Introduction
The day-to-day variability in the vertical distribution of ozone
(O3) above a fixed location is often characterized by the presence
of transient, stratified features (e.g., Dütsch, 1966). The
stratification occurs in the form of layered maxima and minima in the
observed vertical profile of ozone, with typical vertical scales between
about ∼0.2 and ∼3 km (e.g., Dobson, 1973; Ehhalt et al., 1983).
These features are generally called ozone laminae (e.g., Reid and Vaughan,
1991; Teitelbaum et al., 1994; Orsolini, 1995; Appenzeller and Holton, 1997;
Manney et al., 1998, 2000). Laminar structures in O3 have been
observed in both the troposphere and stratosphere, and their generation can
be linked to a wide range of mechanisms such as stratosphere–troposphere
exchange, tropical and monsoon-related deep convection, gravity waves,
differential advection of ozone fields within natural spatial gradients,
photochemical production or loss, and advection of urban plumes (e.g.,
Thompson et al., 2011; and references therein). The horizontal scales of
laminae can vary significantly, but generally they are observed over tens to
hundreds of kilometers, leading to tracer features such as tongues or
filaments appearing in quasi-horizontal coordinates (e.g., Randel et al.,
1993; Waugh, 1996; Bowman et al., 2007; Fairlie et al., 2007; Manney et al.,
1998).
The most important dynamical processes that generate ozone laminae in the
midlatitude upper troposphere (UT, defined here from ∼5 km
altitude to the tropopause) are gravity and Rossby waves, convective lofting
and detrainment of either high or low O3 from the lower atmosphere, and
intrusions of air masses with high ozone concentrations from the
stratosphere (e.g., Langford and Reid, 1998; Thompson et al., 2007b; Selkirk
et al., 2010). These generating mechanisms often involve nonlocal dynamics
and long-range transport by UT jets, and in some cases the ozone anomalies
have been traced back to dynamical events occurring thousands of kilometers
from the measurement location (e.g., Vogel et al., 2014; Minschwaner et al.,
2015). In the midlatitude lower stratosphere (LS, defined here from the
tropopause to ∼22 km), gravity waves, tropospheric
intrusions, and differential advection have been identified as drivers of
ozone laminae (Teitelbaum et al., 1994; Manney et al., 1998, 2000; Pierce
and Grant, 1998; Tomikawa et al., 2002; Pan et al., 2009; Olson et al.,
2010). For regions of the atmosphere where the time constants for
photochemical production and loss of ozone are longer than dynamical timescales, e.g., at least a week in the UT (Liu et al., 1980) and a month in the
LS (e.g., Shimizaki, 1984), observations of ozone laminae are evidence of
predominantly transport-related phenomena.
A better understanding of the characteristics of ozone laminae and their
generating mechanisms is needed in order to fully characterize ozone
variability and long-term changes in the upper troposphere and lower
stratosphere (UTLS). This understanding is critical for assessing the radiative forcing
of climate by ozone and for evaluating the impact of transport on regional air quality. Here, we describe
a new method for identifying and classifying ozone laminae from high vertical
resolution measurements (∼100 m) of ozone, pressure, and temperature.
The techniques have been derived and tested on vertical profiles obtained
from balloon soundings, but they can be generalized to other trace gas
datasets with sufficient vertical resolution. We present an application of
this method to the long-term record (1991–present) of ozonesonde profiles
from Boulder, Colorado.
Dataset
Ozonesonde data are obtained from an in situ sensor that is flown on a
balloon in a package that includes radiosonde and GPS devices (Komhyr, 1986;
Komhyr at al., 1995). An ozonesonde consists of a Teflon air pump and an
electrochemical ozone sensor (ECC) with two platinum electrodes in separate
cells of potassium iodide solutions with different concentrations. Ambient
air is drawn through one cell and the presence of O3 drives chemical
reactions that give rise to a microampere current between the electrodes. A
complete description of the ECC ozonesonde is given in Komhyr et al. (1995).
Output from the ECC is interfaced to a meteorological radiosonde, which
measures air temperature, pressure, relative humidity, and GPS position, and
transmits all of the ozone and meteorological data back to a ground
receiving station during the ∼2 h balloon ascent. Raw data
are taken at ∼1 s resolution during the flight up to the
burst altitude, which is typically at or above 30 km. The precision in ozone
mixing ratios in the UTLS region is 3 %–5 % (1σ), and the absolute
accuracy is about 10 %. The combined effect from the sensor time response
in the UTLS (∼25 s) and the balloon ascent rate (4–5 m s-1) gives an effective vertical resolution of about 100 m (Hassler et
al., 2014, and references therein). Although some data may be available
during the parachute descent phase of the sounding, the ascending flight
data are considered the highest quality; mixing ratio profiles used here are
from ascent only and are vertically averaged within 100 m thick layers.
Ozonesonde data from Boulder, Colorado (40∘ N, 105∘ W;
1.7 km a.s.l.), are available from 1978 to present, with approximately
weekly sampling. The data since 1991 have been homogenized by applying
instrumental corrections including effects of different buffer solutions
(Komhyr et al., 1995; Smit et al., 2007; Deshler et al., 2008) and effects
from Teflon air pump efficiencies (Johnson et al., 2002; Deshler et al.,
2017). Homogenization of NOAA ozonesonde records to remove instrumental
inconsistencies is described by Sterling et al. (2018). Prior to 1991, the
data are digitized from charts and are available at 1 min time resolution
(∼250 m effective vertical resolution). For consistency in vertical
resolution and data quality, we limit our analysis here to the post-1991
ozone data from Boulder.
Methods
A qualitative description of laminae in a vertical profile of O3 can
usually be made by visual inspection, but a quantitative and objective
assessment requires a set of criteria for defining ozone perturbations as
deviations from some basic state. Figure 1 shows balloon profiles of ozone
mixing ratio (χ) and potential temperature (Θ) observed from
Boulder on 10 June 2008. Both profiles contain laminar structures that are
easily discernible by eye. For a quantitative analysis of such profiles, we
developed an analysis package called RIO SOL (Robust Identification of
Observed Signatures in Ozone Laminae), which applies a consistent filtering
method (described below) to every profile in order to find basic states for
ozone mixing ratio (χs) and potential temperature (Θs). All perturbations are then defined in terms of differences (i.e.,
χ′=χ-χs), and a lamina is identified when the
relative anomaly in ozone is at least 10 % (i.e., |χ′/χs|≥0.1; see Fig. 1). This amplitude
threshold for defining laminae is broadly consistent with previous analyses
(Teitelbaum et al., 1994; Grant et al., 1998; Thompson et al., 2007a), but
our approach for deriving the basic state is modified to improve detection
and identification of laminae located within a few kilometers of the thermal
tropopause.
Vertical profiles of ozone (a, solid blue) and potential
temperature (b, solid red) measured from Boulder, CO on 10 June
2008. The respective basic states are indicated by solid black curves in both
panels. Panel (c) shows relative anomalies based on differences
between the measured and basic state profiles for ozone (solid blue) and
potential temperature (solid red, scaled by a factor of 5). Dashed vertical
lines denote the ±10 % threshold in ozone anomaly that is used to
identify lamina.
Dobson (1973) and Reid and Vaughan (1991) used a direct sampling method to
locate extrema in the vertical profile of ozone partial pressure. They
defined a lamina as a local maximum or minimum in ozone that exceeded 20 nb
in peak magnitude, with a full width between 0.2 and 2.0 km (defined with
respect to upper and lower “turning points” bracketing the layer). The use
of an absolute threshold rather than a relative one to define a lamina was
related to their use of ozone partial pressures, as the change in ozone
partial pressure between the troposphere and stratosphere is much less than
the corresponding change in ozone mixing ratio. However, a fixed 20 nb
threshold in partial pressure is roughly comparable to our 10 % threshold
in mixing ratio only in the middle stratosphere, between about 20 and 30 km
altitude. In the UT, mean ozone partial pressures are much lower (25–40 nb)
and the same 20 nb threshold will only detect those anomalies that are
larger than 50 %–80 %. With such a reduced sensitivity, the number
of lamina detections in the UT should be smaller than the number of UT
laminae we identify using a 10 % mixing ratio threshold. Krizan and
Lastovicka (2005) and Krizan et al. (2015) used an even larger threshold of
40 nb in peak magnitude to examine “strong” ozone laminae in vertical
profiles. Alternatively, Huang et al. (2015) used a continuous wavelet
transform (CWT) approach to study ozone laminae in lidar ozone vertical
profiles. An interesting feature of the CWT approach is that it does not use
a basic state or reference ozone profile to identify laminae. The laminae
amplitude thresholds used by Huang et al. (2015) were 10 ppbv in the
troposphere and 40 ppbv in the stratosphere, which more closely follows our
10 % threshold than the partial pressure criteria discussed above.
Reid and Vaughan (1991) and Huang et al. (2015) compared their methods to
“filter and difference” techniques that are broadly similar to the
approach used here and in other studies (e.g., Grant et al., 1998; Krizan
and Lastovicka, 2005; Thompson et al., 2007a) and found reasonable agreement
in lamina statistics between the two methods. One advantage of the filter
and difference approach is that basic states are generated for each profile,
as described below, which can provide important information on the
contribution of laminae to the overall variability in ozone.
An important drawback to filtering, however, is directly tied to sharp
changes in the vertical gradients of ozone and potential temperature near the
tropopause. Figure 2 shows observed χ and Θ profiles along with
two sets of basic state profiles, (χs1, Θs1)
and (χs2, Θs2). The first set of basic states
is derived by applying a nonrecursive boxcar filter with a fixed width of
6 km to each observed profile. A fixed-width filter has been employed in a
number of previous studies (e.g., Teitelbaum et al., 1994), and for a 6 km
boxcar the effective low-pass filter cutoff frequency (∼90 % level)
corresponds to vertical scales of 2–3 km. These basic states are thus
smoothed profiles with all features at scales less than ∼2.5 km
effectively removed (dashed curves in Fig. 2). Subsequent differencing with
the observed profiles produces anomaly profiles that emphasize laminar
features less than 2.5 km in width. Note that our 0.1 km
averaging and sampling grid for the measurement
profiles corresponds to an effective Nyquist cutoff for scales less than
0.2 km; thus, this method for laminae identification is focused on features
with widths between about 0.2 and 2.5 km. Features that span a vertical
range larger than about 3 km occupy a significant fraction of the density
scale height, and are more often related to large-scale shifts in air masses
than to processes typically associated with the generation of laminae (Reid
and Vaughan, 1991). At vertical scales below 0.2 km, however, an important
contribution to ozone variability could result from the presence of very thin
laminae. Aircraft measurements of tracer variability have indicated
scale-invariant behavior over a wide range of horizontal scales, ranging from
0.2 to 2700 km (Tuck et al., 2004). Although this suggests that vertical
scales below 0.2 km may be important, the variability in ozone at horizontal
and vertical scales less than 0.2 km is not well characterized in the UTLS
region.
Vertical profiles of ozone (a, solid blue) and potential
temperature (b, solid red) measured from Boulder, CO, on 6 August
2008. Both panels also show basic states calculated using a fixed-width
filter (dashed) and a variable-width filter (solid), as described in the
text. The bottom two panels show anomalies based on the fixed-width (dashed)
and variable-width (solid) filters for ozone (c, blue), and
potential temperature (d, red). Vertical dashed lines for the ozone
anomaly indicate the ±10 % threshold for laminae detection, and the
horizontal dotted lines in all panels indicate the height of the lapse rate
tropopause determined from this sounding.
The method of fixed-width filtering consistently produces an apparent lamina
of negative sign near the tropopause level (Fig. 2). In this case, the
effective O3 and Θ perturbations are always less than basic
state values due to sharp changes in the vertical gradients of both
quantities near the tropopause. Rapid gradient changes near the tropopause
usually occur on scales less than 2.5 km and therefore are smoothed out in a
basic state derived from a 6 km wide filter. A similar effect was noted by
Schmidt et al. (2008) in their analysis of gravity wave activity using GPS
temperature profiles. We explored several alternatives for deriving basic
states and minimizing tropopause-related artifacts, ranging from piecewise
polynomial fitting to the use of climatological means. An important drawback
for many approaches is that they cannot accommodate the large degree of
variability in the altitude of the tropopause; even seasonal climatologies
do not reproduce tropopause variability to the extent needed to remove false
laminae detections. We adopted a method for RIO SOL that identifies the
primary tropopause for each profile using the World Meteorological
Organization (WMO) lapse rate criterion (e.g., Homeyer et al., 2010), and then
employs a variable boxcar with a maximum width of 6 km and a minimum width
of 1.5 km at the tropopause level. The width varies linearly with altitude
within 6 km on either side of the tropopause, such that the boxcar width is
symmetric about the tropopause level. As shown in Fig. 2, this
variable-width filtering method allows the basic states to track sharp
gradient changes at the tropopause while still filtering enough small-scale
variability to identify ozone laminae in the anomaly profiles. The use of a
variable-width-smoothed basic state means that the detection sensitivity for
laminae of varying thickness will change with altitude. Away from the
tropopause where the filtering width is 6 km, all lamina with vertical
scales less than ∼2.5 km can be identified. Near the
tropopause, however, the mean boxcar width is about 2.6 km, which corresponds
to a lamina detection threshold width of about 1.5 km. In addition,
soundings that contain multiple tropopauses (e.g., Schwartz et al., 2015)
are often associated with complex vertical structures in ozone that may not
be fully characterized by this laminae analysis.
The same variable-width smoothing procedure is used to identify laminae in
the measured vertical profile of Θ. A lamina detected in potential
temperature that is coincident with a lamina in ozone provides evidence that
the sampled air parcel was subjected to a vertical displacement associated
with gravity wave (GW) activity. This method has been used extensively to
examine GW signatures in ozonesonde data (e.g., Teitelbaum et al., 1994;
Pierce and Grant, 1998; Thompson et al., 2007a) and in aircraft measurements
of ozone (e.g., Alexander and Pfister, 1995), based on the expectation that
Θ′=χ′∂Θs∂z/∂χs∂z,
where z is altitude. Teitelbaum et al. (1996) discuss the general conditions
under which this relationship holds, including the condition that the timescales for ozone photochemistry are much longer than the timescales
relevant for transport by GW phenomena. They further note that these
coincidences are more readily identified by scaling potential temperature
perturbations to account for differences in the mean vertical gradients of
Θ and χ,
Rz=1χsdχsdz/1ΘsdΘsdz.
A similar scaling was employed by Ehhalt et al. (1983) to compare equivalent
vertical displacements obtained from measured variances in long-lived
stratospheric gases.
One of the most straightforward approaches for identifying coincidences in
ozone and potential temperature laminae involves the spatial correlation
between vertical profiles of χ′/χs and RΘ′/Θs over a limited vertical domain, for example, within 5 km wide
sampling windows (e.g., Teitelbaum et al., 1994). Figure 3 shows a set of
relative anomaly profiles along with the magnitude of the correlation
coefficient computed within a 5 km wide vertical window centered at the
given altitude. A correlation threshold of r>0.7 has been shown
to be a reliable indicator for GW-induced laminae in ozone (e.g., Pierce and
Grant, 1998). One complication with this approach arises when multiple
laminae appear within the same correlation window. For example, in Fig. 3
the central altitudes of laminae labeled 2 through 5 are close enough to
cause interference in gauging the true correlation within individual
laminae. We adopted a different approach for RIO SOL, by correlating over
the extent of the laminar feature (where the amplitude exceeds 10 %) or
over a 2 km window, whichever is larger. Sensitivity experiments indicate
that our approach for deriving basic states and for correlating over more
limited vertical domains is more consistent with previous analyses if we
adopt a threshold of r≥0.65. In Fig. 3, RIO SOL detects GW ozone
lamina (labeled 1 and 3) near 9.5 and 14 km altitude with the application of
the r≥0.65 threshold. Laminae for which ozone anomalies are not
significantly correlated with scaled potential temperature anomalies (r<0.65) are classified as non-gravity wave (NGW) laminae, as there
is no evidence that the generation mechanism is associated with GW activity.
In order to examine the detection sensitivity for laminae, we constructed a
set of 150 simulated ozone and temperature profiles using climatological
values representing tropical, midlatitude summer, and midlatitude winter
means (Anderson et al., 1986) and introduced localized ozone perturbations at
random altitudes and over a random sample of amplitudes and widths. The
perturbations were either triangular or Gaussian in shape. The simulated
profiles were then analyzed using RIO SOL. Figure 4 shows two examples from
the simulations and analysis. In the first example, three laminae were
introduced to a tropical basic state and RIO SOL accurately characterized the
anomalies (Fig. 4a and b). The amplitudes,
widths, and central altitudes of positive and negative laminae are derived to
within a few percent.
Panel (a)
shows vertical profiles of ozone (blue) and scaled potential temperature
anomalies (red) from a Boulder ozonesonde sounding on 4 May 2006. Vertical
dashed lines represent a 10 % amplitude threshold for defining laminae,
and seven identified laminae are indicated by number. Panel (b)
shows the correlation coefficient calculated between ozone and potential
temperature anomalies using a 5 km wide sliding vertical window (solid
curve), and alternatively from windows centered on individual laminae (orange
and green bars). The dashed vertical line indicates the 0.7 threshold used
for identifying gravity wave ozone laminae with the 5 km sliding window
technique. For correlations over individual laminae, a 0.65 threshold value
is adopted, and laminae meeting or exceeding this threshold are indicated by
the green bars and classified as GW laminae, while correlations below 0.65
are indicated by orange bars and classified as NGW laminae.
The second example is taken from a midlatitude simulation and highlights one
of the weaknesses of the filter and difference approach. A large amplitude
lamina (e.g., near 18.5 km in Fig. 4c and d) can
shift the derived basic state enough to produce pairs or triplets of laminae
in the derived perturbation profile. This effect can be seen in Fig. 4 by the
appearance of a false positive lamina near 17 km, which is an artifact
produced by the large negative laminae immediately above it. False lamina
detections accounted for nearly 25 % of the total number of laminae
identified in the simulations, with no altitude dependence in the number of
false detections. This is in contrast to the fixed 6 km width smoothing
method described in Sect. 3, which generates false laminae detections at the
tropopause in nearly every profile. As expected, the proportion of false
detections grows to nearly 50 % as the lamina amplitude threshold is
reduced from 10 % to 5 %. It should be noted that the overall false
detection rate is a direct consequence of how these simulations are designed.
Most false detections are associated with a single large amplitude lamina in
the simulation. Although we expect that the true number of false detections
in observed ozone profiles is likely smaller, this effect is impossible to
quantify because there is no way to directly observe the basic state.
Two simulated ozone profiles with randomly placed laminae applied to
a tropical basic state (a, b), and to a midlatitude basic
state (c, d). In each case, panels (a) and (c)
show the simulated ozone (solid) and the derived basic state (dashed), while
panels (b) and (d) show the actual anomaly profile for each
simulation (solid), along with the derived anomaly profile (dashed).
Horizontal dotted lines in panels (a) and (c) denote the
tropopause level, and vertical dotted lines in panels (b) and
(d) denote the 10 % anomaly threshold used for detecting ozone
laminae.
In terms of positive identification of true features, the detection rate was
79 % for all simulated laminae with amplitudes larger than 10 % and
widths between 0.2 and 2.5 km. The detected fraction was degraded to about
60 % for those laminae within ±2 km of the tropopause, primarily
because of the reduced filtering width used to derive the basic states near
the tropopause. At all other altitudes, roughly half of the non-detections
arose from simulations involving two or more laminae occurring in close
proximity (within a few kilometers' altitude) which were counted as a single
lamina in the identification process. Most of the remaining non-detections
were due to simulated laminae with amplitudes just above the 10 %
threshold that were not counted because the derived amplitudes for these
laminae fell just below 10 %. On average, there is a 2 %–4 % low bias in
derived amplitudes using our version of the filter and difference method,
and there is a tendency to underestimate widths by 0.1 to 0.2 km compared to
the simulated inputs. Both of these small biases can be seen in some of the
simulated laminae shown in Fig. 4, and they are an inevitable result of
low-pass filtering to determine the basic state. Laminae altitudes are,
however, accurately identified to within ±0.1 km.
One factor that may introduce a systematic offset to laminae central
altitudes is the finite response time of the ozonesonde. Sonde ascent rates
are consistently 4–6 m s-1 and response timescales are ∼25 s,
leading to a possible systematic bias of between +100 and +150 m in
altitude. Note that the offset is unlikely to be any bigger than this because
we consistently find gravity wave laminae for which the ozone and Θ
perturbations (which are based on temperature with response times on the
order of a few seconds) are very well correlated on a 100 m grid, with no
systematic altitude offsets. Given the 1 Hz sampling for the raw data, the
effect of variations in ascent rate which can act to smooth measured profiles
or to limit the resolving of laminar features, with scales greater than
0.2 km, is minimal. There are also rare, but documented (e.g., Morris et
al., 2010), measurement artifacts that could be mistakenly identified as
ozone laminae. In the case of SO2 interference observed by Morris
et al. (2010), RIO SOL would interpret apparent ozone “notches” as negative
NGW ozone laminae.
Results
Overall statistics for ozone laminae
The RIO SOL analysis was applied to 1138 ozone soundings from Boulder,
Colorado. As discussed in Sect. 2, these were obtained on a
∼ weekly basis between the years 1991 and 2015. A total of 9952 ozone laminae were identified, corresponding to a mean number of 8.7 laminae
per sounding. The variability in the number of lamina per sounding was very
close to a normal distribution about the mean, with a standard deviation of
2.3 laminae. There were no soundings with fewer than 2 or with more than 16 laminae detections.
There are considerable differences in the frequency of lamina detections
with respect to altitude, season, and lamina type. The number of laminae
observations per sounding within 1 km thick altitude bins relative to the
WMO tropopause is shown in Fig. 5. The occurrence frequency for all ozone
laminae maximizes near the tropopause and is roughly evenly distributed
above and below the tropopause. Over 60 % of all laminae were observed
within 5 km of the tropopause. Our simulations (discussed above) strongly
suggest that this is not an artifact caused by the tropopause, as the false
detection rate for simulated ozone laminae was independent of altitude.
Vertical profiles of ozone laminae characteristics in
altitude coordinates relative to the WMO tropopause. Panel (a) shows
laminae frequency as the number of laminae detected per sounding within 1 km
wide altitude bins. Black squares are for all laminae types and signs. Solid
lines show frequencies of GW laminae, dashed lines indicate NGW laminae, and
red and blue colors indicate positive and negative anomalies, respectively.
Panels (b) and (c) show profiles of rms amplitudes and mean
widths, respectively. The rms amplitudes are derived from the square of the
mean relative anomaly within each lamina and averaged over all laminae
detected within corresponding relative altitude bins. Widths are defined as
the full altitude range in which the anomaly amplitude exceeds 10 %
(along consecutive 100 m sampling intervals), with a minimum restriction of
0.2 km. As with panel (a), solid and dashed curves denote GW and
NGW laminae, respectively.
Figure 5 also displays occurrence frequencies for GW and NGW laminae,
segregated by positive (+GW, +NGW) or negative anomalies (-GW, -NGW)
with respect to the basic states. The most common lamina type is -NGW, which
accounts for nearly half of all laminae detected outside of the tropopause
region. Within 2 km of the tropopause, higher frequencies of +GW and -GW
lamina contribute a more significant amount to the total. Over all
altitudes, 28 % of all laminae are the GW type and 72 % are NGW laminae.
Negative anomaly laminae outnumber positive anomaly laminae at most levels,
and overall we detect about 15 % more negative anomaly laminae.
Two of the most important characteristics of a laminar structure are its
amplitude and thickness (or width). Figure 5 includes panels for the
vertical distributions of the root mean square (rms) amplitudes and widths
of detected lamina. For both rms amplitudes and widths, no significant
differences were found between positive and negative anomaly laminae. The
amplitude of a lamina is defined by the mean of the perturbation taken over
the full altitude range in which the perturbation magnitude exceeds the 10 %
minimum threshold. Figure 5 shows that rms amplitudes are closely matched
between GW and NGW laminae, with values between 15 % and 20 % in the
troposphere and an overall tendency for larger amplitudes in the LS. The
mean rms amplitude taken over all altitudes and laminae type is 20 %. The
amplitude distribution is skewed by the presence of larger-amplitude
(>40 %) laminae that are seen in ∼2 % of the
soundings. These large-amplitude laminae are most often observed in the LS.
We define laminae widths by the continuous range of altitude levels over
which the 10 % minimum amplitude threshold is met in the anomaly profile. Figure 5 shows that average widths
for laminae at Boulder are about 1 km in the troposphere, decreasing to
∼0.7 km near the tropopause and increasing again in the stratosphere
(as noted below, a large fraction of this variation is a result of the
detection method). The largest mean widths (∼1.4 km) were found for
NGW laminae occurring about 5 km above the tropopause. As with amplitudes,
no significant differences were found between the mean widths of positive and
negative anomalies.
The frequency distribution of laminae widths is shown in Fig. 6. It varies
with relative altitude as expected because of the variation in basic state
smoothing parameters with respect to the tropopause. At relative altitudes
larger than ±5 km, the distribution has a significant tail in
which lamina widths up to 2.5 km
are observed. Closer to the tropopause, we find a truncation of the width
distribution around 1.5 km results from changing the filtering parameters
for the basic states. If we assume that distribution of laminae widths far
from the tropopause is representative of the entire profile, then we can
estimate that roughly 16 % of ozone laminae near the tropopause may not
be identified because their widths are larger than our upper detection limit
in this region. This undetected fraction estimated from Fig. 6 is consistent
with the laminae simulations discussed above, in which the fraction of
undetected laminae increased by 19 % within 2 km of the tropopause. It
should be noted, however, that the simulated negative lamina at 18 km in
Fig. 4 is within 1.2 km of the tropical tropopause, and it is accurately
characterized by RIO SOL. On the narrow side of the width distribution,
extrapolation of the smoothly decreasing widths below modal values of ∼0.4 km at all altitudes yields a detection loss rate of about
2 %–4 % due to lamina with widths narrower than 0.2 km.
Probability density function (PDF) of the amplitude distribution for
all ozone laminae (a) and contour PDF of width distribution for
ozone laminae versus altitude relative to the WMO tropopause (b).
For the amplitudes, the standard 10 % detection threshold is indicated by
the vertical dashed line and the solid curve shows the amplitude distribution
using this criterion. The dotted curve shows the extension of the amplitude
PDF if a 5 % detection threshold is employed. For the width PDF, contours
are separated by 0.02, and the black dashed line indicates the tropopause
level.
Figure 6 also shows the frequency distribution of laminae amplitudes. Note
that the distribution is truncated at 10 % by the minimum threshold used
for lamina detection. Sensitivity runs using smaller minimum thresholds
indicate a significant number of small (5 %–10 % amplitude) laminae fall
below our 10 % minimum, as indicated in Fig. 6. A mean of about 12 laminae are detected per sounding using a 5 % minimum amplitude threshold,
an increase of about 40 % laminae over using a 10 % threshold. As
discussed above, the fraction of false detections grows with decreasing
amplitude threshold, so that the frequency estimate for amplitudes between
5 % and 10 % shown in Fig. 6 should be regarded as an upper limit on
the true occurrence of small-amplitude laminae.
The above statistics for Boulder may be contrasted with those obtained using
previous methodologies, namely the use of a fixed width, 6 km boxcar filter
for the basic state and a 5 km wide correlation window for O3 and
Θ anomalies. For this particular method, the total number of laminae
detected is 25 % smaller and their mean widths are more than twice as
large as those from RIO SOL shown in Fig. 5, ranging from 1 km up to a
maximum of 3 km at the tropopause. These differences can be attributed to
the dominating influence of tropopause-induced laminae for the case of a
fixed-width boxcar. The apparent tropopause lamina appears in over half of
the soundings and it is sufficiently wide to mask or absorb any other
individual laminae that may be present within 2–3 km of the tropopause. Not
surprisingly, we also detect fewer overall positive laminae when using the
fixed-width boxcar. There are also changes to the relative fraction of GW
and NGW laminae when using a 5 km wide correlation window; relatively more
GW laminae are detected and this fraction maximizes at the tropopause level
in association with the aforementioned spurious tropopause-induced laminae
in both O3 and Θ.
A preliminary analysis has also been done using RIO SOL in its standard
configuration for other measurement sites at midlatitude and low-latitude stations,
and the results appear to be similar in accuracy to those from Boulder. At
Pago Pago, Samoa, we find comparable statistics with a slightly higher
overall frequency of laminae (nearly 10 per profile), a 30 % GW fraction,
and a similar altitude distribution relative to the tropopause. On the other
hand, when applying RIO SOL to winter–spring soundings in and around the
Antarctic polar vortex or during particular cold periods in the Arctic
winter, the criteria and thresholds for both ozone laminae and the
tropopause would likely require significant changes in order to maintain a
robust analysis, especially under conditions of significant ozone depletion
and/or changes to the thermal structure of the lower stratosphere. A
detailed comparison of ozone laminae from different measurement sites is
planned for future investigations, but in this paper, our emphasis is on a
description of techniques and on the climatology from Boulder.
Basic states and ozone variance
As discussed in Sect. 3, the filter and difference approach produces basic
state profiles that can be used to quantify the fraction of overall
variability in ozone attributable to laminar features in the profile. Figure 7 shows the climatological means and standard deviations of basic states for
each of the four seasons (December–January–February is denoted by DJF, etc.). These are
displayed in altitude coordinates rather than tropopause-relative
coordinates in order to highlight seasonal differences. Because of the
filtering methods used to derive these basic states, all of the basic state
variability in the UT arises from ozone changes occurring on vertical scales
larger than 2–3 km. The mean basic states are nearly identical to
climatological seasonal means obtained from the raw data, so that many of
the expected seasonal effects are seen in the mean basic state profiles. For
example, larger ozone mixing ratios occur during winter and spring in the 10 to
20 km altitude range as a result of stratospheric transport and seasonal
changes in the tropopause height. This seasonality can be quantified by the
standard deviation of the seasonal basic states at each altitude, as shown
in Fig. 7, and can be directly compared with the intra-seasonal (i.e.,
within each season) variability derived from the standard deviation of each
of the seasonal mean profiles. As noted above, the seasonal component of
ozone variability is largest between 12 and 16 km altitude. However, the
intra-seasonal basic state variability tends to follow the climatological
tropopause and maximizes in the UT about 1–2 km below the WMO tropopause.
During winter and spring, there is a secondary increase in LS variability
(12–15 km), which is likely to be related to deep stratospheric intrusions
of tropical/subtropical air like those investigated by Reid et al. (2000).
Seasonal means of ozone basic states profiles from Boulder over the
years 1991–2015 (a) and normalized standard deviations of the
basic states (b). The means and intra-seasonal standard deviations
were taken over the periods December–February (DJF, black), March–May (MAM,
blue), June–August (JJA, green), and September–November (SON, red). The
standard deviations were normalized by mean values at each altitude, and
seasonal mean tropopause heights are indicated by colored triangles. Also
shown is comparable magnitude of the seasonal variation in basic states
(dashed curve, b), estimated from the variance in the four seasonal
basic states and normalized by the annual mean. Note that this seasonal
magnitude is equivalent to Ap/√2 for a cosine seasonal
variation, where Ap is the peak relative amplitude.
In summary, we expect contributions to the total intra-seasonal ozone
variance arising from three types of features: (i) detected laminae with
widths between 0.2 and 2.5 km and amplitudes greater than 10 %, (ii) all
variations with larger vertical scales (>2.5 km), and (iii) small-amplitude (<10 %) features across all vertical scales.
Assuming that the total intra-seasonal ozone variance σT2 can
be effectively decomposed into these components, then
(σT/χ)2=(A‾)2+(σs/χ)2+(δ‾)2,
where A‾ is the rms amplitude of detected laminae,
σs2 is the variance in the basic state profile, and
δ‾ is the normalized variance due to small-amplitude (<10 %) features. The left side and the two largest terms on the right
side of Eq. (3) are shown in Fig. 8 for the seasons of DJF and JJA. Raw ozone
data were used to calculate σT2, while
(A‾)2 and σs2 were derived from the
laminae amplitudes and basic state outputs of the RIO SOL analysis. Figure 8
shows that the total variance in ozone is generally controlled by large
vertical-scale changes near and immediately below the tropopause. Laminae
make up an important fraction of the total variance, however, and these
features can be the dominant mode of ozone variability in the middle
troposphere and lower stratospheric regions. The contribution from
small-amplitude features (δ‾)2 was calculated from the
results of the threshold sensitivity experiments discussed above (or could
also be estimated as a residual from Eq. 3), and this contribution is
typically between 0 % and 5 % of the total variance. Figure 8 also
shows seasonal and altitude means of the contributions from all three terms
on the right side of Eq. (3), indicated within boundaries of a coordinate
system defined by the amplitude and the
vertical scale of ozone variations. Our results indicate that, on average,
more than half of the intra-seasonal variance in ozone between 5 and 25 km
altitude is due to large-scale changes in the basic state, and that slightly
over one-third of ozone variations are due to laminar features that are
identified by RIO SOL.
Normalized seasonal variances in ozone for DJF (a) and
JJA (b). Plotted are the normalized total variance (solid gray),
basic state variance (dotted), laminae variance (solid black), and the sum of
basic state and laminae variances (dashed). Panel (c) shows the
annual mean contributions to the total variance between 5 and 25 km
altitude, as a function of amplitude and the vertical scale of features in the
ozonesonde profile.
Boulder laminae climatology
We examine here how the frequency of detected laminae varies with altitude
and season. Figure 9 shows monthly mean frequencies relative to the WMO
tropopause for GW and for NGW ozone laminae. Consistent with Fig. 5, GW
laminae are most often observed within 2 km of the tropopause, whereas NGW
laminae are more evenly distributed throughout the UTLS. Throughout most of
the year, the GW frequency distribution maximizes slightly above the
tropopause, while the NGW frequency is larger below the tropopause. This
situation reverses during the months of June–September, when more GW laminae
are detected below the tropopause and most NGW laminae are found above the
tropopause.
Climatologies of gravity wave momentum fluxes indicate a wintertime maximum
in the LS for this location (e.g., Geller et al., 2013). However, it should
be noted that while our ozone GW laminae climatology is expected to be
related to the overall level of gravity wave activity, there are other
factors that can influence whether a GW lamina in ozone is generated at the
location of an ozonesonde profile in the first place, and then whether it
will be detected by RIO SOL. For example, our simulations suggest that GW
laminae are more readily detected and identified as such in regions where
background vertical gradients of ozone and potential temperature are both
large, such as in the LS region.
Climatology of ozone laminae frequency at Boulder, CO, as a function
of month and altitude relative to the WMO tropopause for GW (a) and
NGW (b) laminae. Frequency is expressed as the percent of soundings
that contain one or more GW or NGW laminae within 1 km altitude bins
relative to the tropopause. Note the different scales between GW and NGW
frequencies.
The distribution of NGW laminae stands in stark contrast to that of GW
laminae, and, as noted in the Introduction, the generating mechanisms for NGW
laminae are much more uncertain. Previous analyses have used maximum
correlation threshold criteria between ozone and potential temperature to
infer the influence of Rossby waves on ozone (e.g., Pierce and Grant, 1998;
Thompson et al., 2007a). We have not adopted this approach in RIO SOL due to
larger uncertainties in positively classifying these laminae using ozone and
potential temperature alone, particularly since the connection between
O3 and Θ is not as clear as indicated in Eq. (1) for GW
ozone laminae. However, it is plausible that a significant fraction of NGW
laminae are generated in processes associated with Rossby wave activity. The
seasonality of Rossby wave breaking (RWB) in the UTLS at northern
midlatitudes (e.g., Hitchman and Huesmann, 2007; Isotta et al., 2008) is
similar to the seasonality of UT NGW ozone laminae seen in Fig. 9. Rossby
wave breaking and stratosphere–troposphere exchange (STE) are both prevalent
along the flanks of UT jets (Gettelman et al., 2011 and references therein),
and studies of jets using meteorological reanalysis data show a maximum in
subtropical UT jet frequencies near 30∘ latitude from November
through April in the Northern Hemisphere (Manney et al., 2011, 2014). An associated phenomenon of multiple
tropopause events, which are often linked to tropopause folds and
extratropical STE (e.g., Sprenger et al., 2003), also shows maximum
frequencies during December–March on the northern flank of the subtropical
jet maximum (e.g., Manney et al., 2014), and these events are responsible for
a significant fraction of the variability in ozone and other trace gases in
the tropopause region (Schwartz et al., 2015).
Mechanisms leading to the maximum in NGW laminae frequency in the LS during
summer are more uncertain. Jing and Banerjee (2018) found a maximum in
anticyclonic RWB on the 350 and 370 K
Θ surfaces during NH summer, and both of these surfaces are typically
at or above the tropopause level over Boulder during summer. In addition,
they showed that the zonal distribution of summer RWB favored those regions
above and immediately upstream of Boulder. However, the production of laminar
features in summertime LS ozone from other mechanisms cannot be ignored.
Impacts on the composition of the midlatitude summer LS have been
demonstrated from monsoon-related dynamics (e.g., Randel et al., 2010), deep
summertime convection (e.g., Weinstock et al., 2007), and meridional
transport from the tropical UT (e.g., Bönisch et al., 2009). Clearly,
more work is needed to understand the full range of dynamical and chemical
processes that may produce the range of laminar ozone features seen in these
balloon profiles and in other ozone measurements. The development of methods
to further classify NGW laminae and to associate mechanisms with their
generation is a focus of ongoing work using RIO SOL.
Conclusions
We have described the RIO SOL analysis package for characterizing ozone
laminae in balloon soundings and presented an analysis of the
∼25-year ozonesonde dataset from Boulder, Colorado. RIO SOL
involves an adaptation of the filter and difference approach used in
previous studies of ozonesonde profiles, in which a unique basic state is
generated for each ozone profile and laminae are identified as deviations
from this basic state. The major improvements in RIO SOL include methods for
improved sensitivity in identifying GW laminae using potential temperature
from each sounding and for avoiding false detections of GW laminae near the
thermal tropopause. The vertical gridding of the ozonesonde data and the
filtering method constrain the range of vertical scales for identified
laminae to between 0.2 and 2.5 km. Simulations indicate that RIO SOL can
reliably identify most of the ozone laminae with relative amplitudes greater
than 10 %, and virtually all laminae above 20 % amplitude.
The mean number of ozone laminae observed per sounding at Boulder is about
nine. This is much higher than the number (one–two) reported by Reid and
Vaughan (1991) and Krizan et al. (2015) from analyses of northern midlatitude
soundings, but as noted in the Introduction, the fixed detection threshold
used in these studies emphasized stratospheric ozone laminae at the expense
of tropospheric laminae. Huang et al. (2015) used separate thresholds for the
troposphere and the stratosphere and found a mean of 2.5 laminae per profile
in the ozonesonde dataset from Huntsville, Alabama. This is still
significantly less than the number of laminae detected at Boulder. The method
used by Huang et al. (2015) limited the smallest scale of detected laminae to
0.5 km as compared to the 0.2 km limit used here; thus, it is likely that
the difference can largely be explained by the detection of laminae at
smaller scales and with smaller amplitudes (due to the use of a relative
amplitude threshold in RIO SOL). The root-mean-square laminae amplitude at
Boulder is about 20 % relative to the basic state. This mean amplitude
does not vary significantly with altitude. It is slightly larger than the
∼15 % mean amplitude determined by Pierce and Grant (1998) for
ozonesondes from Wallops Island, Virginia, although their identification
method could have been impacted by interference near the tropopause. The mean
width of ozone laminae, defined by the altitude range in which the anomaly
amplitude exceeds 10 %, varies between 0.7 and 1.4 km depending on the
altitude relative to the tropopause and is generally smallest near the
tropopause. Some of the variation in mean width with altitude is a result of
the filtering procedure used in RIO SOL.
Laminae statistics have been examined on a tropopause-relative altitude grid
rather than on standard altitudes relative to the surface. This gridding
better delineates the subset of laminae generated by primarily tropospheric
mechanisms from those resulting from mainly stratospheric phenomena and
facilitates the identification of STE processes. The occurrence frequency
for ozone laminae shows a distinct maximum within ∼2 km of
the tropopause and is nearly symmetric above and below the tropopause. GW
laminae make up about one-third of all ozone laminae. These are most often
detected near the tropopause in the lower stratosphere. NGW laminae are more
abundant, and negative NGW are the most dominant laminar feature throughout
the UTLS region.
The total variance in the Boulder ozonesonde dataset was decomposed into
terms representing changes in the ozone basic state, changes due to the
presence of ozone laminae, and changes due to weaker-amplitude (<10 %) features. Large-scale changes in the basic state account for
60 % of the total intra-seasonal ozone variance. The magnitudes of
intra-seasonal variations in basic states are comparable to those of the
seasonal cycle. Laminae detected by RIO SOL are responsible for 37 % of
the total variance in ozone, and the remaining 3 % is estimated to
originate from smaller-scale features. Although they are not the dominant
form of ozone variability, laminae must be considered in order to quantify
ozone variability and trends in the UTLS region. Future research in this
area should be directed towards methods for obtaining global laminae
datasets, either from satellite measurements or from ozonesonde networks,
and towards the development of improved techniques for unambiguous identification of
the mechanisms responsible for generating NGW ozone laminae.