AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus PublicationsGöttingen, Germany10.5194/amt-10-4979-2017Retrieving vertical ozone profiles from measurements of global spectral irradianceBernhardGermarbernhard@biospherical.comhttps://orcid.org/0000-0002-1264-0756PetropavlovskikhIrinahttps://orcid.org/0000-0001-5352-1369MayerBernhardBiospherical Instruments Inc., San Diego, CA 92110, USACooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, CO 80309, USANOAA Earth System Research Laboratory, Global Monitoring Division, Boulder, CO 80305, USALudwig-Maximilians-Universität, 80333 Munich, GermanyGermar Bernhard (bernhard@biospherical.com)20December20171012497949946June20176November201724October201725July2017This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/This article is available from https://amt.copernicus.org/articles/10/4979/2017/amt-10-4979-2017.htmlThe full text article is available as a PDF file from https://amt.copernicus.org/articles/10/4979/2017/amt-10-4979-2017.pdf
A new method is presented to determine vertical ozone profiles from
measurements of spectral global (direct Sun plus upper hemisphere) irradiance
in the ultraviolet. The method is similar to the widely used Umkehr
technique, which inverts measurements of zenith sky radiance. The procedure
was applied to measurements of a high-resolution spectroradiometer installed
near the centre of the Greenland ice sheet. Retrieved profiles were validated
with balloon-sonde observations and ozone profiles from the space-borne
Microwave Limb Sounder (MLS). Depending on altitude, the bias between
retrieval results presented in this paper and MLS observations ranges between
-5 and +3 %. The magnitude of this bias is comparable, if not
smaller, to values reported in the literature for the standard Dobson Umkehr
method. Total ozone columns (TOCs) calculated from the retrieved profiles
agree to within 0.7±2.0 % (±1σ) with TOCs measured by the
Ozone Monitoring Instrument on board the Aura satellite. The new method is
called the “Global-Umkehr” method.
Introduction
The Umkehr method for determining the vertical distribution of ozone in the
atmosphere was first introduced in the 1930s (Götz et al., 1934) and is
now routinely applied to measurements taken with Dobson (e.g. Dütsch,
1959; Mateer and DeLuisi, 1992; Petropavlovskikh et al., 2005) and Brewer
(McElroy and Kerr, 1995; Petropavlovskikh et al., 2011) spectrophotometers.
The method is typically based on analysing ratios of zenith-sky radiances at
two wavelengths in the ultraviolet (UV), one strongly and one weakly
attenuated by ozone, that are measured at solar zenith angles (SZAs) between
60 and 90∘. Here we explore using a similar optimal statistical
approach to obtain vertical ozone information from measurements of spectrally
resolved global irradiance, i.e. the irradiance received by a horizontal
cosine collector from direct Sun and sky (upper hemisphere, from zenith to
horizon). Such measurements were started by several groups in the early 1990s
to monitor changes in UV radiation at the Earth's surface. These activities
were motivated by concerns that decreases in atmospheric ozone
concentrations, which were caused by ozone-depleting substances released by
man into the atmosphere, could lead to increases in UV radiation with
detrimental effects on human health, and terrestrial and aquatic ecosystems
(e.g. Bais et al., 2015). Measurements of global spectral irradiance have
been routinely performed by several UV monitoring networks sponsored by the
National Science Foundation (NSF; http://uv.biospherical.com/), NOAA
(http://www.esrl.noaa.gov/gmd/grad/antuv/), the Network for the
Detection of Atmospheric Composition Change (NDACC;
http://www.ndsc.ncep.noaa.gov/), Environment Canada
http://exp-studies.tor.ec.gc.ca/e/ozone/ozonecanada.htm), the European
Union (http://uvdb.fmi.fi/uvdb/), and others. The proposed method has
the potential to make these long-term data sets available for assessing
vertical ozone information in an approach similar to standard zenith-sky
Umkehr retrievals. This is particularly interesting for locations where
zenith-sky observations are not available.
Compared to other methods (e.g. Lidar observations, Megie et al., 1977;
balloon-sondes, and microwave spectrometers, Parrish et al., 1992; Waters
et al., 2006), the Umkehr technique provides a relatively inexpensive way of
measuring the vertical distribution of ozone in the atmosphere. The method is
most sensitive to the altitude range of 20 to 45 km and has
a resolution of about 10 km within this range. For midlatitude
sites, Brewer Umkehr data have a precision of about 15 % in the 20 to
40 km region, with larger departures outside this altitude range
(McElroy and Kerr, 1995). Umkehr data are routinely used for monitoring the
drift of sensors measuring the vertical distribution of ozone from space
(Newchurch et al., 1987; DeLuisi et al., 1994; Miller et al., 1997;
Krzyścin et al., 2009; Petropavlovskikh et al., 2005, 2011).
The use of measurements of global irradiance instead of zenith-sky radiance
for Umkehr retrievals is of no advantage per se. First, global irradiance
includes the direct solar beam, which is attenuated according to Beer's law
and therefore does not contain information on the profile. Second, global
irradiance includes photons received from directions close to the horizon and
multiple-scattering effects are therefore not negligible. We will show that
both challenges can be overcome, resulting in profiles of similar accuracy
to those inverted from zenith-sky observations. The main advantage of the
method presented here is that the vertical distribution of ozone can be
derived for locations where no other ground-based data exist from which
profiles could be calculated. The new method is called the “Global-Umkehr”
method.
The Global-Umkehr method was tested using data from the NSF UV Monitoring
Network (Booth et al., 1994), which has been measuring UV and visible global
spectral irradiance (290–600 nm) at six high-latitude sites since
1990. For this study we used data from Summit, Greenland
(72∘35′ N, 38∘27′ W,
3202 ma.s.l.), where ozone profiles have been routinely measured
also by balloon-sondes. The method can also be applied to measurements at
lower-latitude sites. We estimate that about 25 spectroradiometers that are
part of the various UV monitoring networks mentioned earlier provide data of
sufficient quality for the Global-Umkehr method. Some of these instruments
were established in the early 1990s at locations around the globe, including
the Arctic, North America, Hawaii, Europe, New Zealand, Australia, and
Antarctica.
MethodRetrieval method
The retrieval method is based on the optimal estimation approach
(Gauss–Newton method) developed by Rodgers (2000). In brief, the solution
(i.e. the ozone concentration as a function of altitude or pressure) is
determined iteratively with the matrix equation:
xi+1=xi+Si+1[KiTSε-1(y-F(xi))-Sa-1(xi-xa)],
where
Si+1=(Sa-1+KiTSε-1Ki)-1.
Equations () and () contain the following parameters:
xi
is the state vector of iteration i. In our implementation, it is defined as the average ozone concentration in 11 layers with
a layer thickness of 5 km.
y
is the measurement vector, which is composed of ratios of global spectral irradiance E(λ) measured at 310 nm (a wavelength strongly attenuated by ozone) and 337 nm (a wavelength weakly attenuated by ozone) for SZAs ranging between 70 and 90∘.
F(xi)
is the solution of the forward model (Sect. 2.3), which simulates the measurements using the state vector as input.
Ki
is the Jacobian matrix of the partial derivatives of the forward model results and the state vector.
Sε
is the covariance matrix quantifying the uncertainty of the measurements.
xa
is the a priori state vector. The iteration starts by setting x0=xa.
Sa
is the covariance matrix pertaining to the a priori state vector.
Si+1
is the solution error covariance matrix at iteration i+1, which can be exploited to calculate the uncertainty of the retrieval.
We chose 310 nm as the lower wavelength because measurements at this
wavelength are at least a factor of 50 larger than the spectroradiometer's
detection limit of 0.001 mWm-2nm-1 for all SZAs and ozone
columns of interest. The upper wavelength of 337 nm was chosen
because the temperature sensitivity of the ozone absorption cross section has
a local minimum at about this wavelength (Bass and Paur, 1985). We also
tested other wavelength pairs or combinations of several pairs of wavelengths
– e.g. combinations of E(305)/E(337); E(310)/E(337); E(325)/E(337) – when developing the method. We found that the use of multiple pairs
improved the information content only minimally but increased the
computational time considerably.
The SZA range chosen for Umkehr observations is a trade-off between the
additional information content resulting from a larger range and the risk
that environmental conditions (e.g. clouds, ozone profile) may change
substantially over the longer observation time that a larger SZA range
requires. During development, we tried several SZA ranges and found that
a range of 70 to 90∘ is a good compromise. This observation
is consistent with the conclusion by Petropavlovskikh et al. (2005) that
information in the upper layers is not degraded by changing the SZA range
from 60–90 to 70–90∘ in the standard zenith-sky Umkehr
method. We also omitted observations with SZAs larger than 90∘
because of potential systematic errors in the forward model results
(Sect. 2.3) when the Sun is below the horizon. At the latitude of Summit,
a SZA range of 70 to 90∘ is available in spring between 27
March and 8 May and in autumn between 4 August and 15 September.
The Jacobian matrix Ki has the elements [Ki]mn=[∂F(xi)]m/[∂xi]n and is calculated for every iteration step.
The measurement error covariance matrix Sε is
a diagonal matrix and is constructed by assuming that elements of the
measurement vector have an uncertainty of σε=3 %
and are independent of wavelength and SZA:
[Sε]mn=σε2[y]m[y]nfor m=n0for m≠n.
The value of 3 % was chosen based on the uncertainty budget of the
spectroradiometer installed at Summit (Sect. 2.2). The choice of 3 % was
further supported by analysing the residuals of the retrieval results
(y-F(x^)) where x^
indicates the solution state vector after the final iteration.
A priori state vectors xa were constructed by combining
balloon-sonde profiles for altitudes below 10 km and profiles
measured by the Microwave Limb Sounder (MLS) on NASA's Aura satellite for
altitudes above 10 km (see Sect. 2.5 for additional information on
these profiles). Separate a priori profiles were used for processing data
from spring (27 March–8 May) and autumn (4 August–15 September). Profiles for
both seasons were constructed by calculating the median of a large number of
sonde and MLS profiles measured during the two periods using data from the
years 2004 to 2014.
The covariance matrix pertaining to the a priori state vector, Sa, was
constructed as suggested by Bhartia et al. (2013):
[Sa]mn=σa2[xa]m[xa]nexp(-|m-n|/d).
The parameter σa specifies the anticipated variability of
the retrieved profiles about the a priori profile and can be interpreted as
the relative standard deviation (SD) of the profiles' distribution. The correlation length d was
set to two, which is equivalent to 10 km for our definition of the
state vector.
When σa is set to a small value (e.g. 0.1), the solution
of the inversion becomes very sensitive to the a priori profile. In
contrast, when σa is set to a large value, the solution is mostly
determined by the measurements. Choosing the optimum value for
σa is a trade-off between two competing effects: a large
value of σa ensures correct inversion result even if the
true profile deviates greatly from the a priori profile. On the other hand,
a small value of σa reduces the risk that the retrieval
result is grossly incorrect if measurements are affected by unanticipated
errors.
We calculated profiles for σa=0.1 and 0.4 and compare
the results in Sect. 3. The value of σa=0.1 was chosen by
analysing the variability of MLS profiles relative to the spring and autumn a priori profiles introduced above. For Umkehr layers 3 to 7 (the
layers to which the Umkehr method is most sensitive) the relative SDs
calculated from the MLS profiles vary between 0.05 and 0.15; averaged over
layers 3 to 7, the relative SD is 0.12 for the spring and 0.09 for the
autumn period. The value of σa=0.4 was chosen as the other
extreme. With this value, the a priori profile has little influence on the
inversion result and the effect of errors in the measurement vector
y becomes more prominent. The retrieval results depend
technically on the ratio γ≡(σε/σa)2 as opposed to
σa (Bhartia et al., 2013). Because the measurement
uncertainty σε is well defined, we discuss the results
using σa instead of γ.
The iteration is repeated until two conditions are met: first, the norms of
xi+1 and xi must differ by less than
0.5 %, and second, the values of consecutive results of the cost function
Ψ(x) must agree to within 5.0 %, where
Ψ(x)=(y-F(x))TSε-1(y-F(x))+(xa-x)TSa-1(xa-x).
These convergence criteria were adopted from Tzortziou et al. (2008). We
confirmed that these criteria are also appropriate for our application by
analysing changes of the two convergence metrics as a function of iteration
i. The two criteria are always met in two to four iterations.
The uncertainty em of each element of the solution's state vector was
calculated according to Goering et al. (2005) from the diagonal elements of
the solution error covariance matrix and the solution state vector:
em=[S^]mm[x^]m,
where the caret (^) above the symbols x and
S indicates the values of xi and
Si of the final iteration.
The performance of an inversion based on the optimal estimation approach is
often assessed with the averaging kernel matrix A≡S^KiTSε-1Ki, which quantifies the sensitivity of the retrieved state
x^ to perturbations in the true state x. For
an ideal observing system, A is the identity matrix. In reality, the
rows of the averaging kernel matrix are peaked with a finite width, which can
be regarded as a measure of the vertical resolution of the retrieved profile.
Similarity to the identity matrix, it indicates that the retrieval solution has
been determined using the observations rather than the a priori
information, and as such, the retrieval has provided new information about
the actual state.
Elements of A can have large positive and negative values for layers
where the ozone concentration is close to zero. To prevent this predicament,
Bhartia et al. (2013) suggested illustrating the performance of the
algorithm with relative averaging kernels (RAK or
AR), which quantify the relative change of the
retrieved state x^ to the perturbations in the true state
x. AR is defined by
[AR]mn=[A]mn[x^]n[x^]m.
The optimal estimation technique provides several diagnostics in addition to
the averaging kernels about the quality of the retrieved profile. The
diagnostic used here is ds, which expresses the number of
degrees of freedom for signal and indicates the number of useful
independent observations in the measurement vector y.
ds was calculated as suggested by Rodgers (2000) and Goering
et al. (2005) from the singular values λm of the error-weighted
weighting function matrix K̃≡Sε-1/2KSa-1/2 via
ds=∑mλm21+λm2.
The diagnostic ds depends on Sa and in turn on
σa. We will show in Sect. 3 that ds is considerably
smaller for profiles calculated with σa=0.1 than 0.4.
Measurements
The method was tested using measurements of global spectral irradiance
performed at Summit with a SUV-150B spectroradiometer designed by
Biospherical Instruments Inc. The instrument has a spectral resolution of
0.63 nm, is part of the US National Science Foundation's Arctic
Observing Network, and contributes data to NDACC. The expanded uncertainty
(coverage factor k=2, equivalent to uncertainties at the 2σ-level
or a confidence interval of 95 %) of global spectral irradiance
measurements for wavelengths between 310 and 337 nm is between 6.0
and 6.7 %. More information on the instrument is provided by Bernhard
et al. (2008) and a detailed uncertainty budget is available at
http://uv.biospherical.com/Version2/Uncertainty_SUV150B.pdf.
Data used in this paper are from the version 2 data edition (Bernhard
et al., 2004) and are corrected for the cosine error of the instrument's
entrance optics. The wavelength mapping was determined with a Fraunhofer-line
correlation method and the wavelength uncertainty (k=2) of processed data
is 0.02 nm. Measured spectra and spectra calculated with the forward
model (Sect. 2.3) were convolved with a triangular function of 2 nm
bandwidth to further reduce uncertainties resulting from potential wavelength
shifts between measured and modelled spectra.
The SUV-150B is a scanning instrument, which measures each wavelength at
a different time. The time required to scan between 310 and 340 nm is
about 140 s. Changing cloud condition will therefore affect the ratio of
measurements at these wavelengths and in turn the accuracy of the retrieval
result. The effect of clouds on the ratio of E(310)/E(337) can be reduced
using measurements of a filtered photodiode, which is illuminated via a beam
splitter located between the entrance optics and monochromator of the
SUV-150B system. The sensitivity of the diode is centred at 330 nm
and measurements are preformed continuously during the recording of spectra.
Because attenuation by thin clouds is fairly uniform in the 310 to
337 nm range (Seckmeyer et al., 1996), measurements of the photodiode
can be used to correct for variable cloud attenuation. Specifically, spectral
measurements at λ=310nm or λ=337nm are
multiplied with a correction factor C(λ,t), defined as
C(λ,t)=DC(θ(t))D(t),
where t is the time of the spectral measurement, θ(t) is the SZA at
time t, and D(t) is the measurement of the photodiode at time t. DC(θ(t)) is the hypothetical clear-sky photodiode measurement at time
t. The function was parameterized as a function of SZA using measurement of
the photodiode obtained during clear skies. Clear-sky periods were determined
based on temporal variability using the method described by Bernhard
et al. (2008). The correction takes into account that the SZA changes between
measurements at 310 and 337 nm. This technique cannot be
applied in the presence of optical thick clouds which increase ozone
absorption of tropospheric ozone due to path length enhancement (Mayer
et al., 1998). This restriction does not apply to Summit, where clouds are
always optically thin (Bernhard et al., 2008). Measurement vectors were
inverted both with and without the cloud correction, and results are compared
in Sect. 3.2.
Spectral irradiances at 310 and 337 nm were calculated for all
spectra measured during a given period of Umkehr observations and
interpolated to a common SZA grid (70, 75, 80, 85, 87, 88, 89, and
90∘) using an approximating (smoothing) spline. Compared to an
interpolating spline, an approximating spline has the advantage of reducing
noise in the measurement vector further. Tests indicated that retrieval
results do not change significantly by adding measurements at additional
SZAs.
The measurement vector is only constructed from spectra measured in the
afternoon (between 15:00 and 20:00 UTC) because solar measurements have gaps
in the morning when the system performs diagnostics scans with internal lamps
(wavelength and irradiance standards).
Forward model
Forward modelling was performed with Version 1.01 of the pseudospherical
discrete ordinate (SDISORT) radiative transfer solver of the
UVSPEC/libRadtran model (Mayer and Kylling, 2005). The number of streams was
set to 12. The model's results are spectra of global irradiance. Model input
parameters include the extraterrestrial spectrum (as defined by Bernhard
et al. (2004) and available at
http://uv.biospherical.com/Version2/Paper/2004JD004937-ETS_GUEYMARD.txt),
surface albedo, atmospheric pressure, and the ozone absorption cross section
(Bass and Paur, 1985). While more accurate ozone absorption cross sections
are now available (Gorshelev et al., 2014; Orphal et al., 2016), we used Bass
and Paur (1985) data to facilitate validation with OMI total ozone column
measurements, which are also based on Bass and Paur (1985). The surface
albedo at Summit was set to 0.97 in good agreement with recent measurements
(Carmagnola et al., 2013). Aerosol optical depth was set to stratospheric
background conditions. Atmospheric pressure and profiles of gases other than
ozone (O2, H2O, CO2, and NO2) were taken from
the Air Force Geophysics Laboratory (AFGL) atmospheric constituent profile
for subarctic summer (Anderson et al., 1986), which defines the atmosphere at
51 levels. The vertical distribution of ozone in this standard profile was
replaced with the profile defined by the state vector xi and
updated in every iteration.
The SDISORT solver has been successfully validated using data of the NSF UV
Monitoring Network (e.g. Bernhard et al., 2004, 2008) and for a large range
of conditions at other sites (e.g. Mayer and Kylling, 2005, and references
therein). However to the best of our knowledge, rigorous validation for the
large SZAs required for Umkehr retrievals has not been conducted. The
pseudospherical approximation used by SDISORT correctly describes the
attenuation of the direct beam in spherical geometry but the diffuse radiance
is computed in plane-parallel geometry (Mayer et al., 2015). This
approximation can lead to significant errors at large SZAs (Petropavlovskikh
et al., 2000; Emde and Mayer, 2007). To quantify these errors for our
application, we have compared spectra of global irradiance calculated with
SDISORT with the spherical solver of the MYSTIC (Monte Carlo code for the
phYSically correct Tracing of photons In Cloudy atmospheres) model, which
fully solves the spherical geometry without any approximations (Mayer, 2009).
Both models were run with the same set of input parameters (AFGL subarctic
summer with a priori ozone profile for spring at Summit) for wavelengths
between 307 and 313 nm and between 334 and 340 nm in
0.5 nm steps. The MYSTIC model was run with 84 million photons per
wavelength and per SZA, resulting in photon noise of less than 0.5 % at
SZA =90∘ (worst case). Resulting spectra of both models were
convolved with a triangular function of 2 nm bandwidth to further
reduce noise and to be consistent with the method used in the Umkehr code.
Comparison of results calculated with the SDISORT and MYSTIC models.
(a) Ratio of SDISORT and MYSTIC spectra calculated for eight SZAs
(see legend). (b) Ratio R(θ). See text for definition.
Validation of the ozone profile retrieved for 19 April 2014. (a–d) Results
for σa=0.4 and uncorrected forward model. (e–h) Results of σa=0.4 and corrected forward model.
(i–l)σa=0.1, and corrected forward model. First
column: ozone concentration as a function of pressure for a priori profile
(grey), balloon-sonde profile (blue), MLS profile for day of retrieval (MLS
1, dark green), MLS profile of the following day (MLS 2, light green), and
retrieved profile (red). Solid or open circles indicate, for each data set,
ozone concentrations averaged over each of the 11 Umkehr layers defined
in Table 1. Grey error bars indicate the diagonal elements of
Sa. Red error bars indicate the uncertainty of the retrieval
em. TOCs measured by OMI and calculated from the retrieved profile are
indicated in the legend. Second column: layer ozone as a function of pressure
for a priori profile, balloon-sonde profile, MLS profile for day of
retrieval, MLS profile of the following day, and retrieved profile. Third
column: difference between the retrieval and sonde, MLS 1 and MLS 2 data
averaged over each Umkehr layer. Fourth column: relative averaging kernels.
Validation of ozone profile retrieved for 11 April 2007. (a–d) Results
of σa=0.4 and corrected forward model. (e–h)σa=0.1, and
corrected forward model. (a, e) Ozone concentration as a function of pressure. (b, f) Layer ozone as
a function of pressure. (c, g) Difference between the retrieval and
sonde, MLS 1 and MLS 2 data sets averaged over each Umkehr layer. (d, h) Relative
averaging kernels. Labelling of the different data sets is identical
to that of Fig. 2.
Validation of ozone profile retrieved for 14 August 2009. The
retrieved profile was calculated with σa=0.1 using the
corrected forward model. (a) Ozone concentration, (b) layer
ozone, (c) difference between the retrieval and sonde, MLS 1 and MLS
2 data sets averaged over each Umkehr layer, (d) relative averaging
kernels. Labelling of the different data sets is identical to that of Fig. 2.
Figure 1a shows the ratio of SDISORT and MYSTIC spectra calculated for the
eight SZAs used in our implementation of the Global-Umkehr method. SDISORT
overestimates spectral irradiances relative to MYSTIC at all wavelengths and
SZAs. For SZA ≤ 88∘, the bias is less than 2 % but increases
to up to 6.5 % for SZA =90∘. For the Umkehr retrieval, only
the ratio q(θ)≡E(310,θ)E(337,θ) is important
where θ again indicates the SZA. The ratio R(θ)≡qSDISORT(θ)qMYSTIC(θ) resulting
from calculating q(θ) with SDISORT and MYSTIC is shown in Fig. 1b.
R(θ) ranges between 0.998 at 80∘ and 1.019 at 90∘.
Calculations with the MYSTIC model can be considered the most accurate
results attainable because the Monte Carlo code does not use approximations.
The model has been validated by comparison with other spherical radiative
transfer models and by simulating the radiance distribution of the sky during
a total solar eclipse. For such calculations, a spherical solver without
approximations is required because light entering the atmosphere more than
1000 km away may impact the radiance in the centre of the umbral
shadow (Emde and Mayer, 2007).
Relative to MYSTIC, SDISORT overestimates q(θ) for SZA larger than
88∘. In our Umkehr code, we scale the results of the forward model
with 1/R(θ) to account for the bias of the SDISORT model. Note that
the MYSTIC model is too slow to be used for Umkehr retrievals: the
calculation of the eight spectra used for Fig. 1a required a run time of over
3 days.
Assignment of Umkehr layers.
UmkehrAltitude rangePressurelayerforward model (km)range (hPa)1050.0–55.00.987–0.537945.0–50.01.82–0.987840.0–45.03.40–1.82735.0–40.06.61–3.40630.0–35.013.4–6.61525.0–30.027.8–13.4420.0–25.059.0–27.8315.0–20.0126.0–59.0210.0–15.0267.7–126.015.0–10.0541.0–267.703.202–5.0664–541
The forward model requires that the vertical structure of the atmosphere is
defined as a function of altitude. The association between altitude and
pressure is defined in the AFGL profile and this relationship may differ from
the actual pressure profile at the time of Umkehr observation. Because our
measurements do not allow the pressure profile to be reconstructed, we report all
ozone profiles as a function of pressure and compare the retrieved profile
with sonde and MLS profiles, which are also provided as a function of
pressure. The standard zenith-sky Umkehr technique (Petropavlovskikh et al.,
2005) uses a similar approach. Table 1 provides altitude and pressure ranges
for each Umkehr layer. Note that Layer 0 starts at the elevation of Summit
(3202 m).
Validation method
The retrieved Umkehr profiles were validated using ozone profiles measured at
Summit with balloon-sondes by NOAA/GMD (Oltmans et al., 2010) and ozone
profiles provided by MLS on Aura. Sondes are typically launched between 12:00
and 20:00 UTC. MLS measures thermal emissions from rotational lines of ozone
through the limb of the atmosphere. Ozone measurements have a vertical range
of 12–73 km with a vertical resolution of 2–3 km below
65 km. The horizontal resolution is about 200 km and the
accuracy is about 5–10 % between 16 and 60 km (Froidevaux
et al., 2008). The average horizontal distance between the locations of
Summit and MLS data is 160 km. Sonde and MLS profiles were downloaded
from ftp://ftp.cmdl.noaa.gov/ozwv/Ozonesonde/Summit,%20Greenland/ and
http://avdc.gsfc.nasa.gov/pub/data/satellite/Aura/MLS/V04/L2GPOVP_Prof/O3/Summit/,
respectively. Sonde profiles are only available for 2 to 4 days per month,
whereas MLS profiles are available on a daily basis. MLS measurements at
Summit take place either between 05:28 and 06:26 UTC or between 14:11 and
15:10 UTC. There is only one data file per day in the NASA archive.
The total ozone column (TOC) was calculated from the retrieved Umkehr
profiles and compared with measurements from the Ozone Monitoring Instrument
(OMI) on board NASA's Aura spacecraft. OMI overpass data were downloaded from
http://avdc.gsfc.nasa.gov/index.phpfisite=1593048672&id=28. OMI data
use the Bass and Paur (1985) ozone absorption cross section (David Haffner,
NASA, personal communication) like the forward model.
Good validation results can only be expected if the actual ozone profile does
not change over the period of Umkehr observations. We therefore only
considered periods in which the TOC measured by OMI did not change by more than
20 DU between 15:00 UTC on the day of the comparison and the first
observation on the following day. This criterion ensures that changes in the
ozone profile remain below about 4 % for all Umkehr layers. Retrieved
Umkehr profiles were compared with the sonde profile measured on the same day
(if available) and with the MLS profiles measured on this day (labelled “MLS
1” in the following) as well as the next day (labelled “MLS 2”).
Results
We first show retrieval results for 3 sample days with greatly different
conditions and compare these results with profiles measured by balloon-sondes
and MLS (Sect. 3.1). We then discuss in Sect. 3.2 statistics for all profiles
that were retrieved under sufficiently stable conditions (variation in total
ozone of less than ±20DU).
Comparison with balloon-sonde and MLS profiles – sample profilesValidation for 19 April 2014
Figure 2 compares the retrieved ozone profile for 19 April 2014 with the
a priori balloon-sonde and MLS profiles. OMI measured a TOC of 461 DU on
this day, which was the third highest TOC of the data set and the highest TOC
of days when balloon-sonde data were available. Therefore, the profile
represents one of the highest departures from the spring a priori profile.
Results are shown for three sets of retrieval parameters: (1)
σa=0.4, forward model, not corrected (top row of Fig. 2);
(2) σa=0.4, forward model, corrected by scaling with
1/R(θ) (centre row of Fig. 2); and (3) σa=0.1,
forward model, corrected (bottom row of Fig. 2). For each set of parameters,
we show profiles of ozone concentrations (first column of Fig. 2), layer ozone
(second column of Fig. 2), the difference between the retrieved profile and the
profiles measured by sondes and MLS (third column of Fig. 2), and the relative
averaging kernels (RAKs) of the retrieval (fourth column of Fig. 2).
Layer ozone (Fig. 2b, f, and j) was calculated by integrating average ozone
concentrations of each Umkehr layer over height. Note that ozone
concentrations (Fig. 2a, e, and i) are plotted on a linear scale to highlight
differences in the troposphere and lower stratosphere, while layer ozone
(Fig. 2b, f, and j) is plotted on a logarithmic scale to better distinguish
differences in the upper stratosphere.
Figure 2c, g, and k shows differences in the average ozone concentrations for
the 11 Umkehr layers. Two MLS data sets are considered. The data set labelled
MLS 1 is from the same day as the retrieval, while the data set labelled
MLS 2 is from the following day.
When plotting ozone concentrations on a linear scale (Fig. 2a, e, and i),
results for the three sets of parameters look similar. As expected, the
resolution of the retrieval is not sufficient to capture the large
fluctuation in the ozone concentrations between about 100 and 300 hPa
indicated by sonde and MLS measurements. Furthermore, the retrieved profiles
overestimate the ozone concentration at the peak of the profile at about
100 hPa and underestimate the profile in the 7 to 28 hPa
range (layers 5 and 6). The difference of -22.5 % between the retrieval
and MLS 1 seen in Fig. 2c for Layer 5 is one of the largest negative biases
of all profiles processed. This large bias may partially be caused by errors
in the measurement vector due to clouds (the photodiode used for cloud
correction was not available on this day). The large deviation of
52 % for Layer 0 is not surprising considering that this layer is only 1.8 km
thick and the sensitivity of the Umkehr method to ozone concentrations close
to the surface is poor.
The bias of the retrieval becomes smaller when the forward model is corrected
for the systematic error resulting from the pseudospherical approximation
(compare Fig. 2c and g), indicating that the correction is appropriate.
The smallest difference between the retrieval on one hand and sonde and MLS
measurements on the other is observed for σa=0.1
(Fig. 2k). This suggests that a relatively small value for
σa is advantageous even though the sample profile deviates
considerably from the a priori profile. For layers 5 to 9, the magnitude of
the bias is comparable in magnitude to the difference between the two MLS
profiles, suggesting that a portion of the bias could be due to changes in
the ozone profile occurring during the period of Umkehr observations.
When σa is set to 0.4, the RAKs of layers 3 to 7 peak at
the correct layer and drop to zero within two layers, suggesting that ozone
concentrations in this altitude range can be easily resolved (Fig. 2d and h).
In contrast, RAKs for layers 0, 1, and 2 are similar and peak at about the
same altitude. Hence, ozone concentrations in these layers cannot be easily
separated. The altitude resolution of the standard zenith-sky Umkehr method
is also poor in these layers, and results for layers 0 and 1 are typically
combined when reporting data. RAKs for layers 8–10 peak at the same
altitude, indicating that ozone concentrations above the 3 hPa level
(about 45 km) cannot be resolved and the retrieval is predominantly
driven by the a priori profile. This is not surprising considering the
small ozone concentrations in these layers. Also, the traditional zenith-sky
Umkehr method has little sensitivity at these altitudes.
When σa is set to 0.1, the RAKs become rather broad
(Fig. 2l). The solution is therefore more determined by the a priori
profile than the observations. The reduced importance of the measurements is
also reflected in the value of ds: ds is 3.02 for
σa=0.4 and 2.15 for σa=0.1.
TOCs calculated from the retrieved profiles agree well with the OMI
measurements and depend only little on the choice of retrieval parameters:
absolute and relative biases are 7 DU (1.5 %) for parameter set (1),
6 DU (1.3 %) for set (2), and 1 DU (0.2 %) for set (3).
Comparison for 11 April 2007
Figure 3 shows results for 11 April 2007. On this day, ozone concentrations
measured by sonde and MLS were consistently below the a priori profile
between 5 and 100 hPa, but between 100 and 300 hPa, the
actual profile exceeded the a priori. Figure 3a–d shows results calculated
with σa=0.4, while calculations for Fig. 3e–h used
σa=0.1. The forward model was corrected by scaling with
1/R(θ) in both cases. Note that the MLS 1 and MLS 2 data sets are
almost identical, indicating that the actual ozone profile was constant over
the observation period. RAKs are very similar to those for 19 April 2014
(compare Fig. 2h with Fig. 3d and Fig. 2l with Fig. 3h).
For both settings of σa, the retrieved profile is narrower
than the a priori profile and matches the MLS profile almost ideally for
layers 3–9. This is an example of the retrieval result not simply being the
a priori profile scaled with a constant factor. Instead, the information
contained in the measurement vector is sufficient to modify the shape of the
profile to match the actual, narrower shape. However, like in the case of the
first example, the resolution of the Umkehr method is not sufficient to
reproduce the fluctuation of the actual ozone profile between 70 and
300 hPa. The most obvious difference between the results calculated
with σa=0.4 and 0.1 is the difference at 183 hPa
(Layer 2). Because the Umkehr method has little sensitivity at this pressure
level, the retrieved ozone concentration is mostly determined by the
a priori profile for σa=0.1 (Fig. 3g). In contrast,
when setting σa=0.4, measurements “pull” the retrieval to the
higher concentrations of the actual profile, resulting in a smaller bias
relative to sonde and MLS data (Fig. 3c). The TOCs of both retrievals agree
to within 7 DU (or 2.1 %) with OMI.
Comparison for 14 August 2009
The third example (Fig. 4) shows results from 14 August 2009 when the ozone
profile was almost identical with the autumn a priori profile. Note that this
a priori profile is considerably below that for spring (e.g. Fig. 3d).
Calculations were performed with σa=0.1 and the
corrected forward model. Results agree with sonde and MLS profiles to within
±13 % for layers 1–10 and the TOC of the retrieval is virtually
identical to the OMI measurement. The effect of changing
σa from 0.4 to 0.1 are similar for spring and autumn profiles and results for σa=0.4 were therefore omitted
in Fig. 4.
In summary, Umkehr profiles replicate the general pattern in the sonde and
MLS data but cannot resolve the fine structure in the ozone distribution, in
particular below 100 hPa. The relatively poor resolution in the
troposphere and lower stratosphere is similar for the standard zenith-sky
Umkehr method.
Box-and-whisker plots showing the difference between Umkehr retrieval
results and sonde measurements (first column), MLS observations for day of
retrieval (MLS 1 data set, second column), and MLS observations for the
following day (MLS 2 data set, third column). The fourth column illustrates the
difference between the MLS 2 and MLS 1 data sets. Each plot shows the
minimum and maximum difference (black dots), median (black line), average
(red dot) interquartile range (box) and the 10th–90th percentile range
(whiskers) for each layer. Results for layers 0 and 1 and layers 2 and 3 were
combined. The N in the headers of each plot indicates the number of
profiles used for computing the statistics. Results in each row were
calculated with a different set of parameters. First row (panels
a–d): forward model not corrected, no cloud correction, σa=0.4. Second row (panels e–h): forward model corrected
by scaling with 1/R(θ), no cloud correction, σa=0.4. Third row (panels i–l): forward model corrected, no cloud
correction, σa=0.1. Fourth row (panels m–p):
forward model corrected, cloud correction using data of photodiode,
σa=0.1.
Comparison with balloon-sonde and MLS profiles – statistics
While the results for the three profiles discussed above are promising, they
do not allow a comprehensive assessment of the Global-Umkehr technique. To
fully validate the method, we compared a large number of sonde and MLS
profiles with our retrievals using measurements from the years 2004 to 2014,
and calculated statistics. We only considered periods in which the TOC was
constant to within ±20DU as indicated by OMI. This criterion
restricted the number of comparisons with sonde profiles to 57 and with MLS
profiles to 552. Data were processed with and without the model correction
discussed in Sect. 2.3 and with and without the cloud correction, discussed in
Sect. 2.2. The latter correction requires measurements of the photodiode
internal to the SUV-150B instrument. Unfortunately, these measurements were
not available during all days, reducing the number of retrieval–sonde and
retrieval–MLS comparisons to 38 and 396, respectively. Results from layers 0
and 1 and layers 2 and 3 were combined because of the poor vertical
resolution of the Umkehr methods in the troposphere and lower stratosphere
discussed earlier. Differences between retrieval and sonde, MLS 1, and MLS 2
data are illustrated with box-and-whisker plots (Fig. 5), which show the minimum
and maximum difference (black dots), median (black line), average (red dot),
interquartile (i.e. 25th–75th percentile) range (box), and the 10th–90th
percentile range (whiskers) for each layer or combination of layers. We also
plotted statistics for the difference of the MLS 1 and MLS 2 data sets to
indicate the variability of the actual ozone profile over the course of 1
day. Figure 5 includes results from spring and autumn combined. Table 2
provides statistics calculated separately for spring and autumn.
Bias and interquartile range (in parenthesis) of retrieval–MLS 1
comparison, average and SD of the difference between total ozone calculated
from retrieved profiles and measured by OMI (TOC), and average number of
degrees of freedom for signal (〈ds〉) for spring
and autumn periods. The second column provides the number of profiles (N)
contributing to the statistics.
The first row (panels a–d) of Fig. 5 shows results calculated without the
model and cloud corrections; σa was set to 0.4. The
average and median biases between retrieval and MLS data vary between
-8 and +5 % (Fig. 5b and c). The largest negative bias is
observed for layers 5 and 6, while the largest positive bias of 5 % is
observed closest to the surface (layer 2 and 3). Biases relative to the sonde
measurements (Fig. 5a) are by and large consistent with biases relative to
MLS data, although the comparatively small number of sonde observations makes
the statistics less robust. Figure 5d confirms that there is no systematic
difference between the MLS measurements on the day of Umkehr observations
(MLS 1) and the following day (MLS 2).
For the retrieval–MLS comparisons, the interquartile ranges vary between 7
and 12 % and depend only modestly on the layer. With the exception of
the results for the highest layer, the interquartile ranges for the MLS 2–MLS 1 comparison vary between 5 and 10 %. Differences between the 10th
and 90th percentiles vary between 14 and 24 % for the retrieval–MLS
comparisons (whiskers in Fig. 5b and c) and between 12 and 17 % for the
MLS 2–MLS 1 comparison, excluding the highest layer (Fig. 5d). The similarity
of the ranges for the retrieval–MLS and MLS 2–MLS 1 comparisons suggests that
a large portion of the observed retrieval–MLS differences can be attributed
to changes in the actual ozone profile over the time periods relevant for
these comparisons. Lastly, the large interquartile range for the
retrieval–sonde comparison observed in layer 0 and 1 (Fig. 5a) is again
a manifestation of the fact that the Umkehr method has little sensitivity for
the layers closest to the surface.
To assess the effect of the forward model correction on our Umkehr
retrievals, we repeated the calculations with this correction. Results are
presented in the second row (panels e–h) of Fig. 5. As before, no cloud
correction was applied and σa was set to 0.4. By comparing
the original results (Fig. 5b and c) with the corrected results
(Fig. 5f and g) it can be observed that the bias between retrieval and
MLS data has diminished and now varies between -5 % (layers 5 and 6)
and +3 % (layers 2 and 3), suggesting that the model correction is
justified. The interquartile ranges with and without the correction are
virtually indistinguishable. Note that the correction has no effect on the
MLS 2–MLS 1 comparison and Fig. 5d and h are therefore identical.
To explore the effect of σa on the results, we repeated
the calculations using σa=0.1 instead of
σa=0.4. Results are shown in the third row (panels i–l)
of Fig. 5. For σa=0.1, the bias between retrieval and
MLS data has decreased further and now varies between -4 and +1 %
(Fig. 5j and k). Differences between retrieval and sondes (Fig. 5i) have also
decreased compared to calculations with σa=0.4, except
for layer 0 and 1. The observation that biases are larger for a larger value
of σa could be caused by systematic errors in the
measurement vector or an incomplete correction of the forward model results.
Changing σa from 0.4 to 0.1 had almost no effect on the
interquartile range. However, minimum and maximum differences (black dots)
contracted somewhat.
Finally, the calculations were repeated with the cloud correction turned on
(fourth row of Fig. 5, panels m–p). For the retrieval–MLS comparison, biases
and interquartile ranges with and without the cloud correction agree to
within 1 %. Results for the retrieval to sonde comparison (Fig. 5m) are
affected by the small sample size of N=38. (Note that results shown for
Layer 6 are only based on eight samples because most balloons burst before
they reach this layer.)
The difference between uncorrected and cloud-corrected statistics is very
small, suggesting that clouds affect the accuracy of the retrievals only
marginally. However, this conclusion may not apply to locations with thicker
clouds and should be tested if the method is used at other sites.
Table 2 allows the assessment of retrievals for spring and autumn periods
separately. Because statistics are more robust for the retrieval–MLS than
retrieval–sonde comparisons, Table 2 only presents results for the former.
Biases and interquartile ranges are provided with and without the model and
cloud corrections, and with σa set to either 0.4 or 0.1.
Biases for spring and autumn agree to within 3 % for all layers. When no
corrections are applied and σa=0.4, biases range between
–10 % (Layer 6 for spring) and +6 % (layers 2 and 3 for autumn). The
model correction decreases this range to between -6 and 4 %. By reducing
σa from 0.4 to 0.1, the range decreases further to between
-5 to 2 %. The cloud correction has a negligible (≤1 %) effect
on the biases. Interquartile ranges vary from 7 to 16 % and depend only
little (≤3 %) on σa and on whether or not
corrections are applied.
Table 2 also includes a column comparing TOCs derived from the retrieved
profiles with measurements by OMI. Depending on σa and the
correction method, the average difference between the retrieved and OMI TOCs
varies between -0.2 and 0.7 %, and the SD varies between 1.7 and
2.0 %.
Lastly, the average value of ds is about 3.0 for
σa=0.4 and 2.1 for σa=0.1. A value
of ds=3.0 may seem low, but it is consistent with values of
ds resulting from the standard zenith-sky Umkehr technique. For
example, Stone et al. (2015) reported a value of ds=3.1 for
Dobson zenith-sky Umkehr retrievals using the Dobson C wavelength pair (311.4
and 332.4 nm) and the standard Dobson SZAs ranging from 60
to 90∘.
Discussion
When the forward model is corrected, the bias of our retrievals relative to
MLS data is smaller than ±6 % for all layers. This level of agreement
compares favourably with published results of the standard zenith-sky Umkehr
method. For example, McElroy and Kerr (1995) compared Umkehr profiles derived
from a Brewer spectrophotometer with concurrent measurements of a lidar,
a microwave radiometer and ozone sondes, which were performed during
a 1-month campaign at the Table Mountain Observatory in California. The
mean bias between the Brewer zenith-sky Umkehr results and the mean of the
other instruments varied to within ±10 % for altitudes between 20 and
35 km. Between 37 and 47 km, the Brewer data were low by 15
to 20 % (Fig. 9 of McElroy and Kerr, 1995).
Nair et al. (2011) compared stratospheric ozone vertical distribution
measured by a large number of ground-based and satellite sensors at the
Haute-Provence Observatory, France. They found that zenith-sky Umkehr data
from an automated Dobson spectrophotometer systematically underestimate the
stratospheric ozone concentration with a near-zero bias at about 30 km, but
increase to 7 % at 21 and 34 km, and to 14 % at 40 km (Fig. 8 of
Nair et al., 2011). Despite these large biases, Nair et al. (2011)
concluded that Umkehr data are useful for studies of long-term ozone
evolution and for detecting drifts in satellite observations.
Miyagawa et al. (2014) compared Dobson zenith-sky Umkehr measurements with
homogenized NOAA SBUV (Solar Backscatter Ultraviolet instrument) (/2) 8.6
overpass data measured between 1977 and 2011. The mean bias between Dobson
and SBUV partial ozone column varied between -12 % for Layer 7 and
+3 % for Layer 2 (Fig. 1a of Miyagawa et al., 2014).
The biases reported in the three studies quoted above are comparable or
larger than the differences between our Global-Umkehr retrievals and MLS and
sonde measurements, suggesting that Umkehr results derived from global
spectral irradiance can provide data with similar accuracy to the established
zenith-sky method. A portion of the retrieval–MLS difference could also be
caused by systematic errors in the MLS data set, considering that the MLS
accuracy specified by Froidevaux et al. (2008) is in the 5 to 10 % range.
Results presented in Fig. 5 illustrate that interquartile and 10th–90th
percentile ranges for the retrieval–MLS comparison on one hand and the MLS
2–MLS 1 comparison on the other are similar for most layers. This suggests
that a large portion of the observed retrieval–MLS differences can be
attributed to actual changes in the ozone profile over the time periods
relevant for these comparisons. However, a portion of the change in the MLS
profile from one day to the next may be caused by the relatively poor
horizontal resolution of MLS profiles of about 200 km. In addition,
some variability in the MLS data set can be attributed to the slightly
different geolocations of two consecutive overpass profiles. For example, the
average horizontal distance between the locations of Summit and the MLS
overpass is 160 km. Further analysis revealed that the difference
between the MLS 1 and MLS 2 data sets also depends on the time at which the
daily MLS observation takes place. For example, when MLS 2 data are from the
observation period close to local solar noon (14:11 to 15:10 UTC) and MLS 1
data are measured close to sunrise (05:28 to 06:26 UTC), MLS 2 data for
layers 7–9 have a high bias of 3–6 % relative to the MLS 1 data set,
while MLS 2 data for Layer 10 have a low bias of 8 %. This time-of-day
dependency and its variation with altitude is by and large consistent with
diurnal variations of the ozone profile measured by various instruments at
Mauna Loa, Hawaii (Parrish et al., 2014), and by a microwave radiometer at
Bern, Switzerland (Studer et al., 2014). This suggests that the time-of-day
effect observed at Summit is caused by actual diurnal changes of the ozone
profile rather than potential time-dependent systematic errors in the MLS
data set.
Another source of variability in the retrieval–MLS and retrieval–sonde
comparisons is the different vertical resolutions of MLS (about
2–3 km), sondes (0.1 km), and our Umkehr retrievals (about
10 km for σa=0.4 and about 25 km for
σa=0.1). If the measurements and forward model were without
error, an Umkehr profile would resemble the actual profile smoothed by the
AKs. To reduce the effect of the differing resolution, the higher-resolution
MLS profiles could be convolved with the AKs of the Umkehr profile prior to
comparing the two profiles. This technique has been applied by
Nair et al. (2011) when comparing lidar and SBUV profiles. We did not use
this method because it artificially reduces the true difference that is
observed when comparing a high-resolution profile (sonde, MLS) with a low-resolution
(Umkehr) profile. Nair et al. (2011) found that the smoothing
technique does not make a significant difference to seasonally averaged data
such as those presented in Fig. 5 and Table 2.
The bias between Umkehr retrievals and MLS or sonde data is reduced when
correcting the forward model for the systematic error presented by the
pseudospherical approximation. It is interesting to note that the correction
is only in the –0.5 to 2.0 % range (Fig. 1b) but reduces the retrieval
bias by up to 4 % (Layer 6 in spring; see Table 2). Considering that the
uncertainty of our measurements is 3 % (1σ), systematic errors in
the measurement vector in the 2–3 % range could conceivably be
responsible for the remaining bias of Umkehr and MLS profiles indicated in
Fig. 5 and Table 2. To test this hypothesis, we modified the measurement
vector within reasonable limits and recalculated the profiles. We found that
the bias between Umkehr and MLS profiles cannot be significantly reduced
further, suggesting that the bias cannot be attributed to measurement errors
alone.
The difference between results corrected for cloud effects and uncorrected
results is very small, implying that clouds affect the accuracy of the
retrievals only marginally. However, this conclusion may not apply to
locations with thicker clouds or locations affected by aerosols and should be
tested if the method is used at other sites.
If Sε is well defined, the most important
parameter that optimizes the results is σa. The objective is
to find the right balance between sensitivity to the a priori profile on
one hand and sensitivity to (unavoidable) errors in the measurement vector or
forward model on the other. We chose σa=0.1 and 0.4. The
smaller value quantifies the SD of the actual variability of the ozone
profile at Summit. While calculations with this value lead to good results,
the solution may not be optimal for profiles at the fringe of the
distribution (e.g. result for Layer 3 in Fig. 3). A small
σa also results in a small value of ds.
However, statistics for results calculated with σa=0.1
and 0.4 are quite similar (Table 2), suggesting that any value for
σa between 0.1 and 0.4 leads to acceptable profiles.
Determining the best value for sites other than Summit requires consideration
of the measurement system and variability of the ozone profile at this site.
There are various ways to optimize the Global-Umkehr method for specific
applications or locations. For example, if two instruments were to take
measurements side by side, the uncertainty used to set up Sε
could be better estimated by comparing the measurements of the two systems.
Furthermore, the method to set up Sa could be modified to
take into account the dependence of the variability of the ozone profile on
altitude (Eq. uses the same SD σa for all
layers). Ozone absorption cross section data could be used (e.g.
Orphal et al., 2016) that are more current than the Bass and Paur (1985) data implemented in this
work and by OMI. If temperature profile data are available, these could be
utilized to account for the temperature dependence of the ozone absorption
cross section. Wavelengths, bandpass, and SZAs used for the measurement
vector could be further optimized to reduce uncertainties related to the Ring
effect or the temperature dependence of the ozone absorption cross section.
For example, by degrading the spectral resolution (currently set to
2 nm), the impact of the Ring effect could be diminished. Finally,
the MYSTIC Monte Carlo model, which was used to calculate the correction
function R(θ) (see Fig. 1b), was run with a scalar radiative transfer
solver, which did not take polarization into account. Lacis et al. (1998)
calculated that modelling errors for irradiance resulting from the omission
of polarization in these calculations can be as large as 1.3 % for
a Rayleigh atmosphere. However, errors for 310 and 337 nm (i.e. the
wavelengths used in the Global-Umkehr method) agree to within 0.1 %. We
therefore conclude that the omission of polarization is not an import error
source in our calculations.
We used a priori profiles that are independent of the total ozone column.
Zenith-sky Umkehr retrievals from Dobson instruments that have historically
been processed with the algorithm developed by Mateer and DeLuisi (1992) used
TOC-dependent a priori profiles to constrain the retrieval. While this
practice can lead to artefacts when calculating trends (Petropavlovskikh
et al., 2005; Stone et al., 2015), the approach may be the best choice if
a profile with the smallest uncertainty possible is sought for a specific
purpose.
The Global-Umkehr method was tested with spectroradiometric measurements from
a polar location because we only operate instruments at high-latitude sites.
Inversions using high-latitude data are more challenging compared to
retrievals for lower latitudes because of the limited range of SZAs at polar
regions, the long time that is required to scan the range of SZAs necessary
for the retrieval, and the high short- and long-term variability of the ozone
profile. We therefore have confidence that the method would work well for
midlatitude and low-latitude locations. Confirmation of this assertion is subject
to future tests.
Conclusions
An optimal estimation method has been developed to retrieve vertical ozone
profiles from measurements of global spectral irradiance in the UV. The
method is similar to the widely used zenith-sky Umkehr technique, which
inverts measurements of zenith sky radiance. To our knowledge, this is the
first time that the Umkehr technique was applied to measurements of global
irradiance. High-quality measurements of global spectral irradiance are now
available for more than 25 years at several NDACC locations (De Mazière
et al., 2017), and the Global-Umkehr method has the potential to make these
long-term data sets available for studying changes in the vertical
distribution of ozone.
Compared to the standard zenith-sky Umkehr method, multiple scattering
effects become more important when exploiting global irradiance measurements,
which also include contributions from photons received from directions close
to the horizon. Therefore, the sphericity of the viewing geometry needs to be
taken into account. We have shown that this challenge can be overcome by
using a forward model with pseudospherical approximation plus additional
corrections.
The method was evaluated with spectroradiometric measurements from Summit,
Greenland, and validated with balloon-sonde and MLS observations. For
calculations using the corrected forward model, the bias between our
retrieved profiles and MLS observations ranges between -5 % (layers 5
and 6) and +3 % (layers 2 and 3). The magnitude of this bias is
comparable, if not smaller, to values reported in the literature for the
standard zenith-sky Umkehr method. The distribution of the difference between
retrieval and MLS observations was quantified with the interquartile and
10th–90th percentile ranges. Depending on altitude, the interquartile ranges
vary between 7 and 13 % and the 10th–90th percentile ranges run between
14 and 24 %. Interquartile ranges calculated from the
differences of two MLS profiles that were measured on consecutive days vary
between 5 and 10 %, suggesting that a considerable portion of the
retrieval–MLS differences can be attributed to real changes in the ozone
profile. For Umkehr layers 2 and higher, retrieval–MLS and retrieval–sonde
differences are by and large consistent. The poor sensitivity of the Umkehr
method to the altitude range of layer 0 and 1 leads to relatively large
scatter (e.g. the interquartile range is 25 %) of the retrieval–sonde
differences for this layer.
The effect of the parameter σa, which controls the
sensitivity of the solution on the a priori profile, was extensively
assessed. It was found that results calculated with a small value of
σa=0.1 (emphasis on a priori) generally agree to
within 2–3 % of those calculated with a large value of
σa=0.4 (emphasis on measurements). By setting
σa to a large value, retrieval errors may occasionally
become large if the measurement vector is affected by unforeseen conditions
(e.g. changing ozone, variable clouds). For example, the maximum
retrieval–MLS difference was 50 % for σa=0.4 but
only 32 % for σa=0.1.
The retrieved ozone profiles were integrated over altitude. The resulting
TOCs agreed almost perfectly with TOCs measured by OMI: depending on the
correction method, the retrieval/OMI bias ranged between -0.2 and 0.7 %
with a SD of less than 2.0 %.
While the Global-Umkehr method was only tested for a high-latitude site, we
are confident that it will also work at lower latitudes, but this assertion
requires confirmation by future tests.
Version 2 spectra from the SUV-150B spectroradiometer
at Summit are available from the Arctic Data Center at
https://arcticdata.io/. Profiles of ozone retrieved with the
Global-Umkehr method are available at
http://uv.biospherical.com/Version2/data.asp.
The authors declare that they have no conflict of
interest.
Acknowledgements
Funding for this study was provided by the US National Science Foundation's
Office of Polar Programs Arctic Sciences Section (award ARC-1203250,
Ultraviolet Radiation in the Arctic: 2012–2015). We are grateful to the
numerous dedicated individuals who operated the UV radiometers at
Summit. We also thank Bryan Johnson of NOAA for providing ozone profiles
collected by balloon ozonesondes that were launched at Summit on a weekly
bases. NSF provided funding for the ozonesonde measurements at Summit. We
thank two anonymous reviewers for their thoughtful
comments. Edited by: Pawan K. Bhartia Reviewed by: two anonymous referees
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