ and $1.4 \times 10^{-6}$, respectively) have not been added to HITRAN at this time as they are not expected to contribute significantly to terrestrial atmospheric spectra.

NO also absorbs strongly in the near ultraviolet. In particular, in the 200–230 nm (44,000–50,000 cm<sup>-1</sup>) region its spectrum overlaps those of ammonia, $O_2$ and $O_3$. Qu et al. have recently developed a spectroscopic model which covers the $\beta$, $\gamma$ and $\delta$ bands of NO [348] and associated line list [349] which will be considered for future inclusion in the database.

## 2.9. SO₂: sulfur dioxide (molecule 9)

Sulfur dioxide is an abundant pollutant in the terrestrial atmosphere, being produced by natural (such as volcanoes [350]) and anthropogenic (including coal burning [351]) sources. Characterization of SO₂ is necessary for atmospheric chemistry and climate models, due to its large effect on sulfate aerosols [350]. It is present on Venus, contributing to the Venusian sulfur cycle [352], and SO₂ is also being actively searched for in the atmosphere of Mars [353,354] as it is believed to play an important role in the atmospheres of rocky planets, including exoplanets

[355]. The recently selected NASA DaVinci+ mission to Venus will be equipped with the Tunable Laser Spectrometer (TLS), which will be specifically targeting transitions of different isotopologues of SO₂ to obtain information on sulfur isotope ratios [356]. It is therefore important to expand the amount of the isotopologues of this molecule in HITRAN.

### 2.9.1. Description of new line lists

Recent developments in SO₂ spectroscopy have laid the groundwork for a major update and expansion of the corresponding line list in HITRAN. In particular, semi-empirical line lists from Huang et al. [357], and Naumenko et al. [358], have been identified as major sources for the potential improvement. Both line lists actively employed *ab initio* intensities (sometimes adjusted with empirical values) and systematically verified energy levels available from MARVEL analyses. In the MARVEL work on the SO₂ molecule [58,59], three sulfur isotopologues, <sup>32</sup>S<sup>16</sup>O₂, <sup>33</sup>S<sup>16</sup>O₂, and <sup>34</sup>S<sup>16</sup>O₂, were analyzed, resulting in 15,130, 5852, and 10,893 validated empirical ro-vibrational energy levels, respectively [359]. The <sup>32</sup>S<sup>16</sup>O₂, <sup>33</sup>S<sup>16</sup>O₂, and <sup>34</sup>S<sup>16</sup>O₂ MARVEL datasets, collated from the literature, contain 40,269, 15,628, 31,080 ro-vibrational lines, respectively [359]. Both Huang et al. [357], (hereafter referred to as Ames) and Naumenko et al. [358] (hereafter referred to as Naumenko) line lists and their evaluations against available laboratory spectra are briefly described below.

From 2014 to 2016, NASA Ames-296K *ab initio* IR line lists were published for <sup>32</sup>S<sup>16</sup>O₂, <sup>33</sup>S<sup>16</sup>O₂, <sup>34</sup>S<sup>16</sup>O₂ [360,361], and <sup>16</sup>O<sup>32</sup>S<sup>18</sup>O [362]. They were computed on a PES empirically refined with selected lines taken from HITRAN2012 with line position uncertainty codes ≥4 (see Table 2) [15] (unchanged in HITRAN2016 [16]), and an original *ab initio* dipole moment surface determined at the CCSD(T)/aug-cc-pV(Q+d)Z level of theory. Compared to the bands in HITRAN2012 [15], the agreement for intensities was usually better than 90-95% [360,361]. The consistency of the Ames-296K line lists has been systematically investigated to explore the possibility of further improvements [363,364]. Using the same potential and dipole surfaces, Underwood et al. [365] reported a hot <sup>32</sup>S<sup>16</sup>O₂ line list containing 1.3 billion lines. With more complete calculations at higher $J$ values and extending to a higher energy range, the list was expected to provide the most complete coverage for 0-8000 cm<sup>-1</sup> and temperatures up to 2000 K.

Although line position predictions from the *ab initio* works described above have matched recent experiments with $\sigma_{RMS} = 0.01-0.02$ cm<sup>-1</sup>, this accuracy is not sufficient for atmospheric applications. In order to improve the line positions, experimental line positions and Effective Hamiltonian (EH) models based upon ro-vibrational energy levels published between 2009 and 2017 were collected and analyzed for <sup>32</sup>S<sup>16</sup>O₂ [366–373], <sup>33</sup>S<sup>16</sup>O₂ [374,375], <sup>34</sup>S<sup>16</sup>O₂ [376–379], and <sup>16</sup>O<sup>32</sup>S<sup>18</sup>O [380–384]. With $J \le 75$ (the limit of the Ames-296K line lists) and S<sub>296K</sub> $\ge 10^{-26}$ cm/molecule, 26,464, 25,089, 20,820 lines can be matched for <sup>32</sup>S<sup>16</sup>O₂, <sup>34</sup>S<sup>16</sup>O₂, and <sup>16</sup>O<sup>32</sup>S<sup>18</sup>O, respectively. These “New Line Sets” and other <sup>32</sup>S<sup>16</sup>O₂ and <sup>34</sup>S<sup>16</sup>O₂ data from HITRAN2016 [16] were updated with reliable ground state EH models [371,384,385]. A complete list of observed and calculated energy levels of <sup>33</sup>S<sup>16</sup>O₂ [386] was incorporated at this stage. The resulting energy levels and other published EH model based levels were taken as the “corrected” reference energy set. Transitions were extracted from the Ames-296K line lists if their lower and upper state energy levels could be matched and replaced by the reference set values. Those extracted lines formed the “Expanded Line Sets”. These contain 195,425/162,403/242,889/123,441 lines for <sup>32</sup>S<sup>16</sup>O₂/<sup>34</sup>S<sup>16</sup>O₂/<sup>16</sup>O<sup>32</sup>S<sup>18</sup>O/<sup>33</sup>S<sup>16</sup>O₂, in the range of 0–4151/3465/2974/2625 cm<sup>-1</sup>, with maximum $K''_a = 42/39/32/35$ for 16/13/11/6 vibrational states and 79/59/39/20 bands. Similarly, an “Ames+MARVEL” line set was extracted from the Ames-296K line lists.