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JOURNAL OF THE ATMOSPHERIC SCIENCES
VOLUME 67
Insights into Cloud-Top Height and Dynamics from the Seasonal Cycle
of Cloud-Top Heights Observed by MISR in the West Pacific Region
JUNG HYO CHAE* AND STEVEN C. SHERWOOD1
Department of Geology and Geophysics, Yale University, New Haven, Connecticut
(Manuscript received 5 February 2009, in final form 7 July 2009)
ABSTRACT
The connection between environmental stability and the height of tropical deep convective clouds is analyzed using stereo cloud height data from the Multiangle Imaging Spectroradiometer (MISR), focusing on
the seasonal cycle of clouds over the western Pacific Ocean. Three peaks in cloud-top height representing low,
mid-topped, and deep convective clouds are found as in previous studies. The optically thickest cloud heights
are roughly 2 km higher on the summer side of the equator, where CAPE is higher, than on the winter
side. Overall cloud height, however, is about the same on both sides of the equator, but ;600 m higher in
December–February (DJF) than in June–August (JJA). Because of variations in stratospheric upwelling,
temperatures near the tropopause exhibit a significant seasonal cycle, mainly above 13 km. Using an ensemble of simulations by the Weather Research and Forecasting (WRF) cloud-resolving model and a simple
overshooting parcel calculation, the authors show that the cloud height variation can be explained by that of
near-tropopause stability changes, including influence from heights above 14 km, even though the cloud
height peaks only near 12 km. This suggests that mixing above cloud top—not typically accounted for in
simple models of convection—is important in setting the height of the laminar (anvil) high clouds that result.
The MISR data indicate a seasonal variation in peak cloud-top temperature of ;5 K, despite the recent
proposal that cloud-top heights should track a fixed isotherm. That proposal must therefore be applied with
caution to any climate-change scenario that may involve significant changes in stratospheric upwelling.
1. Introduction
Tropical deep convective clouds have long been investigated and play an important role in the tropospheric energy cycle, Earth’s radiation budget, and the
transport of mass and water vapor into the stratosphere
(e.g., Sherwood and Dessler 2001). These roles are sensitive to the altitude reached by convection. Such heights
vary substantially throughout the tropics, accompanied
by qualitative differences in storms between different
regions (Liu and Zipser 2005), for reasons that are not
fully understood at present (see Sherwood et al. 2004a)
although variations in moist instability, relative humid-
* Current affiliation: Jet Propulsion Laboratory, Pasadena,
California.
1 Current affiliation: Climate Change Research Centre, University of New South Wales, Sydney, Australia.
Corresponding author address: Dr. Jung Hyo Chae, Jet Propulsion Laboratory, Pasadena, CA 91109.
E-mail: junghyo.chae@aya.yale.edu
DOI: 10.1175/2009JAS3099.1
Ó 2010 American Meteorological Society
ity, boundary layer thickness, and surface heterogeneity
have all been suggested.
Several studies have examined the sensitivity of convective frequency and strength to various thermodynamic
factors. Although early studies emphasized correlations
between convective properties and local surface temperature, Lau et al. (1994) and many others have argued that
convection is much more sensitive to large-scale motion
(correlated with surface temperature in the present-day
tropics) than to the temperature itself. Tompkins and
Craig (1999) also found in modeled radiative–convective
equilibrium that convective mass flux and cloud cover are
not sensitive to SST for a given large-scale ascent; however, cloud-top temperature increases when SST increases. Hartmann and Larson (2002) argued that the top
temperature of detrained anvil cloud should be climateinvariant, because the anvil forms where clear-sky radiative cooling from water vapor drops off in the upper
troposphere, and saturated water vapor depends on temperature according to the Clausius–Clapeyron relation.
Kuang and Hartmann (2007) supported this hypothesis
with a three-dimensional cloud-resolving model (CRM)
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CHAE AND SHERWOOD
simulation. The hypothesis has been tested with observations by Kubar et al. (2007), who noted that anvil
cloud-top temperatures could vary if relative humidity
changes, possibly by as much as 6–7 K. They tested for
this by comparing cloud heights in different regions, but
since these regions are not energetically closed, and the
hypothesis rests on energy conservation, it is not clear
that this is a good test. We will use our observations to
test this idea differently, by looking at variation in time
over a large area.
A number of processes occur in the tropical tropopause
layer (TTL)—a layer that we take to extend from a typical cloud outflow level to the highest levels affected by
clouds—that could challenge the validity of conclusions
based on simple models of convection. These include
the steady upwelling through the tropical tropopause
(Brewer 1949); evident vertical mixing and entrainment
effects within the TTL (Sherwood and Dessler 2001,
2003; Robinson and Sherwood 2006); and cirrus clouds,
which exert significant radiative effects (e.g., Ackerman
et al. 1988) and can form either in situ or as remnants of
previous anvil clouds (Webster and Heymsfield 2003).
In this paper, we will exploit seasonal variations in
tropical deep convective cloud-top height to investigate
the mechanisms that control the typical cloud-top height
reached. In particular, this should reveal whether convective cloud-top heights are affected by changes in the
TTL thermal structure, which exhibit a large seasonal
cycle of up to 88C variation just above the cold point. By
comparison, seasonal variations in tropospheric temperature near the equator are small, enabling something
approaching a controlled experiment. This seasonal cycle of temperature in the TTL is almost certainly caused
by a similar cycle in the ascent rate through the tropical
tropopause, remotely forced by dynamical mechanisms
(Rosenlof 1995; Highwood and Hoskins 1998; Norton
2006) and evident all across the tropical belt. The temperature cycle can, at least at 80 hPa and above, be
quantitatively explained by high-latitude wave-driving
of the Brewer–Dobson circulation and ozone, although
additional drivers exist at lower altitudes (Chae and
Sherwood 2007). We hypothesize here that the seasonal
variation of tropical convective cloud-top height can be
affected not only by that of the surface conditions but
also by the thermal conditions in the TTL and that it will
be evident in the response of clouds to the remotely
forced perturbation.
The seasonal variation of tropical deep convective
cloud-top height has not been thoroughly investigated.
Zhang (1993) investigated the seasonal variation of the
tropical deep convective cloud cover using geostationary
satellite data. He found that the highest and coldest clouds,
having top infrared temperatures ,200 K (.15 km),
249
showed prominent seasonal cycles. The maximum cloud
fraction occurred during Northern Hemisphere winter
when the tropopause was highest and coldest in the
tropics, but no significant seasonal cycle was found for
the tropical cloud fraction in the range of 12.5 to 15 km.
Folkins et al. (2006) argued that there is a significant
seasonal cycle of convective outflow near the tropical
tropopause calculated indirectly from the mass flux required to balance clear-sky radiative cooling, and they
inferred that the seasonal cycle of tropical deep convection is caused by SST (e.g., Salby et al. 2003; Salby and
Callaghan 2004). The highest and coldest convection
over the western Pacific occurs when the warmest equatorial sea surface temperature is in Northern Hemisphere
winter.
The most common technique for measuring deep
convective cloud-top height is to obtain a satellite-based
measure of the thermal brightness temperature. Deep
clouds that contain significant condensed water densities
are assumed to radiate as a blackbody. Satellite measurements of temperature are obtained in the infrared
window wavelength of 10–12 mm, which is then compared to local temperature sounding data to obtain the
cloud-top height (Fritz and Winston 1962; Smith and
Platt 1978). This method has several problems, including
those related to emissions from below the cloud top,
inexact knowledge of the environmental temperature
profile, and likely differences between the cloud and
environmental temperatures. Moreover, Sherwood et al.
(2004b) found that thermally estimated cloud tops are
typically 1–2 km too low compared to lidar data even for
optically thicker clouds; this systematic error depends
on cloud properties and thus may not be the same everywhere (Minnis et al. 2008). Because we seek to quantify cloud height changes in the presence of large changes
in the above factors that may bias thermal retrievals, we
have chosen not to use thermal cloud-top estimates in
this study.
The Multiangle Imaging Spectroradiometer (MISR)
measures geometric height directly from multiple directions and needs no other additional information on
temperature, making it a promising alternative. Although
it may be subject to other kinds of errors, we will argue
that these are less likely to be systematic. MISR has a
sufficient lateral sweep to yield large numbers of height
estimates in a few years of flight. Although MISR data
are available only in the morning, this is useful for observing maritime convection. An important advantage
of this over continental convection is that maritime environmental conditions are much less variable on small
time and space scales and are not complicated by topography, thus being easier to characterize. In this paper, we present an analysis of MISR data in section 3 and
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compare the seasonal cycle of cloud-top height to those
of key atmospheric environmental conditions in section
4. In section 5, we introduce simulations by an explicit
numerical cloud model driven by the observed changes
in temperature structure in order to explain the changes
in cloud-top height; we describe the results of this in
section 6.
2. Data and analysis methods
a. MISR
The MISR is carried onboard NASA’s Terra satellite,
which was launched into sun-synchronous Earth orbit on
18 December 1999 with equatorial overpasses near 10:30
a.m. and p.m. local time. The MISR obtains a 360-kmwide swath of imagery, allowing the entire Earth surface
to be viewed in a period of nine days at the equator and
two days at the poles. The intrinsic cross-track pixel dimension is 275 m at all off-nadir angles and 250 m at nadir.
The MISR has nine discrete cameras facing different
angles, with one pointing to nadir and four each viewing
forward and aft directions (26.18, 45.68, 60.08, and 70.58).
Each camera observes four spectral bands (446, 558, 672,
and 866 nm). The general concept of MISR cloud-top
height retrieval is as follows: A cloud can be detected by
cameras at two different angles and positions; the height
of the cloud relative to the surface can then be calculated
from the apparent change in position. However, it takes
7 min to view a given cloud top from all nine angles.
During this time, the cloud can move significantly. Because significant errors in cloud-top height can arise if
cloud motion is ignored, cloud motion (wind) data are
needed for accurate cloud-top height retrieval. Therefore, the first processing step for MISR cloud-top height
is to infer wind velocity at multiple angles. Stereo
heights are then calculated using a stereo-matching algorithm. To reduce the processing time, three cameras
are used to obtain wind vectors, and only two cameras
(one facing nadir and one at 626.18) are used to calculate cloud-top height. Detailed descriptions of the MISR
stereo cloud-top height retrieval algorithm have been
provided by Diner et al. (1999), Moroney et al. (2002),
and Muller et al. (2002). Further information on MISR
may also be found in Diner et al. (2002).
We analyzed version 16 of the stereo heights of
MISR’s level-2, top-of-atmosphere (TOA) cloud data
product; this version was stage-2 validated against Atmospheric Radiation Measurement (ARM) site data.
The horizontal resolution of the product is 1.1 km and
the vertical resolution is 560 m. We used only the ‘‘best
wind’’ stereo heights, on the advice of MISR science
team members (C. Maroney and R. Davies 2007, personal communication) and on the basis of our own tests
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(not shown), which included comparison to Moderate
Resolution Imaging Spectroradiometer (MODIS) cloud
height data. Of the total pixels, approximately 45%–
50% qualified as best wind.
We analyzed tropical cloud-top heights from the following six months: December 2004 and January and
February 2005 for Northern Hemisphere winter, and
June, July, and August 2005 for Northern Hemisphere
summer. Previous studies have found that tropical deep
convection, including overshooting over continents, has
a strong diurnal cycle (Hendon and Woodberry 1993;
Nesbitt et al. 2000; Alcala and Dessler 2002). Cloud-top
heights are low in the morning and highest in the afternoon over land. In contrast, clouds over the ocean
show little diurnal cycle. The Tropical Rainfall Measuring Mission (TRMM) dataset revealed that mean
tropical deep convective cloud-top height is much higher
over the ocean than over land at 10 a.m. local time when
the MISR passes over the equator (Liu and Zipser
2005). Therefore, in MISR observations, overshooting
convection over 14 and 17 km is frequent only over
water, especially over the warm pool area in both seasons. For this reason, and because of relative uniformity
of surface temperatures, we focus on the western Pacific
warm pool area (208S–208N, 1008–2008E).
It must be noted that MISR, like many other instruments, has difficulty retrieving the height of optically
thin cloud. When thicker cloud is present below, thin
overlying clouds (optical depth of as high as 5) can be
missed. However, even optically thin cirrus cloud (t ’
0.5) can be retrieved in cases without lower clouds or
bright surfaces (Marchand et al. 2007).
Cirrus and anvil cloud should be considered separately from deep convective cloud when examining
tropical cloud in the upper tropopause and TTL. Optically thin cirrus clouds with t ’ 0.5 are distributed between 14 and 18 km in the tropics and are frequently
collocated with deep convective clouds (Winker and
Trepte 1998; Comstock et al. 2002; Garrett et al. 2004;
Dessler et al. 2006a). Anvil cloud detrained from deep
convection also forms near the neutral buoyancy level
(Salby et al. 2003; Salby and Callaghan 2004).
Therefore, we divide the cloud types into two thickness categories using local albedo from the MISR level-2
TOA cloud red-channel albedo. Cloud albedo is generally determined by cloud optical depth and can be
used to establish cloud thickness, although there is
a nonlinear relationship between the two (Cahalan et al.
1994). We distinguish thicker-to-moderate clouds with
albedos .0.3 and thinner-to-moderate clouds with albedos ,0.3. Hereafter, we refer to these categories
simply as ‘‘thick’’ and ‘‘thin.’’ The thick category should
include all deep cumulus clouds and the thicker anvil
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CHAE AND SHERWOOD
251
FIG. 1. Radiosonde station from IGRA (208S–208N, 1008–2008E).
outflows, whereas the thin category will include all thin
cirrus and some thinner outflow clouds.
The results presented here were tested by doing
a similar analysis with the Cloud–Aerosol Lidar Infrared
Pathfinder Satellite Observations (CALIPSO)/Cloudsat
data, which are collected in the afternoon. Preliminary
results for the ocean closely match those given here and
will be presented elsewhere.
b. Radiosonde
Radiosonde data from same time period were used to
investigate the typical thermodynamic environmental
conditions in which the convection observed by MISR
developed. Sounding data were obtained from the Integrated Global Radiosonde Archive (IGRA). The IGRA
gathers global radiosonde data from various dataset
sources, as described in detail by Durre et al. (2006). We
used data from 44 stations in the west Pacific warm pool
area (208S–208N, 1008–2008E; Fig. 1). Convective available potential energy (CAPE; see section 4a) was computed for every sounding at each station for the same
time as the MISR observations. The first level of data
was required to be below the 800-hPa pressure surface
and the highest level of data was required to be above
the 100-hPa pressure surface; in addition, at least 50% of
the mandatory pressure levels specified by the World
Meteorological Organization (WMO 1996) had to be
valid. With these conditions, 4836 soundings were used
to calculate the CAPE in June–August (JJA), and 4178
were used for December–February (DJF). We assumed
an initial parcel starting point of 950 hPa in computing
CAPE.
3. MISR cloud-top height
The cloud-top height distribution in the warm pool
area shows three main peaks: near 2, 6, and 13 km
(Fig. 2). This trimodal distribution is clearly consistent
with the findings of previous studies (Johnson et al. 1999;
Jensen and Del Genio 2006; Dessler et al. 2006b; Kubar
et al. 2007; Kubar and Hartmann 2008). Johnson et al.
(1999) noted three abundant cloud types in the tropics,
corresponding to prominent stable layers: shallow trade
FIG. 2. The probability distribution of cloud-top height in warm
pool area (208S–208N, 1008–2008E). The solid line indicates all
cloud; the dashed line, thin cloud; and the dashed–dotted line, thick
cloud. Bins of 500 m are used for the histogram.
cumulus near the stable layer between 1 and 2 km, cumulus congestus near the 08C level at approximately
5 km, and cumulonimbus below the tropopause near
15 km.
The peak in thick cloud is higher than that of thin
cloud, such that thick cloud amounts are greater above
15 km, despite the fact that thin cirrus is widespread near
the tropopause. The main reason is that the MISR cannot detect very thin cirrus cloud of t , 0.5 (Marchand
et al. 2007), which includes many of the clouds at these
levels (e.g., Dessler et al. 2006b). Another likely reason is
that although MISR can detect the relatively optically
thin cloud above 15 km, this thin cloud can have a higher
albedo if optically thick cloud occurs beneath it, and the
latter may be detected instead. Lidar observations indicate that 50% of thin cirrus near the TTL overlap with
thick clouds (McFarquhar et al. 2000). This result shows
that the thin cloud peak could represent anvil cloud top
height, which also agrees with MODIS (see Figs. 3 and 8
in Kubar et al. 2007).
Figure 3 shows the seasonal cloud-top height distributions of thin (dashed line) and thick (solid line) clouds
over 10 km, normalized by the total number of clouds
over that height. The overall warm pool area (the same as
in Fig. 2) is shown in Fig. 3a. Profiles are also shown within
two subregions of the warm pool area: the areas where
deep convection occurs frequently in JJA (08–208N, 1008–
1608E; Fig. 3b), and DJF (208S–08, 1408–2008E; Fig. 3c).
The seasonal fractions of thick and thin clouds in the two
regions are shown in Table 1. Deep convective clouds
cover about 65% in each region in the dominant season.
Clearly, thin clouds are at least twice as frequent as thick
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TABLE 1. The seasonal fractions of thick and thin clouds over
10 km normalized by each region.
North of equator
Thick
Thin
South of equator
DJF
JJA
DJF
JJA
8.7%
28.0%
21.9%
41.2%
20.8%
43.9%
12.1%
23.0%
clouds and determine the positions of the peak in overall
cloud heights regardless of location or season.
The thick cloud peaks are about the same in the two
seasons over the whole warm pool area (Fig. 3a), occurring near 14 km, which is approximately 1 km higher
than the thin cloud peaks. In the two subregions, however (Figs. 3b,c), the seasonal distributions of thick
cloud differ. The thick cloud fraction above 14 km is
relatively greater in JJA north of the equator (Fig. 3b)
but greater in DJF south of the equator (Fig. 3c). The
thick cloud peak is thus about 2 km higher in the summer season of either hemisphere than in winter, and is
2–3 km higher than that of the thin clouds, whereas the
winter peaks of thick and thin categories are close together. Overshooting might be dominant in the warm
pool when deep convection is frequent, although the
fraction of thick cloud may be contaminated by albedo
limitations and might contain many thin cirrus clouds.
A more surprising result in Fig. 3 is that the peak for thin
cloud is consistently ;500 m lower in JJA than in DJF in
both regions. Even though deep convection can reach
higher in JJA than in DJF north of the equator, the peak
of thin clouds is lower in JJA than in DJF (Fig. 3b). This is
shown more clearly in Fig. 4, which shows only the thincloud results for both seasons. The seasonal shift occurs
together in the two regions (although the peaks show
slight differences), regardless of the behavior of deep
convection. This is peculiar, since our ‘‘thin’’ clouds are
presumed to be mostly thinner parts of anvils and other
convective debris rather than genuine thin-cirrus types
that might form independently of convection. The latter
cannot easily be detected by MISR and would be expected
to occur at higher levels. Instead, our ‘‘thin’’ cloud peak
matches well with the level of peak mass divergence from
tropical cloud systems (e.g., Folkins et al. 1999).
Why do these clouds disregard the strong seasonality
of convection evident in the thicker clouds and instead
show a common trend to occur higher in DJF? We now
explore this with radiosonde data and a cloud model.
FIG. 3. As in Fig. 2, but analyzing over 10 km and separating with
two seasons. Each seasonal cloud-top height is normalized by total
number of respective seasonal cloud pixels above 10 km. (a)
Overall warm pool area (208S–208N, 1008–2008E); (b) 08–208N,
1008–1608E; (c) 208S–08, 1408–2008E.
4. Environmental thermodynamic conditions
from radiosondes
Predictions of convective penetrations typically begin
with parcel theory. An air parcel with greater temperature
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CHAE AND SHERWOOD
be described as the work done on the air parcel by the
environment, from the level of free convection (LFC) to
the level of neutral buoyancy (LNB):
ð LNB
CAPE 5
LFC
FIG. 4. As in Fig. 3, but for thin clouds only from Fig. 3b (solid
line) and Fig. 3c (dashed line). Diamonds indicate JJA; triangles
indicate DJF.
and less density than its environment will move upward,
and this buoyant convection leads to cloud formation. In
principle, some of this energy will be available for conversion back to potential energy in an overshoot. An air
parcel ascending with positive buoyancy has its own
potential energy that changes into kinetic energy as it
rises, peaking at the neutral buoyancy level.
However, cloud-top heights, especially overshooting
tops, are usually observed far below such theoretical
values (e.g., Jorgensen and Lemone 1989; Sherwood
et al. 2004a). This is because parcel theory is confined by
many assumptions. For example, the calculation for
maximum cloud-top height in section 4b does not consider mixing between a parcel and environment, friction,
or compensating motion of the atmosphere.
a. CAPE
Studies have examined the cloud-top heights of
tropical deep convective cloud by using CAPE to represent convection strength (Emanuel 1994). CAPE can
(T y
T ya )Rd dlnP.
(1)
The virtual temperatures of an upwelling parcel and the
ambient air are represented by Ty and Tya, respectively,
and Rd is the gas constant of dry air. Tropical deep convection is often observed in high-CAPE conditions (e.g.,
Sherwood 1999; Jensen and Del Genio 2003). However,
mixing with environmental air and the retention of condensed water during uplift contaminate the idealized
parcel theory represented by CAPE (Jorgensen and
Lemone 1989; Lucas et al. 1994). Jorgensen and Lemone
(1989) reported that the cloud-top height is lower than
the idealized maximum cloud-top estimated from
CAPE, which converts kinetic energy without any loss.
Some observed variations in convective behavior cannot be explained by CAPE. For example, tropical convection over land is generally stronger than oceanic
convection, whereas CAPE is not much different in two
regions (LeMone and Zipser 1980; Jorgensen et al. 1985;
Lucas et al. 1994), and Sherwood et al. (2004a) found that
diurnal and regional variations of cloud-top height in the
Florida region are not explained by CAPE. Many other
significant factors have been suggested: midtroposphere
moisture (Brown and Zhang 1997; Takemi et al. 2004),
evaporation of precipitation (Khairoutdinov and Randall
2006), height of thermal inversion (Redelsperger et al.
2002), and surface thermal heterogeneity (Robinson et al.
2008). For the moment we focus on CAPE.
Figure 5 shows the probability distribution of CAPE
in the same seasons and regions as before. In the northern
part (Fig. 5b) CAPE is ;100 J kg21 higher in JJA than in
DJF, whereas south of the equator it is ;350 J kg21
lower. These changes are qualitatively consistent with the
latitudinal variations in the thick-cloud peaks in Fig. 3,
suggesting that the seasonal cycle in surface heating by
FIG. 5. (a)–(c) The relative probability distribution of CAPE in the same region as Figs. 3a–c, respectively.
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JOURNAL OF THE ATMOSPHERIC SCIENCES
FIG. 6. Lapse rate profiles from radiosonde. The solid line indicates DJF and the dashed line JJA; the dashed–dotted line shows
subtraction of JJA from DJF.
the sun is probably driving the north–south variations in
the peak height attained by convective clouds. Relative
humidity is also higher in the summer season, which
probably contributes further to this seasonal difference.
Averaged over the whole region, however (Fig. 5a),
the CAPE in both seasons is the same, approximately
900–1000 J kg21; the relative humidity, vertical buoyancy profiles (‘‘shape of the CAPE’’), and parcel neutral
buoyancy levels are also similar (not shown). However,
the observed cloud peak is always lower in JJA than
DJF. This indicates that low-to-mid-tropospheric conditions are not able to explain the hemispherically
symmetric component of the cloud changes, and some
other influence must be dominant.
b. Stability in the TTL
There is strong a seasonal thermodynamic cycle in
the TTL that is driven by seasonal variations in upwelling through the tropical tropopause (Rosenlof 1995;
Fueglistaler et al. 2009). On a tropics-wide basis, these
variations can be accounted for quantitatively by variations in midlatitude wave-driving of the stratosphere
(see Chae and Sherwood 2007), although locally other
factors such as the seasonal shifts of tropospheric convective heating can cause departures from the zonal
mean (Highwood and Hoskins 1998). Figure 6 shows
how static stability varies by season in the region of
study here. The lapse rate is almost invariant from the
surface to 200 hPa (near 12.5 km), where it attains its
maximum in both seasons. However, from here through
the TTL (up to ;70 hPa) the lapse rate is smaller (more
stable) in JJA than in DJF, with the largest difference
(1 K km21) at 100 hPa (the JJA cold point). The dif-
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FIG. 7. The maximum overshooting heights of each CAPE at
12 km. The triangle indicates an averaged January sounding; the
diamond, an averaged July sounding. A horizontal line indicates
the cold point height of each month (dotted line is DJF; dashed line
is JJA).
ference changes sign above 70 hPa. The seasonal change
in the lapse rate in both subregions is practically the
same as that for the overall warm pool area (not shown).
We explore how stability in the upper troposphere
might affect the overshooting cloud-top height, first using a simple parcel model. Suppose that the integral of
negative buoyancy from the LNB to the maximum
overshooting height (the work required to lift a parcel
from the LNB to this height) equals the CAPE, or parcel
kinetic energy at the LNB, and that an overshooting air
parcel undergoes a dry adiabatic process with no mixing
or friction:
ðh
max u
u
1
a
dz 5 CAPE ’ w2 ,
(2)
g
u
2
LNB
a
where ua and u are the ambient and overshooting parcel
potential temperature, respectively, and w is the vertical
velocity at LNB (taken here to be 12 km). We solve (2)
for hmax, using a prescribed CAPE ranging from 0 to
2500 J kg21, to obtain an estimated maximum overshoot height.
Figure 7 shows hmax as a function of CAPE given each
season’s mean sounding. The maximum overshooting
height increases with CAPE as expected. More importantly, provided that CAPE is near or above its observed
mean seasonal value, parcels can overshoot ;500 m
higher in DJF than JJA because of the environmental
stability difference. This difference is somewhat less
than the difference in cold-point altitude (also shown)
but—intriguingly—closely matches the observed seasonal
difference of convective outflow height. This motivates
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CHAE AND SHERWOOD
a more careful study of the impact of TTL stability using
a more sophisticated model.
5. Model and experiment setup
We seek to simulate tropical deep convection as
simply as possible, using short runs from a prescribed
initial condition. We do not run to equilibrium because
our interest is in how the convective evolution is controlled by the environment into which it grows (essentially the problem faced by a GCM convective scheme).
We thus avoid the more complicated question of how
this environment came about or may be modified subsequently by the convection, except to reiterate that the
TTL temperature changes are caused by remote influences, such that prescribing them in a good model
should produce the same results found in nature.
We used the Weather Research and Forecasting
(WRF) model, version 2, to perform the cloud-resolving
simulations. This model solves the fully compressible
hydrostatic equations (Wicker and Skamarock 2002).
The WRF can run with idealized or real initial data using
a periodic, symmetric, or open lateral boundary condition. Skamarock et al. (2005) have described the model
in detail.
Thus, we chose an idealized two-dimensional version
that had no atmospheric radiation and lacked important short convection time-scale effects, and we used a
Kessler microphysics scheme (Kessler 1969) including
cloud, water vapor, and rain, and no horizontal mean
flow (see below for a sensitivity test concerning this).
The initial model setting was the same as that used by
Robinson and Sherwood (2006) except for the forced
heating and different initial sounding. The model was
configured with 1200 points in the horizontal direction
and 200 points in the vertical direction. The horizontal
grid had constant spacing of 500 m, whereas the vertical
grid had stretched spacing varying from 500 m at the
surface to 70 m near the TTL. The domain was 28 km
high and 600 km wide. The model time step was 3 s, with
open lateral boundaries and free-slip upper and lower
boundaries. The uppermost 6 km included diffusive
damping to absorb vertical-propagating disturbances
without reflection.
Convection was initiated using localized surface heating of Gaussian shape, defined by
"
P 5 A exp
0.5)2
(x
b
255
a critical time. Perturbation heating was set to zero after
the critical time (approximately 1 h), and A and b were
set so that the maximum temperature perturbation at
the center was approximately 5 K, with 75% of surface
perturbation added to temperature at the second-lowest
level and 50% at the third-lowest level. While such hot
spots would not be expected realistically to form in ocean
surface waters, this artifice serves to initiate convection in
the model.
The intent here was to investigate how stability in the
upper troposphere influences the tropical deep convective cloud-top height. For this purpose, the only difference between the experiments was the background
soundings. Monthly averaged Southern Hemisphere
Additional Ozonesondes (SHADOZ) data were input
as the soundings. Because the lapse rate from the surface
to 200 hPa (12 km) averaged over the tropics is almost
same in the two seasons, as demonstrated in section 4b
(Fig. 6), we used the same sounding (that of January
2005) from the surface to 200 hPa for all runs to eliminate any other effects in the low and middle troposphere
in individual soundings. Any systematic differences between simulations must, therefore, arise from the profiles above 200 hPa.
Of 84 soundings, we chose the 22 monthly averaged
soundings that had the smallest temperature difference
from the standard sounding at 200 hPa; we then shifted
the soundings slightly to coincide with the standard
temperature profile to prevent a sharp temperature
change at 200 hPa. Because of the seasonal cycle of the
Brewer–Dobson circulation, the upper troposphere is
usually more stable in Northern Hemisphere summer
than in winter, up to the cold point in Northern Hemisphere winter (solid line in Fig. 8). However, stability
can sometimes change within the upper troposphere, as
shown for the temperature difference of April 2005
minus January 2005 (dashed line in Fig. 8). The April
sounding was much more unstable than the sounding
taken in January from 12 to 15 km, although the April
sounding had a lower and warmer cold point. The part of
the stability that plays an important role in determining
cloud-top height can be tested statistically using several
different soundings. Water vapor was saturated below
1.5 km, and 50% relative humidity was used from 2 km
until the cold point. The smallest mixing ratio was used
everywhere above the cold point.
#
dt,
(3)
where x is the horizontal coordinate scaled such that the
maximum heating is at the center of the domain and dt is
the time scale to maintain and increase heating within
6. Model results
a. Evolution of convective clouds
Some previous studies have employed CAPE with
values between 2000 and ;3000 J kg21 to simulate
overshooting convection reaching near or above the cold
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JOURNAL OF THE ATMOSPHERIC SCIENCES
VOLUME 67
FIG. 8. Temperature difference of input sounding between July
and January 2005 (solid) and between April and January 2005
(dashed).
FIG. 9. Time series of temperature (solid) and CAPE (dashed) with
a parcel starting at 950 hPa in the center of domain.
point (e.g., Lane et al. 2003; Robinson and Sherwood
2006). However, because we are interested in typical
rather than extreme convection, we used a more typical
CAPE value so that cloud reached approximately 14–
15 km, near the predominant peak in the observations.
Simulated cloud height will be sensitive to many uncontrolled factors including model resolution and dimensionality, ice physics, and so on. Ensuring that the
‘‘control’’ simulation produces clouds near the right
level is important for simulating realistically the sensitivity to small perturbations. Figure 9 shows the time
series of simulated changes in temperature and CAPE
(with an initial parcel level of 950 hPa). The maximum
CAPE is approximately 1500 J kg21, which is 200 J kg21
greater than the average measured environmental CAPE
of 1300 J kg21, and the near-surface temperature has
a maximum of 302 K at 50 min and then decreases to
295 K by rainfall after a few hours of simulation. Averaged temperature and humidity within 20 km from the
center of the heat source were used to calculate CAPE
and temperature. CAPE can differ depending on which
air parcel is used as the initial updraft position. CAPE
values are about 500 J kg21 higher if parcels are lifted
from 980 hPa, but seasonal differences are unaffected.
Surface temperature at the center of the heated area
increased until 50 min and then decreased until 220 min.
CAPE did not peak until almost an hour later than
temperature. Figure 10 shows four snapshots of the
formation and spread of deep convective cloud. The
cloud started to form immediately after the maximum
CAPE. One hour after formation, the cloud reached the
lower level of the TTL. The deep convective cloud then
spread out, creating a broad anvil cloud.
b. Stability and cloud-top height
We considered the cloud-top height at a horizontal
location and time to be where the cumulative water
content from above reached .0.2 g kg21 in a column
(roughly unit optical depth). We were particularly interested in two statistics of this cloud-top height field.
One is the maximum cloud-top height (MCH), which is
the uppermost height that convection reaches during the
simulation. The cloud usually reaches this height before
spreading out. The other is the detrainment cloud-top
height of convection (DCH), which is calculated as the
height with the largest number of cloud-top occurrences
after convection has reached the MCH. This is a measure of the height of detrained anvil cloud. Figure 11
shows the relationship between these two measures
among the 22 WRF runs. The MCH ranges from 13 to
15 km, and the DHC ranges from 11 to 14 km, or ;1 km
lower than the MCH. The MCH heights are similar to
those observed for thick cloud in each hemisphere’s
summer as shown by MISR observations, and the DCH
is similar to the peak of thin cloud.
The correlation between the local lapse rate and
cloud-top height among the 22 model runs is shown in
Fig. 12. Both cloud-top heights correlate positively up to
18 km and negatively above. This profile closely resembles the seasonal variation of lapse rate (Fig. 6),
indicating that the dominant variation in soundings and
simulated cloud response is seasonal and that the simulated cloud heights are deeper in DJF. However, this
means that a more careful statistical analysis will be
required to determine which aspects of the sounding
control cloud height.
JANUARY 2010
CHAE AND SHERWOOD
257
FIG. 10. Four snapshots of the cloud water (dark shading) and potential temperature contours at (a) 140, (b) 170,
(c) 200, and (d) 230 min.
7. Simple statistical model
The input soundings can have different lapse rate behavior at different heights, as illustrated by the monthly
average soundings in Fig. 8. For example, the simulated
MCH and DCH for the April 2005 sounding (14.6/
13.4 km) are 800 m higher than the respective quantities
predicted for in January 2005 (14.1/13.1 km) although
the average lapse rate from 12 km to cold point is greater
(more unstable) in January. This shows that stability
from 12 to 15 km is more important than that higher up,
at least for this case.
To distinguish contributions from different heights we
created a simple multiple regression model between the
cloud detrainment height and stability in several layers:
DCH 5 c1 S1 1 c2 S2 1 c3 S3 1 const.
(4)
In Eq. (4), S1, S2, and S3 indicate mean lapse rates in the
200–150-, 150–100-, and 100–70-hPa layers, respectively.
Regression of the 22 simulation results yields c1, c2, and
c3 of 0.37, 0.55, and 20.13 (km2 K21), respectively, with
a constant of 7.36 km. Stability in layers 1 and 2 evidently reduces outflow heights. However, the 1-sigma
uncertainties of c1, c2, and c3 are 0.56, 0.19, and 0.15,
respectively, so that only the coefficient for layer 2 is
highly significant. According to the linear regression
model, ;50% of the variance in cloud height can be
attributed to influences at 14–16 km (layer 2), well
above the mean outflow height.
Figure 13 shows the distribution of simulated DHC
values using the statistical model (4) and DJF versus JJA
radiosonde soundings as lapse rates input. The JJA result is approximately 600 m lower than the DJF result
(peak height: 12.9 versus 12.2 km), in agreement with
the observed seasonal difference for detrained cloud
(Fig. 4). Thus, WRF is able to reproduce the observed
result, based only on lapse rate changes above 11.5 km,
and with a significant contribution from lapse rates at
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VOLUME 67
FIG. 11. Scatterplot between maximum cloud-top and outflow
anvil heights.
FIG. 12. Correlation coefficient between lapse rate profile and
two cloud tops (solid line is detrainment layer; dashed line is
highest cloud top).
14–16 km, or 1–4 km above the outflow peak. The simulated peak is narrower than observed, but this is expected because we used only a single representative
sounding below 200 hPa, whereas in the real atmosphere
a wider variety of conditions would occur (see Fig. 5),
broadening the distribution.
We tested the robustness of the seasonal difference by
repeating the DJF and JJA simulations with the Ferrier
ice microphysics scheme instead of the Kessler (no ice)
scheme. Although the Ferrier scheme produced a lower
cloud top, the seasonal difference was the same as with
the Kessler scheme (not shown).
1) The MISR cloud-top height distribution shows three
peaks near 2, 6, and 13 km. This trimodal distribution
agrees well with the findings of previous studies
(Johnson et al. 1999; Jensen and Del Genio 2006;
Dessler et al. 2006b; Kubar et al. 2007).
2) The deepest, optically thickest clouds in the warm
pool area were observed in the summer season of
each hemisphere, consistent with higher CAPE, with
a height variation of ;2 km.
3) The optically thinner, anvil top heights observed by
MISR were higher by ;500 m in DJF than in JJA
regardless of hemisphere/CAPE. This cannot be explained by standard parcel theory but was reproduced
by WRF. This is evidently caused by the seasonal
8. Discussion and summary
We analyzed the tropical deep convective cloud-top
height observed from the Multiangle Imaging Spectroradiometer (MISR) with separate consideration of
optically thicker and thinner clouds (defined by their
visible albedo). Tropical deep convection (above 10 km)
made up at least 2% of coverage throughout the tropical
convergence zone, except in the eastern Pacific. However, ‘‘overshooting’’ clouds penetrating 14 km were
found mainly in the western Pacific warm pool area in
both seasons. Less tropical deep convection occurred
over land areas because convection has a strong diurnal
cycle over land and is weak when the MISR passes
the equator (10:30 a.m.). We also used a simple overshooting parcel calculation and a suite of simulations
with the cloud-resolving WRF numerical model to understand the results.
From this analysis, we have drawn the following
conclusions:
FIG. 13. Probability distribution of cloud outflow heights [for
DJF (solid) and JJA (dashed)], applied with a statistical model to
radiosonde data.
JANUARY 2010
CHAE AND SHERWOOD
259
change in stability near and above the outflow height
(which in turn results from variations in strength of
upwelling through the tropopause) and is independent
of any small differences below 10.5 km or 200 hPa.
The model results clearly indicate that changes in
stability up to the cold point affect the height of the main
cloud deck 2–4 km below the cold point. The simulated
seasonal cycle was similar to MISR observations, approximately 600 m. A simple statistic model, built from
the relationship between simulated convective outflow
height and stability in the TTL, well represented the
seasonal difference in MISR observations, despite some
limitations.
It is not fully understood yet how stability influences
anvil cloud-top height, but one plausible theory is that
mixing between overshooting convection and environment is the key and that stability plays an important role
in this mixing process. It has been known that convective
cooling and downward motion exist above tropical deep
convection (Sherwood 2000; Kuang and Bretherton 2004).
Sherwood and Dessler (2001) built a conceptual model
demonstrating how an overshooting air parcel descends
after mixing with environment, where the mixture of
cold cloud and warm environmental air descends to a
new, neutrally buoyant level. Since the temperature difference between overshooting cloud and environmental
air is greater in JJA than in DJF, mixtures should descend farther and outflow should be lower in JJA than in
DJF. The observed and simulated seasonal variations are
consistent with a simple exploratory calculation of this.
One puzzling finding in the MISR observations is that
substantial increases in deep convective height do not
seem to affect those of the later outflows, and it is only
the latter that respond to stability changes. One would
expect the thickest clouds to respond and the thinner
ones to follow them. One possible explanation is that the
key mixing/buoyancy sorting processes occur after the
initial updraft has collapsed. The WRF simulations
showed all measures of cloud-top height responding to
the stability, so the behavior of peak heights of thickest
clouds in MISR requires further study.
Hartmann and Larson (2002) argued that the tropical
anvil cloud-top temperature is not changed by global-scale
increases in the sea surface temperature (SST). This is
referred to as the fixed anvil temperature (FAT) hypothesis. They pointed out that the rapid decrease in radiative
cooling rate is governed by water vapor, the main emitter
in the upper troposphere, and saturation specific humidity
is a function of temperature from the Clausius–Clapeyron
relationship. Therefore, they argued, anvil clouds at the
same height as the rapidly decreasing radiative cooling
in clear-sky regions should remain on the same temper-
FIG. 14. The same as the solid line of Fig. 3a (both thick and thin
clouds), except as a function of temperature.
ature surface. This hypothesis is supported by numerical
simulations (Kuang and Hartmann 2007) but depends on
relative humidity being constant, which may cause differences in some circumstances (Kubar et al. 2007).
The seasonal variation in the cloud outflow level
found here cannot be explained by the FAT hypothesis,
as the temperature at the peak cloud-top height is approximately 5 K higher in JJA than in DJF (Fig. 14).
Hartmann and Larson (2002) did not consider the Brewer–
Dobson circulation or overshooting convection, assuming
that the temperature profile is in equilibrium with moist
adiabatic processes. Our result shows that the seasonal
variations of mean upwelling near the tropopause are
sufficient to cause relatively large departures from the
predicted behavior by perturbing the energy budget in
a way not considered in that study.
The seasonal cycle of convective outflow height is
linked with ozone near the tropopause. For example, this
is reduced in Northern Hemisphere winter when convective outflow is high (Folkins et al. 2006) and reduced
ozone events are observed in deep convection conditions
(Solomon et al. 2005). Because ozone heats the TTL by
absorbing both solar and infrared radiation, its seasonal
cycle significantly amplifies (and slightly delays) that of
temperature in the TTL (Chae and Sherwood 2007).
Randel et al. (2004, 2006) found that stratospheric
water vapor dropped suddenly from 2001 and that this
drop was well correlated with the colder tropical tropopause and lower ozone mixing ratio. They explained this
water vapor drop by increasing Brewer–Dobson circulation. If the intensity of Brewer–Dobson circulation
changes with future climate change, the tropical anvil
cloud-top height and its radiative effects may also
change. According to our result, this should have reduced the stability and caused convective outflow height
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JOURNAL OF THE ATMOSPHERIC SCIENCES
to move upward. This should produce a positive feedback on temperature in TTL because higher convective
outflows would reduce ozone, further cooling the TTL.
MISR has limited ability to detect thin cirrus, cloud
optical depth and multilayer clouds, and convection
over tropical landmasses, which occurs mainly in the
afternoon. The recently launched CloudSat/CALIPSO
satellite pair will help to investigate the seasonal cloudtop height variation further and with better resolution
of various cloud types. Their ability to measure cloud
information in the afternoon as opposed to MISR’s
morning overpasses will allow a complementary study
with respect to the marked diurnal variation of clouds,
especially over land.
Acknowledgments. We thank F. Robinson for his help
in running the WRF model, and C. Maroney and the rest
of the MISR science team for help and advice. This research was funded by NASA IDS Grant NNG04GH66G.
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