ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-19-1207-2019Atmospheric band fitting coefficients derived from a self-consistent
rocket-borne experimentAtmospheric band fitting coefficientsGrygalashvylyMykhaylogryga@iap-kborn.dehttps://orcid.org/0000-0002-6702-3587EberhartMartinHedinJonashttps://orcid.org/0000-0001-5338-1538StrelnikovBorisLübkenFranz-JosefRappMarkushttps://orcid.org/0000-0003-1508-5900LöhleStefanhttps://orcid.org/0000-0002-1484-0532FasoulasStefanosKhaplanovMikhailGumbelJörgVorobevaEkaterinahttps://orcid.org/0000-0001-7680-5014Leibniz-Institute of Atmospheric Physics at the University Rostock in Kühlungsborn, Schloss-Str. 6, 18225 Ostseebad Kühlungsborn, GermanyDeutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, GermanyDepartment of Atmospheric Physics, Saint-Petersburg State University, Universitetskaya Emb. 7/9, 199034, Saint-Petersburg, RussiaDepartment of Meteorology (MISU), Stockholm University, Stockholm, SwedenUniversity of Stuttgart, Institute of Space Systems, Stuttgart, Germanyformerly at: Department of Meteorology (MISU), Stockholm University, Stockholm, SwedendeceasedMykhaylo Grygalashvyly (gryga@iap-kborn.de)31January20191921207122019July201812October201811January201914January2019This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://acp.copernicus.org/articles/19/1207/2019/acp-19-1207-2019.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/19/1207/2019/acp-19-1207-2019.pdf
Based on self-consistent rocket-borne measurements of temperature, the
densities of atomic oxygen and neutral air, and the volume emission of the
atmospheric band (762 nm), we examined the one-step and two-step excitation
mechanism of O2b1Σg+ for nighttime
conditions. Following McDade et al. (1986), we derived the empirical fitting
coefficients, which parameterize the atmospheric band emission
O2b1Σg+-X3Σg-0,0. This allows us to derive the atomic oxygen concentration from
nighttime observations of atmospheric band emission O2b1Σg+-X3Σg-0,0. The
derived empirical parameters can also be utilized for atmospheric band
modeling. Additionally, we derived the fit function and corresponding
coefficients for the combined (one- and two-step) mechanism. The simultaneous
common volume measurements of all the parameters involved in the theoretical
calculation of the observed O2b1Σg+-X3Σg-0,0
emission, i.e., temperature and density of the background air, atomic oxygen
density, and volume emission rate, is the novelty and the advantage of this
work.
Introduction
The mesopause region is essential to understanding the chemical
and physical processes in the upper atmosphere because this is the region of
coldest temperature (during summer at high latitudes) and highest turbulence
in the atmosphere (e.g., Lübken, 1997), the region of formation of such
phenomena as noctilucent clouds (NLCs) and polar mesospheric summer echoes
(PMSEs) (e.g., Rapp and Lübken, 2004), the region of gravity wave (GW)
breaking and the formation of secondary GWs (Becker and Vadas, 2018), and
the region of coupling between the mesosphere and thermosphere. This region is
characterized by different airglow emissions and, particularly, by the
emissions of the atmospheric band, which is produced by the excited state of
molecular oxygen O2b1Σg+. Airglow
observation in the atmospheric band is a useful method to study dynamical
processes in the mesopause region. There have been a number of reports of
GW detection in this band (Noxon, 1978; Viereck and Deehr,
1989; Zhang et al., 1993). Planetary wave climatology has been investigated
by the Spectral Airglow Temperature Imager (SATI) instrument
(López-González et al., 2009). In addition, the parameters of tides
have been reported from SATI (López-González et al., 2005) and high-resolution
Doppler imager (HRDI) observations (Marsh et al., 1999). In number
of works Sheese et al. (2010, 2011) inferred temperature from atmospheric
band observation. Furthermore, the response of mesopause temperature and
atomic oxygen during major sudden stratospheric warming was studied utilizing
atmospheric band emission by Shepherd et al. (2010). Various works have
focused on atmospheric band emission modeling with respect to gravity waves
and tides (e.g., Hickey et al., 1993; Leko et al., 2002; Liu and Swenson,
2003). The specific theory of the gravity wave effects on O2b1Σg+ emission was derived in Tarasick and Shepherd
(1992). Moreover, atmospheric band observations have been widely utilized to
infer atomic oxygen, which is an essential chemical constituent for energetic
balance in the extended mesopause region (e.g., Hedin et al., 2009, and
references there in), and ozone concentration (Mlynczak et al., 2001).
Although there is a large field of application of atmospheric band emissions,
there is a lack of knowledge on the processes of the O2b1Σg+ population. Two main mechanisms of nighttime
population (note that the daytime mechanisms are quite different; see, e.g.,
Zarboo et al., 2018) were proposed: the first is the direct population from a
three-body recombination of atomic oxygen (e. g. Deans et al., 1976); the
second is the so-called two-step mechanism, which assumes an intermediate
excited precursor O2* (e. g. Witt et al., 1984; Greer et
al., 1981). It has been shown by laboratory experiments that the first
mechanism alone has not explained observed emissions (Young and Sharpless,
1963; Clyne at al., 1965; Young and Black, 1966; Bates, 1988). The second
mechanism entails a discussion about the precursor excited state and
additional ambiguities in their parameters (e.g., Greer et al., 1981; Ogryzlo
et al., 1984). Thus, Witt et al. (1984) proposed the hypothesis that the
O2c1Σu- state is, possibly, the
precursor; López-González et al. (1992a) suppose that the precursor
could be O2(5Πg); and Wildt et al. (1991) found through laboratory
measurements that it could be O2A3Σu+.
Hence, the problem of identification is still not solved. The essential step
in this direction has been made after the ETON 2 (Energy Transfer in the
Oxygen Nightglow) rocket experiment. The ETON 2 mission yielded empirical fitting
parameters that allow us to either quantify the O2b1Σg+ (and consequently volume emission) by known
O or atomic oxygen by known volume emission values (McDade et
al., 1986). Despite the significance of this work, the temperature and
density of air (necessary for derivation) were taken from the CIRA-72 and MSIS-83
(Hedin, 1983) models. This leads to some degree of uncertainty (e.g., Murtagh
et al., 1990). Thus, more solid knowledge on these fitting coefficients based
on consistent measurements of atomic oxygen, the volume emission of the atmospheric
band, and temperature and density of the background atmosphere is desirable. In
this paper we present common volume measurements of these parameters
performed in the course of the WADIS-2 sounding rocket mission. In the next
section, we describe the rocket experiment and obtained data relevant for our
study. In Sect. 3, to make the paper easier to understand, we repeat some
theoretical approximations from McDade et al. (1986). The obtained results of
our calculations are discussed in Sect. 4. Concluding remarks and a summary are
given in the last section.
Rocket experiment description
The WADIS (Wave propagation and dissipation in the middle atmosphere: Energy
budget and distribution of trace constituents) sounding rocket mission aimed
to simultaneously study the propagation and dissipation of GWs and measure
the concentration of atomic oxygen. It comprised two field campaigns
conducted at the Andøya Space Center (ASC) in northern Norway
(69∘ N, 16∘ E). The WADIS-2 sounding rocket was launched
during the second campaign on 5 March 2015 at 01:44:00 UTC under
nighttime conditions. For a more detailed mission description, the reader is
referred to Strelnikov et al. (2017) and the accompanying paper by Strelnikov
et al. (2018).
The WADIS-2 sounding rocket was equipped with the CONE instrument to measure
absolute neutral air density and temperature with high spatial resolution,
an instrument for atomic oxygen density measurements (FIPEX; Flux Probe
Experiment), and an airglow photometer for atmospheric band (762 nm) volume
emission observation.
CONE (COmbined measurement of Neutrals and Electrons), operated by IAP
(Leibniz Institute of Atmospheric Physics at Rostock University), is a
classical triode-type ionization gauge optimized for a pressure range between
10-5 and 1 mbar. The triode system is surrounded by two electrodes:
whilst the outermost grid is biased to +3 to +6 V to measure electron
densities at a high spatial resolution, the next inner grid (-15 V) is
meant to shield the ionization gauge from ionospheric plasma. CONE is
suitable for measuring absolute neutral air number densities at an altitude
range between 70 and 120 km. To obtain absolute densities, the gauges are
calibrated in the laboratory using a high-quality pressure sensor, like a
Baratron. The measured density profile can be further converted to a
temperature profile assuming hydrostatic equilibrium. For a detailed
description of the CONE instrument, see Giebeler et al. (1993) and Strelnikov
et al. (2013). Molecular oxygen and molecular nitrogen are derived from CONE
atmospheric number density measurements and partitioning according to
the NRLMSISE-00 reference atmosphere (Picone et al., 2002).
The airglow photometer operated by MISU (Stockholm University, Department of
Meteorology) measures the emission of the molecular oxygen atmospheric band
around 762 nm from the overhead column, from which the volume emission rate
is inferred by differentiation. For airglow measurements in general, a filter
photometer is positioned under the nose cone viewing along the rocket axis
with a defined field of view (FOV). For WADIS-2, however, the FOV of ±3∘ was tilted from the rocket axis by 3∘ to avoid having
other parts of the payload within the FOV and at the same time roughly view
the same volume as the other instruments. The optical design is a standard
radiometer-type system with an objective lens, a field lens, aperture, and
stops, which provide an even illumination over a large portion of the
detector surface (photomultiplier tube) and a defined FOV. At the entrance of
the photometer there is an interference filter with a passband of 6 nm
centered at 762 nm. During ascent, after the nose cone ejection, the
photometer then counts the incoming photons from the overhead column (or
actually the overhead cone). When the rocket passes through the layer the
measured photon flux drops and above the emission layer only weak background
emissions are present (e.g., the zodiacal and galactic light). After the
profile has been corrected for background emissions and attitude (van Rhijn
effect) it is converted from counts to radiance using preflight laboratory
calibrations. The calibration considers the spectral shape of the 0–0 band
of the O2b1Σg+-X3Σg-0,0 atmospheric band system and the overlap of the
interference filter passband. The profile is then smoothed and numerically
differentiated with respect to altitude to yield the volume emission rate of
the emitting layer. The data were sampled with 1085 Hz, which results in an
altitude resolution of about 0.75 m during the passage of the airglow layer
(the velocity was ∼800 m s-1 at 95 km). However, because of the
high noise level, the profile needed to be averaged to a vertical resolution
of at least 3 km in order to get satisfactory results after the
differentiation. A more detailed description and review of this measurement
technique is given by Hedin et al. (2009).
The aim of the FIPEX developed by the IRS (Institute of Space Systems,
University of Stuttgart) is to measure the atomic oxygen density along the
rocket trajectory with high spatial resolution. It employs a solid electrolyte
sensor, which has a selective sensitivity to atomic oxygen. A low voltage is
applied between anode and cathode pumping oxygen ions through the electrolyte
ceramic (yttria-stabilized zirconia). The current measured is proportional to
the oxygen density. Sampling is realized with a frequency of 100 Hz and
enables a spatial resolution of ∼10 m. Laboratory calibrations were
done for molecular and atomic oxygen. For a detailed description of the FIPEX
instruments and their calibration techniques, see Eberhart et al. (2015,
2018).
Theory
Here, we are repeating the theory of O2b1Σg+-X3Σg-0,0 nighttime emissions
following McDade et al. (1986) to make our paper more readable, using all
nomenclature as in the original paper. All utilized reactions are listed in
Table 1, together with corresponding reaction rates, branching ratios,
quenching rates, and spontaneous emission coefficients. Some components have
been updated according to modern knowledge, thus deviating from the work of
McDade et al. (1986).
List of reactions with corresponding reaction rates (for three-body
reactions [cm6 molecule-2 s-1] and for two-body reactions
[cm3 molecule-1 s-1]), quenching coefficients, and
spontaneous emission coefficients (s-1) used in the paper.
ReactionCoefficientReference(R1)O+O+M⟶εk1O2b1Σg++Mk1=4.7×10-33(300/T)2ε – unknownCampbell and Gray (1973)(R2)O2b1Σg++O2⟶k2O2productsk2O2=7.4×10-17T0.5e-1104.7TZagidullin et al. (2017)(R3)O2b1Σg++N2⟶k2N2productsk2N2=8×10-20T1.5e503TZagidullin et al. (2017)(R4)O2b1Σg++O⟶k2Oproductsk2O=8×10-14Slanger and Black (1979)(R5)O2b1Σg+⟶A1O2+hv(762nm)A1=0.0834Newnham and Ballard (1998)(R6)O2b1Σg+⟶A2O2+hv(total)A2=0.088158Yankovsky et al. (2016)(R7)O+O+M⟶αk1O2*+Mα – unknown(R8)O2*+O2⟶γk3O2O2b1Σg++O2γ – unknown(R9)O2*+O2,N2,O⟶k3O2,k3N2,k3Oprodk3O2, k3N2, k3O – unknown(R10)O2*⟶A3O2+hvA3 – unknown
Assuming a direct one-step mechanism as the main one for the population and
that O2b1Σg+ is in photochemical
equilibrium, we can write its concentration as a ratio of production to the
loss term:
O2b1Σg+=εk1O2MA2+k2O2O2+k2N2N2+k2OO,
where k1 is the reaction rate for the three-body recombination of atomic
oxygen, ε is the corresponding quantum yield of O2b1Σg+ formation, A2 represents the spontaneous
emission coefficient, and k2O2, k2N2,
k2O are the quenching coefficients for reactions with
O2, N2, and O, respectively. Then the volume emission,
Vat, is obtained by multiplying the O2b1Σg+ concentration by the spontaneous emission
coefficient, A1, of Reaction (R5) (hereafter, nomenclature RX means the
reaction X for Table 1).
In the case of known temperature, volume emission, and concentrations of
O, O2, N2, and M, the quantum yield of
O2b1Σg+ formation can be calculated as
follows:
ε=VatA2+k2O2O2+k2N2N2+k2OOA1k1O2M.
In the case of the two-step mechanism, the unknown excited-state
O2* is populated at the first step from Reaction (R7). Then,
it can be deactivated by quenching (Reaction R9), spontaneous emission
(Reaction R10), or producing O2b1Σg+ by
Reaction (R8). Note that Reaction (R8) is one pathway of the overall
quenching Reaction (R9).
In the second step, O2* is transformed into O2b1Σg+, which can be deactivated by quenching
(Reactions R2–R4) and by spontaneous emission (Reaction R6). Assuming
photochemical equilibrium for O2* and, as before, for
O2b1Σg+, the volume emission in the
case of O2b1Σg+-X3Σg-0,0 is
Vat=A1αk1O2Mγk3O2O2A2+k2O2O2+k2N2N2+k2OOA3+k3O2O2+k3N2N2+k3OO,
where the quantum yield of O2* formation is α, the
quantum yield of O2b1Σg+ formation is
γ, the spontaneous emission coefficient is A3, and
k3O2, k3N2, k3O are unknown
quenching rates of O2*. Note that the assumption about
photochemical equilibrium for O2* and O2b1Σg+ is valid because the O2b1Σg+ radiative lifetime is less than 12 s and all
potential candidates for O2* have lifetimes less than several
seconds (e.g., López-González et al., 1992a, b, c; Yankovsky et
al., 2016, and references therein).
Collecting all known values on the right-hand side (RHS), all unknown
summands on the left-hand side (LHS), and omitting emissive summand A3
as noneffective loss (McDade et al., 1986), Eq. (3) can be rearranged as
follows:
CO2O2+COO=A1k1O2MO2VatA2+k2O2O2+k2N2N2+k2OO,
where CO2=1+k3N2N2k3O2O2αγ and CO=k3Oαγk3O2 are the fitting coefficients that can be calculated
by the least-squares fit (LSF) procedure. Such derivation assumes that the
coefficients are temperature independent (or temperature dependence is weak).
This means that the reaction rates k3 are assumed to be temperature
independent (dependence is weak) or have the same temperature dependency for
all quenching partners (N2, O2, O). Currently, this
statement on the basis of available information about potential precursors is
assumed true, but solid evidence is absent. We calculated them based on our
measurements and will discuss the results in the following section.
In a more general case the population of O2b1Σg+ occurs via both channels: one-step and two-step. We discuss such
processes in Sect. 4.3 and derive an expression for the corresponding
fit function in Appendix A.
Results and discussion
Figure 1 shows input data for our calculations: temperature from the CONE
instrument (Fig. 1a), number density of air (Fig. 1b), atomic oxygen
concentration measured by FIPEX (Fig. 1c), and volume emission at 762 nm
from the photometric instrument (Fig. 1d). A temperature minimum of ∼158 K was observed at 104.2 km. A local temperature peak was measured at
98.9 km with values of 204.5 K. The secondary temperature minimum was
visible at 95.4 km and amounted to ∼173 K. The atomic oxygen
concentration (Fig. 1c) had a peak of ∼4.7×1011 [cm-3] at
97.2 km and approximately coincided with the secondary temperature peak. The
peak of volume emission was detected between 95 and 97 km with values of
more than 1700 [phot. cm-3 s-1]; this is slightly beneath the
atomic oxygen corresponding maximum and slightly above the secondary
temperature minimum. Note that this points to the competition of temperature
and the atomic oxygen concentration in processes of atomic oxygen
excited-state O2b1Σg+ formation.
Independently of the mechanism of atmospheric band emission (Eq. 1 or Eq. 3),
the numerator is directly proportional to the square of the atomic oxygen
concentration and inversely proportional to the third power of the
temperature (via reaction rate k1 and M, considering the ideal gas
low). Our rocket experiment shows an essential difference of emissions
between ascending and descending flights (see Strelnikov et al., 2018). It
also demonstrates significant variability in other measured parameters,
including neutral temperature and density as well as atomic oxygen density
(Strelnikov et al., 2017, 2018). This suggests that, in the case of the
ETON 2 experiments, the temporal extrapolation of atomic oxygen for the time
of the emission measurement flight (which was approximately 20 min earlier)
may lead to serious biases in estimations because, as one can see from
Eqs. (1) and (3), volume emission depends on the atomic oxygen concentration
quadratically. Since the best-quality data were obtained during the descent
of the WADIS-2 rocket flight, we chose this data set for our analysis
(Strelnikov et al., 2018). The region above 104 km is subject to auroral
contamination. In the region below 92 km, negative values may occur in the
volume emission profile as a result of self-absorption in the denser
atmosphere below the emission layer. Hence, we considered the region near the
emission peak between 92 and 104 km as most appropriate for our study. The
comparisons of our measurements with other observations, as well as with the
results of modeling, are presented in several papers (e.g., Eberhart et
al., 2018; Strelnikov et al., 2018).
Measurements of (a) temperature (CONE), (b) number
density of air (CONE), (c) atomic oxygen concentration (FIPEX), and
(d) volume emission at 762 nm (photometer).
One-step mechanism
Figure 2 shows the quantum yield of O2b1Σg+ formation ε calculated according to Eq. (2), which is
necessary to form O2b1Σg+ under the
assumption that the direct three-body recombination of atomic oxygen is the
main mechanism. The uncertainties for this figure (as well as for other
figures) were calculated according to a sensitivity analysis (von Clarmann,
2014; Yankovsky and Manuilova, 2018, their
Appendix 1; Vorobeva et al., 2018), for which the errors represent error propagation from
the experimental data. Calculated values of ε are placed in the
range [0.07; 0.13], which is in good agreement with the values derived by
McDade et al. (1986). The averaged value amounts to 0.11±0.02. The range
of values, taking into account both the variance and the error range, amounts
to [0.02; 0.22]. By the physical nature of this value, the quantum yield of
O2b1Σg+ formation should not depend on
altitude. Figure 2 shows some altitude dependence of central values of
ε, but considering the large error range, there is no clear
altitude dependence. The variability of the data points is much smaller than
the errors of the individual points. Hence, in light of the analysis of our
rocket experiment, we may not reject the direct excitation mechanism.
Quantum yield of O2(b1Σg+) formation
ε for the case of the one-step mechanism.
Although the population via the one-step mechanism alone is, generally speaking,
possible, it is improbable because laboratory experiments show that
direct excitation alone may not explain observed emissions (Young and
Sharpless, 1963; Clyne at al., 1965; Young and Black, 1966; Bates, 1988).
This conclusion is in agreement with the conclusion from McDade et
al. (1986), which stated that the one-step excitation mechanism is not
sufficient to explain the O2b1Σg+
population. Hence, in the following, we check the second energy transfer
mechanism.
Two-step mechanism
Figure 3 depicts the altitude profile of the RHS of Eq. (4)
and the profile calculated by the LSF. The fitting
coefficients, CO2 and CO, resulting from this fit
amount to 9.8+6.5-5.3 and 2.1-0.6+0.3, respectively. The
uncertainties were calculated, as is common for LSF (Bevington and Robinson,
2003), based on error propagation from the RHS as provided in Fig. 3. Our
CO2 coefficient is partially, within the error range, in agreement
with CO2 coefficients given in McDade et al. (1986), which amount
to 4.8±0.3 and 6.6±0.4 for temperature from CIRA-72 and MSIS-83,
respectively. The CO coefficient is approximately 1 order lower.
There are several possible reasons for the large discrepancy in CO,
for example the temperature dependence of the O quenching or that, in
the case of ETON 2 experiments, mean temperature profiles from the models
CIRA-72 and MSIS-83 were utilized, which does not reproduce any short-time
dynamical fluctuations, solar cycle conditions, etc. In the framework of our
analysis, we may not identify the reason for the large discrepancy in
CO more precisely. Fitting coefficients defined in such a way
(Eq. 4) do not have a direct physical meaning. However, they have a physical
meaning in several limit cases. If the quenching coefficients of a precursor
with molecular nitrogen are much smaller than those with molecular oxygen
k3N2≪k3O2, then αγ=1CO2. The assumption that the quenching of the
precursor with N2 is much slower than quenching with O2 is just
a working hypothesis, which is commonly used for the analysis of possible
precursors
(e.g., McDade et al., 1986; López-González et al., 1992a, b; and
references therein). It is true for such potential precursors as
O2A3Σu+ (Kenner and Ogryzlo, 1983b),
but generally, there is no evidence for or against that. If it is
not true, any definite conclusion on precursors by known CO2 is not
possible. In our case αγ=0.102-0.041+0.120. In other
words, in the case of the two-step formation of O2b1Σg+ with energy transfer agent O2, the total
efficiency η=αγ amounts to 10.2 %, which is the lowest
amongst known values. Based on rocket experiment data analysis (ETON), Witt
et al. (1984) obtained αγ=0.12–0.2. According to McDade et
al. (1986) for the case with k2O=8×10-14, the total
efficiencies are 0.15 and 0.21 for temperature profiles adopted from MSIS-83
and CIRA-72, respectively. The analyses of López-González et
al. (1992a, c), which adopted O2, N2, and temperature profiles from
the model (Rodrigo et al., 1991), showed a total efficiency of 0.16. In
contrast to our work, all investigations mentioned above utilized
temperature and atmospheric density from models that describe a mean state
of the atmosphere. This is a possible reason for discrepancy in the results.
Total efficiency η may serve as an auxiliary quantity to identify the
precursor. According to the physical meaning of efficiency, it may not be
larger than 1. Hence, α and γ, as well as the total efficiency, are
smaller than 1. Consequently, γ=ηα<1, and we
can examine potential candidates for O2* with this criterion.
From an energetic point of view, only four bound states of molecular oxygen
can be considered as an intermediate state for the O2b1Σg+ population: O2A3Σu+, O2A′3Δu, O2c1Σu-, and
O2(5Πg) (Greer et al., 1981; Wraight, 1982; Witt et
al., 1984; McDade et al., 1986; López-González et al., 1992c). For
better readability, we will partially repeat a table from
López-González et al. (1992b, c) with known α in our work
(Table 2). From Table 2, it can be seen that only O2A′3Δu and O2(5Πg) fit the
criterion of γ=0.102α<1. At a lower limit of
uncertainty γ=0.061α<1O2A′3Δu and
O25Πg satisfy the criterion and,
considering the upper limit (γ=0.222α<1), only
O2(5Πg) may serve as a precursor.
Efficiencies α of the different excited states of
O2.
O2(c1Σu-)O2(A′3Δu)O2(A3Σu+)O2(5Πg)Reference0.030.120.040.66Wraight (1982), Smith (1984)0.040.180.060.5Bates (1988)0.030.180.060.52López-González et al. (1992a, b, c)
RHS (dots) and least-squares fit of LHS (black line) of Eq. (4).
Atomic oxygen concentration: FIPEX (black line); model MSIS00 (red
line); derived from emission observation with McDade et al. (1986)
coefficients (blue line); calculated with newly derived fitting coefficients
for the two-step mechanism (green line).
The second expression that helps to clarify the choice of the precursor is
the ratio of quenching rates. In the limit of low quenching with molecular
nitrogen k3N2≪k3O2, the ratio of
fitting coefficients equals the ratio of the quenching rates of atomic and
molecular oxygen CO/CO2=k3O/k3O2. An analysis from the ETON 2
rocket experiment yields values for the quenching coefficient ratios of potential
precursors of 3.1 and 2.9 for temperature from CIRA-72 and MSIS-83,
respectively. This is close to the value from Ogryzlo et al. (1984), who
found k3O/k3O2=2.6 by laboratory measurements;
however, as was noted in their work, substitution of these values into the
equation for emission yields 16 % of the observed emission (Ogryzlo et
al., 1984). These findings point to the possibility of a too-high measured
ratio k3O/k3O2 as a result of too-strong
quenching of the precursor by atomic oxygen. Our value of quenching ratios
k3O/k3O2 amounts to 0.21-0.12+0.32.
There is not enough information on measured values for bound states of
molecular oxygen. Laboratory measurements for O2A3Σu+(v=0-4), O2A3Σu+(v=2), and O2c1Σu- infer the
values of the k3O/k3O2 ratio to be 30±30,
100±15, and 200±20, respectively (Kenner and Ogryzlo, 1980, 1983a,
b, 1984). On the other hand, Slanger et al. (1984) found that the lower limit of
O2A3Σu+(v=8) quenching by O2
must be ≥8×10-11. If the results from Slanger et al. (1984)
were applied to the results from Kenner and Ogryzlo (1980, 1984) for
k3O2, then the ratio of k3O/k3O2
would be 2 orders lower. This short discussion illustrates a strong
scattering of this ratio. For our two potential candidates (O2A′3Δu and O2(5Πg)), there is
information about the k3O/k3O2 ratio for only
O2A′3Δu. Through the comprehensive
analysis of known rocket experiments, López-González et al. (1992a,
b, c) inferred that the upper limit of the ratio amounts to 1. Hence, our
value of k3O/k3O2=0.21-0.12+0.32
agrees with this result. Consistent information from laboratory experiments
on the ratio for O2(5Πg) is absent. Thus, we can propose
as potential candidates for precursors both O2A′3Δu and O2(5Πg); however, we
are not able to identify which of these two is more preferable.
In order to illustrate the application of the newly derived fitting
coefficients we compare in Fig. 4 the atomic oxygen concentration from FIPEX
(black line), from the NRL MSISE-00 reference atmosphere model (Picone et
al., 2002) (red line) calculated with McDade et al. (1986) coefficients
(blue line), and our fitting coefficients for the two-step mechanism
(green line). In the region 94–98 km, i.e., at atomic oxygen peak and volume
emission peak (see Fig. 1d), fitting coefficients from this paper reproduce observed values better than
the McDade coefficients (MSIS-83 case). Our fitting
coefficients and the fitting coefficients of McDade give a similar approximation
above the atomic oxygen peak (∼98–104 km). The shape of the calculated
profiles appears slightly different, with the peak maximum at a higher
altitude than the observed. In this, our result resembles the McDade results,
probably because in both cases the ratio of two reaction rates is derived,
but not the rates themselves. In the lower part our results and those of
McDade differ because our CO2 value is larger and the term with
molecular oxygen dominates. Nevertheless, the atomic oxygen retrieved with
our fitting coefficients satisfactorily reproduces measurements, especially
at the peak.
Combined mechanism
In the most general case, the O2b1Σg+
population passes through two channels: directly and via a precursor. In fact,
theoretical calculations from Wraight (1982) and laboratory measurements from
Bates (1988) predicted a direct population with efficiencies of 0.015 and
0.03, respectively, which is not sufficient to explain the observed emissions
(Bates, 1988; Greer et al., 1981; Krasnopolsky, 1986). A similar value,
ε=0.02, was shown in the analysis by López-González et
al. (1992b, c). We investigated a combined mechanism based on the LSF
calculation and fit function (derivation in Appendix A):
O2+D1OD2+ε̃1+D1OO2=A1k1O2MO2VatA2+k2O2O2+k2N2N2+k2OO,
where hereafter tildes denote that these are values for the combined
mechanism and do not equal the values for one-step or two-step mechanisms
(Sect. 4.1 and 4.2); D1=k̃3Ok̃3O2 and D2=α̃γ̃ are
the fitting coefficients, which refer to the ratio of quenching rates and
η̃≡α̃γ̃ total efficiency for the
two-step channel, respectively. The fitting coefficients were calculated for
two limit cases, ε̃=0.015 (Wraight, 1982)
ε̃=0.03 (Bates, 1988), and for the averaged case
ε̃=0.022.
The results for the best fit in each case are listed in Table 3. Analogously
to the two-step mechanism (Sect. 4.2), for the case of the combined mechanism
γ̃=η̃α̃<1; hence, the
precursor should satisfy α̃>0.08-0.04+0.12 (see
Table 3). For central values of α̃, only O2A′3Δu and O2(5Πg) satisfy this
criterion (see Table 2). At a lower limit of uncertainty (α̃>0.04)O2A′3Δu, O2A3Σu+, and O2(5Πg) satisfy the
criterion and, considering the upper limit (α̃>0.2), only
O2(5Πg) may serve as a precursor. The upper limit of the
ratio k3Ok3O2<1 for O2A′3Δu, derived by López-González et
al. (1992a, b, c), is in agreement with our calculations
(0.231-0.142+0.358). As noted above, the ratio for
O2(5Πg) is unknown. Consequently, taking into account
both conditions, only O2A′3Δu and
O2(5Πg) may serve as precursors.
Fitting coefficients for the combined mechanism (Eq. 5) at different
efficiencies.
Figure 5 illustrates a sanity check for volume emissions derived (black
lines) with the fitting coefficients of McDade et al. (1986) for the MSIS-83
(Fig. 5c) case, the CIRA-72 case (Fig. 5d), and with our newly derived fitting
coefficients for the two-step (Fig. 5a) and combined ε̃=0.022 mechanisms (Fig. 5b) in comparison with the measured one (red
lines). All of the derived volume emission profiles (black lines) were calculated
based on the temperature, concentration of surrounding air, and concentration
of atomic oxygen from our rocket launch. The calculations with the combined
mechanism (Eq. 5) and two-step energy transfer mechanism (Eq. 4) give almost
identical results. The results obtained with the new fitting coefficients are in
satisfactory agreement with the measured volume emissions at the peak and
above, whereas the McDade coefficients related to temperature from
CIRA-72 give better approximations below the volume emission peak (92 km).
The coefficients of McDade related to temperature from MSIS-83 are in
better agreement with our results and are almost identical above the volume
emission peak. More independent common volume in situ measurements are
necessary to validate these results.
Volume emissions: photometer (red line); derived from atomic oxygen
(black line) with (a) newly derived fitting coefficients for the
two-step mechanism, (b) with fitting coefficients for the combined
mechanism, (c) with McDade et al. (1986) coefficients that
correspond to MSIS-83 temperature, and (d) with McDade et al. (1986)
coefficients that correspond to CIRA-72 temperature.
Summary and conclusions
Based on the rocket-borne common volume
simultaneous observations of atomic oxygen, atmospheric band emission
(762 nm), and density and temperature of the background atmosphere, the
mechanisms of O2b1Σg+ formation were
analyzed. Our calculations show that one-step direct excitation alone is less
probable for the reasons discussed above (Sect. 4.1).
For the case of the two-step mechanism, we found new coefficients for the fit
function in accordance with McDade et al. (1986) based on self-consistent
temperature, atomic oxygen, and volume emission observation. These
coefficients amounted to CO2=9.8+6.5-5.3 and
CO=2.1-0.6+0.3. The CO2 coefficient is partially,
within the error range, in agreement with CO2 coefficients given
in McDade et al. (1986), and the CO coefficient is approximately 1
order lower. The general implication of these results is the parameterization of
volume emission in terms of known atomic oxygen. This can be utilized either
for atmospheric band volume emission modeling or for the estimation of atomic
oxygen by known volume emission. We identified two candidates for the
intermediate state of O2*. Our results show that
O2A′3Δu or
O2(5Πg) may serve as a precursor.
Taking into account both channels of O2b1Σg+ formation, we proposed a combined mechanism. In this case, atomic
oxygen via volume emission or volume emission based on known atomic oxygen
can be calculated by Eq. (5). The recommended fitting coefficients amounted to
D1=0.231-0.142+0.358 and D2=0.08-0.04+0.12, with
the efficiency of the direct channel as ε̃=0.022. These
coefficients have a mean total efficiency
(α̃γ̃=0.08-0.04+0.12) and a ratio of
quenching coefficients (k̃3O/k̃3O2=0.231-0.142+0.358) for the two-step channel. The analysis of their
values indicates that O2A′3Δu and
O2(5Πg) may serve as possible precursors for the two-step
channel in the combined mechanism. In the context of our rocket experiment, we do
not have the possibility to figure out which mechanism is true. Nevertheless,
we consider the combined mechanism as more relevant to nature because it has
a higher generality. This conclusion does not contradict the current point
of view that the two-step mechanism is dominant because ε̃
is assumed to be 1.5 %–3 %. Moreover, it is possible that in
reality the mechanism is much more complex and it has a multichannel or more
than two-step nature. Undoubtedly, more common volume simultaneous
observations of the atmospheric band and atomic oxygen concentrations
would be desirable to confirm and improve these results.
The rocket-borne measurements and calculated data shown in
this paper are available via the IAP ftp server at
ftp://ftp.iap-kborn.de/data-in-publications/GrygalashvylyACP2018 (last
access: 25 January 2019).
We consider photochemical equilibrium for the nighttime O2b1Σg+ concentration. If O2b1Σg+ is produced via both channels, the equilibrium
concentration is given by the following expression:
O2b1Σg+=ε̃k1O2M+γ̃k̃3O2O2O2*A2+k2O2O2+k2N2N2+k2OO,
where the tilde denotes the combined mechanism, A1,
k1k2O2, k2N2, k2O,
k̃3O2 are the ratios for the corresponding processes (see
Table 1), and O2* is the unknown precursor.
Considering this precursor in photochemical equilibrium, we can obtain the
following expression for its concentration:
O2*=α̃k1O2MÃ3+k̃3O2O2+k̃3N2N2+k̃3OO,
where efficiency is α̃, Ã3 is the unknown spontaneous
emission coefficient of O2*, and k̃3O2,
k̃3N2, k̃3O are the unknown
quenching rates for O2*.
Substituting (A2) into (A1) and into the expression for volume emission we
obtain
Vat=A1O2b1Σg+=A1k1O2O2MA2+k2O2O2+k2N2N2+k2OOε̃O2+α̃γ̃k̃3O2Ã3+k̃3O2O2+k̃3N2N2+k̃3OO.
We assume that, in analogy with a two-step mechanism, a spontaneous emission
A3̃ of O2* is much smaller than the quenching, and
we utilized a traditional assumption about low quenching with molecular
nitrogen k̃3N2≪k̃3O2, which is commonly used to analyze a potential precursor. In this
case, Eq. (A3) can be rearranged as follows:
O2+k̃3Ok̃3O2Oα̃γ̃+ε̃1+k̃3Ok̃3O2OO2=A1k1O2MO2VatA2+k2O2O2+k2N2N2+k2OO.
We defined unknown fitting coefficients D1≡k̃3Ok̃3O2 and D2≡α̃γ̃. Expression (A4) was utilized to calculate them
with LSF.
The authors contributed equally to this work.
The authors declare that they have no conflict of
interest.
This article is part of the special issue “Layered phenomena in
the mesopause region (ACP/AMT inter-journal SI)”. It is a result of the LPMR
workshop 2017 (LPMR-2017), Kühlungsborn, Germany, 18–22 September 2017.
Acknowledgements
The authors are thankful to Valentin Andreevich Yankovsky, William Ward, and
Gerd Reinhold Sonnemann for helpful suggestions and useful discussions. This
work was supported by the German Space Agency (DLR) under grant 50 OE 1001
(project WADIS). The authors thank DLR-MORABA for their excellent
contribution to the project by developing the complicated WADIS payload and
campaign support together with the Andøya Space Center, as well as
Hans-Jürgen Heckl and Torsten Köpnick for building the rocket
instrumentation. The authors are thankful to coeditor Bernd Funke for help in
evaluating this paper and to three anonymous referees for their useful
comments and improvements to the paper.
The publication of this article was funded by the Open Access
Fund of the Leibniz Association.
Edited by: Bernd Funke
Reviewed by: Miriam Sinnhuber and two anonymous referees
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