In the atmosphere and ocean, liquid water interacts with solar radiation in the visible wavelength range in a variety of ways. Its absorption spectrum, which is called, in the following, the H2Oliq spectrum, results from vibrational transitions (overtone and combination bands), and is relatively smooth in shape e.g.,. It causes the characteristic blue color of clear water. Suspended matter, so-called yellow substances or colored dissolved organic matter (CDOM), often dominates the water color, but this is not the focus of this study. In addition, inelastic scattering processes, both vibrational Raman and Brillouin scattering, by water molecules, result in a change in the photon energy, and thus change the spectrum of the incident light . Inelastic scattering produces a filling-in of Fraunhofer lines, similar to the Ring effect in the atmosphere that results from rotational Raman scattering .

This study is concerned with the well-known remote sensing technique of differential optical absorption spectroscopy (DOAS) e.g.,. The DOAS method has been used for many years in order to detect atmospheric trace gases, e.g., NO2, O3, IO, BrO, HCHO, and CHOCHO, from space e.g., as well as from the ground, ships and aircafts e.g.,.

In remote sensing observations (such as DOAS) of atmospheric trace gases in the visible wavelength range over water surfaces, both liquid water absorption and filling-in of Fraunhofer lines by liquid water are necessarily present, and may disturb the trace gas retrieval if insufficiently compensated for. Obvious examples are satellite nadir measurements such as from the GOME, SCIAMACHY, GOME-2, and OMI instruments e.g.,. As an example, the liquid water absorption in the NO2 DOAS analysis of OMI measurements (see Sect. ) is shown in Fig. a. It is important to mention that phytoplankton pigment absorption (which is not included in the DOAS analysis performed here) dominates the color of the water and, consequently, the pattern of liquid water absorption shown in Fig. a is very similar to the pattern of clear natural water having low chlorophyll concentration. However, if the liquid water absorption spectrum is not considered in the DOAS analysis, the rms of the fit reproduces the pattern of clear water as shown in Fig. b, while no enhanced rms is observed in regions where chlorophyll is present in higher amounts. Thus, the compensation of liquid water effects seems to limit the DOAS fit quality in the spectral region used here (425–497 nm), rather than chlorophyll absorption.

Several previous studies demonstrated the presence of liquid water effects in satellite observations. Most of them addressed the topic of vibrational Raman scattering (VRS). For example, modeled ocean Raman scattering in the UV, and described a method to account for the effect on satellite measurements. used for many years in order to detect studied the impact of VRS on trace gas retrievals from the GOME satellite instrument, and found that neglecting VRS can cause significant errors in the DOAS analysis, e.g., more than 30 % for BrO slant columns over clear ocean scenarios. In the UV spectral range, the filling-in of Fraunhofer lines by VRS in the ocean is decreased by chlorophyll and dissolved organic matter (DOM) as they absorb UV radiation (also, the pure water absorption increases drastically with decreasing wavelength in the UV). This was used to retrieve the oceanic chlorophyll content by . Different phytoplankton groups have been derived from SCIAMACHY satellite measurements using their absorption characteristics in an adapted (phyto-)DOAS analysis . More recently, modeled the effect of inelastic Raman scattering in ocean water using the SCIATRAN radiative transfer model. With this, VRS was used in satellite data as a proxy for the abundance of light in the global ocean, which is an important parameter for modeling phytoplankton primary production . However, spectral effects of liquid water are not only present in satellite nadir observations, but also in ground-based MAX-DOAS (Multi-AXis differential optical absorption spectroscopy) measurements towards the water surface, close to the horizon and even at small elevation angles above the horizon, as some photons observed under these viewing directions have traveled some distance within the water before being scattered into the line of sight. For example, included a VRS spectrum to improve their MAX-DOAS fit of IO in the marine boundary layer over the remote ocean.

In small DOAS fitting windows, the smooth liquid water absorption spectrum is often assumed to be sufficiently compensated for by the DOAS polynomial. This is most likely the reason for the variety of studies on VRS, while studies concerning the absorption structure are rare. However, for large fitting windows (> 40 nm in the visible wavelength range, depending on the actual fit settings and the order of the DOAS polynomial), liquid water absorption should be considered in the fit as demonstrated by Fig. b. This is supported by , who found that including the H2Oliq spectrum in the GOME-2 DOAS fit for NO2 (425–497 nm) improves the fit quality. However, even in small fitting windows, H2Oliq can cause problems for the retrieval of weak absorptions if it is not compensated for. For example, for CHOCHO, which is mostly retrieved in the range of ≈ 435–460 nm, developed a two-step approach, fixing the liquid water slant columns in the small glyoxal fitting window to results obtained in a larger fitting window where the smooth shape of the liquid water absorption spectrum can be retrieved more reliably.

Laboratory measurements of the pure liquid water absorption coefficient were performed, for example, by . Unfortunately, this absorption coefficient is given only in 2.5 nm steps, and the spectral resolution is even lower (≈ 7 nm). Even though the absorption structure is smooth, the coarse resolution blurs the exact position of shoulders in the H2Oliq spectrum. If the liquid water absorption is strong, this uncertainty can cause severe problems for the retrieval of trace gases using the DOAS method that requires a spectral resolution in the range of less than 1 nm. In addition, the liquid water absorption spectra as measured by different groups differ clearly from each other in the 400–500 nm range e.g., see, which is a result of the weak absorption strength in the visible wavelength range. As a consequence, very long light paths are needed to obtain reliable measurements. For the DOAS analysis, the 400–500 nm range is crucial, as many trace gases (O3, NO2, CHOCHO, IO) are retrieved here. Furthermore, laboratory measurements of liquid water absorption were made using pure water under standard conditions (i.e., for fixed temperature and pressure). In contrast, the water absorption that is present in field or satellite measurements is not pure, and does not apply to standard conditions.

In this study, we report on MAX-DOAS observations, pointing towards the water surface during the ship-borne TransBrom campaign in the western Pacific in 2009 where regions of remarkably clear water and low chlorophyll concentrations were encountered (see Fig. a). These measurements were designed in a way that minimizes atmospheric contributions to the resulting optical depth, while at the same time maximizing the liquid water influence. From these measurements, we retrieve a H2Ocorr spectrum (< 1 nm resolution) compensating simultaneously for broad-banded VRS structures and uncertainties in currently available literature cross sections of liquid water absorption. The influence and the potential improvement of the retrieved spectrum on the NO2 fit using atmospheric MAX-DOAS measurements close to and above the horizon taken during the same campaign are investigated. In addition, the H2Ocorr spectrum was included in satellite DOAS fits, and the resulting fit factors (slant columns) were successfully found over the clear ocean.

The following Sect.  gives the theoretical background of liquid water spectral effects. Detailed information about the measurements performed as well as the DOAS method and the instrumentation is provided in Sect. . Section  reports on different attempts to retrieve empirical H2Oliq and VRS cross sections as well as the retrieval of the finally used H2Ocorr spectrum. The influence of this spectrum on the NO2 fit in atmospheric MAX-DOAS measurements is investigated in Sect. . Finally, the presence of the H2Ocorr spectral signature in OMI satellite data is demonstrated in Sect. .

The most important spectral feature of liquid water is its absorption H2Oliq, which is different from the absorption spectrum of water vapor. Whereas the latter one is dominated by a large number of distinct vibrational–rotational absorption lines (caused by numerous rotational levels due to the H2O molecule's different moments of inertia for rotation around different spatial axes), in the liquid phase, rotations are suppressed as a result of intermolecular hydrogen bonding, and are limited to so-called librations (rocking, wagging and twisting). Also, in contrast to most other substances, the absorption of liquid water in the visible wavelength range is not based on electronic transitions. Instead, it is caused by overtones of the three fundamental vibrational modes: symmetric stretch (ν1), asymmetric stretch (ν3) and bending or scissors mode (ν2). The result is a continuous absorption spectrum that is smooth in shape, with small values in the blue range and increasing values towards longer wavelengths. Thus, water absorbs more strongly in the red part of the spectrum that produces the blue color of the ocean. The absorption spectrum is plotted in Fig.  (green line). The dominant stretch modes of the OH bond (ν1, ν3) occur at wave numbers of ≈ 3400 cm-1 (≈ 3 µm), and the bend or scissors mode (ν2) appears at ≈ 1600 cm-1 (≈ 6 µm), which is in the infrared region. The absorption in the visible wavelength range is caused by harmonics, and linear combinations of these fundamental modes and strong transitions can be identified as shoulders in the absorption spectrum. For example, the shoulder at ≈ 450 nm corresponds to the seventh harmonic of the OH stretch seeand references therein. Hydrogen bonds developing between adjacent H2O molecules in the liquid phase decrease the vibrational energy levels of OH stretches, and thus cause a red shift in vibrational transition energies and references therein. With increasing temperature, hydrogen bonding decreases in importance, as a larger fraction of bonds is broken. As a result, the red shift and therefore the exact position of absorption features (shoulders) is slightly temperature dependent (lower temperatures lead to larger red shifts).

In atmospheric remote sensing, the effect of rotational Raman scattering (RRS) on air molecules (predominantly N2) is well known. RRS is an inelastic scattering process that produces wavelength shifts in the spectrum. For example, found that the strongest Raman lines are typically 50 cm-1 from the frequency of the incident light. With this, a rough estimation yields a wavelength shift of ≈ 1 nm for an initial wavelength of 450 nm. As this is comparable to the width of strong Fraunhofer lines (and is also in the range of typical DOAS instrumental resolution), more intensity is shifted from the wing of a Fraunhofer line to its core than from the core to the wing, simply because there is less intensity in the minimum that can be shifted. The result is a filling-in of Fraunhofer lines that was first observed by and that is known as the Ring effect.

Similarly, inelastic vibrational Raman scattering (VRS) can also occur in molecules that have vibrational modes, but the mechanism of filling-in of Fraunhofer lines is less efficient and, therefore, VRS in the atmosphere can be neglected. In contrast, in liquid water, the VRS effect on H2O molecules becomes important because of its high density. At the same time, no RRS can occur in liquid water, because no rotations are allowed. The final energy Efin, or wavelength λfin, of an inelastic VRS scattered photon is Efin=Eint-h⋅c⋅ν̃↔1λfin=1λint-ν̃. As the energy of the dominant OH stretch is in the range of ν̃ ≈ 3400 cm-1 (see Fig. ), for an initial wavelength λint of 400 nm, Eq. () yields a final wavelength of ≈ 460 nm (for the Stokes–Raman band); i.e., the VRS produces a wavelength shift of about 60 nm in the visible wavelength range. This maps larger structures of the initial sunlight spectrum to different positions, is much larger than the wavelength shift due to RRS on N2 molecules in the air, and is also much larger than the width of any Fraunhofer line. Consequently, the mechanism of filling in Fraunhofer lines from VRS is different from RRS, and results from the large line width of the VRS Raman band. First, the line width is large because of broadening effects in the liquid phase. In addition, the Raman band shape is a superposition of different Gauss curves associated with monomer (single H2O molecules) and polymer formation because of intermolecular hydrogen bonding. As this decreases the energy of the OH stretch (as mentioned above), the Raman band of polymers is centered at a different energy. For example, and described the Raman band as a superposition of four different Gauss curves (the resulting shape is plotted in Fig. ). As the overall line width (≈ 8 nm in the visible wavelength range) is much greater than any Fraunhofer line, the level of both the wing and the core are raised by roughly the same amount; i.e., the core is less deep relative to the wing after the VRS . As the number of hydrogen bonds is temperature dependent, the shape of the Raman band is also temperature dependent. This has been used for remote sensing of the ocean temperature using LIDAR systems e.g.,.

To conclude, the resulting cross section of VRS is both small banded because of the filling-in of Fraunhofer lines as well as broad banded because of the large intensity shift that maps larger structures of the initial sunlight spectrum. An example of the cross section of VRS is given in Fig.  (Sect. ). The prominent increase (step) around 460 nm results from the relatively sharp increase in intensity of the solar spectrum shortly before 400 nm (after the strong K and H Fraunhofer lines from Ca+).

Another inelastic scattering effect is the so-called Brillouin scattering that is caused by density fluctuations (phonons) in water e.g.,. In principle, Brillouin scattering can also produce a filling-in of Fraunhofer structures, but the spectral shift is only several 10-3 nm in the visible wavelength range . This is much smaller than the shift of VRS or even RRS, and also smaller than the width of Fraunhofer lines that can be resolved with current (MAX-)DOAS instruments. Also, the Brillouin line width in the visible wavelength range (≈ 10-4 nm) is much smaller than for VRS . To conclude, the Ring effect caused by Brillouin scattering can be neglected for current DOAS applications. More details can be found in , but they are not reproduced here, since the findings only confirm the intuitive assumption above.

The original objective of retrieving empirical cross sections of liquid water absorption and VRS had only limited success, as discussed in Sects.  and . However, the obtained findings suggested the retrieval of correction spectra for (potentially non-perfect) literature cross sections (Sect. ).

For all approaches discussed in this section, the I and I0 spectra (clear water, or white caps) were used in DOAS fits, and a polynomial was fitted to the optical depths ln⁡ (I/I0) to account for instrumental and elastic scattering effects. No trace gases were included in the fits, as the difference between I and I0 is considered to be liquid water effects only. In addition, in Sects.  and , a liquid water absorption spectrum (H2Oliq) from the literature was used in order to retrieve a correction spectrum for it. This H2Oliq spectrum had to be adapted to our DOAS routine requirements as described in Sect. . To ensure that atmospheric conditions are as constant as possible, for each measurement I, the closest-in-time reference measurement I0 was always selected. As a cut-off criterion, only measurements I were taken for which a reference spectrum I0 exists within ΔSZA less than 2∘ (SZA = solar zenith angle). Also, only spectra recorded at SZA less than 85∘ were used. After applying the color index selection and these restrictions, about 5000 measurements remained and could be analyzed. In addition, even stronger restrictions were tested: the individual 100 ms measurements for each intergration time were averaged according to their color index. Then, all spectra I were rejected if no I0 exists within a period of 1 min. While this reduces the number of observations (predominantly because of the averaging), the results were always the same as in the first case.

In this section, the effect of the retrieved H2Ocorr spectrum on tropospheric NO2 fits in off-axis measurements close to the horizon is evaluated (elevation angles between -3 and 30∘ and zenith measurements as reference I0, see Sect. ). These viewing directions are suitable for the detection of tropospheric absorbers, as they provide a long light path (i.e., enhanced sensitivity) close to the ground e.g.,.

Four different MAX-DOAS fits of tropospheric NO2 were performed. Fit1 is mainly based on the MAX-DOAS NO2 fit settings used during the NO2 intercomparison campaign CINDI . It contains neither VRS nor liquid water absorption. Fit2 uses the same settings, but this time, the H2Oliq spectrum is included. In addition to H2Oliq, Fit3 contains the H2Ocorr spectrum retrieved in Sect. . Fit4 equals Fit3, but the H2Ocorr spectrum is replaced by the SCIATRAN-simulated VRS spectrum shown in Fig. . To avoid contributions of stratospheric NO2 in the measurements, the closest-in-time zenith observation was always used as reference spectrum I0. If no zenith spectrum was available within ΔSZA = 2∘ around the measurement I, the respective measurement was rejected. The detailed fit settings are summarized in Table .

For measurements at the -3∘ elevation angle, the H2Oliq slant columns (or fit factors) of Fit2 are plotted in Fig. a in blue for the example of 14 October 2009, which was the day of best weather, viewing conditions and also clearest water during TransBrom. A distinct diurnal shape is found, which is mainly the result of the position of the Sun. Obviously, average underwater light paths of longer than 20 m occur around noon, although only slightly pointing towards the sea surface. In addition to the H2Oliq slant columns of Fit2, the (absolute values of) H2Ocorr slant columns of Fit3 as well as the (absolute values of) VRS slant columns of Fit4 are plotted in Fig. a in red and green, respectively. The latter two lines have been scaled to the blue line in order to match into the figure according to a1=y1,y2y2,y2a2=y1,y3y3,y3, where (⋅) is the inner product, a1 and a2 are the scaling factors for the red and green lines, and y1, y2, and y3 are the slant columns of H2Oliq, H2Ocorr and VRS, respectively.

Obviously, the diurnal shape of H2Oliq slant columns in Fig. a is reproduced by the H2Ocorr slant columns of Fit3 as well as the VRS slant columns of Fit4, indicating that all spectra describe effects that scale very similarly with the length of the light path under water. This was already concluded in Sect. , and it is the prerequisite for using the H2Ocorr spectrum to account simultaneously for both broadband structures of VRS as well as uncertainties in liquid water absorption.

In Fig. b, the corresponding rms of the fits shown in Fig. a is plotted in the same color coding. Apparently, the rms of Fit2 is dominated by some water-related effects that are missing in the fit, as the rms reproduces the diurnal cycle of H2Oliq slant columns in Fig. a (note that the H2Oliq cross section from the literature is already included in Fit2). The rms of Fit1 (no H2Oliq) is outside the range of the figure, and therefore is not displayed, but it again reproduces the same shape. If the SCIATRAN-simulated VRS cross section is included in addition to H2Oliq (Fit4, green line), the rms is considerably smaller than in Fit2 (by a factor of up to 2 around noon). However, the same diurnal cycle is present in the rms, meaning that some water-related optical depth is still not accounted for. Finally, if the SCIATRAN VRS cross section is replaced by the H2Ocorr spectrum (Fit3, red line), absolute values decrease again by a factor of up to 2 around noon and – even more importantly – the diurnal shape of liquid water absorption is no longer present. This indicates that in Fit3, all water-related effects are compensated for – at least those that scale with the light path under water and that are detectable with our instrument (this is the objective of this study). To conclude, the H2Ocorr spectrum works as intended, and compensates (together with the straylight correction) for VRS as well as uncertainties in the applied liquid water absorption cross section from the literature.

Figure  shows the effect of the H2Ocorr spectrum on the retrieved NO2 slant columns. The TransBrom campaign encountered marine-polluted regions of enhanced NO2 as well as very clean open ocean regions of very low NO2 ≈ 50 ppt, see. Figure a and b are correlation plots between NO2 slant columns from Fit2 vs. Fit1 and Fit3 vs. Fit1, respectively. In these plots, all measurements in the vertical scanning directions from the whole campaign are plotted using color coding: measurements at elevation angles from -3 to -1∘, i.e., slightly towards the water surface, are displayed in red, 0 to 1∘ in green, and 2 to 30∘ in blue. Figure c and d are correlation plots of the corresponding rms values of the different fits (same color coding).

Only measurements taken under appropriate wind directions were used for Fit1 to Fit4; i.e., measurements were rejected if the wind direction would blow the ship's plume into the line of sight. This is true for both, the off-axis measurements I as well as the zenith reference measurements I0, meaning that the reference I0 should not contain more NO2 than the spectrum I. Thus, only positive NO2 slant columns should be retrieved from the DOAS fits, while negative slant columns indicate some problems in the fit (the fit would use the NO2 cross section to compensate for some other effects). In Fig. a, comparing the NO2 slant columns retrieved from the basic NO2 Fit1 and those from Fit2, two different cases have to be distinguished.

Positive NO2 slant columns from Fit1: in this case, all data points are located close to the 1 : 1 line, independent of the elevation angle. In particular, this means that (a) both fits find the same NO2 signal even if no liquid water absorption is included, but the measurements certainly contain liquid water structures, because they slightly point towards the water surface (red data points). Furthermore (b), if (almost) no liquid water structures are present in the measurements, but the H2Oliq cross section is included (Fit2), this does not affect the retrieved NO2 slant columns (blue data points are also on the 1 : 1 line); i.e., no mismatch of NO2 is introduced by including H2Oliq if this effect is not present in reality.

Using the H2Ocorr spectrum overcomes this problem, as Fig. b demonstrates. In Fit3, containing not only H2Oliq, but also the H2Ocorr spectrum, formally negative NO2 slant columns (from Fit1 and Fit2) scatter around zero within the detection limit (DL) of 2 × 1015 molec cm-2 (see the inset of Fig. b), which is more realistic and likely to be closer to the truth. This is not only the case for measurements towards the water (red data points), but also for measurements slightly above the horizon (green data points). Thus, when using zenith measurements as a reference (which is normally done for MAX-DOAS measurements), the resulting optical depth apparently contains water-related spectral structures at small elevation angles above the horizon (from photons that have been partly under water before being scattered into the instrument's line of sight). Consequently, NO2 can be misfit in these directions, but the H2Ocorr spectrum in combination with H2Oliq overcomes this problem. As small elevation angles provide the longest light path through the boundary layer and therefore the highest sensitivity to tropospheric NO2, these are the most important MAX-DOAS directions. Thus, the achieved improvement is important for the reliability of MAX-DOAS measurements, especially of low NO2 concentrations above the ocean.

As in Fig. a, all positive NO2 slant columns in Fig. b are close to the 1 : 1 line; i.e., if a NO2 signal is present in the measurements, the use of the H2Ocorr spectrum does not affect the retrieved slant columns. To conclude, both H2Oliq as well as H2Ocorr can be used in the MAX-DOAS NO2 fit presented here without unintended side effects, but increasing the reliability of retrieved NO2 slant columns over water.

Figure c and d demonstrate that the rms values of Fit2 and Fit3 are smaller than in Fit1. This is true for all elevation angles, but especially for those pointing slightly towards the water (red data points). Obviously, using the H2Ocorr spectrum (Fit3) produces a much smaller rms than using liquid water absorption only (Fit2). Interestingly, the rms of Fit3 (Fig. d) is highest at the 0 and 1∘ elevation angles (green data points). This is because the dominating effect on the rms is no longer errors introduced by liquid water effects, but misfits of water vapor in the atmosphere, which was present in large amounts in the humid air above the open ocean, and for which the largest slant columns occur at the 0 and 1∘ elevation angles.

In order to quantify the improvement of the fit quality, the rms values of the different fits were compared to each other. First, for each single measurement, the difference between the rms in two fits was calculated and normalized by the rms of the first fit; e.g., (Fit1 - Fit2) / Fit1 gives the relative rms decrease of Fit2 with respect to Fit1. Afterwards, the obtained values of single measurements were averaged in certain ranges of elevation angles (-3 to -1∘, 0 to 1∘, 2 to 30∘) for the whole campaign. The results are summarized in Table , supporting the findings above. The largest rms reduction is obtained by Fit3 with respect to Fit1 in the range of -3 to -1∘, which is on average ≈ 52.5 %, i.e., a factor of 2. For the same range of elevation angles, the comparison between Fit3 and Fit2 yields an rms reduction of up to 30 % that is achieved by using the H2Ocorr spectrum. In general, for all ranges of elevation angles, the rms reduction using the simulated VRS spectrum (Fit4) instead of the H2Ocorr spectrum is smaller. Fit3 and Fit4 were compared directly, yielding on average a better performance of Fit3 of 11.7 % in -3 to -1∘, 4.1 % in 0 to 1∘, and 3.2 % in 2 to 30∘. Obviously, the improvement using the H2Ocorr spectrum instead of the simulated VRS spectrum is larger in viewing directions containing more liquid water structures, which is reasonable, since the H2Ocorr spectrum compensates for insufficiencies in H2Oliq.

Finally, it has to be mentioned that the numbers in Table  are averages of a specific campaign encountering specific conditions (e.g., if more measurements in regions of very clean water had been performed, the value of (Fit1 - Fit3) / Fit1 would have been even larger than it is here). Thus, the exact numbers do not necessarily apply to other measurements (under other conditions), but might represent typical values that can be expected for ship-based MAX-DOAS measurements over clear water.

In addition to MAX-DOAS data, the retrieved H2Ocorr spectrum was also tested on OMI satellite data (see Sect. ). For this purpose, the four MAX-DOAS NO2 fits from Sect.  (425–497 nm, see Table ) have been adapted to satellite requirements. In particular, for OMI-Fit4, a VRS cross section has been simulated with SCIATRAN using the satellite's nadir measurement geometry. The DOAS fits have been performed on OMI data for August 2007, i.e., for a different period than the TransBrom campaign. The fit details are summarized in Table .

Figure a shows the resulting slant columns of the H2Ocorr spectrum in OMI-Fit3 on a global scale. Obviously, locations at which the H2Ocorr structure is found coincide with the pattern of clear natural water and low chlorophyll content (compare to Fig. a showing the H2Oliq slant columns from OMI-Fit2); i.e., the H2Ocorr spectrum is successfully found in measurements of a different instrument on a different platform using data from a different period. This demonstrates again that the H2Ocorr spectrum describes real liquid water residual effects, and is not due to any MAX-DOAS instrumental effect.

Interestingly, the (broad-banded) H2Ocorr spectrum is not only found over the ocean, but also over some desert regions in northern Africa and the Arabian Peninsula (this is not visible in Fig. a, as continents are masked out). The reason is most likely interference with broadband sand structures that have already been found in GOME-2 data by over the desert. Nevertheless, this finding indicates that the H2Ocorr spectrum should probably not be used in satellite observations over continents.

In Fig. b, the improvement of the rms of OMI-Fit3, i.e., using the H2Ocorr spectrum, with respect to OMI-Fit4 (simulated VRS instead of H2Ocorr) is shown, and again reproduces the pattern of clear water regions. For this purpose, the differences between the rms of OMI-Fit4 and OMI-Fit3 have been calculated and normalized by the rms of OMI-Fit4 (similar to Sect. ). In the same way, the changes in rms between the other fits were calculated. Averages of the calculated rms reduction over specific regions are summarized in Table . Region1 (latitudes -20 to 45∘ N, longitudes 140 to 160∘ E) is a box around the TransBrom cruise track, while region2 (latitudes 0–30∘ N, longitudes 130 to 180∘ E) is a large oceanic region of clear water, i.e., where the amount of liquid water absorption is large. These regions are indicated in Fig. b by dashed or solid rectangles. In addition, the global mean over all oceans is reported in Table .

Including liquid water absorption (comparing OMI-Fit2 to OMI-Fit1) leads on average to ≈ 12 % smaller rms globally over the ocean and ≈ 36 % smaller rms in the specified region2 of very clear water and low chlorophyll content. Also taking VRS into account, either by including a simulated VRS cross section (OMI-Fit4) or the H2Ocorr spectrum (OMI-Fit3), reduces the rms with respect to OMI-Fit2 in region2 by 7.9 and 10.8 %, respectively. In all regions, the H2Ocorr spectrum performs better than the simulated VRS spectrum (3.3 % better in region2 and still 0.7 % better on a global scale). Again, this is most likely because the H2Ocorr spectrum is compensating not only for broad-banded VRS structures, but also for residual H2Oliq structures, which the simulated VRS spectrum is not doing.

Pure liquid water interacts with incident (solar) radiation in the visible wavelength range in terms of absorption (H2Oliq) and scattering (VRS, Brillouin), which has an impact on scattered light measured above the ocean (e.g., Fig. a). While Brillouin scattering can be neglected for current DOAS instrument resolutions, the effects of liquid water absorption and VRS need to be compensated for in DOAS retrievals. This is not fully achieved using currently available cross sections of H2Oliq and VRS (Figs.  and b). In contrast, phytoplankton pigment absorption seems not to increase the rms of the atmospheric NO2 DOAS fit in the visible spectral range, and is therefore neglected here.

In order to investigate pure liquid water effects, MAX-DOAS measurements pointing directly to very clear natural waters (i.e., low chlorophyll concentrations) were taken during the TransBrom field campaign across the western Pacific in October 2009. Based on these measurements, it was not possible to retrieve independent empirical spectra of H2Oliq and VRS, because both effects depend in a similar way on the underwater light path (Fig. a). However, it turned out to be possible to apply a simultaneous correction to both effects by using only one correction spectrum. In addition, the intensity offset or straylight correction, which is routinely included in the DOAS analysis as an additional pseudo absorber (Sect. ), was found to compensate very efficiently for small-banded (incompletely removed Fraunhofer) structures produced by VRS. Thus, only broadband VRS structures need to be accounted for, which are broader than Fraunhofer lines, but still too narrowly banded to be compensated for by the DOAS polynomial.

From MAX-DOAS measurements, we retrieved an empirical residual correction spectrum (H2Ocorr) that compensates for uncertainties in the literature H2Oliq spectrum as well as broadband structures of VRS. Using the H2Ocorr spectrum together with H2Oliq in the MAX-DOAS NO2 fit compensates entirely for pure liquid water absorption as well as VRS (Fig. b). In unpolluted marine environments where unrealistic negative NO2 slant columns are retrieved in a standard evaluation, inclusion of the H2Ocorr spectrum yields meaningful NO2 slant columns scattered around zero within the detection limit (Fig. ). On the other hand, the H2Ocorr spectrum was found to have no effect on NO2 slant columns in measurements containing no liquid water effects; i.e., no unwanted side effects arise. At the same time, the rms decreased by up to 29.7 %, depending on the elevation angle. For the most important elevation angles of MAX-DOAS measurements of tropospheric trace gases (0 and 1∘ direction), the H2Ocorr spectrum was found to decrease the rms by 11.1 %, and it performs 4.1 % better than a simulated VRS spectrum (Table ).

Apart from the improvement to MAX-DOAS measurements in a marine environment, the retrieved H2Ocorr spectrum potentially also improves nadir measurements from air-borne or space-borne platforms over clean water surfaces. In order to investigate this, the H2Ocorr spectrum was tested on OMI satellite data over the ocean, and was successfully found, with a global distribution resembling the pattern of liquid water absorption (and low chlorophyll concentration), meaning that a potential improvement to satellite retrievals by our method is realistic (but not the topic of the present study). The average rms reduction of the NO2 DOAS fit due to the H2Ocorr spectrum was found to be 10.8 % in a region of very clear water (region2), where it performs on average 3.3 % better than when using a simulated VRS spectrum instead (Table ).

It cannot be strictly ruled out that the H2Ocorr spectrum is contaminated by any bio-optical property of water. However, this is unlikely, since (a) the H2Ocorr spectrum was retrieved in a region of very clear water, (b) no similarity with chlorophyll absorption was found, and (c) when applied in satellite data, the locations at which H2Ocorr is found resemble the pattern of low chlorophyll and large liquid water absorption, while no correlation with locations of larger chlorophyll concentrations is found.

As our H2Ocorr spectrum replaces the VRS spectrum, no radiative transfer modeling of VRS is necessary, and the number of degrees of freedom of the DOAS fit stays constant (no additional cross section is included). The retrieved H2Ocorr spectrum can be used in other DOAS applications that have similar settings (spectral range, order of polynomial) and use the same H2Oliq cross section as our retrieval fit.