TOA reflectances
As a first exercise, a base case calculation and comparison of TOA
reflectances was made to assess the performance of the four RTMs and to
obtain the structural uncertainty in TOA reflectance modelling. The base case
comparison allowed us to establish the best possible level of agreement
between RTMs by identifying differences in the RTMs performance that in more
complex settings would be difficult to recognise. Furthermore, total and
ozone optical thickness were compared to evaluate how the models agreed in
their treatment of scattering and absorption processes and whether
differences in scattering and absorption can explain possible differences
between the TOA reflectances.
Basic model parameters were established as input in all RTMs (details can be
found in Table S1 in the Supplement). The basic atmospheric profile was a
33-layer midlatitude summer atmosphere , and every group
performed their own vertical discretisation of this profile.
In the RT modelling, we considered a clear-sky atmosphere, so clouds and
aerosols were not included. Rayleigh scattering and O3 absorption were
included, but Raman scattering was not included. The temperature dependence
of the ozone cross section was neglected in the reflectance calculation. TOA
reflectances were calculated at seven wavelengths, including 440 and 340 nm
which are relevant for the retrievals of NO2 and HCHO, respectively. Both
scalar (i.e. without polarisation) and vector (i.e. with polarisation)
calculations were performed in most of the cases. All models applied their
particular sphericity treatments to the calculations. The surface was
considered to be a Lambertian reflector by all the RTMs. This approximation
assumes that surface reflectivity is isotropic (i.e it does not consider the
directionality of the surface reflectance distribution). The selected
geometries covered a wide range of values for solar zenith angle (SZA,
θ0), viewing zenith angle (VZA, θ) and relative azimuth angle
(RAA, φ=180∘-|ϕ-ϕ0|, where ϕ-ϕ0 is the
viewing direction minus solar direction). All the angles are specified with
respect to the surface. The values for SZA span the typical range of what
UV/Vis sensors are encountering in orbit, and the maximum value of VZA is
related to the higher possible values of this parameter for the future
TROPOMI instrument (72.5∘) .
TOA reflectances simulated by four RTMs for θ0=37∘
(μ0=0.8), off-nadir viewing angle θ=72.5∘ (μ=0.3) and
φ=0∘ as a function of wavelength (in 20 nm steps). Dashed
lines represent total optical thickness computed by each RTM. Grey bands
indicate the relevant wavelengths for HCHO (340 nm) and NO2 (440 nm).
Surface albedo is 0 and surface pressure is 1013 hPa.
![]()
All models calculate the same spectral dependency of TOA reflectance, as
shown in Fig. (solid line). TOA reflectance increases towards
shorter wavelengths due to stronger Rayleigh scattering. TOA reflectance
simulated by the different models agrees within 1.3 % for the geometries
included in Fig. . The dashed line in Fig. shows the
total optical thickness as a function of wavelength for DAK, SCIATRAN and
VLIDORT (McArtim does not provide this output), and is generally consistent
within 0.15 % for all wavelengths except 340 nm, where the differences are
0.5 %.
Distribution of relative model differences between TOA reflectances
simulated by four RTMs including polarisation (DAK-VLIDORT, DAK-SCIATRAN,
DAK-McArtim, VLIDORT-SCIATRAN, VLIDORT-McArtim, SCIATRAN-VLIDORT and reversed
combinations) for all geometry combinations (0∘<θ0<90∘, θ=0∘, 72.5∘ and φ=0, 60, 90, 120, 180∘)
(see Table S1 for exact values) at 340 nm (left panel) and 440 nm (right
panel). The dashed lines represent the median plus/minus the standard
deviation of the distribution. Surface albedo is 0 and surface pressure is
1013 hPa. Sample size in each distribution is 960.
![]()
Figure shows the distribution of relative differences (defined as
(100(a-b)/a)) between TOA reflectances simulated by the four RTMs at 340
and 440 nm. The distribution is determined by the relative differences
between all combinations of model differences, including all simulated
geometry scenarios for a surface albedo of 0 and terrain pressure of
1013 hPa. According to the standard deviation in both distributions (dashed
lines in Fig. 3), the relative differences are below 1.5 % at 340 nm and
1.1 % at 440 nm in most geometry configurations (80 % of the samples of
the distribution), including the most common retrieval scenarios. The tails
of the distributions at both wavelengths correspond to extreme viewing
geometries, i.e. for scenarios in which solar and viewing zenith angles are
both large. Mean relative differences over all RTM pairs are at most 6.4 %
for extreme geometries (θ0=87∘,θ=72.5∘),
and for shorter wavelengths. For nadir view (θ=0∘) relative
differences are on average two times smaller than for larger VZA (θ≥60∘) at both 340 and 440 nm.
The results show strong consistency of TOA reflectance calculations for the
most common moderate viewing geometry retrieval scenarios. Relative
differences are somewhat higher for larger VZA, SZA and shorter wavelengths.
For the more extreme geometries, the light path through the atmosphere is
generally longer and photons have a higher probability of undergoing
interactions (scattering, absorption) with the atmosphere. Furthermore,
differences in the treatment of the Earth's sphericity for the extreme geometries
have a stronger influence than in close to nadir viewing geometries. These
differences will still be present in the box-AMF comparison in Sect. 3.2.
Rayleigh scattering also affects the effective photon path and it is stronger
at 340 nm than at 440 nm. Thus, small differences in the description of
Rayleigh scattering in the RTMs are more likely to lead to differences for
the extreme geometries and shorter wavelengths. The standard deviation of
differences between modelled TOA reflectances of 1.5 % (at 340 nm) and
1.1 % (at 440 nm) in this comparison can be considered to be the reflectance
structural uncertainty. The agreement in this study is better than in
previous RTM comparisons like and which
reported differences of 5 %. The detailed RTM comparison will serve as a
test bed to analyse the performance of other RTMs.
NO<inline-formula><mml:math id="M125" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">2</mml:mn></mml:msub></mml:math></inline-formula> and HCHO altitude-dependent (box-) air mass factors
Box-AMF dependencies on forward model parameters for NO2 at
440 nm (solid lines) and HCHO at 338 nm (dashed lines)
for a clear-sky atmosphere. (a) Box-AMFs vertical profile,
(b) 950 hPa box-AMF as a function of surface albedo,
(c) 797 hPa box-AMF as a function of surface pressure,
(d) 950 hPa box-AMF as a function of cosine of SZA,
(e) 950 hPa box-AMF as a function of cosine of VZA,
(f) 950 hPa box-AMF as a function of RAA. In all panels the fixed
parameters are μ0=μ=0.8 (θ0=θ=37∘),
φ=60∘, surface albedo = 0.05, surface
pressure = 1013 hPa.
![]()
To calculate box-AMFs, a common vertical grid was agreed between the groups
in order to reduce the sources that might cause differences between the RTMs.
The common profile resolution was 0.1 km from the surface up to 10 km,
1 km resolution from 10 to 60 and 2 km resolution from 60 to 100 km.
NO2 box-AMFs were calculated at 440 nm and HCHO box-AMFs were calculated
at 338, 341 and 344 nm to investigate the wavelength dependency (not shown).
Box-AMFs were calculated accounting for the polarisation of light and the Earth's sphericity. The number of reference points for surface albedo was increased
and several surface pressures were added relative to the TOA reflectance
simulations in the previous section to cover a wider range of scenarios. All
settings are detailed in Table S2.
Figure 4a shows that the four participating groups generally agree well on the
vertical profile shape of NO2 and HCHO box-AMFs in the troposphere.
Measurement sensitivity decreases towards the surface due to the increase of
light scattering in the lower troposphere. Measurement sensitivity to HCHO is
substantially lower than to NO2, because of stronger Rayleigh scattering
at shorter wavelengths. McArtim box-AMFs have lower values in the
stratosphere (pink line), presumably reflecting the more realistic
description of atmosphere's sphericity in McArtim relative to the other
models (see Sect. 3.4 for specific sphericity effect on AMFs). The vertical
profile of McArtim shows a wavering line due to the statistical noise in the
Monte Carlo simulations (which can be reduced by increasing the number of
simulations). Figure 4b, d–f shows the NO2 and HCHO box-AMF dependency on
forward model parameters (surface albedo, surface pressure, SZA, VZA and RAA)
in the lower troposphere at 950 hPa. This pressure level (close to the
surface) is especially relevant because this is where trace gas
concentrations are enhanced in polluted conditions. The sensitivity to
surface albedo at 950 hPa (Fig. 4b) is similar for all four RTMs. Box-AMFs
increase with surface albedo due to a stronger reflection of light at the
surface. This increase is particularly strong for low values of surface
albedo. For an albedo of 0.05, an increase of 0.01 in the surface albedo
results in an increase of 11 % in the NO2 box-AMF at 440 nm and of
9 % in the case of HCHO at 338 nm. The increase in the box-AMFs is less
steep for higher values of surface albedo. Thus, an accurate knowledge of
surface albedo is required, especially for low albedo values. For surface
pressure (Fig. 4c), the box-AMF (at 797 hPa) decreases with decreasing
surface pressure. For increasing terrain height, the amount of light
scattered and reflected from below 797 hPa decreases. In a more elevated
terrain, the photons undergo fewer scattering events, which tends to reduce
box-AMFs at a specific level. Models agree well in representing this
sensitivity. An error in the surface pressure of 10 hPa leads to ±2 %
errors in the lower tropospheric box-AMF values, which indicates the
importance of accurate surface pressure information that is representative
of the entire pixel area. Box-AMFs at 950 hPa show relatively weak
dependency on VZA (Fig. 4e) and RAA (Fig. 4f) and stronger dependency on high
values of SZA (Fig. 4d), but all RTMs agree well on measurement sensitivity
to geometry parameters.
Vertical profile of mean relative differences between NO2
box-AMFs (left) and HCHO box-AMFs (right) from DAK, McArtim, SCIATRAN and
VLIDORT for a wide range of satellite viewing geometry (0∘<θ0<75∘, 0∘<θ<72.5∘, 0∘<φ<180∘), surface albedo = 0.05 and surface pressure 1013 hPa. Grey
bands indicate a 950 hPa atmospheric layer.
![]()
Figure shows the vertical profile of mean relative
differences in NO2 (left panel) and HCHO (right panel) box-AMFs between
all the models, for a specific surface albedo and surface height and a wide
range of solar and viewing geometries. Generally, models reproduce box-AMFs
to within 2 % for NO2 and 2.6 % for HCHO. Mean relative differences
are higher at the lowest layers and around 300 hPa. This is due to
unavoidable slight differences in vertical discretisation of the
surface–atmosphere boundary and where the resolution changes from 0.1 to
1 km at 10 km altitude in the different models. Specific differences were
also found in the mid-troposphere to upper troposphere and stratosphere, where McArtim is on
average lower than the other RTMs. Those differences illustrate the different
treatments of multiple scattering within the models. McArtim accounts for
multiple scattering in a fully spherical atmosphere, whereas DAK, VLIDORT and
SCIATRAN simulate multiple scattering in a plane parallel atmosphere. In a
spherical atmosphere, less light is horizontally scattered into the line of
sight of the instrument than in a plane parallel atmosphere (see Fig. S2),
which is one of the reasons for lower box-AMFs by McArtim in the stratosphere
(visible in Fig. 4a between 200 and 0 hPa).
Relative differences for 950 hPa box-AMFs are below 1.1 % for NO2 and
below 2.6 % for HCHO in most geometry configurations (according to the
standard deviation of relative differences distribution for 950 hPa
box-AMFs, not shown). Higher relative differences mainly occur between
McArtim and the other models. The highest relative differences occur for
scenarios with high VZAs (θ=72.5∘) (not shown), again
indicating that different Rayleigh scattering descriptions and sphericity
treatments in the radiative transfer modelling of the atmosphere are
important.
This comparison indicates a good agreement between box-AMF LUTs computed
using different RTMs. The structural uncertainty in the AMF calculation due
to the choice of RTM and different interpolation schemes is 2 % for NO2
and 2.6 % for HCHO. These results suggest that a correct treatment of the
processes affecting the effective light path in the atmosphere is important
for box-AMF calculation. The vertical discretisation is also relevant in
box-AMF calculations, as demonstrated by the differences at specific
altitudes (Fig. 5) and by the box-AMF sensitivity to altitude (Fig. 4a).
Therefore, the vertical sampling of the LUT should have a fine resolution,
especially in the lower troposphere where strong gradients in NO2 and HCHO
concentrations occur. The dependencies of the box-AMFs at low surface albedo
values (Fig. 4b) and to surface pressure (Fig. 4c), suggest that the number
of reference points in the LUT for these parameters should be large.
Tropospheric air mass factors
In order to compute tropospheric AMFs via Eq. () we
need to interpolate the box-AMFs from the LUT for the best estimate of the
forward model parameters b. Generally a 6-D linear interpolation
(or 5-D if the vertical resolution of the LUT and the a priori profile
vertical grid are equal) is done over all the parameters on which the box-AMF
depend. For each dimension, the two closest values to the exact pixel
parameters are used to obtain the interpolated box-AMF (ml in
Eq. ). This approach will introduce systematic errors
in case of non-linear dependencies of the parameters in the LUT.
Pixel-by-pixel online calculations of box-AMFs would avoid interpolation
errors. estimated the differences between online and
LUT-derived AMFs to be on average less than 1 %, for individual
measurements less than 8 %, with an upper bound of the difference of 20 %
over South America. found 1–5 % differences on
retrieved VCDs with and without LUT over China.
Upper panels: total NO2 tropospheric AMFs calculated by BIRA,
IUP-UB, MPI-C and WUR. Lower panels: NO2 model tropospheric vertical
column (from a priori TM4 profile), climatological surface albedo (from
Kleipool et al., 2008), cloud fraction (from O2-O2) and an
example of the relative differences between MPI-C and WUR AMFs. Only pixels
for SZA < 70∘ are shown. The selected OMI orbit is from 2
February 2005 (2005m0202-o02949-v003).
![]()
Harmonised settings
Four groups used the same settings (forward model parameters, a priori
profiles, temperature and cloud correction) to calculate clear-sky and total
tropospheric NO2 AMFs for one specific OMI orbit over Australia and
East Asia on 2 February 2005 (see Fig. 6). The selected harmonised
settings were those from KNMI/WUR (see Table ). All groups
applied the same temperature correction (from Boersma et al., 2004, see
Eq. S1) and cloud correction via the independent pixel approximation. The aim
of this comparison was to obtain an estimate of the structural AMF
uncertainty introduced by different vertical discretisations and by different
interpolation schemes, assuming that the values of the selected forward model
parameters are true.
All groups calculate similar AMF spatial patterns for the selected orbit.
Figure 6 (upper panels) shows total tropospheric NO2 AMFs calculated by
each group. The distribution of the AMF values along the orbit is determined
by the different parameters on which AMFs depend. Lower panels in Fig. 6 show
NO2 (a priori) model vertical column, surface albedo and cloud fraction in
the orbit. At high latitudes, where surface albedo is high, AMFs are up to
3–5. Surfaces with high albedo (usually covered by snow or ice) reflect more
radiation than surfaces with lower surface albedo, and this increases the AMF
values. The effect of clouds and the a priori profile is also visible: AMFs
are generally low in cloudy regions and over polluted regions in eastern China
(∼ 30∘ N), indicative of reduced sensitivity to NO2 in the
lowest layers of the atmosphere.
The correlation between AMFs calculated by the different retrieval groups is
excellent (R2>0.99). Overall, tropospheric AMFs calculated by each of
the groups agree within 6.5 % in polluted areas and within 2.5 % in clean
remote areas for most retrieval scenarios, in line with the results from the
box-AMF LUT comparison. BIRA AMFs are on average higher than AMFs calculated by the
other groups, generally by a few percent, and IUP-UB AMFs are on average
lower for polluted and unpolluted conditions. Table 2 summarises the results
of the comparison.
The largest differences are found at the edges of the OMI orbit, where viewing
zenith angles are large and light paths are long. This can be seen in the
lower right panel of Fig. 6, where the relative differences of tropospheric
NO2 AMFs between MPI-C and WUR are clearly visible at the edges of the
orbit. These differences are consistent with the higher sensitivity to
tropospheric trace gases for extreme viewing zenith angles (also shown in
Fig. 4e) in McArtim compared to DAK. Figure S1 in the Supplement shows the
relative differences between all AMFs calculated by the groups. Relative
difference distributions show patterns that reflect the spatial distribution
of surface albedo, clouds and NO2 (e.g. over south-eastern Australia,
eastern China and Korea). Large differences between the groups are found in cloudy
conditions. These effects reflect the uncertainties arising from the use of
different RTM as well as from the interpolation and the vertical
discretisation of the LUT when calculating the AMFs.
Statistical parameters for the comparison of total tropospheric
NO2 AMFs for polluted and unpolluted pixels (pixels with model NO2
vertical column higher or lower than 1×1015 molec cm-2
respectively) between the different retrieval groups for one complete orbit
from 2 February 2005 (2005m0202t0339-o02940 v003). Only pixels with effective
(i.e. radiometrically equivalent) cloud fraction ≤0.2 are considered.
Mean, median and sigma are relative differences in % (100(a-b)/a).
Polluted pixels (#1983)
Diff. between
Mean (rel. diff.)
Median (rel. diff.)
σ(rel. diff.)
R2
Slope
Offset
IUP-WUR
-3.8 ± 0.3
-2.5
6.4
0.9968
0.96
0.08
BIRA-WUR
0.5 ± 0.02
0.5
0.8
0.9996
0.98
0.02
BIRA-IUP
3.9 ± 0.7
2.9
4.8
0.9967
1.02
-0.07
MPIC-WUR
-1.5 ± 0.1
-0.9
4.7
0.9957
0.99
0.03
MPIC-IUP
2.1 ± 0.9
0.5
4.9
0.9955
1.03
-0.06
MPIC-BIRA
-2.0 ± 0.1
-1.2
4.7
0.9957
1.01
0.01
Unpolluted pixels (#23744)
IUP-WUR
-0.4 ± -0.3
-0.3
2.4
0.9983
0.96
0.06
BIRA-WUR
0.6 ± 0.004
0.3
0.8
0.9995
0.98
0.03
BIRA-IUP
1.0 ± 0.04
0.7
1.9
0.9989
1.01
-0.04
MPIC-WUR
-0.5 ± 0.02
-0.4
2.1
0.9985
0.97
0.06
MPIC-IUP
-0.1 ± 0.06
-0.4
2.2
0.9981
1.01
-0.01
MPIC-BIRA
-1.1 ± 0.02
-0.9
1.7
0.9990
0.99
0.03
Mean relative differences between IPA and clear-sky NO2
tropospheric AMFs for different cloud fraction intervals at different cloud
pressures ranges (different colours) for a complete day of OMI measurements (2
February 2005). Left panel is for polluted conditions and right panel for
unpolluted conditions (pixels with model NO2 vertical column higher or
lower than 1×1015 molec cm-2 respectively). The stars with
the black dashed lines show the average difference for all the cloud
pressures. Pixels with surface albedo less than 0.3 and SZA < 70∘
are considered.
![]()
These results demonstrate that, even when similar RTMs, box-AMFs and
identical forward model parameters are used to calculate the AMFs, there is
structural uncertainty that is introduced by the specific implementation of
different groups. First, the choice of a RTM introduces uncertainty in the
box-AMF calculation. Second, there are interpolation errors that are
intrinsic to the calculation method using Eq. (), i.e.
interpolation errors in finding the AMF value from the 6-D LUT and the
vertical discretisation of the a priori profile. Overall, the average
differences between the AMFs (always below 6.5 % for cloud fractions less
than 0.2) are somewhat higher than the differences from the LUT comparison
(2 %). This means that in successive steps of the AMF calculation sources
of systematic uncertainty are added that propagate throughout the AMF
calculation process. These sources directly affect the agreement between the
AMF calculated by different groups and hence affect the AMF structural uncertainty.
6.5 % represents an upper limit value for the differences that
different RTMs and LUTs may introduce to the final AMF calculation.
Overview of AMF calculation methods and ancillary data used in the
round-robin experiment by various research groups.
Group andreference
RTM
LUTinterpolation
Surfacereflectivity
Surface pressure
Cloud parameters
Cloud correction
Aerosolcorrection
A prioriprofile
BIRA-IASB(Sect. S1.1)
VLIDORT
Linearin 6-D space
MODIS BSA and OMI Min LER
GMTED2010a
O2-O2
IPA: CF > 0.2CS: CF < 0.2
Implicit
DailyTM5(1∘ × 1∘)
IUP-UB(Sect. S1.2)
SCIATRAN
Linearin 6-D space
Min LER () (v003)
GMTED2010agridded to0.25∘ × 0.25∘
O2-O2
IPA: CF > 0.1CS: CF < 0.1
Implicit
MACC-II dailyreanalysisd(1.125∘ × 1.125∘)
KNMI/WUR ()
DAK v3.31
Linear in 6-D space
Min LER () (v002)
Global 3 kmDEMbPixel average
O2-O2
IPA
Implicit
DailyTM4(3∘ × 2∘)
Uni. Leicester (, , )
LIDORT v2.3
Linearin 4-D space
Mode LER () (v002)
GEOS-Chem surface pressure
O2-O2
IPA
Implicit
DailyGEOS-Chem(2∘ × 2.5∘)
MPI-C(Sect. S1.3)
McArtim
Linearin 6-D space
Min LER
() (v002)
Global 3 kmDEMc Pixel average
O2-O2
IPA > 3 kmCS: CF < 0.1between 2–3 km
Explicitcfor cloudsbelow 2 km
DailyTM4(3∘ × 2∘)
NASA-GFSC
TOMRAD
Linearin 6-D space
Min LER () (v002)
Global 3 kmDEMPixel center
O2-O2
IPA
Implicit
Monthlymean GMI(2.5∘ × 2∘)
Peking Uni. (, )
LIDORT v3.6
Online calculations
MCD43C2 BRDF
GEOS-Chem(0.5∘ × 0.667∘)
POMINO retrieval
IPA
Explicit GEOS-Chemdaily AOD
DailyGEOS-Chem(0.5∘ × 0.667∘)
a Global multi-resolution terrain
elevation data.
b Digital elevation model data.
c See Sect. S1 in the Supplement for more detailed
information.
d .
Cloud correction: IPA vs. clear-sky AMF
It is important to account for the effect of clouds on the photon path
lengths in the troposphere when calculating tropospheric AMFs. There are
various approaches that are commonly used to calculate AMFs in (partly)
cloudy conditions. The independent pixel approximation (IPA), introduced in
Eq. (4) (e.g. ), is motivated by the fact that few pixels
are completely cloud-free. Many pixels still have some degree of cloud cover,
and even small cloud fractions strongly affect the sensitivity to the trace
gas. The relevant physical effect of clouds (reduced sensitivity to trace gas
below the cloud and enhanced sensitivity to trace gas above and in the top
layer of the cloud) is explicitly taken into account in the IPA. Another
approach is to consider clear-sky AMF for scenes with a sufficiently
small cloud fraction (e.g. ). The motivation for
using clear-sky AMFs instead of IPA is that for scenes with small cloud
fractions (e.g. <0.2), retrieved cloud parameters (cloud fraction and
cloud pressure) have relatively high uncertainty. This inhibits the reliable
modelling of the effect of clouds on photon path lengths and, consequently, a
clear-sky AMF is used.
To quantify the differences between the two approaches, here we compare
tropospheric NO2 AMFs calculated by WUR (see Table 3) with the IPA
approach and the clear-sky AMFs, for two complete days of OMI measurements (2
February and 16 August 2005). In polluted conditions, IPA AMFs are smaller
than clear-sky AMFs on average, with differences as large as -40 % for cloud
fractions approaching the threshold value of 0.2 (left panel of Fig. 7). The
negative differences between IPA and clear-sky AMFs are largest for the highest
clouds, illustrating the reduced sensitivity to tropospheric NO2 below the
cloud in the IPA. IPA AMFs are larger than clear-sky AMFs for clouds situated
in the lower troposphere (cloud pressure > 900 hPa), where most NO2
pollution resides. These positive differences can be understood from the
albedo effect of residual clouds. Low, bright clouds lead to enhanced photon
scattering through the NO2 layers above the cloud level and also inside
the cloud top layer, and this increases the sensitivity to NO2. For
polluted conditions, IPA AMFs are on average smaller than clear-sky AMFs by 20 %
for cloud fractions of 0.05–0.2, and smaller by 11 % for cloud fractions
between 0.0 and 0.2.
In unpolluted conditions, IPA and clear-sky AMFs are generally quite similar, with
average relative differences within 5 %. Still, there are important
differences between the two approaches. In unpolluted conditions with clouds
in the free and upper troposphere (cloud pressure < 600 hPa), IPA AMFs
are smaller because of reduced sensitivity to NO2 (right panel of Fig. 7).
For clouds in the lower troposphere, IPA AMFs are larger because of the
albedo effect. The change of sign in the differences between IPA and clear-sky AMFs
now occurs near 700 hPa (instead of near 900 hPa for polluted scenes),
reflecting the more even vertical distribution of NO2 in pristine
conditions compared to polluted scenes in which most NO2 resides in the
polluted boundary layer.
These results indicate that the differences between using IPA or clear-sky
AMFs are especially substantial for polluted conditions and small residual
cloud fractions. Selecting a particular cloud correction approach implies
that AMF values that will be systematically different from values obtained
with the other method. In polluted conditions, the mean differences are
20–40 % for cloud fractions between 0.1 and 0.2, with cloud pressure largely
explaining the magnitude and sign of the differences. Note that the a priori
profiles used to calculate the AMFs in this section have been obtained from a
specific CTM. If a different CTM were used, the values for the differences
between IPA and clear-sky AMFs would be different, in line with the structural
uncertainty that is being discussed in this study (See Sect. 3.3.3). A
previous study by reported 30 % higher GOME tropospheric
NO2 columns retrieved using the IPA compared to retrievals using clear-sky
AMFs. Such differences are in line with the systematically lower IPA AMFs
found here. However, like the study by , we cannot clearly
recommend one AMF approach over the other. In order to make such a
recommendation, a more detailed analysis of the cloud parameter uncertainties
is needed, along with a validation of tropospheric NO2 retrievals using
different AMF approaches against independent reference data. Such a
validation exercise should preferably focus on polluted conditions with small
(0.05–0.2) residual cloud fractions.
Round-robin comparison
For the round-robin comparison, each group calculated tropospheric NO2
AMFs using their preferred settings (i.e. their own preference for source of
forward model parameters, cloud and aerosol correction). We extended the
comparison and included other leading international retrieval groups
(University of Leicester, NASA and Peking University). We now have a wider
range of approaches and assumptions to better evaluate the impact that the
calculation methods and choices of forward model parameters have on the
structural uncertainty.
Table 3 summarises the AMF algorithms included in this comparison. There are
several differences with the harmonised settings used in the previous
section. IUP-UB and BIRA now apply IPA only when cloud fraction exceeds 0.1
and 0.2, respectively, motivated by the high uncertainty of cloud parameters
for scenes with small cloud fractions (see Sect. 3.3.2). Peking University
accounts for the surface reflectance anisotropy and does pixel-by-pixel
online radiative transfer calculations. They also include an explicit aerosol
correction, motivated by the fact that the implicit aerosol correction breaks
down under conditions of high aerosol optical thickness and strongly absorbing
particles (), which is particularly
significant in East China. MPIC applies IPA cloud correction for clouds
higher than 3 km and clear-sky AMFs for clouds between 2 and 3 km when
cloud fraction is less than 0.1. For clouds below 2 km they include a
parameterised aerosol-cloud layer in order to account for the possibility of
cloud aerosol mixtures, which might be especially relevant for AMF
calculation in scenarios where trace gas is most abundant in the lowest part
of the troposphere. Among all the groups, five different chemistry transport
models for the a priori NO2 profiles are used.
Different groups use different LUTs for their AMF calculations, and POMINO
uses pixel-by-pixel online radiative transfer calculations. The LUTs are
different in several aspects, such as the RTMs used to create them and the number of
reference points for each dimension. All these differences affect the AMF
structural uncertainty. Based on the discussion in previous sections we
consider that the use of different LUTs introduces a structural uncertainty
of the order of 6.5 %.
Most of the surface albedo values used in the retrievals come from the
database, which is based on OMI surface reflectance
climatology. However, due to the different representations of surface
reflectance within this database (mode and min LER), only three retrieval
groups use the exact same albedo values. We investigated whether this could bias
the estimation of the AMF structural uncertainty. We recalculated the AMF
structural uncertainty with two retrievals that use the exact same albedo
values and with three that use different albedo values. These estimated that AMF
structural uncertainties were of similar magnitude and therefore we can
conclude that the fact that the surface albedo values come from the
database is not a clear driver of the overall structural
uncertainty calculation.
The agreement of AMFs from this round-robin exercise quantifies the overall
AMF structural uncertainty. The comparison with seven groups allowed us to
calculate a mean AMF as a reference (which is not necessarily the true AMF)
value which can be considered a state-of-the-art AMF value. For a
representative ensemble mean AMF, we required all groups to have a valid
(unflagged) AMF value at a pixel location. We selected two different days (2
February and 16 August 2005) in winter and summer to identify possible
seasonality effects in the agreement of the AMFs.
Tropospheric NO2 AMFs calculated by each of the groups for a
complete day of OMI measurements (2 February 2005). Lower panels show an
example of cloud fraction and surface albedo used by KNMI/WUR (showed as
example; see Table ) to calculate the AMFs. Groups apply
different filters to the measurements which explains the different gaps
(grey).
![]()
Ratio of tropospheric NO2 AMFs by each group to the ensemble mean
(left axis, bars) and the correlation coefficient (right axis, cross) for two
complete days of OMI measurements on 2 February 2005 (blue) and 16 August 2005
(green) over the globe for polluted (left panel) and unpolluted (right
panel) pixels. The error bars correspond to the standard deviation. Only
pixels for SZA < 60∘ and cloud fraction < 0.2 are
considered in the analysis.
![]()
Round robin: identical cloud parameters
First we compare the six groups that use the same cloud parameters. In contrast
to what we found in the harmonised settings comparison, the global maps of
tropospheric AMF calculated by each group using their preferred settings
(Fig. ) show pronounced differences in several regions. For
example, over the Sahara desert, where surface albedo is high (see lower
panel on Fig. ), AMFs differ by up to 15 %. Small
differences in the albedo values can lead to high differences in the AMFs,
especially for surface albedos lower than 0.3 (see Fig. 4b). Over central
Africa, AMFs differ in situations where cloud fraction is close to the
typically applied threshold of 0.2 (left lower panel in Fig. ).
We compared global AMF calculations from all individual groups against the
pixel mean AMF from six groups (Peking University only calculates AMFs over
China). Figure 9 shows the average ratio of the AMF by each group to the
ensemble mean AMF (bars) and the correlation (crosses) for polluted conditions (NO2>115 molec cm-2, left panel) and unpolluted conditions (NO2<115 molec cm-2, right panel). Over polluted
regions (for pixels with SZA < 60∘ and effective cloud
fraction < 0.2), the agreement between the six groups is within (minimum–maximum) 12–42 %
in February and within 10–31 % in August. BIRA AMFs are 14 % higher than
the ensemble mean, and WUR AMFs are 18 % lower, suggesting considerable
structural uncertainty.
Over unpolluted regions the agreement is better: AMFs from the different
groups agree within 8.5–18 % in both February and August, which implies a
smaller structural uncertainty (Table S6 provides a detailed summary of the
comparison).
In order to assess which forward model parameters explain most of the AMF
structural uncertainty, we analysed AMF differences from groups that use
identical cloud parameters and implicit aerosol correction (BIRA, University
of Leicester, NASA and WUR). Between these four groups, the only different
forward model parameters are surface albedo, a priori NO2 profile and
surface pressure. To investigate which of these parameters best explains the
AMF variability, we correlated differences between a particular parameter
(ΔAs, ΔNO2 and ΔPs) with the
corresponding AMF differences (ΔAMF). For each particular parameter,
we required the differences in the other parameters to be small (surface
albedo within ±0.02, surface pressure within ±50 hPa and a priori
NO2 vertical columns within ±0.2×1015 molec cm-2) so we could
isolate the effect of one parameter only while keeping sufficient pixels for
statistical significance.
We focus on explaining the differences between BIRA and WUR here, since these
were of the order of 30 % (Fig. 9). We explored the correlations between
BIRA-WUR AMF differences and differences between assumed surface pressures,
albedos and NO2vertical columns and profile shapes; results are shown in
Fig. S3 and Table S3. We find that surface pressure differences do not
explain the large systematic AMF differences, and that surface albedo
differences explain WUR and BIRA AMF differences, especially in winter when
NO2 is found close to the surface and AMFs are more sensitive to albedo
variations than in summer. In our ensemble, the WUR-BIRA AMF differences are
highly sensitive to the differences between the a priori NO2 profiles
used, especially in summer. NO2 profiles are vertically more elevated in
TM5 (used by BIRA) than in TM4 (used by WUR) (right panel of Fig. S3), as
diagnosed by their 20 hPa lower effective NO2 pressures (pressure levels
weighted by NO2 sub-column in that level). The confinement of the trace
gas to lower atmospheric layers and the higher concentrations explains the
systematically lower AMF values for WUR compared to BIRA.
Tropospheric NO2 AMFs calculated by each of the groups for a
complete day of OMI measurements (2 February 2005) over China
(20–53∘ N/80–130∘ W). Only pixels for
SZA < 60∘, effective cloud fraction < 0.5 and surface
albedo < 0.3 are shown.
![]()
Selecting a specific chemistry transport model thus influences the AMF
structural uncertainty via differences in the profile shape. These
differences in the profile shape depend on the different characteristics of
the models (e.g. spatial and temporal resolution and parameterisation of
different processes in the atmosphere). Previous studies analysed how using
different CTMs influences the NO2 retrievals due to the change in the
profile shapes used to calculate the AMF values. compared
retrievals using fine- and coarse-resolution models and concluded that using
one AMF value for a large heterogeneous scene can lead to a 50 % bias in the
retrieved NO2 columns. reported much smaller average
differences of 10 % in retrieved NO2 columns, mainly due to different
emission inventories used in TM4 (3∘ × 2∘) and GEOS-Chem
(0.5∘ × 0.67∘). According to ,
temporal resolution also influences a priori profile shapes; they
found differences in the retrieved NO2 column for individual days up to
40 % that were mostly explained by day-to-day wind direction variations
that were not captured in the monthly averages.
All these aspects influence the estimation of retrieval (and AMF) theoretical
uncertainties. In order to quantitatively estimate the effect of one model
characteristic alone (e.g. the spatial resolution) on the AMF structural
uncertainty it would be necessary to compare AMF calculated with the same
approach but with just that specific characteristic being different in the
profile shapes generated by the CTM. Such a specific sensitivity analysis has
not been done in this study but should be considered in future AMF
comparisons. To test the robustness of our structural uncertainty estimate,
we did some experiments by simulating the effect of high-resolution a priori
profiles on AMF values. , and
reported that AMFs calculated using coarse-resolution a
priori profiles are overestimated over polluted areas by approximately
50 %. Over remote locations, there is little spatial variability in NO2
distributions, and the a priori profile spatial resolution is less important
in the AMF calculation. When including synthetic AMF emulating the use of
high-resolution a priori profiles over polluted areas, the estimated AMF
structural uncertainty is not strongly affected (increases by 3–6 %). This
indicates that with the ensemble of retrievals used in our comparison the
estimate of the structural uncertainty in the AMF calculation may be
considered a robust estimate.
The findings in this subsection indicate that quality assurance efforts for
retrievals should not focus just on column validation,
but also target the validation of the a priori NO2 profiles used in the
AMF calculations. It is worth noting that using averaging kernels in satellite applications
(e.g. when comparing retrieved NO2 columns with modelled NO2 distributions
or observed NO2 profiles) will reduce the representativeness errors in the
comparisons associated with the a priori trace gas profile used in the
retrieval scheme (e.g. ).
Ratio of tropospheric NO2 AMFs by each group to the ensemble mean
(left axis, bars) and the correlation coefficient (right axis, cross) for two
complete days of OMI measurements on 2 February 2005 (blue) and 16 August 2005
(green) for polluted (left panel) and unpolluted (right panel) pixels over
China. The error bars correspond to the standard deviation. Only pixels for
SZA < 60∘ and cloud fraction < 0.2 are considered in the
analysis.
![]()
Round robin: different cloud parameters
In the previous section, we found that differences between a priori NO2
profiles and surface albedo values are the main cause of AMF structural
uncertainty when cloud parameters are identical in AMF calculation
approaches. Here we extend our round-robin experiment by including AMF
calculations from Peking University
() that were done with different
cloud parameters (Table ) to the O2-O2 cloud parameters
used by all other groups. The comparison of Peking University and WUR AMFs
thus allowed us to investigate the relative importance of differences in
cloud parameters in driving AMF structural uncertainty. Our comparison of
AMFs is confined to China, since Peking University calculations are only
available over that region.
All groups calculate similar spatial patterns for the AMFs over China
(Fig. 10). In the polluted north-east (Beijing area) AMFs are lower due to
the reduced sensitivity to NO2 in the lower troposphere. In the western
part over the Tibet region, AMFs are higher due to the presence of ice and
snow in February. Figure 11 shows the average ratio of each group's AMF to
the ensemble mean AMF (bars) and the correlation (crosses) for polluted conditions (left panel) and unpolluted conditions (right panel). In polluted
regions, AMFs generally agree within 37 % in February and within 20 % in
August, and correlations are 0.7–0.9. Peking University AMFs are higher than
the ensemble mean AMF, especially in August when they are 25 % higher. WUR
and MPI-C AMFs are lower than the mean AMF, especially in August (20 %
lower). In unpolluted regions the agreement is better: within 26 % in
February and within 16 % in August, with a correlation of 0.8–0.95 (see
Table S7).
Box-AMFs at 25 hPa as a function of cosine of SZA (left panel) and
as a function of cosine of VZA (right panel). In the left panel, VZA is
constant at 37∘ (μ=0.8), and in the right panel, SZA is
constant at 37∘ (μ0=0.8).
![]()
To estimate the effect of differences in cloud parameters on AMF structural
uncertainty, we analysed differences in AMF calculated by WUR and Peking
University. The Peking University AMF calculations (and the cloud parameters)
were based on a version of the POMINO retrieval using clouds retrieved with
an implicit aerosol treatment (i.e. similar to KNMI/WUR). We explored the
correlations between Peking University and WUR AMFs differences and
differences in cloud pressure (Pc) and NO2 vertical columns by
requiring the differences in other forward model parameters to be relatively
small. Results are shown in Fig. S4 and Table S4. AMF differences are partly
explained by differences in the effective cloud pressures (Table S4): the
O2-O2 cloud pressures used by WUR are systematically lower (by
100 hPa) than those by Peking University, in line with .
This results in stronger screening of below-cloud NO2 pollution, and
consequently lower AMFs by WUR compared to Peking University AMFs. Peking
University uses NO2 profiles from GEOS-Chem. These profiles tend to peak
at higher vertical levels than those from TM4
(), thus contributing to higher AMFs by
Peking University compared to WUR AMFs. In summary, the more elevated NO2
profiles in combination with less elevated clouds explain the substantially
higher AMF by Peking University than WUR AMFs.
Round robin: explicit aerosol correction
The POMINO retrieval by Peking University explicitly corrects for the
presence of aerosols in the atmosphere by including profiles of aerosol
optical properties simulated by the GEOS-Chem model (and constrained by MODIS
AOD on a monthly basis) in the radiative transfer model and in the cloud
retrieval (). All the other groups
except MPIC-C (see Table and Sect. S1.3) assume that the
aerosol effects are implicitly accounted for in the cloud retrievals
(). Including an explicit aerosol correction
influences AMF values indirectly through changes in cloud fraction and cloud
pressure and directly in the radiative transfer simulations. We quantify the
effect of the choice of aerosol correction in AMF structural uncertainty by
comparing AMFs calculated by Peking University with (abbreviated
AMFaer hereafter) and without (AMF) explicit aerosol correction.
In conditions with substantial aerosol pollution (AOD > 0.5), the selection
of one aerosol correction approach over another can result in an AMF
structural uncertainty of 45 % over China. The sign of the AMF differences
depends mainly on the altitude of the aerosol layer relative to the NO2
profile (see e.g. ). We find that AMFaer are
on average 55 % smaller in situations when aerosols are located above the
NO2 layer, mainly because cloud pressures are lower on average (more than
350 hPa), resulting in stronger screening of NO2 (upper panel of Fig. S5;
Table S5). When the aerosol vertical distribution is similar to that of
NO2, AMFaer are on average 45 % higher, mostly because of
much smaller cloud fractions, resulting in reduced screening of below-cloud
NO2 (lower panel in Fig. S5; Table S5). An additional factor is that when
aerosols are mixed with NO2, they increase the optical light path and
enhance AMF values. These results are in line with where an
evaluation of the influence of the aerosols in the NO2 retrieval is
analysed for 2012.
Stratospheric air mass factors
We pointed out in Sect. 3.2 that differences in the description of the
atmosphere's sphericity could lead to differences in stratospheric AMFs,
especially for extreme geometries. Here we investigate the differences
between stratospheric NO2 AMFs calculated with DAK and McArtim radiative
transfer models. The McArtim model simulates the radiative transfer in an
atmosphere that is spherical for incoming, single-scattered and
multiple-scattered light. DAK's atmosphere is spherical for incoming
sunlight, but plane-parallel for scattered sunlight. Based on these
differences, we may expect the average photon paths at high altitudes in
McArtim to be shorter than in DAK, as diffuse photon contributions (from
near-horizontal directions) in McArtim are bound to finite spherical
atmosphere (as illustrated in Fig. S2). Consequently, stratospheric AMFs in
McArtim are smaller (Fig. 4a). Figure 12 shows that McArtim box-AMFs (at
25 hPa) are systematically lower than those from DAK by 1–2 % for
moderate viewing geometries, with more significant differences (up to -5 to
-10 %) when solar zenith and viewing angles are large.
A direct validation of stratospheric NO2 AMFs is difficult, but comparing
simulated stratospheric slant column densities against observed NO2 SCDs
constitutes a test of the radiative transfer models. Here we use OMI-observed
(un-destriped) SCDs over the Pacific from the OMNO2A v1 product
() as a benchmark. The NO2 columns over the
Pacific Ocean are dominated by stratospheric NO2, so we expect simulated
stratospheric SCD values to be similar or somewhat smaller than the observed,
total SCDs. Simulated SCDs are the product of modelled VCDs (from data
assimilation in TM4) and the stratospheric AMFs calculated with DAK and
McArtim. Figure 13 (left panel) indicates (for high solar and viewing zenith
angles) that stratospheric SCDs simulated with McArtim are close to, or
slightly below the OMI SCDs. In contrast, the stratospheric SCDs simulated
with DAK overtop the OMI SCDs, because of the higher stratospheric AMFs from
that model. This inevitably leads to negative values for
SCD-SCDstrat, and consequently to reduced or even negative
tropospheric NO2 VCDs at high latitudes. Indeed, DOMINO v2 retrievals
(using DAK stratospheric AMFs) are known to suffer from negative tropospheric
VCDs at high latitudes especially in the summer hemisphere
when solar zenith angles are largest. For small solar zenith angles in the
tropics, the differences between DAK and McArtim stratospheric slant columns
are smaller, but still appreciable at the edges of the swath (Fig. 13, right
panel).
Averaged OMI total NO2 SCD (black line) as a function of viewing
zenith angle for solar zenith angles between 70 and 80∘ (left panel) and
20–30∘ (right panel) (OMI orbit 02940 on 2 February 2005). The blue
line indicates the estimated stratospheric SCDs based on DOMINO v2
stratospheric VCDs and DAK stratospheric AMFs, and the purple line represents
the stratospheric SCDs based on DOMINO v2 stratospheric VCDs and McArtim
stratospheric AMFs. The only difference between the DAK and McArtim-based
stratospheric slant columns is the use of the radiative transfer model; all
other relevant parameters (TM4 assimilated stratospheric column, cloud
parameters, albedo, NO2 profile shape) are identical.
![]()
We tested whether possible errors in the diurnal cycle of stratospheric
NO2 could explain the overestimated slant columns for extreme viewing
geometries. We did so by imposing stratospheric NO2 vertical columns that
are either constant with OMI row number (i.e. with local time) or increase
(as N2O5 photolysis, NO2 concentrations build up) at a rate of
approximately 0.15×1015 molec cm-2 h-1, i.e. by 1×1015 molec cm-2 from the left to the right side of the
orbit (Fig. S6a). These estimates correspond to the range of increase rates
at high latitudes in summer reported in the literature (e.g.
). Our tests show that, for these
scenarios, simulated SCDs based on McArtim generally stay within the
observational constraints of the OMI SCD patterns but that the simulated SCDs
based on DAK are still exceeding the observed SCDs (Fig. S6b–c). McArtim
provides a better physical description of photon transport in the
stratosphere. The results above are not yet fully conclusive; a complete test
would require the implementation of McArtim (instead of DAK) in the data
assimilation scheme, or a dedicated validation of NO2 columns with
independent reference data in situations with extreme viewing geometries.
Nevertheless, our results clearly hint at McArtim as the RTM providing the
more realistic stratospheric AMFs, and we will test this assumption further
in the remainder of the QA4ECV project.