Total column water vapour has been retrieved from TROPOMI measurements
in the visible blue spectral range and compared to a variety of different
reference data sets for clear-sky conditions during boreal summer and
winter. The retrieval consists of the common two-step DOAS approach:
first the spectral analysis is performed within a linearized scheme
and then the retrieved slant column densities are converted to vertical
columns using an iterative scheme for the water vapour a priori profile
shape, which is based on an empirical parameterization of the water
vapour scale height. Moreover, a modified albedo map was used
combining the OMI LER albedo and scaled MODIS albedo map. The use of
the alternative albedo is especially important over regions with very
low albedo and high probability of clouds like the Amazon region.
The errors of the total column water vapour (TCWV) retrieval have been theoretically estimated considering the contribution of a variety of different uncertainty
sources. For observations during clear-sky conditions, over ocean surface, and at low solar zenith angles the error typically is around values of 10 %–20 %, and during cloudy-sky conditions, over land surface, and
at high solar zenith angles it reaches values around 20 %–50 %.
In the framework of a validation study the retrieval demonstrates
that it can well capture the global water vapour distribution:
the retrieved H2O vertical column
densities (VCDs) show very good agreement with the reference data sets over ocean for boreal summer and winter whereby the modified albedo map substantially improves the retrieval's consistency to the
reference data sets, in particular over tropical land masses. However, over land the retrieval underestimates the VCD by about 10 %, particularly
during summertime. Our investigations show that this underestimation
is likely caused by uncertainties within the surface albedo and
the cloud input data: low-level clouds cause an underestimation, but for mid- to high-level clouds good agreement is found.
In addition, our investigations indicate that these
biases can probably be further reduced by the use of improved
cloud input data. For the general purpose we recommend only using VCDs with cloud fraction <20% and AMF >0.1, which
represents a good compromise between spatial coverage and
retrieval accuracy.
The TCWV retrieval can be easily applied to further satellite
sensors (e.g. GOME-2 or OMI) for creating uniform, long-term measurement data sets, which is particularly interesting for climate and trend studies
of water vapour.
Introduction
Water vapour is the most important natural greenhouse gas in the atmosphere
and plays a key role in the atmospheric energy balance via radiative
effects and latent heat transport . Due to its high
spatiotemporal variability on all atmospheric scales, accurate knowledge of the
amount and distribution of water vapour is essential for numerical weather
prediction and climate monitoring.
Several in situ and remote sensing measurement techniques have been
developed in the past decades, enabling the observation of the water vapour distribution from platforms like radiosondes, balloons, aircrafts, and satellites. The particular absorption properties of water vapour
allow for the retrieval of the water vapour content via satellites for several different spectral ranges from the radio , microwave, e.g. AMSU , thermal infrared,
e.g. AIRS , near and shortwave infrared, e.g. MODIS , MERIS , and
TROPOMI , to the visible, e.g. GOME ,
SCIAMACHY , and GOME-2 .
The visible spectral range is particularly interesting for the
retrieval of total column water vapour (TCWV): in contrast to
the microwave range it has a similar sensitivity for the ocean and land surface, allowing for global coverage. Also, it is possible to conduct retrievals
under partly-cloudy conditions and, in comparison to the thermal infrared, it has a much higher sensitivity for the near-surface layers. Furthermore, the
spectral analysis is straightforward; i.e. no forward model calculations are necessary.
So far TCWV has been retrieved mostly in the visible “red” spectral
range because the absorption is strongest there. However, for this
spectral range the ocean surface albedo is relatively low, leading to a low
sensitivity for the lowermost troposphere, where the highest water vapour
concentrations occur. In addition, current and past satellite sensors can not
resolve the fine absorption structure of water vapour in this spectral range, causing non-linear absorption effects (e.g. saturation) which have to be
accounted for in post-processing. Thus, suggested applying retrievals in the “blue” spectral range (around 442 nm) where
the absorption is much weaker than in the red, making the retrieval problem quasi-linear. In addition, the ocean surface albedo is much higher, leading
to a higher sensitivity of the near-surface layers. The first operational analyses of a similar approach have been performed by
for measurements of the Ozone Monitoring Instrument
(OMI, ).
In October 2017 the TROPOspheric Monitoring
Instrument (TROPOMI, ) onboard ESA's
Sentinel-5 Precursor (S-5P) satellite was launched in a Sun-synchronous polar orbit with an Equator crossing time of 13:30 LT (local time). TROPOMI is a UV-Vis-NIR push-broom spectrometer and consists of 450 detectors/rows
covering a swath width of 2600 km. The outstanding property of TROPOMI is
that its spectral bands in the visible combine a high signal-to-noise ratio with an unprecedented spatial resolution of 3.5×7.5 km2
(and 3.5×5.6 km2 since August
2019; ) at nadir, which allows for the performance of spectral analyses at a never seen before accuracy even on small spatial scales.
In this paper we introduce a TCWV retrieval based on the spectral analysis
approach of to S-5P/TROPOMI observations.
The paper is organized as follows: in Sect.
we give an overview of the retrieval describing general retrieval
principles and presenting the retrieval setup. In Sect. we present an empirical parameterization of the a priori water vapour
profile shape and an iterative scheme making use of the relation between
the water vapour profile shape and TCWV. In Sect. we evaluate
different input albedo products and in Sect. we perform a
detailed uncertainty analysis including a variety of different error sources.
In Sect. we present first TCWV results retrieved from TROPOMI measurements and perform a validation study using data sets from satellites, ground-based measurements, and reanalysis models as reference. In Sect.
we draw conclusions and summarize the outcomes of our investigations.
Retrieval principlesWavelength calibration and spectral analysis
In a first step the wavelength alignment of the daily measured irradiance
is calibrated for each of the 450 TROPOMI detectors/rows via a non-linear least-squares fit in intensity space using the solar spectrum
from as reference. Simultaneously, the instrumental spectral response function (ISRF) is approximated assuming an asymmetric
Super-Gaussian following the definition of :
Sasym(x)=exp-xw-awkfor x≤0,exp-xw+awkfor x>0.
Next, we perform a spectral analysis using the differential optical absorption
spectroscopy (DOAS; ) scheme in which
the attenuation along the light path is calculated via the Beer–Lambert law in optical depth space:
lnII0=τ≈-∑iσi(λ)⋅SCDi+Φ,
where i denotes the index of a trace gas of interest, σi(λ)
its respective absorption cross section, SCDi=∫scids its
concentration integrated along the light path s (the so-called slant column density), and Φ a closure polynomial accounting for
Mie and Rayleigh scattering as well as low-frequency contributions.
Table summarizes the fit setup of the
retrieval's spectral analysis. The retrieval's fit window ranges
from 430 to 450 nm and accounts for molecular absorption by water vapour (HITRAN 2008, ),
NO2 at 220 K ,
ozone , and the O2–O2 dimer . In order to account for the Ring effect we include two Ring spectra , and for Φ we use a fifth-order polynomial. Furthermore, we include
pseudo-absorbers accounting for intensity offset, for shift and
stretch effects , and for ISRF changes along the orbit for ISRF parameters w and k
in Eq. (). All molecular absorption cross sections are
convolved with the ISRF of the corresponding TROPOMI row/detector
determined during the calibration process.
DOAS fit settings for the H2O slant column retrievals.
ParameterDescriptionFit window430–450 nmAbsorption crossWater vapour, 296 K sectionsNO2, 220 K O3, 243 K O4, 293 K Ring effectTwo Ring spectra calculated from dailyirradiancePolynomial5th orderPseudo-absorbersintensity offset (inverse spectrum)shift and stretch ISRF parameter changes
The molecular absorption by water vapour within our fit window is relatively
weak, and hence the modelled line lists vary systematically from HITRAN 2008 to HITRAN 2012 and
to HITRAN 2016 . Thus,
the choice of line list is afflicted by a high degree
of uncertainty. found out that HITRAN 2012 underestimates
the water vapour concentration derived from long-path DOAS observations by approximately 10 % and that the previous version, HITRAN 2008, agrees better
with the reference measurements. Further long-path DOAS measurements taken during the CINDI-2 campaign also confirm the findings from (see Appendix for more details).
Hence, combining the findings from and , we conclude that HITRAN 2008 fits best our needs and is superior to the most recent
version of the HITRAN line lists (HITRAN 2016).
Due to the high daily data volume of the TROPOMI L1B radiances, the execution of a non-linear fit without high-performance infrastructure
is demanding in computation time. For instance, TROPOMI's UVIS Band 4, which covers the spectral range of 400–499 nm, generates about 40 GB every day. Therefore, we implemented a weighted linear least-squares fit for our retrieval, in which the weights are the fractional coverage of the
spectral pixel within the fit window (details in Appendix ).
This weighting of the outermost pixels of the fit window avoids “jumps”
of pixels included in the DOAS fit, as they would occur for a fixed fit window due to the changing pixel-to-wavelength mapping across-track. Thus, across-track “stripes” in the SCDs are avoided. According to
the computational speed increases by 3 orders of magnitude by going from
non-linear to linear fits for their MATLAB routine (see Table 3 in their paper).
Example of a typical spectral analysis of a
TROPOMI measurement spectrum (rms: 0.5 ‰, orbit: 6930, -7.41∘ N, -111.97∘ E). The black line indicates the fit result
for the respective trace gas and the red line indicates the residual
spectrum and residual noise for each constituent.
Figure illustrates a typical example of
such a spectral analysis of a TROPOMI measurement spectrum in which the
absorption structures of water vapour, NO2, and the Ring effect can be well identified and the residual spectrum shows a mainly noisy structure. Figure depicts the distribution of the H2O SCD
from one TROPOMI orbit (orbit number 6930) on 13 February 2019. It
demonstrates that the TROPOMI retrieval is able to capture the meso-
to macro-scale water vapour patterns like convective updrafts in the tropics and
atmospheric rivers in the midlatitudes, whereby the small H2O SCD values
in the tropics are caused by cloud shielding.
H2O SCD distribution retrieved from
TROPOMI measurements (orbit: 6930) on 13 February 2019 during an atmospheric river event at the western US coast.
Vertical column
density conversion and Box-AMF simulations
To convert the slant column density to a vertical column
density (VCD), we apply the so-called air-mass factor (AMF):
VCD=SCDAMF.
The air-mass factor accounts for the non-trivial effects of the atmospheric radiative transfer and is usually based on radiative transfer
model (RTM) simulations. In our case we used the 3D Monte Carlo RTM McArtim and performed simulations at
a wavelength of 442 nm for different retrieval scenarios (summarized
in Table ) assuming an aerosol-free atmosphere. These
simulations yield a Jacobian vector J=∂lnI∂μ
(with the absorption coefficient μ and the simulated intensity I at TOA normalized by the solar spectrum I0) defined at each grid box k. The altitude-dependent AMFs (BAMF) can then be calculated according to the formula
BAMFk=-JkIΔh,
with the box thickness Δh. These BAMF profiles have to be
combined with the partial vertical columns ck of an a priori
water vapour profile:
AMF=∑kBAMFk⋅ck∑kck,
with ∑kck=VCD. For the case of a cloud-contaminated pixel we assume that the cloud is a Lambertian reflector with an
albedo of 80 % and use the cloud top height as surface altitude
input for the AMF. Under the assumption of the independent pixel
approximation, the resulting cloud-affected AMF can then be calculated as a linear combination of the AMF for a clear-sky
scenario and the AMF for a cloudy-sky scenario weighted by the respective
simulated intensities I and the effective cloud fractions ζ as follows:
AMF=1-ζIclearAMFclear+ζ⋅IcloudAMFcloud1-ζIclear+ζ⋅Icloud.
Figure depicts typical examples of BAMF profiles
for different clear- and cloudy-sky scenarios. The AMFs for the
cloudy-sky scenarios were calculated assuming a surface albedo
of 7 % and an effective cloud fraction of 20 %. For the clear-sky
scenario (panel a) the sensitivity decreases towards the surface. For the cloudy-sky scenarios (panel b) the BAMF
profiles slightly increase towards the (bright) cloud top surface
of the respective scenario. Below the cloud, the sensitivity is 0,
because the atmosphere is shielded. Since high clouds shield large
fractions of the atmosphere and hence also of the water vapour
column below the cloud (see the black dashed curve), the AMF has to be corrected correspondingly and thus decreases for increasing
cloud top heights.
Parameter list and nodes for the BAMF profile simulations.
Examples of typical BAMF profiles for
different observation scenarios under clear- (a) and cloudy-sky (b) conditions. For all profiles we assume a solar zenith
angle of 0∘, a line-of-sight angle of -90∘, and a solar relative azimuth angle of 0∘. For the clear-sky
case the BAMF profile is illustrated for a surface
albedo of 7 %. For the cloudy-sky cases the profiles are depicted as cloud top heights of 2 and 8 km and the respective
AMFs are calculated assuming a surface albedo of 7 % and an
effective cloud fraction of 20 %. The black dashed lines indicate
relative water vapour concentrations with a scale height of 2 km.
A priori water vapour profile shape
As described in Sect. and Eq. (),
knowledge of the a priori water vapour profile shape is necessary for
accurate calculations of the AMF from the BAMF profile. However, simply assuming the same a priori profile shape for the whole globe might cause biases because it
can not account for the atmospheric variability of water vapour, such as
latitudinal variation, seasonal cycles, or different profile shapes over maritime
and continental regions due to different water vapour sources (e.g.
evapotranspiration by plants). Also, simply using profiles from numerical weather
models is not uncritical: for instance, found out that their calculated AMF changes strongly, depending on which reanalysis model
data they were using.
approximated the water vapour profile
by an exponential decay with altitude:
nv(z)=n0e-z/Hv,
where Hv is the scale height of water vapour, which they defined as
Hv=RvT2LΓ,
where T denotes the mean air temperature
within an atmospheric column, Γ the
mean lapse rate within the same atmospheric column, Rv the gas
constant of water vapour, and L the specific latent heat.
However, this definition requires knowledge of the mean air temperature and/or
the lapse rate and that the relative humidity is constant with altitude.
The former can be only estimated using numerical weather models and
the latter is very unlikely to occur in the atmosphere.
Thus, we investigate to find an empirical parameterization of the scale
height and thereby focus on its dependency on the H2O VCD and
the aforementioned atmospheric variabilities, i.e. dependencies of
latitude, seasonal cycle, and surface properties (such as vegetation effects).
We proceed as follows: first, we evaluate how well the method used to
calculate the water vapour scale height can reproduce the COSMIC profiles
via an AMF comparison. Then we examine how the scale height can be
parameterized globally and investigate for a parameterization over
ocean and land separately. Finally, we implement the parameterization in an iterative retrieval scheme and evaluate the new estimates of
the H2O VCD.
COSMIC water vapour profiles
For our investigations we use profile data retrieved from measurements of the
Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC,
) program provided by the Radio Occultation Meteorology
Satellite Application Facility (ROMSAF). The COSMIC data are
based on the GPS radio occultation (RO) technique, which provides high-resolution vertical profiles of bending angles that can be used to
retrieve the atmospheric refractivity. Since the atmospheric
refractivity is dependent on the air pressure,
the air temperature, and the water vapour pressure , GPS RO allows for the retrieval of profile information under
all-weather conditions with a high vertical resolution of
approximately 100 m in the lower troposphere up to 1 km in the stratosphere and an accuracy of
around 1 g kg-1 while having an
almost uniform global distribution .
The ROMSAF profiles have been retrieved via a 1D-VAR scheme within a reprocessing initiative for creating climate data record (CDR) v1.0. Given the strict product requirements and the validation studies with ERA-Interim and radiosondes , biases associated with using COSMIC should be of secondary order.
We use data retrieved between 2013 and 2016, which accumulates to
approximately 1.6×106 profiles.
Calculation of scale height
For the calculation of the scale height we high-sample the COSMIC profile to a 100 m grid up to 14 km, or rather only consider profile data below 150 hPa (close to the tropopause height). Then we sum up all the
partial columns of the COSMIC profile data from the ground up to a (scale) height Hsum where the H2O VCD reaches 1-1e:
∫0Hsumn(z)dz∫0TOAn(z)dz>1-1e≈63%.
To evaluate this scale height approach, we performed a synthetic study
in which we compared AMFs calculated for the original COSMIC water
vapour profile measurements with AMFs for an exponential profile using the
corresponding calculated scale height Hsum. For the simulation of
the BAMF profiles we assume an albedo of 7 %, which is a representative value for the ocean surface albedo . The
solar zenith angle is calculated for the location of the COSMIC
profile assuming an hour angle of 90∘, and the line-of-sight angles are prescribed for -90, -70, and -50∘.
2D histograms comparing synthetic
AMFs (calculated via the sum method) for different line-of-sight angles (a: -90∘, b: -70∘, and c: -50∘) assuming clear-sky conditions. The colour depicts the number of observations within one defined bin of the 2D histogram and the red dashed line represents the 1-to-1 diagonal.
Histogram of the relative deviation
of the calculated synthetic AMFs between the exponential profile and COSMIC profile for selected latitude bins (0 to 10, -30 to -20, and -70 to -60∘ N) assuming clear-sky conditions and nadir-viewing geometry.
The results of the intercomparison are given in
Fig. . The 2D histograms reveal that the AMFs
derived with the exponential profile agree well with the AMFs calculated
directly from the COSMIC profiles, indicating that the chosen method can well reproduce the shapes of the COSMIC profiles. This good agreement can also be
observed in the histograms of Fig. , which illustrate distributions of relative deviation between the AMFs for selected latitude bins. These distributions have a sharp shape and peak around values of 0 %, indicating that the AMFs from the exponential shape are almost unbiased to the reference AMFs.
In addition, Fig. S1 in the Supplement
shows exemplary profiles for cases of good and bad agreement with the reference AMFs for the same selected latitude
bins as in Fig. . In general,
bad agreement (left column) occurs for profile shapes in
which a sharp gradient is observed in the
lower troposphere and from that quasi-constant values with
altitude. Such profiles usually occur when a moist boundary
layer is topped by a dry free atmosphere.
Nevertheless, the maximal absolute relative AMF deviations only have values around 15 %. In contrast, good agreement (right column) is found for profile shapes following an exponential decay with
altitude, which indicates a well-mixed troposphere.
The results of the intercomparison for prescribed cloudy-sky conditions
and nadir-viewing geometry are illustrated in Fig. S2, in which the panels show histograms of the relative AMF deviation
for the same selected latitude bins as in
Fig. but for different cloud fraction (10 %, 20 % and 50 %; left to right column) and cloud
top height (1, 2, and 5 km; top to bottom rows) scenarios. For a cloud top height of 1 km the AMFs calculated from the exponential profiles are generally biased negative for all cloud
fractions, in particular for the latitude bin of -30 to -20∘ N.
However, for higher clouds the AMFs agree well with the reference AMFs for almost
all cloud scenarios except the extreme case with a cloud fraction of 50 % and a
cloud top height of 5 km or more.
Alternative methods for calculating the scale height yielded systematic
overestimations of the AMF for clear-sky conditions
(Fig. ) and higher scatter within the
AMF for cloudy-sky conditions (Fig. S8)
in comparison to the sum method, as shown in detail
in Appendix .
Parameterization of scale height
Figure depicts the distribution of the calculated
COSMIC scale height Hsum against the COSMIC TCWV for boreal summer
over ocean for latitude bins of 10∘. The regression fits (solid red lines) are based on orthogonal distance regression (ODR)
using the “scipy.odr” package built on ODRPACK .
For low latitudes (tropics and subtropics) the scale height shows a
high linear correlation with the H2O VCD, with slopes around 0.04 and Pearson correlation coefficients R of 70 % and above.
In contrast, for high latitudes the slope increases up to 0.1, and the scatter also increases distinctively; i.e. the correlation coefficient only reaches values of around 0.3 in the polar regions. This decrease in
linear agreement is likely caused by the higher atmospheric variability due to
higher atmospheric dynamics in the midlatitudes. Also, the uncertainty is higher
in the COSMIC profile because a drier atmosphere leads to a smaller sensitivity of the COSMIC profile retrieval to water vapour concentrations
(compare ).
2D histograms depicting the relation between
calculated scale height and TCWV from COSMIC profiles for boreal summer
(June, July, and August) only over ocean summarized in 10∘ latitude bins. Only latitude bins with a sample size of 1500 data points are illustrated. The colour indicates the relative share of total points within one bin of the histogram and the red line indicates the fit
results of the orthogonal distance regression with detailed results
in the legend of each subplot. In addition the Pearson correlation
coefficient for each data set is given in the title of each subplot.
Same as Fig. but for data over land.
Figure illustrates the same panels
as Fig. but for data over land. In
general, the scatter for all latitude bins has increased distinctively, resulting in an inferior linear agreement between the H2O VCD and
the scale height compared to the data over ocean, especially for deserts and northern polar regions. Fortunately, the surface albedo
of these regions is usually high, and thus the AMF is less dependent on the a priori profile shape. In addition, these regions are governed by an
arid climate, and thus the retrieved H2O VCDs are expected to be small. Correspondingly, the absolute H2O VCD errors due to
uncertainties in the AMF are still relatively small.
In the following we investigate a parameterization of the scale height
with respect to H2O VCD, latitude, and season for ocean and land separately. To distinguish between ocean and land surface, we use a land–sea mask derived from GSHHS coastline data .
Summary of the results of the ODR
fit between COSMIC scale height and COSMIC TCWV as a function of latitude and month
for data over ocean. Panel (a) illustrates the fitted slopes and panel (b) the corresponding fitted intercepts whereby the coloured points
represent the fit results and the lines represent the approximations
for α(θ,t) and β(θ,t) for each month.
Ocean
The regression line parameters of the ODR fit results between COSMIC TCWV and
COSMIC scale height for each latitude bin for each month for data over ocean are illustrated in Fig. . The values for the
fitted slopes (Fig. a) indicate a quadratic dependency with latitude and reveal a seasonal shift towards higher
latitudes during July, August, and September. Also, the values for the fitted intercept vary with latitude and season.
Thus, the scale height over ocean Hocean can be approximated as follows:
Hocean(VCD,θ,t)=α(θ,t)⋅VCD+β(θ,t),
with
α(θ,t)=a0(t)+a1(t)⋅θ+a2(t)⋅θ2,β(θ,t)=b0(t)+b1(t)⋅θ+b2(t)⋅θ-θ0(t),
with the latitude θ and the day of year t. The annual variation
of the function parameters ai, bi, and θ0 from Eq. () fitted for the monthly data sets
(illustrated in Fig. ) is depicted
in Fig. S9.
Most function parameters reveal an
annual and semi-annual cycle over the year. Hence, these function
parameters can be approximated by a superposition of two simple
cosine functions with prescribed frequencies:
ai(t)=ai1⋅cosai2+ωt+ai3⋅cosai4+2ωt+ai5,
with t as the day of year and ω=2π365. Such functions have
also been fitted and
illustrated for the monthly data in Fig. S9
(solid orange lines), whereby we assumed that the day of year representing the month is the first day of the month. For most function parameters
the fits coincide well with the data points, and in the cases of suboptimal fit results the annual variation of the data is
relatively small, indicating that our choice of parameterization
is valid.
2D histograms of the distribution
between the parameterized scale height and the COSMIC scale height over ocean for selected global latitude zones.
Altogether, we have to fit 35 parameters to the complete data set of calculated
COSMIC scale heights for the parameterization of the scale height over ocean. The goodness of the parameterization in approximating the scale height is
illustrated in Fig. for different latitude
zones. For the latitude zones including the tropics (-15
to 15∘ N) and subtropics (-35 to 35∘ N) we find
a good agreement between the parameterization and the calculated
COSMIC scale height, with R2 of 0.72 and 0.60 respectively. However, including
higher latitudes in the evaluation, i.e. midlatitudes (-60 to
60∘ N) and polar regions (-90 to 90∘ N), leads to
an increased scatter and a worsening of the parameterization (R2 of
0.45 and 0.44 respectively). This inferior agreement is likely
caused by the larger atmospheric variability in the midlatitudes (e.g. higher
atmospheric dynamics) as well as an increased uncertainty in the COSMIC water
vapour profile measurements due to lower water vapour concentrations.
Land
Figure already revealed much larger scatter in
the distribution of COSMIC TCWV and COSMIC scale height for data over land,
indicating that the water vapour profile shape over land surface is less homogeneous than over ocean, likely due to further heterogeneously distributed water vapour sources, such as evapotranspiration by plants and soil.
Thus, the H2O VCD and scale height are likely to be dependent
on the amount of vegetation; i.e. high vegetation is associated with high evapotranspiration and high water vapour concentrations near the ground, and thus the scale height should be close to the scale height over
ocean. In contrast, low amounts of vegetation are associated with less
evapotranspiration and a usually drier atmosphere, indicating that the scale height should be higher than over ocean.
To quantify the amount of vegetation, we use the Normalized Difference Vegetation Index (NDVI), where a value of 1.0 indicates high vegetation and a value around 0.0 indicates low vegetation.
As data source for the NDVI, we use data within the MODIS Aqua MYDC13C2 Version 6 product and continue as follows: first, we calculate the parameterized scale height Hocean assuming an ocean surface globally. Then
we calculate the ratio of the calculated COSMIC scale height over land Hland
and the parameterized scale height Hocean.
2D histograms of the distribution between
the ratio Hland/Hocean against the NDVI for different
filtered data sets: panel (a) includes all data points, panel (b) includes all points except those with MODIS landcover
type 15 (corresponding to deserts), and panel (c)
includes all points except landcover types 7 (corresponding to open
shrublands) and 15. The red solid line represents the fit result using
the Siegel algorithm with details of the fit results in the legends
of each panel.
Figure shows the ratio Hland/Hocean as a
function of the NDVI for data sets filtered by different landcover types
and the solid red lines represent the robust regression results (summarized
in Table ) using the model from .
Panel (a) depicts the distribution for which no filter is applied. Except for low NDVI values, a linear relation between the ratio and NDVI is observable; however, for NDVI values around 0.1 the ratio varies strongly,
between 0.7 and 3.0. In the centre panel we use the landcover classification from the MODIS Aqua MCD12C1 Version 6 product
to filter measurements for locations classified as
landcover type 15 (corresponding to a desert). With this filter the ratio now
only varies between 0.7 and 1.5, with a weak dependence on the NDVI. If we further filter locations of landcover type 7 (corresponding to open
shrublands), the fit results of the robust regression change only slightly
compared to the first filtered data set.
Fit results of the robust regression between the ratio of scale heights Hland/Hsum and the NDVI for different filtered data sets.
Data setslopeinterceptAll data-0.471.35No landcover type 15-0.381.28No landcover type 7 & 15-0.331.25
Hence the scale height over land Hland can be approximated as the scale
height over ocean Hocean multiplied by a first-order polynomial of the NDVI:
Hland=Hocean(VCD,θ,t)⋅γland+δland⋅NDVI,
whereby in the following we use the results for the data set filtered for
landcover types 7 and 15 globally. Since regions of landcover types 7 or 15 are usually arid, the retrieved H2O VCD is small, and thus the error due to an inadequate parameterization of the AMF is much smaller than the fit error of the
spectral analysis.
Iterative retrieval scheme
For the calculation of the H2O VCD we precomputed AMF look-up
tables (LUTs) for the different water vapour profile shapes with scale heights ranging from 0.5 to 5.0 km. These LUTs can then be used within a fixed-point iteration. In our case the iterative
retrieval scheme is based on a fixed-point iteration according to
Steffensen's method :
VCDi+1=VCDi-f(VCDi)-VCDi2ff(VCDi)-2⋅f(VCDi)+VCDi,
where f is a function calculating the scale height for a given VCD using Eqs. () and (), applying it to the precomputed AMF
look-up tables and from that returning a new VCD. The advantage of Steffensen's
method is that it does not need a derivative and is able to determine
the fixed point even for the case of a non-contractive function . For the first guess we derived the initial
VCD from the SCD using a geometric
AMF AMFgeo=1cos(SZA)+1cos(VZA)
and stop the iteration as soon as the logarithmic difference
between two consecutive results is smaller than 5 % (approximately
1 kg m-2 assuming an average H2O VCD of 20 kg m-2)
or after six iteration steps. We also checked other values
for the first guess and could confirm that the convergence of the iterative
scheme is independent of them.
Comparison of the H2O VCD calculated
using a global constant a priori profile shape of 2 km (a) and the iterative scale height method (b) for all-sky conditions. Panel (c) illustrates the water vapour scale height estimated within the retrieval's VCD conversion. All panels show an atmospheric river hitting the eastern Pacific/western US coast on 13 February 2019. Invalid pixels are coloured grey.
Figure illustrates a comparison of H2O VCD
distributions for the cases of using a global constant a priori water
vapour profile shape (panel a) with a scale height of 2 km (in accordance with ) and using the iterative
scale height approach (centre panel) for all-sky conditions (i.e. no cloud filter applied) during an atmospheric
river event at the western coast of the US on 13 February 2019. Figure c depicts the distribution of the water vapour scale height yielded during the iterative VCD conversion. The water vapour scale height
varies a lot along the orbit and differs
distinctively from 2 km, causing large deviations between the two
approaches, particularly at pixels with high TCWV values and for clouded
pixels. However, in contrast to the approach with a constant scale height, the iterative approach is still able to give reasonable
TCWV results and does not exceed values higher than 80 kg m-2.
Comparison of the H2O VCD
calculated using a global constant a priori profile shape of 2 km
(first from left), ERA-5 profiles (second from left), and the
iterative scale height method (third from left) for clear-sky
(effective cloud fraction <20 %; top row) and cloudy-sky conditions
(effective cloud fraction ≤100 %; bottom row) with TCWV from
SSMIS f16 (right) for the same scenery as in Fig. . Invalid pixels are coloured grey. The solid black lines indicate the edges
of the TROPOMI swath.
Figure illustrates the H2O VCD
distributions from calculations using constant, ERA-5, and iterative profile shapes for the same scenario for clear-sky (effective
cloud fraction CF<20 %, top row) and all-sky
(CF≤100 %, bottom row) conditions.
For ERA-5 we used the data provided by on an hourly
0.25∘×0.25∘ grid and interpolated
the model profile data to the TROPOMI pixel centre coordinates. In addition to the TROPOMI H2O VCDs,
Fig. also depicts the TCWV distribution
from microwave sensor SSMIS f16, which has a temporal difference of around +2.3 h.
For the clear-sky case (top row) the VCD distributions between all profile
approaches are almost identical, whereby for the constant scale height approach (first panel from the left) very high VCDs
(exceeding values higher than 80 kg m-2)
can be observed at the edges of the cloudy regions in the
northern subtropics. For the all-sky case (bottom row) the differences between all approaches are largest in cloudy
regions: for instance, in the region of the atmospheric river, the VCDs from the constant and ERA-5 profiles distinctively overestimate the VCD
and exceed values higher than 80 kg m-2. In contrast,
even under these unfavourable observation conditions the
iterative approach is still able to give reasonable VCD values.
Furthermore, the iterative approach shows an overall good
agreement with the SSMIS observations.
Mean normalized Box-VCD profiles of ERA-5 and the iterative scale height approach for cases of distinctive VCD disagreement within the region of the atmospheric river. Panel (a) illustrates the mean of the selected profiles from the ground up to 15 km and panel (b) the mean of the same profiles, but from the cloud top up to 6 km above the cloud top. The solid lines indicate the mean profiles and the shaded areas the corresponding 1σ standard deviation.
Taking a closer a look at the reasons for the deviations of
the results retrieved for the ERA-5 profiles,
Fig. depicts the mean of the normalized water
vapour profiles of ERA-5 and the iterative scale height approach for the AR region
(around 30∘ N). Figure a shows the water vapour profile from the ground up to 15 km. In comparison to the iterative approach, ERA-5 is much drier above
approximately 2.5 km for these particular cases, indicating
that ERA-5 might systematically
underestimate the water vapour content above the cloud within
the region of the atmospheric river.
This finding is further supported by Fig. b, which illustrates the normalized water vapour profiles above the cloud top: ERA-5 profiles are close to 0 and show only small variations, whereas the profiles of the
iterative approach indicate higher water vapour concentrations
along with a much higher variability. One potential reason for the
discrepancies of ERA-5 could be the missing observational input data for the reanalysis: without observations,
the reanalysis model is dominated by its a priori information (e.g. a
climatological mean), so that it can be systematically
distorted from the real atmosphere. However, further
investigations of possible ERA-5 biases are beyond the scope of this paper.
Evaluation of different surface albedo input data
The surface albedo has a strong impact on the radiative transfer and
thus also on the AMF. Hence we investigated the impact of different albedo
products on the TCWV retrieval: the OMI monthly (a) mean
and (b) minimum Lambertian equivalent reflectance (LER)
at 442 nm from and (c) MODIS
Aqua blue surface reflectance from the MODIS MYD13C2 Version
6 product . The MODIS reflectance covers a
broad spectral window from 459 to 479 nm. Thus, to account for the different spectral windows of the albedo products, we scale
the MODIS albedo by factor of 0.9. This factor was estimated by
calculating the ratio between 472 and 442 nm of the OMI yearly minimum LER over parts of Australia where cloud contamination is
generally low and hence the OMI LER has reasonably accurate values.
Comparison of the effect of different
land albedo input data on the mean H2O VCD for boreal summer
2018 (a: OMI monthly mean LER, b: OMI monthly minimum
LER, c: scaled MODIS Aqua blue surface reflectance). Only
pixels with an effective cloud fraction smaller than 20 % are included.
Figure illustrates the global mean H2O
VCD of boreal summer 2018 for the different albedo input data over
land (top row: monthly mean OMI LER, middle row: monthly minimum OMI
LER, bottom row: scaled monthly MODIS Aqua blue surface reflectance).
In the tropical and subtropical regions the OMI albedos cause a distinctive
separation of the VCDs between land and ocean, in particular at the
coasts of South America, Africa, and Indonesia. These aforementioned regions are often affected by cloud cover, which might
cause the OMI albedo statistics to be unable to filter cloudy cases correctly, so that cloud-contaminated observations are used within the albedo
calculations. As a consequence, the values in the OMI albedo are too high
and lead to an overestimation of the AMF, which in turn causes an underestimation of the H2O VCD.
In contrast, MODIS pixels have a much higher spatial
resolution and MODIS' NIR channels are more sensitive to cloud contamination, yielding a higher sample size and allowing for correct cloud filtering. Hence,
the H2O VCD distribution using the MODIS surface reflectance
results in a much smoother transition from ocean to land and in general much higher VCD values over land along the Equator. Thus, in the following we use a combination of the MODIS and OMI albedos:
the scaled MODIS Aqua blue surface reflectance over land and the monthly
minimum OMI albedo over ocean.
Uncertainty estimation
The error budget of the H2O VCD is determined by the propagation of the
main error sources of the fitted SCD and the precalculated AMF. Errors in the SCD
are mainly caused by random errors, like the photon noise, and systematic errors, e.g. the uncertainty of the absorption cross section, whereas errors in the AMF are mostly systematic with random contributions.
Uncertainties in the slant column density
Table summarizes the different error sources for the
H2O SCD and the corresponding estimated uncertainties. As demonstrated in
Sect. and Appendix
the water vapour absorption cross section varies systematically
between the different HITRAN versions. Hence, we assumed that the
uncertainty of the water vapour cross section is of the same order
of magnitude as the changes between the different cross-section versions, i.e. approximately around 10 %. Considering the LP-DOAS comparisons
(see Sect. and Appendix )
we estimate these errors to be around 5 % for this study.
Summary of the different error sources considered in the H2O SCD uncertainty.
Histograms of the standard H2O SCD fit
error distribution for small (SZA<20∘, a, c) and large
(70∘<SZA≤90∘, b, d) solar zenith angles
for relatively small (<3 %, orange) and high (>15 %, blue) surface albedo
values for clear-sky (cloud fraction <5 %, a, b) and cloudy-sky
(cloud fraction >20 %, c, d) conditions. The coloured dashed
lines represent the median of the respective distributions and
their values are given in the legend of each panel.
The retrieval's spectral analysis directly yields the 1σ standard
fit error of the H2O SCD, which is usually dominated by noise. For a better understanding of these fit errors, we separated
them into data for small/large solar zenith angles (SZA<20∘ and
70∘<SZA≤90∘ respectively), low/high surface albedo (<3 % and >15 % respectively), and clear-/cloudy-sky observation
conditions (CF<5 % and CF>20 % respectively). The distributions of the standard and relative fit errors of the spectral analysis are given in
Figs. and respectively. The median values in Fig.
indicate that the standard errors for high SZA
(around 0.3×1023 molec cm-2) are
twice as high as for small SZA (around 0.15×1023 molec cm-2).
Under clear-sky conditions the standard error for small surface
albedo values is larger than for high surface albedo, but for cloudy
conditions it does not depend on the surface albedo.
Histograms of the relative H2O SCD fit
error distribution for small (SZA<20∘, a, c) and large (70∘<SZA≤90∘, b, d) solar zenith angles for relatively small (<3 %, orange) and high (>15 %, blue) surface albedo values for clear-sky (cloud fraction <5 %, a, b) and cloudy-sky (cloud fraction >20 %, c, d) conditions. The coloured dashed
lines represent the median of the respective distributions and
the solid lines represent the location of maximal probability density
(values given in the legend of each panel).
Figure reveals that the relative fit errors for
high SZAs are higher than for low SZAs. However, the locations of maximal probability density and the medians also indicate that the distributions
are right-skewed, in particular for high SZA scenarios: for these scenarios the relative errors easily exceed values of 100 %. Nevertheless, using the
locations of maximal probability density as a rule-of-thumb
estimate, relative fit errors have values around 10 % for low SZAs
and approximately 30 % for high SZAs.
To estimate errors associated with ISRF biases, we calculated
the H2O SCD using a Gaussian ISRF (instead of an asymmetric Super-Gaussian) for orbit 6930 and compared them to the SCDs from
the “standard” retrieval setup for SZA<88∘. The comparison depicted in Fig. S3 reveals that the SCDs using
the Gaussian ISRF highly correlate with the “standard” SCDs and
only differ by approximately 1 %. Considering the much higher
fit errors, errors due to biases in the ISRF are negligible.
Uncertainties in the AMF
The uncertainty in the AMF depends on the uncertainty of its input parameters. Because the parameters of the viewing geometry (i.e. solar zenith angle, line-of-sight angle, and solar relative azimuth angle) are known with high accuracy, the most important uncertainties are uncertainties of the surface albedo, cloud fraction, cloud top height, and water vapour profile shape. In order to estimate the contribution of each input parameter to the overall AMF uncertainty, we define standard scenarios (summarized in Table ) for which we calculate the AMF from the precalculated LUT. Then we vary the input
parameter for each scenario according to its uncertainty assumption listed in
Table . The uncertainties of the water vapour scale height
have been derived from the fit results of the intercomparisons
between the measured COSMIC scale height and the parameterized scale
height over ocean (see Fig. ) and land (see Fig. ).
Standard retrieval scenarios for the estimation of AMF error.
Figure depicts box–whisker plots of the relative AMF error due to uncertainties in surface albedo and scale height for the standard clear-sky scenarios of surface albedo, solar zenith angle, and scale height. It reveals that uncertainties in surface albedo and scale height over low vegetation have the strongest impact on the AMF and can cause AMF errors larger than 30 %, in particular for scenarios with low surface albedo or high solar zenith angle. On average the median values of the AMF errors typically vary around
approximately 10 %.
Box–whisker plots of the relative AMF errors for clear-sky conditions due to uncertainties within the retrieval's input parameters (blue: surface albedo, orange: scale height over high vegetation, green: scale height over low vegetation, red: scale height over ocean) according to the uncertainty assumptions in Table and simulated for the standard scenarios of the surface albedo, solar zenith angle, and scale height given in Table .
Box–whisker plots of the relative AMF errors for cloudy-sky conditions due to uncertainties within the retrieval's input parameters according to the uncertainty assumptions in Table and simulated for the standard scenarios given in Table .
Figure illustrates box–whisker plots of the relative AMF error due to uncertainties in surface albedo, scale height, cloud fraction, and cloud top height for all standard scenarios listed in Table . In
contrast to the clear-sky scenarios, the impact of the surface albedo uncertainties has strongly decreased, but in general the contributions of all AMF errors have
increased distinctively. The main source of the AMF errors is still the uncertainty of the scale height over low vegetation, whose median
values vary between 20 % and 50 % but can also cause AMF errors larger than 60 %.
Table summarizes the results of the different error sources
considered in the AMF uncertainty for clear- and cloudy-sky conditions.
For clear-sky conditions one can typically assume a relative AMF error
around 10 %–15 % and for cloudy-sky conditions around 10 %–25 %.
Total H2O VCD uncertainty
The total relative H2O VCD uncertainty can be approximated by
ΔVCDVCD=ΔAMFAMF2+ΔSCDSCD2.
With our findings of typical relative AMF and H2O SCD uncertainties, the total relative VCD uncertainty is typically around 10 %–20 % for
observations during clear-sky conditions, over ocean surface, and at low solar zenith angles. During partly cloudy-sky conditions, over land surface, and at high solar zenith angles the error reaches values of
approximately 20 %–50 %.
Validation study
In order to evaluate the retrieval's performance, we conducted a validation study for the time ranges of boreal summer (June, July, and August)
2018 and boreal winter (December, January, and February) 2018/2019 whereby we only include clear-sky observations (i.e. pixels with an effective
cloud fraction smaller than 20 %) and ice- and snow-free pixels. To avoid extreme outliers, we only include observations with
an AMF>0.1. As reference data
for the validation we use TCWV from the Special
Sensor Microwave Imager/Sounder (SSMIS), from the reanalysis model ERA-5, and the ground-based GPS network SuomiNet.
For the sake of completeness, we also briefly investigate
higher cloud fractions at the end of each subsection
and provide the results in the Supplement.
As cloud input data we use the cloud information (effective cloud
fraction at 440 nm and cloud top height) as well as the surface
altitude from the TROPOMI L2 NO2 product and
as surface albedo input data we use the combination of the modified MODIS
and OMI albedo described in Sect. . To distinguish
between ocean and land surface, we use a land–sea mask derived from GSHHS coastline data , in which we use
the pixel centre coordinates for the separation into land and ocean. As the NDVI is not available over lakes, we treat them as ocean.
SSMIS comparison
For the evaluation we use measurements from SSMIS onboard NOAA's f16 and f17
satellites processed by Remote Sensing Systems (RSS) and provided by the NASA Global Hydrology Resource Center on a daily 0.25∘×0.25∘
grid. SSMIS can observe the TCWV distribution under all-sky conditions over
ocean with an accuracy of around 1 kg m-2. Since SSMIS changes its Equator crossing time (ECT), we only include SSMIS observations whose ECT is within 3 h (and 5 h for f17 respectively) with respect to TROPOMI's ECT of 13:30 LT. For the
intercomparison we only include SSMIS measurements that are not affected by rain.
2D histograms for the comparison between TROPOMI
and SSMIS f16 (a, b) and f17 (c, d) for clear-sky conditions (CF<20 %)
for boreal summer (a, c) and boreal winter (b, d), where the colour indicates the relative share of total data points. The black dotted line indicates the 1-to-1 diagonal and the red solid line represents the results of the linear regression. The parameters of the linear regression and the coefficient of determination are given in the box in each
panel.
Figure depicts the comparison between SSMIS (f16, top row, and f17, bottom row) and TROPOMI for boreal summer (left column) and winter
(right column). For f16 (top row) the scatter is distributed closely along the
1-to-1 diagonal (dashed lines) for both seasons and the fitted regression lines
(red solid lines) indicate a very good agreement between both data, with slopes around 0.96, intercepts around
-1.6 kg m-2 for summer and -1.7 kg m-2 for winter, and coefficients of determination of R2=0.91. For f17 the comparison
reveals similar agreement, with slopes around 0.97 and intercepts around -1.5 kg m-2 with R2=0.89 for both
seasons. Overall, considering the differences in collocation time (3 and 5 h for f16 and f17 respectively), the comparison shows that the TROPOMI TCWV retrieval can well capture the water vapour distribution over ocean.
2D histograms of the difference (TROPOMI - SSMIS
f16, a, b) and relative difference (TROPOMI-f16)/f16(c, d) as a function of the input cloud top height (CTH) for
clear-sky conditions (CF<20 %) for summer (a, c) and winter (b, d).
The blue dashed line represents the median over the whole CTH range.
The blue dots represent the median within a 1 km CTH and the
error bars represent their respective 1σ standard deviation.
Same as Fig. but for SSMIS f17.
To investigate the influence of clouds on our retrieval, we plot
the difference (top row) and relative difference (bottom
row) between TROPOMI and SSMIS as a function of the input cloud top
height (CTH) in Figs. and
for f16 and f17 respectively. The median over the whole CTH range (blue dashed line) indicates an
underestimation of the TROPOMI H2O VCD of approximately 12 %–13 %
(2.6 kg m-2). However, the large majority
of data points is distributed within the CTH bin between 0 and 1 km, revealing that the underestimation of the TROPOMI TCWV is mainly caused by low
clouds. For mid-level clouds the median difference almost cancels out, whereas for high clouds it first increases and then remains
almost constant with cloud top height.
Further validation results for SSMIS f16 and f17 separated into different cloud
fraction and cloud top height bins for July 2018 are given in
Figs. S10 and S11 respectively. The results indicate that
there is no dependency with cloud fraction but a distinctive dependency
with cloud top height: the retrieval underestimates for clouds below 1 km, is in very good agreement for mid-level clouds (1–4 km), and overestimates for higher clouds.
ERA-5 comparison
For the intercomparison between the reanalysis model ERA-5 and TROPOMI, we use ERA-5 TCWV data provided by on a 0.25∘×0.25∘ grid. We only take into account values which are within
+1 h with respect to the starting sensing time of the TROPOMI orbit and separate the data into data over ocean and data over land.
2D histograms for the comparison between TROPOMI
and ERA-5 for data over ocean (a, b) and over land (c, d) for clear-sky conditions (CF<20 %) for boreal summer (a, c)
and boreal winter (b, d), where the colour indicates the relative share of total data points. The
black dotted line indicates the 1-to-1
diagonal and the red solid line represents the results of the linear
regression. The parameters of the linear regression and the coefficient
of determination are given in the box in each panel.
The results of the intercomparison are summarized in Fig. .
Over ocean (top row in Fig. ) the results are similar to the results from the comparison between TROPOMI and SSMIS:
apart from slopes close to 0.95 and intercepts close to zero, the linear regression yields R2 of 94 % for summer and 95 %
for winter respectively. Over land the linear regression still yields high values of the coefficient of determination R2,
but the TROPOMI retrieval generally underestimates the H2O VCD by
approximately 12 % during summer (and 7 % during winter). Since the values of
the correlation coefficient are still high and the values over ocean coincide very well with the reference data sets, we assume that this underestimation has to
be caused by a systematic uncertainty within the input parameters for our
retrieval.
2D histograms of the difference (TROPOMI - ERA-5, a, b) and relative difference (TROPOMI-ERA-5)/ERA-5(c, d) as a function of the input cloud top height (CTH) for
clear-sky conditions (CF<20 %) for summer (a, c) and winter (b, d) for data over ocean. The blue dashed line represents the median over the whole CTH range. The
blue dots represent the median within a 1 km CTH and the error bars
represent their respective 1σ standard deviation.
The influence of the cloud top height input is illustrated in
Fig. for data over ocean. The median is around -1.6 kg m-2 (-7.1 %)
and -1.3 kg m-2 (-6.7 %) during summer and winter respectively, whereby similarly to SSMIS, these underestimations are caused by the majority of data points within the 0–1 km CTH bin. For increasing
CTH the deviation from the reference increases and leads to an overestimation. For
data over land (Fig. ) the CTH variability is much
larger than over ocean; i.e. most data points are now distributed between 0 and 3 km and the median is around values of -1.5 kg m-2 (-10.3 %) and -0.4 kg m-2 (-4.0 %) during summer and winter respectively. Furthermore, low clouds still cause an underestimation, and for mid- to high-level clouds the deviations almost cancel out, but one can also observe an increasing scatter
for winter data.
Same as Fig. but for data over land.
All these findings reveal that the combination of albedo uncertainties
and uncertainties in the cloud properties (cloud fraction and cloud
top height) as well as in the scale height parameterization have a
distinctive influence on the AMF. The cloud products from TROPOMI rely
on the OMI albedo which, as we have demonstrated in Sect. ,
has several problems over land surface. In addition, the uncertainty of the OMI albedo over land surface is higher than over ocean due to a highly spatiotemporal variability of the scenery, and the differences between the monthly
minimum and the monthly mean albedo are higher over land than over ocean. Furthermore, the cloud top height is calculated via the cloud top pressure and has
to be combined with the surface pressure. Thus, the uncertainty of the cloud top
height over land is higher than over ocean, since over ocean the topography is much simpler.
Nevertheless, the complex radiative interactions between albedo and clouds might
amplify or cancel out these deviations and thus make it difficult to draw clear
conclusions.
As for the SSMIS comparison, further validation results for ERA-5 over ocean and land separated into different cloud fraction and cloud top height bins for July
2018 are given in Figs. S12 and S13.
Similarly to SSMIS, the results over ocean reveal an underestimation for low clouds and an overestimation
for high clouds and that there is almost no dependency with cloud
fraction. Over land low clouds still cause an underestimation; however, for cloud top heights above 2 km the retrieval shows very good agreement with ERA-5, indicating that the input cloud top height for our retrieval is too low.
SuomiNet/GPS comparison
For the intercomparison with TCWV from ground-based GPS we use data from the
SuomiNet network provided by UCAR. SuomiNet stations are distributed over North and Central America and provide data every 30 min
with a typical accuracy of 2 kg m-2.
Thus, we only take into account TROPOMI pixels within a distance of
0.1∘ to the GPS station and within 2 h with respect to the GPS
measurement.
Scatter plots of the intercomparisons between TROPOMI and SuomiNet for clear-sky conditions (CF<20 %) for boreal summer (a) and boreal winter (b). The black dashed line indicates the 1-to-1
diagonal and the orange solid line represents the results of the robust regression based on . The parameters of the regression and the coefficient of correlation are given in the box in each panel.
Figure illustrates scatter plots of the
intercomparison between TROPOMI and SuomiNet for boreal summer and winter. For
both seasons the robust regression indicates an underestimation of around 20 %
(i.e. slopes of 0.82 and 0.84) with high Pearson correlation
coefficients of 88 %. In order to investigate the influence of clouds on our
retrieval, we plot the difference (top row) and the relative difference (bottom
row) between TROPOMI and Suominet as a function of the input cloud top height
(CTH) in Fig. . The median
over the whole CTH range (blue dashed line) indicates an underestimation
of the TROPOMI H2O VCD of approximately 14 % (3.5 kg m-2)
during summer and of 8 % (0.8 kg m-2) during winter. However,
during summer the median values for each 1 km CTH bin (blue dots)
reveal that the underestimation is mainly caused by low clouds, whereas for
mid- and high-level clouds the median difference almost cancels out. During winter this pattern is not clearly observable due to much larger scatter, but also
here low clouds mainly cause the underestimation in TCWV, whereby the
difference is generally within the range of accuracy of the SuomiNet retrieval.
Scatter plot of the
difference (TROPOMI - SuomiNet, a, b) and relative
difference (TROPOMI-SuomiNet)/SuomiNet(c, d)
as a function of the input cloud top height (CTH) for clear-sky
conditions (CF<20 %) for summer (a, c) and winter (b, d).
The blue dashed line represents
the median over the whole CTH range. The blue dots represent the median
within a 1 km CTH and the error bars represent their respective
1σ standard deviation.
Figure S14 depicts further validation results
separated into different cloud fraction and cloud top height bins
for boreal summer 2018. Though the sample size is much smaller,
similar results to SSMIS and ERA-5 are obtained: independent of the cloud fraction, low clouds cause an underestimation of around 15 %–20 %, whereas for mid-level clouds the TROPOMI H2O VCDs show much better agreement with the SuomiNet TCWV, and for high clouds TROPOMI overestimates by around 10 %.
Summary and conclusions
In this paper, we introduce a total column water vapour retrieval
from TROPOMI spectra in the visible blue spectral range using an iterative
vertical column conversion scheme and provide a detailed characterization
of our retrieved H2O VCD by performing a detailed uncertainty
analysis and intercomparisons to reference data sets from the microwave sensor SSMIS, from the reanalysis model ERA-5, and from the ground-based GPS network SuomiNet.
For the iteration scheme we describe the a priori water vapour profile
as an exponential decay with a scale height H and developed an
empirical parameterization for this scale height. This parameterization is
based on COSMIC water vapour profile data and relates the a priori water
vapour profile shape to the H2O VCD, the seasonal cycle, the latitude, and the vegetation (and NDVI respectively). We demonstrate that we can correctly reproduce the scale heights, in particular for data at low
latitudes (tropics and subtropics). However, we also observe an increasing
scatter if higher latitudes are included in the comparison,
likely because of the higher variability in H2O VCD due to
midlatitudinal cyclone dynamics and a general higher uncertainty in the
COSMIC profile data for drier atmospheric conditions. Overall, the retrieved
profile heights are very reasonable, and we obtain a substantial improvement using the new parameterization compared to the use of a prescribed constant water vapour profile.
For the uncertainty analysis we investigated the impact of several error
sources on the H2O SCD and AMF, like clouds, surface albedo, profile shape, and instrument properties. The error estimation reveals that the main SCD
uncertainty is the fit error of the spectral analysis and that
the main AMF uncertainties are caused by uncertainties in the
surface albedo and water vapour profile shape.
For the H2O VCD we estimated a typical total relative error
of around 10 %–20 % for observations during clear-sky conditions, over ocean surface, and at low solar zenith angles. For observations during cloudy-sky
conditions, over land surface, and high solar zenith angles the error reaches values of approximately 20 %–50 %. Thus, the theoretically estimated errors are
of the same order of magnitude as the deviations found during the
retrieval's evaluation. However, uncertainties in the absorption cross
section of water vapour are a further systematic error source that can
additionally contribute up to 10 %. Based on the LP-DOAS comparisons
we estimate these errors to be around 5 % for this study, so that they are
negligible compared to the other error sources.
In the validation study we demonstrate that for clear-sky conditions the
retrieved TROPOMI H2O VCDs over ocean are in very good agreement with the reference data sets and can correctly capture the global water vapour distribution. Over land the TROPOMI retrieval can reproduce the TCWV
distribution; however, we also observe a distinctive underestimation of around 10 %, in particular during boreal summer.
Nevertheless, these underestimations might be caused by the uncertainties
of the external input data for the retrieval: for instance, the OMI LERs from are too high over tropical land masses, likely due to incorrect cloud filtering which causes too high AMFs, leading to too
low H2O VCDs. Although we tried to overcome this issue by using a
surface reflectance product from MODIS Aqua, the cloud products from
the TROPOMI L2 NO2 product still rely on the OMI LER to calculate the effective cloud fraction and cloud top height and thus also have a large
uncertainty. The intercomparisons to the reference data sets
show that these uncertainties in the cloud products have a substantial
impact on the H2O VCD: our investigations reveal that the input cloud top height is probably too low, which in turn leads to higher AMFs and
consequently to an underestimation in TCWV. However, one has to consider that the radiative properties of the cloud and albedo products interact at
a high degree of complexity, so that a clear explanation or suggestion on how to overcome these issues is beyond the scope of this paper.
Because of all these uncertainties we recommend for general purposes to only use VCDs with an effective cloud fraction <20 % and
AMF>0.1, which represents a good compromise between
spatial coverage and retrieval accuracy.
Overall, the successful application of the TCWV retrieval in the
visible blue spectral range to TROPOMI measurements is very promising for further investigations, including application to further satellite sensors
such as OMI, SCIAMACHY, and GOME-1/2 or the upcoming Sentinel-4 and
Sentinel-5 instruments and expanding the retrieval to measurements
contaminated by higher cloud fractions. As the retrieval allows
for a fast execution of large data sets, investigations of long-term trends using a TCWV data set of merged time series of different satellite sensors are easily possible. However, since these data
sets have to be uniform, they require consistent input
data across the different satellite sensors, in particular for
cloud products.
Weighted linear least-squares fit for spectral analysis
To handle the daily high data volume of TROPOMI and to avoid “jumps” of pixels
included in the fit window, we implemented a weighted linear least-squares fit for the DOAS analysis. The weights W are the fractional coverage of the
pixel within the fit window (see also Fig. ):
W(λ)=1-λ-λlowΔλλ-λlowΔλ<1∧λ-λlow<0,1λlow<λ<λup1-λ-λupΔλλ-λupΔλ<1∧λ-λup>0,0else
with λlow and λup the lower and upper boundaries of the fit window and Δλ the average wavelength increment within
the fit window. The elements of the weight matrix are then given
as wii=Wii(λi). Hence Eq. () can
be solved by simple linear algebra:
y′=M′x,x^=M′TM′-1M′Ty,S=M′TM′-1χ2,βi=Sii,
with the solution of the linear problem x^ containing
the SCDs, y′=diag(w)y the weighted
measurement spectrum, M′=diag(w)M the
weighted absorption structures to fit, βi the estimated 1σ fit error of the results for each fitted
parameter, and χ2 the reduced chi square.
Schematic illustration of the weights used during the retrieval's spectral analysis.
Evaluation of the water vapour absorption cross section
Figure depicts intercomparisons between LP-DOAS and
meteorological measurements of water vapour volume mixing ratios (WVMRs) at different altitudes (10, 40, and 200 m) at the CESAR Tower for daytime and nighttime during the Cabauw Intercomparison of Nitrogen Dioxide Measuring
Instruments 2 (CINDI-2) campaign. The results of the regression methods indicate
that for every altitude the LP-DOAS underestimates WVMRs by around 17 % during day and 11 % during night. These findings independently confirm the results
of further LP-DOAS measurements taken at the Cape Verde Atmospheric
Observatory, for which observed an underestimation
of around 8 % when using the water vapour line lists from HITRAN 2012.
However, when using the water vapour line lists from HITRAN 2008, observe an excellent agreement with the reference
meteorological measurements at the observatory (see Table 8 in their paper).
Figure compares the absorption cross sections of the different HITRAN versions. For the high-resolution cross section (panel a), the differences between the versions are hardly visible; however, after the convolution with the TROPOMI ISRF (panel b), distinctive differences in the peak absorption are clearly visible: in comparison
to HITRAN 2008, the absorption peak of HITRAN 2012 is approximately
7 %–9 % higher than HITRAN 2008, and the absorption peak of HITRAN 2016 is approximately 7 %–9 % lower than HITRAN 2008.
Scatter plots of water vapour volume
mixing ratios (WVMRs) derived from LP-DOAS measurements and meteorological measurements at different altitudes
(10, 40, and 200 m) at the CESAR Tower for day and night during the CINDI-2 campaign. Water vapour absorption cross sections have been
calculated from the HITRAN 2012 line list. The dashed red line represents the 1-to-1 diagonal, the solid blue line
the results from the robust regression , and the solid orange line the results from the weighted linear regression.
Comparison of the water vapour absorption cross section derived from different HITRAN versions
(2008, 2012, and 2016) for a temperature of 296 K. Panel (a) depicts the high-resolution cross sections and the difference between HITRAN2008 and HITRAN2012. Panel (b)
depicts the same cross sections but convolved with a typical TROPOMI Super-Gaussian ISRF (values from ).
Combining these findings with the shortcomings of HITRAN 2016
indicated by and the observational evidence from
the LP-DOAS measurements, we conclude that it is most adequate to use
the water vapour line list from HITRAN 2008.
Evaluation of methods for calculating water vapour scale height
The water vapour scale height can be calculated in different ways. Here, we
compare two different approaches: the first method is the calculation of the scale height via a weighted non-linear fit:
min∑iyi-fzi,n0,Hnl2σi2fz,n0,Hnl=n0e-zHnl,
where yi are the COSMIC profile data points, f(z,n0,H)
is the approximation of the exponential function, and σi
is the inverse of the layer thickness at the observation yi.
The second method consists of summing up all the partial columns of the
COSMIC profile data until a defined threshold is reached, which in
our case is 63 % of the H2O VCD:
∫0Hsumn(z)dz∫0TOAn(z)dz>1-1e≈63%.
Figure S4 depicts the mean profile shapes
calculated using both methods as well as the mean profile shape of
the COSMIC data for different latitude bins for the year 2013 for
which the sample size is largest. Further statistics of goodness are given
in Fig. S5 (bias), Fig. S6 (mean absolute error), and Fig. S7 (standard deviation).
In general, the profile shapes of both methods agree well with
the COSMIC measurements; however, Figs. S5 and S6 also reveal that the largest
deviations occur in the lowermost troposphere, in particular for the
southern polar regions. Nevertheless, the profiles of standard deviations
in Fig. S7 also demonstrate that both methods
are able to well capture the vertical and temporal variations in
the water vapour profile shape and that these variations are within the same
range of the variation of the COSMIC profile data.
Histogram of the relative deviation
of the calculated synthetic AMFs between the sum method (blue)/non-linear fit (orange) and the COSMIC profile for selected latitude bins (0 to
10, -30 to -20, and -70 to -60∘ N)
assuming clear-sky conditions and nadir-viewing geometry.
Figure depicts histograms of the relative
AMF deviation for both methods for selected latitude regions assuming
nadir-viewing geometry and clear-sky conditions (like in Sect. and Fig. ). The peaks of the histograms for the sum method are close to the 0 % line, indicating very good agreement with AMF calculated from the COSMIC
profiles. In contrast, the histograms for the non-linear fit peak at
values around 2 % and show a broader distribution than the histogram
of the sum method, thus revealing an inferior agreement with the reference AMFs. For cloudy-sky conditions (see Fig. S8),
both methods are biased to smaller AMF values (deviations of around -5 %) for a cloud top height of 1 km, but for higher clouds both
methods show similar good agreement with the reference AMFs. However, the variance in the AMFs for the sum method is much smaller than in
the AMFs for the non-linear fit.
In summary, the sum method is to be preferred because it provides more
consistent results for clear-sky and cloudy-sky scenarios than the
non-linear fit.
Data availability
The TROPOMI TCWV data presented here are available upon request.
The supplement related to this article is available online at: https://doi.org/10.5194/amt-13-2751-2020-supplement.
Author contributions
CB performed all calculations for this work and prepared the
manuscript together with SB and TW and in collaboration with all the
coauthors. SB developed the concept of the linearized retrieval scheme
and CB and SB implemented most of the retrieval code. SD
helped with the McArtim calculations and HS helped with the
tessellation of the TROPOMI H2O VCD orbit data to a
regular grid. TW supervised this study.
Competing interests
The authors declare that they have no conflict of interest.
Special issue statement
This article is part of the special issue “TROPOMI on Sentinel-5 Precursor: first year in operation (AMT/ACP inter-journal SI)”. It is not associated with a conference.
Acknowledgements
We would like to thank ESA and the S-5P/TROPOMI level 1 and level 2 teams
for their great work in initiating and realizing TROPOMI and for
providing the respective data sets. We also thank NASA for providing
MODIS and SSMI data and ECMWF for providing reanalysis data. Furthermore,
we acknowledge UCAR and ROMSAF for providing SuomiNet and COSMIC data.
We also would like to thank Stefan Schmitt and Johannes Lampel from
the Institute of Environmental Physics at the University of Heidelberg for
performing the analysis of the LP-DOAS measurements during CINDI-2 and for
providing the WVMR results in a very useful format.
Financial support
The article processing charges for this open-access publication were covered by the Max Planck Society.
Review statement
This paper was edited by Ben Veihelmann and reviewed by Ruediger Lang and one anonymous referee.
ReferencesAnthes, R. A.: Exploring Earth's atmosphere with radio occultation: contributions to weather, climate and space weather, Atmos. Meas. Tech., 4, 1077–1103, 10.5194/amt-4-1077-2011, 2011.
Anthes, R. A., Bernhardt, P. A., Chen, Y., Cucurull, L., Dymond, K. F., Ector, D., Healy, S. B., Ho, S.-P., Hunt, D. C., Kuo, Y.-H., Liu,
H., Manning, K., McCormick, C., Meehan, T. K., Randel, W. J., Rocken, C., Schreiner, W. S., Sokolovskiy, S. V., Syndergaard, S.,
Thompson, D. C., Trenberth, K. E.,Wee, T.-K., Yen, N. L., and Zeng, Z.: The COSMIC/FORMOSAT-3
mission: Early results, B. Am. Meteorol. Soc., 89,
313–334, 2008.Beirle, S., Sihler, H., and Wagner, T.: Linearisation of the effects of spectral shift and stretch in DOAS analysis, Atmos. Meas. Tech., 6, 661–675, 10.5194/amt-6-661-2013, 2013.Beirle, S., Lampel, J., Lerot, C., Sihler, H., and Wagner, T.: Parameterizing the instrumental spectral response function and its changes by a super-Gaussian and its derivatives, Atmos. Meas. Tech., 10, 581–598, 10.5194/amt-10-581-2017, 2017.
Bennartz, R. and Fischer, J.: Retrieval of columnar water vapour over land from
backscattered solar radiation using the Medium Resolution Imaging
Spectrometer, Remote Sens.Environ., 78, 274–283, 2001.Boggs, P. T., Boggs, P. T., Rogers, J. E., and Schnabel, R. B.: User's
reference guide for odrpack version 2.01: Software for weighted orthogonal
distance regression, US Department of Commerce, National Institute of Standards and Technology, available at: https://docs.scipy.org/doc/external/odrpack_guide.pdf
(last access: 19 May 2020),
1992.Copernicus Climate Change Service: ERA5 hourly data on pressure levels from 1979 to present, Copernicus
Climate Change Service Climate Data Store (CDS), 10.24381/cds.bd0915c6, 2018a.Copernicus Climate Change Service: ERA5 hourly data on single levels from 1979 to present, Copernicus
Climate Change Service Climate Data Store (CDS), 10.24381/cds.adbb2d47, 2018b.
Deutschmann, T., Beirle, S., Frieß, U., Grzegorski, M., Kern, C., Kritten, L., Platt, U., Prados-Román, C., Puk, ı, J., Wagner, T., Werner, B.,
and Pfeilsticker, K.:
The Monte Carlo atmospheric radiative transfer model McArtim: Introduction
and validation of Jacobians and 3D features, J. Quant.
Spectrosc. Ra., 112, 1119–1137, 2011.Didan, K., Munoz, A. B., Solano, R., and Huete, A.: MODIS vegetation index
user's guide (MOD13 series), Tech. rep., Vegetation Index and PhenologyLab,
10.5067/MODIS/MYD13C2.006,
2015.Duan, J., Bevis, M., Fang, P., Bock, Y., Chiswell, S., Businger, S., Rocken,
C., Solheim, F., van Hove, T., Ware, R., McClusky, S., Herring, T. A., and
King, R. W.: GPS Meteorology: Direct Estimation of the Absolute Value of
Precipitable Water, J. Appl. Meteorol., 35, 830–838,
10.1175/1520-0450(1996)035<0830:GMDEOT>2.0.CO;2,
1996.Fang, P., Bevis, M., Bock, Y., Gutman, S., and Wolfe, D.: GPS meteorology:
Reducing systematic errors in geodetic estimates for zenith delay,
Geophys. Res. Lett., 25, 3583–3586, 10.1029/98GL02755,
1998.Gao, B.-C. and Kaufman, Y. J.: Water vapor retrievals using Moderate Resolution
Imaging Spectroradiometer (MODIS) near-infrared channels, J.
Geophys. Res.-Atmos., 108, 4389, 10.1029/2002JD003023, 2003.Gordon, I., Rothman, L., Hill, C., Kochanov, R., Tan, Y., Bernath, P., Birk,
M., Boudon, V., Campargue, A., Chance, K., Drouin, B., Flaud, J.-M., Gamache,
R., Hodges, J., Jacquemart, D., Perevalov, V., Perrin, A., Shine, K., Smith,
M.-A., Tennyson, J., Toon, G., Tran, H., Tyuterev, V., Barbe, A., Császár,
A., Devi, V., Furtenbacher, T., Harrison, J., Hartmann, J.-M., Jolly, A.,
Johnson, T., Karman, T., Kleiner, I., Kyuberis, A., Loos, J., Lyulin, O.,
Massie, S., Mikhailenko, S., Moazzen-Ahmadi, N., Müller, H., Naumenko, O.,
Nikitin, A., Polyansky, O., Rey, M., Rotger, M., Sharpe, S., Sung, K.,
Starikova, E., Tashkun, S., Auwera, J. V., Wagner, G., Wilzewski, J.,
Wcisło, P., Yu, S., and Zak, E.: The HITRAN2016 molecular spectroscopic
database, J. Quant. Spectrosc. Ra., 203, 3–69, 10.1016/j.jqsrt.2017.06.038, 2017.Grossi, M., Valks, P., Loyola, D., Aberle, B., Slijkhuis, S., Wagner, T., Beirle, S., and Lang, R.: Total column water vapour measurements from GOME-2 MetOp-A and MetOp-B, Atmos. Meas. Tech., 8, 1111–1133, 10.5194/amt-8-1111-2015, 2015.Hajj, G., Kursinski, E., Romans, L., Bertiger, W., and Leroy, S.: A technical
description of atmospheric sounding by GPS occultation, J.
Atmos. Sol.-Terr. Phy., 64, 451–469,
10.1016/S1364-6826(01)00114-6,
2002.Heise, S., Wickert, J., Beyerle, G., Schmidt, T., and Reigber, C.: Global
monitoring of tropospheric water vapor with GPS radio occultation aboard
CHAMP, Adv. Space Res., 37, 2222–2227,
10.1016/j.asr.2005.06.066, 2006.Held, I. M. and Soden, B. J.: Water Vapor Feedback and Global Warming, Annu.
Rev. Energ. Env., 25, 441–475,
10.1146/annurev.energy.25.1.441, 2000.
Ho, S.-P., Kuo, Y.-H., Schreiner, W., and Zhou, X.: Using SI-traceable global
positioning system radio occultation measurements for climate monitoring, B. Am. Meteorol.
Soc., 91, S36–S37, 2010a.Ho, S.-P., Zhou, X., Kuo, Y.-H., Hunt, D., and Wang, J.-H.: Global Evaluation
of Radiosonde Water Vapor Systematic Biases using GPS Radio Occultation from
COSMIC and ECMWF Analysis, Remote Sens., 2, 1320–1330,
10.3390/rs2051320, 2010b.Kleipool, Q., Dobber, M., de Haan, J., and Levelt, P.: Earth surface
reflectance climatology from 3 years of OMI data, J. Geophys.
Res.-Atmos., 113, D18308, 10.1029/2008JD010290, 2008.
Kursinski, E., Hajj, G., Schofield, J., Linfield, R., and Hardy, K. R.:
Observing Earth's atmosphere with radio occultation measurements using the
Global Positioning System, J. Geophys. Res.-Atmos., 102,
23429–23465, 1997.
Kurucz, R. L., Furenlid, I., Brault, J., and Testerman, L.: Solar flux atlas from 296 to 1300 nm, National Solar Observatory Atlas, US.
National Solar Observatory, Sunspot, NM, USA, 1984.Lampel, J., Pöhler, D., Tschritter, J., Frieß, U., and Platt, U.: On the relative absorption strengths of water vapour in the blue wavelength range, Atmos. Meas. Tech., 8, 4329–4346, 10.5194/amt-8-4329-2015, 2015.Lang, R., Casadio, S., Maurellis, A. N., and Lawrence, M. G.: Evaluation of the
GOME Water Vapor Climatology 1995–2002, J. Geophys. Res.-Atmos., 112, 10.1029/2006JD008246,
2007.
Levelt, P. F., van den Oord, G. H., Dobber, M. R., Malkki, A., Visser, H.,
de Vries, J., Stammes, P., Lundell, J. O., and Saari, H.: The ozone
monitoring instrument, IEEE T. Geosci. Remote,
44, 1093–1101, 2006.
Mears, C. A., Wang, J., Smith, D., and Wentz, F. J.: Intercomparison of total
precipitable water measurements made by satellite-borne microwave radiometers
and ground-based GPS instruments, J. Geophys. Res.-Atmos., 120, 2492–2504, 2015.Nielsen, J., Gleisner, H., and Lauritsen, K.: Validation Report: Reprocessed
Level 2B and 2C 1D-Var products, Tech. Rep. SAF/ROM/DMI/REP/1DVAR/001,
ROMSAF, product version 1.0, available at: https://www.romsaf.org/product_documents.php (last access: 19 May 2020), 2018.Noël, S., Buchwitz, M., Bovensmann, H., Hoogen, R., and Burrows, J. P.:
Atmospheric water vapor amounts retrieved from GOME satellite data,
Geophys. Res. Lett., 26, 1841–1844, 10.1029/1999GL900437,
1999.Noël, S., Buchwitz, M., and Burrows, J. P.: First retrieval of global water vapour column amounts from SCIAMACHY measurements, Atmos. Chem. Phys., 4, 111–125, 10.5194/acp-4-111-2004, 2004.Platt, U. and Stutz, J.: Differential Optical Absorption Spectroscopy:
Principles and Applications, Physics of Earth and Space Environments,
Springer Berlin Heidelberg, 10.1007/978-3-540-75776-4, 2008.
Rosenkranz, P. W.: Retrieval of temperature and moisture profiles from AMSU-A
and AMSU-B measurements, IEEE T. Geosci. Remote,
39, 2429–2435, 2001.
Rothman, L., Gordon, I., Barbe, A., Benner, D., Bernath, P., Birk, M., Boudon, V., Brown, L., Campargue, A., Champion, J.-P., Chance,
K., Coudert, L., Dana, V., Devi, V., Fally, S., Flaud, J.-M., Gamache, R., Goldman, A., Jacquemart, D., Kleiner, I., Lacome, N., Lafferty,
W., Mandin, J.-Y., Massie, S., Mikhailenko, S., Miller, C., Moazzen-Ahmadi, N., Naumenko, O., Nikitin, A., Orphal, J., Perevalov, V.,
Perrin, A., Predoi-Cross, A., Rinsland, C., Rotger, M., Šimečková, M., Smith, M., Sung, K., Tashkun, S., Tennyson, J., Toth, R., Vandaele, A., and Vander Auwera, J.: The
HITRAN 2008 molecular spectroscopic database, J. Quant.
Spectrosc. Ra., 110, 533–572, 2009.Rothman, L., Gordon, I., Babikov, Y., Barbe, A., Benner, D. C., Bernath, P.,
Birk, M., Bizzocchi, L., Boudon, V., Brown, L., Campargue, A., Chance, K.,
Cohen, E., Coudert, L., Devi, V., Drouin, B., Fayt, A., Flaud, J.-M.,
Gamache, R., Harrison, J., Hartmann, J.-M., Hill, C., Hodges, J., Jacquemart,
D., Jolly, A., Lamouroux, J., Roy, R. L., Li, G., Long, D., Lyulin, O.,
Mackie, C., Massie, S., Mikhailenko, S., Müller, H., Naumenko, O., Nikitin,
A., Orphal, J., Perevalov, V., Perrin, A., Polovtseva, E., Richard, C.,
Smith, M., Starikova, E., Sung, K., Tashkun, S., Tennyson, J., Toon, G.,
Tyuterev, V., and Wagner, G.: The HITRAN2012 molecular spectroscopic
database, J. Quant. Spectrosc. Ra., 130, 4–50, 10.1016/j.jqsrt.2013.07.002, 2013.Rozemeijer, N. and Kleipool, Q.: S5P Mission Performance Centre Level 1b
Readme, Tech. Rep. S5P-MPC-KNMI-PRF-L1B,
product version V01.00.00, available at:
https://sentinel.esa.int/documents/247904/3541451/Sentinel-5P-Level-1b-Product-Readme-File (last access: 19 May 2020), 2019.Schneider, A., Borsdorff, T., aan de Brugh, J., Aemisegger, F., Feist, D. G., Kivi, R., Hase, F., Schneider, M., and Landgraf, J.: First data set of H2O/HDO columns from the Tropospheric Monitoring Instrument (TROPOMI), Atmos. Meas. Tech., 13, 85–100, 10.5194/amt-13-85-2020, 2020.Serdyuchenko, A., Gorshelev, V., Weber, M., Chehade, W., and Burrows, J. P.: High spectral resolution ozone absorption cross-sections – Part 2: Temperature dependence, Atmos. Meas. Tech., 7, 625–636, 10.5194/amt-7-625-2014, 2014.Siegel, A. F.: Robust regression using repeated medians, Biometrika, 69,
242–244, 10.1093/biomet/69.1.242, 1982.Smith, E. K. and Weintraub, S.: The Constants in the Equation for
Atmospheric Refractive Index at Radio Frequencies, P. IRE,
41, 1035–1037, 10.1109/JRPROC.1953.274297, 1953.Steffensen, J. F.: Remarks on iteration, Scand. Actuar. J., 1933, 64–72, 10.1080/03461238.1933.10419209, 1933.Sulla-Menashe, D., Gray, J. M., Abercrombie, S. P., and Friedl, M. A.:
Hierarchical mapping of annual global land cover 2001 to present: The MODIS
Collection 6 Land Cover product, Remote Sens. Environ., 222, 183–194, 10.1016/j.rse.2018.12.013,
2019.
Susskind, J., Barnet, C. D., and Blaisdell, J. M.: Retrieval of atmospheric and
surface parameters from AIRS/AMSU/HSB data in the presence of clouds, IEEE
T. Geosci. Remote, 41, 390–409, 2003.Thalman, R. and Volkamer, R.: Temperature dependent absorption cross-sections
of O2-O2 collision pairs between 340 and 630 nm and at atmospherically
relevant pressure, Phys. Chem. Chem. Phys., 15, 15371–15381,
10.1039/C3CP50968K, 2013.Tilstra, L. G., Tuinder, O. N. E., Wang, P., and Stammes, P.: Surface
reflectivity climatologies from UV to NIR determined from Earth observations
by GOME-2 and SCIAMACHY, J. Geophys. Res.-Atmos., 122,
4084–4111, 10.1002/2016JD025940,
2017.Vandaele, A., Hermans, C., Simon, P., Carleer, M., Colin, R., Fally, S.,
Merienne, M., Jenouvrier, A., and Coquart, B.: Measurements of the NO2 absorption cross-section from 42 000 cm-1 to 10 000 cm-1 (238–1000 nm) at 220 K and 294 K, J. Quant. Spectrosc. Ra., 59, 171–184, 10.1016/S0022-4073(97)00168-4, 1998.Van Geffen, J., Boersma, K., Eskes, H., Maasakkers, J., and Veefkind, J.:
TROPOMI ATBD of the total and tropospheric NO2 data products, Tech. Rep.
S5P-KNMI-L2-0005-RP, Royal Netherlands Meteorological Institute, available at:
https://sentinel.esa.int/documents/247904/2476257/Sentinel-5P-TROPOMI-ATBD-NO2-data-products (last access: 19 May 2020),
2019.Veefkind, J., Aben, I., McMullan, K., Förster, H., de Vries, J., Otter, G.,
Claas, J., Eskes, H., de Haan, J., Kleipool, Q., van Weele, M., Hasekamp, O.,
Hoogeveen, R., Landgraf, J., Snel, R., Tol, P., Ingmann, P., Voors, R.,
Kruizinga, B., Vink, R., Visser, H., and Levelt, P.: TROPOMI on the ESA
Sentinel-5 Precursor: A GMES mission for global observations of the
atmospheric composition for climate, air quality and ozone layer
applications, Remote Sens. Environ., 120, 70–83,
10.1016/j.rse.2011.09.027, 2012.
Veefkind, J. P., de Haan, J. F., Sneep, M., and Levelt, P. F.: Improvements to the OMI O2-O2 operational cloud algorithm and comparisons with ground-based radar–lidar observations, Atmos. Meas. Tech., 9, 6035–6049, 10.5194/amt-9-6035-2016, 2016.Wagner, T., Heland, J., Zöger, M., and Platt, U.: A fast H2O total column density product from GOME – Validation with in-situ aircraft measurements, Atmos. Chem. Phys., 3, 651–663, 10.5194/acp-3-651-2003, 2003.Wagner, T., Beirle, S., and Deutschmann, T.: Three-dimensional simulation of the Ring effect in observations of scattered sun light using Monte Carlo radiative transfer models, Atmos. Meas. Tech., 2, 113–124, 10.5194/amt-2-113-2009, 2009.Wagner, T., Beirle, S., Sihler, H., and Mies, K.: A feasibility study for the retrieval of the total column precipitable water vapour from satellite observations in the blue spectral range, Atmos. Meas. Tech., 6, 2593–2605, 10.5194/amt-6-2593-2013, 2013.Wang, H., Souri, A. H., González Abad, G., Liu, X., and Chance, K.: Ozone Monitoring Instrument (OMI) Total Column Water Vapor version 4 validation and applications, Atmos. Meas. Tech., 12, 5183–5199, 10.5194/amt-12-5183-2019, 2019.
Ware, R. H., Fulker, D. W., Stein, S. A., Anderson, D. N., Avery, S. K., Clark,
R. D., Droegemeier, K. K., Kuettner, J. P., Minster, J. B., and Sorooshian,
S.: SuomiNet: A real-time national GPS network for atmospheric research and
education, B. Am. Meteorol. Soc., 81, 677–694,
2000.
Weaver, C. and Ramanathan, V.: Deductions from a simple climate model: Factors governing surface temperature and atmospheric thermal structure, J. Geophys. Res.-Atmos., 100, 11585–11591, 1995.Wendland, W. and Steinbach, O.: Analysis: Integral- und Differentialrechnung,
gewöhnliche Differentialgleichungen, komplexe Funktionentheorie, Lehrbuch: Mathematik, Vieweg+Teubner Verlag, 10.1007/978-3-322-82962-7, 2005.
Wentz, F. J.: A well-calibrated ocean algorithm for special sensor
microwave/imager, J. Geophys. Res.-Oceans, 102, 8703–8718,
1997.Wessel, P. and Smith, W. H. F.: A global, self-consistent, hierarchical,
high-resolution shoreline database, J. Geophys. Res.-Sol. Ea., 101, 8741–8743, 10.1029/96JB00104,
1996.