Introduction
Nitrous acid (HONO) is an important precursor of the OH radical, which
prominently controls the self-cleaning capacity of the troposphere (Alicke et
al., 2003; Kleffmann et al., 2005; Acker et al., 2006; Monks et al., 2009;
Elshorbany et al., 2010). The gas-phase reaction of NO with the OH radical
(Stuhl and Niki, 1972; Pagsberg et al., 1997) mostly determines the daytime
HONO concentration. However, recent field measurements (Neftel et al., 1996;
Kleffmann et al., 2005; Sörgel et al., 2011; Li et al., 2012, 2014; Wong
et al., 2012) and laboratory studies (Akimoto et al., 1987; Rohrer et al.,
2005) reported much larger HONO concentrations than predicted by the
gas-phase reactions. These findings imply some missing daytime sources of
HONO. Laboratory and field studies suggest that the missing daytime sources
consist of heterogeneous reactions on various surfaces such as the ground,
forests, buildings and aerosols (Su et al., 2008, 2011; Li et al., 2014, and
references therein), emissions from soil (Su et al., 2011, and references
therein) and a potential gas-phase reaction between HOx and NOx
(Li et al., 2014).
The overall effect of the proposed missing HONO sources in the troposphere
remains widely unknown because of the lack of measurements of HONO and its
relevant precursor species at higher altitudes above the ground (Li et al.,
2014). The surface HONO concentrations can be well quantified by ground-based
in situ instruments, like the LOPAP (long-path absorption photometer)
technique (Heland et al., 2001; Kleffmann et al., 2006; Li et al., 2012) and
long-path DOAS (Trick, 2004, and references therein). Besides these
techniques, four other optical absorption techniques have been used for the
detection of HONO, i.e. cavity ring-down spectroscopy (Wang and Zhang,
2000), Fourier transform infrared spectroscopy (Hanst et al., 1982), tunable diode laser
spectroscopy (Schiller et al., 2001) and cavity-enhanced (CE)-DOAS (Hoch et al., 2014). To
quantify the distribution of HONO in elevated layers of the troposphere, the
in situ LOPAP technique has been mounted aboard on an airship Zeppelin
platform (Li et al., 2014). However, because of the large cost of operating
such a flight platform, the corresponding data sets are limited in time and
space.
Since about 15 years ago, the multi-axis differential optical absorption
spectroscopy (MAX-DOAS) technique, which is based on the DOAS spectral
analysis technique (Platt and Stutz, 2008, and references therein), has been
widely used owing to its potential to retrieve the vertical distribution of
trace gases and aerosols in the lower part of the troposphere from scattered
sunlight spectra recorded at multiple elevation angles using relatively
simple and low-cost ground-based instrumentation (Hönninger and Platt,
2002; Bobrowski et al., 2003; Van Roozendael et al., 2003; Hönninger et
al., 2004; Wagner et al., 2004; Wittrock et al., 2004). Hendrick et
al. (2014) reported the first MAX-DOAS measurements of vertical column
densities (VCDs) and near-surface volume mixing ratios (VMRs) of HONO in the
Beijing area, China. Because of its simple and automatic operation at the
ground, MAX-DOAS is well suited to continuously acquire HONO vertical
distributions over longer time periods. However, due to the typically low
HONO VMRs in the troposphere (between about 50 and 2000 ppt near the surface
in urban areas; Li et al., 2012) and the moderate cross section with the
maximum of about 5 × 10-19 cm2 molecules-1 in the
UV range, the atmospheric HONO absorption is rather weak, and it can also be
systematically interfered by strong absorptions of other trace gases (e.g.
O3 and NO2) and instrument-related spectral structures. So far few
efforts have been devoted to study these error sources in HONO DOAS fits of
MAX-DOAS spectra. Furthermore, many research groups have developed their own
MAX-DOAS instruments equipped with various types of spectrometers, detectors
and entrance optics. Thus the inter-comparison of HONO measurements and
retrieval results from different MAX-DOAS instruments is essential to
evaluate MAX-DOAS HONO results and associated uncertainties.
The Multi Axis DOAS – Comparison campaign for Aerosols and Trace gases
(MAD-CAT) was conducted at the Max Planck Institute for Chemistry in Mainz, Germany, in
June and July 2013 (http://joseba.mpch-mainz.mpg.de/mad_cat.htm).
During the MAD-CAT campaign, 11 MAX-DOAS instruments from different groups
(listed on the website of
http://joseba.mpch-mainz.mpg.de/equipment.htm) were operated in
parallel, providing an opportunity to assess the consistency of different
HONO measuring MAX-DOAS systems for the first time. In this study, only the
direct output values, namely the slant column density (SCD) of HONO in the
troposphere, derived from the spectral analysis (DOAS fit) of the acquired
MAX-DOAS spectra, are compared between the instruments and discussed with
respect to their systematic error sources based on sensitivity tests. The
inter-comparison activities in this study follow similar work done for
NO2 and HCHO during the Cabauw Intercomparison campaign of Nitrogen
Dioxide measuring Instruments (CINDI) (Piters et al., 2012) in the
Netherlands in June–July 2009 (Roscoe et al., 2010; Pinardi et al., 2013).
In addition to the measured spectra, a set of synthetic spectra generated by
the SCIATRAN radiative transfer model (RTM) (Rozanov et al., 2014) was
analysed for the first time. These spectra are simulated based on various
atmospheric scenarios including not only HONO but also other relevant trace
gases and aerosols. Because the HONO SCDs of the synthetic spectra are
known, the bias of the retrieved SCDs from the true values can be easily
quantified.
This paper is structured as follows. Section 2 gives an overview of the
MAD-CAT campaign and participating instruments. Section 3 presents
inter-comparison results of the HONO SCD derived from real measurements and
synthetic spectra between the participants. In Sect. 4 we focus on
sensitivity tests to assess possible interferences in the HONO SCD
retrievals. Recommended analysis settings are given together with an error
budget in Sect. 5. The conclusions are presented in Sect. 6.
Overview on instrumental properties and analysis software used by
the different institutes participating in the HONO comparison activity.
Institute
Detector
Observed
FWHM
Pixel
Integration
Field of
Manufac-
Instrument
Fit
Inter-comparison
characteristics
wavelengths (nm)
(nm)
Sampling (nm)
time per spectrum (s)
view(∘ FWHM)
turer
reference
software
activitye
Real Meas.
Synth.
Heidelberg
AvaSpec-ULS 2048 pixels back-thinned Hamamatsu S11071-1106 CCD
294–459
0.59 at 334 nm
∼ 0.09
∼ 60
0.2
Envimes
Lampel etal. (2015)
DOASIS1
×
×
BIRA
2-D back-illuminated CCD, 2048 × 512 pixels (-40 ∘C)
300–386
0.49
∼ 0.04
∼ 55
0.5
in-house
Clémer etal. (2010)
QDOAS2
×
×
Bremen
2-D back-illuminated CCD, 1340 × 400 pixels (-35 ∘C)
308–376
0.43
∼ 0.05
∼ 20
0.8
in-house
Peters et al. (2012)
NLIN3
×
×
AIOFMa
2-D back-illuminated CCD, 2048 × 512 pixels (-40 ∘C)
288–410
0.35
∼ 0.06
∼ 25
0.4
in-house
Wang et al. (2014)
×
×
Boulder
2-D back-illuminated CCD, 1340 × 400 pixels (-30 ∘C)
329–472
0.78
∼ 0.07
∼ 25
0.95
in-house
Ortega etal. (2015,2016)
WINDOAS4
×
MPICb
DV420A-BU, Andor 2-D back-illuminated CCD, 1024 × 255 pixels (-30∘)
319–457
0.6–0.8
∼ 0.14
∼ 10
0.6
in-house
Krautwurst (2010)
WINDOAS4/ MDOAS5
×(WINDOAS4)
×(MDOAS5)
CMAc
2048 pixel, Sony ILX511 CCD
292–447
0.6–0.8
< = 60
0.8
Hoffmann Messtechnik GmbH
Jin et al.(2016a, b)
WINDOAS4
×
×
INTAd
–
–
–
–
–
–
–
–
LANA6
×
a Anhui Institute of Optics and Fine Mechanics, Chinese Academy of
Sciences.
b Max Planck Institute for Chemistry.
c China Meteorological Administration.
d Área de Investigación e Instrumentación Atmosférica,
Madrid, Spain.
e The flag indicates whether the group participates in the inter-comparison
activity of the real measurements and the synthetic spectra or not.
1 Reference: Kraus (2006).
2 Reference: Danckaert et al. (2012).
3 Reference: Richter (1997).
4 Reference: Fayt and van Roozendael (2009).
5 Reference: J. Remmers, DOAS fits implemented by MATLAB (personal
communication, 2013).
6 Reference: Gil et al. (2008).
Results and inter-comparison
HONO presents prominent absorption structures in the spectral range from 335
to 390 nm. The DOAS technique (Platt and Stutz, 2008, and references
therein) can be applied to spectra of scattered sunlight to retrieve SCDs of
HONO. In this section we present the inter-comparison of HONO SCD results
derived from real measurements and synthetic spectra between the
participants. For the analyses of both sets of spectra, recommended baseline
settings for the DOAS spectral analysis are provided. These baseline settings
are derived from the sensitivity studies outlined in Sect. 4 and also based
on the experiences in Hendrick et al. (2014). Details of the baseline
settings are given in Table 2 and described in Sect. 3.1.
Baseline HONO analysis settings
The sensitivity studies in Sect. 4 indicate that the wavelength range of 335
to 373 nm is the optimal choice for the baseline DOAS settings because of the
low systematic error in that wavelength range. A similar wavelength range of
337 to 375 nm was also used in Hendrick et al. (2014). The slightly
different wavelength range compared to Hendrick et al. (2014) is due to the
limitation of the upper edge of the wavelength range of the Bremen
instrument. Absorption cross sections of HONO, NO2, O3, BrO,
O4 and HCHO were convolved to the spectral resolution of the individual
instruments and included in the fit. The solar I0 correction was applied
to the O3 and NO2 cross sections (Aliwell et al., 2002). To correct
the wavelength dependence of the NO2 AMF (see Sect. 4.5), the Taylor
series terms of λσNO2 and
σNO22 (with λ the wavelength, and σNO2 the NO2 cross section) (Puķīte et al., 2010)
(the details are given in Sect. 4.5) were included in the fit. The effect of
rotational Raman scattering was considered by including a Ring spectrum
(Shefov, 1959; Grainger and Ring, 1962; Chance and Spurr, 1997; Solomon et
al., 1987; Wagner et al., 2009). The Ring spectrum was calculated according
to Chance and Spurr (1997) based on the high-resolution solar atlas of Kurucz
et al. (1984) for a temperature of 250 K and convoluted to the respective
instrumental resolution. To account for different wavelength dependencies of
the filling-in in clear and cloudy skies, an additional Ring spectrum as
described in Wagner et al. (2009) was included.
To correct for the strong Fraunhofer lines, a Fraunhofer reference spectrum
(FRS) IFRS was included in the DOAS fit of a measured spectrum
Im as indicated in Eq. (1):
Im=IFRS×e-σ×(SCDm-SCDFRS)+P=IFRS×e-σ×dSCD+P,
where σ is HONO cross section, SCDm and SCDFRS
are the SCD of HONO of the measured spectra and the FRS, respectively, and P
represents absorptions of other trace gases and scatterings. Therefore the
difference of SCDm and SCDFRS is retrieved from the DOAS
fits and is usually referred to as differential SCD (dSCD).
Thus the SCDs from the DOAS fits actually represent the difference between
the SCD of the measured spectra and the FRS. This difference is usually
referred to as differential SCD (dSCD).
Equation (1) can be further written as
Im=IFRS×e-σ×(SCDmTrop+SCDmStrat-SCDFRSTrop-SCDFRSStrat)+P,
where SCDm and SCDFRS are separated
as tropospheric (SCDmTrop and
SCDFRSTrop) and stratospheric
(SCDmStrat and
SCDFRSStrat) SCDs. If the zenith measurement
in the same elevation sequence as the off-axis spectra is used as
IFRS such a FRS is referred to as “sequential FRS” in this
study, Because the stratospheric light path only substantially depends on the
solar zenith angle (SZA) but not the elevation angle (Clémer et al., 2010; Peters et al.,
2012; Hendrick et al., 2014), it follows that
SCDmStrop≈SCDFRSStrop.
Therefore Eq. (2) can be written as
Im≈IFRS×e-σ×(SCDmTrop-SCDFRSTrop)+P.
This indicates the difference of the tropospheric SCDs and is extracted from
the DOAS fit with a sequential Fraunhofer reference; it is usually referred
to as delta SCDs (Hönninger et al., 2004).
The delta SCDs can be also extracted by another approach. First retrieving
the dSCDs for all the elevation angles (including zenith view) using a single
zenith spectrum (typically around noon) on 1 day. This FRS is referred to
as “daily noon FRS” in this study. The dSCDs for off-zenith
(dSCDm) and zenith views
(dSCDzenith) in the same elevation sequence are
expressed as
dSCDm=SCDmTrop+SCDmStrat-SCDFRSTrop-SCDFRSStratdSCDzenith=SCDzenithTrop+SCDzenithStrat-SCDFRSTrop-SCDFRSStrat.
Subtracting dSCDzenith from the respective
dSCDm in the corresponding elevation sequence
(Hönninger et al., 2004; Pinardi et al., 2013; Ma et al., 2013) gives
dSCDm-dSCDzenith=SCDmTrop+SCDmStrat-SCDzenithTrop-SCDzenithStrat.
As with Eq. (3), SCDmStrat≈SCDzenithStrat because of the similar light
path in the stratosphere for the off-zenith and zenith view in the same
elevation sequence.
Examples of HONO fits of a spectrum acquired by the AIOFM instrument
at around 04:00 UTC on 18 June 2013 for 1∘ elevation angle and
50∘ azimuth angle. A sequential FRS around 03:58 UTC (a) or
a noon FRS around 11:30 UTC (b) is used.
Therefore the delta SCDs is derived as
δSCD=dSCDm-dSCDzenith≈SCDmTrop-SCDzenithTrop.
In principle the delta SCDs from the two schemes should be the same, but the
fits using a daily noon FRS are usually more strongly affected by changes of
instrumental properties and interferences of stratospheric absorptions (e.g.
O3) than those using a sequential FRS. To quantify the effect of the
different types of FRS, we compare the HONO delta SCDs from both methods.
Results of HONO delta SCDs and dSCDs, and fit errors
Figure 1 presents examples of DOAS fits of one spectrum measured by the AIOFM
instrument using the baseline setting with either the sequential FRS (left)
or daily noon FRS (right). The fits were performed using the
WINDOAS software (Fayt and van Roozendael, 2009). The HONO absorption
structures are well retrieved using both types of FRS. The difference of the
retrieved HONO dSCDs between the two fits is mainly due to the different HONO
absorption in the two FRS. The same reason also leads to the differences of
the retrieved dSCDs of the other trace gases. The difference is substantially
larger for the trace gases with considerable stratospheric contributions,
e.g. O3 and BrO, because the stratospheric light paths around noon for
the daily noon FRS are much shorter than those during sunset or sunrise.
Also, the root mean square (RMS) of the fit residual of 4.5×10-4
(corresponding to a HONO dSCD error of
2.6 × 1014 molecules cm-2) using a sequential FRS is
slightly smaller than the RMS of 5.7 × 10-4 (corresponding to
HONO dSCD error of 3.1 × 1014 molecules cm-2) using a
daily noon FRS.
(a) The hourly averaged HONO and O4 delta SCDs for
1∘ elevation angle (using a sequential FRS) derived from the
measurements of the AIOFM instrument during the whole comparison period.
(b) For the same data, the averaged diurnal variations and the
respective standard deviations (error bars) in each hour are given.
Figure 2a shows the hourly averaged HONO delta SCDs at 1∘ elevation
angle derived from the measurements of the AIOFM instrument during the whole
comparison period; Fig. 2b shows the corresponding averaged diurnal
variation. A large variability of the HONO delta SCDs is found between
-1×1015 molecules cm-2 (negative value probably due to the
effect of water vapour absorption – see Sect. 4.1) and
5 × 1015 molecules cm-2. In general, the highest values
are found in the morning. In addition to the HONO delta SCDs, delta SCDs of
oxygen dimer (O4) are also shown in Fig. 2. Since the atmospheric
O4 mixing ratio is constant and well known, variations of the
O4 delta SCDs can be used as an indicator for variations of the
atmospheric absorption path length (e.g. Erle et al., 1995; Hönninger et
al., 2004; Sinreich et al., 2013; Wang et al., 2014; and references therein).
As can be seen in Fig. 2b, the delta SCDs of HONO and O4 show
systematically different diurnal variations indicating that the observed
variation of the HONO delta SCDs is not an artefact caused by the variation
of the light path length but mainly reflects the variation of the atmospheric
HONO concentration.
Time series of the hourly averaged values of HONO delta SCDs using a
sequential FRS and a daily noon FRS as well as the HONO dSCDs with a daily
noon FRS for different elevation angles and participating instruments on
3 July 2013.
HONO dSCDs are retrieved by each group using the same baseline analysis
settings as shown in Table 2. For the inter-comparison of the different data
sets, we first averaged the HONO dSCDs for individual elevation angles of
each instrument during periods of 1 h, in which all the instruments have
more than two measurement sequences (see Fig. S1 in the Supplement).
Figure 3 shows an example of the time series of the hourly averaged HONO
delta SCDs for individual elevation angles derived from each instrument using
the fits with a sequential or a daily noon FRS as well as the HONO dSCDs
using a daily noon FRS on 3 July 2013. The results for the five selected
elevation angles are shown in Fig. 3. Similar results are also found for the
other elevation angles – see Fig. S2 in the Supplement. On this day all the
instruments provide credible data, and also rather large HONO dSCDs and delta
SCDs are observed in the morning, in particular at lower elevation angles.
The large HONO values in the morning could be due to a high NO2
concentration (NO2 dSCD of up to
1 × 1017 molecules cm-2) and a fast photolysis of HONO
(e.g. Hendrick et al., 2014). Note, however, that because of unknown
instrumental problems, CMA and Boulder did not participate in the comparisons
of the delta SCDs for a sequential FRS and dSCDs for a daily noon FRS,
respectively, but other instruments are not affected. As can be seen in
Fig. 3, much better agreements between the instruments are obtained for the
delta SCDs than for the dSCDs. From all instruments a similar diurnal
evolution and elevation angle dependence of the HONO delta SCDs is retrieved.
A detailed quantitative analysis of the deviations of the HONO results
between the instruments is provided in the statistical analysis in Sect. 3.3
Comparison of different fit errors as a function of the SZA between
participating instruments: (a) Averaged HONO dSCD fit errors for
spectra at 1∘ elevation angle using a daily noon FRS,
(b) integration time, (c) normalized HONO dSCD fit errors
according to an integration time of 1 min, (d) differences of
the HONO dSCD fit errors with either a daily noon FRS or a sequential FRS.
Figure 4a presents the hourly averaged fit errors of the HONO dSCDs using a
daily noon FRS plotted against the SZA for the whole
comparison period. The fit errors depend on the random and systematic
structures of the spectral residual. Systematic structures are mainly caused
by instrumental shortcomings and possible non-considered atmospheric absorption
structures, as well as imperfect corrections of rotational Raman scattering,
temperature dependences of atmospheric absorptions, and wavelength
dependences of absorption light paths (namely air mass factor, AMF).
Increasing fit errors with increasing SZA are found for all the instruments
due to the reduction of the solar radiance and the increase in stratospheric
absorptions (e.g. ozone). In addition fit errors of HONO dSCD under cloudy
and clear days are quite similar due to the fact that the MAX-DOAS
instruments automatically change the exposure time of spectrometer based on
the brightness of the sky. Therefore the similar exposure saturation level is
reached during clear and cloudy days. The largest fit error is found for the
CMA instrument due to the relatively low signal-to-noise ratio of the
detector. The second largest fit error is found for the MPIC instrument due
to the very short integration time (Fig. 4b). The fit errors of other
instruments are similar and in the range 0.15 × 1015 to
0.5 × 1015 molecules cm-2 for SZA < 60∘.
Because the random noise of an instrument depends on integration time, which
is different for different instruments (see Fig. 4b), the fit errors are
scaled to a typical integration time of 1 min in order to make the results
directly comparable (see Fig. 4c). Note that we applied a linear scaling,
which is not strictly correct since the photon noise shows a square-root
dependency of the number of observed photons. However, since the MAX-DOAS
instruments are not radiometrically calibrated, we applied a linear scaling
to achieve a first-order normalization for the effect of the integration
time. Similar normalized fit errors are found for the instruments using
cooled large-size detectors (BIRA, Bremen, AIOFM, Boulder and MPIC). Although
both the Heidelberg and CMA instruments use compact spectrometers, Fig. 4c
demonstrates that the Avantes spectrometer (http://www.avantes.com) in
the Heidelberg instrument has a much lower noise level than the ocean optics
USB 2000 (http://oceanoptics.com/) in the CMA instrument. Figure 4d
also indicates that the fit errors with daily noon FRS are generally higher
than those with sequential FRS for all instruments. The difference is
especially large for the Bremen instrument, probably due to a known
temperature stability problem of the spectrometer during the MAD-CAT campaign.
Mean differences and standard deviations as well as correlation
coefficients, slopes and intercepts of linear regressions derived from
comparisons of the HONO delta SCDs and dSCDs retrieved from different
instruments with reference values as function of the elevation angle. The
HONO delta SCDs are derived from fits with a sequential FRS (red curves) and
a daily noon FRS (green curves). The HONO dSCDs are derived from fits with a
daily noon FRS (blue curves).
Because of the instrumental stray light, possible imperfect correction of the
dark current and electronic offset signal in the measured spectra, and
vibrational Raman scattering (Lampel et al., 2015), usually an intensity
offset correction is included in the DOAS fit procedure (e.g. Noxon, 1975;
Fayt and van Roozendael, 2009). However, the effect of spectral stray light
and its correction by the intensity offset fit could interfere with
retrievals of the species with low optical depths (Coburn, 2011). It is known
that spectral stray light typically depends on the sky colour. Thus the
strength of the corresponding spectral interferences also depends on the
actual sky condition during the measurement. The fitted intensity offsets for
most of the instruments are lower than 1 % of the mean intensity in the
fit window for analyses with both types of FRS (details can be found in
Fig. S3a and b in the Supplement). Much larger offsets are found only for the
CMA instrument, especially in the morning and afternoon.
The shift of the wavelength calibration of the measured spectra with respect
to the FRS is mathematically determined and corrected in the DOAS fit
procedure. The wavelength shift can be caused by the tilt effect (typically
< 2 pm) (Lampel et
al., 2017a) and dominated by the mechanical deformation of a spectrometer,
which is usually sensitive to variations of the ambient temperature. The
averaged diurnal variations of the shifts derived from the fits with a daily
noon FRS and a sequential FRS are smaller than 0.015 and 0.05 nm,
respectively (the detailed results can be found in Fig. S3c and d in the
Supplement, respectively). As expected, the shifts for the sequential FRS are
much smaller than those for the daily noon FRS.
Statistical inter-comparisons
In this section, we apply the statistical analysis method introduced in
Roscoe et al. (2010) and Pinardi et al. (2013) to the inter-comparison of
HONO results (delta SCDs and dSCDs) from the individual instruments. The
results from the Heidelberg, BIRA, Bremen and AIOFM instruments are averaged
as reference values because of their almost full-time coverage, low fitting
errors and good agreement. The selection is also because the
Boulder and CMA instruments are affected by some unknown instrumental
problems. In the following discussions, we assume the reference values as the
truth, but this is not necessarily the case. We implement two methods for the
comparisons:
To derive an overview of the general agreement between the retrieval
results by different instruments for the whole measurement period, mean
absolute differences and standard deviations of HONO results from the
reference values are summarized for individual elevation angles. In addition, a
set of histograms of the absolute differences is prepared.
To investigate how well the different instruments capture the diurnal
variation of the HONO dSCDs, for 8 selected days with pronounced diurnal
variations of the HONO dSCDs and delta SCDs (12, 15, 17, 18 and 30 June as
well as 1, 2 and 3 July 2013), a set of scatter plots with linear regressions
of the results from the different instruments against the reference values is
prepared.
We performed the two comparisons for the two HONO delta SCDs from the fits
with a sequential FRS or a daily noon FRS as well as for the HONO dSCDs with
a daily noon FRS. Note that in the figures below, only the results for the
elevation angles 1, 3, 5, 8, and 15∘ (also 90∘ only for dSCDs
with a daily noon FRS) are shown, but similar conclusions can be drawn for
the other elevation angles. The mean absolute differences and standard
deviations as well as the correlation coefficients, slopes and intercepts of
the linear regressions derived from comparisons of HONO dSCDs (noon FRS) and
delta SCDs of different instruments with respect to the reference values are
presented in Fig. 5. In general, linear correlations of the three HONO results
decrease with an increase in elevation angle for all the instruments,
probably due to the low values and small value ranges. However, there are no
dependences of the absolute differences and standard deviations on the
elevation angles for most of the instruments, except the CMA instrument. The
comparison results of HONO delta SCDs derived from the fits with either a sequential FRS or a daily noon FRS are quite similar to each other; however
they are mostly different from those of HONO dSCDs with a daily noon FRS, for
individual instruments. In the following we separately discuss the
comparisons of three HONO results.
For the HONO delta SCDs with a sequential FRS, Fig. 5 indicates that larger
standard deviations are found for MPIC
(∼ 0.6 × 1015 molecules cm-2), Boulder
(∼ 0.3 × 1015 molecules cm-2) and Bremen
(∼ 0.3 × 1015 molecules cm-2) compared to the
other instruments (∼ 0.16 to
∼ 0.28 × 1015 molecules cm-2), consistent with the
fit errors shown in Fig. 4. Different absolute differences are also found for
the different instruments: MPIC (∼ -0.53 × 1015 molecules cm-2), BIRA
(∼ 0.34 × 1015 molecules cm-2) and Bremen
(∼ -0.23 × 1015 molecules cm-2) display larger
differences than the other instruments (∼ -0.1 to
∼ 0.04 × 1015 molecules cm-2). The different
absolute differences might be related to possible errors of the elevation
angles, interferences of systematic instrumental structures in the fits
(e.g. nonlinearity of the detector response and stray light) and differences
in the implementations of DOAS fits. The histograms of the absolute
differences from the reference values for each instrument are shown in
Fig. S4 in the Supplement. A symmetric and quasi-Gaussian shape of the
histograms is found for all the instruments. From the histograms the same
standard deviation and the mean absolute differences between the instruments
as in Fig. 5 are derived. In addition, for the eight selected days with
pronounced diurnal variations of the HONO values, linear regressions are
performed and slopes and correlation coefficients are derived from the
scatter plots of the HONO delta SCDs with a sequential FRS for each
instrument against the reference values. The results of the linear
regressions and the linear correlation coefficients are displayed in Fig. 5
(the corresponding scatter plots are provided in Fig. S5 in the Supplement).
As can be seen for 1∘ elevation angle, all instruments agree well:
the scatter plots show compact correlations with correlation coefficients
mostly larger than 0.95 (a lower value of 0.86 is only found for the MPIC
instrument); the slopes are close to unity with deviations smaller than
16 % and intercepts smaller than
0.5 × 1015 molecules cm-2. Smaller correlation
coefficients and larger deviations of the slopes and intercepts are found for
large elevation angles due to the rather low values and the small range of
HONO delta SCDs.
Correlation coefficients, slopes and intercepts of linear
regressions as well as mean differences and standard deviations derived from
the comparisons of the HONO delta SCDs retrieved by fits between with a daily
noon FRS and a sequential FRS as function of the elevation angle for
individual instruments. The colour curves indicate different instruments.
For the HONO delta SCDs derived from fits with a daily noon FRS, we follow
the same comparison procedures as for the HONO delta SCDs from fits with a
sequential FRS. All five parameters shown in Fig. 5 are quite similar to the
results for the sequential FRS for all the instruments. Only the slopes for
15∘ elevation angle are different, but this phenomenon is due to the
low HONO delta SCDs and small value ranges. To directly show the agreement of
the HONO delta SCDs from the fits with the two types of FRS, the mean biases
and standard deviations as well as the correlation coefficients, slopes and
intercepts of linear regressions derived from the comparisons of two HONO
delta SCDs are presented in Fig. 6 (the corresponding histograms of absolute
differences between them and their scatter plots are presented in Figs. S6
and S7 in the Supplement, respectively). Figure 6 indicates that for each
instrument and each elevation angle there are no significant mean differences
(< ±0.04 × 1015 molecules cm-2) and standard
deviations (< 0.23 × 1015 molecules cm-2). The
correlation coefficients (> 0.92) and slopes (deviations < 13 %)
are quite close to unity for all the instruments. Only moderate deterioration
of correlation coefficients and slopes for the 15∘ elevation angle
are found for some of the instruments.
For the HONO dSCDs derived from fits with a daily noon FRS shown in Fig. 5,
the standard deviations are slightly larger than those for the comparisons of
the two HONO delta SCDs. This could be caused by the different HONO
absorptions in the daily noon FRS of the different instruments and
interferences by the stratospheric species, e.g. ozone. The correlation
coefficients are mostly slightly better than for HONO delta SCDs (except for
the BIRA instrument) probably due to the slightly larger values of the HONO
dSCDs especially for high elevation angles. For the off-zenith observations,
Bremen, AIOFM and MPIC have similar mean differences and intercepts for the
HONO dSCDs as those for the HONO delta SCDs, while Heidelberg and BIRA show
larger and smaller values. This finding is probably caused by differences of
the HONO dSCDs for zenith view between the different instruments. For the CMA
instrument, its agreement with the other instruments is better for the HONO
dSCDs than for the HONO delta SCDs. The reason could be an unknown
instrumental problem of the zenith observations of the CMA instrument.
In general a consistent temporal variation and elevation angle dependence of
the HONO delta SCDs and dSCDs has been retrieved from the different
instruments. The discrepancy of HONO dSCDs from the fits with a daily noon
FRS between the instruments is systematically larger than those of the HONO
delta SCDs, which can be consistently retrieved from the fits with a daily
noon or a sequential FRS.
Synthetic spectra and inter-comparisons
In general it is difficult to quantify the biases of the retrieved HONO dSCDs
with respect to the true atmospheric state for real MAX-DOAS measurements as
the true HONO column is not known. Thus, to assess these biases in more
detail, we generated a set of synthetic spectra using the RTM SCIATRAN,
version 3.6.0 (3 December 2015), in a pseudo-spherical atmosphere (Rozanov et
al., 2014) for the same measurement geometries (elevation angles and azimuth
angle) and similar sun geometries (16 combinations of SZA and solar azimuth
angle, SAA) as the real measurements. Detailed information on the RTM
simulations is given in Sect. S1 of the Supplement. The simulated delta SCDs
at 355 nm corresponding to the synthetic spectra are in the range 0.4 to
6 × 1015 molecules cm-2 (see Fig. S8b in the
Supplement), covering the range of values of the real measurements (see
Fig. 2a). Note that there is no random noise added into the synthetic spectra
since the main objective of this study is to quantify the systematic
difference of the retrieved values from the truth. It was also found that
noise has a negligible effect on the systematic differences – see Sect. 4.9.
Two versions of synthetic spectra were generated with different input of
water vapour cross sections. The H2O cross section from the HITRAN 2012
(Rothman et al., 2013) database and from the newly published POKAZATEL line
lists (Polyansky et al., 2018) are used by the RTM to generate version (V) 1
and 2 of the synthetic spectra, respectively. Note that absorption structures
below 388 nm exist in the POKAZATEL H2O cross section, but not in
HITRAN. Thus there is no H2O absorption included in the UV
range (used in this study) of V1 synthetic spectra. The POKAZATEL H2O
absorption around 363 nm was recently identified in MAX-DOAS and long-path
(LP)-DOAS measurements and could impact the HONO retrieval (Lampel et al.,
2017b). In addition, they also found
that the POKAZATEL line lists underestimate the real H2O cross section
by a factor of about 2.6. Thus the POKAZATEL H2O cross section
multiplied by 2.6 is used in the RTM. Both the V1 and V2 synthetic spectra
are used in the sensitivity studies presented in Sect. 4, while only the V1
data set is used for the inter-comparison activities.
Example of a HONO fit of a V1 synthetic spectrum for a SAA of
166∘ and EA of 1∘ using the DOAS setting with a sequential
FRS without the intensity offset correction (setting #4 in Table 3).
Correlation coefficients, slopes and intercepts of linear
regressions as well as mean differences and standard deviations derived from
the comparisons of the HONO delta SCDs and dSCDs between retrieved from the
V1 synthetic spectra and the simulated real values as function of the DOAS
fit setting number for individual institutes. The colour curves indicate
different institutes. “a#1”, “a#2”, “a#3” and “a#4” in
the labels of the x axis indicate the HONO delta SCD retrieved by fits with
DOAS setting #1, #2, #3 and #4 (see Table 4), respectively. And
“d#1” and “d#2” indicate the HONO dSCDs retrieved by fits with DOAS
setting #1 and #2, respectively.
Six institutes analysed the V1 synthetic spectra using their respective fit
software (see Table 1). The DOAS settings are almost the same as those for
the inter-comparison of the real measurements presented in Table 2. The only
difference is that the retrievals are implemented with and without including
an intensity offset in the fits. Analyses are performed using a noon (for SAA
of 166∘) and a sequential FRS. The four settings of the DOAS fits are
listed in Table 3. Note that only a constant term is used for the setting of
including intensity offset correction in the fit, because of the negligible
impact on the analyses when including a linear term. Figure 7 shows an
example of DOAS fit of the V1 synthetic spectrum for a SAA of 166∘
and EA of 1∘ using the setting #4 in Table 3. The retrieved
optical depths of the relevant species are comparable to those for the real
measurement shown in Fig. 1a. Furthermore, the residual structure is smaller than half
of that for the real measurement due to the absence of random noise in the
synthetic spectrum. We did the comparisons between the results from the
different institutes for the HONO delta SCDs (all four fit settings) and
for the HONO dSCDs (only setting #1 and #2 (noon FRS)). The mean biases
and standard deviations as well as the correlation coefficients, slopes and
intercepts of the linear regressions derived from the comparisons of HONO
dSCDs (noon FRS) and delta SCDs of different groups with respect to the
simulated real values are presented in Fig. 8. The comparison results are
plotted against labels of the different DOAS settings in Table 3 (the
corresponding histograms of the absolute differences and scatter plots are
also provided in Figs. S9 and S10 in the Supplement, respectively). In
general, Fig. 8 indicates that much larger mean absolute differences for the
dSCDs than for the delta SCDs are found; at the same time, much lower correlations
are found for the HONO dSCDs than for the delta SCDs, mainly due to the
interference of stratospheric species, e.g. ozone. Correlation coefficients
(> 0.91) for the HONO delta SCDs are close to unity for all the groups.
The similar mean absolute differences and slopes of HONO delta SCDs between
settings #1 and #4 as well as between settings #2 and #3 indicate
that the effect of using different FRS on the HONO delta SCDs is negligible
for all the groups. However, the effect of intensity offset correction
(comparisons between settings #1 and #2 as well as between settings #3
and #4) on the HONO delta SCDs is found to be considerable (about 0.3 to
0.7 × 1015 molecules cm-2) for all the groups. The
smallest mean absolute differences of the HONO delta SCDs with respect to the
real values are smaller than 0.23 × 1015 molecules cm-2,
which are found for settings #1 and #4 (without intensity offset
correction) for BIRA, Bremen, AIOFM, MPIC and CMA, and for setting #2 and
#3 (with intensity offset correction) for Heidelberg and INTA. The
different phenomenon of the intensity offset effect on HONO delta SCD between
the two groups of institutes might be caused by differences in the
implementation of intensity offset correction in the DOAS fit software codes.
Peters et al. (2017) have already demonstrated that different linear fit approach
of the intensity offset correction implemented in the DOAS fit can
considerably impact the retrieved dSCDs. However nonlinear fits used in
QDOAS, WINDOAS and MDOAS were not included in their study. The difference of
the nonlinear and linear fit of the intensity offset correction could also be
considerable. However, apart from the effect of intensity offset correction
by excluding Heidelberg and INTA, the systematic difference of HONO delta
SCDs between the groups with the same DOAS setting is smaller than
0.3 × 1015 molecules cm-2.
Four DOAS fit settings for the synthetic spectra.
Setting
Intensity offset
Noon
Sequential
fit (constant)
FRS
FRS
#1
No
Yes
No
#2
Yes
Yes
No
#3
Yes
No
Yes
#4
No
No
Yes
Sensitivity studies
In this section we perform sensitivity studies to assess the systematic
effect of the absorptions of H2O, O4 and NO2, the Ring
spectrum, polynomial, intensity offset and shift corrections on the HONO
delta SCD retrievals. We also evaluate the effect of variations of the
instrument properties including the wavelength calibration, the instrumental
resolution and random noise. The studies are implemented on both the V1 and
V2 synthetic spectra. In addition measurements of the AIOFM instrument on the two
days of 16 and 18 June 2013 are analysed, which were selected because of the
low and high HONO delta SCDs observed on the 2 days, respectively. The
WINDOAS software is used to implement DOAS fits in the study. And a
sequential FRS is used in the DOAS fits.
Residual around 363 nm and the effect of the H2O absorption
in the UV spectral range
In the baseline fit of HONO, a systematic large residual structure around
363 nm was found as shown in Fig. 9. If the fit spectral range extends to
390 nm, the residual structure becomes more prominent. Lampel et
al. (2017b) demonstrated that a considerable
H2O absorption can be found in MAX-DOAS observations around 363 nm.
They also showed that the POKAZATEL H2O cross section (Polyansky et al.,
2018) can well represent this absorption structure. In Fig. 10a for a
measured spectrum by the AIOFM instrument, the residual structures from the
fits with and without the POKAZATEL H2O cross section are compared.
Especially for the large fit range the residual structures around 363 nm can
be minimized by including the POKAZATEL H2O cross section. The
corresponding fit results of the H2O absorptions are also shown in
Fig. 10a. In Fig. 10b the corresponding results for the fits of the V2
synthetic spectra are shown. Compared to the results of the measured spectra,
the residuals do not contain noise, and the improvement of the residual for
the fits by including the H2O cross section becomes even more obvious.
The fit results of the V1 synthetic spectra, in which no H2O absorption
below 388 nm is included, are also shown in Fig. 10c for comparison with
those of the V2 synthetic spectra in Fig. 10b. The effect of including
H2O cross section on the fit residual and the artificially fitted
H2O absorption are quite low. In addition we compared HONO delta SCDs
from fits with and without the H2O cross section for the selected AIOFM
measurements on 16 and 18 June 2013, and for the V2 and V1 synthetic spectra
(for details see Fig. S11 in the Supplement). The difference is up to
1.5 × 1015 molecules cm-2 and is and linearly correlated
with the retrieved H2O delta SCDs with a correlation coefficient of one.
These findings demonstrate that the H2O absorption could mainly
contribute to the residual structure around 363 nm if the H2O cross section is not included in the DOAS fit, and can considerably interfere with
the HONO absorption. Moreover, the interference is stronger for larger H2O
absorptions. Thus we conclude that the POKAZATEL H2O cross section
should be included in the DOAS fits. However, it also needs to be noted that
the effect of including H2O cross section on the HONO delta SCDs is
found not only for the V2 synthetic spectra (with UV H2O absorption)
but also for the V1 synthetic spectra (without UV H2O absorption). This
indicates a possible spectral interference of the POKAZATEL H2O cross section with the structures of other absorptions, e.g. O4 (also reported
in Lampel et al., 2017b). Figure 9 indicates that the absorption peak of
H2O around 363 nm overlaps with the O4 structures. Further
investigations, improved O4 cross sections and H2O cross sections
for UV wavelengths are needed to clarify this hypothesis. In addition it is
important to note that the POKAZATEL H2O cross section scaled by 2.6 is
used in the fits for the real measurements and synthetic spectra because of
the known underestimation (Lampel et al., 2017b).
(a) Residual structure from baseline fits with a sequential FRS of
the measured spectrum at 1∘ elevation angle around noon on 16 June 2013
in the spectral range of 335–390 nm (black) and 335–373 nm (red).
(b) Normalized absorption cross sections used in the HONO baseline fit.
(a) Residual structures (left) and H2O fit results
(right) for the same measured spectrum as in Fig. 9 for the fits either with
(red) or without (black) the POKAZATEL H2O cross section. The upper and
lower two subfigures represent fits in the spectral range of 335–390 nm and
335–373 nm, respectively. Panels (b, c) are same as (a),
but for the V2 and V1 synthetic spectra for a SAA of 166∘ and EA of
1∘, respectively.
Candidate fit spectral ranges and interference species
There are four prominent absorption bands of HONO in the spectral range of
335 to 390 nm (see Fig. 11a). Thus fits of HONO absorptions could be
implemented in different spectral ranges covering, for example, two, three or four
HONO absorption bands. Note that it is unreasonable to extend to the
wavelength range below 335 nm as strong ozone absorptions and low signal-to-noise ratios can significantly deteriorate the retrievals and the magnitude
of the differential absorption cross section of HONO decreases here
significantly. We compared the HONO delta SCDs retrieved in the three
spectral ranges of 335–361, 335–373 and 335–390 nm for the V1 synthetic
spectra and the selected AIOFM measurements (see Fig. S12 in the Supplement).
The difference is about 0.6 × 1015 molecules cm-2 on
average and cannot be explained by the wavelength dependence of AMF, since
this effect can only cause differences of the HONO SCDs of up to
0.03 × 1015 molecules cm-2 on average (for details see
Fig. S13 in the Supplement). Therefore the dependence of the retrieved HONO
delta SCDs on the fit ranges can be mainly attributed to spectral
interferences of the HONO absorption with other absorption structures or
instrumental issues. Typical optical depths of the species (based on the
measurements during the whole campaign) included in the HONO retrievals are
shown in Fig. 11a. In order to assess the possibility of spectral
interferences with HONO, we calculated the correlation coefficients of the
cross sections of different species with HONO. The determined correlation
coefficients are then scaled with typical atmospheric optical depths of the
respective species to roughly estimate their potential for spectral
interferences with the HONO absorption. The results shown in Fig. 11b
indicate that the strongest interferences are expected from NO2, O4
and the Ring effect. Their individual effects on the HONO retrieval are
discussed in the following Sect. 4.3 to 4.5.
(a) Typical optical depths of the absorption species as the
function of wavelength in the wavelength range for HONO retrieval; the dashed
coloured squares in the lower subplot indicate the wavelength ranges 335 up to
360, 373 and 390 nm, respectively; (b) correlation coefficients of
the different cross sections multiplied with typical optical depths of
respective species (based on the measurements during the whole campaign) with
the HONO cross sections in the spectral range 335–373 nm.
Influence of the O4 absorption on the HONO analysis
Lampel et al. (2017b) reported considerable differences between the three
currently available literature O4 cross sections (Greenblatt et al.,
1990; Hermans et al., 1999; Thalman and Volkamer, 2013). For a typical
O4 dSCD of 2 × 1043 molecules2 cm-5, the
optical depths of the differences amount to up to 1 × 10-3,
which is comparable with typical HONO optical depths of up to
3 × 10-3. Considering the known wavelength calibration problem
of the Greenblatt O4 cross section (Piters et al., 2012), the other two
cross sections are probably the best candidates for DOAS fits. We investigate
the effects of changing the O4 cross sections, in the fits on the HONO
delta SCDs for the synthetic spectra and the selected AIOFM measurements on
16 June. Similar diurnal variation of the differences of the HONO delta SCDs
between the analyses with the Thalman and the Hermans O4 cross section
are found for both the synthetic spectra and the measured spectra (see
Fig. S14a in the Supplement). Since the synthetic spectra are simulated using
the Thalman and Volkamer (2013) O4 cross section, this finding indicates that the
atmospheric O4 absorption is best described by the Thalman and
Volkamer (2013)
O4 cross section. In addition we found that the differences of the HONO
delta SCDs are linearly well correlated with the differences of the O4
delta SCDs with a correlation coefficient of about 0.96 (the scatter plots
are provided in the Fig. S14b in the Supplement). This finding indicates a
spectral interference between (errors of the) O4 absorption and the
retrieved HONO delta SCDs.
The temperature dependence of the O4 cross section is reported in
Thalman and Volkamer (2013). The difference of the O4 cross sections
at 203 and at 293 K is about 20 % around 360 nm. The Thalman
O4 cross section at 203 K is orthogonalized to
that at 293 K based on Gram–Schmitt's algorithm
using a polynomial of second degree. The orthogonalized O4 cross section
is normalized by an arbitrary factor to be shown in a comparable scale with
the other cross sections in Fig. 9. The prominent structure at 203 K
indicates that the temperature dependence of O4 cross section probably
interferes with the HONO absorption. Moreover, the overlap of the structures
of the temperature dependence of O4 cross section with the H2O
absorption band around 363 nm indicates the potential interplay of the
O4 temperature dependence, the H2O absorption and the HONO
absorption.
DOAS fit settings for the sensitivity studies with respect to
O4, Ring, NO2, polynomial and intensity offset correction in
Sect. 4.
Item
Type
Fit setting
O4
#1
O4 at 293 K
#2
O4 at 293 K + Taylor linear term of O4
#3
O4 at 293 K + Taylor linear term of O4 + Taylor square term of O4
#4
O4 at 293 and 203 K
#5
O4 at 293 and 203 K + Taylor linear term of O4 at 293 K
#6
O4 at 293 and 203 K + Taylor linear term of O4 at 293 K + Taylor square term of O4 at 293 K
Ring
#1
Ring at 250 K
#2
Ring at 273 K
#3
Ring at 250 and 273 K
NO2
#1
NO2
#2
NO2 + Taylor linear term of NO2
#3
NO2 + Taylor linear term of NO2 + Taylor square term of NO2
Polynomial
#1
Polynomial of degree 5
#2
Polynomial of degree 4
#3
Polynomial of degree 3
Offset
#1
No offset correction
#2
Polynomial of degree 0
#3
Polynomial of degree 1
#4
Polynomial of degree 2
In the DOAS fit it is assumed that the AMF (or atmospheric light path) in a
spectral range of the fit is constant. However, it is well known that the
light path actually depends on the wavelength (Richter, 1997; Marquard et
al., 2000; Puķīte et al., 2010; and references therein). This
problem could also play a role for the fit of the O4 absorption in the
HONO retrievals. The so-called Taylor series approach (TSA) developed by
Puķīte et al. (2010) could approximately solve this problem by
including a linear term (λσO4) and a square term
(σO42) of the O4 cross section in the fit
(λ and σO4 are the wavelength and absorption
cross section of O4, respectively). The two TSA terms of O4
orthogonalized to the O4 cross section are shown in Fig. 9. The
interplay of Taylor terms of the O4, the structure of the O4
temperature dependence, and the H2O absorption could impact the
retrieved HONO delta SCDs. To test these interference effects in more detail,
we compare the HONO delta SCDs from the fits with six different settings for
the O4 absorptions (listed in Table 4) for the V1/V2 synthetic spectra
and for the selected AIOFM spectra. In these sensitivity studies all other
fit settings are kept unchanged (baseline DOAS settings, but without an
intensity offset included for the synthetic spectra). For the synthetic
spectra, we calculate the differences of the retrieved HONO delta SCDs using
the six O4 settings and three spectral ranges with respect to the real
HONO delta SCDs (as used in the calculation of the synthetic spectra). We
also calculated similar differences, but with respect to the results of the
baseline retrieval (O4 setting #1 in 335–373 nm – see Table 4) for
the synthetic spectra and the measured spectra. In general the smallest
differences of fitted HONO delta SCDs from the real values are found for the
wavelength range 335–373 nm. For this wavelength range, also the variation
of the fitted HONO delta SCDs by changing the O4 setting is smallest.
Similar differences are found with respect to the real HONO delta SCDs of the
synthetic spectra and the retrieved HONO delta SCDs using the baseline
settings (the detailed results are provided in the Fig. S15a, b). Therefore
we conclude that the wavelength range 335–373 nm is the best suited
spectral range to minimize the O4-related interference effects on the
HONO retrievals. Another important finding is that for the wavelength ranges
335–373 and 335–390 nm the results for the real measurements and the
synthetic spectra are similar. Thus we recommend using one Thalman O4
cross section at 293 K in the fits. The variation of the HONO delta SCDs by
changing the O4 setting indicates the remaining systematic uncertainty
related to the O4 effects.
Influence of the Ring spectrum
The temperature dependence of the Ring spectrum can contribute to a
difference of optical depth of about 5 × 10-5 K-1 around
355 nm (with respect to a typical Ring optical depth shown in Fig. 11a) based
on the study of Lampel et al. (2017b). For the analysis of absorbers with
small optical depths, Lampel et al. (2017b) recommend including two Ring
spectra representing two different temperatures in the fits. To test the
effect of the temperature dependence of the Ring effect on the HONO
retrievals, we compare the HONO delta SCDs derived using three different Ring
settings (see Table 4), which are either a Ring spectrum for 250 K, for
273 K or both of them (one is orthogonalized to the other).
The Ring effect on the retrieved HONO delta SCDs is quite different
for the measured and synthetic spectra in the three spectral ranges,
especially for Ring setting #3 (the detailed results are provided in
Fig. S16 in the Supplement). Based on the obtained results we recommend using
a Ring spectrum at one temperature in HONO retrievals. Furthermore, due to the
small difference of HONO delta SCDs between Ring settings #1 and #2, it
is reasonable to arbitrarily select 250 K for the generation of Ring
spectrum. The variations of the HONO delta SCDs for different Ring settings
(about 0.35, 0.2 and 0.12 × 1015 molecules cm-2 in the
spectral ranges of 335–361, 335–373 and 335–390 nm, respectively on
average) indicate the remaining systematic uncertainty to be related to the Ring
effect.
AMF wavelength dependence caused by the NO2 absorption
The optical depth of the NO2 absorption can be large, up to about 0.15,
which is much larger than the typical optical depth of HONO (up to 0.003).
Similar to O4, wavelength dependence of absorption caused by NO2 is
also expected. The TSA method (Puķīte et al., 2010) could also be
applied for NO2. We compare the HONO delta SCDs from the three fits with
different NO2 settings listed in Table 4, which are (a) the original
NO2 cross section, (b) also including the linear Taylor term and
(c) the linear and square Taylor terms, for both the synthetic
and measured spectra. The results indicate that the NO2 effect on HONO
delta SCDs is negligible in the wavelength range 335–373 nm, but
considerable in the other two ranges. Also, very consistent results for the
synthetic spectra and measured spectra are found. Reduction of residual
spectral structures related to the NO2 absorption by a use of the TSA
method in DOAS fits can be found in the three wavelength ranges. Thus to
minimize the NO2 effects, we recommend including the two additional
Taylor terms of NO2 in the HONO fit. The detailed results are provided
in Fig. S17 in the Supplement.
Influence of the degree of the polynomial
To account for the broad spectral structures, e.g. related to atmospheric
scattering processes, polynomial fits are included in DOAS retrievals. The
polynomial degree is usually chosen depending on the spectral range and
spectral characteristics of the target species. To quantify the uncertainty
of the retrieved HONO delta SCDs related to the choice of the degree of the
polynomial in the three spectral ranges, we compare the HONO delta SCDs
retrieved by the three fits with different degree of the polynomial (see
Table 4), including degree 3, 4 and 5, for both the synthetic and measured
spectra. The variation of the HONO delta SCDs for different polynomial
degrees is smaller in the wavelength range 335–373 nm than in the other two
spectral ranges. Also, the deviation of the retrieved HONO delta SCDs from the
real delta SCDs is generally smallest in the wavelength range 335–373 nm
(the detailed results are provided in Fig. S18 in the Supplement). Based on
the obtained results the wavelength range 335–373 nm is the best suited
spectral range to minimize the polynomial-related uncertainty of HONO
retrievals. The effect of the degree of the polynomial on the HONO results in
the wavelength range 335–373 nm is small. However, because in some cases
short time variations of the sky conditions might happen in real
measurements, we recommend selecting a higher polynomial degree, which can
better account for such changes. A fifth-degree polynomial is used for HONO
retrievals in this study.
Effect of the intensity offset
To compensate for additional artificial intensity signals like instrumental
stray light or insufficient corrections of the dark current or electric
offset, an intensity offset correction is normally included in the DOAS fits.
The intensity offset correction is implemented by a nonlinear fit in the
WINDOAS software (Fayt and van Roozendael, 2009) in this study. Considerable
interferences of the intensity offset with the retrievals of trace gases,
especially with small optical depths, were reported, for example, by Coburn et
al. (2011). To test the effect of the intensity offset on the HONO analysis
in the three spectral ranges, we compare the HONO delta SCDs for different
degrees of polynomial for the intensity offset correction (see Table 4),
including fits without an offset correction and with polynomials of degree 0,
1 and 2 for the offset correction, for both the synthetic and measured
spectra. Significant changes of the HONO delta SCDs by including an intensity
offset compared to a fit without an intensity offset are found for both
synthetic and measured spectra (for details see Fig. S19 in the Supplement).
Because the intensity offset is expected to be zero for the synthetic
spectra, the retrieved non-zero intensity offsets and their influence on the
HONO delta SCDs imply a significant interference with HONO retrievals. In
spite of these possible interferences, taking into account typical
instrumental problems (like spectrograph stray light), the consideration of an
intensity offset correction in the fit is still recommended for the HONO
retrieval. The effect of spectrograph stray light cannot be quantified here
because it needs a sophisticated lab measurement, which was not available
during the campaign. In addition it should be noted that the interference
between the fitted intensity offset and the retrieved HONO delta SCDs as
found for the synthetic spectra constitutes a relevant systematic uncertainty
of the HONO retrieval, which causes deviations of 0.55, 0.35 and
0.25 × 1015 molecules cm-2 in the spectral ranges of
335–361, 335–373 and 335–390 nm, respectively on average.
Comparison of the averaged fit errors of the HONO delta SCDs
for synthetic spectra with and without noise (black and red dots), and the
averaged differences of the HONO delta SCDs derived from the two
synthetic spectra (blue dots). The error bars indicate the corresponding
standard deviations of the differences.
Effect of the wavelength calibration and instrumental slit
function
In this section the effect of changes of wavelength calibration on the HONO
delta SCDs is tested. The tests are done for either excluding or including a
wavelength shift in the fit. In a particular test, we manually shifted the
synthetic spectra by 0.025 nm because changes of the wavelength calibration
of the MAX-DOAS instruments are smaller than 0.015 nm during 1 day in the
campaign (see Fig. S3c in the Supplement). The HONO delta SCDs derived from
the shifted spectra are compared to those derived from the original spectra.
The differences are only considerable for the fits not including the
wavelength shift correction in the fit (leading to differences of 0.2 to
0.4 × 1015 molecules cm-2, in the three spectral
ranges). The differences are negligible once the shift correction is
accounted for in the fit.
(a) Systematic uncertainties of the HONO delta SCDs with
respect to different error sources for the three spectral ranges.
(b) Systematic biases from the real values, of the retrieved HONO
delta SCDs (black dots) derived from the synthetic spectra in the three
spectral ranges; black and red bars indicate typical total systematic and
random uncertainties (for a SNR of 3000) of the retrieved HONO delta SCDs.
In addition, changes of the instrumental slit function could occur. We test
the effect of changes of the slit function on the HONO retrieval using the
synthetic spectra. The cross sections were convoluted with a wrong Gaussian
slit function with a FWHM of 0.525 nm (instead of 0.50 nm). Then we
analysed the synthetic spectra with the new convoluted cross sections. The
HONO delta SCDs derived from the new fits are compared with those using the
correct slit function. The systematic differences are only around -0.02 to
-0.13 × 1015 molecules cm-2. Here it should be noted
that actual changes of the slit function are usually smaller than assumed in
this test. For example, a change of only 0.004 nm is found for the AIOFM
instrument during the whole comparison period. Thus we conclude that the
changes of the slit function are usually not important for the HONO analysis.
But it needs to be noted that asymmetric changes and wavelength dependence
changes of the slit function are not considered in the test study.
Effect of random noise
The measured spectra are subject to several sources of random noise (i.e.
photon noise or electronic noise). To quantify the effect of noise on the
HONO analysis, Gaussian random noise with a signal-to-noise ratio (SNR) of
3000 is added into the V1 synthetic spectra. We compare the HONO delta SCDs
and the fit errors of the synthetic spectra with noise and without noise. The
comparison results are shown in Fig. 12. The results indicate that the fit
errors increase from around 0.1 × 1015 molecules cm-2
for spectra without noise to
∼ 0.24 × 1015 molecules cm-2 for the noisy
spectra. The largest increase in the fit error is found for the wavelength
range 335–361 nm. However, it should be noted that in the spectral range of
335–373 nm the fit error for the synthetic spectra with noise is rather low
(about 0.15 × 1015 molecules cm-2), which is similar to
that of the real measurements of the best instruments as shown in Fig. 4. We
find no considerable systematic effect of noise on the HONO delta SCDs.
However, the standard deviations of the HONO delta SCDs for the spectra
either including or excluding noise are considerable and in the range of
0.12 × 1015 molecules cm-2 to
0.22 × 1015 molecules cm-2. The largest standard
deviation is found in the wavelength range 335–361 nm.
Conclusions
HONO dSCDs and delta SCDs derived from the seven MAX-DOAS instruments during
the MAD-CAT campaign held in Mainz were systematically compared. The fit
errors of the HONO dSCDs derived from the instruments with cooled large-size
detectors were found to be in the range of about 0.1 to
0.3 × 1015 molecules cm-2 for an integration time of 1 min, while the fit error for the mini MAX-DOAS instrument is around
0.7 × 1015 molecules cm-2. Although the HONO delta SCDs
(the difference of the HONO SCDs for the non-zenith observations and the
zenith observation of the same elevation sequence) are usually smaller than
6 × 1015 molecules cm-2, time series of the HONO delta
SCDs retrieved from different instruments are consistent. Similar
consistent results between the instruments are found for the fits with a
sequential FRS and a daily noon FRS. Except for the mini-MAX-DOAS instrument,
the systematic absolute differences of the HONO delta SCDs between the
instruments are smaller than 0.63 × 1015 molecules cm-2,
while the standard deviations are smaller than
0.68 × 1015 molecules cm-2. The correlation coefficients
of the HONO delta SCDs from the different instruments with respect to the
reference values are higher than 0.7 and the slopes of linear regressions
deviate from unity by less than 16 % for the elevation angle of
1∘, but the correlations decrease with increasing elevation angles.
All instruments can well observe the temporal variation of the HONO delta
SCDs for low elevation angles. The maximum value of the HONO delta SCDs of
about 6 × 1015 molecules cm-2 is usually found in the
morning. The HONO delta SCD rapidly decrease after sunrise due to the
photolysis of HONO. They are typically below the detection limit of
0.2 × 1015 molecules cm-2 in the afternoon. In addition,
the deviations of the HONO dSCDs derived from the fits with daily noon FRS
between the instruments are generally larger than those of the HONO delta
SCDs mainly due to the different HONO absorptions in the noon FRS and the
interferences by the stratospheric species, e.g. ozone. Furthermore, there
are no considerable systematic differences of the HONO delta SCDs from the
fits with the sequential FRS and the daily noon FRS for all the instruments
except the mini MAX-DOAS instrument. The standard deviations are lower than
0.23 × 1015 molecules cm-2.
We evaluated the consistency of the DOAS fits by the different groups by
using synthetic spectra, for which the real HONO dSCD and delta SCDs are
known. The differences of the HONO dSCDs from the real values are much larger
than those of the HONO delta SCDs for all groups mainly due to the
interferences by the stratospheric species. The smallest differences
(< 0.23 × 1015 molecules cm-2) of the HONO delta SCDs
from the real values are found for the DOAS settings without the intensity
offset correction for most groups, but for two groups the smallest
differences are found if the intensity offset correction was included. The
different effect of the intensity offset correction might be due to the
different implementation of intensity offset correction in the software codes
of DOAS fits. Apart from the effect of intensity offset correction, the
systematic differences of HONO delta SCDs for the synthetic spectra between
the groups (caused by implementation of DOAS fits in the software packages)
are smaller than 0.3 × 1015 molecules cm-2, about half
of the systematic differences of the real measurements between the different
instruments. However, the exact reason in the codes of software, which cause
the difference, is unknown here. We can only generally attribute the
differences of HONO results to the differences of the codes of DOAS software.
We compared the HONO delta SCDs obtained from fits with a sequential FRS in
three spectral ranges (335–361, 335–373 and 335–390 nm) and found
significant differences. The HONO delta SCDs in the wavelength ranges
335–361 and 335–390 nm are systematically different from those in the
wavelength range 335–373 nm by -0.08 × 1015 and
+0.57 × 1015 molecules cm-2, respectively. To
characterize the dominant systematic error sources and to find the best-suited DOAS settings for the HONO analysis, we performed various sensitivity
studies based on the synthetic spectra and selected measurements from the
AIOFM instrument. The main findings are outlined below.
Systematic residual structures are found around 363 nm, which are most
probably caused by the H2O absorption around this wavelength. Moreover,
if the POKAZATEL H2O cross section is included in the spectral analysis,
a systematic increase in the HONO delta SCDs of up to
1.5 × 1015 molecules cm-2 is found. Because of the two
phenomena, we recommend including the POKAZATEL H2O cross section in
the fits. The uncertainty caused by the potential interference of the
absorption of H2O and other species (in particular O4) with the
HONO absorption is found to be about
0.13 × 1015 molecules cm-2 in the wavelength range
335–373 nm and 0.5 × 1015 molecules cm-2 in the
wavelength range 335–390 nm.
We investigated further potential interferences with all spectral structures
included in the HONO analysis and found strong effects also from
interferences of NO2, O4, and the Ring spectrum.
Analysis results using different O4 cross sections indicated that the
O4 Thalman cross section describes the real atmospheric O4
absorptions best and should be used in the HONO analysis. Systematic
uncertainties related to the wavelength dependence of the AMF caused by the
O4 absorptions and its temperature dependence are about
0.5 × 1015 molecules cm-2 in the wavelength range
335–361 nm, 0.1 × 1015 molecules cm-2 in the
wavelength range 335–373 nm and
0.2 × 1015 molecules cm-2 in the wavelength range
335–390 nm.
The uncertainties related to the temperature dependence of Ring effect are
about 0.35 × 1015 molecules cm-2 in the wavelength range
335–361 nm, 0.2 × 1015 molecules cm-2 in the
wavelength range 335–373 nm and
0.12 × 1015 molecules cm-2 in the wavelength range
335–390 nm. However, the results of the sensitivity tests are not
conclusive. Thus we still recommend simply using a Ring
spectrum only for one temperature in the HONO analysis.
We also investigated the wavelength dependence of the AMF caused by the
NO2 absorption. We found that the effect on the HONO retrievals can be
well compensated by the Taylor series approach from Puķīte et
al. (2010). Thus we suggest including the linear and square Taylor terms in
the HONO analysis.
The systematic uncertainties related to the choice of the polynomial are
about 0.2 × 1015 molecules cm-2 in the wavelength range
335–361 nm, 0.04 × 1015 molecules cm-2 in the
wavelength range 335–373 nm and
0.25 × 1015 molecules cm-2 in the wavelength range
335–390 nm. Thus we conclude that the spectral range 335–373 nm is the
best choice to minimize the influence of the choice of the polynomial on the
HONO results.
The systematic uncertainties related to the intensity offset are about
0.55 × 1015 molecules cm-2 in the wavelength range
335–361 nm, 0.35 × 1015 molecules cm-2 in the
wavelength range 335–373 nm and
0.25 × 1015 molecules cm-2 in the wavelength range
335–390 nm. Although the results from the synthetic spectra (which are not
subject to any artificial offsets) indicate a systematic interference between
the fitted intensity offset and the retrieved HONO delta SCDs, we still
recommend including the intensity offset in the fit, because for real
measurements it can correct instrumental shortcomings like spectrograph
stray light.
Variations of the instrumental wavelength calibration, the instrument slit
function and random noise have only little contribution to the systematic
uncertainties of the HONO retrievals.
In summary we find that the total systematic uncertainty from the different
error sources is much smaller in the spectral range 335–373 nm
(0.87 × 1015 molecules cm-2) compared to that in the
other two investigated spectral ranges. Moreover, the systematic bias of the
measured HONO delta SCDs from the simulated real values in the synthetic
spectra are also smallest in the wavelength range 335–373 nm (about
0.02 × 1015 molecules cm-2). Thus 335–373 nm is the
recommended fit range for HONO retrievals.
In this spectral range, the typical random uncertainty is about
0.16 × 1015 molecules cm-2, which is only 25 % of
the total systematic uncertainty. These results are obtained for an assumed
SNR of 3000, which is close to what the best instruments considered achieved
in this study. As a final result we conclude that most of the MAX-DOAS
instruments can well observe atmospheric HONO absorptions in situations with
HONO delta SCDs higher than 0.2 × 1015 molecules cm-2.
Further work should aim to better quantify the spectral interferences between
the absorptions of HONO and other absorbers in the selected spectral range.
Further studies on the interference between the HONO absorption and the
intensity offset correction are also recommended.