Horizontal transport and the dehydration of the stratosphere

Horizontal transport and the dehydration of the stratosphere
James R. Holton
University of Washington, Seattle, Washington
Andrew Gettelman
National Center for Atmospheric Research, Boulder, Colorado
Abstract. The coldest tropopause temperatures occur over the
equatorial West Pacific during Northern Hemisphere winter. Horizontal transport through this “cold trap” region causes air parcels
that reach the tropopause at other longitudes to be dehydrated to
the very low saturation mixing ratios characteristic of the cold
trap, and hence can explain why observed tropical stratospheric
water vapor mixing ratios are often lower than the saturation mixing ratio at the mean tropopause temperature. Horizontal transport of water vapor can also explain how a persistent layer of
subvisible cirrus can exist near the tropopause in the cold trap
even though observations suggest that there is diabatic cooling
and subsidence, rather than diabatic heating and rising through
the tropopause in this region. Thus, horizontal transport in the
tropical transition layer in the vicinity of the tropopause plays an
important role in the water balance of the stratosphere.
1. Introduction
It is now recognized [e.g., Highwood and Hoskins, 1998] that
the tropical tropopause is not a sharp boundary. Rather, there is a
tropical transition layer (TTL) between about 14-19 km, in which
the dynamical and chemical properties of the atmosphere gradually change from those characteristic of the troposphere to those
characteristic of the stratosphere. The purpose of this paper is to
demonstrate that horizontal motion within the TTL plays an important role in the dehydration of the stratosphere.
Since the work of Brewer [1949] explanations for the observed
aridity of the stratosphere have focused on vertical transport across
the tropical tropopause accompanied by freeze drying to the saturation mixing ratio characteristic of the local tropopause. Although
Brewer’s qualitative model is now generally accepted, the space
and time scales of the motions, and the dynamical, radiative, and
physical processes involved remain controversial. In focusing
solely on vertical motions, previous studies have ignored the fact
that the ratio of the characteristic horizontal velocity (~5 m s-1) to
the global-scale mean vertical velocity (~0.5 mm s-1) is about 104
near the tropical tropopause. Thus, air parcels moving with the
mean wind in the TTL travel horizontally several thousand kilometers while ascending only a few hundred meters. Saturation
mixing ratios for such parcels will be influenced by horizontal
temperature gradients as well as by vertical gradients. Hence, insofar as large-scale motions dominate transport in the TTL, it is
not appropriate to consider only vertical advection of air parcels.
If, however, overshooting cumulus convective turrets were to account for the bulk of the irreversible transport across the tropical
tropopause, the ratio of horizontal to vertical displacement would
be far smaller, and processes associated with horizontal advection would be secondary.
Some studies [e.g., Danielsen, 1982; Sherwood and Dessler,
2001] have in fact suggested that dehydration is controlled by
convective scale motions. In this model, convective overshooting creates anomalously cold air parcels with very low ice saturation mixing ratios. This is followed by detrainment and subsequent mixing of cloud air with stratospheric air. Efficient dehydration requires, however, that an air parcel remain at or near the
temperature of the tropical tropopause for sufficiently long so
that ice crystals formed by the freeze drying process can sediment out. It is by no means clear that the convective overshooting model could meet this requirement. Furthermore, recent studies
[e.g., Highwood and Hoskins, 1998; Folkins et al., 1999;
Gettelman et al., 2001] suggest that overshooting of tropical convection into the interior of the TTL is not a common occurrence,
and that the characteristics of the bulk of the TTL are not primarily controlled by convective fluxes. Detrainment from convection does, however, apparently provide a significant fraction of
the mass input into the lower half of the TTL [Dessler, 2001],
though there is little evidence for convective input above about
the 16 km level.
Thus, the bulk of evidence suggests that large-scale slow vertical ascent dominates mass transport across the tropical tropopause, and that slow ascent is required for effective dehydration.
It has long been generally believed, however, that the ice saturation mixing ratio at the mean temperature of the tropical tropopause is too high to account for observed stratospheric mixing
ratios if cross-tropopause motion occurs uniformly throughout
the tropics [e.g., Newell and Gould-Stewart, 1981]. This belief
is not universally accepted; Dessler [1998] argued, on the contrary, that dehydration of air to the saturation mixing ratio at the
mean tropical tropopause temperature could indeed account for
the observed stratospheric humidity. Other recent analyses [e.g.,
Michelsen et al., 2000; Zhou et al., 2001] suggest, however, that
the mean mixing ratio of water vapor at entry to the stratosphere
(~3.8 ppmv), is indeed lower than the ice saturation mixing ratio
at the mean tropopause temperature (~4.5 ppmv).
The apparent inability of freeze drying at the mean tropical
tropopause temperature to dehydrate the stratosphere to observed
water vapor mixing ratios led Newell and Gould-Stewart [1981]
to propose the “stratospheric fountain” hypothesis. According to
this hypothesis transport of air into the stratosphere occurs preferentially in areas where the tropical tropopause temperatures are
below their annual and longitudinal mean values. The coldest
tropopause conditions are in the tropical West Pacific in Northern Hemisphere winter. This region has come to be commonly
known as the “fountain” region. Recent observational and model
results suggest, however, that the tropical Western Pacific is actually an area with net subsidence at the tropopause [e.g.,
Sherwood, 2000; Gettelman et al., 2000] despite the fact that in
this region the tropopause is colder than the tropical mean and
subvisible cirrus clouds are commonly observed.
Thus, there is a paradox: Freeze drying to the saturation mixing ratio characteristic of the exceptionally cold tropopause of
the tropical Western Pacific is apparently required to account for
the observed very low stratospheric water vapor mixing ratios.
Such freeze drying would appear to require slow upwelling in
that region to produce cooling and condensation and to allow time
for the ice crystals formed in the freezing process to sediment
out. Observations, however, suggest that the mean vertical motion is downward at the tropopause over the Western Pacific, not
upward. Thus the term “fountain” is not appropriate. Rather, this
region will be referred to below as the “cold trap”.
2. An Alternative Hypothesis for Dehydration
An explanation for the observed characteristics of the cold trap
region was recently proposed by Hartmann et al. [2001]. They
showed that when thin cirrus clouds occur just below the tropopause, but above a thick layer of convective anvil clouds that
extend to about 14 km in altitude, the tropopause layer cirrus are
radiatively cooled, leading to subsidence and an anomalously low
tropopause temperature. Hartmann et al. [2001] suggested that
horizontal advection of air parcels that crossed the tropopause
upstream of the cold trap could provide the moisture source for
maintenance of the thin cirrus near the tropopause in the cold
trap. At the same time, owing to particle sedimentation in the thin
cirrus, passage of air through this region would dehydrate air to
mixing ratios less than the saturation mixing ratio at the tropopause outside the cold trap region.
For a typical horizontal velocity of 5 m s-1 and a cooling rate
of 0.5 K day-1, a cooling of order 5 K would occur during passage
of a parcel from the edge to the center of the cold trap (~5000
km). Owing to the relatively long time scales (several days) associated with horizontal advection in this region, ice crystals formed
would be able to undergo significant sedimentation [Jensen et
al., 1996; Boehm et al., 1999] and irreversible dehydration would
occur. Downstream of the cold trap the newly dehydrated parcels
would again become subject to diabatic heating and rise irreversibly into the stratosphere.
In this alternative model, the equatorial Western Pacific region continues to play a crucial role in dehydration, but not as a
preferred region of net uplifting at the tropopause. In order to
elucidate the role of this region it will be necessary to contrast
conditions in the TTL in the Western Pacific to those at other
Climatological analyses [e.g., Highwood and Hoskins, 1998;
Simmons et al., 1999] show that during Northern Hemisphere
winter the equatorial tropopause is indeed coldest over the Western Pacific. The altitude of the tropical tropopause has a relatively small longitudinal variation [Seidel et al., 2001]. Thus, the
potential temperature at the tropical tropopause has a distinct minimum in the Western Pacific; isentropic surfaces are displaced
upward in this region. Air parcels that have ascended to the tropopause at other longitudes will be adiabatically cooled as they are
advected into the West Pacific cold trap. More importantly, once
such parcels enter the TTL over the Western Pacific, where high
altitude anvil clouds are prevalent in the troposphere, they will,
as shown by Hartmann et al. [2001], undergo significant diabatic
cooling and subsidence. Hence, they will have reduced ice saturation mixing ratios owing both to the temperature decrease and
the pressure increase.
The mean Northern Hemisphere winter circulation in the TTL
over the tropical Western Pacific and Maritime Continent region
features a subtropical anticyclone in each hemisphere bounded
on the poleward side by a subtropical westerly jet and on the equatorial side by equatorial easterlies. Back trajectory calculations
[Pfister et al., 2001] indicate that air parcels in the TTL over the
Indian Ocean during northern winter can be advected poleward
into the subtropical jet. They are then rapidly advected eastward
into the Central Pacific, where they drift equatorward. They then
can return westward through the cold trap region and, if they are
sufficiently close to the cold point tropopause can be dehydrated
to the very low saturation mixing ratio characteristic of that region. In other words, there is potential for air that has entered the
TTL in regions of warmer tropopause temperatures to be dehy-
drated by quasi-horizontal transport through the cold trap. This
dehydration by horizontal transport can also explain how thin cirrus can exist near the tropopause in the cold trap even in the presence of net sinking motion. The thin cirrus in turn provide evidence that dehydration is occurring in this region, and through
their effect on the radiation budget provide a feedback process to
maintain the cold anomaly. Thus, processing of air by horizontal
transport through the cold trap has the potential to explain the
observed features of the TTL in the Western Pacific and the observed water vapor budget of the stratosphere.
3. A Simple Illustration of the West Pacific Cold
Trap Hypothesis
The essential features of the cold trap hypothesis can be illustrated in a simple two-dimensional (longitude-height) transport
model for the equatorial tropopause region. In this model an annually varying temperature distribution T(x,z,t), and zonal mean
horizontal and vertical wind components (u,w) are specified; the
humidity is specified at the 14-km level, and the evolution of the
water vapor (qv) and the cloud ice (qi) distributions in the TTL
between 14-19 km are predicted. In order to focus on the effects
of the annual variation of the West Pacific cold trap a temperature
distribution based on Seidel et al. [2001] is specified consisting
of a time-independent standard atmosphere zonal mean, T0(z) and
a seasonally varying temperature perturbation centered at x = 0, z
= 16 km:
  z − ztrop  2 
  x2
T ( x, z, t ) = T0 ( z ) + Tc exp −
  exp −  
d  
 
 L 
(1 + cos(πt / 180)) / 2
where T0 has a minimum of 193 K at the tropopause (ztrop = 16.5
km), Tc = 4 K, d = 1 km, L = 2500 km, and t is the time in days.
The specified temperature distribution of (1) represents the seasonally varying West Pacific cold trap, but for simplicity it does
not include an annual variation of the tropopause temperature outside of the cold trap region. The cold trap temperature perturbation has a maximum negative value of 4 K, and has Gaussian
distributions in the horizontal and vertical directions (see Plate
1). The background zonal and vertical velocities are specified as
u = -10 m s-1, and w0 = +0.3 mm s-1, independent of longitude,
height, and time. To represent the observed sinking in the cold
trap region, which is assumed to be associated with the radiative
cooling of subvisible cirrus lying above deep convective anvil
clouds, we use the simple parameterization:
 x 2
w( x, z, t ) = w0 − ( 4 × 10 6 )qi exp −  
  L  
which for an ice mixing ratio of qi = 10-6 yields a maximum air
subsidence in the cold trap of about 0.1 mm s-1. The specification
of vertical velocity is based on the studies of Rosenlof [1995] and
Sherwood [2000], while the ice mixing ratio is based on ice water
content for thin cirrus reported by Heymsfield and McFarquhar
Water vapor and cloud ice are assumed to satisfy the following
∂ 2 qv
= −α ( qv − q˜ ) + K
∂z 2
∂ 2 qi
= −αqi + K
∂z 2
Here, q̃ (= 6 ppmv) designates the mean subtropical lower
stratospheric water vapor mixing ratio [Randel et al., 2001]. E
and C stand for evaporation and condensation, respectively. E=qi/
τE and C is zero unless qv>qs, in which case C=(qv–qs)/δt. The
time scale for E is τE =1 day and the time scale for C is δt =1 hr.
The rate coefficient for mixing with the subtropical air, α and
the vertical diffusion coefficient, K, are based on the estimates of
Mote et al. [1998]. Here α is assumed to decrease linearly from
3.1 × 10-7 s-1 at 14 km to 2.0 × 10-8 s-1 at 19 km, and K is set to the
constant value of 0.003 m2 s-1. Sedimentation of ice particles is
represented by adding a fall speed of 4 mm s-1 to the vertical velocity used in (2) for computing the advection of cloud ice. This
fall speed is consistent with a 5 µm particle radius [Boehm et al.,
Temperature and potential temperature: Winter
x 10-6
Vapor mixing ratio: Winter
x 10-6
Ice mixing ratio: Winter
Height (km)
Height (km)
ics. This upward advection of the water vapor minimum produced
by the winter cold trap produces an annual cycle with alternating
upward propagating vapor minimum and maxima. During Northern Hemisphere summer the lack of a cold trap allows the air to
maintain a higher mixing ratio, and at that season the hygropause
(level of minimum water vapor mixing ratio) occurs well above
the cold point tropopause.
The seasonal cycles of temperature, water vapor mixing ratio,
and ice mixing ratio at the center of the cold trap (x = 0) are
shown in Figures 1-3, respectively. During the three seasons when
there is a temperature minimum in the vicinity of x = 0 there is
substantial dehydration, and the water vapor minimum occurs at
the tropopause level, with a minimum value of about 3 ppmv at
the tropopause in winter. Owing to the effect of particle sedimentation there is very little cloud ice at the tropopause. Maximum
ice particle mixing ratios occur about 1 km below the cold point,
which is qualitatively in accord with observations [Pfister et al.,
The model presented here is a highly simplified representation of the equatorial stratosphere. In reality the background tropopause has an annual cycle both in temperature and in altitude; the
Plate 1. Longitude-height cross sections showing the specified
temperature distribution (color), potential temperature (isolines,
K), water vapor mixing ratio (ppmv), and ice mixing ratio for
Northern Hemisphere winter.
Equations (3) and (4) are solved for the time evolution of qv
and qi using a semi-Lagrangian algorithm with biquadratic interpolation (see Durran [1999], page 309). Humidity in the TTL is
poorly constrained by observations. For simplicity the model is
here initialized at 50% relative humidity, and is maintained at that
value at the lower boundary (14 km). The domain is assumed to
have a zonal scale of 18 000 km, with periodic boundary conditions. This represents the approximate distance for recirculation
of air transported through the tropopause level subtropical anticyclone over the Western Pacific [Pfister et al., 2001]. After integrating (3) and (4) for less than 360 days, the transient effects of
the initial condition have disappeared and a repeatable annual cycle
occurs. Longitude-height sections of the temperature, the water
vapor mixing ratio, and the ice-mixing ratio at winter solstice are
shown in Plate 1. As expected, there are low values of water
vapor mixing ratio and a thin cirrus cloud in the cold trap region.
Ice particles in the cirrus descend relative to the air as parcels
traverse the cold trap. This particle sedimentation causes a net
dehydration of the parcels, which is clearly visible downstream
of the cold trap. As air parcels move further downstream they
gradually ascend and are modified by mixing from the subtrop-
Temperature (K)
Figure 1. Vertical profiles of temperature for the four Northern
Hemisphere seasons at x = 0, the longitude of maximum temperature deviation from the zonal mean. The temperature profiles
are the same for autumn and spring.
Height (km)
14 —8000 —6000 —4000 —2000
Distance (km)
Vapor mixing ratio (ppmv)
Figure 2. Vertical profiles of water vapor mixing ratio for the
four Northern Hemisphere seasons at the same location as in Fig.
Height (km)
0.4 0.5
0.6 0.7
Ice mixing ratio (ppmv)
Figure 3. Vertical profiles of ice particle mixing ratio for the
four Northern Hemisphere seasons at the same location as in Fig.
zonal mean upwelling motion depends on season and altitude;
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the horizontal transport. Nevertheless, this model supports the
hypothesis that horizontal processing of air by passage through
the Western Pacific cold trap is an effective means to explain the
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A. Gettelman, NCAR, PO Box 3000, Boulder, Colorado,
80307-3000 (e-mail: andrew@ucar.edu)
J. R. Holton, Department of Atmospheric Sciences, Box
351640, University of Washington, Seattle WA 98195-1640 (email: holton@atmos.washington.edu)
(Received xxxx xx, 2001; revised xxxx xx, 2001;
accepted xxxx xx, 2001.)