On the Retrieval of Atmospheric Profiles

FINNISH METEOROLOGICAL INSTITUTE Erik Palménin aukio 1 P.O.Box 503 FI-00101 HELSINKI 123 tel. +358 29 539 1000 CONTRIBUTIONS WWW.FMI.FI

FINNISH METEOROLOGICAL INSTITUTE CONTRIBUTIONS No. 123 ISBN 978-951-697-891-1 (paperback) ISSN 0782-6117 Erweko Helsinki 2016

ISBN 978-951-697-892-8 (pdf) Helsinki 2016

ON THE RETRIEVAL OF ATMOSPHERIC PROFILES

SIMO TUKIAINEN FINNISH METEOROLOGICAL INSTITUTE CONTRIBUTIONS

No. 123

ON THE RETRIEVAL OF ATMOSPHERIC PROFILES

Simo Tukiainen

Department of Physics Faculty of Science University of Helsinki Helsinki, Finland

ACADEMIC DISSERTATION in meteorology

To be presented, with the permission of the Faculty of Science of the University of Helsinki, for public criticism in Brainstorm auditorium at Dynamicum (Erik Palm´enin Aukio 1) on September 28th, 2016, at 12 o'clock noon.

Finnish Meteorological Institute Helsinki, 2016 Supervisors Professor Erkki Kyrölä Earth Observation Unit Finnish Meteorological Institute, Finland

Professor Johanna Tamminen Earth Observation Unit Finnish Meteorological Institute, Finland

Reviewers Professor Jouni Pulliainen Arctic Research Centre Finnish Meteorological Institute, Finland

Dr. Pawan K. Bhartia Goddard Space Flight Center National Aeronautics and Space Administration, USA

Custos Professor Gerrit de Leeuw Department of Physics University of Helsinki, Finland

Opponent Professor Doug Degenstein Science Department University of Saskatchewan, Canada

ISBN 978-951-697-891-1 (paperback) ISBN 978-951-697-892-8 (pdf) ISSN 0782-6117

Erweko Helsinki, 2016 Series title, number and report code of publication Published by Finnish Meteorological Institute Finnish Meteorological Institute (Erik Palm´enin aukio 1), P.O. Box 503 Contributions 123, FMI-CONT-123 FIN-00101 Helsinki, Finland Date September 2016

Author Simo Tukiainen Title On the retrieval of atmospheric proles Abstract Measurements of the Earth's atmosphere are crucial for understanding the behavior of the atmosphere and the underlying chemical and dynamical processes. Adequate monitoring of stratospheric ozone and greenhouse gases, for example, requires continuous global observations. Although expensive to build and complicated to operate, satellite instruments provide the best means for the global monitoring. Satellite data are oen supplemented by ground-based measurements, which have limited coverage but typically provide more accurate data. Many atmospheric processes are altitude-dependent. Hence, the most useful atmospheric measurements provide information about the vertical distribution of the trace gases. Satellite instruments that observe Earth's limb are especially suitable for measuring atmospheric proles. Satellite instruments looking down from the orbit, and remote sensing instruments looking up from the ground, generally provide considerably less information about the vertical distribution. Remote sensing measurements are indirect. e instruments observe electromagnetic radiation, but it is ozone, for example, that we are interested in. Interpreting the measured data requires a forward model that contains physical laws governing the measurement. Furthermore, to infer meaningful information from the data, we have to solve the corresponding inverse problem. Atmospheric inverse problems are typically nonlinear and ill-posed, requiring numerical treatment and prior assumptions. In this work, we developed inversion methods for the retrieval of atmospheric proles. We used measurements by Optical Spectrograph and InfraRed Imager System (OSIRIS) on board the Odin satellite, Global Ozone Monitoring by Occultation of Stars (GOMOS) on board the Envisat satellite, and ground-based Fourier transform spectrometer (FTS) at Sodankylä, Finland. For OSIRIS and GOMOS, we developed an onion peeling inversion method and retrieved ozone, aerosol, and neutral air proles. From the OSIRIS data, we also retrieved NO2 proles. For the FTS data, we developed a dimension reduction inversion method and used Markov chain Monte Carlo (MCMC) statistical estimation to retrieve methane proles. Main contributions of this work are the retrieved OSIRIS and GOMOS satellite data sets, and the novel retrieval method applied to the FTS data. Long satellite data records are useful for trends studies and for distinguishing between anthropogenic eﬀects and natural variations. Before this work, GOMOS daytime ozone proles were missing from scientic studies because the operational GOMOS daytime occultation product contains large biases. e GOMOS bright limb ozone product vastly improves the stratospheric part of the GOMOS daytime ozone. On the other hand, the dimension reduction method is a promising new technique for the retrieval of atmospheric proles, especially when the measurement contains little information about the vertical distribution of gases. Publishing unit Finnish Meteorological Institute Classication (UDC) Keywords 517.956 Inverse problems 52.64 Radiative transfer ISSN and series title 0782-6117 Finnish Meteorological Institute Contributions ISBN Language Pages 978-951-697-891-1 (paperback), 978-951-697-892-8 (pdf) English 110 Julkaisun sarja, numero ja raporttikoodi Julkaisija Ilmatieteen laitos Finnish Meteorological Institute (Erik Palm´enin aukio 1), PL 503 Contributions 123, FMI-CONT-123 00101 Helsinki Julkaisuaika Syyskuu 2016

Tekijä Simo Tukiainen Nimike Ilmakehän pystyproilien ratkaisemisesta Tiivistelmä Ilmakehän mittaukset ovat tärkeitä, jotta ymmärtäisimme paremmin ilmakehään liittyviä kemiallisia ja dynaamisia prosesseja. Esimerkiksi otsonikerros ja kasvihuonekaasut ovat kohteita, jotka vaativat jatkuvaa ja koko maapallon kattavaa havainnointia. Satelliiteissa olevat mittalaitteet ovat yleensä hankalia totetuttaa ja kalliita, mutta tarjoavat parhaat mahdollisuudet tällaiseen havainnointiin. Satelliittimittauksia täydennetään usein maanpintamittauksilla, jotka ovat paikallisia mutta yleensä tarkkoja. Monet ilmakehän ilmiöt ovat tärkeitä vain tietyillä ilmakehän korkeuk- silla. Siksi hyödyllisimmät mittalaitteet tuottavat tietoa kaasujen jakaumasta korkeuden suhteen. Satelliiteissa olevat mittalaitteet, jotka katsovat maan ilmakehän läpi avaruuteen tuottavat yleensä parasta tietoa ilmakehän pystyjakau- masta. Mittalaitteet, jotka katsovat ilmakehän läpi ylös maanpinnalta tai alas kiertoradalta soveltuvat huonommin pystyjakauman tutkimiseen. Kaukokartoitusmittaukset ovat aina epäsuoria. Mittalaitteet havaitsevat sähkömagneettista säteilyä, mutta kiin- nostava suure on esimerkiksi ilmakehän otsoni. Mittausten tulkinta vaatii ilmakehän säteilyn kulun mallintamista ja havaintoon liittyvän käänteisongelman ratkaisua. Ilmakehään liittyvät käänteisongelmat ovat yleensä epälineaa- risia ja niiden ratkaisemiseen tarvitaan numeerisia menetelmiä ja ennakko-oletuksia. Tässä väitöstyössä kehitettiin menetelmiä ilmakehän kaasujen pystyjakaumien ratkaisemiseen. Työssä käytettiin Odin-satelliitissa olevaa OSIRIS- mittalaitetta (Optical Spectrograph and InfraRed Imager System) ja Envisat-satelliitissa olevaa GOMOS-mittalaitetta (Global Ozone Monitoring by Occultation of Stars). Lisäksi käytettiin Sodankylässä sijaitsevaa, maan pinnalla olevaa FTS-mittalaitetta. OSIRIS ja GOMOS mittauksista ratkaistiin otsonin, aerosolien ja neutraali-ilman pitoisuuk- sia. OSIRIS mittauksista ratkaistiin lisäksi NO2. FTS-mittauksista ratkaistiin metaanin pystyjakauma rajoittamalla ongelman tila-avaruutta ja käyttämällä hyväksi Markov chain Monte Carlo (MCMC) menetelmää. Tämän väitöstyön tärkeimmät tulokset ovat pitkät OSIRIS ja GOMOS aikasarjat, sekä uusi käänteismenetelmä FTS-mittausten parempaan hyödyntämiseen. Pitkät mittaussarjat ovat tärkeitä ilmakehän muutoksen tutkimiseen ja ihmisen vaikutuksen erottamiseen luonnollisesta vaihtelusta. Tässä työssä kehitetty GOMOS-otsonituote on huo- mattavasti parempi kuin vanha, eri menetelmällä ratkaistu otsonituote. FTS-mittausten hyödyntämiseen kehitetty menetelmä on uusi ja lupaava tapa ratkaista pystyjakaumia mittauksista, joiden informaatiosisältö on rajoitettu. Julkaisijayksikkö Ilmatieteen laitos Luokitus (UDK) Asiasanat 517.956 Käänteisongelmat 52.64 Säteilynkuljetus ISSN ja avainnimike 0782-6117 Finnish Meteorological Institute Contributions ISBN Kieli Sivumäärä 978-951-697-891-1 (nid.), 978-951-697-892-8 (pdf) Englanti 110 A

I would like to thank my supervisors and colleagues Erkki Kyröl¨a and Johanna Tam- minen for their continuous support and help during my time at the Finnish Meteoro- logical Institute. It is hard to imagine a better research group than ours, and in general, FMI is a great place to work. In all these years, I have received a huge amount of help from senior scientists such as Marko Laine and Jukka Kujanpää—I don't think this thesis would have been nished without their help. It has also been my pleasure to work with some young and bright researchers such as Jesse Railo and Janne Hakkarainen. eir enthusiasm and skill level always amazes me. I am also grateful to Jouni Pulliainen and P. K. Bhartia for reviewing the thesis, to Gerrit de Leeuw for acting as a custos, and to Doug Degenstein for accepting to be my opponent. Finally, I would like to thank my wife Hely and my daughter Pihla who remind me every day that there is much more in life than just work.

Simo Tukiainen Helsinki, August 2016 C

Listoforiginalpublications ...... 7 1.Introduction ...... 9 2. Radiative transfer of the atmosphere ...... 13 2.1.Scattering ...... 13 2.2.Absorption ...... 15 2.3. Radiative transfer equation ...... 16 2.4. Forward model ...... 17 3.Instruments ...... 20 3.1. OSIRIS ...... 20 3.2. GOMOS ...... 21 3.3.SodankyläFTS...... 24 4.einverseproblem ...... 27 4.1. Onion peeling method for limb scatter measurements ...... 29 4.2. Dimension reduction method for FTS measurements ...... 32 5.Results ...... 36 5.1. OSIRIS O3 proles ...... 36 5.2. OSIRIS NO2 proles ...... 37 5.3. GOMOS bright limb O3 proles ...... 38 5.4. FTS CH4 proles...... 39 6.Conclusions ...... 44

References ...... 46 L   

I S. Tukiainen, S. Hassinen, H. Auvinen, E. Kyrol¨ ¨a, J. Tamminen, C. Haley, N. Lloyd, and P. T. Verronen, Description and validation of a limb scatter retrieval method for Odin/OSIRIS, J. Geophys. Res. Atmos., 113, 2008.

II S. Tukiainen, E. Kyrol¨ ¨a, P. T. Verronen, D. Fussen, L. Blanot, G. Barrot, A. Hauchecorne, and N. Lloyd, Retrieval of ozone proles from GOMOS limb scattered measurements, Atmos. Meas. Tech., 4, 659–667, 2011.

III S. Tukiainen, E. Kyrol¨ ¨a, J. Tamminen, J. Kujanpää, and L. Blanot, GOMOS bright limb ozone data set, Atmos. Meas. Tech., 8, 3107–3115, 2015.

IV S. Tukiainen, J. Railo, M. Laine, J. Hakkarainen, R. Kivi, P. Heikkinen, H. Chen, and J. Tamminen, Retrieval of atmospheric CH4 proles from Fourier transform infrared data using dimension reduction and MCMC, J. Geophys. Res. Atmos., 121, 2016.

e author is responsible for most of the work and writing in Papers I–IV. In paper I, the author developed the NO2 retrieval part, implemented the method for OSIRIS, and made all the analyzes. In papers II–III, the author applied the retrieval method for GOMOS and made all the analyzes. In paper IV, the author developed and coded the forward model, helped to implement the retrieval method, and analyzed most of the results.

1. I

  are crucial for monitoring the composition of the Earth's Satmosphere on a global scale. For example, the dramatic ozone depletion in the Antarctic, appearing each local spring, could not be properly studied without accurate satellite measurements. Air pollution, greenhouse gases and volcanic ash are a few other examples of important atmospheric constituents, nowadays routinely observed using space borne sensors. ese kind of remote sensing observations are always indirect. For example, instead of measuring the actual number density of an atmospheric trace gas, satellite instruments record electromagnetic radiation transmitted, scattered, or emitted from a limited region of the atmosphere. anks to our understanding of physics, we know how in theory the gas molecules in the region of interest interact with photons and leave their ngerprints to the propagated radiation. It is a typical inverse problem to deduce trace gas concentrations from the measured radiance data. is procedure is also known as retrieval. e physical values are retrieved from the measurements using a suitable inversion method. To solve a physical inverse problem, an accurate forward model is needed—a link between the measured quantity and the parameters of interest. Papers I–III of this thesis focus on certain satellite measurements of the atmosphere called limb scatter measurements. Limb scatter measurements are daytime measurements of the sunlight that is scattered from the Earth's Sun-illuminated limb. Limb scatter measurements are valuable because they provide information about the vertical structure of the atmosphere with good vertical resolution. e drawback of the limb scatter technique is that accurate forward modeling is complicated and may be computationally daunting. Obviously, no nighttime data can be measured either. De- spite its challenges and limitations, the limb scatter method has proven to be a power- ful technique for monitoring the middle atmosphere, the part of the atmosphere that spans between about 12 and 80 km. Papers I–III use limb scatter measurements from two satellite instruments: Optical Spectrograph and InfraRed Imager System (OSIRIS) [Llewellyn et al., 2004, McLinden et al., 2012] on board the Odin spacecra and Global Ozone Monitoring by Occultation of Stars (GOMOS) [Bertaux et al., 2010] on board 10 the Envisat satellite. OSIRIS and GOMOS measurements have already been used in numerous scientic studies, from particle precipitation [e.g., Seppälä et al., 2004, An- dersson et al., 2014] to time series analyzes [e.g., Kyrol¨ ä et al., 2013, Bourassa et al., 2014]. Satellite data are oen supplemented by ground-based measurements. Ground- based instruments are stationary, or have limited mobility, but their mass and dimensions are not restricted in the same way as the spacecra connes the instruments on board. e instruments on the ground can be larger and typically generate better atmospheric data than the instruments in the space. erefore, ground-based measurements are commonly used as a reference in the validation of satellite data. Although ground-based measurements are generally accurate, the quality of the retrieved products depends on the used inversion method, which leaves room for improvement. Pa- per IV of this thesis employs measurements of the ground-based Fourier Transform spectrometer (FTS) instrument, located in Sodankylä, Northern Finland. e spectral resolution of the data produced by the Sodankylä FTS is superior to OSIRIS and GOMOS, but the direct Sun measurement principle provides only little information about the vertical structure of the atmosphere. e dimension reduction retrieval method introduced in Paper IV seeks to exploit this information as much as possible. e method is presented in a general form and it could be used in the future to retrieve atmospheric proles from satellite observations as well. Earth's atmosphere is a relatively thin gaseous layer surrounding the planet and contained by the gravitational pull of the Earth. e 100 km altitude is oen used as a limit between the atmosphere and space but there is no actual clear boundary. e air density merely decreases, exponentially, towards zero as the altitude increases. Its size may be unimpressive, but the atmosphere is a crucial medium for the Earth's ecosystems. e atmosphere provides fundamental elements such as oxygen, nitrogen, and carbon, distributes water, and protects life from the harsh conditions of space. e dry atmosphere is mainly composed on nitrogen (∼78 %, by volume), oxygen (21 %), argon (1 %), and many different minor trace gases whose quantities vary depending on the latitude, season, local time, and other factors. e amount of water vapor in the atmosphere can vary between 0 and around 4 % by volume [Mohanakumar, 2008], most of it being in the tropics. e atmosphere is typically divided into four main layers that are called troposphere (0–12 km), stratosphere (12–50 km), mesosphere (50–80 km), and ther- mosphere (80–700 km). e boundaries between the layers are called tropopause, stratopause, and mesopause, respectively. e stratosphere and mesosphere together produce the so-called middle atmosphere, the most relevant region for this thesis. e altitude limits of the layers are only approximative because the exact values depend, e.g., on the latitude. For example, the altitude of the tropopause is roughly 8 km in 11 the polar regions but around 16 km at the equator [Brasseur and Solomon, 2005]. e atmospheric layers are naturally distinguished from each other by the behavior of the temperature prole. Atmospheric temperature decreases with altitude in the troposphere and mesosphere but increases with altitude in the stratosphere and thermo- sphere. Vertically resolved measurements of the atmospheric trace gases are important for understanding the underlying, and sometimes notoriously complicated, chemical and dynamical processes driving the atmosphere. Many atmospheric phenomena affect certain altitude regions only. Besides, an accurate vertical prole gives a credible estimate of the total number of molecules, which oen is an important variable. While some trace gases are thoroughly mixed in the air and thus have a relatively constant mixing ratio prole, others have a strongly anomalous vertical distribution. For example, around 90 % of the atmospheric ozone is located in a narrow layer in the stratosphere called the ozone layer (Fig. 1). e prole of ozone contains also a secondary maximum around the mesopause region (Fig. 1, panel at right). Also the distribution of atmospheric water is very irregular—around 99 % of water residues in the troposphere. Many other trace gases, such as CO2 and CH4, are usually well mixed in the atmosphere but sometimes their proles too may contain substantial structures.

110

100

Altitude [km] 50

20 0 1 2 3 4 5 0 0.5 1 12 −5 O number density [cm−3] x 10 O mixing ratio x 10 3 3

Figure 1: Example of the vertical distribution of ozone presented in number density (left) and mixing ratio (right). This ozone prole was measured by the GOMOS instrument at the equator in 2003.

In the atmospheric research, in general, a key research question is how the abundances of the trace gases evolve in time. Since the industrial revolution began around 1750, the human race has been exceedingly abusing the atmosphere, releasing enor- 12 mous amounts of pollution, greenhouse gases, and aerosols in the air. A dramatic example of the human inuence on the atmosphere is the ozone hole in the Antarc- tic region, discovered in 1984 [Farman et al., 1985], caused by chlorine and bromine released from man-made chlorouorocarbons (CFCs) and halons. Long data records covering many decades are needed for discovering and monitoring this kind of changes and for distinguishing between anthropogenic effects and natural variations. e world leaders have mostly struggled to agree on effective policies for cutting the emissions. e most successful treaty is the 1987-signed Montreal protocol that banned the use of the CFC compounds aer their potential to destroy stratospheric ozone was understood—and revealed by satellite data from Antarctic. As a result of the Montreal protocol and its revisions, the ozone layer has started to slowly recover [WMO, 2014, Harris et al., 2015]. However, attempts to regulate greenhouse gas emissions have been less effective. e Kyoto protocol, signed in 1997, is the most famous treaty adapted so far, but nevertheless it had little effect on the carbon emissions that have been increasing year aer year. Although we now probably have seen the peak in the CO2 emissions [Jackson et al., 2016], world nations release a staggering ∼35 bil- lion tonnes of CO2 annually, and continue to do so for years. e 2015 United Na- tions Climate Change Conference in Paris resulted in promises that by 2100 the global warming would be limited to 2° C compared to the pre-industrial levels. However, if dramatic reductions in the greenhouse gas emissions are not made, a global warming of 4–6° C is more likely to be foreseen [IPCC, 2013, chap. 12]. e gap between the political actions and recommendations of the research community remains large. 13

2. R    

Measurements of atmospheric radiation are useful only if the physical processes governing the observations are suﬃciently understood. A sound theoretical basis allows us to draw meaningful conclusions from the data. Most remote sensing instruments are sensitive to photons, elementary particles that form electromagnetic radiation. Any physical object with the temperature more than absolute zero emits electromagnetic radiation, but the wavelength and energy distributions of the emitted radiation vary greatly depending on the object. Most photons that passive instruments1 register orig- inate from the Sun or from the Earth's atmosphere, land, and sea. Radiative transfer is a discipline that studies how the atmosphere aﬀects the paths of the photons [e.g., Chandrasekhar, 1960, Goody and Yung, 1995, Liou, 2002]. Accurate modeling is challenging because the photon paths can be very complicated in practice.

2.1. S Electromagnetic radiation interacts with matter through absorption, emission, and scattering. In the scattering process, atoms, molecules, and larger particles in the path of the light beam continuously extract energy from the photons and reradiate that energy in all directions. Clouds in the sky, and the sky itself, are visible to our eyes because air molecules and water droplets scatter photons. However, some directions are more favored than others depending on the scatterer. e resulting angular pattern, or the phase function, denoted P (θ), is mostly determined by the size of the scatterer. Phase function is a function of the scattering angle, θ, which is the angle between the incident direction and the direction of scattering. Phase function can be interpreted as a probability distribution that must satisfy, when integrated over 4π steradians, 2π π π ∫ ∫ P (θ) sin θ dθ dφ = ∫ P (θ)2π sin θ dθ = 1. (1) 0 0 0 Small objects such as molecules mostly scatter energy equally forward and backward with a relatively simple angular pattern, while large particles such as aerosols mostly scatter forward and typically have a complex angular pattern. Because the size of the scatterer is relative to the wavelength of light, it is useful to determine a non- dimensional size parameter − x = 2πrλ 1 (2) where r is the actual radius of the (spherical) scatterer and λ is the wavelength. Light scattering by air molecules can be approximated using the Rayleigh phase function 3 P (θ) = (1 + cos2 θ), (3) air 16π 1Active instruments provide their own radiation to illuminate the target. 14 that generally applies to any particles with the size parameter x ≪ 1. Rayleigh scattering is elastic scattering, i.e., the wavelength of the incident and the scattered light is the same. e scattering by aerosols is a less trivial modeling problem. Because the size and type of atmospheric aerosols vary a lot, there are many ways to model their contribution, which oen complicates the interpretation of measurements. A widespread way to model spherical particles, whose size is comparable to the wavelength, is the Lorenz- Mie theory [see e.g. Bohren and Huﬀman, 1998]. It describes the electromagnetic eld as series expansions of vector spherical wave functions, and thus provides analytical solutions. However, stratospheric aerosols can be modeled in a more straightforward manner. Assuming a known phase function, and wavelength dependency discussed later, the aerosol number density is the only variable that needs to be addressed. is kind of approach does not bring in any knowledge about the aerosol type or size but nevertheless is a reasonable approximation in many cases. It is also possible to take account more detailed aerosol properties such as the size distribution but it would require special methods when interpreting the data [e.g. Bourassa et al., 2008, Rieger et al., 2014] and preferably polarization-sensitive measurements. In Papers I–III, we have modeled the angular dependence of the stratospheric aerosols using the classic Henyey–Greenstein phase function [Henyey and Greenstein, 1941]: 1 − g2 Paer(θ) = (4) 4π(1 + g2 − 2g cos θ)3/2 where θ is the scattering angle and the parameter −1 ≤ g ≤ 1 is the measure for the degree of anisotropy. A value of g = 0 means isotropic scattering and g = 1 means forward-directed scattering (Papers I–III use the value g = 0.75). e mathematical denition of g is the expectation value of the cosine of the scattering angle θ for P (θ)

π g ≡ ⟨cos θ⟩ = ∫ P (θ) cos θ2π sin θ dθ. (5) 0 e Henyey–Greenstein phase function has a clever property

π ∫ Paer(θ) cos θ2π sin θ dθ = g. (6) 0 So it is an identity function: calculation of the expectation value for cos θ returns g. Scattering is also a wavelength-dependent phenomenon. e wavelength dependency is expressed with the scattering cross section, a quantity that depends on the material and size of the scatterer. e SI unit of the scattering cross section is m2, although in practice the form cm2 is typically used.2 It can be thought as a likelihood that the

− 2As is cm 3 with the number density. 15 scattering event happens if the scatterer is in the path of the photon. e scattering cross section of the neutral air is called the Rayleigh scattering cross section. It can be described with the classic equation [e.g. van de Hulst, 1957]: 24π3(n2 − 1)2 6 + 3ρ σ (λ) = s ( ), (7) air 4 2( 2 + )2 − λ Ns ns 2 6 7ρ where ns is the refractive index of air, Ns is the molecular density at standard pressure and temperature, and ρ is the depolarization factor or depolarization ratio describing the eﬀect of molecular anisotropy. e term (6+3ρ)/(6−7ρ) is the called the depolarization term or the King factor—it is the largest source of uncertainty in the Rayleigh scattering calculations. Bodhaine et al. [1999] gives a detailed discussion about the terms of Eq. (7) and their numerical approximations. e strong wavelength dependency makes blue light scatter more than red light, the reason why we perceive the sky as blue (save looking directly towards the Sun). e wavelength dependency of the aerosol scattering depends on the size of the particles. A classic way is to choose, or retrieve from the data, the so-called Ångström − exponent in the λ α dependency, where smaller particles tend to produce a larger exponent. For example, water droplets, which are relatively large particles, scatter different wavelengths equally. Some retrieval methods assume totally diﬀerent spectral shape for the aerosol scattering. For example, the operational GOMOS occultation retrieval uses a second order polynomial with three free parameters. In this thesis, the aerosol scattering cross section is approximated using the Ångström's law with the xed α = 1. e analysis of more detailed aerosol properties is out of the scope of this thesis.

2.2. A Absorption is the other fundamental phenomenon besides scattering that aﬀects electromagnetic radiation in the atmosphere. Materials can absorb photons, transforming electromagnetic energy into internal energy of the absorber, typically heat.3 In the atmosphere, absorption causes photodissociation of molecules, an important mechanism in many chemical reactions and cycles. Absorption causes exponential attenuation of light traveling through gas, a behavior discovered already in the beginning of the 1700-century. Pierre Bouguer, Johann Heinrich Lambert, and August Beer—one aer other—studied the absorption process. ey devised the famous relationship, 4 the Beer–Lambert law , describing the attenuation of the incoming light I0 traveling length l in a homogeneous gas with the concentration N

I = I0 exp ( − σNl), (8)

3e opposite of absorption is emission, a process that produces photons instead of removing them. 4Also known as Beer's law or Beer–Lambert–Bouguer law. 16 where σ is the absorption cross section, a material related parameter describing its ability to absorb radiation. In this sense, it is equivalent to the scattering cross section. Gener- ally the absorption cross section is a function of wavelength and temperature—at least. Cross sections are usually measured in laboratory where ambient air can be accurately controlled, yet the published values disagree slightly with each other. For example, there are many cross sections for ozone [e.g., Chehade et al., 2013, Gorshelev et al., 2014]. e problem is that the different teams working on satellite retrievals are using different cross sections, and the choice can affect several percents of the retrieved number densities. is makes objective validation more difficult. Generally in the UV- visible wavelengths, absorption cross sections are relatively smooth functions (Fig. 2). Instead in the near infrared and shortwave infrared wavelengths, the absorption peaks become narrow and depend also on the pressure. e total attenuation of the light

O3 NO2

−18 10 ] 2

−20 10 Hartley−Huggins bands

Cross section [cm Chappuis band

−22 10

250 300 350 400 450 500 550 600 650 Wavelength [nm]

Figure 2: Cross sections of ozone and NO2 in the UV-visible wavelength region. beam due to the scattering and absorption together is called extinction.

2.3. R   e propagated radiation in any point of the atmosphere can be described by the equation of radiative transfer. It accounts for the removal of radiation by extinction but also for the gain of radiation due to emission and scattering. In the radiative transfer problems considered in this thesis, the gain by emission can be ignored because its contribution is negligible compared to the scattering. us, the general form of the radiative transfer equation can be written ⋅ ∇ ( ) = − ext( )[ ( ) − ( )] Ω Iλ r, Ω kλ r Iλ r, Ω Jλ r, Ω , (9) 17

where the radiance Iλ at wavelength λ is specied by three spatial coordinates r and two angular coordinates Ω. In the right hand side, the rst term is the loss due to extinction and the second term is the source term, i.e., the gain of radiation due to ext scattering. kλ is the total volume extinction coeﬃcient of the medium. e limb scatter problem is convenient to describe with the integral form of the radiative transfer equation [e.g., Chandrasekhar, 1960]

− ( ) − ( ′ ) ′ ( ) = ( ) τ 0,s + ext( ′ ) ( ′ ′ ) τ s ,s Iλ rs, Ωs Iλ r0, Ω0 e ∫ kλ rs Jλ rs , Ωs e ds , (10) LOS where the instrument at rs is looking at direction −Ωs, and the integration of the ′ source term goes over the line of sight (LOS) denoted by s . e so-called optical depth, τ, is dened s2 ′ ( ) = ext( ′ ) τ s1, s2 ∫ kλ rs ds . (11) s1 ere are several diﬀerent numerical approaches to solve Eq. (10)—analytic solutions exist only in some simplied cases. e methods mostly diﬀer in the way they evaluate the source function. Methods that produce more accurate results can be complicated and typically require intensive computing.

2.4. F  Understanding the measured data requires a model that contains the relevant physical processes governing the observation. is model is called forward model. Given the inputs, such as the atmosphere, geometry, and instrument function, the forward model can be used to produce simulated measurements. e relationship is usually denoted

y˜ = F (x), (12) where y˜ ∈ Rm are the simulated data, x ∈ Rn are the model parameters, and F ∶ Rn → Rm is the forward model function that produces the data y˜ from the parameters x. e dimensions m and n are the number of data points and model parameters, respectively. Usually, the corresponding rst-order partial derivatives of the model with respect to the parameters are computed as well. e matrix of the derivatives is typically arranged as ⎡ ∂F ∂F ⎤ ⎢ 1 ⋯ 1 ⎥ ⎢ ∂x1 ∂xn ⎥ = dF = ⎢ ⋮ ⋱ ⋮ ⎥ K ⎢ ⎥ , (13) dx ⎢ ∂F ∂F ⎥ ⎣ m ⋯ m ⎦ ∂x1 ∂xn which is a m × n matrix called Jacobian. To keep the model as simple as possible but still accurate, it is important to recognize variables that are meaningful to the problem and the ones that can be ignored without introducing signicant bias. A forward 18 model implemented for the retrieval purposes is always a simplied realization of the complex reality. For example, a vertical distribution of an atmospheric gas is an utterly complicated structure, constantly changing due to the motion of molecules and inu- encing chemical processes. Hence, the distribution of the gas must be approximated using a parametrized function or a discrete prole that is dened using a nite number of altitude levels. In both cases, we have a nite number of parameters that dene the observation and are the unknowns in the corresponding inverse problem (see Sect. 4.). A forward model that uses single scattering (SS) approximation to solve the radiative transfer problem is relatively simple to implement. e SS model is a straightforward numerical integration of Eq. (10). A typical implementation is to rst calculate path lengths in each (homogeneous) layer, when the solution becomes a trivial and computationally inexpensive summation. However, modeling of the multiple scattering (MS) contribution is a crucial part of the bright limb radiative transfer. Photons that have scattered multiple times before entering the instrument can make up even 50 % of the measured radiance in the visible wavelengths [Oikarinen et al., 1999]. e exact amount depends strongly on the wavelength, though. In the UV wavelengths shorter than 310 nm, the strong ozone absorption drastically reduces the relative proportion of the multiple scattered light. Moreover, in the wavelengths longer than 1 µm, − scattering decreases naturally due to the λ 4 dependence of the Rayleigh cross section. e MS proportion depends also on the solar zenith and azimuth angles, albedo, and the composition of the atmosphere. To estimate the multiple scattering proportion, we have used two different radiative transfer models. In Paper I, we used a pseudo three-dimensional (3-D) radiative transfer model called LIMBTRAN [Griffioen and Oikarinen, 2000]. In Papers II and III, we used a more accurate, fully 3-D Monte Carlo model Siro [Oikarinen et al., 1999]. Siro solves the radiative transfer problem by simulating photon trajectories in the model atmosphere. Random scattering events naturally yield a proper estimate for the multiple scattering contribution [Loughman et al., 2004]. However, Siro is slow to run and in practice we have tabulated the multiple scattering fraction as a look-up table. Figure 3 shows an example of the photon paths in the model atmosphere simulated using Siro. In Paper IV, we modeled the shortwave infrared (SWIR) band, and the FTS instrument points directly towards the Sun. In this case, scattering from the neutral air and aerosols is negligible and can be ignored from the forward model. e SWIR region absorption coefficients were calculated using the HITRAN 2012 database and the Voigt line shape. e Voigt prole is a function of pressure and temperature, i.e., a function of altitude, which makes it possible to retrieve vertical information from a single spectral measurement of the whole atmospheric column. e forward model that was used in Paper IV, including various retrieval methods, is available at https://github.com/tukiains/swirlab/. 19

Figure 3: Siro simulation of the photon paths in the atmosphere in limb-viewing geometry. Upper panel: view from the instrument. Lower panel: view from above. The simulation was run for the 30 km tangent height using 1000 photons. 20

3. I

Instruments that measure atmospheric radiation at many wavelengths provide the most useful data for the prole retrieval purposes. A spectrum with low noise and good spectral resolution gives the best chances to distinguish contributions of diﬀer- ent trace gases. e number of gases that can be retrieved depends on the wavelength band and other properties of the measuring instrument.

3.1. OSIRIS OSIRIS [Llewellyn et al., 2004, McLinden et al., 2012] is one of the two instruments on board the Swedish Odin satellite [Murtagh et al., 2002], launched on 20th February 2001. e OSIRIS instrument consists of a UV-visible spectrometer (OS-part) and three infrared channels (IRIS). e spectrometer measures in the 274-810 nm band with approximately 1 nm spectral resolution and the infrared channels are centered at 1.263, 1.273 and 1.530 µm. e spectrometer and the IR-imager are aligned so that they always point at the same part of the atmosphere, a useful arrangement for some applications. In this thesis, I regularly use the name “OSIRIS” but concentrate on the UV-visible spectrometer measurements only. e other instrument on board Odin, besides OSIRIS, is the SubMillimeter Radiometer (SMR). Also SMR data are not used in this thesis. Odin was launched in a Sun-synchronous 6 p.m./6 a.m. local time orbit at ∼600 km altitude resulting in a period of 96 min and 15 revolutions each day. is kind of orbit, where the satellite is always riding between the day and night, is also known as a dawn/tusk orbit or a terminator orbit. It is a natural conguration for Odin because OSIRIS needs sunlight for the measurements. Using the terminator orbit, OSIRIS data can be collected in the ascending (evening) and descending (morning) phases of the orbit. In the Odin mission, the observation time was originally divided between the

Sun

Odin/OSIRIS Line of sight

Solid Earth Atmosphere

Figure 4: OSIRIS measurement geometry. The arrows represent some of the possible ray paths from the Sun to the instrument. 21 separate aeronomy and astronomy missions, but since July 2007 the Odin spacecra is dedicated to the aeronomy mission only. e measurement principle of OSIRIS, the limb-viewing technique, is shown in Fig. 4. e sunlit tangent point is scanned between 10 and 100 km with around 25–45 individual radiance measurements. Figure 5 shows a simplied view of the tangent point where the (hypothetical) layers of the atmosphere are measured with the distinct line of sights originating from the spacecra. OSIRIS explores about 300 tangent points daily and these events are referred as scans from now on. Because the tangent point is inspected independently at several tangent heights, the vertical proles of diﬀerent trace gases (and aerosols) can be estimated with good vertical resolution (2–3 km). It is evident that the limb-viewing technique acquires considerably more information about the vertical structure than, for example, nadir- viewing instruments, which probe the whole atmospheric column at once. Examples

Solid Earth

Figure 5: Mapping of the tangent point using the limb-viewing technique, and the layering of the atmosphere for the retrieval. of the actual recorded UV-visible OSIRIS spectra are shown in Fig. 6. By visual in- spection, one can note a few interesting details such as the exponentially increasing radiance level towards the lower altitudes, the zigzag structures (Fraunhofer lines from the Sun atmosphere), and the so-called oxygen A-band absorption/emission peak at ∼762 nm. For humankind, the most relevant feature is the strong reduction of the signal in the UV wavelengths less than 320 nm. In this region, atmospheric ozone absorbs eﬃciently the dangerous UV radiation of the Sun, enabling and protecting all life on Earth.

3.2. GOMOS GOMOS [Bertaux et al., 2010] is one of the 10 instruments on board the European Space Agency's (ESA) Envisat satellite, launched in 2002. Envisat/GOMOS provided over a decade of measurements before the mission ended abruptly on 8th of April 2012 when the communication with the satellite was suddenly lost. Envisat has a 22

13 10

/nm/sr] 20 km 2

12 10 30 km

40 km 11 10 50 km Radiance [photons/s/cm

10 60 km 10 300 400 500 600 700 800 900 Wavelength [nm]

Figure 6: Example of the OSIRIS radiances at a few tangent heights. The instrument does not record spectrum in the shaded region.

Sun-synchronous 10 p.m./10 a.m. polar orbit at ∼790 km with the orbital period of ∼101 min. GOMOS is a stellar occultation instrument, it looks one star at time as it “oc- cultates” through the Earth's limb. Altogether about 180 diﬀerent stars are followed this way, in nighttime and daytime conditions. While stars are relatively weak signal sources, the measurement principle works ne in the dark limb conditions during the nighttime [Kyrol¨ ¨a et al., 2010]. However, during the daytime the star signal is over- whelmed by the limb scatter contribution from the Sun. GOMOS measures the limb using three separate optical bands. e central band measures the combined contribution of the star and the limb scatter light, while the two other bands—below and above the central band—measure only the limb scatter signal (Fig. 7). In principle, subtracting the mean of the upper and lower bands from the central band should result in a pure star spectrum which could be used in the standard occultation retrieval [Bertaux et al., 2010]. However, it seems that this removal produces large and poorly characterized uncertainties in the resulting star spectrum. Papers II and III introduce a method for retrieving ozone proles from the GOMOS upper/lower band radiances. ese data are called GOMOS bright limb (GBL). e retrieval method is similar than the one we already used with OSIRIS (Pa- per I). However, as the GOMOS instrument was not optimized to measure radiances but star light, the data has some serious defects that complicate the retrieval. First of all, the GOMOS radiances are badly contaminated by stray light. Stray light is superuous light entering the instrument, originating from some other part(s) of the atmosphere than the tangent point. For example, it may be light reected from the spacecra itself 23

Sun

Star Envisat/GOMOS

Solid Earth Atmosphere

Figure 7: GOMOS measurement principle during the daytime. The arrows present the single scattering photon paths from the Sun and from the star. The star contributes only to the central band of the instrument. or clouds below. Figure 8 shows a comparison of co-located (in time and space) OSIRIS and GOMOS radiances, having approximately the same solar zenith, azimuth, and scattering angles. e diﬀerence is dened as (GOMOS-OSIRIS)/GOMOS*100 [%], and Fig. 8 shows a median of those individual relative diﬀerences. GOMOS radiances are considerably larger especially in the visible wavelengths above 40 km, but there are also substantial excess radiance below 40 km in the UV wavelengths shorter than 320 nm. is extra signal is stray light. e visible region of the GOMOS spectrum can be mostly corrected by subtracting the mean spectrum of the topmost tangent heights (above 100 km) from all other altitudes (Fig. 9). However, the stray light in the UV

60 50 GOMOS 55 is larger

50 25

40 0

35 Altitude [km] Difference [%] 30 −25

25 OSIRIS is larger 20 −50 300 350 400 450 500 550 600 650 Wavelength [nm]

Figure 8: Median relative difference of the six co-located OSIRIS and GOMOS radiances before stray light correction. The difference in distance was less than 300 km and in time less than one day, and the difference in solar zenith, azimuth, and scattering angles was less than two degrees. The zenith angles were between 66° and 69°. 24

60 50 GOMOS 55 is larger

50 25

40 0

35 Altitude [km] Difference [%] 30 −25

25 OSIRIS is larger 20 −50 300 350 400 450 500 550 600 650 Wavelength [nm]

Figure 9: Same as Fig. 8 but after the stray light correction. region is more diﬃcult to characterize and correct. We have no good understanding of the mechanism that leads to excess scattering in the UV region when GOMOS is looking at the lower tangent heights (Fig. 10).

306 nm radiance 60 OSIRIS 55 GOMOS

35 Altitude [km]

20 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 2 11 Radiance [photons/s/cm /nm/sterad] x 10

Figure 10: 306 nm OSIRIS and GOMOS radiances from Fig. 9 as a function of altitude. The GOMOS radiances have a substantial positive bias.

3.3. S FTS Fourier transform spectrometers are instruments that divide the incoming light into two parts: the direct beam that simply hits the detector and the second beam that, by 25 reecting from a moving mirror, travels a longer optical path before entering the detector. e result is an interferogram, intensity as a function of the optical path diﬀer- ence (Fig. 11). e spectrum is then obtained by performing Fourier transform to the measured interferogram. e measurement method is also called Fourier Transform Infrared Spectroscopy (FTIR).

0.292

0.29

0.288

0.286

0.284

0.282

0.28

0.278 0 5 10 15 5 x 10

Figure 11: Sodankylä FTS instrument (left) and an example of the measured interferogram (right).

e Sodankylä FTS is located at the Finnish Meteorological Institute's Arctic Re- search Centre in Sodankylä, Northern Finland (67.4°N, 26.6°E). e instrument has been operational since February 2009, providing direct Sun measurements (Fig. 12) from February to November. Up to several hundred measurements a day are recorded depending on the season and cloudiness. e instrument does not operate during the winter because there is no sunlight. e Sodankylä FTS is a Bruker IFS 125 HR with a A547N solar tracker. It − − has three detectors: InGaAs (12,800–4,000 cm 1), Si (25,000–9,000 cm 1), and InSb − (10,000–1,850 cm 1). e instrument operates on the optical path difference of 45 cm, − with the 2.3923 mrad eld of view, leading to the spectral resolution of ∼0.02 cm 1. e FTS at Sodankylä is part of the Total Carbon Column Observing Network (TCCON), a global network that observes solar spectra in near-infrared wavelengths and provides column-averaged dry-air mole fractions [Wunch et al., 2011]. ere are more than 20 TCCON sites around the world and the TCCON data are extensively used in the validation of satellite data and models. 26

Sun

Atmosphere FTS Solid Earth

Figure 12: Direct Sun measurement principle of the Sodankylä ground-based FTS. 27

4. T  

In an inverse problem, we start from the measurement results and try to infer causes. In atmospheric applications, this process typically can be described as a parameter estimation task. We try nd the input parameters that cause the forward model to produce the observed data. us, the inverse problem is the opposite of the forward problem discussed in Sect. 2.4. (Fig. 13). Inverse problem research has become a widely spread

forward problem parameters data inverse problem

Figure 13: Diﬀerence between the forward and inverse problems. branch of mathematics. Besides a large amount of important theoretical results, inverse problems are present in many practical areas like remote sensing of the Earth, weather forecast, and medical imaging. In the retrieval of vertical atmospheric proles from the limb scatter or FTIR data, the starting point is the measured solar spectrum y ∈ Rm, where m is the number of wavelengths.5 e goal is to estimate the vertical prole of a trace gas at n altitude levels. e problem can be written as

y = F (x) + ε, (14) where F ∶ Rn → Rm is the forward model, x ∈ Rn is the vector of unknowns called state vector and ε ∈ Rm is the measurement error. If Eq. (14) is a linear problem, we can try to use matrix operations from linear algebra to solve x, albeit a direct matrix inversion is usually not possible due to the lack of data to uniquely determine x. Anyhow, in atmospheric inverse problems F is generally a nonlinear operator, and attempts to linearize the problem can cause other issues. us, x is usually estimated using methods from numerical optimization or using sampling based approach like Monte Carlo methods. A standard measure of the agreement between the noisy data and the model (parameters) is the cost function 2 = ∥ − ( )∥2 = [ − ( )]T −1[ − ( )] χ y F x Cy y F x Cy y F x , (15) m×m where Cy ∈ R is the covariance matrix including measurement and modeling errors. Cy is oen assumed diagonal but it needs not to be. In fact, in many problems a diagonal Cy would be an overly optimistic assumption. Nevertheless, to nd the optimal x, usually denoted xˆ, a traditional estimation process starts from some ini- 2 tial state x0 and iteratively seeks parameters that locally minimize χ . e estimator

5In some problems we have several spectra that are stacked in the data vector—m can be quite large. 28 can be found, for example, by the simplex method or, preferably, by some derivative- based optimization technique. A awless physical forward model and noise-free data would result in a perfect agreement between the data and model. However, in practice, the estimation of xˆ from the measured spectrum can be ambiguous. Accord- ing to Hadamard6, an inverse problem is well-posed if the solution exists, the solution is unique, and the solution depends continuously on data and parameters. e Hadamard conditions are usually not satised with real, noisy data. For example, even if we have considerably more data points than parameters, m >> n, there might not be enough information to reasonably retrieve n parameters. All data points do not neces- sarily bring in unique information to the system, they hardly ever do. Inverse problems that do not fulll the Hadamard conditions are called ill-posed. Furthermore, even a well-posed inverse problem can be ill-conditioned. is means that small errors in the input data can result in large errors in the answer. Ill-posed inverse problems are commonly tuned towards more sensible solutions using some kind of a priori information of the measurement system. For example, the retrieval process can be regularized by requiring certain smoothness for the solution. Some variables such as the temperature and pressure proles may be taken elsewhere and kept xed. Indeed, it oen makes sense to use expert knowledge about the measurement system and emphasize certain results. Nowadays, a widely used approach is the Bayesian analysis. e unknowns, a priori data, and solution are considered as probability distributions, and the estimated parameters and the measurement errors are considered as random processes. e Bayes formula supposes that the state vector x has the prior probability density p(x), which characterizes properties like physically possible values and vertical smoothness. e conditional probability y∣x has the likelihood probability density p(y∣x), which is typically calculated using Eq. (15). en, the posterior probability density is

p(y∣x)p(x) p(x∣y) = , (16) p(y) which is the famous equation called Bayes' theorem or rule and the solution of the statistical inverse problem. e Bayes' theorem allows new evidence to update our current beliefs. e marginal probability density p(y) is a scaling constant that can be neglected from the analysis as the minimization of Eq. (16) is more relevant than the exact form of the posterior distribution. e commonly used point estimator is the maximum a posteriori (MAP)

xMAP = argmin p(x∣y) (17) x

6Jacques Hadamard (1865–1963), a French mathematician. 29 and sometimes the maximum likelihood (ML)

xML = argmin p(y∣x). (18) x e ML estimate gives the same result as MAP with uninformative (at) prior distribution or when the amount of data increases towards innity.

4.1. O       e limb-viewing technique is a useful way to measure the vertical composition of the tangent point atmosphere. Different retrieval strategies can be used to extract the maximum amount of information from the measurements. e chosen retrieval method should be feasible in terms of accuracy and numerical performance, but usually there are many possible ways to approach the problem. Used wavelengths, retrieved parameters, etc., are important choices affecting the retrieval. In addition, the methods typically treat the prior information differently, which is a crucial—and oen somewhat subjective—part of the inversion. e rst limb scatter ozone retrievals were made using the Ultraviolet Spectrom- eter (UVS) instrument on board the Solar Mesospheric Explorer (SME) [Rusch et al., 1984], launched in 1981. Further measurements were made by the Shuttle Ozone Limb Sounding Experiment (SOLSE) and Limb Ozone Retrieval Experiment (LORE) instruments [McPeters et al., 2000] on board of the Space Shuttle ight STS-87 in 1997. e SOLSE/LORE ozone proles were retrieved using the method described by Flittner et al. [2000] which uses wavelength pairs in the UV, and wavelength triplets in the visible, i.e., ratios that are only weakly affected by other trace gases and aerosols. e authors use the so-called optimal estimation method [Rodgers, 2000] to solve the actual inverse problem. e SOLSE/LORE instrument was lost, along with the crew, when Space Shuttle Columbia disintegrated during reentry into the atmosphere in 2003. More serious limb scatter instrumentation started to appear in the beginning of the 21st century. In addition to OSIRIS on Odin, the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) instrument [Bovens- mann et al., 1999] on board the Envisat satellite was also able to measure limb scatter data. e SCIAMACHY limb ozone retrieval [Jia et al., 2015] combines information from the UV and visible wavelengths: In the visible spectral range, the triplet method is used, and in the UV spectral range, the method described by Rohen et al. [2008] is used. Alternative retrieval methods that use OSIRIS data can be found, e.g., for ozone [Degenstein et al., 2009], for NO2 [Bourassa et al., 2011], and for aerosols [Bourassa et al., 2012]. e OSIRIS ozone retrieval by Degenstein et al. [2009] uses rather similar wavelength pairs and triplets than Flittner et al. [2000], but utilizes weighting functions for the pairs and triplets. is way the UV and visible bands can be combined 30 in a smooth way, which prevents unwanted discontinuities in the retrieved proles. e retrieval itself is a variant of the multiplicative algebraic reconstruction technique [Gordon et al., 1970] which is originally a two dimensional tomographic algorithm. In addition, the GOMOS bright limb ozone proles are previously retrieved by Taha et al. [2008]. Again the authors use the approach by Flittner et al. [2000] to combine the UV and visible regions, and an optimal estimation scheme [Rodgers, 2000] for the retrieval. In this thesis, the fundamental ozone retrieval strategy is to use a large wavelength band (280–680 nm) for the retrieval. It naturally combines the UV and visible bands and allows retrievals for different altitude regions. Because we do not use wavelength pairs or triplets, the smooth base line of the spectrum (due to air and aerosol scattering) must be taken account as well. To perform the retrieval, we use the the so-called onion peeling method. In onion peeling, the layers of the atmosphere are assumed to be homogeneous and the prole is estimated starting from the topmost layer, solving it, and proceeding layer by layer to the lowermost layer. During the process, the layers already solved above the current layer are assumed to be known and xed. In the end, the separately retrieved layer densities produce the complete vertical prole. In Papers I–III, we use the onion peeling method to retrieve proles from OSIRIS and GOMOS bright limb data [see also Auvinen, 2009]. At each layer, the state vector x ∈ Rp presents densities of the p trace gases, the unknowns in the inverse problem. Weuse uninformative prior for the parameters and assume that our measurement error estimates are independent and normally distributed. Hence, the minimization of χ2 in Eq. (15) becomes a weighted least squares problem. e onion peeling solution is relatively fast to compute—typically the parameters of one layer can be estimated in a few iterations. e lightweight inverse problem allows us to use more wavelengths in the forward model without hindering the performance too much. In principle, a large number of data points increases the signal to noise ratio, and especially with ozone, a large wavelength band allows retrievals for a wide altitude range. e downside of a large wavelength band is that the aerosols and stray light, for example, can cause additional challenges for the retrieval. In this kind of retrieval set up, we assume that the there is no correlation between the residuals, even if this might be a somewhat naive assumption. e correlation of the residuals is hard to avoid entirely when a large wavelength band is used in the retrieval (Fig. 14). For example, an incorrect aerosol model or stray light contamination in the data, would cause a smooth modeling error component and a poor agreement between the model and data. How- ever, the modeling error component is troublesome to estimate and would require at least a comprehensive analysis of the residuals. e contribution of the modeling error can be reduced by using a narrow wavelength band in the retrieval. It is a useful solution especially when the spectral ngerprint of the retrieved gas is important only in 31

OSIRIS fit at 30 km 20

10 Ratio

5 Measurement Fitted model 0 10

0 Residual −5

−10 300 350 400 450 500 550 600 650 Wavelength [nm]

Figure 14: OSIRIS O3 retrieval band. Shown are OSIRIS data at one tangent height (30 km) and the model at the optimum (upper panel), and the corresponding residuals (lower panel). The retrieved gases were O3, neutral air, and aerosols.

some limited parts of the measured spectrum. To retrieve NO2, which is a minor absorber compared to ozone, we use a narrow wavelength band between 430 and 450 nm (Fig. 15). is kind of retrieval closely resembles the Diﬀerential Optical Absorption Spectroscopy (DOAS) technique [Platt and Stutz, 2008] that is widely used in atmospheric data analyzes. Because of the diﬀerent spectral ranges, the OSIRIS O3 and NO2 retrievals are done in separate peeling loops. With the GOMOS daytime radiances, the large measurement noise prevents reasonable NO2 retrievals. To solve the weighted least squares problem of Eq. (15), we use the Leven- berg–Marquardt (LM) method. It is a derivative based optimization method commonly used to solve nonlinear least squares problems. e LM method was initially proposed by Levenberg [1944] and further developed by Marquardt [1963]. e LM iteration is dened

= + [ T + ( T )]−1 T [ − ( )] xi+1 xi Ki Ki γidiag Ki Ki Ki y F xi (19) where Ki is the Jacobian of xi, and y − F (xi) is the residual. To account for the observation uncertainty, Eq. (19) becomes

= + [ T −1 + ( T −1 )]−1 T −1[ − ( )] xi+1 xi Ki Cy Ki γidiag Ki Cy Ki Ki Cy y F xi , (20) where Cy is the covariance matrix of the measurement uncertainty. e method needs a starting point, x0, which should be roughly near the correct solution, especially if the 32

OSIRIS fit at 30 km 31.5 Measurement Fitted model 31 Ratio 30.5

30 3 2 1 0

Residual −1 −2 −3 430 432 434 436 438 440 442 444 446 448 450 Wavelength [nm]

Figure 15: OSIRIS NO2 retrieval band. Shown are OSIRIS data at one tangent height (30 km) and the model at the optimum (upper panel), and the corresponding residuals (lower panel). The retrieved gases were NO2, neutral air, and aerosols. residual function, y −F (x), contains multiple local minima. e damping parameter, γi, is adjusted at each iteration until the sum of squared residuals (RSS) decreases before moving to the next iteration. e LM algorithm stops when the RSS decreases less than the user-dened threshold, and xi = xˆ is returned as the solution. A useful statistics for the goodness of t is the reduced chi square χ2 χ2 = , (21) red m − p where χ2 is the weighted sum of squared errors, i.e., Eq. (15), m is the number of wavelengths, and p is the number of tted parameters. Ideally, the model and data agree 2 ≈ 2 within the measurement uncertainty and χred 1 at the optimum. A χred value considerably larger or smaller than one suggests some kind of imbalance between the data, model, and measurement error. Finally, the uncertainty of the estimated parameters can be approximated from the Jacobian at the optimum 2 = ( T −1 )−1 2 σx diag K Cy K χred, (22) 2 where the scaling factor, χred, accounts for the disagreement in the t.

4.2. D    FTS  A single FTIR spectrum contains considerably less information about the vertical structure of the atmosphere at the tangent point than a complete limb scatter scan con- 33 taining many independent spectra. Nevertheless, with the FTIR data too, the retrieval is generally performed using a relatively dense vertical grid. Although the choice is arbitrary, an adequate grid, in general, extracts most information provided by the measurement and gives a good visual representation of the prole [Ceccherini et al., 2016]. In any case, the retrieval method must carefully connect the grid, retrieved parameters, and vertical sensitivity. Mediocre vertical resolution and low sensitivity to some altitudes are common issues for ground-based instruments and nadir-viewing satellite instruments. ese issues typically complicate the prole retrieval eﬀorts considerably. e most common retrieval approaches are the prior prole scaling [e.g. Wunch et al., 2011], and optimal estimation [e.g. O'Dell et al., 2012]. e former method does not even try to provide any prole information, and the latter scheme typically depends on tight prior in order to provide reasonable proles. In this thesis, the idea was to implement a method that would be less dependent on the prior but would still provide information about the vertical structure and realistic proles. Because the measured FTIR data allows us to retrieve around 2–3 independent pieces of information about the vertical structure of CH4, we construct the inverse problem so that there are 2–3 estimated parameters only. is kind of parametrization simplies and stabilizes the inverse problem, and eases the computation. e parameters needs to be chosen so that they manifest the information content of the measurement, and we need a way to project the low-parameter prole back to the full space. e idea of solving inversion problems by the means of dimension reduction is not new. For example, the so-called truncated singular value decomposition technique [see e.g. Kaipio and Somersalo, 2005] is a well-known numerical trick to regularize an ill-posed inverse problem. In his classic book Rodgers [2000] discusses the dimension reduction option also, but without details how the actual projection to the lower dimension is made. e dimension reduction approach that we apply to the FTIR data in Paper IV is based on Marzouk and Najm [2009] and Solonen et al. [2016]. e fundamental concept of the method is to express the prole x ∈ Rn in terms of the parameter vector α as

x = x0 + Pα, (23)

n where x0 ∈ R is a priori mean prole, P is a matrix that can be used such that PPT = C, where C is a n × n positive denite prior covariance matrix, and α ∈ Rn are the unknown parameters. Next, to have a dimension reduction, the key operation ̃ is to replace matrix C by its low-rank version, denoted C. It can be approximated using the singular value decomposition and considering only k (1 ≤ k < n) largest singular values and the corresponding singular vectors. us, the low-dimensional 34 parametrization of x is x = x0 + Pkαk, (24) where αk is a k-dimensional vector whose prior distribution will be a k-dimensional n×k k n Gaussian N (0, Ik), and Pk ∈ R , k < n, is a projection matrix from R to R . Using the Bayesian analysis for the estimation of αk, the posterior density is of form 1 2 2 p(α∣y) ∝ exp (− (∥y − f(x0 + P α )∥ + ∥α∥ )) , (25) 2 k k Cy Ik where y ∈ Rm is the measurement vector, f∶ Rn → Rm is the forward model and m×m Cy ∈ R is the measurement error covariance. An important part of the dimension reduction technique presented above is the estimation of the original prior covariance matrix C. Ideally, C would be estimated from a large number of accurate prole measurements, e.g., in-situ balloon soundings, that would characterize the natural variability of the particular trace gas. Because we do not have this kind of data set for methane over Sodankylä, we construct C from general assumptions and use satellite prole measurements to check our assumptions (see details in Paper IV). e prior covariance for CH4 that we have used is shown in Fig. 16. To estimate the α parameters, we use Markov chain Monte Carlo (MCMC) statistical estimation. e MCMC method is an eﬃcient way to sample multidimensional spaces and to nd regions of statistical signicance [Tarantola, 2005]. e most general MCMC algorithm is the Metropolis-Hastings (MH), based on the work of Metropolis et al. [1953] and Hastings [1970]. In modern applications, it is popular to use adaptive versions of MH [see Tamminen, 2004, Laine, 2008, and references therein]. In this work, we use MCMC to sample the posterior distribution of Eq. (25), thus obtaining a full Bayesian uncertainty quantication. MCMC is a clever way to do Monte Carlo sampling because the full posterior distribution can be analyzed without needing to calculate the normalizing constant in the Bayes' formula. It should be mentioned that MCMC is eﬃcient here because we only have a few estimated parameters (1–3 for each gas). e decrease in the number of estimated parameters is an important feature of the dimension reduction method. Instead, running MCMC in full state space would be computationally demanding. 35

Log of prior covariance Singular values −14 −13 −10 −12 −9 40 2 −4 −8 −2 1.5 30 −3 −7 −6 −5 −5 20 1 −3

Altitude [km] −4 10 0.5 −6 −13 −12 0 10 20 30 40 0 1 2 3 4 5 Altitude [km] N Singular vectors Draws from the prior (N=3)

40 40

30 30

20 20 1st Altitude [km] 10 2nd 10 3rd 0 0 −0.4 −0.2 0 0.2 0.4 500 1000 1500 2000 2500 CH mole fraction [ppb] 4

Figure 16: Prior covariance of CH4 (from Paper IV). Shown are the covariance matrix (upper left), its singular values (upper right), three largest singular vectors (lower left), and random draws from the prior (lower right). 36

5. R

Retrieved proles are considered useful for scientic work once their properties are characterized using reference measurements of known and good quality. A standard way to validate satellite proles is to compare spatially and temporally co-located proles, and calculate the relative diﬀerence for each prole pair as

(xprof − xref ) ∆ = × 100 [%] (26) xref where xprof is the prole whose quality we are interested in and xref is the reference prole of “known” quality. e distribution of ∆ can be used as an estimate for bias when we have a suﬃcient amount of co-located proles. Proper coincidence criteria for the prole pairs depend on the sampling of the instruments and the variability of the measured trace gas. e prole pairs should be as near as possible in time and space, yet producing enough matches for credible statistics. Typical limits in the comparison of satellite proles are around 100–500 km in distance and 1–24 h in time. In addition to other satellite instruments, in-situ balloon soundings are oen used as a reference in the validation studies. In-situ instruments sample local air achieving typically an excellent vertical resolution, and generally obtain better accuracy and precision than satellite measurements. However, balloon soundings typically only reach altitudes up to ∼30 km or less. Furthermore, soundings provide less data than satellite instruments and cover only xed locations. In this thesis, we used in-situ balloon soundings to validate the GBL ozone proles (Sect. 5.3.) and FTIR CH4 proles (Sect. 5. 4.).

5.1. OSIRIS O3 

A commonly used reference satellite data set for ozone proles was measured by the Stratospheric Aerosol and Gas Experiment II (SAGE II) instrument [Damadeo et al., 2013], operational between 1984 and 2005. SAGE II is a solar occultation instrument, achieving high signal-to noise ratio by measuring the direct Sun beam through the atmosphere. SAGE II is oen referred as “the gold standard” in ozone (prole) monitoring. On the other hand, using the solar occultation technique only two measurements per orbit can be recorded leading to a modest spatial coverage. In addition to SAGE II, also the GOMOS nighttime ozone proles are considered to have a good accuracy in the stratosphere, typically better than 5 %. It is a similar accuracy than of SAGE II ozone [see Kyrol¨ ä et al., 2013]. In Paper I, we compared the OSIRIS ozone proles with the GOMOS nighttime proles. Since then, the whole OSIRIS data set has been processed and I will present 37 here updated validation results against SAGE II and GOMOS nighttime data. Statisti- cally, OSIRIS and SAGE II ozone proles have a better than 5 % agreement between 15 and 55 km (Fig. 17). In this comparison, I set the spatial difference less than 200 km and time difference less than 3 h. Because of the short temporal separation, the OSIRIS morning measurements are compared with the corresponding SAGE II sunrise measurements, and the evening measurements with the corresponding sunset measurements. is minimizes possible effects of the diurnal variation of ozone. e OSIRIS and SAGE II matches are from 2001–2005 which is the common measurement period of the instruments. e agreement between the OSIRIS morning measurements and the GOMOS nighttime ozone proles in the 20–55 km range is similar (Fig. 18) than in the comparison with SAGE II. In this comparison, the spatial difference is less than 150 km and the time difference less than 12 h. e OSIRIS evening measurements were omitted because the well known aernoon maximum of ozone [Sakazaki et al., 2013] would cause an additional around 5 % positive bias at around 45 km.

35 Altitude [km] 30

15 −20 −15 −10 −5 0 5 10 15 20 (OSIRIS−SAGE II)/SAGE II [%]

Figure 17: Comparison of OSIRIS and SAGE II ozone proles. Left: median (blue) and interquartile range (shaded region) of the individual relative diﬀerences. There were 122 co- located proles. Right: locations of the matches.

5.2. OSIRIS NO2 

e validation of OSIRIS NO2 is a bit more ambiguous than the validation of ozone. e retrieved NO2 proles are expected to be less accurate than the ozone proles due to the challenges in the corresponding inverse problem. NO2 has a considerably 38

Altitude [km] 35

20 −20 −15 −10 −5 0 5 10 15 20 (OSIRIS−GOMOS)/GOMOS [%]

Figure 18: Comparison of OSIRIS and GOMOS nighttime ozone proles. Left: median (blue) and interquartile range (shaded region) of the individual relative differences. There were 555 co-located proles. Right: locations of the matches. smaller spectral ngerprint than ozone, inducing more sensitivity to the noise, prior, and other factors in the retrieval process. Furthermore, NO2 has a strong diurnal variation in the stratosphere, an aspect that complicates the comparison between measurements made at different local times and viewing geometries. In Paper I, we compared OSIRIS NO2 with data from Halogen Occultation Ex- periment (HALOE), another space-borne instrument using solar occultation. In this section, I perform an additional comparison with SAGE II sunset measurements, a data set that is considered good for scientic work (there are known issues in the SAGE II sunrise NO2 data [see Damadeo et al., 2013]). Examples of the individual, co-located OSIRIS and SAGE II NO2 proles are shown in Fig. 19. On average, the proles deviate less than 10 % between 26 and 39 km (Fig. 20). Below 26 km the increasing negative bias is mainly due to the diurnal effects caused by the different viewing geometry of the instruments [McLinden et al., 2006]. In this comparison, the spatial difference is less than 250 km and time difference less than 30 min.

5.3. GOMOS   O3 

e GOMOS bright limb ozone proles were thoroughly validated in Paper III. e result was that the GBL proles are always signicantly better than the corresponding day occultation proles (see, e.g., Fig. 21). e day occultation retrieval is corrupted by biases and outliers in the measured transmission spectra. Hence, the stratospheric 39

30 Altitude [km]

0 2e9 4e9 OSIRIS NO [cm−3] SAGE II 2

Figure 19: Examples of the co-located OSIRIS and SAGE II NO2 proles. part of the day occultation proles is useless in most cases. e retrieval from the limb scattered radiance is less sensitive to these kind of problems because of the better signal to noise ratio. e retrieved GBL proles agree relative well with the SAGE II measurements (Fig. 22). e relative diﬀerence is (mostly) below 10 % between 20 and 50 km but the bias has a distinct shape. e GBL proles tends to have a negative bias at 40 km and a positive bias at 50 km. Below 35 km the bias in the GBL data is oen below 5 %, according to the comparison with ozone soundings (Fig. 23). e 40 km bias is due to the stray light in the GOMOS spectrum, which causes inconsistency between the UV and visible wavelength regions. A better method for combining information from the two bands should be developed for the next GBL reprocessing.

5.4. FTS 

To validate the retrieved CH4 proles, we use balloon-borne measurements made with the AirCore system [Karion et al., 2010]. AirCore is a long metallic tube that slowly lls with ambient air during the balloon descent. Aer the landing, vertical proles of several gases such as CO2, CH4, and H2O, can be derived from the sampled air. For the ten investigated days, the retrieved FTS proles agree well with the Air- Core proles (Fig. 24). On 19 March 2014 and 8 May 2014 the dimension reduction 40

28 Altitude [km] 26

20 −50 −40 −30 −20 −10 0 10 20 30 40 50 (OSIRIS−SAGE II)/SAGE II [%]

Figure 20: Comparison of OSIRIS and SAGE II sunset NO2 proles. Left: median (blue) and interquartile range (shaded region) of the individual relative diﬀerences. There were 29 co- located proles. Right: locations of the matches.

method is able to nd the steep gradient in the CH4 prole. On these days, air over Sodankylä was inuenced by a strong stratospheric polar vortex, which explains the large discrepancy between the default prior prole and the truth. e oﬃcial TCCON retrieval simply scales the default prior, which will lead to large uncertainties if the shape of the prior prole is clearly wrong. In Paper IV we also demonstrate that the wrong prior prole will also cause large solar zenith dependence and bias in the total column estimate. 41

110

100

90 Day occultation Night occultation 80 GBL 70

Altitude [km] 50

−5 0 5 10 15 Ozone mixing ratio [ppmv]

Figure 21: Three diﬀerent GOMOS ozone prole products (from Paper III). The proles were measured approximately at the same location within 12 h.

Altitude [km] 35

20 −20 −15 −10 −5 0 5 10 15 20 (GBL−SAGE II)/SAGE II [%]

Figure 22: Comparison of GBL and SAGE II ozone proles. Left: median (blue) and interquartile range (shaded region) of the individual relative diﬀerences. There were 590 co- located proles. Right: locations of the matches. 42

60−90N 60−90S 35 77 35 6 165 28 296 48 426 72 508 88 30 541 30 98 572 100 587 105 599 106 609 102 25 611 25 93

Altitude [km] 608 81 567 69 479 55 366 39 20 240 20 23 34 4 −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30

30−60N 30−60S 35 44 35 95 214 5 349 15 412 25 30 446 30 27 465 30 479 33 489 33 492 32 25 486 25 29

Altitude [km] 465 28 398 23 315 17 183 11 20 83 20 5 8 −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30

30S−30N 90S−90N 35 35 128 4 292 14 577 36 898 54 1087 30 58 30 1170 60 1229 60 1270 61 1294 60 1302 25 60 25 1286

Altitude [km] 57 1246 55 1119 47 920 28 634 20 3 20 358 2 48 −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 Difference [%] Difference [%]

Figure 23: Comparison of GBL and ozone soundings proles (from Paper III). The panels represent diﬀerent latitude bands. The numbers inside the panels show how many proles were compared at diﬀerent altitudes. 43

10 o o Altitude [km] 03−Sep−2013, SZA: 78 22−Oct−2013, SZA: 79 0 30

10 o o Altitude [km] 19−Mar−2014, SZA: 72 09−Apr−2014, SZA: 72 0 30

10 o o Altitude [km] 08−May−2014, SZA: 66 14−Jul−2014, SZA: 66 0 30

10 o o Altitude [km] 15−Jul−2014, SZA: 60 16−Jul−2014, SZA: 67 0 30

10 o o Altitude [km] 02−Sep−2014, SZA: 61 05−Nov−2014, SZA: 85 0 300 600 900 1200 1500 1800 300 600 900 1200 1500 1800 CH [ppb] CH [ppb] 4 95% Posterior 4 Prior mean AirCore AirCore (smoothed)

Figure 24: Comparison of the retrieved CH4 proles and AirCore proles (from Paper IV). 44

6. C

Vertically resolved measurements of the Earth's atmosphere are highly relevant data for the research community. Many research questions, such as the behavior of the stratospheric ozone layer or polar vortex, require understanding of the vertical structure of the atmosphere. Accurate prole data are necessary input for the secondary products like total column estimates, too. More general results, such as the global distributions of the gases—and especially trends—are important background infomation for policy makers negotiating international treaties, for example. Papers I–III of this thesis explore the retrieval of vertical atmospheric proles from the limb scatter satellite measurement of OSIRIS/Odin and GOMOS/Envisat. In these studies, an onion peeling type inversion method was used to retrieve stratospheric ozone with high vertical resolution. In addition, also NO2 and aerosols were retrieved from the OSIRIS data. e quality of the retrieved OSIRIS proles is comparable with the best reference data such as the measurements of the Microwave Limb Sounder (MLS) on EOS/Aura satellite and GOMOS nighttime occultations [see, e.g, Kauppi et al., 2016]. OSIRIS provides such excellent radiance measurements that, in terms of ozone, the used inverse method is perhaps less crucial. For example, the OSIRIS ozone from the onion peeling is generally very similar than the other OSIRIS data set, retrieved by Degenstein et al. [2009], which is processed using a completely diﬀerent inverse method. Even so, any physical inverse method would still require an accurate forward model to produce valid results. e quality of the GOMOS daytime proles was vastly improved aer using the limb scattered radiance data instead of the star spectra in the retrieval. GOMOS daytime radiances suﬀer from severe stray light corruption and saturation but these problems can be mostly avoided with a dedicated retrieval method developed in Pa- pers II–III. e GOMOS bright limb ozone data set produced within this thesis approximately doubles the amount of useful ozone data from GOMOS. e GBL data set was recently included in the ESA project OZONE Climate Change Initiative which uses high quality ozone proles from instruments like OSIRIS, SCIAMACHY, and GOMOS. Paper IV used ground-based direct Sun measurements of the Sodankylä FTS instrument. In this study, a dimension reduction retrieval method was used to retrieve methane proles. e motivation came from the fact that the current operational TCCON retrieval does not obtain any prole information. e operational TCCON retrieval is performed simply by scaling default prior proles. is kind of retrieval scheme leads to problems when the prior prole shape is incorrect. Our study shows that the FTIR measurement indeed contains information about the vertical prole and this information can be exploited with a proper retrieval method. An additional ben- et of the dimension reduction method is that the MCMC method can be used for the 45 uncertainty quantication. Using MCMC would be too unpractical with most other prole retrieval methods. 46

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Reprinted, with permission, from Journal of Geophysical Research: Atmospheres, 113, D04308, doi:10.1029/2007JD008591

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D04308, doi:10.1029/2007JD008591, 2008

Description and validation of a limb scatter retrieval method for Odin/OSIRIS S. Tukiainen,1 S. Hassinen,1 A. Seppa¨la¨,1 H. Auvinen,2 E. Kyro¨la¨,1 J. Tamminen,1 C. S. Haley,3 N. Lloyd,4 and P. T. Verronen1 Received 26 February 2007; revised 12 October 2007; accepted 3 December 2007; published 29 February 2008.

[1] In this paper we present the Modified Onion Peeling (MOP) inversion method, which is for the first time used to retrieve vertical profiles of stratospheric trace gases from Odin/OSIRIS limb scatter measurements. Since the original publication of the method in 2002, the method has undergone major modifications discussed here. The MOP method now uses a spectral microwindow for the NO2 retrieval, instead of the wide UV-visible band used for the ozone, air, and aerosol retrievals. We give a brief description of the algorithm itself and show its performance with both simulated and real data. Retrieved ozone and NO2 profiles from the OSIRIS measurements were compared with data from the GOMOS and HALOE instruments. No more than 5% difference was found between OSIRIS daytime and GOMOS nighttime ozone profiles between 21 and 45 km. The difference between OSIRIS and HALOE sunset NO2 mixing ratio profiles was at most 25% between 20 and 40 km. The neutral air density was compared with the ECMWF analyzed data and around 5% difference was found at altitudes from 20 to 55 km. However, OSIRIS observations yield as much as 80% greater aerosols number density than GOMOS observations between 15 and 35 km. These validation results indicate that the quality of MOP ozone, NO2, and neutral air is good. The new version of the method introduced here is also easily expanded to retrieve additional species of interest. Citation: Tukiainen, S., S. Hassinen, A. Seppa¨la¨, H. Auvinen, E. Kyro¨la¨, J. Tamminen, C. S. Haley, N. Lloyd, and P. T. Verronen (2008), Description and validation of a limb scatter retrieval method for Odin/OSIRIS, J. Geophys. Res., 113, D04308, doi:10.1029/2007JD008591.

1. Introduction [3] The UV-visible wavelength band of OSIRIS carries information of several atmospheric trace gases including [2] OSIRIS (Optical Spectrograph and Infrared Imager ozone (O ), nitrogen dioxide (NO ), nitrogen trioxide System) is one of the two instruments on board the Swedish 3 2 (NO3), chlorine dioxide (OClO), and bromine monoxide Odin satellite, launched in February 2001 Llewellyn et al. (BrO). Trace gases leave their absorption fingerprints in the [2004]. The spectrograph part of the instrument measures solar spectrum, which is scattered by the neutral molecules limb-scattered solar light (radiance) in the wavelength of the atmosphere. Stratospheric aerosol loading and direct region of 280–800 nm with around 1 nm spectral resolu- emissions from excited molecules also contribute to the tion. Odin scans toward the Earth’s limb from 7 to 110 km shape of the observed spectrum. through a controlled nodding motion. The effective Field of [4] In addition to OSIRIS, several other spaceborne View(FOV)is1–2kmduetomotionofthe1km instruments have been deployed in recent decades to ob- Instantaneous Field of View (IFOV) during the integration serve chemical composition of the middle atmosphere. period. In turn, the FOV is sampled discretely with 1–3 km Occultation and limb-viewing instruments have been used vertical spacing. OSIRIS is the first dedicated satellite to measure vertical profiles, while nadir instruments provide instrument to measure continuously the vertical composi- mainly total column abundances of the compounds. The tion of the atmosphere using the limb scatter technique and first spaceborne UV-visible limb scatter measurements were by recording the full spectrum from UV to visible wave- done by instruments on board SME (Solar Mesospheric lengths with a good spectral resolution. Explorer) in the beginning of the 1980s [Rusch et al., 1983, 1984]. The SOLSE and LORE instruments on the Space 1Finnish Meteorological Institute, Earth Observation, Helsinki, Finland. Shuttle flight STS-87 further proved the limb scatter tech- 2Lappeenranta University of Technology, Lappeenranta, Finland. nique to be feasible [McPeters et al., 2000; Flittner et al., 3Centre for Research in Earth and Space Science, York University, 2000]. Examples of more recent space instruments, capable Canada. 4 of doing UV-visible limb scatter measurements, are SCIA- Department of Physics and Engineering Physics, University of MACHY [Bovensmann et al., 1999], GOMOS [Kyro¨la¨et Saskatchewan, Saskatoon, Canada. al., 2004], and SAGE III [Rault, 2005]. As the measurement Copyright 2008 by the American Geophysical Union. principle of remote sensing instruments is always indirect, 0148-0227/08/2007JD008591

D04308 1of12 D04308 TUKIAINEN ET AL.: LIMB SCATTER RETRIEVAL METHOD D04308 data inversion methods are needed to extract information available wavelengths and try to retrieve various species from the physical measurements. simultaneously. [5] Several inversion methods have been developed to [12] The theoretical basis of the MOP inversion method is retrieve trace gas densities from the OSIRIS measurements. a Bayesian approach. However, using a flat a priori distri- The so-called Triplet method was developed by Flittner et bution and assuming Gaussian noise, the solution reduces to al. [2000] and McPeters et al. [2000] and was adapted to the a simple weighted least squares fit to the data [e.g., Rodgers, OSIRIS limb scatter measurements by von Savigny et al. 2000]. Non-linear problems, such as the one related to [2003]. The Triplet method uses wavelength triplets in the OSIRIS, require an iterative fitting procedure. Chappuis absorption band near 600 nm to retrieve strato- [13] Following Auvinen et al. [2002], it is advantageous spheric ozone. According to Petelina et al. [2004], the not to use directly measured radiances but the ratio validated altitude range for the OSIRIS triplet ozone is 15–32 km. I ðÞl; j R ðÞl; j ¼ obs ; ð1Þ [6] The DOAS (Differential Optical Absorption Spectros- obs ref IobsðÞl copy) method is one widely used approach for the retrieval of several different species. The basic DOAS approach was where Iobs(l, j) are measured radiances at tangent heights j proposed by Platt [1994] and the method was applied to ref and Iobs(l) is a reference measurement from the same scan simulated limb scatter measurements by McDade et al. at high tangent altitude. Radiance is a function of [2002] and Strong et al. [2002]. Haley et al. [2003] applied wavelength l. We have chosen to use the first measurement the DOAS technique to retrieve ozone from OSIRIS data below 50 km as the reference. It would be possible to try and found good agreement with the Triplet method. other tangent heights as well, but that around 50 km seems [7] The DOAS method has been also used to retrieve to yield the best results in practice. It is already high enough stratospheric NO2 from the OSIRIS data. Haley et al. [2004] to exclude spectral fingerprints from minor trace gases (such and Sioris et al. [2003] used slightly different DOAS as NO2, OClO, and BrO) making it easier to model. variants and obtained quite consistent results. They also Furthermore, straylight contamination in OSIRIS increases made preliminary validation against sonde and POAM III as a function of tangent height making high altitude measurements proving the method feasible. measurements less unreliable to use [Llewellyn et al., 2004]. [8] The Triplet method and the various DOAS algorithms [14] The use of the so-called transfer spectrum (1) is exploit only a small fraction of the available UV-visible useful because it diminishes systematic errors due to surface spectrum. There have also been efforts to analyze the limb albedo, clouds, and polarization [Flittner et al., 2000; scatter spectra without reduction to differential structures. Oikarinen, 2001]. It also reduces errors due to imperfect For example, Kaiser et al. [2004] used this principle to instrument calibration. retrieve satellite pointing from limb scatter measurements. [15] The modeled transfer spectrum is defined as In addition, Rohen et al. [2005] retrieved mesospheric ozone using the Hartley band in 240–310 nm. ImodðÞl; j; r [9] The method used in this study is the Modified Onion RmodðÞl; j ¼ ; ð2Þ I ref ðÞl; r Peeling (MOP) method. It was originally developed by mod ref Auvinen et al. [2002], but the method has later undergone ref significant modifications discussed in Section 2. In partic- where Imod(l, j, r) are modeled radiances and Imod(l, rref) is a model reference spectrum. The gas density profiles r ular, the NO2 retrieval part has been revised since the original publication of the method. The MOP method are adjusted iteratively, and after every iteration a new and should offer at least one advantage compared with the other better agreement is obtained between (1) and (2). retrieval techniques: The advantage of the MOP method, [16] A typical background atmosphere is assumed when compared with the other retrieval techniques, is that using we calculate the model reference spectrum. Obviously, even information from the whole spectral band of the OSIRIS the best estimate differs from the true state of the atmo- instrument, we are able to retrieve ozone by one method sphere and typically produces systematic bias to the re- between 15 and 70 km. trieved profiles. This effect is studied later in Section 3. [10] After the original MOP method was modified, we 2.1. Spectral Fitting tested the sensitivity of the new version using simulated [17] At every layer, assuming that the measured transfer data (Section 3). Finally, we validated the outcome of the spectra (1) are independent, the sum of squared residuals is MOP method using real OSIRIS data. Inverted vertical defined as profiles were compared with data from other instruments measuring the middle atmosphere (Section 4). 2 T À1 c ¼ ðÞRmod À Robs C ðÞRmod À Robs ; ð3Þ

2. MOP Inversion Method where C is a covariance matrix. The covariance matrix [11] The general idea of onion peeling inversion methods includes contributions from the measurement and modeling is to divide the atmosphere into separate layers and solve the errors. The errors at different wavelengths are assumed to be inversion problem layer by layer from top of the atmosphere uncorrelated, which leads to a diagonal covariance matrix. downward. This way we can construct the vertical profiles The modeling error describes our inability to model limb of different trace gases. In the MOP method, as described scatter observations perfectly, mainly because of multiple by Auvinen et al. [2002], we can use any number of scattering of the atmosphere (see Section 2.3). The modeling error is estimated as a function of wavelength

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Figure 1. OSIRIS spectral fits in the UV-visible region after the first peeling loop (upper panel) and the corresponding residuals (lower panel). The NO2 profile is kept fixed during the iterations while ozone, air density, and aerosols are allowed to vary. Note that OSIRIS does not record the spectra between 470 and 530 nm and the wavelengths beyond 680 nm are not used in the fitting. and altitude using the Monte Carlo radiative transfer model for example, a missing gas, incorrect cross sections (e.g., an Siro [Oikarinen et al., 1999]. uncertain temperature profile), too simplified aerosol model, [18] The fitting problem (3) is solved using an initial or incorrect albedo model. Furthermore, an insufficient guess for the densities and the Levenberg-Marquardt algo- modeling of the diurnal effects and errors due to geometry rithm [Levenberg, 1944; Marquardt, 1963; Gill et al., 1981] simplifications may contribute. The (current) model to find the best fit. The Levenberg-Marquardt algorithm is presents our best understanding of the physics behind the commonly used in non-linear curve fitting problems. It finds observations. The clear structures in the residuals indicate the minimum of (3) by combining techniques of gradient that there is still work to do in order to improve the model in descent and the inverse-Hessian optimization. The algo- the future. rithm also provides error estimates for the fitted parameter [21] In addition, the measurement data contain errors and values. therefore the model is not able to describe observations [19] Figure 1 presents examples of the spectral fits after exactly. The spectral fit to the OSIRIS data shown in the first peeling loop. The relative differences increase at Figure 1 was done with a model including an accurate lower altitudes, but generally a good consistency can be single scattering model and an approximate multiple scat- found between the model and the measurement. Completely tering correction. The model will be described more exten- flawless agreement is very difficult to achieve because the sively in Section 2.3. wavelength band used is relatively wide (over 400 nm) and the radiance is governed by numerous wavelength-dependent 2.2. Improved NO2 Retrieval phenomena. [22] The original idea by Auvinen et al. [2002] was to use [20] Limb scatter measurements include relatively small the whole spectral range of OSIRIS and retrieve all the noise, but the model is unable to describe observations desired trace gas densities simultaneously. However, this perfectly. Because the modeling of the atmosphere is a very approach seemed to work only with simulated data. When complex problem indeed, it is possible (or even evident) inverting real OSIRIS data, the NO2 retrievals were usually that the model lacks some processes, or that they have been of poor quality although the inverted ozone profiles were taken account in too simplified way. These factors can be, proper. The old retrieval often produced a bias of several

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Figure 2. Fits in the NO2 retrieval band after the second peeling loop (upper panel) and the corresponding residuals (lower panel). The 30 km and 40 km spectra are scaled to fit in the figure with the 20.5 km spectra. The ozone profile (retrieved from the first peeling loop) is kept fixed during the iterations while NO2, air density and aerosols are allowed to vary.

hundreds of percent to the NO2 profiles below 30 km the Fraunhofer lines should cancel out when we apply compared with the results from the other OSIRIS retrieval equation (1), but a small residual may still be left over. algorithms or NO2 measurements by other instruments This is the tilt effect recognized by Sioris et al. [2003]. It [Tukiainen, 2006]. basically arises from the different spectral slopes of the [23] Using the whole spectrum for the fit has both radiances at different tangent heights and from the finite advantages and disadvantages. When a large wavelength spectral resolution of the instrument. Thus it is safest to band is used, the information content can naturally be avoid strong Fraunhofer lines where the effect is largest. In maximized, but on the other hand the modeling issues this wavelength band, all of the 50 available wavelengths become more critical. Since ozone is a strong absorber, were used in the spectral fitting. minor modeling uncertainties are not as crucial for the [25] Because of the distinct fitting windows for the strong ozone retrieval as they are for minor absorbers like NO2. and weak absorbers, we have to run two separate peeling As there are uncertainties in the OSIRIS modeling, we loops. During the first peeling loop, we retrieve only ozone, noticed that the NO2 retrieval benefits from using a shorter aerosol, and neutral air. The NO2 profile is summoned from wavelength band where the signal-to-noise ratio is more a climatology (U.S. Standard Atmosphere 1976). During the optimal for the NO2 retrieval. Also the band should be short second loop, we retrieve NO2. The ozone profile, retrieved enough that the wavelength dependent modeling errors are from the first peeling loop, is now fixed, but aerosols and not dominating the retrieval. neutral air are again allowed to vary freely to obtain a good [24] In the present version of MOP, the retrieval of major NO2 fit. Figure 2 shows NO2 fits from a single scan at three absorbers and scatterers (ozone, air, aerosols) is separated different tangent heights. from the retrieval of minor ones (NO2, and others). For [26] This kind of iterative solving of the parameters is NO2, the wavelength band of 430–450 nm is selected due justified, because the use of the fixed NO2 profile in the first to strong NO2 absorption fingerprint in this region. Further- peeling loop has little effect on the outcomes. Nevertheless, more, ozone as well as other species absorb weakly in this it is not totally insignificant. The use of the NO2 climatol- band and it is also free of strong Fraunhofer lines. In theory, ogy in the first peeling loop seems to result in roughly 2%

4of12 D04308 TUKIAINEN ET AL.: LIMB SCATTER RETRIEVAL METHOD D04308 bias at the ozone peak. This bias is possible to eliminate by [32] In order to take advantage of the precalculated look- adding a third peeling loop and retrieve ozone, neutral air, up tables, we divide the modeled transfer spectra (2) into and aerosols again with the retrieved NO2 profile, but this two parts: would double the required computing time. With just two peeling loops, it already takes a couple of minutes to invert I ref I ss ðÞl; j; r R mod mod M l; j ; 4 one scan (AMD Athlon 1800+ CPU). This means that we mod ¼ ¼ ref ðÞ ð Þ Imod I ðÞl; r need around six months to process the current OSIRIS data mod ref set (2001–2007) with the present computing facilities for ss where Imod(l, j, r) is the dynamic single scattering term OSIRIS at Finnish Meteorological Institute. The third peel- which is adjusted iteratively during the fitting procedure. ing loop is possible to implement later in the future, if more ref The model reference radiance Imod(l, rref) in the denomi- computing resources are provided to the operative OSIRIS nator of (4) is also calculated with LIMBTRAN (including processing. multiple scattering). The second term on the right side, 2.3. Multiple Scattering Correction M(l, j), is the static part which comes from the look-up tables and is kept fixed during the iterations. This correction [27] Taking account the multiple scattering effects is a crucial part of limb scatter retrieval methods. Therefore the term is defined as the modeled multiple scattering radiance multiple scattering correction of the MOP method is given (total radiance) divided by the corresponding single here, though the correction method has remained the same scattering radiance: since the previous paper by Auvinen et al. [2002]. [28] In the limb scatter geometry, multiple scattering can Ims l; j; rprior constitute 10–50% of the observed radiance at visible MðÞ¼l; j : ð5Þ wavelengths [Oikarinen et al., 1999]. Its proportion of the Iss l; j; rprior total radiance is strongly dependent on wavelength as the ratio of multiple to total scattering increases steeply at where rprior are the gas densities for the standard atmosphere wavelengths greater than 310 nm [Oikarinen et al., 1999]. used in the LIMBTRAN radiance simulations. In addition, the multiple scattering contribution depends on the tangent height, surface albedo, solar angles, and com- 3. Sensitivity Study position of the atmosphere itself. For these reasons, a mere single scattering radiative transfer model is not generally [33] The calculation of the model reference spectrum ref satisfactory to describe scattering and absorption effects in Imod(l, rref) requires at least ozone and neutral air profiles limb scatter problems. However, taking the multiple scat- up to the upper limit of the LIMBTRAN atmosphere (90 km). tering effects into account complicates limb scatter prob- Other species can be ignored as they have a negligible impact lems significantly and certainly increases computational on the radiance at 50 km. The effect of possibly incorrect costs, which leads to some kind of compromise between ozone and neutral air profiles in the model reference was the modeling accuracy and the available computation time. studied using single scattering simulations and a 50 km [29] During the fitting procedure in each layer, we have to reference tangent height. use a few (usually 2–10) iterations, and as many forward [34] Radiances were first simulated using the internal model calls, before the Levenberg-Marquard algorithm single scattering kernel of the MOP algorithm for a given finds good enough agreement between the model and the atmospheric composition. These simulated radiances were measurement. A full 3-D radiative transfer model operating then used as an input, and the MOP algorithm was run to in multiple scattering mode would be too slow to use and resolve the original number densities. The model reference hence we must seek faster solutions. One way would be to spectrum was also simulated with the single scattering reduce the total number of wavelengths used (from around model, but with slightly modified ozone and air profiles 300 to only a few) in the first peeling loop. This solution to study the effect on the outcomes. would not exploit the whole bandwidth of the OSIRIS [35] The results from the simulations are shown in instrument and the altitude range of the ozone retrieval Figure 3 and Figure 4. We clearly see how the modified would shrink. ozone density profile in the model reference creates biased [30] A practical approach, discussed in the original pub- ozone profiles after inversion at the upper layers (Figure 3). lication by Auvinen et al. [2002], is to use a single scattering This bias diminishes rapidly, and is already negligible below forward model during the fitting iterations and include the 45 km altitude. The effect on the NO2, air, and aerosol multiple scattering effects using precalculated look-up profiles is not as large. Instead, if the neutral air profile of tables. The single scattering forward model built into the the reference differs from truth, it creates a roughly equal MOP-inversion module solves the radiative transfer by difference in the inverted air product (Figure 4). The aerosol numerical integration and is computationally efficient to product is also affected considerably, but NO2 and ozone run. errors are only a few percent at most. It should be noticed [31] The look-up tables used in the MOP inversion from Figure 4 that the MOP neutral air and aerosols are contain modeled (single- and multiple scattered) radiances anticorrelated. calculated as a function of tangent height, solar angles, [36] As a summary, if the ozone estimate in the reference season, albedo, and latitude. The look-up tables are pro- calculation is wrong, it will produce a bias in the retrieved duced using the LIMBTRAN [Griffioen and Oikarinen, ozone profile, but the effect is large only at the few 2000] forward model. uppermost layers. An incorrect air density estimate, on the other hand, creates a corresponding bias in the retrieved air

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Figure 3. Effect of ozone density in the model reference calculation. The plots present the relative difference between the true and the inverted profiles. Ozone densities in the model reference were modified by À10% (red), À5% (blue), À1% (green), +1% (green dashed), +5% (blue dashed), and +10% (red dashed) compared with the true state of the atmosphere. The simulation was run with single scattering and using 50 km as the reference altitude. density and can also affect the retrieved aerosol profile by retrieval. There are several other possible sources of error tens of percent. such as incorrect albedo or aerosol model, imprecise satel- [37] A faulty ozone or air density profile in the model lite pointing, and polarization sensitivity. The impact of reference calculation is not the only uncertainty in the these on the limb scatter ozone retrievals has been studied

Figure 4. Same as Figure 3 but for the effect of air densities in the model reference.

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Figure 5. Comparison of GOMOS nighttime and OSIRIS daytime ozone profiles in the stratosphere between latitudes 35°S and 35°N. The coincidence criteria for the individual matches in time was less than one day, in latitude less than 1°, and in longitude less than 1°. The blue and red curves on the left present the medians of 121 coincidences and the dashed curves are the corresponding standard deviations. The green solid curve is the median of the individual relative differences defined as Comparison of OSIRIS and GOMOS aerosols between latitudes 35°S and 35°N. Coincidence limits for the individual matches are the same than in Figure 5. The blue and red curves present the medians of 110 coincidences and the dashed curves are the corresponding standard deviations. The green solid curve is the median of the individual relative differences defined as (OSIRIS-GOMOS)/GOMOS100%. The green dashed curves around the median show the semi-interquartile deviation of the differences. The blue and red dashed curves around the median show the corresponding deviations of the OSIRIS and GOMOS profiles. comprehensively by Loughman et al. [2005], von Savigny et less than 5% bias in the GOMOS nighttime ozone profiles. al. [2005], and Oikarinen [2001]. GOMOS nighttime measurements are very accurate and there is less than 5% bias in the ozone profiles. 4. Validation of Profiles [41] Coincidences were selected from the year 2003 using a latitude band from 35°Sto35°N. The latitude and [38] A preliminary validation of ozone, NO2, neutral air, longitude difference of the 121 matches was less than 1°, and aerosol profiles was carried out using OSIRIS data from and the time difference less than one day. The local time of the year 2003. The NO2 profiles are now much more the OSIRIS coincidences is close to either 6 am or 6 pm. reasonable than with the earlier version of the MOP method. [42] Figure 5 shows the result of the comparison. Median The ozone, air, and aerosol profiles also seem to be realistic. profiles of both distributions are plotted with the 4.1. Ozone corresponding standard deviations. The green solid curve on the right panel shows the median of the individual [39] The diurnal variation of stratospheric ozone is insig- relative differences. The individual differences were defined nificant below around 45 km [Brasseur and Solomon, as (OSIRIS-GOMOS)/GOMOS100%. The green dashed 2005]. Thus we can compare day and nighttime profiles lines around the median present the semi-interquartile with similar geolocation if the time difference of measure- deviation (SID): ments is on the order of days. Ozone is also generally more stable at low and midlatitudes than in polar regions. jQ3 À Q1j [40] OSIRIS ozone profiles inverted using the MOP SID ¼ ; ð6Þ method were compared with the GOMOS (Global Ozone 2 Monitoring by Occultation of Stars) nighttime profiles where Q1 and Q3 are the 25th and 75th percentiles. The area between 20 and 45 km. GOMOS is a stellar occultation between the ±1 SID lines includes 50% of the data points. instrument on board the ESA’s Envisat satellite, launched in The blue dashed lines around the median present the relative February 2002 [Kyro¨la¨etal., 2004]. The vertical sampling semi-interquartile deviation of the retrieved OSIRIS profiles resolution of GOMOS is 0.5–1.7 km and the vertical (i.e., the natural variability of the atmosphere). See also the resolution of GOMOS ozone profiles is 2–3 km depending upper panels of Figure 6 for examples of typical individual on the altitude. According to Meijer et al. [2004], there is comparisons between OSIRIS and GOMOS ozone profiles.

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Figure 6. Upper panels: typical individual ozone profile comparisons between OSIRIS (solid) and GOMOS (dashed). Lower panels: typical individual NO2 profile comparisons between OSIRIS (solid) and HALOE (dashed).

[43] The mean could be also used instead of the median, HALOE retrieval gives the NO2 volume mixing ratio while but more attention should be paid to flag abnormal data the outcomes of the MOP method are number densities. points. In practice, there was no significant difference Therefore OSIRIS NO2 densities were converted into mix- between the two (mean or median). The median of the ing ratios using retrieved neutral air profiles. The vertical individual relative differences was less than 5% between 21 resolution of HALOE NO2 profiles is about 2–3 km, which and 45 km proving that the two different instruments is similar to the resolution of OSIRIS profiles inverted with provide very consistent observations of stratospheric ozone. the MOP method. The median difference increases up to 15% at the lowest [46] The coincidence criteria for a comparable OSIRIS layer (OSIRIS measuring less ozone than GOMOS). and HALOE measurement in time was less than 30 min, in latitude less than 2°, and in longitude less than 3°. The solar 4.2. Nitrogen Dioxide zenith angles of the OSIRIS measurements were chosen to [44] The behavior of stratospheric NO2 is characterized by be between 85° and 90°. With this kind of differences in strong diurnal variation. The NO2 concentration decreases time and space, we found 28 OSIRIS and HALOE matches. rapidly in the morning as the sun rises. A similar, but positive, Thus we get reasonable statistics for the validation and the change happens when the sun sets in the evening. Thus if we profiles still describe roughly the same air mass. The compare NO2 measurements with the solar zenith angles coincidences were found between latitudes 15°S and 50°N close to 90°, the difference from the diurnal cycle should be from the year 2003. In all these cases, the OSIRIS mea- minimized as well as possible. surement comes first in the time domain. The local times of [45] OSIRIS NO2 measurements were compared with the the OSIRIS coincidences are between 5.30 pm and 6.15 pm. sunset measurements of the HALOE (The Halogen Occul- [47] As we compare NO2 profiles from solar occultation tation Experiment) instrument [Russell et al., 1993]. and limb scatter instruments, we are forced to accept a small HALOE was a solar occultation instrument launched in difference in the solar zenith angles. This will inevitably 1991 and it was operational until November 2005. The produce some difference to the results, but the effect should

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Figure 7. Comparison of HALOE sunset measurements and OSIRIS NO2 profiles in the stratosphere. The coincidence criteria for the individual matches was in time less than 30 min, in latitude less than 2°, and in longitude less than 3°. The blue and red curves on the left present the medians of 28 coincidences and the dashed curves are the corresponding standard deviations. The green solid curve is the median of the individual relative differences defined as (OSIRIS-HALOE)/HALOE100%. The green dashed curves around the median show the semi-interquartile deviation of the differences. The blue and red dashed curves around the median show the corresponding deviations of the OSIRIS and HALOE profiles. be only small because the solar zenith angles of the OSIRIS the analysis data from European Center for Medium-Range profiles used in this study are close to 90°. The other source Weather Forecast (ECMWF). The MOP air profiles are from of error is the impact of the lack of horizontal homogeneity the first peeling loop, inverted together with ozone and on limb scatter retrievals [McLinden et al., 2006]. The solar aerosols. The profiles were selected randomly covering all zenith angle may vary along the line of sight causing latitudes from the year 2003. species with diurnal cycle to vary as well, and the horizontal [50] Figure 8 shows results of the neutral air comparison. homogeneity assumption fails. This effect is generally The profiles were compared for altitudes between 20 and largest during twilight and below 25 km. The diurnal effects 65 km. The median of the relative individual differences is due to changing solar zenith angle along the line of sight are around 5% at almost all altitudes. OSIRIS appears to be not taken account in the MOP retrieval. For occultation biased low compared with the ECMWF data. The compar- instruments, the problem is less complicated and the ison result indicates that the neutral air retrieval of the MOP HALOE retrieval does account for it. This may explain method is also quite accurate. some of the differences between OSIRIS and HALOE NO2 below 25 km, but the total effect is rather hard to quantify. 4.4. Aerosols [48] Figure 7 shows the comparison of the 28 OSIRIS and [51] Stratospheric aerosols contribute to radiance through HALOE NO profiles between 20 and 40 km. The obser- scattering and absorption. The aerosol modeling in the MOP 2 À1 vations of the instruments are quite consistent and there is method is done using l scattering cross section and well- no particular bias between the instruments. The median known Henyey-Greenstein phase function. This is the difference of the individual profiles is usually less than classical, but not very sophisticated, way to model strato- 20%, which is a quite good agreement. OSIRIS seems to spheric aerosols. 52 measure more NO2 than HALOE at the peak and less than [ ] Figure 9 shows the comparison of GOMOS and HALOE at the lower stratosphere. The lower panels of OSIRIS aerosol number density profiles. The MOP aerosol Figure 6 show typical individual comparisons between profiles are from the first peeling loop. OSIRIS seems to OSIRIS and HALOE NO2 profiles. observe as much as 80% more aerosols than GOMOS. The shapes of the median profiles are rather similar but the 4.3. Air reason for the bias has yet to be worked out. [49] Scattering from the neutral molecules of the atmo- [53] These results indicate (partly expected) difficulties in sphere follows Rayleigh theory with approximately lÀ4 the validation of the MOP aerosol product. As noticed dependency. This basically determines the signal level of earlier, the outcome of the MOP aerosol retrieval is sensitive the observed radiative transfer spectrum. Air density pro- to the model reference spectrum. It should also be noted that files retrieved with the MOP method were compared with the GOMOS retrieval method uses a second-order polyno-

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Figure 8. Comparison of OSIRIS neutral air density and ECMWF analysis data. The blue and red curves on the left present the medians of 412 coincidences and the dashed curves are the corresponding standard deviations. The green solid curve is the median of the individual relative differences defined as (OSIRIS-ECMWF)/ECMWF100%. The green dashed curves around the median show the semi- interquartile deviation of the differences. The blue and red dashed curves around the median show the corresponding deviations of the OSIRIS and ECMWF profiles. mial aerosol model instead of the lÀ1 form used here. This tion about GOMOS aerosols, see Vanhellemont et al. polynomial model could be also tried with OSIRIS as it [2005a, 2005b]. might explain some of the differences. For more informa- [54] However, the underlying difficulty is the unknown (aerosol) particle shape and size distribution in the atmo-

Figure 9. Comparison of OSIRIS and GOMOS aerosols between latitudes 35°S and 35°N. Coincidence limits for the individual matches are the same than in Figure 5. The blue and red curves present the medians of 110 coincidences and the dashed curves are the corresponding standard deviations. The green solid curve is the median of the individual relative differences defined as (OSIRIS-GOMOS)/ GOMOS100%. The green dashed curves around the median show the semi-interquartile deviation of the differences. The blue and red dashed curves around the median show the corresponding deviations of the OSIRIS and GOMOS profiles.

10 of 12 D04308 TUKIAINEN ET AL.: LIMB SCATTER RETRIEVAL METHOD D04308 sphere, which makes the problem notoriously difficult. We easily expanded to retrieve also other trace gases such as are forced to do simplifications in the retrieval, and in the BrO and OClO by selecting another wavelength window end we still lack a reliable reference for the basis of the and adding an extra peeling iteration loop. The retrieved validation. The aerosol model selection itself is a difficult ozone and NO2 profiles may then be used in this iteration. decision. One promising idea is to apply Bayesian model The underlying challenge is that the concentrations of BrO selection by using a Markov chain Monte Carlo technique and OClO are an order of magnitude smaller than that of as proposed by Laine et al. [2007]. NO2 and the absorption fingerprint is easily masked by noise. However, Krecl et al. [2006] have shown that the 5. Conclusions retrieval of OClO should be possible. [61] It should also be noted that with the current Level 1 [55] In this study, the MOP inversion method was used to data we do not find any altitude shift between OSIRIS and retrieve ozone, NO2, neutral air, and aerosol densities from GOMOS ozone profiles. GOMOS uses a star tracker to the OSIRIS limb scatter measurements. Compared with the achieve a pointing accuracy of some tens of meters. Thus it other limb scatter retrieval methods, there are a few unique provides a good reference to validate the pointing perfor- aspects in MOP. The MOP method uses a wide spectral mance of Odin/OSIRIS. band and several hundreds wavelengths to retrieve ozone, air, and aerosol number densities. Thus the maximum [62] Acknowledgments. The authors wish to thank the OSIRIS team amount of information from the data is used, while the at the University of Saskatchewan for the Level 1 data, Sodankyla¨ Data use of a priori information is minimized. The same method Center for the processing support, and Samuel Brohede for the validation help. We would also like to thank the GOMOS and HALOE teams for the is also used for the whole altitude range of the retrievals. data. Finally, we would like to thank the anonymous referees for the [56] A sensitivity study with the simulated data showed corrections and suggestions that improved the paper considerably. Odin is a that the upper part of the retrieved ozone profile becomes Swedish-led satellite project funded jointly by Sweden (SNSB), Canada biased if the ozone estimate in the model reference spectrum (CSA), France (CNES), and Finland (TEKES). is incorrect. The aerosol retrieval is quite sensitive to a References faulty neutral air estimate in the reference calculation and Auvinen, H., L. Oikarinen, and E. Kyro¨la¨ (2002), Inversion algorithms for this can lead to errors up to tens of percents. Roughly equal recovering minor species densities from limb scatter measurements at error in the retrieved neutral air is also produced at all UV-visible wavelengths, J. Geophys. Res., 107(D13), 4172, altitudes. However, errors in the NO profile due to incor- doi:10.1029/2001JD000407. 2 Bovensmann, H., J. P. Burrows, M. Buchwitz, J. Frerick, S. Noel, V. V. rect model reference are always insignificant. Rozanov, K. V. Chance, and A. P. H. Goede (1999), SCIAMACHY: [57] Validation against other satellite instruments demon- Mission objectives and measurement modes, J. Atmos. Sci., 56, 127– strated the strength of the MOP method in practice. A good 150, doi:10.1175/1520-0469. Brasseur, G. P., and S. Solomon (2005), Aeronomy of the Middle Atmo- agreement was found between OSIRIS daytime and sphere, 3rd revised and enlarged ed., Springer, Dordrecht. GOMOS nighttime ozone profiles. The median of the Flittner, D. E., P. K. Bhartia, and B. M. Herman (2000), O3 profiles re- relative individual differences is less than 5% between 21 trieved from limb scatter measurements: Theory, Geophys. Res. Lett., 27, and 45 km. Above 45 km the diurnal variation of ozone 2601–2604, doi:10.1029/1999GL011343. Gill, P. R., W. Murray, and M. H. Wright (Eds.) (1981), Practical Optimi- prevented comparisons between the instruments. The qual- zation, Academic Press. ity of this mesospheric part of the ozone retrieval should be Griffioen, E., and L. Oikarinen (2000), LIMBTRAN: A pseudo three- confirmed in the future. dimensional radiative transfer model for the limb-viewing imager OSIRIS on the Odin satellite, J. Geophys. Res., 105(D24), 29,717– [58] OSIRIS NO2 profiles between 20 and 40 km were 29,730, doi:10.1029/2000JD900566. consistent with the HALOE profiles despite the challenging Haley, C. S., C. von Savigny, S. Brohede, C. E. Sioris, I. C. McDade, E. J. twilight conditions for OSIRIS. The comparison between Llewellyn, and D. P. Murtagh (2003), A comparison of methods for retrieving stratospheric ozone profiles from OSIRIS limb-scatter mea- solar occultation and limb viewing instruments is always surements, Adv. Space Res., 34, 769–774. difficult because the NO2 concentration experiences a large Haley, C. S., S. M. Brohede, C. E. Sioris, E. Griffioen, D. P. Murtagh, I. C. transition near sunrise and sunset. McDade, P. Eriksson, E. J. Llewellyn, A. Bazureau, and F. Goutail (2004), Retrieval of stratospheric O and NO profiles from Odin Optical [59] The MOP neutral air retrieval seems to result in 3 2 Spectrograph and Infrared Imager System (OSIRIS) limb-scattered sun- roughly 5% negative bias compared with the ECMWF light measurements, J. Geophys. Res., 109, D16303, doi:10.1029/ analysis data. On the other hand, there is a 20–80% positive 2004JD004588. bias in the MOP aerosol number densities compared with Kaiser, J., C. von Savigny, K.-U. Eichmann, S. Noel, H. Bovensmann, and J. Burrows (2004), Satellite-pointing retrieval from atmospheric limb- the GOMOS aerosols. The anticorrelation between neutral scattering of solar UV-B radiation, Can. J. Phys., 82, doi:10.1139/P04- air and aerosols, which is apparent from the sensitivity 071. study in Section 3 (see, e.g., Figure 4), could explain most Krecl, P., C. S. Haley, J. Stegman, S. M. Brohede, and G. Berthet (2006), Retrieving the vertical distribution of stratospheric OClO from Odin/ of the observed differences. Thus it could be possible to get OSIRIS limb-scattered sunlight measurements, Atmos. Chem. Phys, 6, better aerosol results by fixing the MOP neutral air density 1879–1894. to the ECMWF data, or by setting some interval for the Kyro¨la¨, E., et al. (2004), GOMOS on Envisat: An overview, Adv. Space MOP air density values to vary around the ECMWF values. Res., 33, 1020–1028. Laine, M., J. Tamminen, E. Kyro¨la¨, and H. 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Phys., 83, 957–972, doi:10.1139/ 110, D09309, doi:10.1029/2004JD004970. P05-041. Rodgers, C. D. (2000), Inverse Methods for Atmospheric sounding: Theory and Practice, World Scientific, Singapore. ÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀÀ Rohen, G., C. Savigny, M. Sinnhuber, E. J. Llewellyn, J. W. Kaiser, C. H. H. Auvinen, Lappeenranta University of Technology, P.O. Box 20, FI- Jackman, M.-B. Kallenrode, J. Schro¨ter, K.-U. Eichmann, H. Bovens- 53851, Lappeenranta, Finland. mann, and J. P. Burrows (2005), Ozone deflection during the solar proton C. S. Haley, Centre for Research in Earth and Space Science (CRESS), events of October/November 2003 as seen by SCIAMACHY, J. Geophys. York University, Toronto, ON M3J 1P3, Canada. Res., 110, A09S39, doi:10.1029/2004JA010984. S. Hassinen, E. Kyro¨la¨, A. Seppa¨la¨, J. Tamminen, S. Tukiainen, and P. T. Rusch, D. W., G. H. Mount, J. M. Zawodny, C. A. Barth, G. J. Rottman, Verronen, Finnish Meteorological Institute, P.O. Box 503, FI-00101, R. J. Thomas, G. E. Thomas, R. W. Sanders, and G. W. Lawrence (1983), Helsinki, Finland. ([email protected]) Temperature measurements in the earth’s stratosphere using a limb scan- N. Lloyd, Institute of Space and Atmospheric Studies, University of ning visible light spectrometer, Geophys. Res. Lett., 10, 261–264. Saskatchewan, Saskatoon, SK S7N 5E2, Canada. Rusch, D. W., G. H. Mount, C. A. Barth, R. J. Thomas, and M. T. Callan (1984), Solar Mesosphere Explorer ultraviolet spectrometer: Measure-

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Atmos. Meas. Tech., 4, 659–667, 2011 www.atmos-meas-tech.net/4/659/2011/ Atmospheric doi:10.5194/amt-4-659-2011 Measurement © Author(s) 2011. CC Attribution 3.0 License. Techniques

Retrieval of ozone proﬁles from GOMOS limb scattered measurements

S. Tukiainen1, E. Kyrol¨ a¨1, P. T. Verronen1, D. Fussen2, L. Blanot3, G. Barrot3, A. Hauchecorne4, and N. Lloyd5 1Finnish Meteorological Institute, Helsinki, Finland 2Belgian Institute for Space Aeronomy, Brussels, Belgium 3ACRI-ST, Sophia-Antipolis, France 4Laboratoire Atmospheres,´ Milieux, Observations Spatiales (LATMOS), Verrieres-le-Buisson,´ France 5University of Saskatchewan, Saskatoon, Canada Received: 26 August 2010 – Published in Atmos. Meas. Tech. Discuss.: 8 October 2010 Revised: 18 March 2011 – Accepted: 23 March 2011 – Published: 4 April 2011

Abstract. The GOMOS (Global Ozone Monitoring by Oc- 1 Introduction cultation of Stars) instrument on board the Envisat satellite measures the vertical composition of the atmosphere using During the last few decades, extensive research efforts have the stellar occultation technique. While the night-time oc- been made to measure the vertical composition of the Earth’s cultations of GOMOS have been proven to be of good qual- atmosphere. Numerous satellite instruments have been de- ity, the daytime occultations are more challenging due to ployed specifically to observe the middle atmosphere using weaker signal-to-noise ratio. During daytime GOMOS mea- different measurement techniques, geometries, and wave- sures limb scattered solar radiation in addition to stellar ra- lengths regions. Limb-viewing instruments can directly ob- diation. In this paper we introduce a retrieval method that serve the solar or stellar signal as the source is occulted by determines ozone profiles between 20–60 km from GOMOS the atmosphere or instead measure the scattered indirect sun- limb scattered solar radiances. GOMOS observations contain light (radiance) and various atmospheric emissions. a considerable amount of stray light at high altitudes. We in- Compared to the nadir looking instruments the limb- troduce a method for removing stray light and demonstrate viewing technique can not achieve as good horizontal spatial its feasibility by comparing the corrected radiances against resolution but it yields superior vertical resolution. The limb those measured by the OSIRIS (Optical Spectrograph & Infra view also offers greater sensitivity to trace constituents than Red Imaging System) instrument. For the retrieval of ozone the nadir view. Cloud interference is often a disadvantage profiles, a standard onion peeling method is used. The first in the limb view, but on the other hand it can be used, for comparisons with other data sets suggest that the retrieved example, to study polar mesospheric clouds and noctilucent ozone profiles in 22–50 km are within 10% compared with clouds (Petelina et al., 2006; Robert et al., 2009; Perot´ et al., the GOMOS night-time occultations and within 15% com- 2010). A detailed information of the past and present middle pared with OSIRIS. GOMOS has measured about 350 000 atmosphere instruments can be found e.g. in Grant (1989); daytime profiles since 2002. The retrieval method presented Shepherd (2002); Qu et al. (2006). here makes this large amount of data available for scientific The obvious advantage of satellite measurements is that use. large quantities of global data can be gathered over long periods of time. Recent middle atmosphere studies, for instance, Jones et al. (2009); Kyrol¨ a¨ et al. (2010); Kiesewetter et al. (2010); Gillett et al. (2011), have increasingly aimed to utilize and sometimes to combine large satellite data sets in or- Correspondence to: S. Tukiainen der to understand how ozone (or other species) are changing (simo.tukiainen@fmi.fi) in time. The goal is to distinguish between natural variations

Published by Copernicus Publications on behalf of the European Geosciences Union. 660 S. Tukiainen et al.: Retrieval of GOMOS limb ozone and anthropogenic forcings in the atmosphere. Furthermore, 24 27km long and consistent satellite data sets are crucial for valida- 22 26km 25km 20 tion of climate models. 24km The GOMOS (Global Ozone Monitoring by Occultation 18 Ratio of Stars) instrument on board the Envisat satellite uses the 16 stellar occultation method to probe the atmosphere between 14

10 and 130 km. Since 2002, GOMOS has performed alto- 12 350 400 450 500 550 gether almost one million measurements. The ozone profiles Wavelength [nm] obtained from the night-time occultations are considered to 24 have typically better than 5% accuracy in the stratosphere 27km (Meijer et al., 2004; Renard et al., 2008; van Gijsel et al., 22 26km 25km 20 2010). However, the majority of the daytime ozone profiles 24km retrieved from occultations are currently of poor quality and 18 Ratio not suitable for scientific use. 16 In addition to the star signal, GOMOS also records the 14 limb scattered sunlight during the daytime in similar way 12 350 400 450 500 550 to e.g. OSIRIS (Optical Spectrograph & Infra Red Imag- Wavelength [nm] ing System) on the Odin satellite (Llewellyn et al., 2004) and SCIAMACHY (SCanning Imaging Absorption SpectroMe- Fig. 1. Saturation in the normalized GOMOS radiances for a few ter for Atmospheric CHartographY) on Envisat (Gottwald altitudes. Upper panel: current Level 1 version, where obviously et al., 2006). The first experiment to retrieve ozone pro- saturated pixels are not flagged. Lower panel: forthcoming Level 1 files from the GOMOS bright limb (GBL) measurements was version including improved saturation flags (data achieved via pri- done by Taha et al. (2008), obtaining promising results. In vate communications with Gilbert Barrot, ACRI-ST). this paper we present a study to retrieve ozone from the GO- MOS radiances and show some initial comparison results. get the pure star signal which is then used for the retrievals. This procedure is performed for the day and twilight observa- 2 GOMOS radiance measurements tions but not for the night measurements when no limb scattered light contribution is present. 2.1 The GOMOS instrument 2.2 Saturation GOMOS is a UV-visible spectrometer covering the wavelength range from 250 to 675 nm with 1.2 nm spectral res- The GOMOS radiance measurements suffer from CCD sat- olution (during night-time observations). Two additional uration below 30 km in the 400–500 nm band. The saturated infrared channels at 756–773 nm and at 926–952 nm with pixels are flagged in the Level 1 data but the flags are not cor- 0.2 nm spectral resolution are also included. GOMOS is rectly implemented in the version 5.00 of the Level 1 data. also equipped with two fast photometers sampling at the The effect of the saturation is clearly seen when looking at frequency of 1 kHz in the ranges 644–705 nm and 466– normalized radiances (measured radiances divided by a radi- 528 nm. GOMOS was designed to measure about 180 dif- ance spectrum from a high altitude). A normalized radiance ferent stars as they occultate through the atmosphere. About is also called radiance ratio. Figure 1 shows normalized radi- 300–400 occultation events are recorded each day between ances between 350 and 550 nm for a single scan (orbit 9758, around 10–130 km. star 83) and for a few altitudes. The upper panel is plotted The vertical sampling distance of GOMOS is 0.5–1.6 km. using the current Level 1 data, and while the signal notably The uncertainty in the tangent height registration is very begins to saturate at 26 km, the version 5.00 flags are wrongly small because stars are point sources whose positions are claiming the data to be good down to 24 km. well known. The only uncertainties come from the satellite The new Level 1 processing version, coming out in 2011, position and the ray path calculation but the impact of these includes improved saturation flags. The lower panel of Fig. 1 on the retrieved profiles is considered negligible ( Tamminen reveals that almost all saturated pixels are now flagged cor- et al., 2010). rectly. It is important to have correct saturation flags for During the daytime, the GOMOS CCDs record light from a successful retrieval. Our strategy in the retrieval is to the limb using three spatial bands. The central band measures take advantage of the whole UV-Visible optical region be- the sum of the star and the limb scattered signal, while the up- tween 280–700 nm and use dozens or even hundreds of wave- per and the lower bands measure only the limb contribution. lengths. This way the profiles can be retrieved for a wide al- In the operational occultation retrieval, the upper/lower band titude range. If the saturation flags are incorrect, and also sat- radiance is removed from the central band measurement to urated pixels are used in the retrieval, errors in the retrieved

Atmos. Meas. Tech., 4, 659–667, 2011 www.atmos-meas-tech.net/4/659/2011/ S. Tukiainen et al.: Retrieval of GOMOS limb ozone 661

proﬁles will greatly increase. In this study, we ignored the Original radiance whole 400–500 nm region to make sure that no saturated pix- 120 Radiance used for fitting Constrained value at 20 km els were used in the retrieval. Stray light estimate at 300 nm 100 Stray light estimate at 350 nm Stray light estimate at 600 nm 2.3 Stray light 80

In addition to the CCD saturation, the GOMOS limb scatter Altitude [km] 60 measurements suffer from severe stray light contamination. External stray light refers to the light whose origin is outside 40 of the nominal field of view of the slit but is nevertheless ob- 20 served by the instrument. There are two major sources of the 10 11 12 13 10 10 10 10 external stray light in GOMOS. One is the solar light scat- Radiance [photons/(cm2 s ster nm)] tered by some Envisat hardware into the baffle and optics of GOMOS. The other is the off-axis scattering coming from Fig. 2. Stray light estimation for 300 nm, 350 nm, and 600 nm. The the sun-illuminated atmosphere. The latter stray light com- spectral shape of the stray light is used to calculate the 20 km points ponent is most probably coming from the zone below the line (red circles), which are then used together with the >100 km radi- of sight between the tangent point and the satellite position. ance values to calculate the stray light estimates for all altitudes. Our preliminary investigations show that there seems to be a positive correlation between cloudiness in this area and the 3. Extrapolate this stray light estimate for the 20 km tan- amount of stray light, specially at the red end of the spec- gent height corresponding to the typical lowest tangent trum. height of the daytime GOMOS scans. We denote these In Taha et al. (2008), the GOMOS stray light was modeled extrapolated 20 km values as Iˆ (λ). by assuming the measured radiances to be entirely stray light ext between 80 and 120 km and by doing a simple linear fit for 4. Recalculate the extrapolated stray light estimates at each wavelength. A similar approach was also used by Rault 20 km, obtained in the previous step, using the spec- (2005) for SAGE III limb scatter. In this study, the stray tral shape S(λ) as a constraint. The best fit in the least light removal method is slightly different. We only consider squares sense is altitudes above 100 km and use the spectral shape of stray light to constrain a polynomial fit. S(λ)T c = Iˆ (λ). (2) The relative amount of stray light in the GOMOS ra- S(λ)T S(λ) ext diances increases with the altitude and above 100 km we consider the signal to be pure stray light. We can deduce The constrained values at 20 km are then the altitude dependence of the GOMOS stray light from ˆ the >100 km spectra, but the extrapolation to lower tangent Ifit (λ) = c S(λ). (3) heights will often lead to unreliable results. To avoid this, we constrain the extrapolation by the spectral shape of the 5. Compute a third degree least squares polynomial fit for stray light. Our stray light correction method consists of the each wavelength using the measurements above 100 km ˆ following steps: and the recalculated 20 km values Ifit (λ).

1. Calculate the mean relative stray light spectrum 6. Evaluate the polynomial for all measurement tangent heights and subtract the obtained stray light estimate n from the radiances. 1 X I (λ, j) S(λ) = , (1) n I (λ ,j) j=1 500 Figure 2 illustrates the stray light calculation for three wavelengths. The red circles are the constrained 20 km val- where I (λ, j) are the measured radiance spectra and ues calculated in Eq. (3). Blue, green, and red lines show I (λ500,j) are the measured radiances at 500 nm. The the final stray light estimates which are subtracted from the tangent height index j goes through the measurements radiances. above 100 km and λ denotes wavelength. Typically, A few things should be noted about this algorithm. Be- GOMOS begins to scan at ∼130 km with ∼1 km ver- cause the >100 km spectra always contain some noise and tical sampling so that the number of I (λ, j) spectra is wavelengths are treated independently radiances become about 30. noisier after the correction. Another issue is that the optimal range and orders for the the polynomial fits are unknown and 2. Compute a linear least squares fit for each wavelength the choices can affect the results, too. In this study, we used using the measurements above 100 km as the fitting a linear fit in Step 2 and a third degree polynomial in Step 5. range. Also, in reality, the amount of stray light may actually vary as www.atmos-meas-tech.net/4/659/2011/ Atmos. Meas. Tech., 4, 659–667, 2011 662 S. Tukiainen et al.: Retrieval of GOMOS limb ozone

0.35 6.75

0.3 6.7 0.25

] 0.2 6.65 −1

[nm 0.15 6.6

0.1 Radiance ratio 6.55 0.05 OSIRIS original OSIRIS convolved GOMOS original 0 6.5 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 430 432 434 436 438 440 442 444 446 448 450 Wavelength [nm] Wavelength [nm]

Fig. 3. GOMOS slit function. Fig. 4. Comparison of GOMOS and OSIRIS spectral resolution in the NO2 retrieval region. Shown are 32 km radiances normalized with the 47 km spectra. The GOMOS ratio is before stray light a function of altitude leading to abnormal results from the ex- correction and scaled to fit in the figure. trapolations. As mentioned earlier, the GOMOS stray light is dependent on the albedo of the underlying reflective surface between the tangent point and the satellite position. Thus, Table 1. Coincidence criteria for the GOMOS and OSIRIS radiance strong albedo gradients during the measurement can disturb matches. the usually quite linear altitude dependence of stray light at ◦ high tangent heights. In these cases, a simple linear fit would Latitude 3 ◦ probably be better than any higher degree polynomial. Longitude 6 Time 24 h Sun zenith angle 2◦ ◦ 3 Radiance comparison Scattering angle 2

In this section we compare GOMOS radiances with OSIRIS radiances. OSIRIS is a combined UV-Visible optical and infrared instrument dedicated to limb scatter measurements. GOMOS data by investigating the oxygen emission line at The instrument is flying on board the Odin satellite, launched 557 nm whose spectral characteristics are well known. in 2001. The OSIRIS Level 1 data is the latest version, re- In addition to the low spectral resolution, the GOMOS ra- processed in the end of 2009. OSIRIS radiances are relatively diances are also much noisier than those of OSIRIS. This ∼ free of stray light below 70 km and therefore OSIRIS is a makes it challenging to retrieve trace gases whose absorp- good reference for the validation of GOMOS radiances and tion fingerprints are relatively small compared to the ozone the stray light correction algorithm. However, it should be fingerprint. For example, NO 2 is routinely retrieved from the noted that stray light is not totally absent from the OSIRIS OSIRIS data using the NO2 absorption features in the 430– measurements either. But according to Llewellyn et al. 450 nm region. Figure 4 shows radiance ratios in this region (2004) and references in it, the contamination is rather small for GOMOS and OSIRIS at 32 km. The absorption lines are and within expected limits. The GOMOS Level 1 is also the barely recognizable in the GOMOS ratio, while the OSIRIS most recent available version 5.00 from 2006. ratio is far cleaner. At higher altitudes the noise in GOMOS The criteria shown in Table 1 were used to find coincident obscures the absorption lines even further and below ∼30 km measurements between GOMOS and OSIRIS. Using the data the region begins to saturate as shown in Fig. 1. from the year 2004, a total of 14 matching observations were found when applying the coincidence criteria and excluding 3.2 Absolute radiance data with solar zenith angle larger than 86◦. These observations are from a very narrow latitude band around 60◦ S from First, we analyzed the differences between GOMOS and January and February 2004. OSIRIS absolute radiances. The radiances were interpolated 3.1 Spectral resolution and noise in wavelength and in altitude using linear interpolation. Ra- diance as a function of altitude changes non-linearly in the The spectral resolution of the GOMOS radiance measure- UV wavelengths but the high vertical sampling of both in- ments is ∼3.5 nm, i.e. relatively low compared to ∼1 nm of struments (1–2 km) allows us to use linear interpolation. OSIRIS. The wider slit of GOMOS allows the tracking of Figure 5 shows an example of an individual OSIRIS (or- occultating stars but it lowers the spectral resolution. There- bit 15702, scan 25) and GOMOS (orbit 9778, star 83) match. fore, we convolved the OSIRIS spectra with the GOMOS slit At 55 km the amount of stray light in the GOMOS ra- function. The best estimate of the slit function is shown in diance is prominent, especially in the wavelengths above Fig. 3. The GOMOS slit function was estimated from the 400 nm. After the stray light removal, the overall agreement

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11 x 10 80 55km OSIRIS 30km 5 GOMOS original 60 4 GOMOS straylight corrected

s ster nm)] 40 2 3

Radiance 2 20

1 Difference [%] 0 [photons/(cm 0 300 350 400 450 500 550 600 650 Wavelength [nm] −20 300 350 400 450 500 550 600 650 Wavelength [nm]

100 Fig. 6. Median relative difference of the 14 OSIRIS and stray light

50 corrected GOMOS absolute radiances at 30 km (blue) and 55 km (red).

0 10 Difference [%] (GOMOS corrected−OSIRIS)/OSIRIS 10 (GOMOS original−OSIRIS)/OSIRIS 8 −50 8 300 350 400 450 500 550 600 650 6 Wavelength [nm] 6 4 4 OSIRIS Radiance ratio Fig. 5. Example of absolute radiances from GOMOS and OSIRIS. 2 OSIRISGOMOS original Upper panel: radiances at 55 km. Lower panel: relative differences. Radiance ratio 2 GOMOSGOMOS originalstraylight corrected 0 300 350 400 450 500 GOMOS550 straylight600 corrected650 0 300 350 400 450Wavelength500 [nm] 550 600 650 Wavelength [nm] is signiﬁcantly better but the removal algorithm has intro-

25 (GOMOS corrected−OSIRIS)/OSIRIS duced some additional noise to the radiance. Figure 6 presents median differences between OSIRIS and 25 (GOMOS(GOMOS corrected−OSIRIS)/OSIRISoriginal−OSIRIS)/OSIRIS stray light corrected GOMOS radiances for two different al- 0 (GOMOS original−OSIRIS)/OSIRIS titudes (55 and 30 km). There seems to be a positive bias in 0 −25 the GOMOS radiance below 350 nm. The bias is increasing Difference [%] −25 towards lower altitudes, being up to around 20% at 55 km Difference [%] −50 and 40–60% at 30 km. 300 350 400 450 500 550 600 650 −50 Wavelength [nm] 300 350 400 450 500 550 600 650 3.3 Radiance ratio Wavelength [nm] Fig. 7. Example of radiance ratios from GOMOS and OSIRIS. Up- Instead of using absolute radiances, a common practice to per panel: ratios of 30 and 47 km. Lower panel: relative differences. counteract uncertainties from calibration and polarization is to normalize radiance spectra by a high altitude measure- 4 Inversion method ment. It may be a full spectrum from one altitude, typically around 50 km, or the reference can come from various alti- A slightly revised version of the inversion method described tudes depending on the wavelength. in detail in Tukiainen et al. (2008) is used for the retrieval. The same match as in Fig. 5 is shown in Fig. 7 but the The fundamental idea is the same. For every measurement radiances are now normalized with the 47 km spectra. The tangent height j, a least squares ﬁt weighted by the standard difference in the UV band is apparent and the stray light cor- deviation of the noise term is done between the model and rected ratio is noisier than the original GOMOS radiance ra- the measurement: tio. Otherwise the agreement between the OSIRIS ratio and ˆ the stray light corrected GOMOS ratio is good. I (j, λ) Iss(j, λ, ρ) = R(j, λ) + , (4) ˆ The median of the differences of the 14 matches is shown Iref(λ) Iref(λ) in Fig. 8 for 55 and 30 km. At 30 km the GOMOS ratio is biased up to +20% below 320 nm and there is an opposed bias where I (j, λ) is the observed radiance and Iref(λ) is the reference measurement at ∼47 km. On the right hand side, at 55 km. At 55 km the red end of the spectrum is quite noisy ˆ Iss(j, λ, ρ) is the modeled single scattering radiance, ad- due to the stray light correction. The bias in the wavelengths ˆ 320–680 nm is 5–10% for both investigated altitudes. justed dynamically during the ﬁtting operations and Iref(λ) is the modeled reference radiance including multiple scattering. The second term on the right:

Iˆ (j, λ) R(j, λ) = tot (5) ˆ Iss(j, λ) www.atmos-meas-tech.net/4/659/2011/ Atmos. Meas. Tech., 4, 659–667, 2011 664 S. Tukiainen et al.: Retrieval of GOMOS limb ozone

30 55km Table 2. Siro look-up table parameters. 30km 20 Parameter Range 10 Zenith angle 40–90◦, 5◦ resolution 0 Azimuth angle 20–180◦, 10◦ resolution Difference [%] −10 Albedo 3 albedos: 0.1, 0.5, 0.9 Climatology 5 regions: tropic, mid latitudes −20 300 350 400 450 500 550 600 650 (summer,winter), arctic Wavelength [nm] (summer), Antarctica (summer) Altitude 12, 14, 16, 18, 21, 23, 25, 27, Fig. 8. Median relative difference of the 14 OSIRIS and stray light 30, 35, 40, 50, 60, 70 km corrected GOMOS radiance ratios at 30 km (blue) and 55 km (red). Radiances were normalized with the 47 km spectrum. Wavelength 123 wavelengths in the 280–680 nm band is the ratio of modeled total to single scattering radiance. This term comes from a look-up-table (see Table 2 and Sect. 4.1) and is kept fixed during iterations. The iterative using much more narrow wavelength windows. It should fitting of the gas densities ρ in Eq. (4) is done using the be noted that, as mentioned earlier, NO2 is not currently re- Levenberg-Marquardt method (Levenberg, 1944; Marquardt, trieved from the GOMOS bright limb measurements due to 1963). The standard deviation of in Eq. (4) is used as a weak spectral performance in the 430–450 nm band of GO- weight in the fitting. At every tangent height, the best fit is MOS. In this study, we did retrieve neutral air and aerosols in the one that minimizes the chi square value the same peeling loop as ozone but the quality of these two 2 T −1 products will be determined in later studies. χ = (Tobs − Tmod) C (Tobs − Tmod), (6) where Tobs is the measurement ratio (left hand side of Eq. 4) 4.1 Radiative transfer model and Tmod is the modeled ratio (right hand side of Eq. 4 without the error term). The covariance matrix C is diagonal and It is straightforward and computationally very effective to includes only the standard deviation of the measurement er- calculate single scattering radiances in limb-viewing geom- ror. The standard deviation of the radiance I (j, λ) is approx- etry. But in the visible wavelengths, a significant part of the imated as photons have scattered multiple times before observed by the instrument. This makes the modeling challenging, and usu- = p + + σrad(j, λ) Ie(j, λ) Isc(λ) Idc(λ) Z(λ), (7) ally approximations are used to simplify the radiative transfer where Ie(j,λ) is the uncorrected radiance as electrons, Isc(λ) calculations. is the approximate variance of the stray light estimate, Idc(λ) Several models have been developed to calculate the mul- is the contribution from the dark charge, and Z(λ) is the ra- tiple scattering radiance in the UV visible wavelengths. diometric sensitivity curve to convert the values into physical Recent models include e.g. SASKTRAN (Bourassa et al., units. The variance of the radiance ratio I (j, λ) is approxi- 2008), McSCIA (Spada et al., 2006), Sciatran (Rozanov Iref(λ) mated as et al., 2005), MCC++ (Postylyakov, 2004), LIMBTRAN 2 2 (Griffioen and Oikarinen , 2000) and Siro (Oikarinen et al., 2 σrad(j,λ) R(j,λ)σrad (jref,λ) 1999). σratio(j,λ) = + , (8) Iref(λ) Iref(λ) We use a revised version of the Monte Carlo (MC) model where Iref(λ) is the measurement reference radiance, R(j, λ) Siro. Siro is a backward MC model – photons are simu- is the modeled tot/ss ratio, and σrad(jref, λ) is the standard lated from the detector towards the atmosphere. The latest deviation of the radiance at the reference altitude. At the mo- Siro version is written in Fortran90 and parallelized using ment, no modeling error is added in the covariance matrix C. OpenMP framework. Options for polarization and refraction The atmosphere between around 60 and 20 km is “peeled” are available, but were not used in this study. from top to down to get the vertical profiles of retrieved The execution time of Siro depends mainly on the tan- species. With this approach, it is possible to retrieve several gent point altitude and wavelength. More multiple scattering species simultaneously. Typically O3, aerosols and neutral means slower execution. The multiple scattering contribu- air are inverted together using tens (or hundreds) of wave- tion is determined by the solar angles, atmospheric composi- lengths in the 280–680 nm band, while NO2 is taken from a tion and albedo. climatology and kept fixed. In this study we used 71 wave- The running time and the precision of the solution are nat- lengths. As shown in Tukiainen et al. (2008), it is better to re- urally proportional to the number of simulated photons. With trieve minor absorbers such as NO2 in separate peeling loops a modern CPU (Xeon E5420) using only a single core, a

Atmos. Meas. Tech., 4, 659–667, 2011 www.atmos-meas-tech.net/4/659/2011/ 10 S. Tukiainen: Retrieval of GOMOS limb ozone

N = 14 60 60 GBL without UV GBL with UV 55 OSIRIS 55 10 50 50 8

6 45 45

4 OSIRIS 40 40 Radiance ratio 2 GOMOS original GOMOS straylight corrected Altitude [km] 35 35 0 300 350 400 450 500 550 600 650 Wavelength [nm] 30 30

25 25 25 (GOMOS corrected−OSIRIS)/OSIRIS (GOMOS original−OSIRIS)/OSIRIS 20 20 0 0 1 2 3 4 −20 −10 0 10 20 −3 12 Ozone Density [cm ] x 10 Difference [%]

−25 Difference [%] Fig. 9. Retrieved ozone proﬁles from the 14 GOMOS and

−50 OSIRIS radiances of Fig. 6 and Fig. 8. Left panel: medians of 300 350 400 450 500 550 600 650 Wavelength [nm] the OSIRIS profiles (blue), GOMOS profiles retrieved with the UV band (red dashed profile) and without using the UV band below 40 km (red solid profile). Right panel: medians of individual rela- Fig. 7. Example of radiance ratios from GOMOS and OSIRIS. Up- tive differences compared to the OSIRIS profiles and the 25th and per panel: ratios of 30 and 47 km. Lower panel: relative differences. 75th percentiles. The red lines show the difference (and deviation) when using the UV band and the green lines show the difference when the UV band is not used.

S. Tukiainen et al.: Retrieval of GOMOS limb ozone 665

N = 14 N = 79 60 60 60 60 GBL without UV GOMOS NIGHT OCC GBL with UV GBL 55 OSIRIS 55 55 55

50 50 50 50 30 55km 30km 4520 45 45 45

4010 40 40 40 Altitude [km] 350 35 Altitude [km] 35 Altitude [km] 35 Difference [%] −10 30 30 30 30

−20 25 300 350 400 450 500 25 550 600 650 25 25 Wavelength [nm]

20 20 20 20 0 1 2 3 4 −20 −10 0 10 20 0 1 2 3 4 5 −20 −10 0 10 20 Fig. 8. Median relative difference−3 of the12 14 OSIRISDifference and stray [%] light −3 12 Difference [%] Ozone Density [cm ] x 10 Ozone density [cm ] x 10 corrected GOMOS radiance ratios at 30 km (blue) and 55 km (red). Radiances were normalized with the 47 km spectrum. Fig. 9. Retrieved ozone profiles from the 14 GOMOS and OSIRIS Fig.Fig. 10. 10. Comparison of the 79 GOMOS bright limb profiles and and radiances of Figs. 6 and 8. Left panel: medians of the OSIRIS GOMOSGOMOS night night occultations occultations at the equator.equator. Left panel: medians of profiles (blue), GOMOS profiles retrieved with the UV band (red thethe distributions. distributions. Right panel: median of the individualindividual relative dashed profile) and without using the UV band below 40 km (red differencesdifferences (solid) (solid) and and the the 25th and 75th percentilespercentiles (dashed). solid profile). Right panel: medians of individual relative differences compared to the OSIRIS profiles and the 25th and 75th percentiles. The red lines show the difference (and deviation) when without the UV band below 40 km (red solid line). The right using the UV band and the green lines show the difference when panel shows the medians of the individual relative differ- the UV band is not used. ences (with OSIRIS being the reference) and the 25th and 75th percentiles. In both cases there is a negative bias below 105 photon simulation for one wavelength takes a few sec- 50 km compared to OSIRIS but flagging the UV wavelengths onds in the UV region. In the visible band, a similar simula- clearly improves the agreement. tion takes typically around 30 s. To better test the statistical accuracy of the retrieved pro- It is computationally too expensive to use Siro directly in files, we compare the GOMOS bright limb profiles with the the operational retrieval. Instead in Eq. (4), we use a fast GOMOS night-time occultation profiles. Due to issues in analytical single scattering model and perform multiple scat- the 400–500 nm band (saturation) and in the UV band below tering correction using a Siro calculated look-up table. The 40 km, we flagged these wavelengths from the retrieval. Fig- Siro look-up table is built with the parameters shown in Ta- ure 10 shows the result of the comparison in the equator between 30◦ S and 30◦ N. The 79 profiles are from 2003 with no ble 2. The sensitivity of the look-up table values to the pa- ◦ ◦ rameters were also studied, and the ranges shown in Table 2 more than 1 difference in latitude, 2 in longitude and 15 h were found sufficient. To get approximately 1% accuracy, in time. The median of the individual relative differences is radiances were simulated with 105 photons. less than 10% between 22 and 50 km. Above 45 km the diurnal variation of ozone starts to take effect, and the GBL values (day) are smaller than the night occultation values, as 5 Ozone profile comparison expected. There is a large bias in the GBL profiles below 22 km compared with the night occultation profiles. This is As there is some discrepancy in the GOMOS and OSIRIS ra- probably because some saturated pixels were still used in the diances below ∼350 nm, differences in retrieved ozone pro- retrieval (outside of the 400–500 nm band). However, GO- files should be expected. Above around 40 km, these wave- MOS daytime profiles at the equator seldom reach to 20 km lengths are required for successful ozone retrievals. But at or lower. During the daytime, when the limb scattering con- lower altitudes, information mainly comes from the Chap- tribution is present, it is difficult to follow occultating stars at puis band around 600 nm, and the UV band can be sup- low tangent heights. The limb signal starts to overwhelm the pressed from the inversion. star signal and the star tracker loses control more easily. Figure 9 shows a comparison of the 14 GOMOS bright limb and OSIRIS ozone profiles retrieved using the radiances shown in Figs. 6 and 8. The profiles were first interpolated into the same 1 km grid and the medians of the distributions are shown in the left panel. The GOMOS profiles were retrieved with the UV band (red dashed line) and

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2004 GOMOS measurements agreement with GOMOS night-time occultations was better 90 night than 10% between 22 and 50 km in the equator. The good 70 day comparison result against the GOMOS night-time occulta-

50 tions, after ﬂagging the UV band, suggests that the UV band is biased indeed in GOMOS and not in OSIRIS. 30 Despite the weaknesses in the Level 1 data, the proposed 10 stray light removal algorithm and the inversion method offer a promising way to utilize the whole GOMOS bright limb

Latitude −10 data set. The processing of the GBL data would roughly dou- −30 ble the amount of useful GOMOS ozone proﬁles between at

−50 least 22 and 50 km. The distribution of GOMOS night-time and daytime measurements in 2004 is shown in Fig. 11. −70 Finally, it should be noted that the comparison for proﬁles −90 shown in this paper is preliminary and should be extended Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec using other reference instruments for all latitudes. Addition- Fig. 11. Distribution of the night and daytime measurements from ally, the robustness and performance of the stray light correc- GOMOS during 2004. tion could be analyzed more carefully in a separate study.

Acknowledgements. This work was funded by the European Space 6 Discussion Agency through the project Trace Gas Retrieval from GOMOS Bright Limb Measurements (AO/1-5301/06/I-OL) and by the There are serious defects in the GOMOS Level 1 bright limb Academy of Finland through the MIDAT project. The authors data that complicate trace gas retrievals. The stray light con- wish to thank Marko Laine, Seppo Hassinen, Benjamin Herman, tamination is a severe problem at high altitudes. In the wave- Anne van Gijsel, and Ankie Piters for their valuable help. The lengths >400 nm, stray light accounts for as much as 10– authors also wish to thank the anonymous reviewers for their helpful comments and suggestions. 50% of the measured signal already at 55 km altitude (see Fig. 5). Thus, it is absolutely necessary to correct for the Edited by: C. von Savigny stray light. The radiance comparisons against OSIRIS suggest that the algorithm presented in Sect. 2.3 is feasible. In addition to the stray light, the signal saturates below References around 30 km in the 400–500 nm region making a large part of the spectrum useless. Current saturation flags are not reli- Bourassa, A. E., Degenstein, D. A., and Llewellyn, E. J.: SASK- able, but the situation is greatly improved with the upcoming TRAN: A spherical geometry radiative transfer code for efficient version of the Level 1 data. estimation of limb scattered sunlight, J. Quant. Spectrosc. Ra., The spectral resolution of GOMOS (bright limb signal) 109, 52–73, doi:10.1016/j.jqsrt.2007.07.007, 2008. is poor, about 3.5 nm compared to the ∼1 nm resolution of Gillett, N. P., Akiyoshi, H., Bekki, S., Braesicke, P., Eyring, V., OSIRIS. The spectra of GOMOS are also noisier than those Garcia, R., Karpechko, A. Yu., McLinden, C. A., Morgen- of OSIRIS. Both the low spectral resolution and the noise stern, O., Plummer, D. A., Pyle, J. A., Rozanov, E., Scinocca, J., and Shibata, K.: Attribution of observed changes in strato- make NO retrievals difficult and so far it has not been suc- 2 spheric ozone and temperature, Atmos. Chem. Phys., 11, 599– cessful. 609, doi:10.5194/acp-11-599-2011, 2011. Furthermore, there seems to be a systematic difference be- Gottwald, M., Bovensmann, H., Lichtenberg, G., Noel, S., von Bar- tween the GOMOS and OSIRIS spectra in the wavelengths gen, A., Slijkhuis, S., Piters, A., Hoogeveen, R., von Savigny, C., below 320 nm. This cannot be explained by the stray light be- Buchwitz, M. A. K., Richter, A., Rozanov, A., Holzer-Popp, T., cause the discrepancy increases at lower altitudes where the Bramstedt, K., Lambert, J.-C., Skupin, J., Wittrock, F., Schrijver, relative amount of stray light decreases. The difference is ap- H., and Burrows, J.: SCIAMACHY, Monitoring the Changing parent in both absolute and normalized radiance (see Figs. 6 Earth’s Atmosphere, DLR, 2006. and 8). Unfortunately, close matches between OSIRIS and Grant, W. B.: Ozone measuring Instruments for the Stratosphere, GOMOS measurement times, tangent point locations, and Optical Society of America, Washington, 1989. solar angles are rare and only 14 cases were investigated in Griffioen, E. and Oikarinen, L.: LIMBTRAN: A pseudo three- dimensional radiative transfer model for the limb-viewing im- this paper. ager OSIRIS on the Odin satellite, J. Geophys. Res., 105, 29717– The disagreement in the UV band leads to a difference in 29730, 2000. the retrieved ozone profiles between GOMOS bright limb Jones, A., Urban, J., Murtagh, D. P., Eriksson, P., Brohede, S., Ha- and OSIRIS. It is possible to cope with the problem by ley, C., Degenstein, D., Bourassa, A., von Savigny, C., Sonkaew, suppressing the UV band in the retrieval below ∼40 km. T., Rozanov, A., Bovensmann, H., and Burrows, J.: Evolu- After flagging the UV band (and the saturation band) the tion of stratospheric ozone and water vapour time series studied

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Reprinted from Atmospheric Measurement Techniques, 8, 3107–3115, doi:10.5194/amt-8-3107-2015

III

Atmos. Meas. Tech., 8, 3107–3115, 2015 www.atmos-meas-tech.net/8/3107/2015/ doi:10.5194/amt-8-3107-2015 © Author(s) 2015. CC Attribution 3.0 License.

GOMOS bright limb ozone data set

S. Tukiainen1, E. Kyrölä1, J. Tamminen1, J. Kujanpää1, and L. Blanot2 1Finnish Meteorological Institute, Earth Observation Unit, Helsinki, Finland 2ACRI-ST, Sophia Antipolis, France

Correspondence to: S. Tukiainen (simo.tukiainen@fmi.ﬁ)

Received: 5 December 2014 – Published in Atmos. Meas. Tech. Discuss.: 27 January 2015 Revised: 26 June 2015 – Accepted: 10 July 2015 – Published: 5 August 2015

Abstract. We have created a daytime ozone profile data set trace gases in the middle atmosphere (Bertaux et al., 2010). from the measurements of the Global Ozone Monitoring by Envisat operated from 2002 to 2012 and during that time Occultation of Stars (GOMOS) instrument on board the En- GOMOS measured altogether around 880 000 occultations. visat satellite. This so-called GOMOS bright limb (GBL) While the GOMOS nighttime ozone profiles have generally data set contains ∼ 358 000 stratospheric daytime ozone less than 5 % bias in the stratosphere (Meijer et al., 2004; profiles measured by GOMOS in 2002–2012. The GBL data van Gijsel et al., 2010; Kyrölä et al., 2013), the majority of set complements the widely used GOMOS nighttime data the daytime occultation profiles are poor due to weak sig- based on stellar occultation measurements. The GBL data nal to noise ratio (Verronen et al., 2007). For this reason, the set is based on the GOMOS daytime occultations but in- GOMOS daytime occultation profiles have not been used in stead of the transmitted star light we use limb-scattered so- scientific studies. lar light. The ozone profiles retrieved from these radiance To improve the GOMOS daytime ozone profiles, Taha spectra cover the 18–60 km altitude range and have approxi- et al.(2008) suggested using atmospheric limb radiance of mately 2–3 km vertical resolution. We show that these pro- scattered sunlight instead of star spectra for the daytime re- files are generally in better than 10 % agreement with the trievals. GOMOS measured limb radiances above and below NDACC (Network for the Detection of Atmospheric Com- the occulting star using a separate optical path so that the position Change) ozonesonde profiles and with the GOMOS star and the limb contributions can be distinguished from nighttime, MLS (Microwave Limb Sounder), and OSIRIS each other (see Bertaux et al., 2010, for a detailed descrip- (Optical Spectrograph and InfraRed Imager System) satellite tion of the instrument). In principle, the subtraction of the measurements. However, there is a 10–13 % negative bias at pure limb signal from the central band, containing both the 40 km altitude and a 10–50 % positive bias at 50 km for so- star and the limb contribution, should produce an uncontam- lar zenith angles > 75◦. These biases are most likely caused inated star spectrum. However, it seems that this removal by stray light which is difficult to characterize and to remove leads to large and poorly understood uncertainties in the day- entirely from the measured spectra. Nevertheless, the GBL time transmission spectra, ruining the operational GOMOS data set approximately doubles the amount of useful GO- occultation retrieval that works fine for the nighttime data. MOS ozone profiles and improves coverage of the summer In their study, Taha et al.(2008) used an optimal-estimation- pole. based method to retrieve ozone from the limb scatter radiances and reported up to 10–15 % agreement with the reference data from Stratospheric Aerosol and Gas Experiment II (SAGE II) between 25–53 km. The authors retrieved separate 1 Introduction ozone profiles from both bands (upper/lower) and obtained consistent results. The GOMOS (Global Ozone Monitoring by Occultation of Following the promising early results of Taha et al.(2008), Stars) instrument on board the Envisat satellite uses the stel- Tukiainen et al.(2011) developed an alternative method for lar occultation technique for monitoring ozone and other

Published by Copernicus Publications on behalf of the European Geosciences Union. 3108 S. Tukiainen et al.: GOMOS bright limb data set retrieving ozone profiles from the GOMOS limb scattered We use an onion peeling retrieval approach to estimate trace radiances, or GOMOS bright limb (GBL) measurements as gas densities, starting from the topmost layer used in the re- they are referred to from now on. This paper is a continuation trieval (at ∼60 km) and proceeding layer by layer towards of that study. We have processed all GOMOS daytime mea- the bottom layer (at ∼18 km). At each layer, we minimize surements and in this study we estimate the quality of this the cost function novel data set. We also tested the sensitivity of the retrieval 2 −1 method to the selected spectral band and decided to use the χ (z) = [H(λ,z) − M(λ,z)]C [H(λ,z) lower band radiance to process the GBL data set. Another −M(λ,z)]T , (1) important decision is the choice of the stray light removal method (GOMOS daytime radiances are badly contaminated where M is the (stray-light-corrected) radiance measurement by stray light). In this work, we adapted a simple method at layer z and a function of wavelength λ. It is normalized that estimates the average stray light from the high tangent with the first measurement below 47 km of the same scan. altitude GOMOS spectra. The structure of this paper is as The diagonal uncertainty covariance matrix C includes the follows. In Sect. 2 we describe the retrieval method, test its standard deviation of the measurement error. Currently, no sensitivity, and explain some general aspects of the GOMOS modeling error is assumed, see details in Tukiainen et al. daytime data. In Sect. 3 we describe the correlative data sets (2011). The modeled radiance, used to validate the retrieved GBL ozone profiles, present the I (λ,z,ρ) comparison method, and show the results of the comparisons. H (λ,z) = R(λ,z) ss , (2) In Sect. 4 we conclude our study and discuss the results. I ref(λ) consists of the modeled total to single scattering ratio R, calculated in advance as a look-up table, and the single scat- 2 GOMOS bright limb data tering radiance I ss divided by the modeled reference spectrum I . R depends only weakly on the actual trace gas pro- ∼ ref The GOMOS bright limb data set consists of 358 000 files, allowing us to keep it fixed during the fitting process. limb-scattered radiance spectra measured around 10:00 LT With this assumption, we only need to solve the single scat- between March 2002 and April 2012, from the launch of En- tering radiance I ss which can be effectively calculated using visat to the communication failure that stopped the mission. simple numerical integration. The reference spectrum I ref is From these measurements we have retrieved vertical ozone estimated using neutral air density from the ECMWF (Eu- profiles in the 18–60 km altitude range. The retrieved profiles ropean Centre for Medium-Range Weather Forecasts) model have approximately 2–3 km vertical resolution. The data are analysis data (MSIS-90 climatology above 1 hPa) and clima- processed using the ESA IPF (Instrument Processing Facil- tological trace gas profiles. ity) Level 1 version 6.01 and the current GBL Level 2 ver- The retrieved gas densities, ρ, include ozone, aerosols, sion 1.2. The Level 2 retrieval scheme is based on Tukiainen and neutral air. NO2 is taken from a climatology and kept et al.(2011) with a few modifications. We describe the re- fixed. The NO2 climatology is based on OSIRIS (Optical trieval method briefly below. Spectrograph and InfraRed Imager System) data (Tukiainen One GOMOS limb “scan” includes typically 120–140 in- et al., 2008). Aerosol scattering is modeled with the Henyey– dividual radiance measurements at different tangent heights. Greenstein phase function and aerosol extinction is modeled Since GOMOS records two separate radiance spectra at each with the Ångström λ−1 law. Rayleigh scattering is assumed tangent height, above and below the central band (which col- for neutral air. The minimization of χ 2 in Eq. (1) is done with lects the combined star and limb signal), there are actually the Levenberg–Marquardt method. The error covariance ma- twice as many spectra. The GBL data set was processed us- trix of the retrieved densities is estimated at the minimum ing the lower band radiances but the upper band, or possibly assuming Gaussian posteriors: a combination of both bands, could be used as well. The upper and lower band radiances are separated by around 1.5 km χ 2 C = (J0J)−1 , (3) in tangent height. One particular advantage of GOMOS is r (n − p) that the tangent height registration is very accurate: on the order of 30 m (Bertaux et al., 2010). Stars are point sources and where J is the Jacobian, n is the number of spectral points their positions are well known. Because the GOMOS central in the fit, and p is the number of retrieved gases. The er- band always follows the occulting star, the uncertainty in the ror estimates of the retrieved densities are the square roots tangent height, which is often a significant problem in limb of the diagonal elements of Cr. An example of the ozone scatter satellite observations, is a negligible issue in the GO- profile errors is shown in the left panel of Fig.1. The rel- MOS retrievals (Tamminen et al., 2010). ative error (error/density×100 (%)) is 2–15 % depending on In the retrieval, the model atmosphere is discretized into the altitude, which is quite a typical range of error values homogeneous layers whose center point heights match the for stratospheric ozone profiles. Scaling the covariance ma- tangent heights of the corresponding radiance measurements. trix with the reduced χ 2 in Eq. (3) leads to more realistic

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Table 1. Wavelength ranges used in the retrieval. 55

50 Tangent height range Wavelength range 45 > 45 km 280–300 nm, 320–330 nm 40 40–45 km 300–330 nm, 420–425 nm < 40 km 420–680 nm 35 Altitude [km] 30

25 55 55 20 0 5 10 15 0 0.5 1 1.5 50 50 Relative error [%] 2 Reduced χ 45 45 Figure 1. Interquartile range of the relative error (left) and reduced χ2 (right). Data from the tropics, year 2004. 40 40

Altitude [km] 35 Altitude [km] 35

2 error bars for the profiles. In theory, the reduced χ should 30 30 be unity but the average χ 2 of GBL is around 0.5 between 20 and 45 km and the scaling is needed (Fig. 1, right panel). 25 25 2 The GBL χ values of less than unity indicate some issue in −15 −10 −5 0 5 10 15 −3 −2 −1 0 1 2 3 the measurement error characterization. Difference [%] Difference [%] GOMOS daytime radiances are significantly contaminated Figure 2. Sensitivity of GBL ozone profile to CCD band (left) and by stray light, especially at visible wavelengths and at high stray light correction method (right). Shown are the mean (solid tangent altitudes. For example, below 40 km at 500 nm the line) and standard deviation (shaded area) of the relative individ- stray light accounts roughly for a few percents of the signal ual differences of the retrieved profiles in both cases. See text for but already several 10 % at 60 km. We remove the stray light details. by calculating the average spectrum above 100 km and by subtracting this constant spectrum from each tangent height. The removal is done independently for each scan. This ap- (Fig. 2 right panel). The difference is defined as (average– proach ignores a possible altitude dependence of the stray constrained) / constrained ×100 (%). As both methods pro- light but, on the other hand, is a simple and robust method. To duce, at least in this case, almost identical ozone profiles it avoid using the most corrupted wavelength regions, we use is probably better to use the average method because of its three different sets of retrieval wavelengths depending on the simplicity. tangent height (Table 1). This reduces bias due to inconsis- Each GBL Level 2 file contains geolocation information, tencies in the GOMOS spectra but also introduces a disconti- ECMWF model values for the temperature and density, a nuity at 40 km where we start using only visible wavelengths. fixed NO2 profile (from the OSIRIS climatology), and resid- We reduce the discontinuity by scaling the amount of stray uals of the fit. Densities and error estimates are provided for light (at layers below 40 km) by an iteratively found constant the three simultaneously retrieved species: ozone, aerosols, factor, requiring that the ozone profile remains smooth in the and neutral air. In this paper we show only the results related 40 km transition. to the ozone profiles. Figure 3 shows the number of GBL We tested the sensitivity of the GBL ozone to the two profiles and GOMOS nighttime occultation profiles during important assumptions in the retrieval: the choice of the the whole Envisat mission. The GBL data set roughly dou- charge-coupled device (CCD) band of the spectrometer (up- bles the amount of useful GOMOS ozone profiles. Figure 4 per or lower) and the stray light correction method. The test shows a typical 1-day coverage of GOMOS day and night data included 10 orbits (142 scans) from 1 April 2004. The measurements, and Fig. 5 shows the number of GBL pro- two available CCD bands yield ozone profiles within 1 % files during 1-year (2004) as a function of latitude. The GBL (Fig. 2 left panel). The difference is calculated, after linear data complements the night occultations in the tropics and interpolation in altitude, as (upper–lower) / lower ×100 (%). mid latitudes and furthermore expands the global coverage This figure visualizes the propagation of the random mea- towards the summer pole. surement error in the GOMOS limb retrieval. For the Figure 6 shows an example of the zonally averaged ver- stray light correction, we tested two methods: the con- tical distribution of ozone from the GOMOS nighttime oc- strained extrapolation method introduced in Tukiainen et al. cultations, GOMOS daytime occultations, and GBL. The (2011) and the simple average method described above. measurements are from January 2005 and from the latitude The difference in the retrieved ozone profiles is below 1 % 35◦ N. The nighttime data are from the star number 2 and www.atmos-meas-tech.net/8/3107/2015/ Atmos. Meas. Tech., 8, 3107–3115, 2015 3110 S. Tukiainen et al.: GOMOS bright limb data set

90 500 3000 night + day day 60 400 2000 30 ] o 300 1000 0

Number of measurements 200 0 Latitude [ 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 −30 Year 100 Figure 3. Number of GOMOS nighttime and GBL measurements −60 Number of measurements (weekly). −90 0 1 2 3 4 5 6 7 8 9 10 11 12 Month Night Day Figure 5. Number of GBL measurements as a function of latitude and time during 2004.

110

100

90 Day occultation Night occultation 80 GBL

70 Figure 4. Typical 1-day coverage of GOMOS night occultations 60 (red) and GBL (blue). Data from 15 December 2004.

Altitude [km] 50

40 the daytime data from the star number 175. As practically always, the shapes of the day occultation profiles are signif- 30 icantly different than the shapes of the GBL and night oc- 20 cultation profiles. The huge fluctuations and large negative −5 0 5 10 15 values seen in the day occultation profiles are not realistic. Ozone mixing ratio [ppmv] At least in the stratosphere, the quality of the day occultation profiles is clearly inferior to the GBL and GOMOS nighttime Figure 6. Example of the vertical distribution of ozone from the data. GOMOS night/day occultations and GBL. Data from January 2005, latitude 35◦ N (zonal medians and interquartile ranges).

3 Correlative data sets For GOMOS night occultations, we used the latest Level 2 First, we compared the retrieved GBL ozone profiles version 6 data. Because the occultation retrieval from cool against NDACC (Network for the Detection of Atmo- and weak stars is also difficult due to low signal to noise ratio spheric Composition Change) balloon-borne ozonesonde and often results in mediocre nighttime occultation profiles measurements. The NDACC data can be downloaded from (see the data disclaimer ESA, 2012), we screened out these http://www.ndacc.org and the stations that were used in the “bad star” profiles from the comparison. comparison are listed in Table 2. While ozonesondes typi- MLS on board the Aura satellite, launched in July 2004, cally reach only about 30–35 km altitude, they measure tro- uses thermal infrared emission to measure the atmosphere pospheric and lower stratospheric ozone with very good ver- between ∼ 0 and 90 km. MLS measures globally during the tical resolution. Also, in general, the accuracy and precision day and night, and the accuracy of the MLS ozone profiles is of ozonesondes is at least as good as satellite measurements. estimated to be better than 5 % in the stratosphere (Froide- To validate the GBL profiles also for altitudes above vaux et al., 2008). In this comparison we used the MLS 35 km, we compared the GBL data against satellite measure- Level 2 version 3.3 data (Livesey et al., 2011). MLS ozone ments from the GOMOS nighttime occultations, MLS (Mi- profiles are mixing ratios as a function of pressure while crowave Limb Sounder) on EOS (Earth Observing System) the GBL profiles are number densities as a function of alti- Aura (Waters et al., 2006), and OSIRIS on Odin (Llewellyn tude. Thus, we converted the GBL densities to mixing ratios et al., 2004; McLinden et al., 2012). and pressures using the ECMWF model analysis data (below

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Table 2. NDACC stations that were used for different latitude zones.

60–90◦ N 30–60◦ N 30◦ S–30◦ N 30–60◦ S 60–90◦ S Scoresby Sound Obs. de Haute Provence Paramaribo Lauder Dumont d’Urville Ny Ålesund Hohenpeißenberg Izana´ Neumayer Sodankylä Legionowo Natal Summit De Bilt Eureka Boulder Alert Wallops Thule Prague

1 hPa) and the MSIS-90 climatology (above 1 hPa), which Table 3. Coincidence criteria for the GBL and correlative measure- are included in the GOMOS Level 1 data. It is convenient to ments. use the neutral density data from the Level 1 product, especially as the ECMWF data below 1 hPa (∼ 50 km) are gen- Instrument 1distance 1time erally very accurate (errors of less than 1 %). The MSIS-90 GOMOS night 250 km 24 h climatology, merged with the ECMWF data, is less accurate MLS 200 km 6 h though. Nevertheless, we estimate that the accuracy of the OSIRIS 200 km 5 h GOMOS Level 1 neutral air product between 50 and 60 km NDACC sounding 300 km 24 h is still better than approximately 5 %. OSIRIS is a UV/visible spectrograph, including a near- infrared imager, on board the Odin satellite. OSIRIS mea- orbiting satellites especially in the Southern Hemisphere. We sures the atmosphere using the limb scatter technique, mea- also calculated the bias against GOMOS night occultations suring scattered sunlight and scanning Earth’s limb between as a function of solar zenith angle. ∼ 10 and 100 km. In this work, we have used two dif- In the median calculation, we used coincidences from ferent OSIRIS ozone profile products. The University of all overlapping years. Possible year-to-year differences due Saskatchewan’s OSIRIS ozone product is retrieved from to e.g., aging of the instruments were found insignificant OSIRIS data using the SaskMART (Saskatchewan mul- (a few percents with no clear pattern) compared to the other tiplicative algebraic reconstruction technique; Degenstein sources of bias. In addition, the vertical resolutions of the et al., 2009). The product has been the target in several vali- four different satellite ozone products are similar (2–3 km for dation studies (e.g., Adams et al., 2012, 2013). In this study GBL, GOMOS night, and OSIRIS, and ∼ 3 km for MLS). we use the version 5.07 of these data. The Finnish Meteoro- Therefore, these profiles were compared without any verti- logical Institute’s (FMI) OSIRIS ozone product is retrieved cal smoothing. The vertical resolution of GBL is determined using the modified onion peeling method (Tukiainen et al., by the field of view of GOMOS and the movement of the 2008), which is similar to the method used in this work. The satellite during the measurement. These lead to an ∼ 2 km present version is 3.2. The two available OSIRIS ozone prod- theoretical resolution in the GBL product, which is further ucts agree with each other within a couple of percents. lowered to ∼ 2–3 km due to the retrieval method, according to our estimate. In the GOMOS occultation retrieval, the 3.1 Comparison method resolution is fixed to 2–3 km (depending on the altitude) using the Tikhonov regularization and target resolution tech- For each co-located profile pair we calculated the difference nique (Tamminen et al., 2010). The vertical resolutions of the as OSIRIS and MLS ozone products are very close to the GO- X − X MOS resolutions and the marginal resolution differences do = GBL ref × 1 100(%), (4) not seem to cause any notable issues in the comparisons. The Xref NDACC ozonesonde profiles, which have significantly bet- where XGBL is a GBL profile and Xref is a reference ter vertical resolution, were smoothed to the approximately (NDACC, GOMOS night, MLS or OSIRIS) profile. The same resolution with the satellite products using a Gaussian coincidence criteria for each instrument are shown in Ta- filter. ble3. To estimate the bias against GOMOS night, MLS and Some of the GBL profiles include outliers especially at OSIRIS, we calculated the median of the individual rela- the lowermost retrieved altitudes. This measurement is often ◦ ◦ tive differences using 10 latitude zones between 70 S and corrupted because GOMOS has lost the tracking of the star. ◦ 70 N. With the NDACC soundings we used only six lati- Before comparisons, we screened the GBL data with the fol- tude zones (see Table2) because the latitude coverage of the lowing criteria: NDACC sounding stations is much sparser than of the polar www.atmos-meas-tech.net/8/3107/2015/ Atmos. Meas. Tech., 8, 3107–3115, 2015 3112 S. Tukiainen et al.: GOMOS bright limb data set

60−90N 60−90S 35 77 35 6 165 28 296 48 55 426 72 508 88 30 541 30 98 572 100 50 587 105 599 106 609 102 25 611 25 93 45

Altitude [km] 608 81 567 69 479 55 366 39 20 240 20 23 40 34 4 40−45 −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 45−50 35 50−55 Altitude [km] 30−60N 30−60S 55−60 35 44 35 60−65 95 30 214 5 65−70 349 15 412 25 70−75 30 446 30 27 25 75−80 465 30 479 33 80−85 489 33 85−90 492 32 20 25 486 25 29 Altitude [km] 465 28 398 23 −20 −10 0 10 20 30 40 50 315 17 183 11 Difference [%] 20 83 20 5 8 −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 Figure 8. Median relative differences of GBL ozone proﬁles against GOMOS nighttime occultations for different solar zenith angles. 30S−30N 90S−90N 35 35 128 4 292 14 577 36 898 54 1087 30 58 30 1170 60 1229 Figure 8 shows the comparison against GOMOS night oc- 60 1270 61 1294 cultations for different solar zenith angles. There is a clear 60 1302 25 60 25 1286

Altitude [km] 57 1246 positive bias at around 50 km when the solar zenith angle is 55 1119 47 920 ◦ 28 634 75 or larger. With smaller solar zenith angles the differences 20 3 20 358 2 48 are rather similar. The large solar zenith angle observations −30 −20 −10 0 10 20 30 −30 −20 −10 0 10 20 30 Difference [%] Difference [%] account for 16 % of the GBL data and the GOMOS measurement geometry is such that these observations appear mostly Figure 7. Interquartile ranges (shaded areas) and medians (solid lines) of the individual relative differences of GBL ozone profiles at mid and high latitudes. We suspect that the 50 km bias is against NDACC ozonesondes for different latitude zones. The num- linked to stray light and its removal. GOMOS daytime data bers are the amount of co-located points at each altitude. suffer from serious stray light contamination and in particular the upper altitudes are sensitive to the accuracy of the removal method. We also note that the solar zenith angle 1. always remove the lowest retrieved point; seems to be the only parameter that clearly correlates with the 50 km bias. Some good individual profiles can be found 2. remove points with the reduced χ 2 > 10; even for high solar zenith angles but there is no clear pattern, or too few profiles to draw conclusions. Because the majority 3. remove points below 35 km where the relative error of the GBL measurements with a large solar zenith angle are O3(error) > 0.1, where O (error) is the error estimate distinctly biased at 50 km, in the remaining comparisons we O3(density) 3 of the retrieved density. only used the GBL data with the solar zenith angle smaller than 75◦. ◦ On average, the χ 2 screening removes ∼ 0.3 points per pro- Figure 9 shows the difference in 10 latitude bins against file and the error screening removes ∼ 1.3 of the remaining GOMOS night, MLS, and OSIRIS measurements. The most points per profile. This kind of screening significantly im- distinctive feature is the 10–15 % negative bias at around proves the agreement in the 20–25 km range against all stud- 40 km, which is present in all comparisons. A few percent ied reference data. of this difference can be explained by the diurnal variation of ozone. The GOMOS day measurements are made 3.2 Results around 10:00 LT, which is in the minimum of the diurnal curve (Sakazaki et al., 2013). In addition, the MLS after- Figure 7 shows the result against NDACC ozonesondes for noon measurements are made around 14:00 LT, which is in the six latitude zones. Shown are interquartile ranges and the quite recently discovered afternoon maximum of ozone medians of the differences. The numbers represent the num- (Sakazaki et al., 2013). We estimate that the diurnal variation bers of co-located pairs at each altitude. In these comparisons explains about 3 % of the 40 km bias against MLS and around the median difference is always less than 10 % except lati- 1–2 % against GOMOS nighttime and OSIRIS. Another no- tudes 60–90◦ S where the negative bias is more than −20 % table structure is the negative bias at southern mid/high lat- at 19 km. itudes, which is several 10 % at 19 km. Large biases exist at

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vs. GOMOS night vs. MLS Table 4. Login information for accessing the GBL data. 55 0 50 10 45 Server ftp.fmi.ﬁ 40 Login gomosGBL 35 1 10 Altitude [km] 30 Pressure [hPa] Password kOs20mos! 25 20 −60 −40 −20 0 20 40 60 −60 −40 −20 0 20 40 60

vs. OSIRIS (Univ. of Saskatchewan) vs. OSIRIS (FMI) In this work, we showed the accuracy of the GBL data as a

55 55 function of latitude, altitude, and solar zenith angle (Figs. 7– 50 50 45 45 9). These are the most important variables affecting the over- 40 40 all quality of the proﬁles. Beside these variables, we have 35 35

Altitude [km] 30 Altitude [km] 30 also studied the effect of season, scattering angle, azimuth 25 25 angle, albedo, and time, but they do not seem to correlate 20 20 −60 −40 −20 0 20 40 60 −60 −40 −20 0 20 40 60 Latitude [o] Latitude [o] substantially with the bias. The quality of the GBL data could be summarized as follows. The accuracy of the GBL data is −20 −15 −10 −5 0 5 10 15 20 Difference [%] better than 10 % between 20 and 35 km. There is a negative bias at 35–45 km that has a consistent shape with all stud- Figure 9. Median relative differences of GBL ozone profiles against ied observation conditions. Because of the regular shape, this GOMOS nighttime occultations (upper left), MLS (upper right), bias is straightforward to correct if the data is used, for exam- OSIRIS University of Saskatoon version (lower left), and OSIRIS FMI version (lower right). ple, in time series studies. Above 45 km, the data is valid with the solar zenith angles of less that 75◦ when the accuracy is approximately 15 % or better. tropic/sub-tropic regions below 21 km but the deviations are The GBL Level 2 files are available from the FMI’s FTP large too. Remaining differences are below 10 % (and often server and the login information is shown in Table 4. The file < 5 %). format is HDF5 (one file for each profile) and the total size of the whole data set is about 22 GB.

4 Discussion and summary Acknowledgements. This study was funded by the European Space We have processed and released a GOMOS bright limb Agency through the SPIN project (http://esa-spin.org) and by the ozone data set. This data set roughly doubles the number Academy of Finland through the MIDAT project. The authors wish of useful GOMOS ozone profiles. In general, the bias in the to thank the three referees for reviewing the manuscript and for GBL ozone is less than 10 %, and often less than 5 %, but suggesting relevant corrections. The authors also appreciate the there is a clear 10–13 % negative bias at 40 km. The reason MLS and OSIRIS teams for sharing their data. Special thanks go to Viktoria Sofieva for valuable suggestions. The (ozone sounding) for this bias is uncertain but the most likely cause is the stray data used in this publication were obtained as part of the Network light contamination in the 300–320 nm band already noted for the Detection of Atmospheric Composition Change (NDACC) by Tukiainen et al. (2011). Above the 45 km tangent height, and are publicly available (see http://www.ndacc.org). we use UV wavelengths to retrieve ozone and below 40 km we use visible wavelengths. The retrieval method is sensitive Edited by: C. von Savigny to the transition from UV to visible and it is easily disturbed by stray light. As explained above, we scale the amount of stray light to get a smooth ozone profile in the 40 km transi- References tion. This ad hoc approach works reasonably well in practice but better ways to switch between the different wavelength Adams, C., Strong, K., Batchelor, R. L., Bernath, P. F., Brohede, domains should be investigated in future. S., Boone, C., Degenstein, D., Daffer, W. H., Drummond, J. R., The diurnal variation explains about 1–3 % of the observed Fogal, P. F., Farahani, E., Fayt, C., Fraser, A., Goutail, F., Hen- 40 km bias as the GOMOS day measurements are made dur- drick, F., Kolonjari, F., Lindenmaier, R., Manney, G., McElroy, ing the minimum of the diurnal cycle. At the 50 km altitude C. T., McLinden, C. A., Mendonca, J., Park, J.-H., Pavlovic, B., we have up to 50 % positive bias depending on the solar Pazmino, A., Roth, C., Savastiouk, V., Walker, K. A., Weaver, D., and Zhao, X.: Validation of ACE and OSIRIS ozone and NO2 zenith angle. This bias cannot be explained by natural vari- ◦ ation; it indicates some problem in the retrieval, most likely measurements using ground-based instruments at 80 N, Atmos. related to the stray light and its correction. Until this issue Meas. Tech., 5, 927–953, doi:10.5194/amt-5-927-2012, 2012. Adams, C., Bourassa, A. E., Bathgate, A. F., McLinden, C. A., is solved, it is recommended to only use GBL measurements ◦ Lloyd, N. D., Roth, C. Z., Llewellyn, E. J., Zawodny, J. M., Flit- with a solar zenith angle of less than 75 when using data tner, D. E., Manney, G. L., Daffer, W. H., and Degenstein, D. A.: from the altitudes above 45 km. Characterization of Odin-OSIRIS ozone profiles with the SAGE www.atmos-meas-tech.net/8/3107/2015/ Atmos. Meas. Tech., 8, 3107–3115, 2015 3114 S. Tukiainen et al.: GOMOS bright limb data set

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Reprinted, with permission, from Journal of Geophysical Research: Atmospheres, 121, doi:10.1002/2015JD024657

Journal of Geophysical Research: Atmospheres

RESEARCH ARTICLE Retrieval of atmospheric CH4 proﬁles from Fourier transform 10.1002/2015JD024657 infrared data using dimension reduction and MCMC

Key Points: 1 2 1 1 3 • Retrieval of CH4 proﬁle information S. Tukiainen , J. Railo , M. Laine , J. Hakkarainen , R. Kivi , from FTIR data, potentially improving P. Heikkinen3, H. Chen4,5, and J. Tamminen1 the total column • Practical and intuitive dimension 1Earth Observation Unit, Finnish Meteorological Institute, Helsinki, Finland, 2Department of Mathematics and Statistics, reduction methodology University of Jyväskylä, Jyväskylä, Finland, 3Arctic Research Center, Finnish Meteorological Institute, Sodankylä, Finland, • Full Bayesian uncertainty 4 quantiﬁcation using Markov chain Centre for Isotope Research (CIO), Energy and Sustainability Research Institute Groningen (ESRIG), University of Monte Carlo Groningen, Groningen, Netherlands, 5Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado Boulder, Boulder, Colorado, USA

Correspondence to: S. Tukiainen, simo.tukiainen@fmi.fi Abstract We introduce an inversion method that uses dimension reduction for the retrieval of atmospheric methane (CH4) profiles. Uncertainty analysis is performed using the Markov chain Monte Carlo (MCMC) statistical estimation. These techniques are used to retrieve CH4 profiles from the ground-based Citation: ∘ Tukiainen, S., J. Railo, M. Laine, spectral measurements by the Fourier Transform Spectrometer (FTS) instrument at Sodankylä (67.4 N, J. Hakkarainen, R. Kivi, P. Heikkinen, 26.6∘E), Northern Finland. The Sodankylä FTS is part of the Total Carbon Column Observing Network H. Chen, and J. Tamminen (2016), (TCCON), a global network that observes solar spectra in near-infrared wavelengths. The high spectral Retrieval of atmospheric CH4 profiles from Fourier transform infrared resolution of the data provides approximately 3 degrees of freedom about the vertical structure of data using dimension reduction CH4 between around 0 and 40 km. We reduce the dimension of the inverse problem by using principal and MCMC, J. Geophys. Res. Atmos., component analysis. Smooth and realistic profiles are sought by estimating three parameters for the 121, doi:10.1002/2015JD024657. profile shape. We use Bayesian framework with adaptive MCMC to better characterize the full posterior distribution of the solution and uncertainties related to the retrieval. The retrieved profiles are validated Received 15 DEC 2015 against in situ AirCore soundings which provide an accurate reference up to 20–30 km. The method is Accepted 11 AUG 2016 Accepted article online 16 AUG 2016 presented in a general form, so that it can easily be adapted for other applications, such as different trace gases or satellite-borne measurements where more accurate profile information and better analysis of the uncertainties would be highly valuable.

1. Introduction Greenhouse gas measurements of the atmosphere are necessary for monitoring and understanding the

observed global warming of the Earth. Greenhouse gases such as water vapor (H2O), carbon dioxide (CO2), and methane (CH4) absorb electromagnetic radiation, originally emitted from the Sun—and reradiated from the Earth—directly affecting the energy balance of the Earth. The theory of this radiative impact is well estab- lished and it has been recently confirmed by direct measurements as well [Feldman et al., 2015]. The current understanding is that the increased greenhouse gas concentrations have warmed the globe approximately by 0.85 K since the end of the 1800 century [Intergovernmental Panel on Climate Change, 2013, section 2.]. Because greenhouse gases are important factors in the behavior of the atmosphere, accurate estimates of the abundances and trends of the greenhouse gases are crucial constraints for meaningful climate model simulations of the future. Greenhouse gas concentrations are traditionally measured by analyzing local air samples or by using ground-based Fourier transform spectrometers (FTS) that use Fourier transform infrared (FTIR) spectroscopy to measure column-integrated values. Examples of the FTS instrumentation include the Total Carbon Column Observing Network (TCCON) network [Wunch et al., 2011] which consists of around 20 measurement sites around the world and the Network for the Detection of Atmospheric Composition Change (NDACC) which has ∼23 stations. More recently, satellite-based measurements have been gathered as well. The SCIAMACHY instrument [Gottwald and Bovensmann, 2011] on board the Envisat satellite (2002–2012) was one of the first satellite equipments to continuously measure atmospheric greenhouse gases on a global scale. The SCIAMACHY data were also used to derive one of the first greenhouse gas trends from space [Frankenberg

©2016. American Geophysical Union. et al., 2011; Schneising et al., 2011] even though the data became noisier in the last years of the mission. All Rights Reserved. SCIAMACHY measured greenhouse gases using nadir geometry and near-infrared/shortwave infrared

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 1 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

(NIR/SWIR) wavelengths. The same concept have been used by the Greenhouse gases Observing SATellite (GOSAT), launched in 2009, and NASA’s Orbiting Carbon Observatory 2 (OCO 2), launched in 2014. GOSAT was

the ﬁrst dedicated satellite mission to measure CO2 and CH4 (and O2 in the oxygen A band), providing about 500 clear sky measurements each day. These measurements are used in various studies of the biosphere, such as in investigations of the water vapor and chlorophyll ﬂuorescence. OCO 2 provides an order of magnitude

more CO2 data than GOSAT, and 2 orders more than SCIAMACHY.The ﬁrst versions of the OCO 2 level 2 data are already released and under investigation by the scientiﬁc community. Several other instruments have measured greenhouse gases from nadir using thermal infrared (TIR) wavelengths. These instruments include, for example, AIRS on the Aqua satellite [Aumann et al., 2003], TES on Aura [Beer, 2006], and IASI on Metop A/B [Airesetal., 2002]. MIPAS on Envisat [Fischer et al., 2008] was a limb-viewing instrument using TIR, and ACE-FTS instrument on SCISAT-1 [Bernath et al., 2005] uses solar occultation, covering wavelengths from SWIR to TIR.

ACE-FTS provides also CH4 proﬁle data with relatively good vertical resolution (3–4 km). The ground-based measurement networks are crucial for validating the satellite-based observations. Espe- cially the TCCON network has been widely used as the reference [e.g., Dils et al., 2014]. The TCCON instruments look directly at the Sun providing good signal-to-noise ratio in clear sky conditions. Furthermore, the TCCON instruments achieve very good spectral resolution (typically ∼0.02 cm−1). The TCCON total column results

are delivered as column-averaged dry air mole fractions (denoted by XCO2,XCH4, etc.), i.e., the gas columns are divided by the dry air column which is approximated from the retrieved O2 column. This is a standard practice to get a more stable quantity, less aﬀected by variations in the air pressure and water vapor. Using

the retrieved O2 as a reference is also useful because it removes some of the systematic errors related to the retrieval and compensates some of the instrumental errors. The same concept is used with the satellite-based columns as well. The accuracy requirements for the retrieved products are exceptionally strict. For example,

the average CO2 column should be retrieved within ∼1 ppm (out of ∼400 ppm) and the CH4 column within ∼5 ppb (out of ∼1800 ppb). These are difficult limits to achieve with remote sensing measurements. Although accurate measurement data with high signal-to-noise ratio and spectral resolution are necessary, accurate forward modeling and inversion methods are crucial as well. The radiative transfer in the shortwave infrared (SWIR) and near-infrared (NIR) wavelengths has been extensively studied in the past. There are more than 20 published SWIR/NIR radiative transfer codes available such as MODTRAN, DISORT, 4A/OP, MOSART and SCIATRAN. The fundamental theory behind the absorption line for- mation and the line shape are covered in numerous textbooks such as Goody and Yung [1995] and Liou [2002]. The line parameters have been derived using laboratory measurements and there are line databases available for a large number of isotopologues and wavelength ranges [e.g., Rothman et al., 2013; Jacquinet-Husson et al., 2011]. Modern retrieval methods are usually based on the Bayesian statistical approach, which exploits the prior information about the state of the atmosphere [e.g., Butz et al., 2011]. A posterior analysis is then performed by combining the prior and the likelihood. A canonical example is the optimal estimation method by Rodgers [2000]. Examples of retrieval methods for satellite-based greenhouse gas measurements are described in Buchwitz et al. [2006] for SCIAMACHY, Yoshida et al. [2011] for GOSAT, and in O’Dell et al. [2012] for OCO 2. The official TCCON retrieval uses the GGG software package [Wunch et al., 2011], which solves the inversion problem by scaling the prior profile densities of the gases that absorb in the wavelength window of interest. Several wavelength windows are used for most of the gases and the final estimate of the profile is an error-weighted average of the individual results. The absorption coefficients are evaluated beforehand, assuming known fixed temperature and pressure profiles. Scaling of a prior profile, the method used in GGG, is an intuitive and robust concept but retrieves only one piece of information and assumes that the shape of the prior profile is known. There have been efforts to

retrieve also proﬁle information from FTIR data. In Kuai et al. [2012], the CO2 prior proﬁle is scaled on three levels instead of having only one common scaling factor. Furthermore, Kuai et al. [2013] assimilate FTIR data

and thermal infrared satellite data to estimate lower tropospheric CO2 columns, and Hase et al. [2004] report optimal estimation-based profile retrievals from high-resolution FTIR measurements. In Senten et al. [2012], the authors use information operator approach (IOA) [Doicu et al., 2007] to retrieve profiles from FTIR data and investigate other common methods as well. In this paper we describe an alternative inversion method for retrieving greenhouse gas profiles from FTIR measurements. We demonstrate a simple and flexible technique to retrieve information about the vertical

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 2 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

structure of the atmosphere, leading to a more accurate estimate of the total column. The retrieval method presented is based on reducing dimension of the state space by a suitable truncation of the prior covariance matrix, hence reducing the dimension of the problem. For the estimation of the unknown parameters we use adaptive Markov chain Monte Carlo (MCMC) methods. The MCMC solution gives a better understanding of the posterior uncertainties, compared to the derivative-based estimation methods. Once the natural variability of the retrieved gas is properly characterized, our retrieval method is only marginally aﬀected by the possibly

incorrect prior proﬁle shape. In this work we retrieve CH4 proﬁles, but the same technique can be used with other trace gases as well.

2. Sodankylä Measurements The Sodankylä FTS station is part of the Finnish Meteorological Institute’s Arctic Research Center in Northern Finland (67.3668∘N, 26.6310∘E). The Sodankylä FTS [Kivi and Heikkinen, 2016] has been operational since February 2009, providing direct Sun measurements from February to November. Up to several hundred measurements a day are recorded depending on the season and cloudiness, but the wintertime measurements are not possible due to the absence of the sunlight. The Sodankylä FTS is a Bruker IFS 125 HR with a A547N solar tracker. It has three detectors: InGaAs (4000–11,000 cm−1), Si (11,000–15,000 cm−1), and InSb (1800–6000 cm−1). The wave number limits are roughly the useful ranges of the detectors. The Sodankylä FTS operates on the optical path diﬀerence of 45 cm, with the 2.3923 mrad ﬁeld of view, leading to the spectral resolution of ∼0.02 cm−1. The measurements are routinely processed using the GGG software and distributed as column-averaged

dry-air mole fractions. The latest version of the algorithm, GGG2014 [Wunch et al., 2015], retrieves CH4 from −1 three separate wavelength windows centered at 5938, 6002, and 6076 cm . In general, the CH4 errors within the GGG2014 retrieval are below 0.5% (about 5 ppb) for solar zenith angles less than 85∘ [Wunch et al., 2015]. One of the main sources of error comes from the prior proﬁle shape. Especially the springtime prior

profiles of CH4 are prone to differ substantially from the truth. The prior profiles for Sodankylä depend on the tropopause height but not on the polar vortex which can largely affect the stratospheric part of the

CH4 proﬁle. In addition to the FTS measurements, a variety of in situ observations, e.g., balloon soundings and tower mea-

surements, are collected at the Sodankylä site. To validate CH4 profiles retrieved from the Sodankylä FTIR data, we use the AirCore profile measurements made along with the FTIR measurements. AirCore is an innovative atmospheric sampling tool made of a long coil of tubing which slowly fills with ambient air during the payload descent of the balloon sounding [Karion et al., 2010]. The vertical profile measurements used in this study were made by an ∼100 m long AirCore and obtained by the analysis of the air samples on the ground using a cav- ity ring-down spectrometer (Picarro Inc. model G2401) within a few hours after landing. In this study we use Sodankylä AirCore version 1.0 data. The AirCore soundings made at Sodankylä are important because there are not much vertically resolved in situ data of the Arctic methane, especially measured in the stratospheric polar vortex conditions.

3. Forward Model The radiative transfer problem of the FTS measurement is solved here with the Matlab code SWIRLAB (https://github.com/tukiains/swirlab) which can be used to calculate absorption coeﬃcients, model short-wave infrared radiative transfer, and perform retrievals from measurement data. So far we have tested SWIRLAB with the ground-based geometry where the instrument is looking directly at the Sun. In this simpli- ﬁed case, the scattering of radiation from air molecules and aerosols is negligible and only the absorption of the atmosphere needs to be considered. The satellite viewing geometry is not utilized in this work. In this study we assume a spherical Earth and atmosphere. The SWIRLAB atmosphere can be discretized with an arbitrary layering but we have mostly used 100 layers between 0 and 70 km. The layering is based on a geometric series, where the layers are thinnest close to the surface (∼800 m) and thickest at the top (∼1.25 km). This kind of layering is rational as the number density of methane decreases exponentially with altitude, although in our tests the retrieval results are not very sensitive to the layering scheme. The layers are homogeneous, i.e., the number density, temperature, and pressure inside each layer are assumed constant. All the layer parameters (densities, temperature, and pressure) are linearly interpolated to the center of each layer.

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For the calculation of the absorption coefficients we use the HITRAN2012 line database [Rothman et al., 2013]. The line intensities and positions are computed according to Rothman et al. [1998] with the total internal partition sums from Laraia et al. [2011]. Isotopologue ratios are taken from the HITRAN2012 database and kept fixed in the retrieval. Line mixing is not taken into account. For the line shape calculation we use the Voigt profile, which is generally a function of temperature and pressure (and marginally the partial pressure of the absorbing gas). In our retrieval, we use the same temperature, pressure, and prior profiles for the trace gases as GGG2014. The solar spectrum is also the same. The GGG2014 prior profiles are generated using National Centers for Environmental Prediction/National Center for Atmospheric Research model analysis data (for temperature, pressure. and humidity), empirical models for the greenhouse gases, and a variety of satellite-based and in situ data [Wunch et al., 2011]. We note that our absorption coefficient calculation is somewhat simplified. For example, in addition to the

HITRAN database, the OCO CO2 retrieval employs results from Devi et al. [2007], Predoi-Cross et al. [2009], and Sung et al. [2009], just for the 1.61 μm band alone. Line mixing, independent isotopologues, and water vapor content of the atmosphere should be taken into account for the best possible results. Also, in some cases,

especially for the O2 retrievals with high solar zenith angles, the Voigt proﬁle might not be the best approximation for the line shape. Nevertheless, our simple forward modeling is enough to adequately model the FTIR data and demonstrate the beneﬁts of our retrieval method.

4. CH4 Proﬁle Retrieval Methane is an important carbon-containing species in the atmosphere. Atmospheric methane is produced by anthropogenic and natural processes at the surface; it has no source in the atmosphere. Methane has a relatively long lifetime (8–10 years) allowing it to be transported from the troposphere to the stratosphere. In

the troposphere, CH4 has a fairly constant mole fraction, but in the stratosphere, CH4 is an excellent tracer to study transport processes [Brasseur and Solomon, 2005]. Thus, it is useful to measure the vertical distribution

of CH4. Besides, an accurate vertical proﬁle gives a credible estimate of the total column, which often is an important variable.

Ground-based FTS instruments measure solar light modified by the whole atmospheric column of CH4 and other interfering trace gases. Our retrieval problem is to estimate the vertical CH4 profile from a single spectrum. The information about the vertical structure comes from the pressure and temperature dependence of the Voigt line shape: absorption lines are wider close to the Earth in high pressure than higher in the atmosphere. Given the measured spectrum y ∈ Rm, where m is the number of wavelengths, we wish to approximate the state vector x ∈ Rn, where n is the number of atmospheric layers times the number of trace gases to be retrieved. Typically, the number of layers is around 50 or more depending on the forward model. Thus, the state vector x represents the densities of the discretized atmosphere in the forward model, and the inverse problem can be formulated in a very general way ̂ , , 𝜽 , x = R(y Cy ) (1) ̂ Rn Rm×m where x ∈ is the retrieved state, R is the retrieval method, and Cy ∈ is the measurement error covariance. Typically, the problem is also affected by some additional parameters, denoted by 𝜽, that can be either fixed or retrieved. If the extra parameters are retrieved, as they often are, they should be part of x̂. Nevertheless, we ignore them in the following to keep the equations simpler to follow. The fundamental problem in the estimation of the vertical profile x̂ from a single spectral measurement is that the measured noisy spectrum does not contain enough information to independently resolve all n altitude levels in a meaningful way (the inverse problem is said to be ill-posed). In other words, without proper prior regularization, there are a vast number of profiles that fit the data but are physically unrealistic, e.g., are oscillating or otherwise unstable. In order to make the problem well posed, we need to regularize, or constrain, the retrieval by using additional information about the solution. For example, we can require a certain degree of smoothness from the retrieved profile or demand the retrieved densities to be positive. A general strategy is to cast the inversion problem in statistical form and consider unknowns and other auxiliary information as probability distributions. In Bayesian statistical approach we assume a priori information about the state vector x and use the Bayes’ theorem to combine information from the prior measurement in the estimation process. In general probability distribution form, this can be written as

p(x|y)∝p(y|x)p(x), (2)

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 4 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

where p(x|y) is the posterior distribution of the state x given the observations y, p(y|x) is the likelihood and Rn p(x) is the prior distribution. In our profile retrieval, the prior is a CH4 profile x0 ∈ having the prior error Rn×n covariance Cx ∈ . Assuming that the prior distribution and the distribution defining the likelihood are independent Gaussian, then the posterior density can be written as ( ( )) | 1 || ||2 || ||2 , p(x y)∝exp − y − f(x) + x − x0 (3) 2 Cy Cx

|| ||2 T −1 Rn → Rm where we use the notation b A = b A b, and f ∶ is the forward model. The Bayesian inversion is, in principle, an elegant way to assimilate prior model information about x and the information in the data y. However, in many cases the prior is mainly used to produce a “well-behaving” posterior, e.g., the desired smoothness in the retrieved proﬁle, instead of a careful statistical analysis of the prior as the information on the natural variability in the proﬁles and the smoothing properties of the measurement system. In the FTIR inverse

problem, the posterior depends significantly on the prior mean profile x0 and the relationship between Cy and Cx. Too loose prior distribution will lead to an unstable solution, and too tight will bias the result if x0 is far from the truth. Nevertheless, the vertical variability allowed by the prior is usually set relatively restricted to substantially regularize the solution and to avoid any superfluous oscillation in the retrieved profile. To make the uncertainty quantification from the posterior distribution valid, the prior should be an honest statistical representation of the model knowledge before the measurement is taken, but it is impractical to use such a prior when the state vector contains many more unknowns than there are degrees of freedom in the signal. 4.1. Dimension Reduction Method In mathematical sense, a vertical profile is a function and as such an infinite-dimensional object. When we discretize the profile with, say, 70 levels, the corresponding retrieval problem has 70 unknowns. The intrinsic dimension of the problem is typically much lower, as the observations contain only limited amount of vertical information. This dimension is a property of the measurement system, and together with the prior constraints posed for the retrieval process, it determines the resolution of the retrieved profile as manifested in the averaging kernel, see section 4.4 later in this paper or, e.g., Rodgers [2000, section 2.4]. The approach presented in this paper is based on the work by Marzouk and Najm [2009] and Solonen et al. [2016]. In atmospheric remote sensing, the dimension reduction techniques have been utilized, e.g., by Masiello et al. [2012] and Cuietal.[2014]. If we want to solve the problem in the full dimension determined by the discretization, we need to use some prior constraints due to the ill-posed nature of the problem. In addition, using the full dimension would make the corresponding estimation problem harder to solve. In this work, we utilize sampling-based uncertainty analysis, which allows the use of the full Bayesian posterior distribution by MCMC simulation. For MCMC, the computational efficiency is heavily affected by the dimension of the unknown and dimension reduction will be of great benefit as the use of a low-rank approximation of the prior covariance matrix will efficiently restrict the MCMC sampling to a lower dimensional space. In dimension reduction, we formulate the problem as a low-dimensional problem that can be mapped back to the original dimension determined by the discretization, which will make the method discretization invariant. If there are only 3 degrees of freedom in the observations, then we can parameterize the problem so that we have only three parameters to estimate, but this parameterization must be chosen so that the information available is retained. In the method presented here, the prior distribution that defines the dimension reduction is selected so that it reflects the information content of the observations. An extreme case would 𝛼 be just to scale the prior profile, x = x0, i.e., to have a one-dimensional problem as in the operational TCCON inversion algorithm. Let us consider a parameterization for the profile x in terms of a parameter vector 𝜶 and a projection matrix P as 𝜶, x = x0 + P (4) Rn where x0 ∈ is a mean profile. Our aim is to define P in such a way that it defines a probability distribution 𝜶  , of x, with as simple as possible. If the prior distribution for x is Gaussian, x ∼ (x0 C), where C is an n × n T 𝜶  , positive definite prior covariance matrix, then we can choose P such that PP = C and ∼ (0 In). Then it follows that 𝜶 𝜶 T T . cov(x)=cov(P )=Pcov( )P = PInP = C (5)

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 5 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

Next, to define the dimension reduction, we will use a similar parameterization, but replace the prior covariance matrix C by its low-rank version C̃ and use it to build a projection from a lower-dimensional subspace to the original n-dimensional space. We factorize the covariance C using the singular value decomposition, ∑n 𝚲 T 𝜆 T , C = U U = iuiui (6) i=1 with , , , 𝚲 𝜆 , ,𝜆 , U =[u1 … un] = diag( 1 … n) (7) , , 𝜆 ≥ 𝜆 ≥ ≥ 𝜆 > where u1 … un are the singular vectors, and 1 2 ··· n 0 are the singular values (or, equivalently, the eigenvalues) of C. The reduced rank version of C of order k, 1 ≤ k < n, is defined as ∑k ̃ 𝜆 T T , C = iuiui = PkPk (8) √ √ i=1 𝜆 , , 𝜆 Rn×k, < Rk Rn where Pk =[ 1u1 … kuk]∈ k n, is a projection matrix from to . The reduced matrix C̃ ∈ Rn×n approximates the original covariance C and it is the best rank k approximation according to the Eckart-Young-Mirsky theorem of numerical linear algebra. ̃ T With the reduced rank covariance matrix C = PkPk , we can define a low-dimensional parameterization for the profile 𝜶 , x = x0 + Pk k (9) 𝜶  , where k is a k-dimensional vector whose prior distribution will be a k-dimensional Gaussian (0 Ik).The optimizer for the parameter estimation problem can now work in the reduced dimension, while the forward model is still run in the full dimension. With a sampling-based approach, such as MCMC, we can make proposal 𝜶 draws for k from the reduced dimension, and then generate full profile using equation (9). If the neglected singular values are small, i.e., whose singular vectors contribute to the variability (and thus to the uncertainty) less than a selected threshold, the original prior information will be represented accurately. In practice, it is useful to estimate the log profile instead of the original, 𝜶 , log(x)=log(x0)+Pk k (10) as this will always lead to positive profiles, which is not the case if we define the estimation problem with the Gaussian prior of equation (9). This means that the prior for x is lognormal, and we have to define the prior covariance matrix C in terms of the log profiles. 𝜶 In the CH4 profile retrieval using FTIR data, we define the posterior distribution in terms of the and retrieve k parameters instead of n. The posterior density of equation (3) now becomes ( ( )) 1 p(𝜶|y)∝exp − ||y − f(x)||2 + ||𝜶||2 , (11) 2 Cy Ik Rm Rn → Rm Rm×m where y ∈ is the measurement vector, f ∶ is the forward model, and Cy ∈ is the mea- 𝜶 Rk×k surement error covariance. As already mentioned, the prior covariance of the parameters is Ik ∈ , i.e., a diagonal unit matrix. While equations (3) and (11) are analogous, the difference is that in the dimension reduction retrieval the likelihood term receives only smooth realization of x, as they are generated by equation (9) or equation (10), but in equation (3) the state vector has no such restriction. Thus, the estimation of the posterior with k parameters in the state vector is numerically much more stable than with n parameters. 4.2. Prior Covariance The important part of the dimension reduction based retrieval is the prior covariance that has to be selected before the estimation. In this work we construct the prior covariance from general assumptions, but we do

use ACE-FTS satellite measurements to check that our assumptions are valid. For CH4, we allow some variability between 0 and ∼10 km, a large variability in the UTLS region (upper troposphere, lower stratosphere) between ∼10 and ∼35 km, and very little variability above ∼35 km. From the UTLS we expect to ﬁnd the

largest gradients in the CH4 mole fraction, a well-known feature visible also in the ACE-FTS version 2.2 data (Figure 1). Note that the ACE-FTS data set we use may overestimate the natural variation because it contains seasonal and year-to-year variations. The altitudes above ∼35 km are “ﬁxed” to the prior proﬁle because the measurement has very little sensitivity to these altitudes. Below the (approximate) tropopause altitude,

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 6 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

𝜎 Figure 1. CH4 proﬁles (grey), mean (solid line), and ±2 (dashed lines) over Sodankylä measured by ACE-FTS in 2004–2010.

we assume that CH4 is rather well mixed and the prior proﬁle has approximately the correct shape at least. In a recent CH4 retrieval paper by Sepúlveda et al. [2014] the authors describe typical CH4 signals between 0 and 25 km and have a similar treatment of the variability than we have. However, they also consider possible

CH4 enhancement on the ground level, a feature that we do not take into account. To set up the prior covariance matrix, we ﬁrst deﬁne its diagonal. The prior standard deviations for each altitude h are calculated using a mixture of two square exponential “bumps” as ( ) ( ) 𝜎 𝜎 2 −2 𝜎 2 −2 . (h)= 1 exp −(h − h1) s1 + 2 exp −(h − h2) s2 (12)

The terms in equation (12) are chosen so that the diagonal elements between 10 and 30 km approximately

resemble the natural variability of CH4 over Sodankylä, measured by ACE-FTS in 2004–2010. We define the prior in logarithmic scale, so in terms of the relative standard deviation of the original profile variability, with 𝜎 . 𝜎 . 1 = 0 01, 2 = 0 4, h1 = 5, h2 = 27, s1 = 9, and s2 = 6. The smoothness of the profiles comes from the off-diagonal entries of the prior covariance, and for these a standard Gaussian covariance function is used. The elements of the prior covariance function are thus ( ) ( )2 1 d(i, j) c = 𝜎(i)𝜎(j) exp − , (13) ij 2 𝜙

where i and j are two altitudes, d(i, j) is the spatial distance between them in kilometers, and the correlation length parameter 𝜙 controls the smoothness, here we set 𝜙 = 12 km. Equation (13) gives rational profiles when we use the positivity condition defined in equation (10). The covariance of equation (13) is shown in Figure 2 (top left). Figure 2 (top right) shows the five first singular values of the decomposed covariance and Figure 2 (bottom left) shows the three largest singular vectors of the original covariance matrix. Any profile suggestion is a linear combination of these three components, weighted by the 𝜶 parameters. Figure 2 (bottom right) shows 20 random draws using the three largest singular vectors. The random draws visualize typical realizations of equation (10) representing candidate profile shapes for our retrieval attempt. 4.3. Transmittance and Jacobian In this section we describe more carefully how we model the FTIR spectra. We show the calculation of the Jacobian, which is needed if we use some derivative-based optimization instead of MCMC. Furthermore, the Jacobian is needed later in section 4.4 where we discuss the averaging kernel. , , , T , , , T Given the forward model f(x), observations y =[y1 y2 … ym] , and the state vector x =[x1 x2 … xn] , the linearized forward model for some reference state xr can be written as 𝜕f(x) y − f(x )= (x − x )+𝜺 = K(x − x )+𝜺, (14) r 𝜕x r r

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 7 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

Figure 2. (top left) Logarithm of the CH4 prior covariance, (top right)ﬁve largest singular values, (bottom left) three largest singular vectors, and (bottom right) random draws from the prior using the three singular vectors.

where 𝜺 is the vector of measurement errors and K is the m × n weighting function matrix also called the 𝜕 𝜕 Jacobian which has the elements Kij = fi(x)∕ xj. With the direct Sun geometry, the derivatives (for each x) can be easily computed analytically. Assuming a discretized atmosphere with n layers, and only one absorbing gas for simplicity, the transmittance in one wavelength is ( ) ∑n 𝜏 𝜎 , = exp − ixili (15) i=1 𝜎 where i is the absorption coeﬃcient, or cross section, of the layer i, and xi and li are the corresponding number density and slant length of the layer. In the matrix notation for the whole spectral window with m points we have the cross-section matrix S ∈ Rm×n, densities x ∈ Rn, and slant lengths l ∈ Rn.Now the slant densities are x̄ = l ∘ x, (16)

where ∘ denotes the pointwise product, and the transmittance

𝝉 = exp(−Sx̄), (17)

𝝉 ∈ Rm, which has the Jacobian 𝜕𝝉 K = =−diag(𝝉)S, (18) 𝜕x̄ with K ∈ Rm×n.However, in the dimension reduction retrieval we estimate 𝜶 parameters instead of gas den-

sities of the individual layers. Using the logarithmic proﬁle, the projection matrix Pk in equation (10) gives the mapping back to the full space 𝜶 , xk = exp(Pk k)∘x0 (19)

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and the Jacobian becomes 𝜕𝝉 Kk = 𝜕𝜶 = Kdiag(l∘xk)Pk (20) k Rm×k with Kk ∈ . In practice, the situation is slightly more complicated. Instead of measuring transmittance, 𝝉, a ground-based FTS observes solar radiation inﬂuenced by the atmosphere and the Fourier transformed spectrum contains a nonphysical baseline (thus, its units are arbitrary). Moreover, an extra additive term called the zero-level oﬀset is usually added to take account the nonlinearity of the detector. Thus, the FTIR spectrum in a narrow wavelength window can be approximated as

𝝉 𝝉 𝚫 , ftir = ∘s∘p + 0 (21) 𝚫 where s denotes the solar irradiance, p is a polynomial describing the (usually smooth) baseline and 0 is the zero-level offset term. The degree of the polynomial term depends on the width and location of the spectral window; a degree of 1 or 2 is generally feasible. We have used the degree of 2 and parameterized p as a Lagrange polynomial so that the three coefficients are between 0 and 1. The baseline fit should not be constrained; hence, the polynomial coefficients will have flat prior distributions. The offset term is practically −3 𝝉 always close to zero; a typical value is around 10 , while ftir is between 0 and 1. Generally, the offset and the polynomial terms identify much better in wider wavelength windows. The downside of a wide window is that a higher-order polynomial may be required for the baseline. 4.4. Averaging Kernel It is useful to investigate the resolution and information content of the dimension reduction retrieval. Following Rodgers [2000], the averaging kernel is defined as 𝜕x̂ A ∶= , (22) 𝜕x

which is a measure of the sensitivity of the retrieved state x̂ to the change in the underlying truth denoted by x. The averaging kernel can be estimated with simulation experiments (when the “truth” is known) or directly from the Jacobian, prior, and related uncertainties. The Jacobian for the vertical proﬁle in full space is . Kv = Kdiag(l) (23) Now using the formulation by Rodgers [2000], and equations (20) and (23), we can write the averaging kernel 𝜶 for the k-parameters ( ) ( ) 𝜕𝜶̂ −1 k T −1 T −1 A𝛼 = = K C K + I K C K , (24) 𝜕x k y k k k y v Rk×n Rm×m Rk×k where A𝛼 ∈ , Cy ∈ is the error covariance of the measurement, and Ik ∈ is the prior covariance 𝜶 of the k parameters. We can further write the density-wise averaging kernel matrix

, A = diag(xk)PkA𝛼 (25)

where A ∈ Rn×n. Equation (25) is useful when the retrieved FTIR proﬁles are compared with the reference measurements having much better vertical resolution (such as AirCore). As given in Rodgers and Connor [2003], a smoothed version of the reference proﬁle is , xsmooth = x0 + A(xhigh − x0) (26)

where x0 is the prior proﬁle and xhigh is the high-resolution proﬁle. The averaging kernel for the total column is

T Ac = lv A (27)

Rn Rn where Ac ∈ and lv ∈ contains the lengths of the layers in the vertical direction. Equation (27) describes the sensitivity of the integrated column, it can be used when column values are compared.

Finally, we mention that SWIRLAB also oﬀers possibility to retrieve CH4 by scaling prior proﬁles. The averaging kernels for the least squares prior scaling retrieval can be derived in the same way as above and omitted here.

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30 4.5. Computation of the Retrieval Most of the remote sensing retrieval 20 algorithms that apply Bayesian for- 10 mulation are based on optimization o o Altitude [km] 03−Sep−2013, SZA: 78 22−Oct−2013, SZA: 79 and on the assumption of approx- 0 30 imately Gaussian posterior distribu-

20 tion around the maximum a posteriori (MAP) point. Here our aim is to apply a 10 o o Monte Carlo sampling scheme to cal- Altitude [km] 19−Mar−2014, SZA: 72 09−Apr−2014, SZA: 72 0 culate the full posterior distribution. 30 In particular, we apply the MCMC 20 methodology, which can be seen as a clever Monte Carlo technique as it 10 o o avoids the direct computation of the Altitude [km] 08−May−2014, SZA: 66 14−Jul−2014, SZA: 66 0 scaling factor needed in the Bayes 30 formula. Note that this factor is not 20 needed when only the MAP point is searched, as, e.g., in the optimal esti- 10 o o Altitude [km] 15−Jul−2014, SZA: 60 16−Jul−2014, SZA: 67 mation or Levenberg-Marquardt (LM) 0 algorithms. 30 The MCMC algorithm has previously 20 been applied to atmospheric remote 10 sensing problems by, e.g., Tamminen o o Altitude [km] 02−Sep−2014, SZA: 61 05−Nov−2014, SZA: 85 0 and Kyrölä [2001], Haario et al. [2004], 300 600 900 1200 1500 1800 300 600 900 1200 1500 1800 CH [ppb] CH [ppb] and Laine and Tamminen [2008]. The 4 4 advantages of MCMC methodology, in addition to computing the full posterior distribution, include the flexibil- ity to perform the inversion without Figure 3. Comparison of the original AirCore in situ profiles (red), smoothed AirCore profiles (black), prior profiles (blue dashed, taken from typical restrictions of Gaussian prior GGG2014), and the retrieved profiles (green: 95% posterior envelopes of and error distribution. When perform- the profiles accepted by the MCMC chain). ing the sampling in high dimensional problems the convergence may be slow and using dimension reduction with the MCMC is a tempting opportunity, which we will demonstrate here. We have used the efficient adaptive MCMC by Haario et al. [2001, 2006]. Despite that we have used the adaptive MCMC method and we have just a few parameters to estimate, MCMC method is still substantially slower than derivative-based point estimation methods. The computing time necessary for MCMC depends on the number of samples, number of parameters, used wavelength band, and the

computer resources. On a modern desktop PC (Intel Xeon 2.40 GHz), our current CH4 retrieval takes ∼1 min 40 s with 100,000 samples. In comparison, the LM estimation, which we always perform before MCMC to get good initial values, takes just a few seconds. As a Matlab code, SWIRLAB is not optimized for speed, but for user friendliness. It is not intended to be a serious operational processor for large data sets, but rather a tool for research and development. In many cases MCMC and LM give approximately the same results. This is especially true when the error estimate of the FTIR spectrum is correct, which means that the likelihood and the prior are in good balance. If the error estimate is substantially smaller (or larger) than the spectral ﬁt suggests, then the LM results become less reliable. With MCMC, the measurement error needs not to be known beforehand. Our adaptive MCMC algorithm allows estimation of the error during the sampling.

5. Results

In this section we apply the dimension reduction method for the retrieval of CH4 proﬁle information from FTIR data. We use FTIR measurements made at Sodankylä, Northern Finland, on 10 diﬀerent days between 3 September 2013 and 5 November 2014. For all of the investigated days, we have a reference in situ measurement made with the AirCore system. The measurements made on 19 March 2014 and 8 May 2014 are

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 10 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

Figure 4. Example of the full MCMC chain of the sampled parameters. Shown are every 100th sample from the chain of 100,000 samples. The dashed grey lines indicate the burn-in periods.

especially good test cases for our retrieval method, because on these two days the measured AirCore CH4 profile shapes differ substantially from the standard a priori profiles assumed for the stratospheric part of the profiles. This is most probably due to the polar vortex conditions on these days.

Figure 3 shows examples of the retrieved CH4 posteriors from the 10 investigated days using the covariance of equation (13). The three proﬁle shape parameters were estimated running 100,000 samples of MCMC. The ﬁrst 50,000 samples were discarded because the MCMC chain takes some time to adapt (this is called the

burn-in period). The other retrieved parameters were H2O prior location (one parameter), zero-level offset (one parameter), and the polynomial baseline (three parameters). The estimated values of these extra parameters are not so relevant for this study and omitted from the discussion. The profile shapes sampled by the MCMC were compared with the original priors (blue) and the AirCore soundings from the same days (red). To smooth the AirCore data using equation (26), the AirCore profiles were extrapolated to the retrieval grid

Figure 5. (top) Used wavelength band and an example SWIRLAB ﬁt. (bottom) Comparison of the residuals from the prior proﬁle scaling and dimension reduction methods using data from 19 March 2014.

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Figure 6. Examples of the CH4 averaging kernels from 19 March 2014. Shown are averaging kernels (top left) from GGG2014, and (top right) from SWIRLAB using prior proﬁle scaling. Averaging kernels from SWIRLAB using dimension reduction retrieval—(bottom left) for total column and (bottom right) a full averaging kernel matrix.

between 0 and 70 km. Thus, the smoothed AirCore curves (black) are somewhat ambiguous in the upper end of the proﬁles. We also note that AirCore provides dry-air mole fractions but SWIRLAB uses number density.

To convert between units, we used the prior air and H2O number density profiles. The comparison in Figure 3 is in wet-air mole fraction. In general, the agreement between the retrieved profiles and the AirCore profiles is very good. In all cases the 95% posterior envelope overlaps with the AirCore profile at almost all altitude levels. With the 19 March 2014

and 8 May 2014 data, our method correctly ﬁnds the steep gradient in the CH4 mole fraction at 10–20 km. In these polar vortex cases, the stratospheric part of the prior proﬁle is clearly incorrect. The MCMC samples

that generated the 19 March 2014 profile are shown in Figure 4. The three CH4 parameters drift relatively far from the initial point, which suggests strong data-based evidence of the profile information. Note that there is a positivity condition in the offset term. In the spectral fitting, we use a narrow wavelength band between 6003 and 6005.5 cm−1 (Figure 5, top). The

information about the CH4 gradient mainly comes from the two medium-strong lines centered at 6004.65 and 6004.86 cm−1. With an incorrect prior profile shape, the prior scaling method produces large residuals in these two lines, a discrepancy that can be improved by fitting three parameters for the profile shape (Figure 5, bottom). Examples of the averaging kernels from 19 March 2014, defined in equations (25) and (27), are shown in

Figure 6. For comparison, we also show the averaging kernels from the closest CH4 window used by GGG2014 and averaging kernels from the SWIRLAB version that scales prior proﬁles (GGG-type retrieval). Although not exactly from the same wavelength window, the GGG2014 averaging kernels (Figure 6, top left) and the corresponding SWIRLAB averaging kernels (Figure 6, top right) are visually very similar. The averaging kernels of the dimension reduction retrieval for the total column (Figure 6, bottom left) have a slightly diﬀerent shape and smaller variation during the day. In Figure 6 (bottom right) is one example of the full averaging kernel matrix.

To illustrate potential errors in the TCCON XCH4 when the prior proﬁle has incorrect shape, we show a comparison between TCCON, SWIRLAB, and AirCore XCH4 columns for 19 March 2014 (Figure 7). The Sodankylä

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Figure 7. Comparison of the XCH4 columns derived from FTIR and AirCore. Shown are the oﬃcial TCCON (orange) and corresponding AirCore (blue), the SWIRLAB dimension reduction (purple), and corresponding AirCore (brown). Also shown are the AirCore column without smoothing (black dashed) and the SWIRLAB prior scaling solution (green).

FTIR data from that day cover solar zenith angles between 67 and 82∘. TCCON provides averaging kernels in a 5∘ solar zenith angle grid; thus, we interpolated them for the solar zenith angles of the measurements. Both

AirCore and SWIRLAB XCH4 were derived according to the equations given in Wunch et al. [2011]. It would be better to estimate SWIRLAB XCH4 using the retrieved O2, but the current version of SWIRLAB does not yet allow O2 retrievals. There is a notable “U shape” in the TCCON XCH4, which is also visible in the smoothed AirCore. There is also a bias of around 16 ppb. Although the TCCON averaging kernels produce similar solar

zenith angle dependence to the reference measurements, we suspect that the TCCON XCH4 values may contain additional errors when the scaled prior has incorrect shape. The solar zenith angle dependence is substantially smaller in the AirCore columns smoothed using the SWIRLAB dimension reduction averaging

kernels, as expected (see Figure 6). The XCH4 values from SWIRLAB (dimension reduction) agree with AirCore within 5 ppb for solar zenith angles less than 75∘. There is a notable negative bias up to ∼30 ppb with larger solar zenith angles, which is most probably caused by systematic modeling errors remaining in the spectral ﬁt. The slope is even in the diﬀerent direction than the averaging kernels indicate. Finally, we note that the

prior XCH4 is ∼1820 ppb (not shown), quite far from the AirCore value.

6. Discussion The maximum amount of information can be extracted from the measurements using a full nonlinear retrieval and appropriate a priori information [Rodgers, 2000]. Defining an adequate prior is not always an easy task, and is open for criticism. Moreover, special cases like the polar vortex can be difficult to tackle in practice. When a full nonlinear retrieval is used in optimal estimation, it can lead to problems like instability of the vertical profile or physically unrealistic retrieval [Senten et al., 2012]. Several ideas to circumvent these issues have been developed in the literature; see, e.g., Tikhonov regularization and truncated singular value decom-

position discussed in Rodgers [2000]. Not surprisingly, the FTIR CH4 profile retrieval requires substantial regularization. For example, in Senten et al. [2012], the authors compare optimal estimation and Tikhonov regularization to IOA, and conclude that all these methods have some problems with the stability (but IOA is less sensitive to the choice of the prior covariance matrix). The main difference between the dimension reduction approach of this paper and most other approaches is that we solve the problem in low dimensional subspace rather than regularize the profiles in full space. In that sense, the approach used in this paper is closer to methods that use arbitrarily parameterized profile shape [e.g., Kuai et al., 2012; Yang et al., 2010]. The idea of the dimension reduction in atmospheric remote sensing is not new, and, for instance, Rodgers [2000] discusses this option also. However, there the idea is to represent the high-resolution profile with some linear representation and then to use, e.g., truncated singular value

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decomposition to solve the problem. It is left open how the actual projection to the lower dimension is created. In our approach (based on Marzouk and Najm [2009] and Solonen et al. [2016]), the singular value decomposition is applied to the prior covariance matrix, and the retrieval is constrained to the subspace spanned by these singular vectors.

7. Conclusions

In this paper we used the dimension reduction inversion method for the retrieval of CH4 profiles. Similar singular value truncation techniques have been used for decades to solve various ill-posed inversion problems. In our method we formulate the prior constraints so that the prior covariance reflects the information content of the observations and it can be expressed with a few significant principal components. Ideally, the number of these components (parameters) matches the number of degrees of freedom in the measurement. This approach is more flexible than the retrieval in a dense vertical grid with strong regularization, which is necessary when the vertical information content is modest in the measured signal but the number of unknowns in the state vector is large. The retrieval by the dimension reduction is not much constrained by the prior profile itself, its covariance just defines an informed subspace where smooth deviations from the prior profile are sought. In addition, by retrieving only a few parameters the algorithms become efficient to compute. We generated the prior covariance using general assumptions about the variability of atmospheric methane. The tropospheric part of the profile is generally quite well mixed, and stronger gradients are more common in the lower stratosphere. In the future, a large array of AirCore measurements would provide a good database for the construction of a more realistic prior covariance. We used the ACE-FTS satellite data to validate our prior assumption of the natural variability for altitudes between 10 and 30 km and found our constructed covariance reasonable. A more extensive characterization of the prior space would be a useful continuation study.

In this study, we retrieved three parameters to describe the shape of the underlying CH4 profile. The number of parameters depend on the prior covariance and the complexity of the proposal profiles one wishes to generate. More complex prior covariance requires more parameters to represent it. However, with SWIRLAB we can not currently aim for more complex representation of the profile. Although the Sodankylä FTIR data have excellent spectral resolution and signal to noise ratio, the modeling errors in the spectral fit prevent more information to be retrieved reliably. Missing constituents, spectroscopy errors, and uncertainty in the instrument line shape are common factors that complicate the spectral fit, and typically produce correlated residuals. With a too ambitious retrieval scheme, there is a danger of overfitting. Nevertheless, our analysis

shows that there is certainly more than one piece of information about the vertical shape of CH4 in the FTIR spectra. This information can be extracted even with our simplified forward model, at least when the solar zenith angle is less than 75∘. Inversion methods that scale fixed prior profile shape do not fully take advantage of all available information in the spectral data. 𝜶 We used MCMC for the estimation of the k parameters to produce posterior analysis of the CH4 profile. In contrast to using derivative-based optimization and linearized Gaussian uncertainty assumptions, MCMC samples from the true posterior of the solution. MCMC eventually finds the global optimum regardless of the starting point and returns a set of “acceptable” profiles around the optimum. This leads to more realistic uncertainty estimates for the profile shape and further for the total column. MCMC is usable here because we use only a small wavelength window making the forward model extremely fast to compute. In our setup, it 𝜶 takes a few minutes to estimate one profile with 100,000 samples. The k parameters can be estimated (with a few iterations) using the local gradient of the forward model, which could be done if the computation time is a priority. The AirCore system provides valuable data for validating the retrieved profiles. As shown in Figure 3, the agreement between the retrieved posteriors and the AirCore profiles is generally very good. AirCore profiles can be

also used in the validation of XCH4, although the extrapolation of the AirCore profiles causes uncertainty of around 5 ppb. At least in Sodankylä, the springtime TCCON XCH4 values often have a substantial dependence on the solar zenith angle—the values are smaller at noon than in the morning and evening. Because the averaging kernels of the prior scaling retrievals are very solar zenith angle dependent, the retrieved columns have dependency when the prior is far from the truth. This is not a major problem in comparisons, if the averaging kernel is used, but it is troublesome in data analyses that directly use the column values. Moreover, an incorrect prior profile shape causes additional uncertainty in the spectral fit and further in the retrieved column.

TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 14 Journal of Geophysical Research: Atmospheres 10.1002/2015JD024657

Figure 7 shows that in this case the actual XCH4 values may also contain bias, but most probably the discrepancy depends on many factors such as the forward model, used wavelength band, etc. By solving the true proﬁle shape, we are able to reduce the air mass artifact and bias in the integrated total column. Finally, we note that our retrieval method could be easily adapted for satellite measurements also. The signiﬁcant reduction of the state vector, i.e., the number of estimated parameters, would make it possible to use MCMC in the

OCO2CO2 proﬁle retrieval, for example.

Acknowledgments References This study was funded by the Finnish Meteorological Institute and the Aires, F., W. B. Rossow, N. A. Scott, and A. Chdin (2002), Remote sensing from the infrared atmospheric sounding interferometer instrument Academy of Finland (INQUIRE and 1. Compression, denoising, and first-guess retrieval algorithms, J. Geophys. Res. Atmos., 107(D22), 4619, doi:10.1029/2001JD000955. CARB-ARC projects). The authors Aumann, H., et al. (2003), AIRS/AMSU/HSB on the Aqua mission: Design, science objectives, data products, and processing systems, would like to thank the ACE team IEEE Trans. Geosci. Remote Sens., 41(2), 253–264, doi:10.1109/TGRS.2002.808356. for sharing their data (available Beer, R. (2006), TES on the Aura mission: Scientific objectives, measurements, and analysis overview, IEEE Trans. Geosci. Remote Sens., 44(5), at http://www.ace.uwaterloo.ca/ 1102–1105, doi:10.1109/TGRS.2005.863716. public.html). The SWIRLAB code is Bernath, P. F., et al. 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TUKIAINEN ET AL. RETRIEVAL OF FTIR CH4 PROFILES 16 FINNISH METEOROLOGICAL INSTITUTE Erik Palménin aukio 1 P.O.Box 503 FI-00101 HELSINKI 123 tel. +358 29 539 1000 CONTRIBUTIONS WWW.FMI.FI

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ON THE RETRIEVAL OF ATMOSPHERIC PROFILES

SIMO TUKIAINEN