Introduction
Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS) is
a ground-based passive remote sensing technique that is used to detect
tropospheric trace gases such as nitrogen dioxide (NO2), formaldehyde (HCHO),
sulfur dioxide (SO2), nitrous acid (HONO), iodine oxide (IO), glyoxal (CHOCHO),
bromine oxide (BrO) and aerosols (aerosol extinction) e.g..
MAX-DOAS instruments take spectral measurements of scattered sunlight in the
ultraviolet (UV) and visible (Vis) part of the electromagnetic spectrum.
Profile information is obtained from a scan which comprises spectral
measurements at different elevation angles but in the same azimuthal
direction. The main retrieval products are tropospheric column densities,
concentrations near the surface and estimates of the vertical profile shape.
Because of this versatility MAX-DOAS is complementary to ground-based in situ
observations (in a spatial sense) as well as to satellite observations (in
a temporal and spatial sense, i.e. the vertical) and it can play an important
role in bridging the gap between those techniques .
Knowledge of the relationship between surface concentrations and integrated
tropospheric column densities (in urban, suburban and rural regions) is
important for the use of satellite observations in studies of air quality
e.g..
MAX-DOAS has great potential to be used in regional or global networks
similar to the AERONET (sun photometer) and EARLINET (lidar) networks
because of its versatility, the relatively low cost per instrument,
the fact that a radiometric calibration is not required, and the fact
that instruments can operate autonomously. Long-term data sets can be
used for e.g. air quality monitoring, validation of chemical transport
models, validation of satellite tropospheric column density retrievals and
potentially as input in data assimilation systems for air quality
forecasts. With respect to satellite validation it is interesting to
note that MAX-DOAS can provide not only tropospheric trace gas column densities
for direct comparison, but also profile shape estimates for trace gases
and aerosol extinction. These can replace the a priori profile shapes assumed
for the satellite retrieval, such that one can assess the impact of
the a priori profile shape assumption (both for aerosols and for the
trace gas of interest) on the satellite retrieval accuracy
. Proper knowledge of the accuracy of the profile
shape assumptions that are used in the satellite retrieval is crucial
for a realistic estimate of the potential biases in the retrieved
tropospheric column density.
Mostly in the last decade, much progress has been made with respect to
the quantitative interpretation of MAX-DOAS observations
e.g., and MAX-DOAS instrumentation
or similar (like PANDORA ) has been used for a wide
range of gases and applications. In comparison to surface
concentrations and profile shapes, tropospheric column densities are the most
robust retrieval product. Several MAX-DOAS data sets have been used
for validation of satellite observations of tropospheric column densities,
predominantly for NO2
e.g..
Near-surface concentrations are generally associated with higher
uncertainties (primarily because of the quite limited vertical resolution of
MAX-DOAS measurements), but
nevertheless some studies have shown promising comparisons compared to
independent ground-based in situ instrumentation,
see e.g.. Most challenging is the
retrieval of vertical tropospheric profiles, and also their validation.
Quite some groups have developed algorithms for the vertical profiles of
aerosol extinction and trace gases
e.g..
Especially in relation to satellite validation there is a great need for
simultaneously measured trace gas and aerosol extinction profiles, and
MAX-DOAS is one of the few remote sensing methods which can satisfy this
need. At the same time it is well known that the MAX-DOAS profiles are only
first-order estimates, due to the fact that the information content of
MAX-DOAS observations with respect to the vertical distribution of aerosols
and trace gases is very limited: the degrees of freedom for signal typically
varies from 1 to 3, see Sect. 2.5 and .
Comparatively few studies have been published however which directly
address the quality of MAX-DOAS tropospheric profiles obtained from
real observations. This is largely due to the fact that suitable
long-term (multi-year) data sets which can serve as golden standard in
a comparison (e.g. profiles measured with high vertical resolution)
do not exist. In turn, the lack of a thorough validation of MAX-DOAS
profiles limits their usefulness in validation studies
where MAX-DOAS itself would be the reference.
The present study is highly motivated by the need for further
assessment of the quality of MAX-DOAS profiles. Our approach is based
on three pillars. First, the use of two very different profile
retrieval algorithms, both run with various a priori profile shape
assumptions. Second, the use of a 4-year data set covering a wide
range of conditions (e.g. pollution levels, seasons, meteorological
conditions). Third, analysis of profiles for three different components:
formaldehyde, NO2 and aerosols (aerosol extinction profile).
With this we address in this work the following specific questions: how
consistent are the
retrievals of individual profiles with different algorithms? How
consistent are the retrievals on average? Do the column densities and profiles
– on average – show a diurnal and seasonal variation? How strong or
weak is the dependence on a priori assumptions? Which atmospheric
conditions most critically limit the quality of the profile retrieval?
What is the agreement between the profile shapes retrieved for the
different constituents?
The two profile retrieval methods that are compared in this study do not
retrieve profiles on the same vertical grid. One way to perform a profile
comparison would be to interpolate profiles retrieved with both methods to a
common vertical grid. A comparison performed in this way would give results
for all layers which define the common grid. Such an approach would probably
be favourable if the vertical resolution of the measurements (and therefore
the DOFS) was high, but this is not the case for MAX-DOAS measurements, as
noted above. Because of the low DOFS (1–3), it was decided to derive from
each profile three suitable quantities and to compare the two profile
retrieval methods based on those quantities: tropospheric column density,
near-surface concentration and “characteristic profile heights” H75.
The latter quantity is defined as the height below which 75 % of the
integrated profile resides (75 % of the tropospheric column density). An
advantage of this quantity (a scalar) is that it allows a first-order
description of the profile shape of pollutants which reside primarily in the
atmospheric boundary layer.
The paper is structured as follows: in Sect. 2 we describe the data
set of MAX-DOAS observations that is used: the instrument
characteristics and measurement sites; the settings of the DOAS
fitting procedures for the UV and Vis; the two MAX-DOAS profile
retrieval algorithms, both of which are run with different
“internal” settings to test the dependence on a priori
assumptions. The last part of this section describes the criteria that
are applied to select data with sufficient quality. Results for
selected days and the statistical analysis based on the entire data
set are shown and discussed in Sect. 3. Section 4 contains a discussion,
and the conclusions are in the last section.
MAX-DOAS measurements and profile retrieval algorithms
The retrieval of vertical profiles from spectral measurements with
MAX-DOAS typically consists of three steps. First, differential slant
column densities (of O4, NO2 and HCHO) are derived by
applying the DOAS spectral fitting technique to the measured
spectra. Second, differential slant column densities of O4 are used as input
for the aerosol extinction profile retrieval algorithms. Third,
differential slant column densities of the trace gas of interest (in this work:
NO2 and HCHO) are used as input for the trace gas
profile retrieval algorithm, together with the estimated aerosol
extinction profile. In this section each of those steps is described
in more detail.
Instrument and measurement site
The MAX-DOAS instrument used in this study has been designed and
assembled by the Belgian Institute for Space Aeronomy (BIRA-IASB),
see . It consists essentially of a telescope mounted on
a sun-tracker (which can point at any elevation and in any azimuthal
direction) combined with two spectrographs: one
for the UV (300–390 nm), and one for the Vis
(400–720 nm). Although the instrument is also capable of
taking direct sun observations, we use here only the scattered
sunlight observations taken towards the north. The retrievals
described below are based on sequential observations at 2,
4, 6, 8, 10, 12, 15,
30 and 90∘ elevation. During the period analysed in
this work (2008–2012), the instrument was stationed at two different
sites. First it was stationed in Beijing city centre, at the
Institute of Atmospheric Physics (IAP) of the Chinese Academy of
Sciences (39.98∘ N, 116.38∘ E). From 2010 until
present, the instrument was stationed about 55 km away to the
east-southeast, at the meteorological observatory in Xianghe
(39.75∘ N, 116.96∘ E). Compared to Beijing this site has
a more suburban character.
DOAS settings used for the UV and Vis. For more details, see
for the UV and for the Vis.
UV
Vis
Wavelength range (nm)
336.5–359
425–490
Cross-sections
HCHO, O4, O3, NO2, BrO, Ring
NO2, O4, O3, H2O, Ring
Polynomial
3rd order
3rd order
DOAS retrieval of differential slant column densities
The DOAS spectral fitting method is applied to the
spectra measured with the UV and Vis spectrometers. The DOAS
analysis is performed with the QDOAS software that has been developed
at BIRA . Table 1 gives for some relevant parameters
the values used in both of the channels. More details of the DOAS
settings used can be found in for the UV channel,
and for the Vis channel. Note that a scaling
factor of 0.8 is applied to the measured differential slant O4
column densities (see ) in order to obtain sufficient
agreement between simulations and measurements. This scaling factor is
used for both methods A and B. After the DOAS analysis the
differential slant column densities corresponding to each elevation are
linearly interpolated in time (with a 20 min sampling), such
that as input for the profile retrieval code one “scan” can be
provided, as if the measurements were performed at the same
time. Since the DOAS analysis is performed with the zenith-noon
spectrum as a reference, the (interpolated) zenith differential slant
column densities of a scan is subtracted from all the differential slant
column densities. This procedure reduces the sensitivity to trace gases in
the stratosphere and upper part of the free troposphere to almost zero.
Schematic of profile parameterizations for methods A (left) and B
(right). Method A uses 13 layers (not drawn) between 0 and 4 km. The
number of free variables for method B varies, see Table 2.
Method A – algorithm developed at BIRA
The first algorithm (method A) has been developed at BIRA
and makes use of the
optimal estimation method (Rodgers, 2000). Forward simulations of
differential slant column densities and weighting functions are performed using the LIDORT radiative
transfer model . Trace gas and aerosol extinction profiles are
described by partial columns of 13 layers in a fixed altitude grid:
the first 10 layers (below 2 km) each have a vertical extent
of 200 m, between 2 and 3 km there are two layers of
0.5 km, and the uppermost layer of the profile goes from 3 to
4 km. An important input parameter for retrieval model A is
the a priori profile, which is the initial profile from which the
profile retrieval code iteratively searches for a more optimal
solution. Retrieved profile shapes can in principle be very different
from the a priori, but only if the information content of the
measurements is sufficiently high (depending on trace gas and
measurement conditions). If this is not the case, the retrieved
profile shape will be very similar to the a priori. In the original
implementation of the retrieval code () this
a priori profile concentration profile n(z) was described by an
exponential function which is characterized by a specific a priori
scale height Hsprior:
n(z)=NpriorVHsprior⋅exp-zHsprior.
For trace gases, the profile shape is scaled such that the integrated
profile corresponds to the first-order estimate of the tropospheric
trace gas column density (NpriorV), namely the
differential slant column density measurement at 30∘
elevation. The corresponding geometrical differential air mass factor
(see e.g. ) is equal to one. For aerosols the
initial column estimate (the AOD, aerosol optical depth) was set to 0.15 for all retrievals.
A second important input parameter is the a priori error estimate for
each layer. Tests have shown that setting this value high – this
would give the algorithm most flexibility to realize diverse profile
shapes – leads to frequent retrievals of profile shapes showing
oscillations that are not likely to be realistic. For this reason
a relatively low value (20 %) of the a priori is chosen,
although this limits the potential of the algorithm to deviate
significantly from the a priori, see also the discussion in Sect. 4.2.
Tests performed prior to the study presented here have shown that the
interplay between the a priori profile and its error estimate,
combined with the fact that the sensitivity of MAX-DOAS decreases with
altitude, leads to an undesired effect for relatively high a priori
scale heights (>1.5 km), namely that the retrieved
tropospheric trace gas column or AOD in the case of aerosol extinction
retrieval is systematically too high.
This unwanted mechanism works as follows: for a priori scale heights
higher than 1.5 km, the exponentially decreasing a priori
profile does not go to (almost) zero in the upper part of the altitude
grid (4 km). Because above approximately 1.5 km the
information content of the observation is low, the retrieval will have
a tendency to stay close to the a priori and not be allowed to go to
zero. As a consequence, the retrieved profiles will have
a considerable fraction of the partial column above ∼1.5 km,
even when this is not the case in reality. This effect will lift up
the mean profile height, and this goes together with a systematic
overestimation of the integrated trace gas column (or AOD).
By modifying the definition of the a priori profile shape such that it
decreases to zero at the top of the altitude grid, the overestimation of
columns and AOD is greatly reduced. The following profile shape
definition is forced to low values above 1.5 km and even zero
at the top of the altitude grid:
n(z)=NpriorVHsprior⋅exp-zHsprior⋅4-z.
Figure 2 shows a priori profile shapes obtained with this definition,
for Hsprior={0.5,1.0,1.5} km. Note that the range in terms of H75 is different:
{0.6,1.0,1.3} km.
The impact of the a priori profile shape on the retrieved profile can
be quite high. For this reason the profile retrieval with method A is
performed with three different a priori scale heights
(Hsprior={0.5,1.0,1.5}), leading
to three versions: A1, A2 and A3. The final product that is compared
to method B is a composite of the retrievals with these three
a priori: for each retrieval quantity (see Sect. 2.6) the mean of the
values obtained with A1–A3 is taken as the solution, and the
difference between the maximum and minimum as the uncertainty. The
reason to follow this approach is that the impact of the a priori is
substantial and there is no external information available instead
which justifies the choice for one specific a priori. Tests have indicated
that errors estimated in this way are in general considerably larger than the
smoothing error, a commonly used parameter in the optimal estimation
framework to quantify the impact of the a priori on the retrieval error
. The relative smoothing error per layer is typically
less than 20 %, for both the aerosol extinction and the trace gas
retrieval. The a priori based error is about 1.6 times higher in case of the
aerosol extinction retrieval and about 4.8 times higher in case of the
NO2 retrieval (both numbers are median values).
Method A is run with three different a priori profile shapes (see
Eq. 2), each with a different characteristic profile height (H75).
Method B – algorithm developed at KNMI
The profile retrieval approach of method B is
quite different from method A: it makes use of a profile shape
parameterization with just a few (2–4) free parameters; forward
simulations are performed by making use of a look-up table which has
been created with the Doubling Adding KNMI (DAK) radiative transfer model
; a standard least-squares algorithm
is used, without any form of regularization. The main reason to use
a low number of free parameters is that the information content of
MAX-DOAS observations with respect to the vertical distribution of
aerosols and trace gases is quite limited (see Fig. 3). With
a suitable choice of free parameters a sufficiently wide range of
possible profile shapes can be retrieved, especially in combination
with the ensemble approach described below. Compared to the
description in the algorithm has been modified
in the following ways: the profile shape parameterization is slightly
different, this is described below; the look-up table is compiled to
allow for more extreme aerosol optical thicknesses (τ) needed
in China with τ=3.2 as maximum; the look-up table is expanded
with a UV component (central wavelength: 360 nm); no
correction is applied to compensate for the temperature dependence of
the differential cross-section of NO2 (similar strategy
for method A) – a fixed temperature is used (296 K). This will
affect the accuracy of both retrieval methods similarly. The up to
four free parameters that are used to parameterize the profile (see
Fig. 2) are: (i) the tropospheric column density for trace gases and the AOD
in case of aerosols; (ii) the top height of the mixing layer;
(iii) the “shape parameter”, which determines the linear increase or
decrease of the trace gas concentration or aerosol extinction in the
mixing layer; (iv) the fraction of the total trace gas column density which
resides (uniformly distributed) in the layer starting at the top of
the mixing layer up to 2 km above. The vertical extent of
this layer varies with parameter (ii). Parameter (iv) replaces the free
tropospheric layer which in the earlier version of the algorithm
was put at a fixed altitude. Parameter (iii),
already tested and introduced as part of a sensitivity study in
is also newly applied here.
Histograms showing the degrees of freedom for signal (DOFS) for the
profile fits obtained with methods A1–A3, based on all MAX-DOAS scans
analysed for the Xianghe station. The upper row shows results for the UV, the
bottom row shows results for the Vis. The dashed line indicates the threshold
that is used for the quality control: retrievals with DOFS < 1 are
excluded from the comparison.
An important characteristic of this profile shape parameterization is
that with parameter (ii) it can mimic the dynamic behaviour of the cloud-free boundary layer, which can be very shallow in the morning
(especially after a cold, cloud-free night with little wind) and
become quite deep during the day, especially in summer. Parameter (iii)
is included especially to allow for profile shapes which peak at
higher altitudes (e.g. somewhere near the top of the mixing
layer). With parameter (iv) elevated trace gas concentrations at higher
altitudes can be described. From it is known
that the accuracy of this part of the profile is generally low. For
the aerosol extinction profile retrieval, parameter (iv) is not used for practical
reasons (computation time). As a consequence it is not possible to
perform accurate aerosol extinction profile retrievals under measurement
conditions with elevated aerosol layers above the mixing layer
– aerosol extinction profiles which peak near the top of the mixing
layer can be described with the shape parameter (iii). Such cases are
however indicated by high values of χ2 and can therefore be
flagged (or excluded), see below. The cost function used for method B
is defined as
χ2=∑i=18ΔNαiS-ΔNαiS^ϵαi2,
where ΔNαiS is the measured
differential slant column density for elevation i, ΔNαiS^ is the simulated differential slant
column density and ϵαi is the error estimate for the
differential slant column density. Due to the low number of free parameters
used in method B (2 to 4), it is more difficult to get optimal
agreement between simulations and measurements (i.e. to obtain low
residuals) than with method A (13 profile layers). Therefore, and also
because there is no a priori to fall back on, the individual
retrievals with method B tend to be more unstable with respect to one
or more retrieval parameters.
It is important to note that this instability is not necessarily an
unwanted effect: it is an expression of the fact that (under some
conditions) the MAX-DOAS observations contain very limited information
about the profile shape. For such conditions it is desirable to have
a good estimate of the uncertainty. This is obtained by making use of
an ensemble approach: the retrieval code is run 50 times, each time
with slightly different input. The differential slant column density
measurements are perturbed by adding Gaussian noise with a standard
deviation corresponding to 10 % of the original differential
slant column density (obtained with the semi-simultaneous zenith
measurement). For each scan an ensemble of solutions is obtained, and
for each retrieval quantity the median is taken as the final
result. The width of the distribution for each parameter (e.g.
described by the end of the first and beginning of the fourth
quartile) provides an estimate for the retrieval uncertainty. Note
however, that this retrieval uncertainty does not account for the
uncertainty with respect to the profile shape parameterization. For
this reason the retrieval is run for several profile shape
parameterizations at the same time (see Table 2) and a composite
retrieval product is constructed a posteriori. A posteriori selection
of plausible profile shape parameterizations (among B1–B4) is done by
considering the distribution of the reduced χ2
(χν2). This parameter is defined as
χν2=χ2N-M,
where N is the number of observations (differential slant column densities at
various elevations) minus the number of model parameters (i.e. 2 to
4). If the median value of the χν2 distribution (after 50 runs)
for a certain profile shape parameterization is approximately
equal to one, then the selected retrieval model is capable of
producing simulations that agree with the observations within the
estimated measurement error.
Retrieval with method B is performed for different combinations of
free parameters which describe the profile shape. See also Fig. 1.
Profile
Free parameters
parameterization
included
B1
I, II
B2
I, II, III
B3
I, II, IV
B4
I, II, III, IV
After the algorithm is run 50 times for all four models, it is
determined which models are included in the a posteriori composite
retrieval product, namely all models which have a median
χν2<1.5. For each model individually the retrieval outcomes
for a certain quantity (e.g. surface concentration) is defined as the
median value of the distribution (after 50 runs) for that particular
quantity. The lower limit of the corresponding uncertainty estimate is
defined as the value which marks the transition from the first to the
second quartile of the distribution. The upper limit is defined
similarly as the value which marks the transition from the third to
the fourth quartile of the distribution. This implies that
50 % of the retrievals is within the error bar. The composite
product is constructed simply by averaging the medians of the selected
models, and the error bars are constructed by averaging the lower
limits and upper limits separately. The procedure that is followed
here (including all models among B1–B4 which have sufficiently low
median of χν2) yields a more realistic uncertainty estimate
than if only the model with lowest median χν2 would be
used, because it takes into account the uncertainty with respect to
the profile shape.
Histograms of residuals of the profile fits obtained with
methods A1–A3, based on all MAX-DOAS scans analysed for the Xianghe station.
The upper row shows results for the UV, the bottom row shows results for the
Vis. The dashed line indicates the threshold (0.1, or -1 on a logarithmic
scale) that is used for the quality control: retrievals with residuals above
this threshold are excluded from the comparison.
Selection criteria and uncertainty estimates
Comparison of methods A and B is done only for profile pairs which
satisfy three criteria: they should pass the quality control criteria
of method A, and those of method B, and they should coincide with AERONET
observations. The third criterion provides an indirect way of
selecting cloud-free periods. MAX-DOAS profiles are only included in
the comparison if at least three AERONET level 2.0 (cloud screened,
quality controlled) measurements are taken within an hour around the
MAX-DOAS measurement. Quality control for method A is based on
two quantities: the size of the residual of the profile fit and the
degrees of freedom for signal (DOFS, see ). The
residuals are defined as the sum of squared differences between
simulations and measurements, divided by the simulated differential
slant column density for an elevation of 30∘ (this quantity provides
a first-order estimate of the tropospheric vertical column density):
δ=∑i=18ΔNαiS-ΔNαiS^ΔNαi=8S^2.
Figures 3 and 4 show the histograms of these two parameters before the
quality control is applied. These figures illustrate clearly that in
general profile retrieval is more challenging for HCHO than for
NO2: the DOFS for HCHO are often well below 2,
whereas for NO2 the DOFS are often >2. Also the
residuals for HCHO are considerably higher for a considerable
fraction of all data (note that Fig. 4 shows the logarithm of the
residual). The same is illustrated in Fig. 5: the averaging kernels
for HCHO are lower than for NO2 and are less
orthogonal with respect to one another. Profile pairs of A and B are
excluded from the comparison if the minimum value of the DOFS is <1
for one or more of the models A1–A3. Also they are excluded if the
maximum residual of A1–A3 is larger than 0.1. Quality control for
method B consists of selecting only those profiles where the median
value of the reduced χν2 for the profile fit of method B
is <1.5. For aerosol extinction only the median χν2 of the
aerosol extinction profile fits is considered, for the trace gas retrieval also
the median χν2 of the trace gas profile fits.
Examples of averaging kernels for retrievals performed with
method A, both for the UV (left column) and Vis (right column). The upper row
shows averaging kernels for low AOD (representative for the winter season),
the bottom row for high AOD (representative for the summer season).
The impact of the quality control criteria defined above is discussed
in Sect. 4.1.
Examples of NO2 profiles retrieved with method A – grey
(Hs=0.5 km) and black (Hs=1.5 km) – and
method B – parameterizations B1–B4 (see Fig. 1 and Table 2) shown in red,
blue, orange and light blue respectively.
Retrieval quantities
We compare results mostly based on three quantities: the tropospheric
vertical column densities (NV), the concentration
(nsurf) or volume mixing ratio (Xsurf)
of trace gases near the surface and the characteristic height (or
H75, see Sect. 1) of the retrieved profile. Similar quantities
are used in the case of aerosols: aerosol optical depth
(τaer), aerosol extinction near the surface
esurf, and H75. A fourth quantity that is used is
the a posteriori scale height (not to be confused with the scale
height of the a priori profile of
method A (Hsprior), see Sect. 2.3). This
a posteriori scale height Hspost is a first-order
profile height estimate derived from column density (or AOD) and surface
concentration (or aerosol extinction):
Hspost=NVnsurf
for the trace gases, and
Hspost=τesurf
for aerosols. The reason to consider this first-order profile height
estimate in addition to H75 is that, as will be shown in
Sect. 3.2, for method A it depends less on the a priori than
H75. This indicates to some extent that the measurements contain
information about the profile height that is not extracted in an
optimal manner in this particular retrieval set-up.
Results
Example day
Figures 6–8 show retrieval results for 19 May 2012. The individual
profiles obtained with method A and B (Fig. 6) show good agreement in
the sense that in the morning they are all quite low, and in the
afternoon they are all quite high. Nevertheless, this example also
illustrates that retrieved profile shapes can be very different: not
only do the four versions of method B show considerable differences but
so do the two versions of method A, especially those retrieved after
12:00 p.m. LT (bottom row).
Example of quantities derived from the profile retrieval in the Vis
(Xianghe, 19 May 2012). The left column shows the results of
the aerosol retrieval, the right column shows results for the
NO2 retrieval. Grey horizontal bars above each panel indicate periods
that are flagged because of high values of χ2 in the aerosol or in the
trace gas retrieval.
Time lines for the different quantities that can be derived from the
profile retrieval are shown in Fig. 7 for the same example day. Both
for the aerosol extinction retrieval (left column) and the NO2
retrieval (right column) the χν2 are quite low for most of
the day, indicating a good quality of fit. On this particular day, the
retrievals agree quite well for most quantities, especially for the
column densities (row 1) and surface concentrations (row 3). Agreement is worst
for H75NO2 and
HsNO2 in the afternoon, where
method B occasionally shows much higher values. This is
a consequence of the fact that the retrieval is not regularized, in
combination with relatively low surface concentrations in the
afternoon. Because the surface concentration is the denominator in
Eq. (6), one can understand that a small change (error) in the surface
concentration can lead to a much larger change in
HsNO2. This figure also clearly
demonstrates the potential impact of different profile shape
assumptions on H75NO2.
Figure 8 shows results for the same day, but this time for the aerosol
extinction and HCHO retrieval in the UV. In general there is much more
disagreement compared to NO2. There is on this day almost no retrieval
where the agreement is good for all quantities at the same time. The
agreement between most quantities is especially low between 10:00 a.m. and
4:00 p.m. LT. High values for χν2 in
the aerosol extinction retrieval indicate that the retrieval with method B is
not successful and therefore this period is flagged with grey bars on top of
each figure. Quite remarkable is the disagreement in terms of HCHO
column densities in the remaining part of the day (before 10:00 a.m. and
after 4:00 p.m.). In the morning of this day the higher column densities
(for method B compared to A) seem to go along with higher
H75HCHO.
Example of quantities derived from the profile retrieval in the UV
(Xianghe, 19 May 2012). The left column shows the results of
the aerosol retrieval, the right column shows results for the
HCHO retrieval. Grey horizontal bars above each panel indicate
periods that are flagged because of high values of χ2 in the aerosol or
in the trace gas retrieval.
Statistical comparison of methods A and B. The last two columns
refer to median, mean and standard deviation (SD) of percentage relative differences (RD). The linear fit results are
defined for method A on the abscissa. Relative differences have a sign
determined by B - A. Note that the intercepts have unit km for H75
and Hspost, unit 1015moleccm-2 for the
tropospheric column densities, unit ppb for the volume mixing ratio
(vmr) near the surface, and unit km-1 for the aerosol extinction
near the surface.
Quantity
N
Corr.
Slope
Interc.
Median (mean) of RD (%)
SD of RD (%)
UV, aerosols
AOD
2734
0.92
1.20
-0.02
17.16 (22.81)
24.92
H75
2723
0.77
4.08
-2.42
7.55 (6.69)
47.17
Hspost
2735
0.88
1.50
-0.37
10.92 (10.25)
25.91
Extinction near surface
2734
0.93
1.12
0.01
11.44 (14.93)
20.07
UV, HCHO
Trop. column density
2509
0.95
1.02
0.67
9.64 (9.43)
12.14
H75
2498
0.67
7.47
-5.33
22.34 (15.65)
36.93
Hspost
2498
0.77
3.01
-1.47
41.96 (37.87)
35.57
vmr near surface
2504
0.80
0.95
-0.32
-23.03 (-20.70)
27.71
Vis, aerosols
AOD
4001
0.91
1.39
-0.05
18.26 (23.07)
23.54
H75
3936
0.62
2.82
-1.31
5.67 (2.74)
43.63
Hspost
3821
0.63
1.20
0.11
12.65 (14.40)
36.64
Extinction near surface
3907
0.93
1.33
-0.08
11.24 (10.27)
30.43
Vis, NO2
Trop. column density
3360
0.99
1.03
-0.56
0.51 (0.25)
9.26
H75
3298
0.76
1.44
-0.20
8.71 (6.51)
33.18
Hspost
3309
0.80
1.79
-0.35
18.71 (17.30)
38.03
vmr near surface
3313
0.76
1.16
-2.25
-11.82 (-7.92)
32.97
Statistical analysis
Results of both retrieval methods are compared for 16 quantities
in terms of correlation, slope and intercept of linear fit, and
median, mean and standard deviation of relative differences, see
Table 3. The comparison of 12 of these quantities is also shown in
Figs. 10, 14, 15 and 21. We will discuss these results separately in
terms of tropospheric column densities (AOD for aerosols), profile heights and
surface concentrations (or aerosol extinction).
Time series of individual data points and monthly medians of AOD
(Vis), and tropospheric column densities of NO2 and HCHO,
obtained with method A. The black dots refer to individual profiles and the
red lines refer to monthly medians. AOD from AERONET is shown in green (upper
row). In 2008/2009 the instrument was installed in Beijing; from 2010 onwards
it was stationed in Xianghe.
Tropospheric column densities
Figure 9 shows the monthly median values for the column quantities:
AOD, tropospheric NO2 and HCHO column densities. Note that
measurements before 2010 are made in Beijing. From 2010 onwards, the
observations are made in Xianghe. A clear seasonal cycle with a winter
minimum of about 5×1015 moleccm-2 and a summer
maximum roughly five times as high can be seen for
HCHO. Compared to NO2 and aerosols, the
variability per month is quite small. A weaker, but similar seasonal
cycle can be seen for aerosols, with typical winter values around 0.2
and a summer median between 0.5 and 1.0. For NO2 the
seasonal cycle of monthly median values is quite weak as well. Winter
medians are roughly between 20×1015 and
30×1015 moleccm-2, summer medians between
10×1015 and 20×1015 moleccm-2. Noteworthy
is the fact that especially the peak values in winter can be high with
values above 100×1015. Peaks in tropospheric NO2
column densities in midsummer do not exceed 30×1015. Figure 10 and
Table 3 show that very good agreement is found for tropospheric
NO2 column densities. The standard deviation of relative
differences is however considerable: almost 10 %. The third and
fourth columns of Fig. 10 show that the relative difference increases
with increasing tropospheric column density and with increasing profile
height. Also for tropospheric HCHO column densities the agreement is
good. Relative differences are however considerably larger than for NO2. The
dependence of relative differences on the tropospheric column density itself
(second row, third column) shows opposite behaviour as for NO2,
whereas the dependence of relative differences on the profile
height shows a similar increase as for NO2. Despite the
quite high correlation found for the AOD, the agreement between method A and B is moderate, with
slopes 1.20 (UV) and 1.39 (Vis) and substantial mean relative differences. Figure 10 (bottom row) shows
for the Vis that these differences in AOD are strongly related to
the difference in aerosol extinction profile height, but also tend to increase
with the AOD itself. The agreement between method B and AERONET is
much better, which provides confidence in the AOD retrievals obtained
with method B. The frequency distributions of AERONET and AODs
retrieved with method B show good agreement and differ with respect to
method A in the fact that they include much more cases with AOD
between 1.5 and 3.5. But for the highest 25 % of
characteristic profile heights, method B seems to overestimate the AOD
systematically by about 20 %. Figure 11 shows for NO2
and HCHO the relation between AOD (as measured by
AERONET) and tropospheric trace gas column densities for different
seasons. There are clear seasonal differences with largest differences
for NO2 vs. AOD between summer and winter. The two models
show good agreement, with only moderate systematic differences for
HCHO column densities in spring and summer. This is in line with the
example day (Fig. 8) which shows considerable differences between
tropospheric HCHO column densities retrieved by methods A and B. Note that
on this example day the AOD is high, and the differences in
characteristic HCHO profile height are considerable. The quite
linear relationship between NO2 and AOD, and HCHO
and AOD illustrate that trace gas emissions are often accompanied by
aerosol emissions. From that perspective the flattening of the curves
for high AODs (mainly in summer and autumn) is remarkable. Possibly
this is related to aerosols from natural sources (dust), emissions of
which do not go along with emissions of trace gases. Another
explanation would be that high AODs cause systematic underestimation
of the tropospheric column density, but the flattening of the curves is not
seen in winter and spring, even for higher AODs.
Statistics of column density retrievals. The three rows refer to
tropospheric column densities of NO2, HCHO and aerosols
respectively. Left column: frequency distributions obtained with
method A (blue) and B (red). Second column: frequency distribution of
relative differences (B minus A). Lines in orange indicate the quartiles.
Column 3: relative difference sorted as a function of the tropospheric column
density (AOD for row 3) where the three bins refer to the lowest 25 %,
middle 50 % and highest 25 % respectively. Column 4: similar to
column 3, but here sorted as a function of the profile height (H75). The
grey line on the bottom row refers to AODs from AERONET. The relative
differences indicated in grey (bottom row, columns 2–4) refer to method B
minus AERONET.
Median values of the tropospheric NO2 column (upper row) and
HCHO column (bottom row) for a range of AOD bins, specified per
season.
Time series of individual data points and monthly medians of profile
heights (H75) for aerosol (Vis), NO2 and HCHO obtained with
method A. The black dots refer to individual profiles. The red and blue lines
refer to monthly medians for the morning (all observations before
10:00 a.m.) and afternoon respectively (all observations after
12:00 p.m.).
Profile heights
Figures 12 and 13 show for methods A and B monthly median values of
characteristic heights, with a distinction between retrievals before
10:00 a.m. (red) and retrievals after 12:00 p.m. (blue). For all three
species and both retrieval methods, we find higher profiles in the
afternoon than in the morning, especially with method B. Only for
H75HCHO obtained with method A are the differences between
morning and afternoon negligible. This is most likely an artefact,
which is also seen in Fig. 14, and which is discussed in
Sect. 4.2. The morning–afternoon differences found in all other
cases are qualitatively in agreement with the expected diurnal
variation in the mixing layer height, and provide a first-order check
to see if the algorithms behave as expected. Variability per month and
between months is however much larger with method B. Highest monthly
median characteristic profile heights are found with method B for
aerosol extinction profiles in summer. This is in agreement with the general
expectation that mixing layers are more shallow in winter and grow
deeper in summer (see e.g. ). That this effect is
weaker for NO2 might be related to the shorter lifetime
of NO2 in summer which limits the effective transport of
NO2 from the surface to the higher parts of the mixing
layer, see also and
. Figure 14 and Table 3 show that the agreement
between the two methods in terms of profile heights is considerably
lower than the agreement in terms of column densities, which is to be expected
because the information content of MAX-DOAS with respect to the
vertical distribution is limited. The best agreement is found again
for NO2, with for the profile heights correlation 0.76,
slope 1.44, intercept -0.20 km, and mean relative difference
6.51 %. The standard deviation of relative differences is
high: 33.18 %. It can be seen in Fig. 14 that the dynamic
range of NO2 profile heights found with method A is
somewhat lower than with method B. In particular, the fraction of profiles
with height above 1 km is significantly higher with
method B. For the HCHO profile height we have correlation
0.62. This is quite surprising because the dynamic range of profile
heights found with method A is very small compared to method B and
this also explains the exceptional slope (7.47) and intercept
(-5.33 km). Even though no independent data are available, it
is quite safe to conclude that this very limited dynamic range is
unrealistic, and therefore these HCHO profiles should be used
and interpreted with great care. As a result of this effect, it is
difficult to judge the quality of the HCHO profile heights
obtained with method B. One can see that here the dynamic range is
comparable to that of NO2 and aerosols, but the mode of
the histogram has shifted to higher altitudes compared to NO2. Also for aerosols (Vis) the dynamic range found with
method A is limited compared to method B. The correlation (0.62) is
somewhat lower than for NO2 and HCHO, but the
slope and intercept are less extreme than for HCHO (2.82 and
-1.31 respectively). Figure 15 demonstrates that in terms of the
other estimator of the average profile height
(Hspost) the agreement between methods
A and B is better. Especially for HCHO, the slope is less
extreme for Hspost than for H75
which is in line with the higher dynamic range seen for method A in
Fig. 15 compared to Fig. 14. We see a similar effect for
aerosols. This might indicate a retrieval artefact for method A which
means that information about the profile height that is actually
contained in the MAX-DOAS measurements is not efficiently converted
into a noticeable effect on H75NO2.
Similar to Fig. 12, but now for method B.
Statistics of characteristic profile height retrievals. The three
rows refer to profile heights (H75) of NO2, HCHO and
aerosols respectively. Left column: frequency distributions obtained with
method A (blue) and B (red). Second column: frequency distribution of
relative differences (B minus A). Lines in orange indicate the quartiles.
Column 3: relative difference sorted as a function of H75 where the
three bins refer to the lowest 25 %, middle 50 % and highest 25 %
respectively.
Similar to Fig. 14, but here for the a posteriori scale height
(Hspost, Eqs. 6 and 7). The three rows refer NO2,
HCHO and aerosols respectively. Left column: frequency distributions
obtained with method A (blue) and B (red). Second column: frequency
distribution of relative differences (B minus A). Lines in orange indicate
the quartiles.
Three binned scatter plots: aerosol profile heights retrieved in the
Vis, vs. profile heights retrieved in the UV (left), aerosol profile height
retrieved in the Vis vs. NO2 profile heights (middle), aerosol profile
heights retrieved in the UV vs. HCHO profile heights (right). Note
that models A and B have very different frequency distributions of
characteristic profile heights for the three constituents, see Fig. 14.
A different view on the quality of the profile height retrieval
obtained with both methods is given by Fig. 16. From the left
panel we can conclude that for both methods the internal consistency
(UV vs. Vis) of aerosol extinction profile heights below 1.5 km is
quite good, especially for method A. Above 1.5 km we have only
very few cases with method A, and all of these cases show a strong
bias between UV and Vis. For method B the bias appears to be quite
constant over the entire range, with UV profiles that are
approximately 25 % lower than profiles in the Vis. The
middle panel of Fig. 16 shows a comparison of NO2 and
aerosol extinction profiles. In contrast to aerosols, we do not expect a strong
agreement beforehand. What we hope to see, and this is partially the
case, is that the general pattern is similar for both methods. Below
1.5 km the agreement is remarkably good, and this is certainly
a confirmation that the results obtained with both methods make some
sense. As mentioned before, the limited dynamical range of
method A makes it almost impossible to draw conclusions on the
reliability of profile heights above 1.5 km found with
method B. Nevertheless, a possible explanation for the bias between
NO2 and aerosol extinction profile heights in this regime is the
same as mentioned earlier: higher aerosol extinction profiles occur in summer,
but then the lifetime of NO2 can be very short, which
leads to more shallow NO2 profiles.
Median values of the characteristic profile height (H75) for
aerosols (upper row), NO2 (middle row) and HCHO column (bottom
row) for a range of AOD bins, specified per season.
Figure 17 shows for
different seasons the characteristic aerosol extinction, NO2 and
HCHO profile heights as a function of the AOD. For aerosol extinction
profile heights, we see a much stronger seasonal cycle with method B
than with method A. In principle a seasonal cycle is also expected:
higher boundary layers occur in summer, when the thermal convection is
strongest. A possible interpretation of the results seen on the top
row (decline of H75aer with increasing AOD) is that
growth of the boundary layer through convection is weakened by the
presence of high aerosol loadings (see also
). Without independent simultaneous observations
with other techniques, it can however not be excluded that this effect
is related to the measurement technique itself (i.e. a retrieval
artefact). Method B shows a weaker seasonal variation in NO2
than in aerosol extinction profile heights and highest NO2
profiles occur in spring. This might be due to the fact that in spring
the NO2 lifetime is not as short as in summer (allowing
more time for vertical transport), whereas at the same time vertical
transport through convection is stronger than in winter. Results for
HCHO are more difficult to interpret. Because the lifetime is
longer than for NO2, and because formaldehyde sources can
be biogenic and anthropogenic (the relative contribution varies by
season) the profile shapes can be very different from those of
NO2. A quantity that is especially important in the
context of satellite validation and satellite retrievals is the
relative difference in NO2 and aerosol extinction profile
height. The impact of the relative characteristic profile heights on
the slant column density measurement can be high, and lead to systematic
biases if not accounted for in the retrieval. This quantity is shown
for both methods as a function of season in Fig. 18 (also for
HCHO). Similar as for the characteristic heights themselves, we
see in Fig. 18 a higher dynamic range for method B than for
method A. This is partly explained by the lower stability of method B,
but also by the ability to retrieve a wider range of profile
heights. Both methods detect in spring higher characteristic aerosol
than NO2 profile heights. In summer method B finds
systematically higher values for
H75aer-H75NO2 than method A. In
winter and autumn, the systematic bias between H75aer
and H75NO2 is smaller. As argued above, results for
HCHO are more difficult to interpret (because of the artefact
affecting the retrieval with method A). However, based on the results
obtained with method B it appears as if aerosol extinction profiles are higher
than HCHO profiles in spring and summer, and lower in fall and
winter.
Box plots of difference between aerosol and trace gas profile heights
(NO2 left, HCHO right), specified per season and retrieval
method.
Time series of individual data points and monthly medians of
near-surface aerosol extinction (upper row) and volume mixing ratios for
NO2 and HCHO (bottom row), retrieved with method A. Red refers to
morning observations, blue to afternoon observations.
Aerosol extinction and trace gas volume mixing ratios near the
surface
Seasonal variations of volume mixing ratios and aerosol extinction
near the surface are shown in Figs. 19 and 20 for methods A and B
respectively. For NO2 a systematic difference is seen
between morning and afternoon values, and this is clearly related to
the dynamics of the mixing layer. For aerosols a similar effect is
found. For HCHO however, this contrast is almost absent. This
is related to fact that HCHO profiles shapes retrieved with
method A show almost no deviation from the a priori (Sect. 3.2.2). As
a consequence, the main driver of the surface concentration is the
tropospheric column density of HCHO. This explains why for HCHO
retrieval with method A the seasonal variation in volume mixing ratios
is so similar to the seasonal variation in column densities. For method B (not
shown) the results are quite different in winter months, when morning
values are about three to four times higher than afternoon values of
the HCHO volume mixing ratio. In summer months, this effect
appears to be less pronounced, unlike for NO2. It is
difficult to draw conclusions based on method B only, but this weaker
diurnal variation in HCHO surface volume mixing ratios compared
to winter could indicate that in summer local emissions on the surface
have a relatively small impact. Based on this data set only, it can
however not be excluded that absence of a strong morning–afternoon
contrast for HCHO volume mixing ratios in summer is an artefact
of the retrieval. Figure 21 shows the results of the comparison of
methods A and B in terms of trace gas volume mixing ratios and aerosol
extinction near the surface (lowest profile layer). In contrast with
the results found for the profile heights, the agreement is
reasonable, with quite similar histograms for all three
constituents. Nevertheless, the systematic relative differences are
considerable. For NO2 we have a mean relative difference
of -7.92 % with a standard deviation of
32.97 %. For HCHO the relative differences are larger
(-20.70, ±27.71 %) which is mostly explained
by the differences in profile shape, because in terms of column densities the
relative difference is smaller and of opposite sign
(9.43 %). With respect to aerosol extinction near the
surface, the agreement between methods A and B is good, with
correlation 0.93, slope 1.33 and intercept -0.08. The mean relative
difference is however considerable (10.27 %) and the
standard deviation of relative differences is high: 30.43 %.
Time series of individual data points and monthly medians of
near-surface aerosol extinction (upper row) and volume mixing ratios for
NO2 (middle row) and HCHO (bottom row), retrieved with method B. Red refers to
morning observations, blue to afternoon observations.
Discussion
In this section we address the main question of this paper: what can
be concluded on the quality of aerosol extinction and trace gas profiles
retrieved from MAX-DOAS observations. We begin with a discussion of
strength and weaknesses of both profile retrieval methods, draw
conclusions, and then give recommendations for improvements and use.
Impact of quality control
The ideal selection of high-quality data for this comparison study
would be based on a validated cloud screening method which performs
well under a wide range of aerosol conditions. Such a method was not
available when this study was started (in the meantime promising
results have been published by , and
). Therefore a pragmatic approach was chosen, see
Sect. 2.5. A disadvantage of this approach is that a high number of
retrievals is rejected. For example, there are many cases where the
trace gas retrieval is rejected (despite a proper χν2)
because the χν2 in the aerosol extinction retrieval is not
sufficiently low. The criterion used might be more appropriate for
a quality control intended for profiles – and for that reason it is
used in this work – but it is probably too strict for a quality
control intended for column densities only. Several tests have been performed
to check the robustness of findings reported in this paper after
changing the selection criteria. For example, the criterion on
χν2 has been relaxed to χν2<5 and the
number of AERONET observations in the same hour is lowered from 3 or
more to 2 or more. This leads roughly to two times more aerosol extinction
profile pairs (see second column of Table 3) and roughly two and
a half and three times more profile pairs for HCHO and
NO2 respectively. The impact of these relaxed settings is
considerable for the aerosol extinction retrieval (e.g. mean relative difference
in H75aer increases from 2.74 to
12.35 %), but quite small for the trace gas retrieval. For
example, the mean relative difference in H75NO2
increases from 8.71 to 9.85 %, and the mean
relative difference in the volume mixing ratio for NO2
decreases from -7.92 to -4.4 %, which is
a small change compared to the standard deviation
(32.97 %). There are no sign changes for quantities in
Table 3 that are significantly different from zero. It should be noted
that the results for the aerosol extinction retrieval obtained with these relaxed
constraints are clearly considered to be less representative for ideal
clear sky conditions. With every set of quality criteria, the results
presented here will change slightly (largely due to a different the
sampling of the full data set), however the settings used here are
considered to be a reasonable balance between maintaining sufficient
data pairs and rejection of data pairs which are likely to be affected
through clouds.
Strength and weaknesses
In Sect. 3.2 it was shown that both methods show good agreement in
terms of tropospheric NO2 and HCHO column densities: the
correlation is high, the slopes of linear fit are close to 1 and the
intercepts are relatively close to zero. The agreement of
characteristic profile heights is reasonable for NO2 and
aerosols, despite clear biases, especially above 1.5 km. The
main strength of method A is its robustness (stability). This is
a clear advantage especially when differential slant column densities are close
to the detection limit, or when the assumptions that are made about
fixed parameters (or cloud-free conditions) do not hold. In such
cases, the retrieval can rely on the a priori. The characteristic
profile height retrieval with method B is only stable under cloud-free
conditions, and if assumptions about fixed parameters are not too far
from the truth. The number of profiles which passes the quality
control (Sect. 2.5) for method B is significantly smaller than for
method A. A disadvantage of method A is that the combination of
a profile parameterization based on 13 layers and a relatively low
information content of the MAX-DOAS observations forces one to take
measures to stabilize the retrieval. These measures are: (1) a
relatively conservative estimate of the a priori error (for each
profile layer 20 % of the a priori profile estimate) and (2) a
profile which decreases to zero rapidly above 1 km. A consequence
of this approach is that the absolute values of the a priori error
estimate become very low above 1 km. This is believed to be
the main reason why it is almost impossible to retrieve profiles with a
characteristic height (H75) much higher than that of the a priori. In
most cases sufficient agreement between
observations and simulations can be achieved by modifying the profile
shape (compared to the a priori) only below 1.0 km. This
explains why for retrieved NO2 profiles reduction of H75
compared to the a priori is seen much more often than increase. This is
not seen for HCHO. For HCHO it appears that the
information content is too low to obtain profiles (with method A)
which deviate much from the a priori. A strong aspect of method B is
that it can realize a high range of quite different profile shapes,
with just a few free parameters. It can more easily realize profiles
which have a characteristic height (H75) well above
1.0 km. In this study, it is however not possible to fully
judge the quality of these profiles because these cannot be retrieved
with method A. Nevertheless, the monthly averaged morning to afternoon
difference in profile height and the seasonal cycle of aerosol extinction profile
heights (Fig. 13) correspond to the expected behaviour and this is at
least an indirect indication of the quality of the profiles obtained
with method B. Independent (e.g. lidar) observations at the same
measurement site would be needed to say more about the quality of
individual profiles.
Statistics of near-surface concentration retrievals. The three rows
refer to volume mixing ratios of NO2 (row 1) and HCHO (row 2) and
aerosol extinction (row 3). Left column: frequency distributions obtained
with method A (blue) and B (red). Second column: frequency distribution of
relative differences (B minus A). Lines in orange indicate the quartiles.
Column 3: relative differences sorted as a function of the volume mixing
ratio (rows 1 and 2) and aerosol extinction (row 3). Column 4: relative
difference sorted as a function of H75 where the three bins refer to the
lowest 25 %, middle 50 % and highest 25 %
respectively.
This study also makes clear that the main disadvantage of method B is
its instability, despite the limited number of free parameters and
the ensemble approach. Note however that the retrieval is certainly
not always unstable, see for example the retrievals in the Vis on
15 May 2012 (Fig. 7). The advantage of the ensemble approach taken
with method B is that most often the instabilities go along with high-uncertainty estimates, and this provides a means for additional
quality control. Unlikely retrievals with a low-uncertainty estimate
occur also, but these can most often be excluded based on high values
for χ2, either in the aerosol or in the trace gas part of
the retrieval.
Recommendations for algorithm improvements and further validation
Both profile retrieval algorithms have specific strengths and
weaknesses, as described above. The challenge for improved algorithms
is to combine the stability and precision of method A with the ability
of method B to retrieve a high dynamic range of characteristic profile
heights. A possible but not so practical solution could be to use
method B to obtain an initial estimate of the a priori scaling height
for method A and then as a next step to perform a retrieval with
method A. This will work however only under strict cloud-free
conditions because of the limitations for method B. Also it would
transfer the impact of instabilities (for individual cases) from
method B to method A. An alternative is to use the profile
parameterization of method B in the framework of the optimal estimation
method. Such a retrieval algorithm could be better capable of
retrieving a wide range of profile heights and at the same time be
more stable than the present implementation of method B. This would
also lead to an algorithm which is considerably faster because there
would be no need for an ensemble approach. Improving the stability of
the retrieval by making use of a priori data (in combination with the
optimal estimation approach) brings a certain risk, which is that
systematic biases in the a priori climatology remain present in the
a posteriori climatology. An advantage of more simple retrieval
schemes (e.g. method B) is that they are predominantly driven by the
observations themselves and therefore less prone to inheritance of
systematic biases in the a priori, despite a low precision. It is
almost impossible to make a choice which combines the best of both
worlds: a very stable retrieval (i.e. precision of individual
profiles) without introducing systematic biases in a climatological
sense. Stability is important for comparison with satellite
observations if the number of available cases is very limited;
accuracy over a wide range of profile heights is important if MAX-DOAS
would be used to provide a climatology of profile heights for better
a priori estimates in the satellite retrieval. The recent work by
provides indications that the
Phillips–Tikhonov regularization method can be used for MAX-DOAS
profile retrievals which are more stable and at the same time (potentially)
less biased in a climatological sense. To our best knowledge, their method has not
yet been applied to a long data set of real observations with
a similar focus on the ability to retrieve accurate (first order)
profile height estimates. The present study has demonstrated the
benefit of having a large data set covering a wide range of
measurement conditions. Based on a small data set it would have been
very difficult to entangle differences in accuracy and precision. More
thorough validation requires simultaneous co-located observations with
other techniques (lidar, NO2 sonde). Such validation
efforts are especially useful if a sufficiently large data set is
available. In the presence of large differences in spatial
representativity (this is very different for satellite, MAX-DOAS and
in situ techniques) and a high variability in possible NO2
and aerosol extinction profile shapes, it is almost impossible to draw
conclusions about the accuracy of MAX-DOAS profile shapes based on a quite
limited number of co-located observations, even if the precision and
accuracy of the other techniques are high.
Summary and conclusions
A 4-year data set of MAX-DOAS observations in the Beijing area is
analysed with two different methods for the retrieval of tropospheric
NO2, HCHO and aerosol extinction profiles. The objective of
this study is firstly to assess for each constituent (NO2,
HCHO, aerosols) and retrieval quantity (AOD or
tropospheric column density, characteristic profile height (H75),
aerosol extinction or surface concentration) the mutual consistency of
the retrievals with both methods, and secondly to identify the
mechanisms causing the differences. The two profile retrieval methods
differ in many respects. Method A uses a profile parameterization with
13 layers (up to 4 km), on-line forward simulations with the
LIDORT radiative transfer model and an inversion based on optimal
estimation. Method B uses a profile parameterization based on 2 to
4 parameters to describe the profile shape and a look-up table created
with the DAK radiative transfer model. The inversion is based on
a least-squares minimization and an ensemble approach is used to
improve stability of the solutions and to estimate uncertainties. In
the following we summarize the results of the comparison, first in
a qualitative sense, then quantitatively. The strength of method A is
the stability of the profile shape retrieval, even under cloudy
conditions, which is a consequence of the relatively conservative
estimate of the uncertainty of the a priori profile. The choice for
stability is advantageous for the retrieval of tropospheric column densities
and volume mixing ratios near the surface. A negative side effect of
this conservative estimate of the uncertainty of the a priori appears
to be that the retrieved characteristic profile heights have
a relatively small dynamic range. This is most evident for the
HCHO profiles retrieved in the UV, but also for aerosol extinction and
NO2 retrieved in the Vis. Method B is generally less
stable, and this affects the precision of individual retrievals. The
tropospheric column density is least sensitive to instabilities in the profile
retrieval, whereas the characteristic profile height and volume mixing
ratio near the surface are most sensitive. The most pronounced
difference with method A is the higher dynamic range of retrieved
profile heights for aerosols, HCHO and NO2.
Although the higher dynamic range is partly a consequence of
the instability of the retrieval (and therefore not necessarily
meaningful), diurnal and seasonal patterns that show up after
averaging many profiles give some confidence that the retrievals are
meaningful. For example, we see low characteristic profile heights in
the morning, and higher values in the afternoon, especially for
aerosol extinction in summer. This can be related to the periodical cycles of
the boundary layer. Also we find in spring and summer lower aerosol extinction
profile heights with decreasing aerosol optical thickness. Although it
cannot be excluded that this is a retrieval artefact, this might also
be real (and therefore add to the credibility of method B), namely
that higher aerosol loads reduce the thermal convection in the
boundary layer and therefore lead to lower aerosol extinction profile heights.
More quantitatively, we find best agreement for the tropospheric
NO2 column densities (correlation 0.99), with almost no systematic
bias (slope 1.03, intercept -0.56×1015 moleccm-2)
and comparatively small relative differences (mean 0.25 % and
standard deviation 9.3 %). For formaldehyde column densities we find
a high correlation (0.95) and slope close to one (1.02), but also find that
method B is systematically higher than method A: mean relative difference is
9.4 % and standard deviation of relative differences is
12.1 %. Relative differences in formaldehyde column densities are
found to be related to differences in profile height: overestimations
of the tropospheric column density (for method B compared to method A) often
correspond to overestimations of the characteristic profile height
(for method B compared to method A). Volume mixing ratios near the
surface are systematically lower for method B compared to method A:
∼ 8 % relative
difference for NO2 and
∼ 21 % for
HCHO. The differences can again be related
to the differences in profile heights between methods A and B. The
standard deviation of relative differences of surface volume mixing
ratios is much higher than for tropospheric column densities:
33 % for NO2 and 28 % for HCHO. Characteristic
profile heights are systematically higher for method B than for
method A. The mean relative differences are 6.5 % for
NO2, 15.7 % for HCHO and 2.7 %
for aerosols (Vis). The high standard deviation of relative
differences (33, 37 and 44 % for
NO2, HCHO and aerosols respectively) shows that
the precision of characteristic profile heights is low. We find with
method B that in spring and summer aerosol extinction profiles are systematically
higher than NO2 profiles. Also we find that in winter and
summer mornings HCHO profiles are systematically higher than
aerosol extinction profiles, and vice versa in summer afternoons. Note however
that these findings are only indicative, because the limitations with
method A prevent confirmation of the results obtained with
method B. Altogether, this study gives some indications about the
quality of tropospheric column densities, surface concentrations and profile
heights retrieved with MAX-DOAS. Since this study is based solely on
MAX-DOAS observations the scope is limited and a more thorough
validation is needed. In order to obtain robust validation results
which can entangle differences related to accuracy and/or precision
for a wide range of pollution and sky conditions, it is recommended to
station MAX-DOAS instruments close to continuously monitoring surface
in situ monitors (e.g. for NO2), sun photometers and
lidars which are sufficiently sensitive to boundary layer aerosols.