AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus GmbHGöttingen, Germany10.5194/amt-8-3767-2015The impact of vibrational Raman scattering of air on DOAS measurements of atmospheric trace gasesLampelJ.johannes.lampel@iup.uni-heidelberg.dehttps://orcid.org/0000-0001-7370-9342FrießU.https://orcid.org/0000-0001-7176-7936PlattU.Institute of Environmental Physics, University of Heidelberg,
Heidelberg, Germanynow at: Max Planck Institute for Chemistry,
Mainz, GermanyJ. Lampel (johannes.lampel@iup.uni-heidelberg.de)17September2015893767378729January201531March201526August201527August2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/8/3767/2015/amt-8-3767-2015.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/8/3767/2015/amt-8-3767-2015.pdf
In remote sensing applications, such as differential optical absorption
spectroscopy (DOAS), atmospheric scattering processes need to be considered.
After inelastic scattering on N2 and O2 molecules, the
scattered photons occur as additional intensity at a different wavelength,
effectively leading to “filling-in” of both solar Fraunhofer lines and
absorptions of atmospheric constituents, if the inelastic scattering happens
after the absorption.
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 N2 and O2 has often been thought to be
negligible, but it also contributes.
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 O2 and N2,
respectively. We describe how to calculate VRS correction spectra according to the Ring spectrum.
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 O2
and N2 and RRS of air.
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(N2) cross-section at
393 nm amounts to 2.3±0.4 % of the cross-section of RRS at 433 nm under
tropospheric conditions. The contribution of VRS(O2) is also found to
be in agreement with calculated scattering cross-sections. It is concluded,
that this phenomenon has to be included in the spectral evaluation of weak
absorbers as it reduces the measurement error significantly and can cause
apparent differential optical depth of up to 3×10-4. Its influence
on the spectral retrieval of IO, glyoxal, water vapour and NO2 in the
blue wavelength range is evaluated for M91. For measurements with a large
Ring signal a significant and systematic bias of NO2 dSCDs (differential slant column densities) up to
(-3.8 ± 0.4) × 1014 molec cm-2 is observed if this effect
is not considered. The effect is typically negligible for DOAS fits with an
RMS (root mean square) larger than 4×10-4.
Introduction
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 (O3), nitrogen dioxide
(NO2) and many others. Observation geometries include zenith-sky,
direct-sun and off-axis measurement of sunlight scattered in the atmosphere
e.g..
The Multi-Axis (MAX)-DOAS principle allows for the reaching of high sensitivity to tropospheric
absorbers, such as, e.g. NO2, iodine monoxide (IO), bromine monoxide (BrO),
water vapour (H2O), the oxygen dimer (O4), glyoxal (CHOCHO) and
formaldehyde (HCHO) e.g..
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 . While originally several
mechanisms for the Ring effect were proposed and references
therein there is a consensus in recent literature that most
properties of the Ring effect can be described by rotational Raman scattering
.
However, for large amounts of filling-in of Fraunhofer lines, i.e. a strong
Ring signal, reported problems with the spectral
retrieval of IO from satellite measurements at wavelengths above 431 nm.
Unexplained residual optical depths were observed, indicating an effect that
was not considered in the spectral analysis. We propose that this effect is
at least partly due to vibrational Raman scattering (VRS) in the atmosphere.
This spectral region (i.e. 430–440 nm) is actually the location of the
strong Ca lines of the Fraunhofer spectrum, red-shifted by the excitation
energy of the first vibrational eigenstate of N2.
This is a first indication that this effect might indeed be relevant for
measurements of atmospheric absorbers. Additionally,
reported that despite co-adding of measurement spectra, the size of the
residual spectral structures from MAX-DOAS observations in the blue
wavelength range did not reduce as expected from photon statistics. They
suggested that an insufficiently modelled Ring spectrum or a missing
contribution such as vibrational Raman scattering is causing this difference.
In spectral retrievals of trace gases encompassing the wavelength range
between 430 and 440 nm, this effect is currently not explicitly considered.
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 N2 and 0.2 for O2 to reflect their
atmospheric concentrations (see also Table ). The
cross-sections were calculated according to Eq. () at
a scattering angle of Θ=180∘. As a comparison the Raman
response of liquid water according to is also
shown in the plot, scaled arbitrarily.
Figure shows the cross-section of rotational and
vibrational Raman scattering for forward scattering of a monochromatic light
beam at 393 nm (the position of the solar calcium-II K-absorption line).
While the pure rotational Raman lines of N2 or O2 appear in
the vicinity of the wavelength region of 393 nm, the rotational–vibrational
Raman (Stokes) lines of N2 and O2 are considerably
red-shifted according to their different vibrational constants. VRS of
O2 leads to a red-shift of the calcium-II K-absorption line of
25 nm, VRS of N2 to 40 nm. Note that anti-Stokes lines are very
weak under atmospheric conditions, since only a small fraction of the
N2 and O2 molecules is vibrationally excited. The rotational
and vibrational constants are listed in Table . Thus,
strong Fraunhofer lines can give rise to VRS – “ghost” absorption lines in
other parts of the spectrum.
The rotational constant B0 and the vibrational constant ν̃ for
ground state N2 and O2 according to . For
excited vibrational states ν>0 the rotational constant is modified: Bν=B0-ν⋅αe.
These constants are used in Eq. () to calculate the energy of the molecule E(ν,J).
mentioned that VRS of air can lead to apparent ODs
of up to 0.3 % in zenith sky measurements.
estimated the effect of single vibrational Raman
scattering to the filling-in of Fraunhofer lines to be less than
0.3 % and did not discuss it further. and
estimated the filling-in to be 0.02–0.22 %,
which results in 2–14 % of the filling-in due to rotational Raman
scattering. However, none of these publications showed experimental evidence
from DOAS measurements to support their estimates.
In addition, also water vapour exhibits narrow vibrational Raman transitions,
with a frequency shift of around 3654 cm-1 and with a cross-section of 8 (±20 %) ×10-30 cm2sr-1 about 5–10 times as
strong as the vibrational Raman scattering cross-section of the Δν=1 transition of N2 (depending on the scattering angle). This
effectively leads to a wavelength shift of the Ca-Fraunhofer lines to about
460 nm, but this should usually not be observable in current DOAS
measurements since the expected OD would be below 5×10-5 for
a typical tropospheric water vapour column density of 5×1023moleccm-2 along a light path of 10 km. Inelastic
scattering of air and water vapour is however used in LIDAR applications
.
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. , together with
a constant offset (e.g. caused by instrumental stray light) and vibrational
Raman scattering in liquid water .
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 N2 and O2, since the respective cross-subsections
consist of several lines separated by only a few cm-1, which are not
separated in typical DOAS measurements. Vibrational Raman scattering in
liquid water has been reported by and
. Similar to ice, liquid water has a broad Raman spectrum
(Raman shift of ≈3300cm-1 with a FWHM of
≈500cm-1, which converts to a shift of ≈61 nm at
λ=400 nm and a FWHM of ≈11 nm at λ′=461 nm,
according to ) and thus essentially creates an
intensity offset in measurement spectra. Therefore, the VRS (liq. H2O)
correction spectrum for this effect is similar to the intensity offset
polynomial often used in DOAS evaluations to compensate for intensity offsets
caused by instrumental stray-light, but has a broad-band (10 nm) modulation
of its amplitude . This broad Raman response
is shown in Fig. and leads to inelastically scattered
light with a smooth spectrum as shown in Fig. . As shown by , this can
have a significant impact on MAX-DOAS measurements of NO2, especially
when looking downwards into clear water.
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 N2,
O2 and liquid water as well as assumed instrumental stray-light as
a function of wavelength at a spectral resolution of 0.5 nm. The
apparent optical depths Iadd/I0 according to
Eq. () are shown in Fig. . The
relative magnitudes for each of the effects are arbitrarily scaled. Note the
red-shift in the VRS(O2) and VRS(N2) spectrum compared to the
solar atlas; the Ca-II lines and their respective ghost lines for inelastic
scattering on N2, O2 and liquid water are marked gray. For
the absolute magnitudes of the cross-sections compare
Table .
The liquid water Raman cross-section also shows a frequency shift of
≈ 1650 and ≈2100 cm-1, but the relative cross-section
is together about 5 times smaller .
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 N2 and
O2 contain individual and narrow peaks, therefore resulting in
narrow-band contributions to the total measured OD. If vibrational Raman
ghosts of strong Fraunhofer lines happen to occur in a spectral region
which is relevant for the spectral retrieval, these can also affect the
spectral retrieval of trace gases.
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.
Quantitative description of rotational and vibrational Raman scattering by N2 and O2
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 (ν) and rotational (J) quantum numbers
and given by
E(ν,J)=Erot+Evib=hcBJ(J+1)+hcν̃ν+12,
assuming no coupling between rotation and vibration, which is a reasonable
approximation for typical spectral resolutions used in DOAS applications
(0.5–1.0 nm). B is the rotational constant in wavenumbers and
ν̃ is the wavenumber in cm-1 corresponding to the energy
difference between the vibrational states (compare
Table ; see Table for a list of
variables). To avoid confusion with the vibrational quantum number ν, the
vibrational constant of a molecule in units of wavenumbers is denoted
ν̃. Allowed transitions are denoted by ΔJ=0,±2 resulting
in the Q (ΔJ=0), O (ΔJ=-2) and S branches (ΔJ=2) and Δν=1 for vibrational transitions. Due to the temperatures
in the Earth's atmosphere T, only the ground vibrational state is occupied
significantly, thus leading only to Stokes transitions of the vibrational
states. (Evib/kT≈11 and 8 for N2 and
O2, respectively.)
The scattered power density Iν,J→ν′,J′ in
Wm-2 scattered into the full solid angle 4π involving
a transition (v,J→v′,J′) is given, e.g. by :
Iν,J→ν′,J′=IIσν,J→ν′,J′LNgJ(2J+1)1Ze-E(ν,J)/kT,
where II is the incident power density, N the number density of
molecules in the scattering volume, L the length of the scattering volume
(i.e. its extent in the direction of the line of sight of the instrument) and
gJ is the statistical weight factor of the initial rotational state due to
the nuclear spin (see Table ). The sum over states Z is given
below. J and ν describe the initial state and J′ and ν′ describe the
final state. The factor (2J+1) accounts for the degeneracy
due to the magnetic quantum numbers while exp(-E(ν,J)/kT) accounts for
the population of the initial state of the molecule at temperature T. The
absolute cross-section in Eq. () is given by σν,J→ν′,J′ which can be obtained via the integration of the
differential cross-section dσ(Θ)ν,J→ν′,J′dΩ (see Eq. ) over
the entire solid angle (note that the term differential refers here
to the solid angle).
The statistical weight factor gJ due to nuclear spin (I) statistics for
odd and even shell angular momentum J of the respective N2 or
O2 molecule.
MoleculeIgJgJJoddevenN2136O2001
The differential cross-section for an incident light beam with the wavenumber
ν̃in in cm-1 can be written as
dσ(Θ)ν,J→ν′,J′dΩ=8π4(ν̃in+ν̃ν,J→ν′,J′)412J+1∑M,M′∑ij[αij2](ν,J,M→ν′,J′,M′)fij(Θ),
where αij are the entries of the polarizability tensor as given by
. These can be spatially averaged over the magnetic
quantum numbers M,M′ since the molecules' orientations in space are
arbitrary, which results in the spatially averaged squares of the
polarization tensor entries, αij2‾, see
Table , which is given by
[αij2](ν,J→ν′,J′)‾=12J+1∑M,M′[αij2](ν,J,M→ν′,J′,M′).
Averaged polarizability a,a′ and anisotropy γ,γ′ according to
and references therein for incident wavelengths
between 400 and 500 nm. The resulting differential cross-sections
dσ/dΩ are listed in
Table .
ν̃inWavenumber of incident photonλWavelengthνQuantum number of vibrational eigenstateJQuantum number of rotational eigenstateν̃Vibrational constant, in wavenumbers (Table )BRotational constant, in wavenumbers (Table )E(ν,J)Energy of molecule in state (ν,J) (Eq. )Erot(ν,J)Rotational energyEvib(ν,J)Vibrational energyMMagnetic quantum numberΩSolid angleσCross-sectionΘScattering angleα,α′Polarizability and its derivative (Table )γ,γ′Anisotropy and its derivative (Table )IIIncident power densitybJ→J′Placzek–Teller coefficient (Eq. )gJStatistical weight factor (Table )TTemperatureLLength of scattering volumeNNumber density of scattering moleculesZPartitioning function (section )I0Measured Fraunhofer reference spectrumI*Solar atlas τOptical depthH(λ,λ′)Instrument slit function
Spatial averaged polarization tensor according to and corresponding phase functions f(Θ).
The invariants of this tensor are the average polarizability a
and the anisotropy γ
and a′ and γ′, their derivatives with respect to nuclear coordinates for
vibrational–rotational transitions, respectively.
Their contributions to the cross-section corresponding to different transitions are listed
in Table . The wavelength dependence
of a,a′,γ and γ′ is small (for γ less than 5 % variation for wavelengths from 400 to 500 nm, see , for example) and is therefore neglected here.
The Placzek–Teller coefficients bJ,J′ used in
Table can be found at
:
bJ→J=J(J+1)(2J-1)(2J+3)bJ→J+2=3(J+1)(J+2)2(2J+1)(2J+3)bJ→J-2=3J(J-1)2(2J+1)(2J-1).
Sum over states
The sum over states (or partitioning function) Z=ZrotZvib is given by the product of the rotational state sum
Zrot and the vibrational state sum Zvib:
Zrot=∑J∞gJ(2J+1)e-Erot(J)/kTZvib=∑ν∞e-Evib(ν)/kT.
Zvib can be calculated explicitly using a geometric series:
Zvib=e-hcν̃2kT1-e-hcν̃kT.
Phase function
The geometric factors fij(Θ) in Eq. () are
determined by the relative orientations of the incident light polarization,
the polarizability tensor and the direction of observation, given by the
scattering angle Θ. Using
Table the non-normalized phase
function p′(Θ) for each of the scattering processes can be calculated.
p′(Θ)VRS depends thus also on the ratio of b′2=γ′2a′2 and shows more dominant scattering into the forward
and backward direction and differs for N2 and O2, compare
Table . The phase function of
VRS is similar to the Rayleigh phase function.
p′(Θ)RRS=p′(Θ)VRRS=13+cos2(Θ)p′(Θ)VRS=1+745b′2+1+345b′2⋅cos2(Θ)
Total cross-section
From the general expression for the total cross-section
σtotal=∑ν,Jσν,J→ν′,J′1ZgJ(2J+1)e-E(ν,J)/kT
the total cross-section of the Q branch of the vibrational transition can
now be calculated e.g. by summing over all
possible transitions of the Q branch (ΔJ=0;Δν=1) and
averaging the respective phase functions over the full solid
angle:
σQ,total=128π5(ν̃in+ν̃)49(1-e-hcν̃/kT)3a′2+23γ′2SΔJ=0h8cπ2ν̃
using
SΔJ=0=∑J1ZrotgJ(2J+1)bJ,Je-Erot(J)/kT.
σQ,total depends only slightly on the temperature, since
also SΔJ=0 varies by less than 1 % between
T=230K and T=298K and the term
1-e-hcν̃/kT less than 10-4. The numerical values for the
resulting overall cross-section are given in Table .
The important information for passive DOAS applications is
the (ν̃in+ν̃)4-dependency from Eq. (), together
with the spectral shift ν̃ (Table ) itself. This information already
allows the calculation of correction spectra in a first approximation. The remaining calculations are
necessary to obtain the absolute magnitude of the effect. The resulting apparent optical densities
are shown in Fig. . Equation () was used to
calculate the spectra provided in the Supplement. Figure was calculated using Eq. ().
The apparent optical depths according to Eq. ()
related to the additional intensities in
Fig. .
Experimental method
The DOAS method uses the attenuation of light from a
light source by absorbers within the light path according to Lambert–Beer's
law. The optical depth (OD)
τ(λ)=-lnI(λ)I0(λ)
from two spectra I(λ) and I0(λ) is used to determine the
column density of different absorbers in the respective wavelength range.
Each of the absorbers is identified by its specific absorption structures. To
remove broad-band extinction from particles and molecules, the OD is
subdivided into a narrow-band (differential) and a broad-band part, τ=τB+τd. τd can then be
expressed by a sum of the differential parts of possible absorbers with their
differential absorption cross-sections σd,i, assuming that
these are constant with pressure and temperature. ci(l) are the respective
concentrations along the light path L.
τd=∑iσd,i∫0Lci(l)dl
The method of Multi-Axis DOAS (MAX-DOAS) measurements was first described by
and uses scattered sunlight at different
elevation angles, which have each a different sensitivity for absorptions in
different heights in the atmosphere.
The SCD is defined by the integral over the concentration ci along the
light path L and is hence given in the unit molec cm-2.
Differential slant column densities dSCDi can be calculated from MAX-DOAS measurements for each fitted trace gas:
a Fraunhofer reference spectrum I0 is chosen and dSCD(α)=SCD(α)-SCDref is
obtained from the DOAS fit of the OD for each elevation angle α.
Instrumentation
The effect of VRS of N2/O2 is shown for two measurement
campaigns, using two different spectrometers and telescopes at different
locations. The M91 campaign data set shows low NO2 concentrations at
a high spectral resolution using an Acton spectrometer. The measurements took
place on the Pacific. To exclude possible interferences from liquid water
absorption and VRS of liquid water, the MAD-CAT data set was analysed: this
data set was recorded during a MAX-DOAS intercomparison campaign in Mainz.
However, this data set was recorded with a compact spectrometer at lower
spectral resolution and NO2 and glyoxal concentrations were
significantly larger.
M91
The MAX-DOAS measurements used here were recorded during research cruise M91
of the German research vessel Meteor in the Peruvian Upwelling
. The cruise was part of the Surface Ocean Processes in
the Anthropocene (SOPRAN) project as part of SOLAS (Surface Ocean - Lower Atmosphere Study). The ship left Callao
(12∘2′30′′ S, 77∘8′36′′ W), the harbour of Lima, on
1 December 2012. It then sailed north until 5∘ S and continued south
along transects perpendicular to the coastline until 18∘ S and
arrived again in Lima on 26 December 2012. A cruise track is shown in
Fig. .
Track of cruise Meteor M91. From Lima, the ship first
sailed north until about Piura and then continued south along transects from
the open ocean to the coastal upwelling or vice versa until 18∘ S,
from where it returned to Lima.
The MAX-DOAS instrument consisted of three main parts: a telescope unit
mounted on top of the air chemistry lab on RV Meteor headed towards
port side in a height of approximately 28 m, a temperature stabilized
Acton spectrometer located inside the lab and a PC to control the devices.
The same setup was used by .
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
≈0.5∘ while the ship's roll is less than 8∘, which
was the case most of the time. The light from the telescope is focused via
a lens onto a mode mixing fibre which was then connected to 37 circularly
arranged fibres of 100 µm diameter. These fibres are then again
used as the entrance slit of the spectrometer. To avoid the influence of
direct sunlight reflected in the entrance of the telescope, a 5 cm long
baffle was attached.
The spectrometer used was an Acton 300i that was temperature stabilized at
44 ∘C with an Andor CCD camera DU 440-BU. The camera was
used in imaging mode recording 256×2048pixel. The detector
of the camera was cooled to -30 ∘C to reduce the
dark-current signal. This setup covered a wavelength range of 324 nm–467 nm. The full-width-half-maximum resolution was 0.45 nm or 6.5 pixel.
During daylight, spectra were recorded for 1 min each at 8 elevation
angles of 90∘ (zenith), 40, 20, 10, 6, 4, 2, 1∘,
respectively, as long as solar zenith angles (SZAs) were ≤85∘.
During twilight (85∘≤ SZA ≤ 105∘), spectra were
alternatingly recorded at 90 and 2∘ elevation. The exposure
time was adjusted to have spectra at a typical saturation of 50 %. At
night (SZA ≥ 110∘) dark current and offset spectra were
recorded automatically. Mercury discharge lamp spectra to obtain the
instrument slit function H(λ,λ′) were recorded manually. No
significant change of the instrument slit function shape was observed during
the campaign. DOAS fits using one fixed Fraunhofer reference show that the
variation in wavelength calibration during 1 day was less than 0.01 nm.
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 NO2 dSCD of
5×1016moleccm-2 (differential OD at instrument
resolution: 1.6×10-2) in a residual structure of 1×10-4
peak to peak. This NO2 dSCD was exceeded only once during the whole
cruise in the port of Callao, typical values during the cruise were
(2±5)×1014moleccm-2 at a telescope elevation angle
of 3∘, compare also Fig. .
MAD-CAT
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.
http://joseba.mpch-mainz.mpg.de/mad_cat.htm
see
also e.g..
One of the instruments was the Heidelberg Envimes MAX-DOAS. It is based on an
Avantes ultra-low stray-light AvaSpec-ULS2048x64 spectrometer (f=75 mm) using
a back-thinned Hamamatsu S11071-1106 detector. The spectrometer is
temperature stabilized (ΔT<0.02∘C). It covered a spectral range of 294–458 nm at a FWHM spectral resolution of ≈0.6 nm or
≈7 pixel. The spectral stability was typically better than ±3 pm per day and better than ±5 pm for the duration of the
measurements from 6 June 2013 until 31 July 2013. Mercury discharge
lamp spectra to obtain the instrument slit function H(λ,λ′)
were recorded manually. No significant change of the instrument slit function
shape was observed during the campaign. The 1-D-telescope unit measures its
elevation angle constantly using a MEMS acceleration sensor, and corrects the
elevation angle, when it deviates from the nominal elevation angle. It has a
vertical/horizontal field of view (FOV) of 0.2/0.8∘.
During daylight, spectra were recorded for 1 min each at 11 elevation
angles of 90∘ (zenith), 30, 15, 10,
8, 6–1∘ respectively, as long as solar zenith
angles (SZA) were ≤ 87∘. Until a SZA of 100∘ zenith
sky spectra were recorded at 90∘ telescope elevation. The exposure
time was adjusted to have spectra at a typical saturation of 50 %.
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 %.
Spectral retrieval
The aim of the spectral retrieval was to identify the contribution of
inelastic scattering due to VRS(N2/O2) to measured
intensities in MAX-DOAS measurements. The most pronounced signal is expected
between 430 and 440 nm, as the calcium Fraunhofer line ghosts due to
VRS(N2) are expected to be found here. As a number of absorbers show
absorption structures in this spectral range, these had to be included in the
fit or their detection limits had to be determined. An overview over the
respective settings in shown in Table .
The recorded scattered sunlight spectra were analyzed for absorptions using
the software package DOASIS . A measured Fraunhofer
reference spectrum (FRS) I0 from the current elevation sequence at an
elevation angle of 90∘ for MAD-CAT was chosen. For M91 40∘
spectra were used to avoid direct sunlight into the telescope in the southern
part of the cruise track. The measured OD τObs was then
calculated for each spectrum I (Eq. ).
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 7.5×10-5 is
observed. Example fits are shown in Fig. for both
campaigns. Adding more than 16 elevation sequences is typically not possible
due to instrumental instabilities and changing atmospheric conditions and
radiative transfer. For residual spectra dominated by photon shot noise, the
RMS depends on the integrated intensity I as I according to Poisson
statistics. When increasing the number of co-added spectra, the residual will
be eventually dominated by systematic structures. This behaviour can be
visualized in a so-called Allan plot (plotting RMS vs. intensity on a
log-log scale) and was used to find a compromise between time resolution and
low RMS. This led to summing 16 elevation sequences for the M91 data set. For
the MAD-CAT data set more elevation angles were recorded, and therefore only
eight elevation sequences were co-added to obtain a similar time resolution of
1.5 h.
(left) Fit showing the detection of structures from vibrational
Raman scattering of N2 for a spectrum recorded during M91. The main
peak at 430 nm originates from the reciprocal of a Fraunhofer structure at
this wavelength from the Taylor expansion of the optical thickness. It
vanishes when orthogonalizing the spectrum with the stray light compensation
spectrum 1/I0. The two minima to at 432 and 436 nm are the red-shifted
calcium Fraunhofer lines. The grey lines are measured quantities, the red
line is the modelled OD. The spectrum was recorded on 15 December 2012,
starting at 17:38 UTC, at 12∘33′ S, 76∘50′ W at a SZA
of 14∘ and a relative solar azimuth angle (SAA) of 132∘. The
FRS spectrum was recorded at 40∘ elevation. 16 elevation sequences
were co-added, resulting in a time resolution of 2 h and a total
exposure time of 16 min per co-added spectrum. The Fraunhofer reference
spectrum was omitted for clarity. Column densities are given in
moleccm-2. The unit of the measurement spectrum and the intensity
offset correction is given in counts. (right) Detection of
structures from vibrational Raman scattering on N2 in data from
MAD-CAT. The spectrum was recorded on 15 June 2013, starting at
13:32 UTC, in Mainz, Germany at a SZA of 27∘
and a relative SAA of 122∘. The FRS spectrum was recorded at 90∘ elevation. Eight elevation sequences were co-added, resulting in a time resolution of 1.5 h and a total
exposure time of 8 min.
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
and comparing it to a measured spectrum.
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
for each Fraunhofer reference spectrum, agreeing with
the expression given in Eq. (), without vibrational
transitions. A second Ring spectrum, the original one scaled by λ4/λ04-1 to account for radiative transfer effects discussed in
was also included in the fit and was clearly detected in
the measured OD.
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. () and (). However,
if in Eq. () the colour index of I' changes (e.g. due to
scattering on particles), this translates directly to the Ring correction
spectrum. The second Ring spectrum compensates for this effect.
The spectrum was calculated by multiplication of the original Ring spectrum
by (λ4/λ04-1). By construction, this Ring correction
spectrum vanishes at the wavelength λ0, which is used then as the
wavelength of the RRS signal to be compared to the VRS signal. It is almost
orthogonal to the Ring spectrum in the interval from 420 to 440 nm: by
comparison with an explicitly orthogonalized second Ring spectrum (within the
complete fit interval) the change in Ring dSCD was found to be less than
1×1024moleccm-2 for both data sets used. This is
less than 2 % of the range of observed Ring signals, as shown in
Fig. ().
The cross-sections listed in Table were used after
being convolved with the instrument slit function. The instrument slit
function was measured as the response of the spectrometer to the mercury
emission line at 404.7 nm. It was assumed to be constant, in Sect. an error estimate is given for this assumption
for the case of strong NO2 absorption. A parameterization by a
Gaussian function with a wavelength dependent width would have also
introduced uncertainties, since the slit function shape of both spectrometers
is not exactly of Gaussian shape.
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 .
AbsorberSourcedSCD for I0 correctionNO2 294 K1×1015moleccm-2O3 223 K1×1018moleccm-2IO1×1013moleccm-2H2O with corrections 3×1023moleccm-2Glyoxal5×1014moleccm-2O4 293 K3×1043molec-2cm-5Liquid waterVRS(liqu. water)based on Ringby DOASIS and Ring ⋅λ4Solar atlasused for I0 correction andVRS correction spectra
It was not necessary to incorporate tropospheric ozone absorption
cross-sections in the fit, since the expected OD due to stratospheric ozone
is τ≤1×10-4. However, the resulting stratospheric light-path change during morning and evening made it necessary to include an ozone
cross-section measured at 223 K by . The
zeroth order intensity offset correction was realized by including an inverse
reference spectrum in the DOAS fit according to Eq. ().
For water vapour absorptions based on HITEMP , the
relative sizes of the absorption bands in the fit interval were adjusted
according to . This correction was not crucial for the
detection of VRS, but yields reasonable water vapour dSCDs even for the weak
water vapour absorption band at 426 nm.
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 Kitt Peak Flux Atlas 2010 by . No significant differences were
found when determining the shift and squeeze of all cross-sections together using
the Levenberg Marquard implementation of the DOAS-fit within DOASIS as shown
in Table .
Impact on the ratio of VRS(N2) and RRS depending on
different fit
settings for the spectral retrieval, given in % relative to the standard settings, where the
shift of the literature cross-section was determined from a fit using a convolved solar atlas.
The mean RMS for all settings did not vary by more than 5 % around the mean RMS
of 7.5×10-5 for the standard setting.
The effect of vibrational Raman scattering in liquid
water on the spectral retrieval of IO has been discussed in greater detail in
using a spectrum based on . This
correction spectrum was not used here, since it was not clearly identified
for positive elevation angles. If there was any contribution, it is most
likely compensated to a large extend by the intensity offset correction
within this relatively small wavelength interval as discussed in
. Even for a larger fit window (432–460 nm, including a
differential structure of liquid water at 451 nm, see also
Table ) a contribution of VRS of liquid
water and/or liquid water absorption could not be identified for spectra
recorded at positive elevation angles. The maximum ratio of liquid water
absorption and its typical fit error of 0.07 m was 2.9. A mean value of
-0.08 m and a standard deviation of 0.20 m was found. OMI satellite
measurements shown in showed up to 8 m water column
absorption in the remote Pacific, but less than 0.4 m in the Peruvian
upwelling region. This could be explained by high turbidity due to high
bio-productivity in this region (see e.g. ). The
contribution of VRS was not significantly correlated with the liquid water
absorption (R2=0.03, p=0.1) and was not found in measurement data above
a detection limit defined as 4 times the DOAS fit error.
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(N2/O2) signal. Despite previously reported
significant absorption of glyoxal in the eastern Pacific region by
, no absorption of glyoxal during the M91 cruise was
found to exceed our detection limit of 2σ=5×1014moleccm-2 at low elevation angles of 1–3∘ in
the wavelength interval from 432 to 460 nm using the settings from Table . This is in agreement with other
observations listed in . Sensitivity studies for
glyoxal were performed using different O4 literature cross-sections
published by and
. The average observed glyoxal dSCD was found between
(1 and 2±3)×1014moleccm-2, resulting in surface
concentrations of (10±15) ppt. In the wavelength interval used here from
420 to 440 nm this upper limits corresponds to an OD of glyoxal of less than
10-4. Consequently, the glyoxal cross-section was not included in the
final DOAS analysis of the M91 data.
MAD-CAT
On the contrary, glyoxal was found in significant amounts during the MAD-CAT
campaign. Glyoxal dSCDs at low elevation angles of up to
4.5×1015 molec cm-2 were found in both fit intervals listed
in Table .
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 2σ=6×1012 molec cm-2 at low
elevation angles of 1–3∘ in the wavelength interval from
418 to 438 nm. The site of the campaign was inland, and enhanced NO2
concentrations were observed, which could have led to a fast reaction of IO
with NO2, if any IO was initially present. The IO cross-section was
therefore not included in the final DOAS analysis of the MAD-CAT
measurements.
VRS correction spectra
According to Eq. () the intensity correction spectra for
vibrational Raman scattering can be calculated, either based on a solar atlas
or on measured spectra of scattered sunlight. Both
approximations hold, since the filling-in due to RRS is of the order of
2 %
and the inelastic scattering occurs somewhere within the atmosphere. VRS of
N2/O2 contributes by about 2 % of the RRS, the overall OD for
the VRS correction spectrum is then 0.04 %. Therefore, a relative uncertainty
of 2 % of the VRS correction spectrum is typically negligible. However, if this
accuracy is needed, radiative transfer modelling similar to existing
studies on rotational Raman scattering (e.g. ) is indeed
necessary. When calculating the VRS correction spectrum from measurement
spectra, wavelength changes in the instrument slit function and the quantum
efficiency of the spectrometer need to be considered.
Scattering can add an intensity K(λ)=∑iKi(λ) to the
measured intensity I(λ)=I′(λ)+K(λ). This will lead to
an apparent absorption structure in the optical depth
τObs(λ). I is the measured intensity of the
measurement spectrum, I′(λ) would be the intensity without the
contribution of additional intensities Ki(λ) and I0(λ) is
the intensity of the Fraunhofer reference spectrum.
τObs=-lnI′+∑iKiI0≈τ-∑iKiI′≈τ-∑iKiI0
The additional measured intensities Ki(λ) can be caused by RRS of
N2, O2, VRS of N2, O2, water vapour or liquid
water, but also by instrumental stray light leading to an (approximately)
wavelength-independent intensity offset. Equation () is linear
in Ki(λ), therefore the different components can be fitted
separately to the observed OD. KVRS_N2(λ) can be
calculated by shifting a sunlight spectrum in frequency by
ν̃N2 and scaling by
(ν̃in+ν̃N2)4 and
KVRS_O2(λ) respectively (see
Eq. ). Under the assumption that the rotational
constant of N2 and O2 is independent of the vibrational state
(which is the case within 1.2 % for the ν=0,1 states for
O2 and N2, see Table ), the intensity
caused by vibrational–rotational transitions was calculated also using
DOASIS, after a shift of the wavelength axis according to the vibrational
constants for N2 and O2. The calculation within DOASIS agrees
with Eq. () for the rotational transitions.
The optical depth τVRS(λ) can be fitted to correct for
the additional intensity caused by vibrational Raman scattering, in this case
based on solar atlas I*, from which also KVRS(λ) was
calculated (⊗ denotes the convolution operation here):
τVRS=KVRS⊗HI*⊗H.
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.
Results
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 N2 as well as of
O2 from spectral data. It furthermore yields estimates on the impact
of VRS on the calculated dSCDs of other absorbers.
Detection of the VRS signal
(left) Fit coefficients for Ring and vibrational Raman correction
spectrum for N2 and O2 from 702 co-added elevation sequences
from the M91 campaign. The VRS axis shows the optical depth of the of the
Raman-remapped Ca lines. The resulting relative size of the RRS and VRS
cross-sections are listed in Table . The intercept of
the linear fits is in both cases within the typical measurement error shown
as error bars on the left. (right) The same plot from 3264 co-added
elevation sequences from the MAD-CAT campaign.
The VRS correction spectra τVRS for N2 and O2
were calculated according to Eq. () from a solar atlas and then
separately included in the spectral evaluation of the measurements in the
spectral range of 420–440 nm. This wavelength range has been chosen to
avoid the main water vapour absorptions at 416 and 442 nm and to include the
main Fraunhofer ghosts at 433 and 436 nm due to VRS(N2).
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 1.5×10-4 were
used. This ensures that spectra during twilight and/or high NO2
concentrations, which can increase the overall residual of the fit, are not
included in the further analysis.
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 NO2 dSCD of less than 7×1016moleccm-2 to avoid an influence of large NO2
absorptions on the detection of the weak VRS signal. This filter removed
28 %
of all measurements.
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 ). The light paths in Eq. () are thus the same for both effects and cancel out. This
then allows for the estimation of the size of the cross-section of VRS relative to the
cross-section of RRS.
A comparison of the VRS and RRS signal is shown for each campaign in
Fig. . For M91, a clear correlation of the contribution
of rotational Raman scattering with the contribution from vibrational Raman
scattering on N2 is observed (R2=0.8); on is also observed for MAD-CAT (R2=0.7). The contribution from O2 is also positively correlated
with the Raman signal, but the slope is nearly zero within the measurement
error (R2=0.1). For MAD-CAT this correlation is stronger (R2=0.17). For
both campaigns, the contribution from rotational-vibrational inelastic
scattering was not identified in measurement spectra. The relative magnitude of
the cross-sections of RRS and VRS is calculated from the slope of the
linear fits shown in Fig. . In
Table the results are listed and compared to
calculations.
The effective contribution to the measured intensity was estimated by using
the Fraunhofer line at λ=430 nm: The intensity caused by each of the
processes, RRS, VRS N2 and VRS O2 at this wavelength will
create a maximum in the respective pseudo cross-section
IRamani(λ)/I0(λ), which then allows for the
estimation of constant intensity offsets due to these processes.
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 % for N2 and O2. These values are compared to the
results from MAX-DOAS measurements during M91, directly from
Fig. and derived from the solution of a system of
linear equations and resulting in a fit, which is shown in
Fig. . The spectrum obtained from the linear
system of equations had an 1σ-error of about 10 %. The VRRS
contributions were not significant in either case. The theoretical
cross-sections were calculated using Eq. () at 433 nm for RRS
and at 393 nm for VRS.
Calculation dσ/dΩMeasurements M91MAD-CATM91Spectral retrieval Linear regr.Θ=0∘Θ=90∘Fig. Fig. Fig. cm2sr-1molec-1%cm2sr-1molec-1%%%%(1)RRS (N2/O2)3.4×10-291003.2×10-29100100100100(2)N2 VRS1.2×10-303.476.2×10-311.962.5±0.52.5±0.62.1±0.3(3)N2 VRRS2.1×10-310.601.9×10-310.60(4)O2 VRS3.4×10-311.001.9×10-310.600.4±0.51.0±0.60.56±0.2(5)O2 VRRS1.4×10-310.401.25×10-310.39An alternative way of VRS signal detection
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 and correction spectra calculated according to
Eq. (). A schematic of both approaches is shown in
Fig. and is here applied to the M91 data set. From the
underlying properties of VRS described in Sect. a linear
relationship between the observed RRS and VRS signal is expected. This
relationship is found for actual MAX-DOAS measurements as shown in
Fig. . Parameters which can modify this relation are
discussed in Sect. .
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 vi to the residual spectra R that are correlated with the column densities Si. The residual
spectrum vRing, which is found to correlate with the Ring
signal SRing, is then expected to contain the residual
structures caused by VRS, independently of potential influences of other
absorbers on the residual spectra. Insufficiently modelled absorption
cross-sections of the absorber i are found in vi if the
respective dSCDs are not strongly correlated.
The first line of this diagram shows the procedure which led to
Fig. : the VRS correction spectrum is added to the
fit scenario, applied to all spectra and then the obtained fit coefficients
are correlated with the Ring signal. The other approach
(Sect. ) uses a standard DOAS fit (without
VRS correction), correlates the residuals with the obtained coefficients from
the fit and then uses this result to identify a VRS correction spectrum and
its coefficients in one final DOAS fit, which is shown in
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 ), but without the
VRS correction spectra and based on individual spectra with an exposure time
of 1 min.
Only fits with a RMS of <4×10-4 were used for the multi-linear regression.
All channels j from the residual spectra i were stored in the matrix R=Rij.
Regressors were the dSCDs S calculated in the first step, except the magnitude
of the rescaled (λ4/λ04-1) Ring spectrum, as this is only a
correction of the Ring spectrum. Also the size of the intensity offset correction,
exposure time and number of scans are used as regressors. Scan number and exposure time
could indicate here a contribution to the residuals from offset and dark current spectra.
Together, these vectors form the matrix A.
AT⋅V=(SRingSH2O…)T⋅(vRingvH2O…)=R
The overdetermined system of linear equations (Eq. ) was
solved for V using a least-squares approach, minimizing
|AT⋅V-R|2. This yields
V=(AAT)-1AR. The resulting
correction vRing corresponding to the Ring dSCD
SRing was then fitted with the already included absorbers
from the original fit scenario and additionally the pseudo cross-section for
vibrational and vibrational–rotational Raman scattering of N2 and
O2. This fit is shown in Fig. . Adding
the other absorbers to the fit is necessary due to possible compensation of
residual structures due to VRS by other absorbers within the first fits to
obtain the residuals. In other vectors corresponding to other absorbers or
parameters a significant contribution of the structure associated with
VRS(N2/O2) was not found. The vector corresponding to the intensity
offset correction could have contained some contribution of
VRS(N2/O2), as a part of it can be compensated by the intensity
offset correction; however, no correlation of the magnitude of intensity
offset correction and Ring signal was observed. We assume that the intensity
offset correction is mainly affected by instrumental stray light, which, for example, depends on the colour index of the measured spectrum.
Despite the significantly better detection of the VRS signal of O2
and N2, the contribution of VRRS of both species could not be
disentangled from the intensity offset correction.
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, NO2 and O3 are from the original fits
from which the residual spectra were used to solve the system of linear
equations. Their coefficients in the fit above are thus dimensionless or
could be written as molec cm-2 per molec cm-2 Ring-dSCD.
The VRS spectra are calculated from a solar atlas. The VRRS(N2/O2)
component is not significant here in the sense that it is not distinguishable
from the contribution of the intensity offset correction, which is usually
necessary to compensate for instrumental stray light.
The spectrum for VRS(N2) is detected at a size which corresponds to 29 times the fit error, the contribution of VRS(O2)
8 times.
The fit of the Ring-correlated residual structure shown in
Fig. yields more information than only the
contribution of VRS to the observed OD; it also yields approximations for the
changes of other involved trace gases in the respective spectral region,
a factor with which the Ring signal can be multiplied to obtain the averaged
effect on NO2; for example, the fit yields a NO2 fit coefficient of
7.65×10-12. For a large Ring signal of 5×1025moleccm-2 this results in a change of NO2 dSCDs
of (3.8±0.4)×1014moleccm-2. This is larger than
the estimate from individual fits shown in Fig. ,
because Fig. combines all measurements with
different Ring dSCDs.
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 N2 as well as for the weaker O2 signal, which
was not found to be significant in Fig. for individual
elevation sequences.
Discussion
The obtained results from measurements listed in Table
are in agreement with calculations based on
Eq. ()
as shown in Eq. (). Since the average scattering angle is
also between 0 and 180∘, the relative size of the VRS contributions is
found between both extrema of dσ(Θ)/dΩ at
0 and 90∘. While the impact of VRS of N2 is clearly
detected, the spectral signature of VRS of O2 remains close to the
instruments detection limit. For M91, it can be clearly detected by analysing
all residual spectra as described in
Sect. .
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. ) and the narrow
response of VRS(N2) can be identified from DOAS fits, as this leads
to a Fraunhofer ghost of the calcium lines at 393 nm, shifted to 433 nm.
Additionally the signal for VRS of N2 and O2 are linearly
correlated with the magnitude of the Ring signal, which underlines the fact,
that it is indeed an atmospheric effect.
Impact on trace gas retrievals
Ignoring the potentially significant impact of VRS can lead to systematic
biases in the spectral evaluation. Since IO, NO2, water vapour and
glyoxal are trace gases typically absorbing in a spectral range which is
mainly affected by VRS, its effect is exemplary studied for these trace gases
for our M91 data set. Also here 16 elevation sequences were co-added in order
to reduce the overall fit errors. Fit results with an RMS larger than
2×10-4 were not used. We observed an agreement of the results when
not co-adding elevation sequences.
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 χ2 of the evaluation with and
without correcting for VRS is expected to have a linear relationship with the
square of the Ring signal, R:
Δχ2=a⋅R2.
This relation is found in MAX-DOAS data, for example, from M91, with
a=(0.25±0.05)×10-8/(5×1025molec cm-2)2 for
the wavelength interval 420–438 nm, effectively reducing the RMS of a fit
residual of 1×10-4 by about 15 % for a Ring signal of
5×1025moleccm-2. In other words, if no VRS spectrum
is included, the minimum possible RMS for a DOAS fit showing a Ring signal of
this magnitude is larger than 5×10-5. In this case, 30 %
of the VRS signal is already compensated for by other absorbers and the
intensity offset correction.
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 N2 and O2.
From the resulting dSCDs of these two fits the impact of VRS was calculated.
Influence of VRS on the retrieval of IO
To estimate the influence of having ignored the effect of VRS of N2,
MAX-DOAS data from M91 was reanalysed for IO in the wavelength range of 418–438 nm with and without VRS and VRRS (N2) correction
spectra. Except for the wavelength range, the fit used the same settings as
used for the detection of VRS of air listed in Table .
Using an example measurement spectrum with 2×10-4 differential
optical depth caused by VRS from 432 to 438 nm, including the
correction spectra led to a decrease of the fit error by 25 %.
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 N2
within the typical IO measurement error of 1.5×1012moleccm-2.
The use of the linear regression method and the fit shown in
Fig. , while assuming a maximum Ring signal of
5×1025moleccm-2, corresponds to a change in
IO dSCD of 6×1011moleccm-2, which is also within the
typical IO measurement errors.
The effect of the VRRS (Δν=1,ΔJ≠0) transitions was
not observed to be correlated with RRS and could not be distinguished from
the contribution by the intensity offset correction. Therefore, its impact on
IO dSCDs was not studied.
Influence of VRS on the retrieval of NO2
NO2 can be evaluated in the same wavelength range as IO, from
418 to 438 nm. In this wavelength range, NO2 has a relatively large
absorption cross-section of NO2, and the influence of water vapour
absorption is minimal. When retrieving tropospheric NO2 dSCD, negative NO2 values are often observed in clean and remote areas. Since
these negative dSCD are also frequently observed close to local noon, this
excludes an effect of a changing AMF (air mass factor) of stratospheric NO2 within one
elevation sequence. One reason for this negative NO2 dSCDs can be VRS
of liquid water, as discussed in . Its signal is strong for
regions of the ocean with clear water for elevation angles close to the
horizon or downward-looking geometries. In the M91 MAX-DOAS data set in the
Peruvian upwelling region, neither the spectral signature of liquid water VRS nor
liquid water was found (see Sect. ).
Including the VRS correction spectra can lead to a reduction of the fit error
by ≈15% and furthermore the NO2 dSCD changes by
4×1014moleccm-2 per 2×10-4
VRS(N2) contribution. This corresponds typically to a difference of
20 ppt NO2 and can be thus significant for background measurements
of NO2 in clean areas e.g..
Figure shows two histograms for NO2 dSCDs
from M91, without (Reference fit) and with including a correction spectrum
for VRS of N2 and O2.
Histogram of NO2 dSCDs in the wavelength range of 418–438 nm
illustrating the influence of VRS(N2/O2) on the spectral retrieval
of NO2. Twice the fit error is shown as a line on the top of the
figure. The centre of the fitted gaussian curves is shifted from
(-3.5±0.4)×1014moleccm-2 to (-0.7±0.3)×1014moleccm-2.
Usually a wider fit interval e.g. or a fit interval
above 450 nm e.g. is used to fit the absorptions of
tropospheric NO2, which will then reduce the relative effect from
VRS(N2), but the instrument needs to cover this wavelength range and
the significantly stronger influence of water vapour absorption in this
spectral range needs to be considered. The same analysis as shown in
Fig. for a fit range from 432 to 460 nm leads also
to an underestimation of NO2 dSCDs. A shift of the mean dSCD from
1.24×1014moleccm-2 without including VRS(N2)
and VRS(O2) correction spectra to a mean dSCD of 1.72×1014moleccm-2 when including the correction is observed and
is therefore within the typical fit error of 0.8×1014moleccm-2.
Influence of VRS on the retrieval of glyoxal
To retrieve glyoxal, a fit window from 432 to 460 nm was used, with and
without including N2-VRS (see also Table ).
Including a correction spectrum for N2-VRS led to a reduction of
fit RMS of 0–20 %, the glyoxal fit error was reduced by the same
amount. RRS Ring spectrum and N2 VRS also correlated in this
wavelength window, despite the large water vapour absorption. The glyoxal
dSCD increased when including the N2-VRS for strong Ring spectrum
signals of 5×1025moleccm-2 by 6×1013moleccm-2
and is thus clearly within the measurement error of typically 5×1014moleccm-2.
All other influences, such as water vapour and O4 absorption, have
a far stronger influence on the spectral retrieval of glyoxal.
Influence of VRS on the retrieval of water vapour
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 1.5×1021moleccm-2 (0.5 %) for typical
dSCDs of (3±1)×1023moleccm-2 at telescope
elevation angles below 10∘. This is the same magnitude as typical fit
errors, which were reduced by 0–10 %.
For the narrower fit range of 420–440 nm, which is used for the
evaluation shown in Fig. , the changes in apparent
water vapour absorption are larger due to the smaller water vapour
cross-section. Here the VRS would have changed the water vapour dSCD by up to
5×1022moleccm-2 (typically more than 10 %)
for a Ring signal of 5×1025moleccm-2.
The results from reporting significant deviations of
the relative absorption strengths for water vapour absorption in the blue
wavelength range do not change significantly when applying correction spectra
for N2 and O2 VRS in the spectral retrieval of the MAX-DOAS
data.
Implications for other wavelength intervals
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
1/λ4 according to Eq. (). This is
compensated, however, by the fact that Fraunhofer lines below
390nm are less pronounced. In the wavelength range of
332–380 nm it was not possible to clearly identify the contribution
of VRS of N2/O2. The residual spectra were dominated by systematic
residual structures correlated with the dSCD of O4 with typical ODs
of (4-8)×10-4 for light-path lengths of ≈10km.
The structures were observed independently of the employed O4
literature cross-section. We expect an apparent differential OD due to the
contribution by VRS of N2 to measured ODs of about 3×10-4
at 360 nm (see also Fig. ) for a large
Ring signal of 5×1025moleccm-2.
If the incident light was attenuated by any strong absorber
before being scattered inelastically, then strong absorbers such as ozone, water vapour or NO2 need to be
considered.
But even without strong Fraunhofer or absorption lines, this effect
contributes to the observed differential OD according to
Eq. (). However, constant or polynomial intensity offset
corrections are included in typical spectral evaluations of DOAS
measurements, compensating in this case for most of the contribution of VRS
and VRRS.
Recommended corrections
Correction spectra for VRS of N2 and O2 need to be included
especially in the spectral retrievals of NO2, IO and glyoxal, but
also water vapour in the blue spectral range, whenever wavelengths between
430 and 440 nm are included and systematic residual structures are smaller than
the optical depths attributed to VRS of N2 and O2. For a
residual RMS of 1×10-4 an improvement of the RMS of up to 15 % was
observed.
Since the atmospheric O2/N2 ratio is constant (at the precision
relevant to correcting spectra for VRS contributions) , it is advisable as
a first approximation to include only a single combined
N2+O2-spectrum compensating for VRS contributions to measured
intensities.
The contribution by VRRS is mostly proportional to the VRS signal and can therefore
be added to the VRS correction spectrum. On the other hand, the contribution of VRRS
is relatively smooth (compare Fig. ) due to the rotational
shifts of the transitions and a large part is already compensated in fit settings by the
intensity offset correction.
Given a Ring signal with an OD of 2 %, for example, this translates to an
additionally measured intensity due to VRRS of 0.8×10-4. Due to
the Raman remapped Ca lines the largest variations are expected for the
spectral region between 414 and 440 nm. The effect is already corrected by the
intensity offset correction except for a remaining part of 30–50 %,
which translates to total differential ODs of <0.4×10-4. This is
currently negligible for most ground-based measurements, but this effect
might need to be considered for geometries where a strong filling-in of
Fraunhofer lines is observed
All calculations for a spectral
resolution of the instrument of 0.5 nm.
.
Due to the observed correlation of the spectral signature of VRS scattering
on N2 and the Ring dSCD shown in Fig. ,
a direct correction of the Ring spectrum together with the VRS signal seems
reasonable, at least in the spectral ranges where an effect has been
observed. The actual values of the cross-sections can be found, for example, in
Table . This would allow furthermore to correct for
VRRS scattering, which is also expected to behave in the same way as the Ring
spectrum, but is often (by coincidence) corrected by the intensity offset
correction (see Eq. ), as estimated above. This correction of
the Ring spectrum would therefore improve how the intensity offset correction
can be interpreted, which usually has been introduced in the first place to
compensate for instrumental stray light. The contribution of the VRRS on
O2 and N2 can then be removed from the intensity offset
correction polynomial, because the dominating factor for determining the Ring
spectrum dSCD is the actual RRS contribution, which is about 50 times
larger.
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 N2 VRS from the Ca-II
K Fraunhofer line at 393 nm, significant relative intensity differences at 393/433 nm
can be observed for different measurement geometries and/or aerosol loads. During
M91, relative intensities at 390 and 432 nm (the so-called colour-index CI(390, 432 nm)) were
observed between 0.3 and 0.8 for zenith sky measurements, even more if the
complete elevation angle sequence is considered. This relation translates directly to the size of
VRS correction spectrum via Eq. (). Therefore, a direct correction of
the Ring spectrum is not possible in general, if not considering these effects explicitly.
The same argumentation can be applied for separating the influence of VRS(N2)
and VRS(O2), since the wavelength shifts are different. However, the influence
of VRS(O2) is hardly detected in current measurement spectra. A potential
dependence of VRS(N2)-OD on the colour-index was not observed in
measurements.
The phase functions of RRS, VRS and VRRS differ. Different contributions
proportional to αij2‾ and αii2‾ in the
cross-section correspond to different phase functions, thus the resulting
filling-in does not need to be correlated exactly.
This needs to be modelled in detail to estimate the error made when assuming
the same phase functions. Since no explicit dependence of the relative VRS
contribution to the Ring signal depending on the measurement geometry was
observed during 1 month of measurements during M91 shown in Table ,
it is estimated to be below 20 % of the OD of the VRS of N2. For a typical
variation of the Ring dSCD of 3×1025moleccm-2 this error is
therefore found to be below 2×10-5 peak-to-peak in the wavelength range
between 430 and 440 nm, where the largest spectral structures were detected. This is
5 times smaller than the typical sizes of residual spectra of current MAX-DOAS evaluations.
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
N2 without including the contribution from VRRS, calculated based on
a solar atlas. Correction for VRS of O2 is only needed if the RMS of
the residual is significantly below 10-4.
Conclusions
Vibrational Raman scattering of N2 and O2 can
contribute significantly to observed optical depths in passive DOAS
applications. This was shown for ground-based and ship-based MAX-DOAS
observations from two different campaigns using two different MAX-DOAS
instruments and is expected to contribute in the same amount to other passive
DOAS techniques, such as airborne or satellite measurements. Optical depths
due to VRS Fraunhofer ghosts were observed to amount to up to 3×10-4 in the blue spectral region. The strong Ca Fraunhofer lines at 393
and 396 nm are shifted by VRS of N2 to 433 and 436 nm, where they
are observed as Fraunhofer ghosts. Their magnitude correlates well
(R2=0.8 for M91, R2=0.7 for MAD-CAT) with the magnitude of inelastic
scattering due to rotational Raman scattering (Ring effect). The relative
contribution of the cross-section of VRS of N2 to the cross-section
of RRS of 2.3 % is in agreement with expected values from the theory (2–3.5 %,
depending on the measurement geometry). The detection of VRS of O2 is
close to its detection limit and amounts to an averaged contribution of
0.55±0.30 % of RRS, and thus it is also in agreement with expected values from
the theory (0.6–1.0 %). The individual MAD-CAT result for the contribution of
VRS of NO2 is also still in agreement with expected values (1.0 %),
but compared to the contribution of VRS of N2, a lower value (as for
M91) would have been expected. The reason for this overestimation could be
interferences with large absorption of NO2 and the absorption of
glyoxal, but could also be caused by the lower spectral resolution and the
less constant instrument function width of the compact spectrometer used
during MAD-CAT, compared with the Acton 300i during M91. A contribution of
vibrational rotational Raman scattering (VRRS) of air could not be identified
for the used data sets.
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(N2/O2) leads to a reduction of the fit RMS (see Eq. ): the RMS of a fit residual of 1×10-4 is
reduced by about 15 % for a Ring signal of 5×1025moleccm-2 when considering VRS(N2/O2)
in the spectral retrieval. For measurements with residual structures
significantly larger than those attributed here to
VRS(N2/O2), it is not advisable to include the correction spectra in the fit, as it will
introduce additional degrees of freedom to the fit. This could lead to
erroneous results. Nevertheless, it is possible to detect this effect using a
compact spectrometer, as shown here for the MAD-CAT data set.
The apparent OD caused by VRS of N2 and O2 can influence the
spectral retrieval of various trace gases. For instance, the large
Ca-II-Fraunhofer lines at 393.4 and 396.8 nm lead to ghost lines at 433.1
and 437.2 nm. The additional measured intensity can influence the spectral
retrieval of NO2, water vapour, IO and glyoxal. This influence
was studied for ship-based MAX-DOAS measurements. While the influence on the
total magnitude of water vapour, IO and glyoxal column densities was
below the detection limit, a significant and systematic negative offset of
NO2 dSCDs by up to 4×1014moleccm-2 was
observed. In all cases, the fit errors were reduced by up to 20 % by
including the VRS spectrum in the DOAS fit. The observed ODs attributed to
VRS of N2 between 430 and 440 nm are of similar size as reported
absorptions of IO in the remote marine boundary layer
e.g. and Antarctica e.g. in
the same wavelength range.
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.
Supplement
We provide the VRS correction spectra
calculated from a solar atlas by using
Eq. () for vacuum wavelengths. It is given in
cm2 molec-1. As the shape of the correction spectrum depends on the
instrument function of the spectrometer, the Raman spectrum and the solar
atlas are given to allow the calculation of the correction spectrum according
to Eq. (). This is necessary, since division and convolution do
not commute. The spectra are interpolated to a common wavelength grid with a
spectral resolution of 0.01 nm.
The Supplement related to this article is available online at doi:10.5194/amt-8-3767-2015-supplement.
Acknowledgements
We thank H. Haug for laying the foundations for this work in his diploma
thesis . We thank Stefan Schmitt, Julia Remmers, two anonymous reviewers and the editor for valuable comments and suggestions.
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
(http://joseba.mpch-mainz.mpg.de/mad_cat.htm),
especially Julia Remmers and Thomas Wagner.
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
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