MIPAS database : new HNO 3 line parameters at 7 . 6 μ m validated with MIPAS satellite measurements

Improved line positions and intensities have been generated for the 7.6 μm spectral region of nitric acid. They were obtained relying on a recent reinvestigation of the nitric acid band system at 7.6 μm and comparisons of HNO3 volume mixing ratio profiles retrieved from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) limb emission radiances in the 11 and 7.6 μm domains. This has led to an improved database called MIPAS-2015. Comparisons with available laboratory information (individual line intensities, integrated absorption cross sections, and absorption cross sections) show that MIPAS-2015 provides an improved description of the 7.6 μm region of nitric acid. This study should help to improve HNO3 satellite retrievals by allowing measurements to be performed simultaneously in the 11 and 7.6 μm micro-windows. In particular, it should be useful to analyze existing MIPAS and IASI spectra as well as spectra to be recorded by the forthcoming Infrared Atmospheric Sounding Interferometer – New Generation (IASING) instrument.


Introduction
Optical remote sensing of nitric acid in the infrared range can be performed using the three strongest band systems of this species, namely the {ν 5 , 2ν 9 }, {ν 3 , ν 4 }, and ν 2 band systems located near 11, 7.6, and 5.8 µm respectively.Focusing on the spectral ranges covered by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) instrument (Fischer et al., 2008) that was operational on board the ENVISAT satellite (Endemann, 1999) in the years from 2002 to 2012, Flaud et al. (2006 and references therein) created a HNO 3 linelist covering the 600-1800 cm −1 region with the aim to provide the best and most consistent possible set of line parameters (positions, intensities, and shape-specific parameters) for this molecular species.Subsequent laboratory and theoretical studies (Gomez et al., 2009;Laraia et al., 2009) revisited this linelist.The updated linelist thus produced and validated (Tran et al., 2009) is implemented in the HITRAN (Rothman et al., 2009(Rothman et al., , 2013) ) and GEISA (Jacquinet-Husson et al., 2011) databases.It will be called MIPAS-OLD in the following.
However, retrievals of nitric acid at altitudes higher than ∼ 35-40 km would benefit from the use of the stronger infrared signatures at 5.8 or 7.6 µm.A thorough error analysis shows that, since the first spectral region overlaps rather strongly with water vapor absorption in atmospheric spectra, it is preferable to use the 7.6 µm band system.However, the quality of retrievals in this spectral range was up to now hampered by the rather poor quality of the HNO 3 line positions and line intensities.The present effort aims to provide for the 7.6 µm spectral region of nitric acid spectroscopic data of the best possible quality in order to allow the retrieval of this species using the 11 and 7.6 µm regions simultaneously.It relies on an improved analysis of the nitric acid band system at 7.6 µm (Perrin, 2013), summarized in Sect.2, and comparisons of HNO 3 volume mixing ratio (VMR) profiles retrieved from MIPAS limb emission radiances using MIPAS-OLD line parameters for the 11 µm region and the updated spectroscopic information generated in the present work for the 7.6 µm range.This work is described in Sect.3. The resulting linelist, called MIPAS-2015, thus contains new and more precise information for the 7.6 µm region of HNO 3 , as compared to MIPAS-OLD.The quality of the update was evaluated by comparisons with available laboratory information (individual line intensities, integrated absorption cross sections, and absorption cross sections).This assessment of the MIPAS-2015 linelist is described in Sect. 4.
2 Improved analysis of the 7.6 µm region of HNO 3 At 7.6 µm, the MIPAS-OLD data originate from two laboratory studies, focused on line positions (Perrin et al., 1989) and line intensities (Perrin et al., 1993).The corresponding linelist is limited to the ν 3 and ν 4 bands of the main isotopologue, H 14 N 16 O 3 , and the quality of the corresponding line positions and intensities is rather poor.Indeed, the theoretical model used to calculate the upper state energy levels accounted only for resonances coupling energy levels belong-ing to the V3 and V4 bright states, neglecting contributions from several dark states present in the same energy range (see Table 1), thus limiting the quality of the frequency analysis (Perrin et al., 1989).The subsequent updates (Godman et al., 1998;Flaud et al., 2006), which consisted only in an absolute intensity calibration, did not improve the situation.
A complete reinvestigation of the ν 3 and ν 4 bands of nitric acid at 7.6 µm was performed recently (Perrin, 2013).Contrary to the previous analysis (Perrin et al., 1989(Perrin et al., , 1993(Perrin et al., , 1989)), the new Hamiltonian model accounts fully for the various vibration-rotation resonances and torsional effects affecting the V3 and V4 bright states and the four dark states 2V6, 3V9, V5 + V9, and V7 + V8.The relative line intensities at 7.6 µm were calculated, also accounting for the observed resonances (Perrin, 2013).Additionally, the ν 3 +ν 9 -ν 9 hot band could be identified for the first time (Perrin, 2013).1) the ν 3 and ν 4 cold bright bands, the 2ν 6 , 3ν 9 , ν 5 + ν 9 , ν 7 + ν 8 cold weak bands, and the ν 3 +ν 9 -ν 9 hot band of the main isotopologue.Line shape parameters (air-and self-broadening coefficients, temperature dependence of the air-broadening coefficient, and air-shift coefficients) were added using the corresponding information available in MIPAS-OLD for the 11 µm spectral range of HNO 3 (Rothman et al., 2009).The HNO 3 linelist at 7.6 µm of the MIPAS-OLD database was completely replaced by the new linelist, leading to the socalled MIPAS-2015 linelist.The remainder of MIPAS-OLD was left unchanged.
Using MIPAS radiances, an absolute intensity calibration was performed to "convert" the relative line intensities at 7.6 µm to absolute intensities.More precisely, this was done by comparing HNO 3 VMR retrieved from MIPAS radiances using the MIPAS-2015 linelist in either the 7.6 or the 11 µm regions.A multiplicative factor was applied to all the line intensities at 7.6 µm so that in the height range of the HNO 3 VMR peak (∼ 21-24 km), the VMR retrieved using the 7.6 µm interval matches that retrieved using the 11 µm region.
The retrieval algorithm used for the tests presented in this work is the so-called optimized retrieval model (ORM) version 7.0, that is, the scientific prototype of the code used by the European Space Agency (ESA) for routine MIPAS data processing (Ridolfi et al., 2000;Raspollini et al., 2006Raspollini et al., , 2013)).The retrieval is based on the inversion of narrow (max 3 cm −1 ) spectral intervals, called micro-windows (MWs).The MWs used in our test retrievals are listed in Table 2.These are selected using the MWMAKE algorithm of Dudhia et al. (2002).Out of a user-supplied broad spectral inter-  Channel is a MIPAS identifier; σ min and σ max (cm −1 ) are the lower and higher wavenumber limits of the micro-windows.
val, this algorithm selects optimized MWs that contain relevant information on the atmospheric target parameters to be retrieved (the HNO 3 VMR in our case).The selection aims at the minimization of the total retrieval error.The latter is evaluated, taking into account the measurement noise, the errors due to the uncertainties in the (previously retrieved) pressure and temperature, the error due to spectral interferences of non-retrieved atmospheric gases, and several instrument and forward model errors.The full list of the considered error components is reported in Dudhia (2007).In order to limit the influence of the error due to the mutual spectral interference of the main atmospheric emitting gases, in the test retrievals presented in this study we adopt the following retrieval strategy: first we jointly retrieve tangent pressures and the temperature profile then, sequentially, we retrieve the VMR profiles of H 2 O, O 3 , HNO 3 , CH 4 , N 2 O, and NO 2 .For the remaining interfering gases we assume the climatological profiles of Remedios et al. (2007).
At the end of the MW selection process, MWMAKE provides estimates of the various error components affecting the HNO 3 VMR profile derived from the inversion of the selected MWs.As an example, at 21 km height, for the MWs listed in Table 2 we get following error estimates.a.When using the MWs at 11 µm we get the total error due to the uncertainties in pressure, temperature, and its horizontal gradient, 4 %.The interference error due to H 2 O is 0.2 %; the interference error due to NH 3 is < 0.1 %.The error due to radiometric and instrument line shape (ILS) calibration is 2 %.Other error sources are much smaller than the above contributions.
b.When using the MWs at 7.6 µm we get the total error due to the uncertainties in pressure, temperature, and its horizontal gradient, 14 %.The interference error due to H 2 O is 6.7 %; the interference error due to N 2 O is 2.3 %; the interference error due to CH 4 is 3.4 %; The error due to radiometric and ILS calibration is 2 %.Other error sources are much smaller than the above contributions.
MWMAKE also provides an estimate of the error due to measurement noise; however, being based on assumed instrument radiometric performance figures, the estimate itself is not extremely accurate.A more reliable estimate of this error is provided by the covariance matrix of the Levenberg-Marquardt inversion method (Ceccherini et al., 2010), that is, based on the actual noise determined by the MIPAS Level 1b processor for each measurement.At the altitude of 21 km this method provides, on average, an error of 1.8 % when using the MWs at 11 µm, and of 2.4 % when using the MWs at 7.6 µm.Note that apart from the error due to radiometric and ILS calibration, all the other error components mentioned above behave randomly when considering a statistically significant set of retrieved profiles spanning the whole globe.
The left panel of Fig. 1 shows averages of 929 HNO 3 VMR profiles retrieved from the MIPAS limb scanning radiances (Level 1b version 7.11) acquired on 24 January 2003 with a Fourier transform spectrometer spectral resolution of 0.025 cm −1 .In this test, the profiles are retrieved using the MIPAS-2015 linelist and MWs, alternately in the 11 µm region (red line) or in the 7.6 µm region (blue line).Being the average of a large number of profiles, the noise error bars are not visible in the plot.We notice that the profiles retrieved from the two spectral regions are in excellent agreement.To better quantify the residual discrepancies, in the right panel of Fig. 1 we show the percentage differences (black line) between the average profiles retrieved using MWs in the 7.6 and in the 11 µm region.The error bars of the black line represent the statistical error of the mean difference.At each altitude, this error is calculated as the standard deviation of the profile differences divided by the square root of the number of samples at the considered altitude.It accounts, therefore, for all the components of the VMR error that, as mentioned above, vary randomly within our sample.Note that, especially in the altitude range from 15 to 30 km, where the individual profile retrievals are more stable due to the larger sensitivity of the limb measurements to the HNO 3 amount, the maximum bias between the average profiles is less than 0.8 %.Being the average of a large number of profiles, the random error on the evaluated bias (error bars of the black line of Fig. 1) is rather small.
An additional (systematic) error on the evaluated bias arises from the inter-band radiometric calibration error in the MIPAS spectra used (Kleinert et al., 2007).The radiometric calibration of MIPAS spectra is constant within the set of measurements considered in the tests of Fig. 1.However, since it is renewed on a weekly basis, to evaluate the impact of this error source in the calibration of the HNO 3 linelist in the 7.6 µm region, we repeated the test illustrated in Fig. 1 with different sets of MIPAS measurements with different radiometric calibrations.We selected MIPAS measurements acquired in three different days of the years 2002 and 2003 (still measurements acquired with the MIPAS full spectral resolution of 0.025 cm −1 ).The results of these additional tests show that, actually, the observed differences between the average HNO 3 VMR retrieved from the 11 and the 7.6 µm regions amount to a maximum of 1.5 % in the height range from 15 to 30 km.This is the accuracy we attribute to our HNO 3 linelist calibration procedure.The blue and red lines in the right panel of Fig. 1 indicate the ± noise error of an individual profile retrieval determined from the covariance matrix of the Levenberg-Marquardt inversion method  (Ceccherini et al., 2010).While the inversion with the MWs in the 11 µm region provides a smaller retrieval error below 23 km, the MWs in the 7.6 µm region provide a smaller error above 30 km.This behavior is due to the larger intensity of the HNO 3 band system in the 7.6 µm region.This effect is however noticeable only at high altitudes.In the troposphere or lower stratosphere the presence of H 2 O emission lines in the 7.6 µm region masks the signal from HNO 3 .
As a term of comparison, to better highlight the achieved improvements, in Fig. 2 we show the results of a test analogous to that of Fig. 1, but using the MIPAS-OLD line database.We see that in this case the agreement between the HNO 3 VMR retrieved from the 11 and 7.6 µm regions is not better than 8-10 %.
Beyond the better consistency between the two HNO 3 band systems at 11 and 7.6 µm, the new HNO 3 linelist at 7.6 µm allows a much more accurate simulation of the MIPAS-observed spectra.The average normalized chisquare value of the inversion fit with the MWs selected in the 7.6 µm region changes from the value of 1.616 achieved with the MIPAS-OLD linelist, to the value of 1.227 with the MIPAS-2015 linelist.This reduction in the chi-square value is clearly due to the improvement of the residuals of the fit, i.e., of the differences between observed and simulated spectra.To show the improvements in the residuals, for the MI-PAS orbit 04712 acquired on 24 January 2003, we computed the average observed spectrum, the average simulated spectrum, and the average residual spectrum for the two test retrievals using the MIPAS-OLD and the MIPAS-2015 HNO 3 linelists.We obtained the average by co-adding the spectra with nominal tangent altitudes of 21, 24, 27, and 30 km.In total, each average spectrum is the result of a co-adding of 288 individual spectra.Since MIPAS measurement noise in the 7.6 µm region is of the order of 14 nW (cm 2 sr cm −1 ) −1 , the noise error on the average residuals is of the order of 0.8 nW (cm 2 sr cm −1 ) −1 , i.e., much smaller than the actual features observed in the residuals themselves.
In Figs.
3-5 we show some average spectra and residuals.In each of these figures the black line is the average observed spectrum; the magenta and orange lines are the average simulations obtained with the MIPAS-OLD and the MIPAS-2015 linelists respectively.For better readability of the plots, the lines representing the average simulated spectra are shifted with respect to the observation as specified in the figure caption.The blue and the red lines represent the average residuals computed as the difference between the average observation and the average simulation using, respectively, the MIPAS-OLD and the MIPAS-2015 HNO 3 linelists.From these figures we can clearly appreciate improvements in the residual spectra achieved with the new HNO 3 linelist.In fact such improvements are due, on the one hand to the fact that thanks to an improved theoretical model which accounts for the resonance effects, the cold bands are much better modeled, and on the other hand to the inclusion of the hot band ν 3 + ν 9 -ν 9 (see Table 3 and Fig. 5).More precisely, Table 3 compares the information available for the 7.6 µm region of HNO 3 in the MIPAS-OLD and MIPAS-2015 databases.It shows that the new database includes lines from four weak bands (2ν 6 , ν 5 +ν 9 , ν 7 +ν 8 and 3ν 9 ) together with those from the ν 3 and ν 4 bands which were already present in MIPAS-  OLD: this is because the theoretical model used in 2013 (Perrin, 2013) to generate the linelist is more sophisticated than in 1993 (Perrin et al., 1993).NB is the number of lines; σ min and σ max (cm −1 ) give the wavenumber range of the bands; S min and S max are the smallest and largest line intensity in cm −1 (molecule cm 2 ) −1 at 296 K; S tot is the sum of the line intensities in cm −1 (molecule cm 2 ) −1 at 296 K.

Individual line intensities at 7.6 µm
To the best of our knowledge, individual line intensities have been measured in the 7.6 µm region of the HNO 3 spectrum in only two contributions (May and Webster, 1989;Perrin et al., 1993).Laboratory measurements of individual line intensities are indeed rather difficult for HNO 3 since the line widths (γ Voigt ∼ 0.002 cm −1 in laboratory conditions usually used for this unstable species (296 K and 0.3 hPa)) are of the same order of magnitude as the separation of adjacent lines (from 0.002 to 0.010 cm −1 ), resulting in a lot of blended lines.
Intensities measured for blended lines being most probably characterized by a reduced precision, the comparison between line intensities reported in these two studies and those included in the MIPAS-2015 database was limited to wellidentified and unblended lines.Table 4 presents the averages of the ratios R = Int(MIPAS-2015) / Int(Obs) of line intensities in MIPAS-2015 with the corresponding measured values.It shows that, on average, the line intensities of MIPAS-2015 are about 27 % weaker and 39 % stronger than measured by May and Webster (1989) and Perrin et al. (1993), respectively.
In view of these diverging results, we decided to measure individual line intensities for nitric acid using a Fourier transform spectrum, recorded in Giessen in 2002 (Perrin The comparison accounts for the temperature conversion to 296 K; no. is the number of line intensities included in the average.The numbers in parentheses are the standard deviations, in the units of the last digit quoted. Figure 6.Comparison between the line intensities measured in this work using a Fourier transform spectrum (Obs, 299.7 K, 0.03 hPa, absorption path length = 302 cm, Perrin et al., 2004;Perrin, 2013) and those available in MIPAS-2015.The comparison, performed as a function of the intensities and wavenumbers (upper and lower panels, respectively), accounts for the temperature correction from 299.7 to 296 K. et al., 2004).This spectrum was recorded in the 718-1436 cm −1 spectral region at 299.7 K, at a pressure of 0.03 hPa and with an absorption path length of 302 cm (more details can be found in Perrin et al., 2004).Assuming a Gaussian line profile and including instrumental effects arising from the maximum optical path difference of 542 cm and the 1.3 mm entrance aperture used, 348 line intensities were measured for well-isolated lines in the 7.6 µm region using the program WSpectra (Carleer et al., 2001).Figure 6 presents an overview of the comparison between these measured line intensities and those available in MIPAS-2015.
No clear trend with respect to line positions or line intensities is noticeable.On average, the intensities quoted in MIPAS-2015 are only 5 % smaller than those measured during the present investigation.As shown in Table 4, this corresponds to a much better agreement than with previous works, although this is not a definite confirmation of the accuracy of the line intensities in MIPAS-2015 because the uncertainty of measurement of the HNO 3 pressure for the Giessen spectrum is not precisely known.It is worth noting that large variations of the ratio R are observed, as shown in Fig. 6; they reflect in the standard deviation on R which is rather large.Similar behaviors were observed for the other two sets of line by line intensity measurements (May and Webster, 1989;Perrin et al., 1993).Possible explanations of these rather large standard deviations include the fact that it is not always possible to avoid blended lines in the congested 7.6 µm spectral region, even if care was taken to avoid them, and that the theoretical model used to compute the line intensities is still imperfect, as discussed in detail in Perrin (2013).Flaud et al. (2006) reviewed the integrated band intensities reported in the literature at 11 and 7.6 µm (Goldman et al., 1971;Giver et al., 1984;Massie et al., 1985;Hjorth et al., 1987;Chackerian et al., 2003).As shown in Table 5, these literature results are in reasonable agreement with each other.

Integrated band intensities
As measured integrated band intensities include the contributions of hot bands and bands from isotopologues other than H 14 N 16 O 3 , comparison of the experimental integrated band intensities with the sum of the individual line intensities listed in the MIPAS databases require use of the following expression (see Appendix A of Flaud et al., 2006 andRotger et al., 2008): where S k is the intensity of line k in the MIPAS database accounting for the isotopic abundance, Z vib (T ) is the vibrational partition function of H 14 N 16 O 3 (Z vib (296 K) = 1.29952) and I a = 0.989 is its isotopic abundance.The summation in Eq. ( 1) runs over all the lines of all the cold bands listed in Table 3.In Table 5, the integrated band intensities calculated using MIPAS-OLD and MIPAS-2015 with Eq. ( 1) are compared with the experimental values reported for the 11 and 7.6 µm regions.Considering their associated uncertainties, one can say that MIPAS-2015 is in agreement with the most recent measurements.

Absorption cross sections
We also performed direct comparisons with the experimental absorption cross sections available in the Pacific Northwest National Laboratory (PNNL) library (Sharpe et al., 2004).Figure 7 compares the PNNL experimental absorption cross sections at 7.6 µm with absorption cross sections calculated at the same conditions using MIPAS-2015 and MIPAS-OLD (assuming that the N 2 -broadening coefficients are the same as the air-broadening coefficients provided in these databases).Figure 7 shows that the agreement is significantly All the intensities are given in 10 −17 cm −1 (molecule cm 2 ) −1 at T = 296 K, 7.6 µm/11 µm R= 7.6 µm S band (296 K)/ 11 µm S band (296 K).  better with MIPAS-2015.In particular, the improvement is really significant at 1331.1, 1341.1, and 1343.8 cm −1 ; this is because the contribution of the ν 3 + ν 9 -ν 9 hot band and of the ν 7 + ν 8 and ν 5 + ν 9 dark bands are correctly accounted for in the new database.

Conclusions
An improved set of line positions and intensities called MIPAS-2015 has been generated for the 7.6 µm spectral region of nitric acid.They were obtained relying on a recent reinvestigation of the nitric acid band system at 7.6 µm and on comparisons of HNO 3 volume mixing ratio profiles retrieved from the MIPAS limb emission radiances in the 11 and 7.6 µm domains.Comparisons with available laboratory information (individual line intensities, integrated absorption cross sections, and absorption cross sections) showed the improvement brought by the new database MIPAS-2015 as compared to the old one clearly.

Figure 1 .
Figure 1.Left panel: average HNO 3 VMR profiles from MIPAS measurements acquired on 24 January 2003, using the MIPAS-2015 linelist.Retrievals using MWs in the 11 µm region (red line) and in the 7.6 µm region (blue line).Right panel: mean percentage differences between HNO 3 profiles retrieved from the 7.6 and 11 µm regions (black line).The red and the blue lines show the noise error of the individual retrievals using MWs in the 11 and in the 7.6 µm spectral regions.

Figure 2 .
Figure 2. Left panel: average HNO 3 VMR profiles from MIPAS measurements acquired on 24 January 2003, using the MIPAS-OLD linelist.Retrievals using MWs in the 11 µm region (red line) and in the 7.6 µm region (blue line).Right panel: mean percentage differences between HNO 3 profiles retrieved from the 7.6 and 11 µm regions (black line).The red and the blue lines show the noise error of the individual retrievals using MWs in the 11 and in the 7.6 µm spectral regions.

Figure 3 .
Figure 3. Average MIPAS-observed spectrum (black) in the 1314-1320 cm −1 spectral region, and spectra simulated with the MIPAS-OLD (magenta line) and the MIPAS-2015 (orange line) HNO 3 linelists.For better readability of the plot, the average orange and magenta lines were shifted by 100 and 200 nW (cm 2 sr cm −1 ) −1 respectively.The blue and the red lines are the residuals obtained with the MIPAS-OLD and the MIPAS-2015 linelists respectively.

Figure 4 .
Figure 4. Average MIPAS-observed spectrum (black) in the 1324.5-1326.5 cm −1 spectral region, and simulated spectra with the MIPAS-OLD (magenta line) and the MIPAS-2015 (orange line) HNO 3 linelists.For better readability of the plot, the average orange and magenta lines were shifted by 50 and 100 nW (cm 2 sr cm −1 ) −1 respectively.The blue and the red lines are the residuals obtained with the MIPAS-OLD and the MIPAS-2015 linelists respectively.

Figure 5 .
Figure 5. Average MIPAS-observed spectrum (black) in the 1329.5-1331.5 cm −1 spectral region, and simulated spectra with the MIPAS-OLD (magenta line) and the MIPAS-2015 (orange line) HNO 3 linelists.For better readability of the plot, the average orange and magenta lines were shifted by 50 and 100 nW (cm 2 sr cm −1 ) −1 respectively.The blue and the red lines are the residuals obtained with the MIPAS-OLD and the MIPAS-2015 linelists respectively.
1 PNNL: Pacific Northwest National Laboratory. 2 To estimate the integrated band intensities for MIPAS-OLD and MIPAS-2015, the sums of the cold band intensities (listed in Table3) are multiplied by 1.314 (see text for details).

Figure 7 .
Figure 7. Upper panel: absorption cross sections from PNNL(Sharpe et al., 2004, black trace), and calculated using MIPAS-OLD (blue trace) and MIPAS-2015 (red trace); lower panel: corresponding residuals.For these calculations, the contributions of hot bands and bands from isotopologues other than H 14 N 16 O 3 were accounted for by multiplying the calculated absorption cross sections by the ratio Z Vib (300 K)/I a = 1.314 (see Eq. 1).

Table 4 .
Average ratios R mean of line intensities included in MIPAS-2015 (at 296 K) and measured in the literature and in this work.