I investigate the nightly mean emission height and width of the
OH* (3–1) layer by comparing nightly mean temperatures measured by
the ground-based spectrometer GRIPS 9 and the Na lidar at ALOMAR. The
data set contains 42 coincident measurements taken between November 2010 and
February 2014, when GRIPS 9 was in operation at the ALOMAR observatory
(69.3∘ N, 16.0∘ E) in northern Norway. To closely resemble the
mean temperature measured by GRIPS 9, I weight each nightly mean temperature
profile measured by the lidar using Gaussian distributions with 40 different
centre altitudes and 40 different full widths at half maximum. In principle,
one can thus determine the altitude and width of an airglow layer by finding
the minimum temperature difference between the two instruments. On most
nights, several combinations of centre altitude and width yield a temperature
difference of ±2 K. The generally assumed altitude of 87 km
and width of 8 km is never an unambiguous, good solution for any of
the measurements. Even for a fixed width of ∼ 8.4 km, one can
sometimes find several centre altitudes that yield equally good temperature
agreement. Weighted temperatures measured by lidar are not suitable to unambiguously
determine the emission height and width of an airglow layer.
However, when actual altitude and width data are lacking, a comparison with
lidars can provide an estimate of how representative a measured rotational
temperature is of an assumed altitude and width. I found the rotational
temperature to represent the temperature at the commonly assumed altitude of
87.4 km and width of 8.4 km to within ±16 K, on
average. This is not a measurement uncertainty.
Introduction
To evaluate whether the common assumption of a nightly mean hydroxyl
(OH) layer emission altitude of 87 km and a fixed width of 8 km is justified, I compare temperatures measured by the Na
lidar at ALOMAR with OH* (3–1) rotational temperature measured by
GRIPS 9. Both instruments were located at the ALOMAR observatory
(69∘ N) in Norway between November 2010 and February 2014, resulting in
42 coincident measurements. To determine the emission altitude and width of
the OH* (3–1) layer, I compute Gaussian-weighted mean lidar
temperatures for different centre altitudes and widths to resemble the
temperatures measured by GRIPS 9. In principle, the minimum of the
temperature difference then yields an estimate of the emission altitude and
width of the OH* (3–1) layer.
The emission altitude and width of the mesospheric OH* layer are
essential quantities not only for the determination of temperature trends
e.g., but also for the comparison with
temperature measurements by meteor radars, satellites, and resonance lidars.
Typically, studies of ground-based infrared observations assume a stationary
emission altitude of 87 km and a full width at half maximum (FWHM) of
about 8 km, which correspond roughly to recommended values given by
.
Apart from satellite-based observations and the direct measurement by
rockets, the OH* emission layer height has been estimated by comparing
ground-based measurements of the OH* rotational temperature with
temperature measurements by lidars. From such a comparison of three nights of
data, found an emission layer altitude of
(86 ± 4) km. The FWHM of Gaussian function was fixed at
8.4 km.
Fig. 4 compared nightly mean temperatures of the
Advanced Mesospheric Temperature Mapper to those measured by an Na lidar located in Logan, Utah.
Their results show that, for a Gaussian-shaped weighting function centred at
87 km and a full width at half maximum of 9.3 km, the
Na lidar temperatures are apparently warmer than those measured by the
OH* imager on average . The centre altitude was
not varied in these studies, and lidar temperatures appear to be warmer by
roughly 10 K on average , while the difference
exceeds 20 K on certain days . Such a
temperature difference can in principle be a systematic measurement error. By
varying the centre altitude and the FWHM of the applied Gaussian function, I
clarify whether such a temperature difference between the Na lidar and
GRIPS 9 can also arise because of the choice of parameters. From the
temperature difference at each day, I estimate how representative the
OH* (3–1) rotational temperature is of the temperature at 87 km, assuming a stationary width of 8.4 km.
Instruments and methods
I use temperature measurements made by the Ground-based Infrared P-branch
Spectrometer (GRIPS) 9, which probes the OH* (3–1) vibrational
transition, and the Na lidar at ALOMAR. The ALOMAR observatory is
located at 69.3∘ N, 16.0∘ E. The time period covered by
GRIPS 9 at ALOMAR extends from October 2010 to May 2014. For this study, I
only analyse lidar data from measurements in darkness, as GRIPS can only
observe the OH* nightglow. This means that there is hardly any or no
data from GRIPS 9 between May and August. Lidar observations are limited to
clear nights. The data set consists of 42 coincident measurements with both
instruments' nightly temperature time series restricted to the same periods
of time. The nightly mean temperatures computed from GRIPS 9 are based on
measurements with a temporal resolution of one minute.
Nightly mean temperature profiles and standard error (grey shaded
areas) measured by the Na lidar at ALOMAR. Also shown is the mean
temperature and the standard error measured by GRIPS 9 during the same period
of time. This temperature is plotted at an altitude of 87.4 km and
the vertical error bars are meant to indicate a hypothetical full width at
half maximum of 8.4 km. Date and common measurement duration:
(a) 13 December 2010, 04:22 h; (b) 22 January 2012,
13:46 h; (c) 8 November 2013, 03:10 h; (d)
8 December 2013, 14:17 h.
The GRIPS instruments were described by . GRIPS uses
an InGaAs array detector to measure the airglow spectrum between
approximately 1522 nm and 1545 nm. Rotational temperatures
are derived from the OH* (3–1) P1-branch. The rotational lines of
this vibrational level are less affected by non-local thermodynamic
equilibrium effects compared to higher vibrational levels
. The analysis of GRIPS data is described in
Sect. 3.3. One detail is worth mentioning: the
derived temperature is sensitive to the Einstein coefficients used in the
analysis e.g.,. To derive temperatures from GRIPS
data, Einstein coefficients published by are used. Using
Einstein coefficients published by instead of those
by leads to apparent OH* (3–1) temperatures colder by
(3.5±0.3) K, on average (Carsten Schmidt, personal
communication, 2015).
The two instruments used in this analysis were co-located, but their fields
of view differed considerably. The Na lidar has a field of view of
600 µrad, which corresponds to 9×10-3km2 at an
altitude of 87 km. The nominal field of view of GRIPS derived from
the F-number of the spectrograph is 15∘. A
laboratory assessment of the field of view of GRIPS revealed that the
effective acceptance angle is slightly smaller (∼ 14∘ instead
of 15∘). Nevertheless, the field of view of GRIPS 9 is larger than
400 km2 at 87 km. Although the fields of view overlap or
are close to each other (depending on the lidar zenith angle), one cannot
expect the measured temperatures to be exactly equal. Due to waves and other
processes, atmospheric temperature varies across the field of view of GRIPS
on various scales, and the lidar probes only a small part of this volume.
Each of the lidar's two beams has 300 altitude channels with a time
resolution of 1 µs, yielding a nominal altitude resolution of 150 m in the zenith direction. Therefore, a temperature profile consists
of many independent measurements. The difference in measured temperature by
the lidar's two beams is an estimate of the horizontal temperature
variability. Usually, one beam points to the north at a zenith angle of
20∘ and the other beam to the east at the same zenith angle. At an
altitude of 92 km, the horizontal distance between the two beams is
approximately 50 km. For each of the 42 nights, I choose lidar data
from the beam with the smallest temperature uncertainty and only
temperatures with an uncertainty smaller than or equal 5 K. Whether
one computes the mean temperature profile from only one beam or from the
average of both, has a negligible effect on this analysis (see Figs. S5 to
S46 in the Supplement); the mean temperature profiles measured by the two
beams differ little in shape and absolute temperature.
The resulting daily mean temperature profile from the chosen beam is then
weighted with a Gaussian function. To identify the parameters of best
agreement between the two instruments, the weighting needs to be performed
with different centre altitudes and FWHM of the Gaussian weighting function.
I choose 40 centre altitudes between 81.8 km and 92.8 km, and
40 FWHM between 4.7 km and 15.7 km. The bins are separated by
282 m, which is twice the altitude resolution of the lidar at a
zenith angle of 20∘.
For each centre altitude z and full width at half maximum d, the weighted
nightly mean temperature T‾ is given by the
following equation:
T‾z,d=∑h=0NfhTh,
where fh is the weighting factor at each altitude h, corresponding to
the choice of z and d, between the lowest and highest useable altitude.
The temperature at a given altitude h in the nightly mean temperature
profile is denoted by Th.
The nightly mean temperatures could have been weighted with their
corresponding uncertainty, but this is not how the nightly mean temperature
is calculated from spectrometer data. Besides, the assumption of a Gaussian
distribution is a simplification. For example, it is possible that the real
OH* layer has a shape best approximated by a skewed or a multi-peak
Gaussian distribution. Individual OH* profiles measured by sounding
rockets generally do not have a Gaussian shape, while
average profiles calculated from rather short observation intervals
can be well-approximated by a Gaussian distribution
Fig. 8. The GRIPS 9 data were taken with a
one-minute resolution, from which I computed a nightly mean temperature.
This is similar to the data shown in , justifying this
simplification of a Gaussian distribution. The effect of using different
weighting functions, despite all of them being approximately Gaussian, to compute an
OH* (3–1) equivalent temperature has been shown to be smaller than
3 K for any of the functions considered .
For nightly mean data, which I consider here, there does not seem to be any
evidence for a distribution substantially different from a Gaussian shape.
See Sect. 4 of the Supplement to this article for a digression on this topic.
Results and discussion
Nightly mean temperature difference between GRIPS 9 and artificial
OH* (3–1) temperatures from the Na lidar at
ALOMAR for the same days shown in Fig. 1. Temperature difference is
shown as △T(z,d)=TOH*(3-1)-T‾z,d
and is a function of chosen centre altitude and full width at half maximum.
Weighted temperatures are calculated despite possibly missing data at the
boundaries. Positive values indicate that GRIPS 9 measured an apparently
warmer temperature than observed by the lidar for the given parameters. The
0-contour line indicates exact agreement. Measurement durations are given in
Fig. .
The nightly mean temperatures, measured by the Na lidar at ALOMAR, for
four arbitrary nights (see the Supplement for full data set) are shown in
Fig. . The nightly mean OH* (3–1) rotational temperature
measured by GRIPS 9 is also shown, but note that I have assumed this
temperature as representative of the OH* (3–1) layer at 87.4 km with a full width at half maximum of 8.4 km.
To determine how well the temperatures, measured independently by the two
instruments, actually agree, I compute the nightly mean Gaussian-weighted Na lidar
temperature from the temperature profiles shown in Fig. for 40
different centre altitudes and 40 different FWHM. To find the altitude of the
best agreement, I calculate the absolute temperature difference between GRIPS
9 and the OH* (3–1)-equivalent temperatures calculated from the
Na lidar data. This allows one, in principle, to find the centre
altitude and full width at half maximum where the temperature difference is
smallest, that is, where the agreement is best.
One may argue that this analysis is too general, because, for instance, I have also chosen
centre altitudes or full widths at half maximum which seldom or never occur
in reality. While this is probably true, at least to some
extent, restricting the analysis to narrower layer widths and fewer centre
altitudes would only change a numerical result, if I were to compute a mean
centre altitude. However, as will be evident, it is not advisable to compute
such statistics from these data because of the inherent ambiguity.
Hypothetically, in case the measured temperature profile were not the true
temperature profile, but offset from the truth by a certain value, the effect
on the results would be similar to that of a different set of Einstein
coefficients: any ambiguity would remain, only the values of the
altitude-dependent
and width-dependent temperature difference would change.
The ambiguity is visible in Fig. , which shows the difference of
the nightly mean temperatures for the different centre altitudes and FWHM for
four nights. The temperature difference is given by the following equation:
△T(z,d)=TOH*(3-1)-T‾z,d,
where z is the centre altitude of the Gaussian weighting function, and d
is its full width at half maximum. Positive temperature differences thus
indicate that the temperatures measured by GRIPS 9 are warmer than the
weighted temperatures measured by the Na lidar.
Figure shows that there is, in most cases, more than one
combination of centre altitude and full width at half maximum that yield the
smallest temperature difference – regardless of the measurement duration. A
temperature agreement of △T≤2K
can often be obtained from several combinations of centre altitude and full
width at half maximum. Even with the width fixed at, say, 8.4 km,
there are nights on which the altitude determination is ambiguous, see
Fig. c: the nightly mean altitude may be either
∼ 84 km or ∼ 90 km. Both are realistic values
. Even if the width of the OH* (3–1) layer is
taken into account, one cannot determine its altitude unambiguously from the
temperature measurements by lidar. However, not taking the FWHM into account
might give false confidence in a so-determined altitude, because the
ambiguity might be invisible.
Temperature differences between the two instruments of |T|≥10K can arise simply from assuming a certain fixed width of
the OH* layer. On a few nights, the mean temperatures differ by more
than 10 K for all sensible combinations of centre altitude and full
width at half maximum (see Fig. b). Thus, I argue that a systematic
temperature offset between the instruments cannot be detected beyond doubt
and that apparent offsets are not necessarily caused by real systematic
effects.
Other notable observations are that the temperature agreement can be almost
independent of the chosen parameters, see Fig. b, and that,
generally, the agreement is not best at a mean centre
altitude of 87.4 km and a
mean full width at half maximum of
8.4 km. Still, the results do not undermine
the assumption that the OH* rotational temperature can be used as an
estimate of the nightly mean temperature at 87 km.
In an ideal case, an emission profile is available for the interpretation of
ground-based rotational temperature measurements. However, this is rather
seldom the case. Whenever the emission altitude and width of an airglow layer
is not readily available, a stationary altitude and width (typically,
∼ 87 km and 8 km, respectively) must be assumed in the
interpretation of ground-based rotational temperatures. In cases where no
measurement of the actual altitude and width is available, a comparison like
this one can be a second-best option, despite the ambiguity in the altitude
determination: assuming a stationary altitude of 87.4 km and a width
of 8.4 km for all 42 nights, I compute the temperature difference for
each of the nights under these assumptions. The results then indicate how
representative the OH* (3–1) temperature is of this altitude and width.
Note that this temperature difference is not a measurement uncertainty or
error.
Figure shows the temperature difference △T for each of
the 42 nights, assuming a fixed centre altitude of 87.4 km and a
fixed FWHM of 8.4 km. It is thus possible to quantify how
representative this proxy is of 87 km and this
width. The maximum and minimum temperature differences are 12 K and
- 20 K (Fig. ). Because the temperature differences
shown in Fig. are not Gaussian-distributed, the mean (and
corresponding standard deviation) of the temperature difference is not a
sensible choice. A more appropriate measure in this case is half the
difference between the maximum and minimum temperature difference, yielding
±16 K, which is specific to this comparison and may be different
for other dates, locations, and instruments. I obtain similar values for
other combinations of altitude and width. What this quantity implies is that,
on any given day, the OH* (3–1) layer may be higher or lower than
87.4 km, or that its thickness is not 8.4 km, or that its
shape is not Gaussian, or any combination of these. Although
±16 K may seem large, it does not seem unrealistic to me for two
reasons. First, I do not have any actual information available about the
OH* (3–1) layer's shape and altitude, I just assumed an altitude and
width I thought was probable. Second, in the mesopause region, temperature
differences of ±16 K may arise from altitude variations of about
3 km, assuming an adiabatic lapse rate of
∼5 Kkm-1; that is, if the OH* (3–1) layer
were at about 84 km or 90 km while I have assumed it to be at
about 87 km. This argument seems more valid for individual days,
though, and such altitude variations do occur Figs. 5 and
8. Keep in mind that this is not a measurement
uncertainty. Also, this is a result specific to this comparison.
Temperature difference for each day, assuming a fixed a centre
altitude of 87.4 km and a full width at half maximum of
8.4 km for each day. See the Supplement for a list of all
measurements.
Even though it may seem tempting to compute the mean centre altitude and FWHM
of the OH* (3–1) layer based on this spectrometer-lidar comparison,
such a result would be misleading and camouflage the ambiguity shown in
Fig. . The main reason for this ambiguity is the nightly mean
temperature profile. To unambiguously determine the altitude of, for example,
the OH* (3–1) layer from a comparison with weighted temperatures
measured by lidar, the nightly mean temperature profile throughout the layer
would have to show certain characteristics. A monotonously increasing or
decreasing temperature profile is not enough. One could then vary the assumed
layer width of the Gaussian arbitrarily without changing the temperature
agreement. A strictly monotonous temperature profile is seldom the case (see
also the mean temperature profiles in the Supplement). Gravity waves, tides,
and turbulence drive the temperature profile away from a perfect adiabatic
lapse rate, for example. Mesospheric inversion layers can persist for several
hours and can be a prominent feature even after
averaging. Thus, measurements shorter than a few hours are not necessarily
the cause of the ambiguity.
An important systematic uncertainty of the method used here is the
uncertainty of the absolute OH* (3–1) rotational temperature due to the
set of Einstein coefficients used in its computation (Carsten Schmidt,
personal communication, 2015). The effect of a different set of Einstein
coefficients is that the best agreement would then appear at a different
centre altitude and FWHM. Despite being an uncertainty, it further
corroborates the results, namely that it is not possible to determine
unambiguously the altitude and width from lidar measurements alone.
Conclusions
I compared nightly mean temperatures from 42 coincident
measurements of the Na lidar at ALOMAR and GRIPS 9, covering the
period from October 2010 to April 2014. To approximate the OH* layer
temperatures measured by GRIPS 9, I weighted the lidar temperatures using
Gaussian functions with 40 different centre altitudes and 40 full widths at
half maximum.
To interpret variations seen in OH* rotational temperatures, be it on
a decadal or hourly scale, the emission altitude must be known. A
climatological OH* (3–1) layer emission altitude of 87 km is
not incompatible with this study, but the nightly OH* layer height
generally cannot be determined unambiguously from temperature measurements by
lidars, regardless of whether a variable layer width is taken into account.
This is probably also true for any other instrument that measures temperature
profiles, and is true for any location. Because different combinations of
centre altitude and full width at half maximum often yield very good
temperature agreement, the parameters of the approximated OH* (3–1)
layer are usually ambiguous. Still, for any such analysis, the width of the
Gaussian should not be fixed at some value, because a fixed width (a) is
incompatible with observations , and (b) gives false
confidence in the altitude determination because the ambiguity may often be
invisible. To determine the emission altitude and width of any – not just of
the OH* (3–1) transition – of the airglow layers unambiguously,
satellite-based or rocket-based observations of the volume emission rate
profiles are necessary . Even though
these measurements do not usually coincide with the spectrometer
measurements, a miss distance of up to 500 km or a miss time of
several hours can be accepted .
In case no altitude and width measurements of an airglow layer are available
for the interpretation of ground-based rotational temperature measurements,
it is possible to estimate from a comparison with lidars (or similar
instruments) how representative a measured temperature is of an assumed
altitude and width. In the present analysis, I assumed a stationary altitude
of 87.4 km and width of 8.4 km. On average, I found the
OH* (3–1) rotational temperature to be representative to within
±16 K of the temperature at this altitude and width. This figure is
specific to this comparison, and is not a measurement uncertainty.
I will provide the code upon request.
The Na lidar data used in this article are archived
at DataverseNO . The airglow observations of GRIPS 9 are archived
at the World Data Center for Remote Sensing of the Atmosphere (Schmidt et
al., 2014). Contact Carsten Schmidt (carsten.schmidt@dlr.de) for
further information on GRIPS 9 data.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-18-6691-2018-supplement.
The author declares that he has no conflict of
interest.
Acknowledgements
I gratefully acknowledge the valuable collaboration and discussions with
Carsten Schmidt of DLR. I am grateful to Michael Bittner of DLR for making my
fruitful working visits with his research group possible, and to Sabine
Wüst, also of DLR, for making the online platform for GRIPS data available.
Numerous discussions with Ulf-Peter Hoppe and Dallas Murphy's comments
greatly improved this manuscript. I thank Katrina Bossert and Bifford P.
Williams, GATS, Inc., as well as the ALOMAR staff, for conducting several of
the lidar measurements. The Research Council of Norway funded this work under
grant 216870/F50, as well as many Na lidar measurements under grant
208020/F50. The Na lidar at ALOMAR is a National Science Foundation
Upper Atmosphere Facility instrument, funded under grant NSF AGS–1136269.
The airglow observations at ALOMAR were partly funded by the Bavarian State
Ministry for Environment and Consumer Protection (project BHEA, grant number
TLK01U–49580). The publication charges for this article were funded by a
grant from the publication fund of UiT The Arctic University of
Norway. Edited by: Franz-Josef
Lübken
Reviewed by: two anonymous referees
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