This paper presents a general approach to quantify absorption model
uncertainty due to uncertainty in the underlying spectroscopic parameters. The
approach is applied to a widely used microwave absorption model (Rosenkranz,
2017) and radiative transfer calculations in the 20–60 GHz range, which are
commonly exploited for atmospheric sounding by microwave radiometer (MWR).
The approach, however, is not limited to any frequency range, observing
geometry, or particular instrument. In the considered frequency range,
relevant uncertainties come from water vapor and oxygen spectroscopic
parameters. The uncertainty of the following parameters is found to dominate:
(for water vapor) self- and foreign-continuum absorption coefficients, line
broadening by dry air, line intensity, the temperature-dependence exponent for
foreign-continuum absorption, and the line shift-to-broadening ratio; (for
oxygen) line intensity, line broadening by dry air, line mixing,
the temperature-dependence exponent for broadening, zero-frequency line
broadening in air, and the temperature-dependence coefficient for line mixing. The
full uncertainty covariance matrix is then computed for the set of
spectroscopic parameters with significant impact. The impact of the
spectroscopic parameter uncertainty covariance matrix on simulated
downwelling microwave brightness temperatures (

Atmospheric absorption models are used to simulate the absorption and emission of electromagnetic radiation by atmospheric constituents. Atmospheric absorption models are thus crucial to compute radiative transfer through the atmosphere (Mätzler, 1997; Saunders et al., 1999; Clough et al., 2005; Buehler et al., 2005; Eriksson et al., 2011), which is needed to simulate and validate passive and active remote sensing observations, such as those from microwave radiometer (MWR) and radar instruments (Hewison et al., 2006; Maschwitz et al., 2013). Absorption and radiative transfer models, representing the forward operator for atmospheric radiometric applications, are also exploited in physical approaches for the solution of the inverse problem, i.e., the retrieval of atmospheric parameters from remote sensing radiometric observations (Westwater, 1978; Rodgers, 2000; Rosenkranz, 2001; Rosenkranz and Barnet, 2006; Cimini et al., 2010). Thus, absorption and radiative transfer models, and their uncertainty, have general implications for atmospheric sciences, including meteorology and climate studies.

Comparisons of different radiative transfer and microwave absorption models
have been performed to quantify the difference in calculated brightness
temperatures (

Absorption models are based on quantum mechanics theory and rely on parameterized equations to compute atmospheric absorption given the thermodynamic conditions and abundance of constituents (Rosenkranz, 1993). The spectroscopic parameters entering the parameterized equations are determined through theoretical calculations or laboratory and field measurements, and their values are continuously refined (Liebe et al., 1989; Rosenkranz, 1998; Liljegren et al., 2005; Turner et al., 2009; Mlawer et al., 2012; Koshelev et al., 2018). Review papers are published occasionally to summarize the proposed modifications (Rothman et al., 2005, 2013; Gordon et al., 2017). The absorption models described in Rosenkranz (1998, 2017) are cited frequently in this paper and are hereafter called R98 and R17, respectively. The review by Tretyakov (2016) is also cited frequently, meaning Tretyakov (2016) and the references therein.

The uncertainty affecting the values of spectroscopic parameters contributes to the uncertainty of the simulated absorption, which in turn affects atmospheric radiative transfer calculations. Thus, the uncertainty affecting spectroscopic parameters contributes to the uncertainty of simulated remote sensing observations and consequently to the uncertainty of remote sensing retrievals of atmospheric thermodynamic and composition profiles (Boukabara et al., 2005a; Verdes et al., 2005). This situation does not apply to microwave radiometry only, but is general to all wavelength regions (Long and Hodges, 2012; Alvarado et al., 2013, 2015; Connor et al., 2016). However, it must be considered that the uncertainty affecting different spectroscopic parameters may be correlated. Therefore, in addition to the uncertainty affecting the single parameters, the full uncertainty covariance matrix should be estimated to account for the correlation in radiative transfer calculations and retrievals (Rosenkranz, 2005; Boukabara et al., 2005b).

In the last decade, the Global Climate Observing System (GCOS) Reference
Upper-Air Network (GRUAN) has evolved from aspiration to reality (Bodeker et
al., 2015). GRUAN is now delivering reference-quality measurement of
essential climate variables (ECVs), for which the uncertainty contributions
are carefully evaluated. In addition to radiosonde observations (Dirksen et
al., 2014), ground-based remote sensing products are planned in GRUAN,
including from microwave radiometer (MWR) profilers. Most common ground-based
MWR profilers operate in the 20–60 GHz range to infer ECVs such as
tropospheric temperature and water vapor profiles and vertically integrated
water vapor and liquid water contents. MWR adds value to GRUAN by providing
redundant measurements with respect to radiosondes, but covering the complete
diurnal cycle at high (e.g., 1 min) temporal resolution. The various sources
of uncertainty for MWR retrievals have been reviewed in the framework of the
GRUAN-related GAIA-CLIM project (

Thus, the main purpose of this paper is to introduce a rigorous approach for
quantifying the absorption model uncertainty. Although the approach is
general and not limited to any particular instrument, observing technique,
or frequency range, we demonstrate its use through the application to
ground-based microwave radiometer simulations and retrievals. The analysis
thus consists of the following four steps:

review recent work concerning water vapor and oxygen spectroscopic parameters and their associated uncertainties;

perform a sensitivity study to investigate the dominant uncertainty contribution to radiative transfer calculations;

estimate the full uncertainty covariance matrix for the dominant parameters; and

propagate the uncertainty covariance matrix to estimate the impact on MWR simulated observations and atmospheric retrievals.

Thus, the paper is organized as follows: Sect. 2 summarizes the equations
used in the considered microwave absorption model and defines their
parameters. Section 3 presents the results of the uncertainty sensitivity
study. Section 4 discusses the approach to estimate the uncertainty
covariance matrix. Section 5 presents the impact of spectroscopic uncertainty
on simulated downwelling 20–60 GHz

Absorption happens when radiation travels through a dissipative medium. The
radiation intensity as a function of the path length

Resonant absorption is modeled by computing the contribution of each
significant absorption line (line by line). Following Rosenkranz (1993), the
power absorption coefficient at frequency

In the frequency range considered here (20–60 GHz), the line-mixing effect
is fundamental for understanding oxygen absorption, while it is
negligible for water vapor (

The van Vleck–Weisskopf profile can also be used for taking into account
zero-frequency transitions by letting

Nonresonant absorption accounts for the absorption characterized by the smooth frequency dependence remaining after considering the effect of resonant lines. The mechanism for nonresonant absorption arises from the nonideality of atmospheric gases and corresponds to the absorption by collisionally interacting molecules. At usual atmospheric conditions only pair interaction is significant. This interaction during a finite time of collision may lead to significant (either positive or negative) deviation of resonance line far wings from the absorption calculated using profiles (3–6). For each molecule, the sum of these deviations over all lines gives absorption smoothly varying with frequency. Another component of nonresonance absorption corresponds to molecular pairs (bimolecular absorption). The latter can be further subdivided into three parts corresponding to free molecular pairs, quasi-bound (metastable) dimers, and true-bound (stable) dimers. All these absorption contributions also vary very smoothly with frequency at atmospheric conditions due to either the short lifetime of bimolecular state (free pairs and quasi-bound dimers) or an extremely dense and collisionally broadened spectrum of loosely bound molecular pairs (quasi-bound dimers and true-bound dimers).

To model nonresonance bimolecular absorption in the atmosphere, it should be taken into account that pair interactions occur in any atmospheric gases and their mixtures. For convenience, the treatment of atmospheric nonresonance absorption is divided in two contributions, one deriving from dry air and the other from water vapor.

The dry contribution is due to the interaction of dry air molecules with
each other. Only molecular nitrogen and oxygen are considered, as they
account for nearly 100 % of the atmospheric mixture and absorption.
Because of the dominant nitrogen contribution this component can be
approximately calculated in the considered frequency range as

Concerning the water vapor contribution to nonresonance absorption, despite
a general understanding of the physical nature (e.g., Shine et al., 2012;
Tretyakov et al., 2014; Serov et al., 2017), there are no sufficiently
accurate theoretical models for calculating the spectra of all necessary
components (especially in gas mixtures) and their temperature dependences.
Therefore, for practical purposes parameters of the observed nonresonant
absorption are determined using simple empirical models, which have not been
supported by accurate theoretical calculations and are based on experimental
data only (Tretyakov, 2016). The so-called continuum absorption is thus
empirically defined as the difference between the total observed absorption
and the calculated contribution of resonance lines:

The spectroscopic parameters appearing in the above equations may depend on
temperature (

For the line intensity, the temperature dependence is given by the total
number of populated molecular states (the partition sum), which can be
calculated numerically (Gamache et al., 2017), and the population of
molecular energy levels corresponding to the transition. The latter is
calculated from the energy of the lower level and the frequency of the
corresponding transition. Thus, calling

For pressure-broadened line coefficients, it is convenient to introduce
normalized coefficients relative to the reference temperature

For water vapor absorption, the line width and the line center frequency are
differently affected in the case of broadening induced by water vapor (self-broadening, indicated by

Similarly, for oxygen it is convenient to introduce normalized broadening
(

Line parameters that most significantly affect the line shape (e.g.,

Concerning the water vapor continuum, it has been established (Liebe and Layton, 1987; Kuhn et al., 2002; Koshelev et al., 2011; Shine et al., 2012) that
the absorption can be represented as two terms corresponding to the
interaction of water molecules with each other (self-continuum component)
and the interaction between water molecules and air molecules (foreign-continuum component). In the frequency range considered here, the continuum
absorption depends quadratically on frequency (R98) and its temperature
dependence is described by a simple exponential function:

For the dry continuum, Rosenkranz et al. (2006) proposed a
frequency-dependent factor

In the frequency range considered here (20–60 GHz) and for tropospheric
conditions, atmospheric clear-air absorption is dominated by oxygen and water
vapor. Oxygen produces strong resonant absorption due to transitions in the
magnetic dipole spin-rotation band between 50 and 70 GHz. Collisional broadening
at increased pressures causes the 60 GHz band lines to blend together and at
pressures approaching atmospheric and higher the band absorption looks like
an unstructured composite feature spreading about

Based on theoretical considerations and laboratory experimental data in the 1960s, the millimeter-wave propagation model (MPM) was developed for the range from 20 GHz to 1 THz, including the 30 strongest water vapor lines, 44 oxygen lines, and an empirically derived water vapor continuum (Liebe and Layton, 1987). This model was later revised, modifying the line parameters (Liebe, 1989), the oxygen line coupling (Liebe et al., 1992), the number of water vapor lines, and the continuum formulation (Liebe et al., 1993; R98). More details on the differences between these, as well as other absorption models, and the comparison with shipborne, aircraft, and ground-based observations can be found in Westwater et al. (2003), Cimini et al. (2004), Hewison (2006a), Hewison et al. (2006), and the references therein. The above models are widely used and have been taken as references for the last 30 years. For example, the parameterized radiative transfer code RTTOV (Saunders et al., 1999), widely used worldwide to assimilate satellite microwave radiometer observations into weather models, is trained against calculations made with the MPM87 (Rayer, 2001) and later modifications (Saunders et al., 2017).

Appendix A gives a summary of the modifications to the R98 water vapor and
oxygen absorption models proposed in the open literature in the last 20 years
and subsequently imported in the current version of the model (R17). Here,
just to show the effects of the adopted modifications, Fig. 1 displays the
20–60 GHz downwelling

The atmospheric absorption calculated from a model has in general a
nonlinear dependence on some spectroscopic parameters, as reviewed in
Sect. 2. With the assumption of small perturbations, however, one can
reasonably linearize that dependence for a given model:

Thus, this section presents a study of the absorption model sensitivity to
the uncertainty of spectroscopic parameters, with the purpose of identifying
the most significant contributions to the total uncertainty of modeled
downwelling

In the 20–60 GHz frequency range under consideration, only two resonant lines (at 22 and 183 GHz) and the continuum contribute non-negligibly to water vapor absorption. For the model parameters associated with these absorption features, the uncertainties were either taken from the spectroscopic literature or, where not available, were estimated from an independent analysis of measurement methods. The resulting uncertainties, as well as nominal values, for the water vapor parameters considered in this sensitivity analysis are listed in Table 1.

List of water vapor parameters perturbed in the sensitivity analysis.

For the resonant absorption, the following parameters are relevant: line
frequency (

For the continuum absorption, four parameters are relevant, namely the self-
and foreign-induced intensity coefficients and their respective
temperature-dependence exponents (

The sensitivity analysis shows that among the 19 model parameters that
were perturbed by the estimated uncertainty (Table 1), only 6 impact the
modeled downwelling 20–60 GHz

Sensitivity of modeled

Oxygen absorption includes the zero-frequency band, fine structure spectrum, and pure rotational resonant transitions. The R17 model includes 49 oxygen absorption lines, of which 37 are within the 60 GHz band, 1 is at 118 GHz and the remaining 11 are in the millimeter to sub-millimeter range (200–900 GHz). Uncertainties for the oxygen parameters were either retrieved from the spectroscopic literature or, where not available, estimated from an independent analysis of measurement methods.

For the resonant absorption, the following parameters are relevant: line
frequency (

The uncertainty estimates for most of these parameters are given by
Tretyakov et al. (2005). In particular, Tretyakov et al. (2005) provide
frequency uncertainty for 27 lines (

Resonant line intensities and lower-state energies are taken from the HITRAN
2004 database (Rothman et al., 2005). Although newer calculations are
available in HITRAN 2016 (Gordon et al., 2017), the differences are within
the assumed uncertainty at 1 % and 0.25 %, respectively. The latter is a
rather conservative estimate, though its contribution turned out to be
irrelevant. Note that the 1 % uncertainty in

Values for oxygen line air-broadening and mixing parameters are taken from
Tretyakov et al. (2005). Line-broadening parameters are measured through
low-pressure laboratory experiments. Since individual lines are isolated at
low pressures, no correlation is considered between parameters of different
lines. Mixing parameters are determined at higher pressures, and their values
are correlated with the previously determined low-pressure parameters. So,
the line-mixing parameters are correlated with both themselves and the line
air-broadening parameters. Because of this relationship, consistency requires
that the number of considered line widths and the number of considered mixing
coefficients should be the same. Tretyakov et al. (2005) derived mixing
coefficients for lines with

For the air-broadening temperature-dependence coefficient, R17 retains a
uniform value (0.8) for all lines (Liebe, 1989). We assume 0.05 uncertainty,
which covers more recent measurements from Makarov et al. (2008) and
Koshelev et al. (2016). Since R17 adopts the water-to-air broadening ratio

For the zero-frequency absorption, two parameters are relevant: the
intensity (

The sensitivity analysis shows that among the model parameters in Table 2,
which were perturbed by the estimated uncertainty, only the following impact
the modeled downwelling 20–60 GHz

List of oxygen parameters perturbed in the sensitivity analysis.

Sensitivity of modeled

The sensitivity analysis of Sect. 3 shows that the absorption model
uncertainty on downwelling 20–60 GHz

Although we use different methods to estimate covariances depending on how
the parameter values were measured, some general principles apply. If a set
of variables

A probability distribution can be conditional, and the uncertainty of one
parameter may be conditioned on an assumed value for a different parameter.
Sometimes reported values of a parameter or set of parameters have been
adjusted to fit measurements, while the experimenters considered other
relevant spectroscopic parameters as fixed. Now if we wish to include in our
analysis the uncertainty of one of the latter parameters (

Section 3.1 shows that for water vapor absorption six spectroscopic
parameters dominate the uncertainty of modeled 20–60 GHz

Covariance

Intensity, width, and shift affect a line profile in different ways. But even
if the original spectroscopic measurements covered the line profile
adequately, a noticeable negative correlation between width and intensity
arises if both are simultaneously estimated from measured absorption. In the
present case, the only water line that survived the sensitivity screening for
the 20–60 GHz band is the one at 22.2 GHz; the intensity used here was
calculated independently from the width (Rothman et al., 2013), and the width
was measured without using that intensity (Payne et al., 2008). Therefore, we
consider errors in those two parameters to be uncorrelated. However, the
absorption model code under investigation here (R17) uses the aforementioned
ratio of shift to width (

By definition, the water vapor continuum is the remainder after the
contribution of local resonant lines has been subtracted. Thus, if a line
width is revised, the continuum should also be revised to compensate for and
reproduce as well as possible the original brightness temperature
measurements of Turner et al. (2009) from which the continuum was derived. That
was done by adjusting the continuum coefficients

Although

For the water vapor continuum, R17 adopts the multipliers proposed by Turner
et al. (2009) to the R98 parameter values of

When brightness temperature measurement errors are uncorrelated, with
variance

Turner et al. (2009) held other parameters constant while adjusting the
continuum coefficients

The sensitivity analysis in Sect. 3.2 shows that for oxygen absorption six
spectroscopic parameter types dominate the uncertainty of modeled 20–60 GHz

Values for oxygen line air broadening are taken from Tretyakov et
al. (2005). They measured

For the remaining lines, Tretyakov et al. (2005) extrapolated the broadening
coefficients by a straight-line graphical method, assuming a pivot value
(hereafter indicated with subscript

Figure 4 represents the sign-adjusted correlation coefficients as a color
image. The extrapolated coefficients (nos. 24–37 in Fig. 4) are strongly
correlated among themselves, although not perfectly. On the other hand, the
uncertainty of the zero-frequency broadening coefficient (no. 3) is assumed
to be uncorrelated with the line air-broadening uncertainties. Figure 5 shows
the

Uncertainty matrix for oxygen absorption as a color-scale
image of sign-adjusted correlation coefficients (

Values for oxygen line-mixing coefficients are taken from Tretyakov et al. (2005), in which mixing coefficients
were determined from measurements made
near 1 atm of pressure and temperatures near 22–24

The mixing coefficient of the

Uncertainty on simulated

The first-order line-mixing parameterization in R17 is given by Eq. (13). Table 5
of Tretyakov et al. (2005) lists coefficients

The discussion in connection with Eqs. (20) and (21) indicates that
corresponding to the second, third, and fourth terms in Eq. (32) for

The uncertainty covariance matrices estimated in Sect. 4 for water vapor
and oxygen spectroscopic parameters are combined together to form

The propagation of the absorption model parameter uncertainty to calculated

As in Table 4 but at 22 central frequencies of MP3000-A channels.

Oxygen line parameters as a function of rotational quantum number

To appreciate the dominant contributions within the frequency range, the
different parameters have been grouped into seven types: intensity

Thus, looking at Figs. 6–7 and Tables 4–5, it seems convenient to discuss
the 20–60 GHz range in four parts: the proximity of the 22.2 GHz water vapor
line (20–26 GHz), the atmospheric window (26–45 GHz), the low-frequency
oxygen wing (45–54 GHz), and the opaque oxygen band (54–60 GHz). In the
following, the contribution dominance is inferred from Fig. 7, while the
typical values are inferred from Fig. 6 and Tables 4–5.

20–26 GHz:

26–45 GHz:

45–54 GHz:

54–60 GHz:

The qualitative conclusions above may sound somewhat obvious, at least to
microwave remote sensing experts. But the quantitative estimates are
unprecedented to our knowledge, especially in light of the evaluation of the
full uncertainty covariance matrix. One may wonder how high the
contribution of covariance matrix off-diagonal terms is. To evaluate it,

Zenith downwelling

Contributions to zenith downwelling

Finally, it shall be noted that the output of this analysis is

Previous studies also reported values for

The uncertainty in absorption model parameters impacts the accuracy of
geophysical variables retrieved from radiometric observations through
inversion methods based on a forward operator. Here, the forward operator is
a radiative transfer model (RTM) relying on the spectroscopic parameters to
compute atmospheric absorption and emission and thus the measurable

Thus, let us consider the OEM formalism. Following Rodgers (2000), the total
uncertainty covariance matrix of the retrieved atmospheric profile

As an example of the spectroscopic contribution to profiling uncertainty we
apply the approach described above to HATPRO channels (as in Table 4),
specifically (i) seven K-band channels (22.24 to 31.40 GHz) and (ii) seven
V-band channels (51.26 to 58.0 GHz), to compute the impact on specific
humidity and temperature profile retrievals, respectively. For the sake of
result reproducibility, simple diagonal

Difference between

Uncertainty in temperature retrievals from ground-based
MWR due to the uncertainty in

The square roots of

With respect to the absorption model parameter contribution in Figs. 10
and 11, the uncertainty due to measurement noise (i.e., the diagonal terms of

Radiative transfer models have general implications for atmospheric sciences,
including meteorology and climate studies. Atmospheric absorption modeling is
a key component of radiative transfer codes, which are extensively used for
the retrieval of atmospheric variables and the assimilation of radiometric
observations into NWP. Uncertainties in atmospheric absorption models thus
contribute to the uncertainty of atmospheric retrievals and observations vs.
background comparison. The analysis above shows a viable approach to quantify
the uncertainties of atmospheric absorption modeling and the impact on
radiative transfer calculations and atmospheric retrievals. The approach
relies on the estimation of the full covariance matrix of parameter
uncertainties, which is necessary to compute the uncertainty of calculated

We have summarized the modifications made in the last 20 years to a
reference absorption model (Rosenkranz, 1998), leading to the current version
of the model R17. We reviewed the spectroscopic literature searching for
uncertainty estimates affecting the spectroscopic parameters entering the
absorption model code. In the considered frequency range, atmospheric
absorption is dominated by water vapor and oxygen. The associated parameters
and their uncertainties are reported in Tables 1 and 2, respectively, for
water vapor and oxygen absorption. We performed a sensitivity analysis by
perturbing each parameter by its estimated uncertainty and quantifying the
impact on simulated

Then, the contribution of the spectroscopic parameter uncertainties, including
the covariance between them, to the uncertainty of simulated downwelling
20–60 GHz

The resulting uncertainty on simulated

Finally, let us underline the fact that the presented uncertainty quantification
contributes to a better understanding of the total uncertainty affecting
radiometric products, thus reducing the chances of systematic errors in NWP
data assimilation and observation-derived climate trends. Note that the
presented uncertainty covariances of spectroscopic parameters are generally
valid, while the

As in Fig. 11, but for specific humidity retrievals.

Uncertainty covariance matrices for the spectroscopic
parameters considered here, as well as the resulting

The following two sections review the set of modifications to the R98 model for water vapor and oxygen absorption, respectively, proposed in the open literature in the last 20 years and subsequently imported in the current R17 version of the model.

The R98 model uses 15 water vapor lines, similar to the strongest lines used
in MPM89, while the other 15 lines have been omitted as they were judged to
have a negligible impact. For the water vapor continuum absorption, the model
combines the foreign-broadened component from MPM87 with the self-broadened
from MPM93, increased by 15 % and 3 %, respectively, to compensate for
the line truncation at cutoff frequency (

Since 2003, the model has included the pressure line shift mechanism
investigated by Tretyakov et al. (2003) and Golubiatnikov et al. (2005). For
the 22.23 and 183.31 GHz absorption lines, the only two relevant for the
frequency range under study here, the main modifications are the adoption of
the air-broadened line widths determined in Payne et al. (2008) using
ground-based radiometric measurements, leading to

Parameters for higher-frequency lines (321–916 GHz) were modified according to different sets of spectroscopic measurements (Colmont et al., 1999; Podobedov et al., 2004; Koshelev et al., 2007; Golubiatnikov et al., 2008; Koshelev, 2011; Tretyakov et al., 2013), leading to modifications in air-broadened line width (order of 1 %–15 %), the temperature exponent of air broadening (2 %–5 %), and self-broadened line width (1 %–9 %). Other line parameters are from the HITRAN 2012 database (Rothman et al., 2013).

Concerning the water vapor continuum, the main modifications follow the
results of Turner et al. (2009) suggested by an analysis of ground-based
observations at 150 GHz. The suggested adjustments to the two components of
the water vapor continuum in the R98 model are in opposite directions (i.e.,
increasing the contribution from the foreign-broadened component while
decreasing the contribution from the self-broadened component). Figure A1
plots

More recently, two papers presented further modifications to the spectroscopy
underlying microwave remote sensing of atmospheric water vapor, i.e.,
Tretyakov (2016) and Koshelev et al. (2018). Tretyakov (2016) presents a
historic review, discussing in chronological order the measurement and
analysis that lead to estimates of spectroscopic parameters for the water
vapor absorption continuum and resonant lines near 22 and 183 GHz.
Tretyakov (2016) also provides an expert assessment of the best estimate for
the spectroscopic parameter values and their uncertainty based on the
analysis of all the available data. These parameter values provide the best
fit of the absorption model to the available data, taking into account the
measurement errors reported by the authors and the probabilities of possible
systematic errors. In almost all cases, with the exception of the 22 GHz
line self-broadening, the estimated parameter values agree within uncertainty
limits with those given in HITRAN, though in most cases HITRAN uncertainty
estimates are more conservative. Concerning the water vapor continuum
absorption, Tretyakov (2016) finds that the adjustments to R98 proposed by
Turner et al. (2009), based on zenith-looking ground-based radiometric
observation, lead to a worse fit to the laboratory and field (parallel to
Earth-surface path) measurements, particularly noticeable in the self
component. However, Fig. A1 shows that the model uncertainties have
appreciable overlap. Finally, Koshelev et al. (2018) present laboratory
measurements devoted to refining the 22 GHz line-shape parameters. Koshelev
et al. (2018) suggest line width values within the uncertainty of those given
by Tretyakov (2016), though with smaller estimated uncertainty by a factor of

The R98 model adopts the same oxygen line parameters as given in MPM92,
except for sub-millimeter frequencies for which frequency and intensity are taken
from the HITRAN 1992 database (Rothman et al., 1992). Other differences with
respect to MPM92 are the temperature dependence (

The line intensities are from the HITRAN 2004 database (Rothman et al.,
2005). The zero-frequency line intensity is from the JPL catalogue
(

The line width and line-mixing coefficients for the 118 GHz line are taken from Tretyakov et al. (2004), who report results of laboratory investigations of the pressure-dependent parameters of the single 118 GHz line. The sub-millimeter line widths are from Golubiatnikov and Krupnov (2003), except the one at the 234 GHz line that comes from Drouin (2007).

Makarov et al. (2011) proposed a model for the 60 GHz absorption band based
on the second-order line-mixing expansion of Smith (1981), showing an
improved fit of observed absorption profiles between 54 and 65 GHz, but this
model is not adopted in R17. In fact, during this analysis, significant
absorption differences (

For the dry continuum, R98 only considered the

In order to consider the broadening of oxygen lines by water vapor with little modifications to the original model, R17 adopts the mean value of the water-to-air broadening ratio suggested by Koshelev et al. (2015).

More recently, Koshelev et al. (2016) report measurements of line widths and
their temperature exponents for 12 oxygen lines (rotational quantum
number

The supplement related to this article is available online at:

DC and PR designed the research, contributed to data processing and analysis, and wrote the original manuscript. MYT, MAK, and FR provided advice and contributed to data analysis. All the co-authors helped to revise the manuscript.

The authors declare that they have no conflict of interest.

This work was partially supported by the EU H2020 project GAIA-CLIM (Ares(2014)3708963, project 640276). Mikhail Y. Tretyakov and Maksim A. Koshelev acknowledge state project no. 0035-2014-009. Domenico Cimini acknowledges the useful advice from Stefan Bühler, Richard Larsson, and Oliver Lemke in the early stage of the analysis. Edited by: Jui-Yuan Christine Chiu Reviewed by: Vivienne Payne and two anonymous referees