In remote sensing applications, such as differential optical absorption
spectroscopy (DOAS), atmospheric scattering processes need to be considered.
After inelastic scattering on

Measured spectra in passive DOAS applications are typically corrected for
rotational Raman scattering (RRS), also called Ring effect, which represents
the main contribution to inelastic scattering. Inelastic scattering can also
occur in liquid water, and its influence on DOAS measurements has been
observed over clear ocean water. In contrast to that, vibrational Raman
scattering (VRS) of

Consequences of VRS are red-shifted Fraunhofer structures in scattered light
spectra and filling-in of Fraunhofer lines, additional to RRS. At 393 nm,
the spectral shift is 25 and 40 nm for VRS of

We use the VRS correction spectra in the spectral range of 420–440 nm to
determine the relative magnitude of the cross-sections of VRS of

The effect of VRS is shown for the first time in spectral evaluations of
Multi-Axis DOAS data from the SOPRAN M91 campaign and the MAD-CAT MAX-DOAS
intercomparison campaign. The measurements yield in agreement with calculated
scattering cross-sections that the observed VRS(

The DOAS-technique (differential optical absorption spectroscopy) is widely
used from different platforms to retrieve the abundance of tropospheric and
stratospheric absorbers, such as ozone (

Solar absorption lines (Fraunhofer lines) have an effect on the evaluation of
scattered sunlight spectra, since inelastic scattering processes in the
atmosphere lead to an effective “filling-in” of these absorption lines. The
reduction of the optical depths (OD) of Fraunhofer lines is known as the Ring
effect

However, for large amounts of filling-in of Fraunhofer lines, i.e. a strong
Ring signal,

This is a first indication that this effect might indeed be relevant for
measurements of atmospheric absorbers. Additionally,

Cross-section of Cabannes line, rotational (RRS – rotational Raman scattering), vibrational (VRS) and
rotational–vibrational Raman scattering (VRRS) for a wavelength of 393 nm
scaled with 0.8 for

Figure

The rotational constant

In addition, also water vapour exhibits narrow vibrational Raman transitions,
with a frequency shift of around 3654

In the atmosphere, not only monochromatic light is scattered by air
molecules, but rather a continuous incident light spectrum from the Sun. The
solar spectrum is highly structured by Fraunhofer lines. These spectral
structures are red-shifted by VRS and will result in so-called “Fraunhofer
ghosts” in another spectral interval. If this additional intensity is not
explicitly corrected for, it can lead to errors in the retrieved trace gas
concentrations. Intensities of elastically and inelastically scattered
sunlight are shown in Fig.

Inelastically scattered light appears as an additional intensity in measured
spectra. When the scattering medium does not exhibit narrow excitation
states, this can lead to a “blurred” remapping of the solar spectrum. This
is the case for some liquids and solids. A blurred remapping of the solar
spectrum is also observed for RRS and vibrational rotational Raman scattering
(VRRS) of

Calculated intensities (in arbitrary units) for purely Rayleigh scattered
light (Cabannes), rotational Raman scattered light (RRS), vibrational Raman
scattered light (VRS), and combined scattering (VRRS) due to

The liquid water Raman cross-section also shows a frequency shift of

The individual lines of the Raman cross-section of RRS and VRRS cannot be resolved by typical DOAS instruments. Therefore the scattered light intensity due to RRS and VRRS is also a smooth function of wavelength, compared to the original Sun spectrum.

In contrast to that, the vibrational Raman spectra of

The additional intensity offset, which is included in several settings for DOAS evaluations of stray-light spectra is typically meant to compensate for a constant contribution to the measured intensity due to instrumental stray-light. As it turns out, this correction term also compensates for a large fraction of the contribution of vibrational Raman scattering in the atmosphere, especially involving transitions due to VRRS.

Inelastic scattering results in a change of the energy of the scattered
photon and of the scattering molecule. The energy of the molecule is
characterized by the vibrational (

The scattered power density

The statistical weight factor

The differential cross-section for an incident light beam with the wavenumber

Averaged polarizability

Variables used in equations

Spatial averaged polarization tensor according to

The invariants of this tensor are the average polarizability

The Placzek–Teller coefficients

The sum over states (or partitioning function)

The geometric factors

From the general expression for the total cross-section

The apparent optical depths according to Eq. (

The DOAS method

The method of Multi-Axis DOAS (MAX-DOAS) measurements was first described by

The SCD is defined by the integral over the concentration

The effect of VRS of

The MAX-DOAS measurements used here were recorded during research cruise M91
of the German research vessel

Track of cruise

The MAX-DOAS instrument consisted of three main parts: a telescope unit
mounted on top of the air chemistry lab on RV

The telescope unit has an inclinometer to correct the ship's roll angle for
elevation angles close to the horizon. Its output is directly fed into the
motor controller and can correct the elevation angle at an accuracy of

The spectrometer used was an Acton 300i that was temperature stabilized at
44

During daylight, spectra were recorded for 1 min each at 8 elevation
angles of 90

The FWHM (full width half maximum) of the mercury emission lines at 404.7,
407.8 and 435.8 nm differed by 2 % assuming a Gaussian shape. A fit of the
measured spectrum to a solar atlas using a Gaussian instrument function with
a linearly wavelength dependent width for the main fit interval from
420 to 440 nm also showed in agreement a variation of the width of the slit
function of less than 2 %. A difference of 2 % error in slit function width
would result for an absorption corresponding to a

The Multi Axis DOAS - Comparison campaign for Aerosols and Trace gases
(MAD-CAT) in Mainz/Germany took place on the roof of the Max Planck Institute
for Chemistry (MPIC). The measurement site is located close to the city of
Mainz and surrounded by Frankfurt as well as several smaller cities. 11 research
groups participated with the MAX-DOAS instruments.

One of the instruments was the Heidelberg Envimes MAX-DOAS. It is based on an
Avantes ultra-low stray-light AvaSpec-ULS2048x64 spectrometer (

During daylight, spectra were recorded for 1 min each at 11 elevation
angles of 90

The FWHM of mercury emission lines at 404.7, 407.8 and 435.8 nm differed by 2.5 % assuming a Gaussian shape. A fit of the measured spectrum to a solar atlas using a Gaussian instrument function with a linearly wavelength dependent width for the main fit interval from 420 to 440 nm also showed in agreement a variation of the width of the slit function of less than 2.5 %.

The aim of the spectral retrieval was to identify the contribution of
inelastic scattering due to VRS(

The recorded scattered sunlight spectra were analyzed for absorptions using
the software package DOASIS

In order to reduce noise of both data sets, several elevation sequences were
co-added. When adding 16 elevation sequences for M91 (corresponding to 2 h measurement time), a mean RMS (root mean square) of the residual of

(left) Fit showing the detection of structures from vibrational
Raman scattering of

The pixel to wavelength mapping for the recorded spectra was performed by
using mercury emission lines. The correctness of the pixel to wavelength
mapping was tested by convoluting a high-resolution sunlight spectrum by

The broad-band contributions to the observed optical depth were compensated
by a polynomial fitted together with the trace gases. The (rotational) Ring
spectrum was taken from DOASIS where it is calculated according to

The second Ring spectrum compensates for additional Ring spectrum structures
which appear with a changing colour index within one elevation sequence, for
example, due to particle scattering at lower elevation angles. The first Ring spectrum is
calculated according to Eqs. (

The spectrum was calculated by multiplication of the original Ring spectrum
by

The cross-sections listed in Table

Cross-sections used for the spectral (DOAS) retrieval. All shift and squeeze
parameters of the cross-sections were linked, those of Ring and reference
spectrum were linked separately. The retrieval interval settings for each
used trace gas are given in Table

It was not necessary to incorporate tropospheric ozone absorption
cross-sections in the fit, since the expected OD due to stratospheric ozone
is

For water vapour absorptions based on HITEMP

While for the Ring spectrum neither shift nor squeeze was allowed, the
remaining cross-sections' shift and squeeze parameter were linked together
and determined by fitting the measurement spectrum against the

Impact on the ratio of VRS(

The effect of vibrational Raman scattering in liquid
water on the spectral retrieval of IO has been discussed in greater detail in

Retrieval wavelength intervals for the MAX-DOAS measurements from
M91 and MAD-CAT using the literature absorption cross-sections listed in
Table

Glyoxal shows absorption structures in the spectral range which is can be
affected by VRS. It could therefore interfere in the spectral retrieval of
the VRS(

On the contrary, glyoxal was found in significant amounts during the MAD-CAT
campaign. Glyoxal dSCDs at low elevation angles of up to

Therefore the glyoxal cross-section had to be included in the final DOAS analysis of the MAD-CAT data.

However, IO could not be identified in this data set exceeding the detection
limit of

According to Eq. (

Scattering can add an intensity

The additional measured intensities

The optical depth

When using a solar atlas, effects caused by the (typically unknown) quantum efficiency of the measuring spectrometer cancel out and do not introduce additional residual structures. As mentioned above, also measurement spectra could be used to calculate the correction spectrum. Here a solar atlas was used.

The following two subsections describe two ways how to detect the VRS
signature in MAX-DOAS measurements: in the first approach the correction
spectra are calculated and directly fitted to the measured optical depths.
The obtained fit coefficients are compared to the Ring signal to determine
the relative sizes of the cross-sections. In the second approach the
residuals from a standard fit are analyzed systematically using
a multi-linear regression. This offers the possibility to average over the
residual spectra of a complete campaign to minimize photon shot noise. It
allows for the detection of the contribution of VRS of

(left) Fit coefficients for Ring and vibrational Raman correction
spectrum for

The VRS correction spectra

The results for M91 of the spectral analysis of 16 co-added elevation
sequences (2 h time resolution) were filtered: only spectra with a low fit
residual with a root mean square (RMS) of less than

The results for MAD-CAT of the spectral analysis of eight co-added elevation
sequences (1.5 h time resolution) were filtered additionally to use only
measurements with a

The absolute cross-section of VRS is small and the mean free path for VRS and
RRS is significantly larger than the scale height of the atmosphere (See
cross-sections in Table

A comparison of the VRS and RRS signal is shown for each campaign in
Fig.

The effective contribution to the measured intensity was estimated by using
the Fraunhofer line at

A perfect correlation of both effects is not expected, because the phase
function for VRS and RRS differ, as shown in Sect.

Cross-sections for different contributions to Raman scattered light. Absolute
values are often listed as well as relative contributions, compared to RRS. The
cross-sections were scaled according to the atmospheric ratio of 80 and
20

Alternatively, the optical depth due to VRS can be extracted from residual
spectra of a DOAS fit using only the cross-sections listed in
Table

In order to linearly decompose the residual spectra based on column densities
obtained from the DOAS fit, a system of linear equations was set up to
determine contributions

The first line of this diagram shows the procedure which led to
Fig.

This approach is based on the following procedure

The complete M91 MAX-DOAS data set was fitted from 420 to 440 nm to avoid the
main water vapour absorptions at 416 and 442 nm. The retrieval was the same
as in the first analysis (see Table

Only fits with a RMS of

All channels

Regressors were the dSCDs

The overdetermined system of linear equations (Eq.

Despite the significantly better detection of the VRS signal of

Fit of the Ring-dSCD-correlated residual structure obtained from a linear
regression of residual spectra and corresponding dSCDs. The cross-sections
for IO, water vapour,

The fit of the Ring-correlated residual structure shown in
Fig.

The main advantage of this approach is that it allows for the obtainment of an average
over the residual structures associated with a certain absorber over the
whole period of a campaign, e.g. a month or a year for a sufficiently stable
instrument. This can reduce the influence of photon shot noise to a minimum.
Furthermore an identification of the VRS signature from spectral data is
possible for

The obtained results from measurements listed in Table

The results agree for both campaigns, M91 over the ocean and MAD-CAT over
land, which excludes an interference with VRS of liquid water. VRS of liquid
water has furthermore a different spectral signature due to its broad Raman
response (compare Fig.

Ignoring the potentially significant impact of VRS can lead to systematic
biases in the spectral evaluation. Since IO,

We found that correcting for the effect of VRS will reduce the total RMS of
the fit residual for a large Ring signal and thus in most cases also the fit
error. It does not significantly lower the RMS for spectra with small Ring
signals. Whether the correction has an impact on the retrieved column
densities has to be tested for each trace gas and also for different spectral
resolutions of the respective MAX-DOAS instruments, which can have an
influence on the way in which the neglected apparent OD was compensated for.
The difference of the squares of the RMS

This relation is found in MAX-DOAS data, for example, from M91, with

The following subsections show the impact on the spectral retrieval of
different trace gases when neglecting this effect. It may vary depending on
fit settings and the spectral resolution of the instrument. Within each of
the comparisons the same retrieval settings and intervals were used, once
without and once with the correction for VRS of

To estimate the influence of having ignored the effect of VRS of

Leaving the size of the correction independent of the Ring spectrum showed that
the IO dSCD is independent of the amount of structures caused by VRS of

The use of the linear regression method and the fit shown in
Fig.

The effect of the VRRS (

Including the VRS correction spectra can lead to a reduction of the fit error
by

Histogram of

Usually a wider fit interval

To retrieve glyoxal, a fit window from 432 to 460 nm was used, with and
without including

The same settings as for glyoxal were used to estimate the influence of VRS
on retrieved water vapour column densities. The observed changes were found
to be below

For the narrower fit range of 420–440 nm, which is used for the
evaluation shown in Fig.

The results from

The influence of VRS on the observed differential OD at 433 and 436 nm is directly visible due to the high OD of the Ca-II-Fraunhofer lines, combined with overall small residual sizes due to large amounts of available light.

Towards shorter wavelengths, the amount of Raman scattered light scales with

If the incident light was attenuated by any strong absorber
before being scattered inelastically, then strong absorbers such as ozone, water vapour or

But even without strong Fraunhofer or absorption lines, this effect
contributes to the observed differential OD according to
Eq. (

Correction spectra for VRS of

Since the atmospheric

All calculations for a spectral
resolution of the instrument of

Due to the observed correlation of the spectral signature of VRS scattering
on

However, the following points need to be considered:

Vibrational Raman scattering leads to a red-shift of solar
radiation, thus the ratio of vibrational Raman scattered and elastically
scattered light is influenced by the wavelength dependency of the aerosol
extinction and Rayleigh scattering. For the case of rotational Raman
scattering (the Ring effect) this is inherently compensated for, since the
frequency shift due to RRS is not significant for the wavelength dependence of
the aerosol extinction. For the shift of 40 nm of

The phase functions of RRS, VRS and VRRS differ. Different contributions
proportional to

A way to avoid these points is to use a measured spectrum to calculate the correction spectra, which includes the effects due to changes in radiative transfer, such as aerosol load and measurement geometry. When using measured spectra, this would require the same quantum efficiency of the instrument at both wavelengths or a radiometrically calibrated instrument, as well as a constant instrument slit function. This is typically not the case.

It is therefore recommended to include the correction spectrum for VRS of

Vibrational Raman scattering of

In spectral regions without large Fraunhofer ghost structures the intensity
offset polynomial typically used in DOAS evaluations can compensate for most
of this effect. Depending on the magnitude of the Ring effect, the correction
of VRS(

The apparent OD caused by VRS of

The systematic biases introduced into DOAS evaluations of different trace gases by neglecting the effect of vibrational Raman scattering shows once more the need for high-precision absorption measurements of trace gases and thorough statistical analysis of residual spectra. Even if individual measurements hardly allow the identification of systematic structures, systematic contribution in the residual spectra might still be identified and point towards possible improvements. Future advances in DOAS evaluations as well as improved DOAS instruments are expected to further reduce the magnitude of residual structures and thus improve detection limits. While the correction of VRS effects already improves the evaluation of several trace species, this correction will be even more important in future advanced DOAS evaluations.

We provide the VRS correction spectra
calculated from a solar atlas by

We thank H. Haug for laying the foundations for this work in his diploma
thesis

We thank the captain, officers and crew for support during research cruise M91.

We want to thank the organizers of the Multi Axis DOAS – Comparison campaign
for Aerosols and Trace gases (MAD-CAT) in summer 2013
(

We thank the German Science foundation DFG for its support within the core program METEOR/MERIAN.

We thank the German ministry of education and research (BMBF) for supporting this work within the SOPRAN (Surface Ocean Processes in the Anthropocene) project (Förderkennzahl: 03F0662F) which is embedded in SOLAS.

We thank the authorities of Peru for the permission to work in their territorial waters.

We thank GEOMAR for logistic support.

Rich Pawlowicz is acknowledged for providing the m_map toolbox. The article processing charges for this open-access publication were covered by the Max Planck Society. Edited by: A. Richter