ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-17-4337-2017Role of vertical and horizontal mixing in the tape recorder signal near the tropical tropopauseGlanvilleAnne A.BirnerThomasthomas.birner@colostate.eduhttps://orcid.org/0000-0002-2966-3428Department of Atmospheric Science, Colorado State University, Fort Collins, CO, USAThomas Birner (thomas.birner@colostate.edu)30March2017176433743539April20169May20165March20176March2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/17/4337/2017/acp-17-4337-2017.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/17/4337/2017/acp-17-4337-2017.pdf
Nearly all air enters the stratosphere through the tropical tropopause layer
(TTL). The TTL therefore exerts a control on stratospheric chemistry and
climate. The hemispheric meridional overturning (Brewer–Dobson) circulation
spreads this TTL influence upward and poleward. Stratospheric water vapor
concentrations are set near the tropical tropopause and are nearly conserved
in the lowermost stratosphere. The resulting upward propagating tracer
transport signal of seasonally varying entry concentrations is known as the
tape recorder signal. Here, we study the roles of vertical and horizontal
mixing in shaping the tape recorder signal in the tropical lowermost
stratosphere, focusing on the 80 hPa level. We analyze the tape recorder
signal using data from satellite observations, a reanalysis, and a
chemistry–climate model (CCM). By modifying past methods, we are able to capture
the seasonal cycle of effective vertical transport velocity in the tropical
lowermost stratosphere. Effective vertical transport velocities are found to
be multiple times stronger than residual vertical velocities for the
reanalysis and the CCM. We also study the tape recorder signal in an
idealized 1-D transport model. By performing a parameter sweep, we
test a range of different strengths of transport contributions by vertical
advection, vertical mixing, and horizontal mixing. By introducing seasonality
into
the transport strengths, we find that the most successful simulation of the
observed tape recorder signal requires vertical
mixing at 80 hPa that is multiple times stronger compared to previous estimates in the literature. Vertical
mixing is especially important during boreal summer when vertical advection
is weak. Simulating the reanalysis tape recorder requires excessive amounts
of vertical mixing compared to observations but also to the CCM, which hints
at the role of spurious dispersion due to data assimilation. Contrasting the
results between pressure and isentropic coordinates allows for further insights
into quasi-adiabatic vertical mixing, e.g., associated with overshooting
convection or breaking gravity waves. Horizontal mixing, which takes place
primarily along isentropes due to Rossby wave breaking, is captured more
consistently in isentropic coordinates. Overall, our study emphasizes the role
of vertical mixing in lowermost tropical stratospheric transport, which
appears to be as important as vertical advection by the residual mass
circulation. This questions the perception of the “tape recorder” as a
manifestation of slow upward transport as opposed to a phenomenon influenced
by quick and intense transport through mixing, at least near the tape head.
However, due to the limitations of the observational dataset used and the
simplicity of the applied transport model, further work is required to more
clearly specify the role of vertical mixing in lowermost stratospheric
transport in the tropics.
Background
Water vapor accounts for less than 0.001 % of stratospheric air, but as a
radiatively active tracer, it plays a major role in shaping its climate. Even
surface temperature can be radiatively affected by changes in stratospheric
water vapor on decadal timescales , and the near-surface
circulation may respond to these changes through downward coupling
.
Most water vapor enters the stratosphere through an interface known as the
tropical tropopause layer (TTL) from where it spreads upward and poleward
along the Brewer–Dobson circulation (BDC) . The
extremely low temperatures in the TTL cause dehydration through freeze-drying and
therefore determine the amount of water vapor that enters the stratosphere
. The water vapor above the TTL behaves nearly like a
passive tracer. Concentrations are stamped at the base of the stratosphere by
the annual cycle in tropical tropopause temperature and moved upward by the
BDC, creating the so-called tape recorder signal in the tropical lower
stratosphere . By exploiting water vapor as a tracer for
lower stratospheric transport, we can investigate the speed of BDC upwelling
and the relative importance of mixing versus advection.
The TTL is a transition region between convective outflow in the upper
troposphere ∼ 200 hPa and the base of the deep branch of the BDC
∼ 70 hPa. This region features a mix of tropospheric and stratospheric
properties and is controlled by complex interactions between dynamics,
clear-sky radiation, and its coupling to transport of radiatively active
tracers, as well as cloud radiative effects and cloud microphysics. Dynamical
control acts on a vast range of scales, including planetary-scale
circulations, equatorial waves, and convection . The
BDC is a measure of aggregated transport on all spatial and temporal scales
and may provide insight into the different transport
contributions at and just above the TTL. There are currently no direct
measurements of the magnitude or variability of tropical upwelling near the
tropical tropopause e.g.,.
The tape recorder signal emerges from time–height plots of zonally averaged water vapor in the tropical lower stratosphere.
Figure shows the tape recorder signal
obtained from microwave limb
sounder (MLS) measurements. Although the transport through the TTL and the
lower stratosphere is strongly guided by slow upward advection due to the
residual mean meridional mass circulation e.g.,, recent
studies have emphasized the importance of vertical and horizontal mixing in
the overall transport
, especially
near the tape head (the tropical tropopause).
The zonal mean tropical (10∘ S–10∘ N) tape
recorder signal of water vapor (the colored mixing ratio in ppmv) from the MLS
observations. The white line marks the 400 K isentrope for reference.
At the tape head, water vapor has a strong seasonal cycle
with anomalously high values during boreal summer and anomalously low values
during boreal winter. This is a direct result of the seasonal cycle in the
temperature of the cold point tropopause (CPT), anomalously warm during
boreal summer and anomalously cold during boreal winter, which affects the
water vapor content of the air through the process of freeze-drying
(dehydration). As a result of tropical upwelling, there is a phase lag
between the signal at the base versus the signal at higher altitudes. The
interannual variability associated with the quasi-biennial oscillation (QBO)
and the El Niño–Southern Oscillation (ENSO) also impacts the water vapor
transport through the TTL and the lower stratosphere e.g.,.
Chemistry–climate models (CCMs) show a large (10 K) spread in annual mean
CPT temperatures, and these discrepancies have been associated with their
differing transport characteristics ( and
) and even the details of the numerical schemes
. As mentioned above, these temperatures control the amount
of water vapor entering the stratosphere with consequences for the models'
radiation budgets. Improved transport characteristics on various scales might help to narrow the CPT temperature spread. More accurate modeling of TTL processes is expected to
result in improved calculations of the global radiation balance, which is
important for future climate predictions. However, accurate simulations of
TTL transport require improved understanding of the dynamics in this region.
Horizontal mixing and slow upwelling near the tropical tropopause are closely
related because both are driven by Rossby wave breaking occurring between the tropics and the
extratropics. On the other hand, vertical mixing in the TTL and the lowermost
stratosphere may be directly or indirectly associated with tropical deep
convection. Overshooting convection directly leads to mixing but is limited
by the depth of the overshoots. Gravity waves and other equatorial waves
associated with deep convective clouds can propagate vertically into the
tropical stratosphere . When these waves dissipate, they
may cause vertical mixing, which is then indirectly associated with the
convection. Deep convection also influences water vapor concentrations in the
TTL either directly through the lofting of ice with subsequent sublimation
e.g., or indirectly through the dehydration associated
with the large-scale tropopause-level cold response to upper tropospheric
heating e.g.,.
The purpose of this study is to quantify the individual contributions to the
total transport of water vapor above the tropical tropopause in the hope of
improving our understanding of the multiscale nature of the dynamics in this
region, from quick, small-scale vertical mixing to slow, large-scale
residual vertical advection. Part of this study takes advantage of an
isentropic coordinate (i.e., quasi-Lagrangian) framework to visualize
transport. Horizontal mixing between the tropics and the midlatitudes is
quasi-adiabatic and therefore best described in isentropic coordinates
e.g.,. Vertical transport in isentropic
coordinates is by definition directly related to diabatic heating. A
component of vertical mixing, e.g., due to overshooting convection or
breaking small-scale gravity waves, may be assumed to take place
quasi-adiabatically
In the region of interest, the tropopause and
the
lower stratosphere, the dominant contribution to diabatic heating is due to
radiation (possibly including cloud radiative effects). We assume that the
timescales for mixing by small-scale processes are generally much shorter
than the relevant radiative timescales. The mixing may then be assumed to
take place quasi-adiabatically.
and will therefore leave different
signatures in isentropic versus pressure or height coordinates.
The paper is organized as follows. Sections 2 and 3 describe the data
and methods used in this study, respectively. Sections 4 and 5 present
the results in pressure and isentropic coordinates, respectively. Our results
are discussed in Sect. 6.
Data
Water vapor is a quasi-conserved tracer in the TTL and the lower stratosphere
and therefore offers insights into total transport. The slope of water vapor
isolines in a time–height plot is a measure of the effective upward speed of
the BDC. The microwave limb sounder (MLS) aboard the NASA Aura satellite,
launched in 2004, offers daily coverage with ∼ 3.5 km vertical
resolution within the TTL and nearly global horizontal coverage. These
measurements are reliable in the presence of aerosol or cirrus clouds. We use
MLS version 3.3 (v3.3) data obtained from the Aura website
(http://disc.gsfc.nasa.gov/datacollection/ML2H2O_003.html) following
the data quality screening given in the MLS data quality document
. The vertical resolution of MLS results in relatively coarse sampling of
the tropical lowermost stratosphere (e.g., the averaging kernel for the
∼80 hPa level includes a ∼20 % contribution from 100 hPa). At a
number of places, we therefore also include results using the older HALOE
dataset , which has doubled vertical resolution compared to
MLS.
We focus on the inner tropics by employing a
10∘ S–10∘ N latitude average, which ensures sufficient
sampling and covers the latitudinal variations in the location of maximum
upwelling. Tests with a slightly bigger latitude range of
15∘ S–15∘ N resulted in only minor quantitative
modifications of our results.
To enhance our understanding of transport processes and to test our methods,
we also employ the European Centre for Medium-Range Weather Forecasts (ECMWF)
Interim Reanalysis (ERA-i) on a Gaussian grid at T255 spectral resolution
(∼ 80 km or ∼ 0.7∘) on the 60 vertical model levels.
The available data spans from 1 January 1979 to the present with 6-hourly
temporal resolution, but we focus on the time frame that overlaps with MLS.
Tropical stratospheric transport in ECMWF's previous reanalysis system,
ERA-40, was twice as fast as that in ERA-i . For example, the
moist and dry signals of ERA-40's tape recorder signal reached 30 hPa only
about 3 months after leaving the 100 hPa level. In ERA-i, the transport
between those surfaces takes 6 months, which is closer to reality. Nonetheless, this
is still at least twice as fast compared to MLS observations as can be seen
in Fig. where the dotted lines roughly indicate
the evolution of the dry signal for each dataset cf..
ERA-i does not assimilate stratospheric water vapor. However, given how
strong of a function of the cold point temperature it is, and given that
temperatures are assimilated, ERA-i's stratospheric water vapor should not be
considered unconstrained. In fact,
Fig. shows that apart from the tape recorder
seasonality (i.e., the transport strength), ERA-i and MLS agree quite well in the
stratosphere (in terms of overall absolute values).
The climatological zonal mean tropical
(10∘ S–10∘ N) tape recorder signal (the water vapor mixing
ratio in ppmv) based on MLS (colors) and ERA-i reanalysis (black contours).
The red and purple dotted lines roughly indicate the evolution of the dry
minima with time for MLS and ERA-i, respectively.
To better understand the influence of data assimilation on transport in
ERA-i, we also analyze the tape recorder in the Goddard Earth Observing
System (GEOS) Chemistry Climate Model (CCM) without data assimilation.
also compared the effective vertical transport
velocities between MLS and the GEOS CCM, so using the same model eases the
comparison to previous work. The GEOS CCM combines atmospheric chemistry and
transport modules with NASA's GEOS circulation model. The GEOS CCM took part
in the Chemistry Climate Model Validation 2 activity (CCMVal-2), which
included other stratosphere-resolving, interactive chemistry models
performing historical (REF-B1) and future (REF-B2) runs. The historical runs
do not overlap with the MLS period. We therefore use the REF-B2 run to
analyze the same time period as available from MLS. Compared to all other
models in CCMVal-2, GEOS CCM was found to produce one of the best simulations
of mean age of air, a measure of the BDC speed. found the
CCM's residual circulation in the lower stratosphere to be somewhat slower
than what is implied through its tape recorder; however, our improved
effective velocity method shows it to be comparable in the annual mean. We will show that the separation
between GEOS CCM and ERA-i residual circulations is much smaller than the
separation between their effective velocities, implying an impact on
transport by data assimilation.
Methods
We use two methods to study transport in the tropical lowermost stratosphere.
First, we analyze the tape recorder signal to estimate the effective vertical
transport velocity as a measure of BDC tropical upwelling just above the
tropical tropopause, expanding on previous work in the literature. Second, we
study the relative roles of residual vertical advection and vertical and
horizontal mixing using a 1-D advection–diffusion–dilution model
similar to that in . We also use this simple, idealized model to
test the efficacy of the first method.
For altitudes higher than 21 km (∼40 hPa), methane oxidation acts as a
source for water vapor. Upon reaching 25 km (∼25 hPa), about
0.25–0.5 ppmv is added to the signal e.g.,.
Here, we focus on the lowermost stratosphere where this effect can be
largely neglected.
Effective vertical transport velocity
We follow and use phase-lagged correlations between
adjacent levels of the tape recorder signal to estimate an effective vertical
transport velocity, a method previously introduced by and
recently used in modified form by . The earlier studies
used large sample sizes (∼1 year) to compute the correlations. These
sample sizes tend to highlight interannual variability (such as due to the
QBO) over seasonal variability. Here, we modify this method to parse out
shorter-duration variability. First, we obtain correlation coefficients
between daily data at consecutive levels. The data at the higher level are
then shifted in 1-day increments up to 14 months to find the largest
correlation coefficient. A strong correlation between the data at the lower
level and the shifted data at the higher level is assumed to follow the tape
recorder. The effective transport vertical velocity, assigned to midpoints
between levels and time steps, is simply the distance between the levels
divided by the time shift associated with the largest correlation
coefficient. We consider effective transport velocities in both pressure and
isentropic coordinates. Vertical velocities in pressure coordinates will be
presented as log–pressure velocities to give the more often used unit of
mm s-1, using a constant scale height of 7 km
A more
appropriate scale height for the tropical lowermost stratosphere would be
6 km (H=RT0/g, where R is the gas constant for dry air, T0 is a
reference temperature, and g is the acceleration due to gravity). However, we
opt for 7 km as this is the most commonly used scale height in the expression
for log–pressure coordinates e.g.,.
.
Instead of using a large (∼365 days) sample size for computing the
correlation coefficients , we have found that a sample size
of ∼180 days is capable of parsing out the seasonal cycle of effective
transport velocity. Further, unlike , we retain high
correlations that occur at lags of less than 1 month. However, lags of less
than 7 days are omitted because they produce unrealistic and temporally
unvarying speeds with low correlations. Our modified phase-lagged correlation
method was tested on a synthetic tape recorder signal with varying advection
scenarios. The results show that the method is more likely to underestimate by
0.05 hPa day-1 below 60 hPa and more likely to overestimate by
0.05 hPa day-1 above 60 hPa. Small vertical velocities in the middle
stratosphere and rapid water vapor changes in time are not fully identified
(e.g., in May when the signal goes from dry to moist). Overall, the method
appears to successfully capture the seasonality and magnitude of the
transport.
We emphasize that this lag correlation method based on the observed tape
recorder signal results in an effective (vertical) transport velocity. When
mixing has negligible influence on the signal, this velocity may be assumed to
be approximately equal to the residual vertical velocity
. However, especially in the lowermost tropical
stratosphere, the effects of horizontal and vertical mixing may be
significant. Vertical mixing will cause the signal to spread between two
levels while reducing the time lag for maximum correlation and therefore
increase the inferred velocity. The influence of horizontal mixing
dilutes the tape recorder signal , but this depends on the horizontal
background structure that varies seasonally.
One-dimensional model
Estimates of the effects of vertical and horizontal mixing on the tape
recorder signal may be obtained by simulating this signal with a
1-D transport model:
∂tχ‾=-ω‾*∂pχ‾+∂p(Kp∂pχ‾)-αp(χ‾-χ‾ML)+S.
Here, χ‾ is the water vapor mixing ratio,
ω‾* is the residual vertical velocity, Kp is the
vertical diffusivity in pressure coordinates, αp is the horizontal
dilution rate in pressure coordinates, χ‾ML is the
midlatitude reference value of χ‾, and the overbars represent
the zonal mean. χ‾ML is obtained from the actual (seasonally varying) water vapor for each dataset, averaged over 30 to
60∘ latitude. We have
tested an alternative latitude range for χ‾ML of 15
to 45∘ and found no significant changes to our results. S is a
chemical source–sink term. We set S to zero because we are only interested
in the tape recorder below the level of methane oxidation, which becomes
important above ∼ 40 hPa . This also neglects cloud
formation or evaporation just above the tropopause, as well as a potential
contribution due to dehydration at the local cold point tropopause. We will
discuss this potential drawback in detail in Sect. 6. Our model is similar
to the one used in , except that it uses pressure coordinates (we
also use a potential temperature coordinate version; see below).
solved for annual mean parameters by defining the tape recorder
as a wave solution and inverse solving for advection, diffusion (vertical
mixing), and dilution (horizontal mixing). Although they tested their model
on synthetic data, the solutions from this approach are restricted because
they rely on the tape recorder fitting a perfect wave at each level, which
may be problematic in the presence of mixing. The most severe restriction,
however, comes from using an annual mean value for the residual vertical
velocity. It is by now well established that the strength of residual
tropical upwelling undergoes a significant seasonal cycle, with smaller
values in boreal summer e.g.,. The vertical transport due
to residual vertical advection alone slows down significantly during boreal
summer, enhancing the relative importance of mixing to total transport,
particularly in this season. Assuming annual mean values for the transport
parameters essentially underestimates the contribution due to mixing. We
therefore introduce seasonality in these parameters by prescribing reductions
and enhancements of 50 % over the course of the seasonal cycle. The 50 %
value results in realistic variations for vertical advection, which corresponds to estimates in the literature
e.g.,.
Seasonal variations in the mixing strengths are less well constrained by past
studies; for these we use the same value of 50 %. We tested other seasonal
cycle amplitudes for the MLS dataset in pressure coordinates by keeping a
50 % amplitude in two of the transport parameters while varying the third
(ranging from 0 to 100 %). Overall, we find that the seasonality in the
transport parameters has little influence on the tape recorder as long as the
amplitude remains below 75 % for the vertical transport parameters. Small
improvements in the simulated tape recorder signal can be obtained by making slight
adjustments to the seasonal cycle amplitude in vertical advection or vertical
mixing. In comparison, the tape recorder signal is hardly affected by changes
in the seasonal cycle amplitude of the horizontal mixing strength. Given the
mostly insignificant changes in the simulated tape recorder signal for modest
changes in seasonal cycle amplitudes, we stick to the 50 % values in this
study for simplicity.
We further remove the perfect wave restriction by running a parameter sweep
with varying strengths of each transport. Control values for the annual mean
solutions (denoted by the subscript “ctrl”) are taken to be the solutions
obtained by , including their vertical structure. Transport
strengths are varied from 0 to 10 times their control value. Apart from these
modifications, our model carries the same assumptions as discussed by
. It assumes that tropical air is horizontally well mixed within
the latitude bounds (here, 10∘ S to 10∘ N) and is
notably different, though not completely isolated, from midlatitude air. The
vertical eddy water vapor flux in the full water vapor budget can be
represented as instantaneous diffusion acting on the vertical gradient of
water vapor (ω′χ′‾≃-Kp∂pχ‾,
with K as a positive constant; further discussed below). Horizontal mixing by
midlatitude air is modeled by a linear relaxation process (dilution) in which
tropical air is relaxed towards χ‾ML with rate
αp. This last assumption represents a crude approximation;
horizontal mixing in the lowermost stratosphere is generally a more complex
process . Note that by taking
χ‾ML from the actual seasonally varying data, we
expect to better represent influences due to the monsoon circulations, e.g.,
during boreal summer e.g.,.
The effective vertical log–pressure transport velocities
(mm s-1; converted from pressure velocities by multiplying by -H/p;
with H=7 km) based on the phase-lagged correlation method (see text).
(a) The MLS observations (colors) vs. the ERA-i reanalysis (black
contours; note the different magnitude). (b) HALOE (colors) vs. MLS (black contours, same as the
colors on the left). The midpoint levels used for lag correlations are
indicated as white (MLS, HALOE) and black (ERA-i) bars on the right of each
panel.
We prescribe the seasonal cycle of advection (ω‾∗) as a
sine wave that peaks during boreal winter (on 1 January) when the
meridional circulation is strongest according to observations. Vertical
diffusion (K) is prescribed with the same seasonality, i.e., strongest
during boreal winter, which is consistent with the results in , and
when convective influence on the TTL is strongest
. While observational estimates of vertical mixing
and its seasonal cycle are sparse to nonexistent, this seasonal cycle can be
considered a plausible first guess and is found not to have a strong
influence on our results (see below). The seasonal cycle of horizontal mixing
αp is opposite from that of vertical advection and vertical mixing.
Horizontal mixing is prescribed to maximize during boreal summer (on 1
July) when the subtropical mixing barrier (jet) is relatively weak
. We tested the model with seasonality in vertical
advection only, which resulted in a somewhat lower performance with respect to
its ability to reproduce the observations; however, the main qualitative features
of our results to be presented in Sect. 4 are not affected.
We also use the 1-D transport model in isentropic coordinates.
This has the advantage that the representation of horizontal mixing becomes
more realistic. This process is driven by Rossby wave breaking and takes
place approximately along isentropes in the real atmosphere. Furthermore,
vertical mixing is partially an adiabatic process (e.g., if driven by
small-scale gravity wave breaking) and is therefore expected to contribute
less to transport through isentropic surfaces. On the other hand, comparison
to our datasets is more straightforward in pressure coordinates, so
additional insight may be gained by comparing the two coordinate systems. In
isentropic coordinates the model may be written as
∂tχ‾∗=-Q‾∗∂θχ‾∗+σ‾-1∂θ(σ‾Kθ∂θχ‾∗)-αθ(χ‾∗-χ‾ML∗)+S,
where Q is the diabatic heating rate and σ is isentropic (mass)
density (also often referred to as thickness). The overbars with asterisks
denote the
mass-weighted zonal averages (e.g.,
χ‾∗≡σχ‾/σ‾).
As measures of the model's performance in simulating the tape recorder, we
analyze the amplitude, phase, and annual mean of the water vapor mixing ratio at
80 hPa and 400 K for each parameter combination. The phase is obtained
using simple Fourier analysis, while the amplitude is obtained simply from
the minimum and maximum values. We introduce a score (out of 100 %; see
equation below) that is a function of the multiplying factors (a,b,c) on
the control values of the residual vertical velocity or the diabatic heating rate,
vertical diffusivity, and the horizontal dilution rate. For example, in pressure
coordinates, the factors (a,b,c) determine the values of
(ω‾∗,Kp,αp)=(aω‾ctrl∗,bKp,ctrl,cαp,ctrl).
Generally, we find that the strengths of vertical advection and horizontal
mixing are not independent, and their variations result in similar structures
(i.e., a=c with the high-scoring combination). This is perhaps not
surprising as both are a function of subtropical Rossby wave breaking
e.g.,. To highlight that typically a=c, we denote the
combined effects of vertical advection and horizontal mixing by G with the
control value Gctrl for a=c=1. There are rare cases in which the
original values for vertical advection and horizontal mixing
must be multiplied by different factors to create the highest score (i.e.,
where a≠c). In these cases, Gctrl represents a. For
example, if an optimal solution requires (a,b,c)=(1,1,3), then 1×Gctrl corresponds to a=1 and c=3, while 2×Gctrl corresponds to a=2 and c=6, and so on. These rare cases
will be discussed separately.
The score as a function of (a,b) (assuming c=a) is
score(a,b)=1001+|As-Ar||Ar|+|ϕs-ϕr||ϕr|+|χs-χr||χr|,
where A is the amplitude, ϕ is the phase, and χ is the water
vapor mixing ratio. The subscripts “s” and “r” refer to the synthetic and
real tape recorder signals, respectively.
Results in pressure coordinatesEffective vertical transport velocity
Both MLS and HALOE show seasonal variations in effective vertical transport
velocity in the TTL and the lower stratosphere, with stronger upwelling during
boreal winter (Fig. ). Boreal winter upward
transport is 2–3 times stronger than during summer in these datasets.
A finer vertical resolution in HALOE results in more consistent vertical
spreading of this seasonality up to ∼50 hPa. The difference in the
depth of the signal may be due to our method of underestimating small speeds,
which may be more pronounced in MLS with its coarser vertical resolution.
Seasonal variations are qualitatively similar in ERA-i, but velocities are
2–4 times greater than in MLS and HALOE.
Figure highlights that the inferred
effective vertical transport velocity is not necessarily the same as the
residual upward velocity. In ERA-i, the effective vertical transport velocity
is about 4 times larger than the residual vertical velocity at 80 hPa, which
points to the role of vertical and/or horizontal mixing in transport just
above the tropical tropopause (and amplified dispersion due to data
assimilation; see below). The MLS- and HALOE-derived transport velocities are
of similar magnitude as the residual circulation velocity in ERA-i. Taking
into account that ERA-i's residual vertical velocity seems biased high near
the tropical tropopause , this indicates that effective
vertical transport is stronger than by the residual circulation alone. The
double-minimum structure between April and August in MLS effective transport
velocity is likely the result of noisy data around the transition between the
wet and the dry part of the signal.
The effective vertical log–pressure transport velocities at
80 hPa (solid; converted from pressure velocities using H=7 km) compared
to the TEM vertical residual velocities (dashed) from ERA-i and GEOS CCM. The ERA-i effective
velocity has been divided by 2 to fit within the shown axis range.
The residual vertical velocity is about 25 % weaker in GEOS CCM (the green
lines in Fig. ) than in ERA-i, albeit with
identical seasonality. Its effective vertical transport velocity, however,
only shows very little seasonal variation and is significantly smaller than in ERA-i, allowing GEOS CCM to be in closer agreement with MLS and HALOE during boreal
winter. The large difference
between the effective transport transport velocities in GEOS CCM and ERA-i (up to 4 times larger in
ERA-i) suggests that excessive vertical dispersion due to data assimilation
dominates in ERA-i. Mixing appears to have a stronger influence on transport
in boreal summer in GEOS CCM (cf. the difference between the green dashed and
solid lines in Fig. ).
One-dimensional transport modeling
Figure shows that a range of
combinations that slightly vary G, but more so K, result in high-scoring
simulations of observed water vapor at 80 hPa for both MLS and HALOE.
Moderately high scores may be achieved by using the control value for
vertical mixing (Kctrl), but this requires increases in vertical
advection and horizontal mixing by more than 50 % of their control values.
Using Gctrl, on the other hand, a near-perfect score (near or
above 90 %) results from increasing K by a factor of 4 for MLS or 5.5 for
HALOE. The strength of vertical advection may be considered better
constrained from past studies e.g.,, while the
strength of vertical mixing remains more ambiguous. Closer inspection of the
individual tape recorder characteristics shows that high-scoring (above
90 %) simulations of its amplitude alone require at least 3×Kctrl. High-scoring simulations of only its phase, on the other
hand, are more sensitive to the strength of vertical advection and to
allowing transport seasonality (particularly vertical advection).
The percentage total scores (see text for details) of the synthetic MLS
(a), HALOE (b), and ERA-i (c) tape recorders at
80 hPa. The white stars mark the combinations producing the highest scores.
Figure compares
the tape recorder signal between our simple model and the satellite
observations using the transport combination (1×Gctrl,4×Kctrl) for MLS and (1×Gctrl,5.5×Kctrl) for HALOE (the white stars in
Fig. ). The time series at 80 hPa
(bottom panels) further shows that our parameter settings better capture the
observed seasonal water vapor evolution than the control
setting, although the seasonal cycle amplitude is still somewhat
underestimated. Note that the solution much better captures the
HALOE time series (on which it was based).
The best synthetic 1-D transport model solutions of the MLS (left;
a=c=1, b=4) and HALOE (right; a=c=1, b=5.5) tape recorders in
pressure coordinates (corresponding to the white stars in the left and middle
panels of Fig. , respectively). The
bottom panels show the annual cycle of the water vapor mixing ratio at
80 hPa produced using the control values (red), the above
synthetic values (blue), and the MLS and HALOE observations (black).
Inspecting the individual transport contributions to the time tendency of
water vapor for MLS (Fig. ) shows that vertical
advection and vertical mixing play equally significant roles in forming the
tape recorder signal at 80 hPa. Vertical mixing plays a particularly large
role during late summer/early fall. The transport contributions based on HALOE
are very similar (see Fig. S2 in the Supplement).
The contributions to the water vapor tendency (ppmv day-1) at
80 hPa from the best synthetic 1-D transport model solution for MLS
(a=c=1, b=4; corresponding to the white star in the left panel of
Fig. ). The red dashed line shows
the tendency due to the vertical residual velocity from ERA-i.
Horizontal mixing generally plays a small role, except during boreal spring.
Note that the tendency due to horizontal mixing is a function of both the
dilution rate αp and the background meridional gradient
(∼χ‾-χ‾ML). The latter becomes small
during boreal summer, when meridional mass transport maximizes, and this
explains why the tendency due to horizontal mixing maximizes during boreal
spring. This is consistent with the results in ; their Fig.
1a shows from trajectory calculations that the difference in the water vapor
mixing ratio between in-mixed extratropical air and tropical air is the largest
during boreal spring and becomes negligible during boreal summer.
Nevertheless, the strongest signature in the tropical mean water vapor will be
found when the accumulated tendency is the strongest; this happens during late
boreal summer when the tendency (the green line in
Fig. ) crosses through zero.
High-scoring simulations of the ERA-i tape recorder signal in pressure
coordinates require much greater amounts of vertical mixing than for the MLS
or HALOE observations (Fig. ).
Based on all parameter combinations tested, vertical mixing needs to be at
least an order of magnitude larger than the control values. We found that
high-scoring solutions also require strongly enhanced horizontal mixing
(multiple times its control value), whereas vertical advection may remain
unchanged from its control value (small changes in it require large changes
in both types of mixing to compensate). Gctrl therefore
corresponds to c=3a in the transport combinations for ERA-i, and the
x axis in Fig. b only extends to
3×Gctrl because changes in transport strength by more than 1
order of magnitude have not been examined.
The effective vertical transport velocities in isentropic coordinates
(effective diabatic heating rate; K day-1) based on the phase-lagged
correlation method. The colors indicate the MLS observations, and the black contours indicate the ERA-i
reanalysis (note the different magnitude). The midpoint levels used for
lag correlations are indicated as white bars on the right (same for MLS and
ERA-i).
The 1-D model results imply that eddy transport in the lowermost
stratosphere is strongly enhanced in ERA-i compared to observations,
especially in the vertical. Amplified vertical advection alone does not
result in very improved tape recorder simulations. In fact, even reduced
vertical advection may easily be compensated for by slight further amplifications
of the vertical and horizontal mixing. The enhanced eddy mixing in ERA-i is
likely a result of spurious dispersion due to data assimilation
, but could also result from diffusive numerical
schemes. In the case of the GEOS CCM, a transport combination more similar to
MLS or HALOE produces the highest scores: enhanced vertical mixing with
vertical advection and horizontal mixing near their control values (not
shown). This difference between the free-running model and the reanalyses
further points to excessive dispersion due to data assimilation in ERA-i. We
also note that our simulations of the GEOS CCM tape recorder signal are not
very sensitive to changes in vertical mixing strength, which is likely due to
its small vertical water vapor gradient so that vertical diffusion remains
small.
Results in isentropic coordinatesEffective vertical transport velocity
In isentropic coordinates, the effective vertical transport velocity
corresponds to diabatic heating. Figure
shows this diabatic effective vertical transport velocity for MLS and ERA-i
using the phase-lagged correlation method as before. The averages (zonally and in
time) in isentropic coordinates are appropriately obtained by applying
mass weighting, which is implicit in pressure coordinates. The seasonal
cycles of diabatic heating rates thus obtained are similar between MLS and
ERA-i, with maxima in the lowermost stratosphere during boreal winter, as
expected. The maximum diabatic heating from MLS is ∼1 K day-1. That
from ERA-i is 4–5 times larger and located slightly higher (at 410 K versus
390 K for MLS, perhaps related to temperature differences in this region).
The enhanced diabatic heating in ERA-i compared to MLS is consistent with
and , who found longwave cloud
radiative heating rates above 200 hPa to be larger in ERA-i compared to
other reanalyses and a detailed radiative transfer model.
note that water vapor contents, and therefore
the treatment of convective anvil clouds in ERA-i, could partially explain the
anomalous heating rates. ERA-i has also been found to exhibit clear-sky radiative heating rates that are ∼40 %
too large . However, the
discrepancy between MLS and ERA-i is likely also due to excessive vertical
and horizontal dispersion, as discussed in the previous section.
The difference between the effective vertical transport velocities and the
contributions due to vertical and horizontal mixing may be better understood
by considering the zonal mean tracer evolution equation, which in pressure
coordinates reads (written in Cartesian coordinates and neglecting sources
and sinks for simplicity)
∂tχ‾+ω‾∂pχ‾+v‾∂yχ‾=-∂yv′χ′‾-∂pω′χ′‾.
Here, v is the meridional velocity and the primes denote deviations from the
zonal mean (denoted by the overbars as before). The effective vertical transport
velocity (ωeff) results formally from establishing that
∂tχ‾+ωeff∂pχ‾=0.
Hence,
ωeff=ω‾+(∂pχ‾)-1(v‾∂yχ‾+∂yv′χ′‾+∂pω′χ′‾).
This shows
how both horizontal and vertical eddy fluxes (∼ mixing) lead to
differences between ω‾ and ωeff (note
that in the residual, transformed Eulerian mean form, horizontal mixing is
partially included in ω‾∗; more precisely, the part
that is aligned with the meridional eddy heat flux , so in
that form it is primarily the vertical mixing that creates differences
between ω‾ and ωeff). Horizontal
advection may cause an additional difference but is generally small in the
deep tropics.
In isentropic coordinates, the corresponding zonal mean tracer evolution equation reads
∂tχ‾∗+Q‾∗∂θχ‾∗+v‾∗∂yχ‾∗=-σ‾-1∂yv^σχ^‾-σ‾-1∂θQ^σχ^‾.
Here, the hats denote deviations from the mass-weighted zonal mean (e.g.,
χ^≡χ-χ‾∗). This is a slightly modified
version of that given in , formulated here for the
mass-weighted tracer mixing ratio. The effective vertical transport velocity
in this case (Qeff) results from
∂tχ‾∗+Qeff∂θχ‾∗=0.
Hence,
Qeff=Q‾∗+(∂θχ‾∗)-1v‾∗∂yχ‾∗+σ‾-1∂yv^σχ^‾+σ‾-1∂θQ^σχ^‾.
In this case, assuming quasi-adiabatic mixing processes (Q^≈0,
e.g., due to Rossby and gravity waves in the horizontal and vertical
direction, respectively) and neglecting horizontal advection, horizontal
mixing is the primary process that leads to differences between
Q‾∗ and Qeff.
Our estimates of Qeff from MLS agree roughly with diabatic
heating rate estimates in the TTL and the lower stratosphere
e.g.,, indicating that horizontal mixing
does not play a big role in the observed tape recorder signal
cf.. However, the difference between Q‾∗ and
Qeff is substantial in ERA-i, indicating excessive
horizontal dispersion in the lowermost stratosphere.
The estimated vertical eddy flux of water vapor based on the difference
in MLS effective vertical transport velocities between pressure and
isentropic coordinates (see text for details).
The total scores (%) of the synthetic MLS and ERA-i tape recorders at
400 K.
The best synthetic 1-D transport model solution (color shading;
a=b=c=1; corresponding to white star in left panel of
Fig. ) of the MLS water vapor tape
recorder signal (black contours for reference) in isentropic coordinates.
The contributions to the water vapor tendency (ppmv day-1) at
400 K from the best synthetic 1-D transport model solution for MLS
(a=b=c=1; corresponding to the white star in the left panel of
Fig. ). The red dashed line shows
the tendency due to vertical advection (diabatic heating) from ERA-i.
Further insight into the role of vertical mixing may be obtained by comparing
the effective vertical transport velocities in pressure and isentropic coordinates.
Specifically, an approximate expression relating their difference to the vertical
eddy tracer flux may be derived (outlined in “Appendix A”):
ω′χ′‾≈ωeff-Qeff(∂pθ‾)-1(∂θ¯χ‾)2∂θ¯θ¯χ‾.
The factor outside the square brackets involves derivatives of the mean
tracer mixing ratio with respect to the mean potential temperature, where
both means are taken in pressure coordinates. This expression suggests that
differences between the effective vertical transport velocities in the
pressure versus isentropic coordinates are directly related to vertical
mixing.
Figure shows the vertical profiles of
this approximate vertical eddy flux of water vapor for DJF and JJA. The flux
is predominantly negative in the lowermost stratosphere (in pressure
coordinates), indicating the expected upward eddy transport from high to low
background concentrations in height coordinates. This may serve as a sanity
check that the above approximation gives physically reasonable results. The
vertical gradient of the shown eddy flux
(∂pω′χ′‾) confirms that vertical
mixing contributes approximately 10-3 to 10-2 ppmv day-1 to
the overall water vapor tendency just above the tropical tropopause.
However, the tendencies resulting from these eddy flux estimates only agree
to within a factor of 10 with those derived from our 1-D model (cf.
Fig. ) and during DJF even have the opposite
sign. This indicates that the approximations going into our eddy flux
estimate at best provide
qualitative results, although uncertainties also exist with our 1-D model
results. Nevertheless, given the lack of observational estimates of vertical
eddy tracer fluxes on a zonal mean scale, our approach, which at its heart
takes advantage of comparing tracer evolutions in pressure and isentropic
coordinates, may prove useful when applied to future higher resolution
datasets.
One-dimensional transport modeling
In Sect. 4.2, we found that a successful simulation of the water vapor tape
recorder signal in pressure coordinates requires strongly enhanced values for
vertical mixing. A different story emerges when simulating the tape recorder
signal in isentropic coordinates. In this case, the original transport
parameters obtained in and translated into isentropic coordinates
cf. also lead to a successful simulation matching the
observations (with a score of ∼90 %, shown in
Fig. ). The corresponding time
tendencies at 400 K (roughly corresponding to 80 hPa), shown in
Fig. , reveal that the total tendency is
explained almost entirely by the contributions due to vertical advection
(∼ diabatic heating; the red line) and horizontal mixing (green), with the
former dominating throughout Northern Hemisphere (NH) winter and the latter dominating through NH
spring and early summer.
Figure a shows the scores for a
range of parameter combinations at 400 K for MLS, similar to
Fig. . The range of high-scoring
solutions is narrower than in pressure coordinates. Other than the reference
or control set of parameters (a=b=c=1), we also find maximum scores for two
other cases. The first case requires zero vertical mixing (b=K=0), while
vertical advection and horizontal mixing are at their control values
(a=c=1). The other case requires vertical mixing to remain at its control
value (b=K=1), while vertical advection and horizontal mixing are reduced
by half of their control values (a=c=0.5). Overall, vertical mixing plays a
smaller role in isentropic coordinates compared to pressure coordinates. This
is expected based on the assumption that vertical mixing takes place
quasi-adiabatically (see the discussion in the previous section).
Simulating the ERA-i tape recorder in isentropic coordinates increases in all
three transports (Fig. b). A
factor of 2–3 increase in vertical advection and horizontal mixing compared
to the control values, together with an increase by at least a factor of 4 in
vertical mixing, leads to maximum scores (>90 %). The increase in
vertical advection points once more to biases in the diabatic heating rates
in ERA-i (presumably due to longwave cloud radiative biases in the TTL, as
stated earlier). The increase in vertical mixing indicates excessive
dispersion even in isentropic coordinates. We have found, however, that large
changes in vertical mixing strength only lead to small changes in the
simulated tape recorder signal (the vertical gradients in the score
distribution in Fig. b are much
smaller than the horizontal gradients), indicating that it is not very
sensitive to this transport contribution.
Discussion
We have employed two methods to study transport contributions to the water
vapor tape recorder signal in the tropical lowermost stratosphere: inferred
effective vertical transport velocities and simple 1-D modeling in pressure
and isentropic coordinates. Both methods indicate a significant
role of vertical mixing in transport near the tropical tropopause. Our
effective vertical transport velocity is larger than residual circulation
upwelling, indicating additional vertical transport due to mixing. Our 1-D
model setup is in principle identical to that used in , with the
important modification of seasonal dependency in the transport parameters.
Residual circulation tropical upwelling is known to be much weaker during NH
summer compared to NH winter e.g.,. Using annual mean
vertical advection as in therefore artificially enhances its
contribution to the total vertical transport during NH summer. It is in
particular during NH summer, then, where vertical mixing (parameterized as
diffusion) plays a dominant role in the upward transport of water vapor,
although we have found it to play a significant role throughout the year. Our
most successful simulations of the observed tape recorder signal at 80 hPa
using our modified idealized 1-D transport model incorporated a vertical
diffusivity multiple times stronger compared to the control
setting.
As a caveat to our results, we stress that the Aura MLS vertical resolution of
∼3 km, and even HALOE's doubled resolution, are coarse relative to the
structures of interest in the lowermost tropical stratosphere. Our results
are not qualitatively different between the two satellite products (and time
periods). Higher resolution datasets are needed to make more definitive
conclusions
about the role of vertical mixing in tracer transport in this
region. Nevertheless, it is instructive to note that vertical mixing alone
can create a fairly realistic tape recorder signal using the 1-D model (not
shown). To the extent that vertical mixing plays an important role in
tropical lower stratospheric transport, the term “tape recorder”, which
refers more accurately to slow vertical advection, is misleading, at least
near the tropopause (the same is true if horizontal mixing is important).
One potential drawback from our model setup is the neglect of the sink
associated with explicit dehydration near the tape head (at the local cold
point tropopause). Although even the lowest cold point pressures are
generally higher than our lowest analyzed pressure level of 80 hPa
e.g.,, the relatively large MLS averaging kernel of
∼3 km means that the 100 hPa level still contributes 20 % to the
diagnosed 80 hPa level
More precisely, the output level is at
82.5 hPa
. This means that some of the dehydration happening at the local
cold point tropopause will be projected onto the 80 hPa MLS level. In fact,
Fig. shows that the absolute minimum in MLS
lower stratospheric water vapor is diagnosed at 80 hPa in February, which
suggests that part of the MLS signal during boreal winter at this level is
due to dehydration. This may be less of an issue with the finer resolution
HALOE dataset (cf. Fig. S1 in the Supplement), although it also shows an
absolute minimum during February at 80 hPa (but less pronounced compared to
MLS).
To test whether dehydration can have a significant effect on our results, we
have repeated our 1-D transport model calculation with a prescribed sink term
(S<0 in Eq. 1) (not shown). We used a seasonal functional form of a sine
wave with the strongest amplitude at 100 hPa that decays exponentially toward
lower pressures and is set to zero at and above 70 hPa. We assumed that
the strongest dehydration of S=-0.05 ppmv day-1 happens at 100 hPa in
January
This dehydration strength is consistent with that inferred
from the Lagrangian transport calculations made by ; Felix Ploeger,
personal communication (2016).
and that S=0 in July. This calculation
with prescribed dehydration results in a more successful simulation of the
water vapor evolution during boreal winter (as expected; our simulation
in Fig.
shows a moist bias during this season). The water vapor evolution during
boreal summer, however, becomes less realistic: the dry bias already evident
without dehydration
(Fig. ) generally
increases due to the propagation of the now dryer boreal winter signal into
boreal summer. We therefore conclude that while the neglect of dehydration in
our presented 1-D transport model results may explain the moist bias during
boreal winter and may question the diagnosed strength of vertical mixing in
that season, it does not improve the overall simulation of the water vapor
evolution throughout the year. In particular, dehydration tends to increase
the dry bias during boreal summer, which would then demand an even greater
contribution to the tape recorder signal due to mixing.
One possible reason for the dry bias during boreal summer is the neglect of
the potential contribution by convective hydration due to overshooting
convection; e.g.,. Estimates of this contribution for the tropics
are difficult, and so it is hard to say something more definitive. However,
hydration due to convective overshooting essentially represents vertical
mixing (of total water with subsequent evaporation of the condensate) and is
therefore partially accounted for by the vertical mixing term in our simple
transport simulations. Convection tends to reach deeper during boreal winter
e.g.,, which is consistent with our prescribed seasonality
for K. Note that the vertical mixing tendency is a function of both K and
the vertical curvature of water vapor; it is the latter that peaks during
boreal summer causing the strongest vertical mixing tendency during that
season.
The influence by dehydration would be expected to vanish at levels above
80 hPa. We have also applied our 1-D transport model to these higher levels
(not shown) and still find a significant impact by vertical mixing in
pressure coordinates, although its amplitude decreases with height. For
example, the top-scoring solution near 70 hPa uses 2×Kctrl
(i.e., half that at 80 hPa) and the control settings for vertical
advection and dilution. This supports our conclusion that vertical mixing is
likely more important than previously estimated, although higher resolution
datasets are needed to confirm this.
Support for the importance of vertical mixing in shaping the tape recorder
signal also comes from comparing pressure and isentropic coordinates. We
obtain physically reasonable differences between these coordinates. To the
extent that vertical mixing involves primarily quasi-adiabatic processes
(e.g., overshooting convection or breaking gravity waves), it is implicit in
isentropic coordinates. It should therefore be less strong relative to other
transport contributions when diagnosed in these coordinates, and this is
confirmed by our results based on both MLS and ERA-i. In fact, the observed
tape recorder signal could be successfully simulated with our simple 1-D
transport model using the control parameter settings translated into
isentropic coordinates. Our results for these coordinates, including the
importance of horizontal mixing for lowermost stratospheric transport, are
also consistent with previous findings in the literature
e.g.,. The contribution from dehydration (or any other
sources or sinks) would be expected to be largely independent of the coordinate
system used; hence, it would show up very similarly in both pressure and
isentropic coordinates. The fact that we find vertical mixing to be much more
important in pressure coordinates, but not so much in isentropic coordinates,
then speaks against it being artificially enhanced due to the neglect of
sources or sinks.
Another advantage of isentropic coordinates is that horizontal mixing, which
is primarily due to Rossby wave breaking taking place along isentropes, is
represented more dynamically consistently. It is conceivable that some of
this mixing gets mapped into the vertical (due to undulating isentropic
surfaces) when diagnosed in pressure coordinates. The simple 1-D formulation
of our transport model as in may misrepresent horizontal
mixing, such that part of our diagnosed vertical mixing in fact represents
masked horizontal mixing. Future work is required to shed more light on this
caveat.
Data assimilation as used in reanalyses is known to cause spurious dispersion
in the lower stratosphere e.g.,. This most likely
explains why our results indicate strongly enhanced vertical and horizontal
mixing in ERA-i relative to observations. The effective vertical transport
velocities inferred from the water vapor tape recorder signal are 3–4 times
greater in ERA-i than in MLS or HALOE. These transport velocities are also
significantly greater than ERA-i's residual circulation upwelling, suggesting
that tropical lower stratospheric transport in ERA-i does not behave like a
tape recorder. We find the vertical mixing in particular to be excessive in
ERA-i, and this makes sense given the strong vertical gradient of water vapor
near the tropical tropopause.
Another indicator for spurious transport caused by data assimilation in ERA-i
is that the transport contributions inferred from the free-running climate
model GEOS CCM are much more in alignment with the MLS or HALOE observations.
We have also simulated the GEOS tape recorder signal using our idealized 1-D
transport model and found similar transport parameter settings for the
highest scoring simulations as in MLS and HALOE (not shown). Preliminary
simulation results using other CCMs, however, show a range of vertical
diffusivities suggesting that vertical mixing plays a more significant role
in some models. Vertical diffusion likely also results numerically due to the
limited resolution in the models, which might lead to the numerical dissipation
of waves as they propagate through the tropical tropopause.
Overall, our results confirm that transport in the tropical lowermost
stratosphere is complicated with significant roles played by vertical
advection, vertical mixing, and horizontal mixing. Vertical advection (residual circulation upwelling) and horizontal mixing are both to a large
extent created by extratropical (Rossby) wave driving. Vertical mixing, on
the other hand, is created by small-scale processes, e.g., associated with
overshooting convection or breaking gravity waves. The details of how
these processes give rise to the inferred mixing are presently unclear.
found vertical eddy heat fluxes due to overshooting convection
to be of leading order importance in determining the temperature structure
around the cold point tropopause in their small-domain cloud model study.
Gravity wave breaking via convective instability has been shown not to be
very effective in mixing heat and constituents vertically
e.g.,. Inertio-gravity waves, on the other hand,
tend to break down more preferentially due to shear instability
e.g., and may give rise to substantially
stronger mixing. Nonlinear effects due to the strong stratification jump at
the tropical tropopause and the associated tropopause inversion layer
may also give rise to enhanced vertical mixing in this
region.
Due to the involved small horizontal and/or vertical scales, vertical mixing
is much less well constrained in global models, but might contribute to
variability and change from seasonal to centennial timescales. Given the
importance of stratospheric water vapor for the climate, it is important to
better constrain the transport processes shaping the tape recorder signal
near its base just above the tropical tropopause.
MLS data can be found at
http://disc.gsfc.nasa.gov/datacollection/ML2H2O_003.html (EOS MLS
Science Team, 2011); HALOE data can be found at
http://haloe.gats-inc.com/download/index.php (HALOE, 2009); and ERA-i
data can be found at
http://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=ml/
(ECMWF, 2014).
The Supplement related to this article is available online at doi:10.5194/acp-17-4337-2017-supplement.
Effective velocity comparison between pressure and isentropic coordinates
Neglecting the local time tendency of the zonal mean potential temperature, the zonal mean diabatic heating is approximately given by
Q‾≈ω‾∗∂pθ‾+∂pω′θ′‾,
where the last term may be thought of as representing the effects of vertical
mixing. Assuming that the θ-perturbations are primarily created by
quasi-adiabatic vertical displacements (e.g., associated with gravity waves)
acting on the background gradient, we can write
θ′≈-ξ∂pθ‾,
where ξ is the vertical displacement in pressure coordinates. Similarly,
perturbations in a quasi-conserved tracer can be written as
χ′≈-ξ∂pχ‾⇒θ′≈χ′∂pθ‾∂pχ‾.
This allows us to write the vertical eddy heat flux as
ω′θ′‾≈ω′χ′‾∂pθ‾∂pχ‾⇒Q‾≈ω‾∗∂pθ‾+∂pω′χ′‾∂pθ‾∂pχ‾.
Now, assuming that the effective vertical transport velocity for χ is primarily composed of a residual circulation contribution and vertical mixing
ωeff≈ω‾∗+∂pω′χ′‾(∂pχ‾)-1,
we can insert ω‾∗ from the expression for Q‾ to give
ωeff≈Q‾(∂pθ‾)-1-∂pω′χ′‾∂pθ‾∂pχ‾(∂pθ‾)-1+∂pω′χ′‾(∂pχ‾)-1=Q‾(∂pθ‾)-1-ω′χ′‾(∂pθ‾)-1∂p∂pθ‾∂pχ‾=Q‾(∂pθ‾)-1+ω′χ′‾∂θ¯θ¯χ‾(∂θ¯χ‾)2.
The last step uses
∂p=∂pθ‾∂θ¯. If
Q‾≈Qeff (neglecting the horizontal transport
contribution and still assuming quasi-adiabatic eddies), this provides an
estimate of the vertical eddy flux of the tracer χω′χ′‾≈ωeff-Qeff(∂pθ‾)-1(∂θ¯χ‾)2∂θ¯θ¯χ‾.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work has been supported by the US National Science Foundation's Climate
Dynamics Program under grant no. 1151768. ERA-Interim data were provided by ECMWF through NCAR. We acknowledge the criticism by one
anonymous reviewer, which sparked the discussion of the potential role of
dehydration in Sect. 6. The comments by another anonymous reviewer helped to
clarify many aspects of our paper. We further thank Timothy Dunkerton
for constructive criticism and for sharing his insights into the transport
processes shaping the tape recorder signal. Helpful comments on an earlier
version were provided by Felix Ploeger. Finally, we are grateful to the
editor, Rolf Müller, for diligently handling our paper. Edited by: R. Müller Reviewed by:
T. J. Dunkerton and two anonymous referees
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