Role of the Convection Scheme in Modeling Initiation and Intensification
of Tropical Depressions over the North Atlantic
J.-P. DUVEL
Laboratoire de Météorologie Dynamique, CNRS, École Normale Supérieure, Paris, France
S. J. CAMARGO
Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York
A. H. SOBEL
Lamont-Doherty Earth Observatory, Palisades, and Department of Applied Physics and Applied Mathematics,
Columbia University, New York, New York
(Manuscript received 6 June 2016, in final form 22 December 2016)
ABSTRACT
The authors analyze how modifications of the convective scheme modify the initiation of tropical de-
pression vortices (TDVs) and their intensification into stronger warm-cored tropical cyclone–like vortices
(TCs) in global climate model (GCM) simulations. The model’s original convection scheme has entrainment
and cloud-base mass flux closures based on moisture convergence. Two modifications are considered: one in
which entrainment is dependent on relative humidity and another in which the closure is based on the con-
vective available potential energy (CAPE).
Compared to reanalysis, TDVs are more numerous and intense in all three simulations, probably as a result of
excessive parameterized deep convection at the expense of convection detraining at midlevel. The relative
humidity–dependent entrainment rate increases both TDV initiation and intensification relative to the control.
This is because this entrainment rate is reduced in the moist center of the TDVs, giving more intense convective
precipitation, and also because it generates a moister environment that may favor the development of early
stage TDVs. The CAPE closure inhibits the parameterized convection in strong TDVs, thus limiting their
development despite a slight increase in the resolved convection. However, the maximum intensity reached by
TC-like TDVs is similar in the three simulations, showing the statistical character of these tendencies.
The simulated TCs develop from TDVs with different dynamical origins than those observed. For instance,
too many TDVs and TCs initiate near or over southern West Africa in the GCM, collocated with the maximum
in easterly wave activity, whose characteristics are also dependent on the convection scheme considered.
1. Introduction
Variations in the large-scale environment may have
important impacts on tropical cyclone (TC) activity,
whether those variations occur on intraseasonal
[Madden–Julian oscillation (MJO)] or interannual [El
Niño–Southern Oscillation (ENSO)] time scales, or in
response to longer-term global climate change. The sen-
sitivity of TCs to the large-scale environment can now be
studied using global climate models (GCMs; see e.g.,
Walsh et al. 2016; Camargo and Wing 2016). Cyclogenesis
is a complex process, however, and it is not trivial to
determine the causes of variations in TC activity, either in
nature or in a GCM. Considering early vortices’ initiation
and intensification processes separately can potentially
lead to a better assessment of the ability of GCMs to
correctly reproduce the sensitivity of TCs to the large-
scale environment.
A tropical cyclone may indeed form locally by con-
vective aggregation processes (not necessarily well
represented in a GCM), or it can be triggered dynami-
cally by preexisting disturbances or vortices. In the
‘‘vortex view’’ of TC genesis (Davis et al. 2008), the
vortices are seen as possible TC seeds that can be initi-
ated by tropical waves or by other mechanisms, related,
for example, to orography (Mozer and Zehnder 1996)
Corresponding author e-mail: J.-P. Duvel, jpduvel@lmd.ens.fr
A
PRIL 2017 D U V E L E T A L . 1495
DOI: 10.1175/MWR-D-16-0201.1
Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright
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well before their intensification to TC strength. If a high
percentage of TCs in a basin are initiated from these
vortices, then the physical source of these vortices be-
comes an important TC assessment criterion. By using
either GCM outputs or meteorological analysis com-
bined with TC observation databases, it is possible to
study the environmental conditions during the forma-
tion of vortices—referred to here as tropical depression
vortices (TDVs)—which can serve as TC seeds. For
example, previous studies (Liebmann et al. 1994; Duvel
2015) have shown that the MJO’s modulation of TC
frequency over the Indian Ocean is mainly due to its
modulation of the number of TDVs and only marginally
to its modulation of intensification processes. We are
interested here in applying the same approach to un-
derstand the sources of variability in TC characteristics
simulated by different GCM formulations. Over the
North Atlantic, African easterly waves (AEWs) are
known to be sources of cyclogenetic TDVs near the
West African coast (e.g., Landsea 1993; Dunkerton et al.
2009) and can be an important factor in the ability of
GCMs to simulate TC activity (Daloz et al. 2012). These
waves have long been studied (i.e., Carlson 1969; Burpee
1972, 1975; Reed et al. 1977), but GCMs still have dif-
ficulty in simulating AEWs, and there are still large
uncertainties regarding possible modifications of AEWs
due to global climate change (Martin and Thorncroft
2015). It is thus likely that part of the misrepresentation
of TCs in a GCM over the North Atlantic can be related
to the TDVs associated with AEWs.
With horizontal resolutions in the range of 0.18–18,a
GCM is able to simulate the initiation and intensification
of TDVs. Some TDVs may become very intense for part
of their path and have characteristics similar to observed
tropical cyclones, even if the cyclone mesoscale structure
is not well rep resented. It is possible to track the TDVs
inaGCMandalsotoselectonlyTDVswithatropical
cyclone–like vertical structure, as is done by the Camargo
and Zebiak (2002, hereinafter CZO2) algorithm, which
detects and tracks warm-core vortices. Previous studies
have analyzed the influence of the convection scheme on
the TC characteristics in GCMs with various spatial res-
olutions (e.g., Vitart et al. 2001; Zhao et al. 2012;
Murakami et al. 2012b; Stan 2012; Kim et al. 2012). In
particular, Murakami et al. (2012a) reported significant
differences in TC characteristics in a 20-km-mesh model
with two different versions of the convection scheme (one
based on an Arakawa–Schubert scheme and one based on
theTiedtkescheme).ThegreaterTCintensityinthe
Tiedtke-based scheme was mostly attributed to its stron-
ger inhibition of the convection, which increased the grid-
scale resolved convection (larger upward motion and
large-scale condensation) and the associated moisture
supply at low levels. A previous study by Vitart et al.
(2001) in a coarser model (T42) also showed that the in-
hibition of the convection enhanced the TC frequency,
but this was mostly attributed to the effect of this in-
hibition on the increase of the background CAPE. As
noted in Vitart et al. (2001), it is possible that larger CAPE
is necessary to produce TCs when the resolution is lower,
to compensate for the inhibition of vertical motion by the
coarse resolution. This large CAPE can increase the
number of TCs, but the most important driver for the TC
intensity appears to be the horizontal resolution. Kim
et al. (201 2) sho wed that in a low-resolution (2832.58)
GCM, the TC frequency was reduced with a larger en-
trainment, while another factor—the rain reevaporation—
was f ound to increase the TC frequency. This ambiguous
influence of the entrainment on the convective inhibition
and TC number is perhaps consistent with the results of
Zhao et al. (2012), showing that the inhibition of the con-
vection favors TC genesis up to certain point but reduces
TC genesis when the entrainment is too strong. This was
attributed to the fact that the resolved convection at first
enhances the TC activity but then can also counteract the
formation of coherent vortices by favoring the spatial
noisiness of the convection.
OtherfactorscanalsoplayaroleintheTCfrequencyand
intensity. For example, Stan (2012) showed that an explicit
representation (the so-called superparameterization) of
cloud processes in a low-resolution T42 GCM increases
the TC activity compared to a conventional parameteri-
zation, by increasing the moistening of the lower tropo-
sphere (850–700 hPa). Reed and Jablownowski (2011)
showed that the growth of an idealized vortex (early stage
TDV) depends on both the spatial resolution and the
manner in which the CAPE (defining the closure of the
convection scheme) is calculated. Using the same ap-
proach, He and Posselt (2015) showed that among 24
different parameters, the convective entrainment rate has
the largest role in TDV intensification with larger in-
tensification for the smaller entrainment rate (i.e., an in-
verse effect compared to TC intensification due to the
convective inhibition effect of the entrainment).
Here we use the Laboratoire de Météorologie Dy-
namique zoom model (LMDZ) to study the sensitivity
of TDV characteristics to different entrainment and
closure formulations of the convection scheme. This
study uses the zoom capability of the LMDZ GCM
with a resolution of about 0.758 over a large region of the
North Atlantic and West Africa. We use the Tiedtke
convection scheme either with entrainment formulation
and overall closure based on moisture convergence or
with an entrainment based on the relative humidity of
the environment, as well as a closure based on CAPE.
Each configuration is run for 10 yr between 2000 and
1496 MONTHLY WEATHER REVIEW VOLUME 145
2009 with prescribed observed SST. The aim is to analyze
the impact of the convection scheme on the initiation stage
of the TDVs and on their probability of surviving and in-
tensifying over the African continent and over the ocean.
The assessment of the different GCM configurations is
done by first comparing TDV characteristics (such as ini-
tiation, duration, strength) to those extracted from the
ECMWF interim reanalyses [ERA-Interim (ERA-I); Dee
et al. 2011]. The approach introduced in Duvel (2015) is
used to define TDV characteristics at the same horizontal
resolution of 0.758 for both LMDZ and ERA-I. In parallel,
the CZ02 tracking algorithm is used to assess more spe-
cifically the activity of mature tropical cyclone–like storms
in the GCM in comparison with IBTrACS observations
(Knapp et al. 2010).
Section 2 presents succinctly LMDZ, the zoom con-
figuration, and the different closure and entrainment
formulations of the convection scheme. The two tracking
algorithms and some metrics are presented in section 3.
The distributions of TDV and TC characteristics (fre-
quency, duration, intensity) are analyzed in section 4.The
initiation locations, the tracks, and the intensity distri-
butions are analyzed in section 5, and the seasonal and
interannual variations in section 7. Potential physical
sources of the differences between the simulations are
analyzed in section 7, and section 8 contains a summary.
2. Model simulations
The simulations are performed using version 4 (v.4) of
LMDZ, as described in Hourdin et al. (2006).Weusethe
Tiedtke (1989) bulk mass flux scheme for moist convection
instead of the Emanuel (1991) convection scheme used in
the standard LMDZ v.4 because it allows us more flexi-
bility in modifying the closure (i.e., the cloud-base mass
flux) and entrainment formulations. We use the zoom ca-
pability of LMDZ (see, e.g., Yang et al. 2016)withares-
olution of about 0.758 overawideareacoveringtheNorth
Atlantic and part of West Africa. The domain encom-
passes West Africa, since this region has been shown to be
important for TC simulations (Caron and Jones 2012). The
model is free to run in a large central part of the zoomed
region, while it is totally constrained to remain close to the
ERA-I meteorological reanalyses outside of this region.
There are intermediate relaxation times in the buffer zone
around the zoom region (Fig. 1). The regular westward
decrease of the nudging intensity over West Africa gives a
smooth boundary condition (compared to a sharp lateral
boundary forcing) for AEWs and TDVs generated over
West Africa and that are susceptible to enter the Atlantic
Ocean. This nudging also ensures comparable lateral
boundary conditions for the three simulations and thus
reduces differences that could be due to biased large-scale
conditions around the zoomed region.
The guidance from ERA-I is applied to the wind,
temperature, and humidity fields. For a field x, the time
evolution is given by
›x
›t
5
›x
›t
GCM
1
x
era
2 x
t
x
, (1)
where the first right-hand-side term is the tendency
given by the GCM and the second right-hand-side term
is the relaxation toward its value in ERA-I (x
era
) with a
relaxation time t
x
. Based on this principle, a relaxation
increment dx 52a
x
(x 2 x
era
) is applied every five dy-
namical time steps. The relaxation factor a
x
is defined as
a
x
5 (1 2 e
25dt/t
x
), (2)
where dt 5 45 s is the model time step for dynamical
processes.
FIG. 1. Model grid points in the zoomed region (dots) and relaxation time t
u
in days for the wind (contours) for t
u
smaller or equal to 10
days (t
u
continues to increase in the zoomed region, but the model may be considered as already free to run for t
u
greater than 10 days).
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PRIL 2017 D U V E L E T A L . 1497
For the wind, the relaxation time is set to a very large
value in the heart of the zoomed region and is at a mini-
mum value of 30 min outside the zoomed region (Fig. 1).
The relaxation factor a
u
is computed with an analytical
function of the horizontal resolution with near-zero
values at the center of the zoomed region and a value of
0.12 outside. The same process is applied to temperature
and humidity, but with larger values of the minimum re-
laxation time (6h and 3 days, respectively) in order to
limit the nudging impact on thermodynamic variables
over West Africa and to avoid model instabilities outside
the zoomed region. For synoptic time scales of interest
here, the relaxation is negligible for relaxation times
greater than 10 days and is already weak for relaxation
times around 2 days. We may thus consider that the wind
is not significantly influenced locally by the nudging over
the Atlantic and near the West African coast. As intended
by our nudging approach, there is a substantial nudging of
the wind near and east of the Greenwich meridian where
AEW and some TDVs are initiated, giving realistic seeds
for possible westward TDV and TC developments in the
three LMDZ simulations. For temperature and humidity,
one may consider that the nudging is negligible west
of 108E.
The vertical redistribution of water and energy in the
Tiedtke convection scheme is based on one single satu-
rated updraft profile and one single downdraft profile
extending from the free sinking level to the cloud base.
The mass flux at the top of the downdraft is a constant
fraction (0.3) of the convective mass flux at the cloud
base. The downdraft remains saturated by evaporating
precipitation. This scheme does not consider convective
momentum transport, but previous studies by Reed and
Jablownowski (2011) and He and Posselt (2015) showed
that it has a small effect on TC intensity for models with a
comparable horizontal resolution. The activation of the
moist convection scheme depends on the buoyancy of the
lifted parcel at the first grid level above the condensation
level. In its original formulation (noted TIE here), both
the closure (i.e., the value of the mass flux at the cloud
base) and the entrainment of environmental air above the
cloud base depend on the moisture divergence profile.
Here, the scheme was modified progressively by first
considering an entrainment that depends on the envi-
ronmental relative humidity following the formulation
described in Bechtold et al. (2008). With this new en-
trainment (noted ENT), the entrainment rate is larger in
drier environments, inhibiting the convection, and smaller
in humid environments, favoring the convection. ENT
thus increases the contrast between dry and wet environ-
ments and the variability of the convective/precipitation
rate compared to TIE. An additional modification
(noted CAPENT) uses a closure b ased on CAPE, as
described in Bechtold et al. (201 4), but without ac-
counting for the imbalance between boundary layer
heating and deep convective overturning. With this new
closure, the primary convective strength (i.e., prior to the
modulation due to entrainment) does not depend on the
low-level moisture convergence (as for TIE and ENT)
but on the static stability of the column.
When active within a TDV or TC, the convective
scheme dries and warms the atmospheric column and
reinforces the vortex intensity. The surface friction under
the vortex generates a low-level convergence that plays
an ambiguous role in the original Tiedtke scheme (TIE)
by increasing both the entrainment above the cloud base
(convection weakening by mixing with the drier envi-
ronment) and the mass flux at the cloud base (convection
strengthening). With the new entrainment (ENT) the
convection will be at the first order inhibited in dry vor-
tices and favored in wet vortices; one may thus anticipate
stronger convection and vortex intensity with ENT for
strong vortices (associated with large low-level moisture
convergence) with nearly saturated centers over the
ocean. With the new closure (CAPENT), there is a dis-
connect between the low-level moisture convergence and
the primary convective intensity. This disconnect is far
from total, however, since in a vortex, the low-level con-
vergence is associated with a resolved upward motion that
tends to increase the temperature gradient and the
CAPE. After strong convective episodes, one may expect
that smaller CAPE tends to inhibit the convection for the
following time steps in CAPENT. If the inhibition of the
convection is too large, the center of the vortex is not
dried out and may become saturated. This can lead to an
unexpected resolved convection in the center of the vor-
tex with excessive upward motion and low-level moisture
convergence compared to the parameterized convection.
The three versions of the convection scheme de-
scribed above—TIE, ENT, and CAPENT—are used for
three AMIP-type simulations with the zoomed grid and
with 39 vertical levels (only 22 levels below 20 km). We
performed 10-yr simulations between 2000 and 2009
forced with ERA-I fields and observed SST. It is thus
possible to study the interannual variability of the TDV
activity related to interannual variability of SST and of
large-scale lateral conditions. As shown below, it is not
trivial to identify the convective scheme giving the best
TDV/TC simulation, since the score can depend on what
criteria are used to evaluate the statistics of the TDVs
and TCs detected by the two tracking algorithms.
3. Tracking algorithms
The TDV tracking is based on the approach described
in Duvel (2015). For each time step (here, every 6 h), a
1498 MONTHLY WEATHER REVIEW VOLUME 145
TDV area is defined as an ensemble of continuous grid
points with geopotential height anomaly (Df)at850hPa
lower than a given threshold. Term Df is defined as the
difference between f and the average f over a region of
67.58 (here 610 grid points). As in Duvel (2015),an
empirical threshold Df
0
5280 m
2
s
22
is set as the mini-
mal geopotential perturbation considered. This relatively
weak threshold allows for the detection of TDVs at an
early stage, but stronger TC-like systems have a too large
TDV area at Df
0
with ill-defined characteristics. The
TDV area is thus computed for a series of deeper
thresholds (i.e., ,280 m
2
s
22
), and the first threshold
giving an equivalent radius of the TDV area lower than 38
of latitude–longitude is retained. For developed cyclones,
this threshold may be less than 21200 m
2
s
22
.
The tracking of a given TDV is performed by con-
sidering the overlap between TDV areas in two con-
secutive time steps. If several TDVs are overlapping,
then only the TDV with the largest overlap is considered
for the continuity of the tracking. Each TDV is thus
represented by a time series of characteristics of over-
lapping TDV areas (barycenter, maximum surface wind,
maximum vorticity at 850 hPa, maximum Df, minimum
surface pressure, etc.).
Here, since we are mostly interested in simulating TC
activity over the North Atlantic Ocean, we consider only
TDVs that are initiated south of 408N and that spend at
least 2 days over the tropical North Atlantic waters.
These TDVs are called Atlantic TDVs, or simply TDVs
here. This means that TDVs that initiate over West
Africa but dissipate before reaching the Atlantic are not
considered. Because of the chosen nudging configura-
tion, TDVs initiated near and east of the Greenwich
meridian (see Fig. 1) are partly forced by the wind
nudging toward ERA-I. However, the dissipation or the
maintenance of these TDVs as they propagate westward
toward the African west coast and over the Atlantic is
fully determined by LMDZ.
The strength of a given TDV is characterized by ac-
cumulated cyclone energy (ACE) computed on the basis
of the maximum surface wind y
max
in the TDV area at
each time step. The values in the model are not directly
comparable to the observed ACE, since the maximum
surface wind perturbations in the simulation and in the
reanalyses are far weaker than the maximum sustained
winds in real observed TCs. The formulation is, how-
ever, the same,
ACE 5 10
24
å
y
2
max
, (3)
where the sum is defined over ev ery 6 h during the TDV
lifetime and y
max
is the maximum surface (10 m) wind speed
in the TDV area expressed in knots (1 kt 5 0.5144 m s
21
).
Note that this definition differs from the standard ACE
in that the latter considers only steps with storm in-
tensities larger than 35 kt (Bell et al. 2000; Maue 2009),
whereas we include all steps in which the TDV is de-
fined by the tracking scheme. The strongest TDVs will
be defined using this ACE metric on a per-storm basis.
To inspect the TDV strength spatial distribution, we
will also sum the ACE over all the TDVs crossing a
particular region.
Tropical cyclone–like vortices are detected and tracked
using the CZ02 algorithm. This tracking algorithm first
identifies TC-like features with a maximum local relative
vorticity (850 hPa), minimum surface pressure, and a
warm core (defined by the local temperature anomaly). To
be considered as a possible TC-like storm, these features
must last at least 2 days (nonconsecutive). Once these
potential TCs are identified, in the second part of the al-
gorithm, these storms are tracked using a relaxed vorticity
threshold (i.e., lower than in the first part of the algorithm)
by connecting the vorticity centroid every 6 h. This algo-
rithm has been extensively used in global (Camargo et al.
2005; Camargo and Barnston 2009; Camargo 2013; Shaevitz
et al. 2014) and regional climate models (Landman et al.
2005; Camargo et al. 2007a). Here, we considered the
same thresholds in all LMDZ simulations, namely, a
minimum of 7.5 3 10
25
s
21
(vorticity), 8.5 m s
21
(wind
speed), and 1.5 K (temperature anomaly over a 5 3 5
gridpoint box) for detection, and 4.5 3 10
25
s
21
vorticity for
thetrackingpartofthealgorithm.
The CZ02 scheme was initially developed to identify
TC-like vortices in low-resolution models, recognizing
that the simulated interannual variations of the activity in
such models could be simulated well enough to be useful
for prediction and some research purposes even when
their intensities are well below those observed in real
TCs. At the resolution considered here, many of the
systems detected by the CZ02 algorithm are weaker than
observed TCs and so the phrase ‘‘TC-like vortices’’ is still
to some extent appropriate. We nonetheless denote them
as ‘‘TCs’’ here, for brevity. The distinction we make be-
tween TCs and TDVs is that the former are defined
using a wider range of criteria appropriate (qualitatively
if not quantitatively) to real tropical cyclones, including a
warm core, while TDVs here are defined using simpler
and less restrictive criteria that allow, for example, cold-
core systems and early stage vortices.
4. TDV and TC statistics
LMDZ tends to generate more TDVs than does ERA-I
with a maximum obtained for ENT (Table 1). Consider-
ing the same constraints (systems lasting more than
2 days over ocean south of 408N), there are 139 TCs in
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![FIG. 2. TDV characteristics averaged or integrated over theN systems with the largest ACE as a function ofN for (a) ACE, (b) number of TCs, (c) maximum wind speed, (d) distance, (e) TDV speed, and (f) duration. The results are also shown for the observed TCs [with ordinates on the right axis for (c)].](/figures/fig-2-tdv-characteristics-averaged-or-integrated-over-then-2wniiil7.webp)
