Precise knowledge of the atmospheric water vapour absorption not only is crucial to calculate Earth's radiation budget since water vapour is the largest contributor to the natural greenhouse effect but also needs to be known at high precision when retrieving other atmospheric absorbers from spectroscopic measurements in the UV/VIS wavelength range. If their absorptions overlap, this can lead to errors in measurements of several trace gases. Due to technical limitations and since the absorption cross-sections are small in the region below 500 nm (above 20 000 cm-1), the body of available experimental data in this spectral interval is sparse. Numerous absorption lines in the blue spectral region included in absorption line databases like HITRAN 2009 , HITRAN 2012 and HITEMP are therefore based on theoretical calculations only. According to and references therein, validation measurements of individual water absorption lines are only available at wavelengths longer than 394.7 nm (25 337 cm-1), but a large fraction of the absorption lines included in the databases in this region is not validated by measurements.

More recently, water vapour absorption was also observed and modelled in the UV range below 370 nm. The HITEMP absorption line database for H2O relies to a large extent on the ab initio line list BT2 calculated by . Including the BT2 data increased the number of absorption lines especially in the blue wavelength region drastically: from 410 to 434 nm (W1 + W2, see Table ) HITRAN 2009 contains 20 absorption lines with intensities above 10-27 cm molec-1 at room temperature, and HITEMP and BT2 contain 382 individual absorption lines. Ratios of absorption line intensities from BT2 and HITEMP are found between 0.5 and 3, because experimental data included in HITRAN 2009 were only combined with the BT2 data when certain criteria were met, as described in . An overview of the cross-sections from HITRAN 2009, HITEMP and BT2 is shown in Fig. . Convolved to a resolution of 0.5 nm, the differences between the HITRAN 2012 cross-section and the HITEMP cross-section are negligible; therefore they are treated as equivalent here.

The vibrational state of the triatomic asymmetric top water molecule can be described in standard normal mode notation by three quantum numbers: ν1 (symmetric stretch), ν2 (bend) and ν3 (asymmetric stretch). The water vapour absorption shown in Fig.  has its structure due to the closeness of the numerous interacting vibrational states. These absorption structures can be named using a convention described in : a polyad is given a label nν, where n is ν1+ν2/2+ν3 for even ν2 and nν+δ for odd ν2.

A widely used approach to measure trace gases in the atmosphere of the Earth is the technique of differential optical absorption spectroscopy (DOAS) . Typically, absorption spectra covering 100–200 nm sections in the UV or visible spectral range are recorded by a grating spectrometer at a spectral resolution of 0.3–1 nm. Suitable evaluation of differential absorption structures allows quantitative determination of column densities and concentrations of numerous trace gas species, even if their spectral features overlap. This allows for simultaneous evaluation of several trace gases in the atmosphere at high temporal resolution.

Absorption path lengths for different DOAS setups range from several hundreds of metres to several tens of kilometres in the free troposphere. Optical densities (ODs) can often be resolved down to 1×10-4 e.g., which in turn means that water absorption lines can be observed up to an accuracy of 5×10-28 cm2 molec-1 at a resolution of typically 0.5 nm when other absorbers in the respective spectral region are well known and/or their total absorptions are small.

While absorption structures due to known absorbers can be readily disentangled, problems can arise from unknown spectral features. One example – as mentioned above – is the uncertainty of the weak absorption features of water vapour in the blue spectral region.

Frequently the actual water vapour content during the measurements is not of primary interest, but nevertheless water needs to be corrected for when evaluating the absorption spectra. For example, weak water absorptions can be found in the typical evaluation range of iodine monoxide (ca. 414–440 nm). Iodine monoxide (IO) plays a role in atmospheric chemistry and creation of cloud condensation nuclei. Elevated IO levels can be found in coastal areas e.g. as well as on the open ocean e.g., in the free troposphere e.g. and in polar regions e.g.. For a typical tropospheric water vapour slant column density (SCD) found in moderate climate of SH2O= 4 × 1023 molec cm-2 the resulting optical density is 2.5 × 10-3 (when taking the cross-section data from HITEMP) at a spectral resolution of 0.5 nm. Optical densities due to IO in the tropical marine boundary layer are 5 times weaker, i.e. of the order of 4 × 10-4; thus to avoid possible errors in the retrieval of IO due to incomplete correction of the water vapour absorption, precise knowledge of the water vapour absorption cross-section is essential. Older versions of HITRAN such as HITRAN 2000 did not even include any absorptions in this spectral range.

Even more important is the correction of water vapour absorptions for the retrieval of glyoxal e.g.and references therein, which can be evaluated in the spectral range from 432 to 458 nm. For a typical tropospheric water vapour SCD SH2O=4×1023 molec cm-2 the resulting OD is 1.7×10-2 in this wavelength range at a spectral resolution of 0.5 nm, while the typical glyoxal differential slant column densities (dSCDs) as reported by for the marine boundary layer of 1.5 × 1015 molec cm-2 correspond to 8×10-4 and thus is 10 times weaker than the water vapour absorption. Moreover, the main spectral absorption features of water vapour and glyoxal overlap in some parts, potentially introducing cross-sensitivities and/or increasing the measurement error. At the spectral region of maximum absorption of glyoxal the difference between the water vapour absorption cross-sections found in HITRAN 2000 and HITEMP for a typical SCD SH2O= 4 × 1023 molec cm-2 is about 4×10-4 and amounts to one-half of the reported glyoxal absorption. Recently the accuracy of glyoxal measurements by CE-DOAS and MAX-DOAS was estimated from chamber measurements by and field measurements by . For their instruments, water vapour absorption can explain an uncertainty of 5 pptv glyoxal and less than 15 pptv glyoxal .

Water vapour absorption can also have an impact on the spectral retrieval of the oxygen dimer O4 (also called O2–O2) around 477 nm. Its column densities can be used to constrain radiative transfer simulations in remote sensing application and to obtain height profile information of aerosol extinction and trace gas concentrations e.g..

Water vapour column densities have been measured in the blue wavelength range from satellite as well as from ground-based instruments . Here the 7ν absorption at 442 nm from HITRAN 2004 has been used for retrieving the atmospheric water vapour column density. These measurements require precise water vapour absorption cross-sections as well to minimise retrieval errors.

If significant absorptions of water vapour were present below 370 nm, these could have an effect on the spectral evaluation of measurements of e.g. BrO, HCHO, HONO, SO2 and O4. Based on currently available cross-section data, no atmospheric water vapour absorptions in this spectral range have been reported for DOAS measurements so far.

The data analysed here were collected during two field campaigns (see Table 1) in which different instruments were used. The DOAS measurements during both campaigns, research cruise SOPRAN M91 off the coast of Peru and HaloCaVe on Cape Verde, aimed to quantify the abundance of reactive trace gases, especially IO and BrO, in the marine boundary layer. HaloCaVe took place parallel to SOPRAN cruise P399 on RV Poseidon in the Mauritanian upwelling region . The absorption of IO is overlayed by water vapour absorption. Therefore proper water vapour correction in the spectral retrieval of IO is crucial to obtain reliable measurements of IO. SOPRAN is embedded in the international Surface Ocean – Lower Atmosphere Study (SOLAS) project.

During the SOPRAN cruise M91 with the research vessel Meteor multi-axis (MAX)-DOAS data were collected in the Peruvian upwelling region in December 2012 .

The sites of both campaigns were located far away from any strong anthropogenic pollution; thus interferences due to e.g. high NO2 mixing ratios on the data evaluation should be negligible.

The DOAS method relies on attenuation of light from suitable light sources by absorbers within the light path according to Lambert–Beer's law I(λ)=I0(λ)exp⁡(-τ(λ)).

The optical density τ(λ) is calculated from a reference spectrum, I0(λ), and a measurement spectrum, I(λ), τ(λ)=-ln⁡I(λ)I0(λ). In order to remove broad-band Mie and Rayleigh extinction, the OD is subdivided into a narrow-band (differential) and a broad-band part, τ(λ)=τB(λ)+τd(λ). τd(λ) is expressed by a sum of the differential parts of possible absorbers with their differential absorption cross-sections σd,i(λ) and concentrations ci of absorber (i.e. trace gas) i. τd(λ)=L∑iciσd,i(λ) The column density Si=L×ci of the trace gas i (with the concentration ci) is calculated by a fitting routine, which is applied to data from a wavelength interval with a width of several nanometres to several tens of nanometres. The absorption path L is known for LP-DOAS measurements and can be estimated or calculated from radiative transfer models for MAX-DOAS measurements. The high-resolution literature cross-sections σL,i are convolved with the instrument function H of the respective setup to obtain σi=H⊗σL,i, the absorption cross-section as it would be determined by the instrument. In an analogous fashion to the optical density, cross-sections can also be subdivided into a broadband and narrow-band (differential) contribution: σi=σB,i+σd,i. The instrument function H is usually measured by observing individual atomic emission lines of mercury, which have a width which is 2 orders of magnitude smaller than the resolution of the instrument . Corrections to this simple convolution procedure are discussed in Sect. .

The water vapour dSCDs derived in different spectral regions of the same measured spectra were compared to each other. In principle the same water vapour dSCD values are expected, but significant differences were found.

Values of the retrieved water vapour SCDs in different spectral intervals were compared to each other. Relative to the differential SCD of W3 SW3, an error-weighted linear regression was done to obtain ax in f(Sx)=ax×SW3. ax is the relative absorption strength of the interval x relative to W3. The results are shown in Table . Typical DOAS fit errors for each cross-section in W0–W5 for individual measurements are summarised in Table . In order to illustrate the differences, one of the data comparison plots with the relative absorption of W1 and W3 for HITEMP is shown in Fig. .

The weights for the linear regression were iteratively calculated according to . A comparison with other methods for error-weighted linear regressions can be found in .

The water vapour absorption at ≈444 nm was used as a reference for the other absorption bands, because it is the strongest absorption in this spectral region (see Table ).

The mathematical error from the regression is small compared to possible systematic errors, which might arise from the DOAS fit itself: its relative size is estimated by using twice the fit error given in Table  following the argumentation of . These errors are then used to calculate the weighted mean deduced from MAX-DOAS and LP-DOAS observations for each of the absorption bands given in Table , when their respective relative fit error is smaller than 25 %.

In order to exclude an impact of glyoxal absorption on the evaluation of water vapour absorptions, the analysis procedure was repeated including glyoxal. The result is comparable to the result without glyoxal absorption, only the amplitude of the weak water absorption around 426 nm was slightly reduced by the additional degree of freedom introduced to the spectral retrieval.

For the LP-DOAS measurements an upper limit of 30 ppt glyoxal see also was determined and its cross-section was also not included in the final analysis.

Other MAX-DOAS observations in the same region showed larger glyoxal dSCDs , which was also detected at various other campaigns in the marine boundary layer as listed in and . The detection limit found here is at the lower range of these observations. As we performed various sensitivity studies for this data set, which could not explain this difference, we assume that this difference could be due to natural variability. The bulk of the measurements published in was not as close to the coast as M91. The measurements by were done in a different region, even north of the equator, which additionally also shows typically larger sea surface temperatures (SSTs) than the data presented here (SST during M91: 14–22 ∘C; ).

The impact on IO dSCDs of the rescaled water vapour absorption is small, as long as the main water vapour absorption feature W3 is not included in the fit interval, which is typically the case as e.g.. The impact on the IO dSCD is found to be smaller than 1 × 1012 molec cm-2 for a fit interval from 418 to 438 nm.

From the fit errors listed in Table  especially for the weak absorption features of water vapour, it can be seen that the development of water vapour absorption compilations from HITRAN 2009 to HITEMP/HITRAN 2012 results in a better fit of the measurement data. The fit errors for the intervals (W0 to W5) of the water vapour absorption cross-section are reduced. Changing from HITRAN 2009 to HITEMP or BT2 reduces nearly all fit errors somewhat; the reduction is dramatic (20–75 %) for the weaker bands (W1, W2 and W4). The smallest relative fit errors are observed for most absorption bands for HITEMP.

The magnitude of the main absorption W3 at 442 nm agrees with data from a meteorological station as shown in Table .

Nevertheless, the relative absorptions of different groups of absorption lines are inconsistent and do not fit our measurements; they are listed relative to W3 in Table . In the BT2 line list and in HITEMP the absorptions from 410 to 434 nm overestimate the observed absorptions approximately by a factor of 2.

noted that the absorption line intensities for transitions involving highly excited vibrational states can depend strongly on the representation of the dipole moment surfaces in the ab initio models, particularly for transitions involving bending modes. This could be in agreement with our observations, since the largest discrepancy between modelled and measured absorptions was observed for the 7ν+δ polyad.

As it turned out in Sect.  a separation of the cross-section into separate cross-sections for different bend mode values ν2 indicates that the difference in relative absorption strength can be attributed to absorption lines with higher bend mode values. Their intensities are systematically overestimated (Table ).

For W0 (394–410 nm) the results from MAX-DOAS and LP-DOAS agree that the magnitude of the absorption at W0 is found to be about 5±6 % smaller in measurements than what is reported in HITEMP.

On the basis of the observed discrepancies in relative absorption band strength, we suggest rescaling the respective water vapour absorption cross-section or including only wavelength intervals in a DOAS analysis where the relative absorption band strengths are sufficiently in agreement with each other. This means e.g. for IO that the water absorption band at 442 nm (W3) should be avoided when the absorption at 426 nm (W2) or even also at 416 nm (W1) is included. For the retrieval of glyoxal with its main spectral absorption features above 440 nm, a wavelength window which does not include water vapour absorption at 426 and 416 nm should be preferred when using these water vapour absorption cross-sections. The same argument applies for choosing a retrieval interval for NO2.

The relative strength of the absorption band W5 around 470 nm and the small fit errors indicate that the water vapour absorption cross-section is unlikely to cause interferences when retrieving O4 dSCDs for radiative transfer modelling in this spectral region.

The water absorptions included in HITEMP below 390 nm were observed in our measurements and found to be smaller than σmax=4×10-27cm2 for the 377 nm region for a spectral resolution of 0.45 nm. Absorptions observed in the 362 nm region might be caused by water vapour or by uncertainties of O4 cross-sections. Here absorptions with ODs of 4×10-4 correspond to water vapour dSCDs of 3 × 1023 molec cm-2 (BT2) or 6 × 1023 molec cm-2 (HITEMP), which are realistic dSCDs in mid-latitude regions. Typical O4 absorptions in MAX-DOAS measurements in this regions are of the order of 2×10-2. Since the O4 absorption is used to retrieve aerosol extinction profiles from MAX-DOAS data, it might be necessary to correctly compensate for water vapour absorption to obtain correct profile information. This would require more theoretical calculations and dedicated validation measurements of the water vapour absorption cross-section below 395 nm.

Another aspect which needs to be considered is the wavelength dependence of the air mass factor in MAX-DOAS measurements covering several significant absorption bands, which implies that low residuals can only be obtained when accounting for these effects. For example, for a water vapour dSCD of 5 × 1023 molec cm-2 these effects will lead to residual structures of ≈2.5×10-4 when including W1–W3 or already ≈1×10-4 within W3 itself (compare also Table ).

The revised line compilations HITEMP and BT2 lead to considerable improvements in DOAS measurements of water vapour and other trace gases. In particular, lowering the threshold above which absorption lines are included in the HITRAN database as well as theoretical and experimental progress led to improved water vapour absorption cross-sections in the blue wavelength range.

We showed that the water vapour absorption fit errors of the DOAS retrieval can be reduced by up to 20–75 % by using current water vapour absorption cross-sections e.g. HITEMP: compared to older versions of HITRAN. This shows that the shape of the water vapour absorption is better reproduced by the HITEMP, reducing the amplitude of residual spectra. When the error in the relative magnitude of several absorption bands are corrected (e.g. by scaling the water vapour absorption cross-sections in the different spectral intervals), the amplitude of residual spectra for larger fit intervals can be reduced significantly (compare e.g. Fig. ), which then allows more reliable retrieval of weak absorbers.

Each of the water vapour absorption cross-sections evaluated here (HITRAN 2009, HITRAN 2012, HITEMP and BT2) was found to have certain limitations for the use in DOAS retrievals in the blue wavelength range. Even after water absorption cross-sections have improved they are still not sufficiently accurate for modern high-precision DOAS measurements of tropospheric trace gases at mid-latitudes. Fit errors obtained from evaluating measurement data were found to become lower for individual absorption features with the improvement of the HITRAN database from HITRAN 2009 to HITEMP and HITRAN 2012. However, we also showed that there are still problems concerning the relative strength of the different absorption bands in the blue wavelength range which need to be addressed.

The correction factor for different absorption bands from 394 to 480 nm, which we derived from our atmospheric measurements listed in Table . They range from 0.5 to 1.9 and are highly significant. Even the most recent water vapour absorption cross-section (HITRAN 2012) still requires the application of correction factors ranging between 0.63 and 1.0. The corrections are necessary for all high-precision DOAS measurements in this spectral range when significant water vapour absorption is present. The here-presented correction factors can be used until better absorption line lists are available. Inclusion of even weaker absorption lines in the databases could further improve the modelling of water vapour optical densities, as indicated by the minimum in fit errors of LP-DOAS data when using the BT2 line list without a threshold for the absolute magnitude of the cross-section of individual absorption lines. From our measurements, water vapour absorptions below 385 nm remain uncertain and do not match current water vapour absorption cross-section data. We could not confirm recent UV water vapour absorption cross-section measurements by and found upper limits for the absorption cross-section which are 2 orders of magnitude lower. Therefore further research to provide more consistent water vapour absorption cross-section data in the UV/VIS range is necessary.

High-quality LP-DOAS measurements along light-path lengths of ≈10 km and a comparably high spectral resolution in a tropical climate seem to be feasible in order to investigate further the relative absorption band strength without the need to correct for radiative transfer effects, especially the study of different vibrational states outlined in Sect. .