Generation of African Easterly Wave Disturbances:
Relationship to the African Easterly Jet
Jen-Shan Hsieh* and Kerry H. Cook
Department of Earth and Atmospheric Sciences, Cornell University
Ithaca NY 14850
Accepted for Monthly Weather Review
October 2004
*Corresponding author: Jen-Shan Hsieh, Department of Earth and Atmospheric Sciences.
3152 Snee Hall, Cornell University, Ithaca, NY14850
Email: jh122@cornell.edu
ABSTRACT
The relationship between African easterly waves and the background climatology in
which they form is studied using a regional climate model. The surface and lateral boundary
conditions in the model are manipulated to modify the background climatology, especially the
African easterly jet and the ITCZ, and the behavior of the waves in these different settings is
evaluated.
Three climate simulations are presented, with monthly mean lateral and surface boundary
conditions. One has a strong jet and a strong ITCZ, the second has a strong jet and a weak ITCZ,
and the third has a weak jet and a strong ITCZ. In these simulations, the presence of wave
activity is more closely associated with the concentration of the ITCZ than the strength of the
African easterly jet. In particular, the simulation with a strong jet accompanied by a weak ITCZ
does not produce significant wave activity, but a weak jet with a strong ITCZ has realistic wave
disturbances. Both the Charney-Stern and the Fjörtoft necessary conditions are satisfied in all
three simulations, suggesting that combined barotropic and baroclinic instability contributes to
the generation of waves. Near the origin of the waves, meridional gradient reversals of isentropic
potential vorticity result from potential vorticity anomalies generated by convective heating
within the ITCZ, implying that the unstable zonal flow may be caused by cumulus convection
within the ITCZ and not by shear instability associate with the jet.
Two additional simulations with 1988 lateral boundary conditions demonstrate that 3-5day wave disturbances can be generated in the absence of the African easterly jet, but with
unrealistically small wavelengths. These results suggest that African easterly waves are initiated
by cumulus convection within the ITCZ, and not by barotropic instability associated with the jet.
1
1. Introduction
African easterly waves are an important synoptic feature of the summer climate in West
Africa and the tropical Atlantic.
Observations during GATE revealed synoptic-scale
disturbances with periods of 3-5-days and wavelengths of 2000-4000 km propagating to the west
across West Africa and the tropical Atlantic with phase speeds of 6-8 m/s (Carlson 1969, Burpee
1972, Reed et al. 1977). The waves regularly traverse the Atlantic to reach the Central and North
American coasts, and are associated with the formation of tropical cyclones in the western
Atlantic Ocean and Caribbean Sea (Riehl 1954, Thorncroft and Hodges 2001). Frank (1970)
showed that about half of the tropical cyclone formation in the Atlantic is related to African
easterly waves. Avila and Pasch (1992) investigated Atlantic tropical systems during the 1991
hurricane season, and found that nearly all of the eastern Pacific tropical cyclones were
associated with African waves.
Diedhiou et al. (1998) distinguish similar periods in the NCEP/NCAR reanalyses, and
find that 3-5-day waves have average wavelengths of 2500 km and phase speeds around 8 m/s.
They note two preferred tracks, one to the north and one to the south of the African easterly jet,
and suggest that these tracks tend to merge over the Atlantic. The 6-9 day waves originate
farther north than 3-5 day waves, have longer wavelengths of about 5500 km, and move
westward at a lower phase speed of approximately 6 m/s.
Numerous studies address the causes and dynamics of African easterly waves, but
outstanding questions remain. Many investigations focus on the hydrodynamic stability of the
zonal flow since African easterly wave activity occurs in the vicinity of the African easterly jet.
This mid-tropospheric feature is centered near 15ºN in summer, and is a consequence of the
2
strong positive meridional temperature and geopotential height gradients that develop over
Sahelian Africa (Thorncroft and Blackburn 1999, Cook 1999).
The relationship between the jet and the waves is investigated here in a series of synoptic
and climate-mode simulations with a regional climate model. A companion paper (Hsieh and
Cook 2004b) presents a thorough energetics analysis of the model output.
Central to the
believability of both investigations is the quality of the African easterly wave simulation in the
model. After a review of the pertinent literature in section 2, the model is described (section 3)
and shown to produce an excellent reproduction of the African easterly wave climatology in
section 4. In section 5, the modeling results are analyzed to investigate the relationship between
the jet and the waves. Section 6 is the summary and conclusions.
2. Background
Much of the theoretical work concerned with the generation of these waves focuses on
the African easterly waves as an expression of hydrodynamic instability associated with
meridional gradient reversal of isentropic potential vorticity (IPV). Fjörtoft (1950) applied
Rayleigh theory to atmospheric flows and obtained a necessary condition for barotropic
instability, which requires that the zonal velocity be positively correlated with the meridional
gradient of potential vorticity. Charney and Stern (1962) generalized the instability problem to
three dimensions and applied it to an internal jet by including horizontal and vertical wind shear
in a stratified atmosphere. They showed that the instability of such a jet requires a sign reversal
of the meridional IPV gradient, i.e., a disturbance cannot grow in zonal flow that has a positive
meridional IPV gradient everywhere in the domain (Eliassen 1983).
3
Burpee (1972) used the Charney-Stern necessary condition to explain the existence of
African easterly waves, even though the African easterly jet cannot be strictly classified as an
internal jet. His study suggested that the generation of African easterly waves is directly related
to the African easterly jet since the Charney-Stern necessary condition is satisfied near the jet.
The theory relating the waves and the jet was further developed in the modeling studies of
Rennick (1976) and Simmons (1977), who considered confined zonal flows and suggested that
the waves grow at the expense of the zonal kinetic energy of the jet without large influences
from latent heat releases.
Thorncroft and Hoskins (1994a, b) and Thorncroft (1995) used the primitive equations
with the hydrostatic condition to study the linear and nonlinear behavior of easterly waves near
the easterly jet. Their studies indicate that initial wave generation occurs through barotropic
conversion but that later growth is supported by baroclinic conversion in a nonlinear process.
They concur that African easterly waves grow by combined barotropic and baroclinic
instabilities associated with the jet, but note that the role of latent heating is important in
increasing the baroclinic conversion and determining the synoptic structure of the waves.
Other investigations emphasize the role of diabatic heating in generating wave
disturbances. Holton (1971) suggested that latent heat released in convection driven by frictional
moisture convergence is of primary importance for waves that form along the ITCZ. Mass
(1979) studied African waves using a linear model and found that convective heating
dramatically increases the perturbations in the lower and upper troposphere, in agreement with
observations (Burpee 1974, Reed et al. 1977). Schubert et al. (1991) investigated the potential
vorticity characteristics of the ITCZ using a simple zonally symmetric balanced inviscid model.
They found that concentrated convective heating can cause large IPV gradient reversals, and
4
suggested that the existence of the African easterly jet is not necessary for the waves to occur.
Ferreira and Schubert (1997) used a nonlinear shallow water model on the sphere to simulate the
ITCZ breakdown and found that ITCZ convection plays an important role in the origin of the
unstable mean flow in which easterly waves form.
Finally, whether the waves are associated with Charney-Stern instability (the reversal of
IPV gradient) is also studied. Chang (1993) studied the unstable waves under the near-neutral
conditions over the Sahara and found that waves in this region occur through baroclinic energy
conversions where the Charney-Stern necessary condition is not satisfied.
3. Model and simulation description
Considering some limitations of simpler models, for example, the hydrostatic
assumption and simple parameterizations of latent heat release, a non-hydrostatic model with the
ability to realistically capture the climatology of northern Africa and the tropical Atlantic may
offer an alternative modeling approach for studying the relationship between African easterly
waves and the jet. In this study, climate mode simulations with a regional model are performed
to study the relationship between the background climatology and wave activity in the absence of
interannual variability. In addition, synoptic mode experiments are conducted to simulate the
summer of 1988. According to Avila and Clark (1989), the African easterly waves of 1988 were
vigorous during the entire summer, with 62 tropical waves, 19 tropical depressions, and 12
tropical storms.
The NCAR/PSU MM5 (Version 3.4) model (Grell et al. 1994) is used. MM5 is a
regional model based on finite differencing in both space and time.
Its non-hydrostatic
dynamics, with 24 vertical σ − levels, allows the model to be valid for meso-scale simulations.
5
Here, large domains are used to position the lateral boundaries far from the area in which the
waves occur and eliminate the possibility that disturbances are propagating into the domain
rather than being generated by the model physics.
Three climate mode simulations are presented. Each is 124 days in length, and a
horizontal resolution of 80 km is used across the domain, shown in Fig. 1. The model is
initialized at 00Z on 15 May using climatological May conditions from the NCEP/NCAR
reanalysis (Kalnay et al. 1996) and run through the middle of September. The first 17 days are
discarded for model spin-up. Lateral boundary conditions for winds, temperature, and moisture
at each vertical level are also taken from the NCEP/NCAR reanalysis, updated every 12 hours
based on a linear interpolation between monthly means as in Vizy and Cook (2002). Thus, the
lateral boundary conditions include the influence of the seasonal cycle, but not the diurnal cycle.
Sea surface temperatures are prescribed and also updated every 12 hours using linear
interpolation of the monthly SST climatology of Shea et al. (1992).
Considerable testing and validation were performed to choose a set of lateral boundary
locations, surface and lateral boundary conditions, and physical parameterizations that produce a
good simulation of West Africa and the adjacent Atlantic Ocean (Vizy and Cook 2002, 2003).
The radiation parameterization used is the Rapid Radiative Transfer Model (RRTM) longwave
scheme (Mlawer et al. 1997). This scheme combines with the cloud-radiation shortwave scheme
and the simple ice explicit moisture scheme (Dudhia 1989) to determine shortwave fluxes and
cloud ice. The RRTM radiation scheme was chosen because it produces a much more realistic
surface radiation budget in our simulation compared to the other radiation parameterization
options in the model. The CCM2 scheme, for example, consistently produces far too little solar
radiation incident at the ground due to its strong interaction with low clouds.
6
Other
parameterizations chosen are the Kain-Fritsch cumulus scheme (Kain and Fritsch 1993), the high
resolution Blackadar planetary boundary layer scheme (Blackadar 1979; Zhang and Anthes
1982), and shallow cumulus parameterization (Grell et al. 1994). The parameterization choices
are based on the work of Vizy and Cook (2002, 2003) in their simulations of Africa and the
tropical Atlantic.
In the three climate mode simulations, changes in soil moisture availability are used to
manipulate the strength of the African easterly jet and then examine changes in the waves. Soil
moisture availability, a dimensionless fraction, is used in the model as a multiplier in the surface
moisture flux equation. Empirical conversion formulae in the soil bucket model are used to
convert the observed or the NCEP soil moisture (in units of mm) to soil moisture availability
though no soil model is used in the present study. Therefore, moisture availability is not exactly
equivalent to the degree of saturation on the ground, but it is related to it. Effects of vertical soil
moisture distributions are not included. One simulation has realistic soil moisture availability,
which is updated every 12 hours by linear interpolation based on the monthly soil moisture
climatology of Willmott et al. (1985). Across northern Africa, the soil moisture availability
ranges from about 0.6 over the West African rain forests to 0.02 over the Sahara, as shown in
Fig. 2a. This range motivates two idealized soil moisture experiments, in which the soil moisture
availability is uniform at values of 0.02 and 0.06, respectively. A land surface model is not used,
and the soil moisture is prescribed and indifferent to the state of the atmosphere.
For the two synoptic mode simulations, 120 km horizontal grid spacing is used on an
even larger domain than in the climate mode simulations, covering 125°W to 70°E in longitude
and 14°S to 51°N in latitude (not shown). The same 24 vertical σ -levels are used. The physical
parameterizations for the synoptic experiments are those used in the climate mode simulations
7
except the CCM2 scheme is used to parameterize radiation (see below) and the Grell scheme for
cumulus convection.
Lateral boundary conditions for wind, temperature, and moisture are taken from the
1988 NCEP reanalysis. The 12 hourly time series is linearly interpolated to generate boundary
conditions for each model time step of 3 minutes. Both of the 124-day synoptic simulations are
initialized at 00Z on 15 May using the May 1988 NCEP reanalysis conditions and run through
the middle of September 1988. As in the climate mode integrations, the first 17 days are
discarded for model spin-up.
Druyan and Fulakeza (2000) and Druyan et al. (2001) have also used a mesoscale
model for synoptic simulations of African easterly waves, but on a smaller domain. They find
that the simulated waves are sensitive to the treatment of initial moisture field and soil moisture
in the model. In the synoptic simulations presented here, we needed 12-hourly soil moisture
values for that particular year (1988). The only available “data” are from the NCEP reanalysis,
even though these values are largely unvalidated and derived solely from the model fields forced
by the data assimilation. Since the 1988 NCEP soil moisture on distribution does not look very
realistic, another synoptic-mode simulation using observed soil moisture climatology (Willmott
et al 1985) was carried out. The small meridional gradient of soil moisture in the 1988 NCEP
values produce a simulation with no jet, consistent with the results of Cook (1999).
Two modifications are made to compensate for the strong radiation interaction with low
clouds that occurs when the CCM2 scheme is used. (The need for these modifications motivated
our change to the RRTM radiation parameterization for the climate mode simulations.) The first,
similar to Giorgi et al. (1993), Vizy and Cook (2002), and Cook et al. (2003), is to specify clouds
below 850 hPa transparent to incoming solar radiation. The second modification is to remove
8
excessive moisture from the upper troposphere by fixing mixing ratio values in the top six σlevels (above 300 hPa) to their initial conditions, as in Vizy and Cook (2002) and similar to
Horel et al. (1994). (The need for these modifications disappears with the use of the RRTM
scheme.)
4. Model validation
Since the focus of this paper is the relationship between African easterly waves and a
feature of the background climatology, namely, the African easterly jet, the model validation
begins with an examination of the basic state in which the waves occur.
Latitude-pressure distributions of the July-August average zonal wind and potential
temperature from the climate mode simulation with realistic soil moisture and the NCEP
reanalysis are displayed in Figs. 3a and b, respectively. Both are averaged from 20°E to 10°W
longitude. Although reanalyses cannot be treated as pure observations, some fields like wind
velocity and air temperature used for validation are strongly constrained by observed data
(Kalnay et al. 1996), and they provide a validation opportunity in data sparse regions such as
West Africa. To compare with the NCEP reanalysis, the model variables are interpolated onto
the coarser grid of the NCEP reanalysis, which is 2.5° by 2.5° for the horizontal resolution and
17 vertical levels.
A more consistent comparison with the NCEP climatology would result from an
ensemble average of the simulations for each year, but that is not practical. The magnitude of
the simulated African easterly jet is 14 m/s, somewhat stronger than the 10 m/s jet in the NCEP
reanalysis, but well-placed at 600 hPa and 13°N. The low-level westerly monsoon flow below
the jet is also stronger in the model, so vertical and meridional wind shears are larger. The
9
average magnitude of the jet in the climatology of the 1983-1992 ECMWF reanalysis is 8 m/s,
and the low level westerly flow is only 2 m/s, as shown in Fig. 3c. Some of the differences
between the ECMWF and NCEP reanalyses may be related to the different averaging periods.
The simulated isentropes are quite similar to those in the reanalyses. All show large deflections
toward the ground north of 15°N, suggesting strong baroclinicity in association with strong
sensible heating over the Sahara.
Figs. 3d and e show the July-August mean zonal wind and potential temperature from
the 1988 NCEP reanalysis and the synoptic mode simulation with Willmott et al. (1985) soil
moisture distributions, respectively. The 1988 jet is weaker than the climatological jet (Fig. 3b).
(The 1988 jet in the ECMWF climatology is similar to that in the NCEP reanalysis, but the low
level westerly flow is weaker.) The 1988 simulated African easterly jet is broader and stronger
than in the reanalyses.
Fig. 3f displays the 1988 synoptic mode simulation with NCEP soil moisture
prescribed. The African easterly jet and the low level westerlies are absent in this simulation.
These differences are related to the use of a different soil moisture distribution, since the soil
moisture’s control on the surface temperature is an important factor determining the jet location
and strength (Cook 1999).
The model produces realistic summer rainfall distributions over Africa and the tropical
Atlantic. Vizy and Cook (2002) compared model results with various observational and satellitegauge estimates and concluded that the model captures the summer rainfall over this region.
Fig. 4 displays the zonal mean power spectral density averaged from 10°W to 20°E
from the realistic climate mode simulation, computed from the time series of the meridional
wind at 725 hPa from mid-June to mid-September. The maximum at a period of about 4.5 days
10
period between 10°N and 15°N indicates the presence of 3-5 day African easterly waves, in
agreement with the spectral analyses of previous studies (Burpee 1974, Diedhiou et al. 1998,
1999). North of about 25°N, there is strong wave activity between 4.5-7 days, and 8-10 days,
consistent with the 6-9 day African easterly waves identified in the reanalyses.
To further validate the modeled waves with the various easterly wave types
distinguished by Viltard et al. (1997) and Diedhiou et al. (1998), band-pass filters are used to
separate wave disturbances with 3-5 day periods from the 6-9 day waves. Fig. 5 shows the
response functions of the two band-pass filters used, which offer steep rolloff characteristics for
the spectral windows. The two filtered time series are used to form composite waves as in
Diedhiou et al. (1998) by selecting and averaging the 725 hPa filtered wind fields with filtered
meridional wind speed magnitudes at 18°N and 0°W greater than 1 ms-1. The composite waves
reflect an average picture of the significantly perturbed fields based on the reference point (18˚N0˚W).
The 3-5 day composite waves are shown in Fig. 6a. They tilt from southeast to
northwest north of the jet (between 10°N and 15°N), and from northeast to southwest south of
the jet, as noted in Diedhiou et al. (1998). The wave trains merge over the Atlantic, similar to
Reed et al.’s (1988) findings from the ECMWF reanalysis. The axis of the cyclonic circulation
at 25˚N between 10˚W and 0˚W tilts from the southwest to the northeast, leading to negative
barotropic conversions ( C k
=−
∆p
∂[u ]
)
[u ' v' ]
g
∂y
since [u ' v' ] > 0 in westerly shears, i.e.,
∂[u ]
>0
∂y
(u is
zonal wind, v is the meridional wind and p is pressure). In contrast to the positive barotropic
conversions near the two sides of the jet, this cyclonic circulation can not be obtaining eddy
kinetic energy from the African easterly jet.
11
The vertical structure of the composite 3-5 day wave (not shown) is also in agreement
with previous investigations (Burpee 1974 and 1975, Reed et al. 1977). The wave trough axis
tilts eastward with increasing height below the jet, and westward above the jet. This structure
implies that energy is being converted from zonal mean to eddy available potential energy.
Fig. 6b displays 6-9 day composite waves. These wave patterns are located further
north, in agreement with observations. Diedhiou et al. (1998) suggested that the 6-9 day waves
originate from the Libyan and the Azores areas, and this is consistent with the modeled waves
since the first anti-cyclonic circulation is centered around 25°N-20°E (Libyan area) and the first
cyclonic circulation is centered further north around 35°N-30°W (near the Azores). The 6-9 day
wind perturbations are weak south of 5°N, and stronger between 10°N and 15°N.
Fig. 7a shows Hovmöller correlation diagrams of the 3-5 day filtered meridional wind
at 725 hPa, computed by correlating the time series of the filtered meridional wind at 15°N-0°W
with that of each grid point along 15°N in different time lags (Liebmann and Hendon 1990). The
slope of the contours indicates the westward propagation of the African easterly waves. At
15˚N, the wavelength increases from 2400 km at 20°E to 3500 km at 10°W. The modeled
wavelength also increases toward the equator, similar to the observational study by Diedhiou et
al. (1999). The slope of the correlation isopleths in Fig. 7a gives the waves’ average phase
speed, which is about 8.3 m/s at 0°W. At 15°N, it increases from 6 m/s at 20°E to 10 m/s at
10°W, similar to those of previous investigations (Reed et al. 1977, and Diedhiou et al. 1998).
Fig. 7b shows a Hovmöller correlation diagram for 6-9 day waves with the reference
point at 22°N-0°W. The distortion of the correlation isopleths near 10°E is due to Tahat
Mountains (see Fig.1). However, since the 6-9-day waves occur east of the Tahat Mountains,
they are clearly not caused by the interaction of the flow with topography.
12
The average
wavelength is around 5300 km, the local phase speed is 6 m/s. The wavelength and phase speed
estimated by Diedhiou et al. (1998) are 5500 km and 6 m/s, respectively.
5. Results
5.1 The climate mode simulations
The relationship between the African easterly jet and the waves in the three climate mode
experiments is examined. As described in section 3, the “realistic case” has soil moisture
availability prescribed based on observations, and two idealized cases have uniform soil moisture
availability of 0.02 and 0.06, the “dry” and “wet” cases, respectively.
Figs. 8a, b and c show horizontal wind vectors and contours of the zonal wind at 625 hPa,
averaged from 15 June to 14 September for the realistic, dry, and wet cases, respectively. In the
realistic and dry cases, the African easterly jet extends to about 30°E, and has maximum wind
speeds of 15 m/s near the west coast, similar to the observations. The jet is a little weaker over
West Africa in the dry case than in the realistic case in association with a slight decrease of the
meridional surface temperature gradient over West Africa.
The jet is quite weak in the wet case, shown in Fig. 8c, with a maximum zonal wind
speed of 9 m/s over Central Africa. This jet structure is associated with a decrease in meridional
geopotential height gradients over West Africa. Strong evaporative cooling over the Sahara due
to the unrealistically wet land surface cools this region and reduces the magnitude of the
(positive) surface and, thereby, lower tropospheric temperature gradient.
Composite 3-5 day waves at 725 hPa for the dry case, computed using 57 snapshots, are
shown in Fig. 9a. The same reference point at 18˚N-0˚W, as in the realistic case, is used for the
composite waves of both the dry and wet cases. The 3-5-day wave disturbances are active off
13
the west coast of Africa, similar to the realistic case, but there is no robust wave structure over
the African continent except, perhaps, within the ITCZ near 5ºN. Thus, the presence of a
realistic African easterly jet in this simulation (Fig. 8b) and, with it, the possibility of barotropic
energy conversions to initiate African waves over the land surface, does not produce significant
wave activity.
Fig. 9b displays composite 3-5 day waves for the wet case. Despite the absence of a
well-defined jet in the west, the waves are quite active. The fact that 204 snapshots exceed the 1
m/s threshold velocity also indicates that the wave activity is stronger than in the dry case. A
realistic tilt of the wave axes is present (compare with Fig. 6a), and the phase speed and
wavelength of the wave disturbances are around 10 m/s and 3700 km, respectively, within the
ranges reported in previous investigations (Burpee 1974, Diedhiou et al. 2001).
Figures 10a, b and c display the seasonal mean power spectral density averaged between
10°N and 15°N of the 725-hPa meridional wind for the realistic, dry, and wet cases, respectively.
(The coast is near 17ºW.) In the realistic case, 3-5 day wave activity occurs as far east as 20˚E,
with a local maximum between 4 and 5 days near 7˚E, and modes with periods between 3 and 4
days appear near the Greenwich meridian and over the eastern Atlantic. The 3-5-day wave
activity is confined west of the Greenwich meridian in the dry case (Fig. 10b), consistent with
the composite analysis (Fig. 9a), with strong activity centered at 11ºW. The wet case, without a
strong jet over West Africa, has the strongest wave activity, centered at about 2ºE and a period of
4.5 days.
Strong waves may weaken the jet temporally through barotropic conversions, as noted by
the previous simple modeling results. However, as long as the strong surface temperature
gradient exists, the jet will restore its strength through a thermally direct ageostrophic meridional
14
circulation (Cook 1999). Therefore, the weak jet in the wet case is not the result of strong waves
but of a weaker surface temperature gradient.
As discussed in section 2, the Charney-Stern and Fjörtoft necessary conditions for
instability have been associated with the generation of African easterly waves. To evaluate this
association in the climate mode simulations, Ertel IPV is computed. As given in Molinari et al.
(1997),
IPV=−g
where σ = −
∂θ
(ς θ + f ) = gσ (ς θ + f )
∂p
−1
∂p
is the mass density, θ is potential temperature,
∂θ
(1)
ς θ is the vertical component of
relative vorticity computed on isentropic surfaces, g is gravitational acceleration, p is pressure,
and f = 2Ωsinø is the Coriolis parameter. Eq. (1) indicates that the IPV anomaly is associated
with both an absolute vorticity anomaly and with by a mass density anomaly. Note that they are
not independent. The former is related to barotropic instability, and the latter to baroclinic
instability.
Fig. 11a shows contours of the seasonal mean potential vorticity (solid line) and pressure
distribution (dash-dotted lines) averaged between 10°E and 25°E on isentropic surfaces for the
realistic climate mode simulation. This averaging region is chosen to emphasize the wave
generation region, and explore the idea that the initial or early wave growth associated with the
IPV gradient reversals is related to the jet’s wind shears. The blank area denotes regions in
which the isentropes dip under ground in the Sahara (Fig. 2a) some time during the summer
analysis period. IPV is maximum at 9°N near the 320 K isentrope on the southern side of the
African easterly jet, which is located near the 318 K isentrope between 10°N and 15°N (Fig. 2a).
The meridional IPV gradient is larger on the southern side of this IPV anomaly than on the
northern side due to the larger planetary vorticity gradient (
15
df
) on the southern side. A second
dy
IPV maximum appears in the upper troposphere near the tropical easterly jet, which is located
around 7°N near the 345 K isentrope, as noted in previous studies (Diedhou et al. 2002).
Shading in Fig. 11a indicates areas with negative IPV gradients. In the region of negative
meridional gradient of IPV between 9˚N and 15˚N, the Fjörtoft necessary condition is also
satisfied since the flow is easterly (see Fig. 2a). Note that this negative IPV gradient region
extends from the lower troposphere to the tropopause, where the IPV increases dramatically as a
result of the smallness of mass density, σ . This structure suggests that the horizontal and
vertical shears of the mean zonal wind (i.e., the African easterly jet) are not the primary cause of
the negative IPV gradients because these shears are confined below the 500 hPa (325 K) level
(Fig. 3a). Thorncroft and Hoskin (1994a) reexamined the analytically defined jet flow (centered
at 15°N) by Simmons (1977) and found that the negative IPV gradient is located between 10°N
and 20°N below 400 hPa. The negative IPV gradient north of 12˚N below 600 hPa (not clearly
shown in Fig. 11a because of the deflection of the isentropes over the Sahara) results from the
IPV minimum north of 12˚N in the lower troposphere in association with to dry convection over
the Sahara, as noted by Thorncroft and Blackburn (1999).
Figs. 11b and c show cross sections of seasonal mean streamlines and diabatic heating,
respectively, averaged between 10°E and 25°E. The zonal mean confluent streamlines tilt
southward with increasing height to 7°N as the warm dry air from the Sahara is lifted over cooler
humid air from the south. Convection in the ITCZ reaches up to the 340 K isentrope (about 300
hPa), with two condensational heating maxima that are approximately proportional to the vertical
p-velocity ω (not shown). The modeled precipitation maximum near 6°N is consistent with the
observation (Nieuwolt 1977) that most of the rainfall within the ITCZ over Africa falls to the
south of the surface convergence zone (18°N, not shown in isentropic coordinate) since the
16
uplifting air condenses near and above the mid-troposphere. Air north of the confluence zone
tends to be warm and dry. Due to the smaller inertial stability (smaller f) and larger moisture
supply on the equatorward side of the ITCZ, there is stronger condensational heating.
Schubert et al. (1991) found that reversed IPV gradients can occur when concentrated
regions of convection produce IPV maxima. Such a reversal would be produced on the poleward
side of the ITCZ at low levels and on the equatorward side of the ITCZ at upper levels. In the
simulation, a positive IPV anomaly occurs to the north of the convergent center near 7°N (Fig.
11a).
A detailed analysis of the IPV budget (Hsieh and Cook 2004a) shows that this IPV
anomaly is a result of IPV stretching and tilting caused by ITCZ convection, which suggests that
the negative IPV gradient near the mid-troposphere is primarily caused by ITCZ convection.
IPV compression, associated with divergence near 345 K, induces anticyclonic vorticity and
leads to the local minimum of IPV near the tropopause. These convective IPV sources in the
mid-troposphere (near 320 K) accompanied by sinking aloft produce the negative IPV gradient
to the north of the ITCZ near middle levels (9°N and 15°N) and to the south at upper levels (4°N
and 7°N).
The spatial and temporal scales of convective system are close to the scales of synopticscale wave disturbances over West Africa due to interactions between the convective scale and
the large-scale flow. For the seasonal mean climatology, synoptic-scale convective systems
along the ITCZ can produce an IPV anomaly with magnitude about 3~ 4 × 10-7 K m2kg-1s-1 south
of the jet (see Fig. 11a).
Figure 12 is the same as Fig. 11, but for the dry case. The magnitude and extent of the
IPV maxima at 9°N in the mid-troposphere are both smaller than in the realistic case, suggesting
a smaller unstable region in the vicinity of the jet (centered at 12°N near the 318 K isentrope).
17
The strength of the African easterly jet is comparable to that of the realistic case, which indicates
that comparable zonal mean kinetic and available potential energy is present. However, there is
no significant 3-5 day wave activity over Africa despite the IPV gradient reversal. Dickinson
and Molinari (2000) obtained a similar result over northern Australia. They found little evidence
for 2-10 day wave disturbances in the region and suggested that this may be because the unstable
region is not long enough to support waves.
According to Figs. 12b and c, convection between 6°N and 9°N in the dry case is much
more shallow and weaker than in the realistic case (Fig. 11b and c). Fig. 12c displays the
diabatic heating distribution for the dry case. This result is similar to that of the observational
analysis of Taylor et al. (2003), who suggest that soil moisture plays an important role in
determining the stability of the atmosphere. The weakening of the ITCZ leads to a weaker IPV
anomaly south of the African easterly jet, causing a smaller region of IPV gradient reversal
between 9°N and 13°N than in the realistic case.
Figure 13 is the same format as Fig. 11, but for the wet case. The IPV maximum near
12°N is comparable in extent to that in the realistic case, but slightly weaker and located about 2°
of latitude farther north. As in the realistic case, IPV gradient reversals occur on the poleward
side of the convergence maximum at lower levels near 9°N, and on the equatorward side aloft
between 6°N and 9°N. The total condensational heating is somewhat larger than that in the
realistic case and nearly double the magnitude in the dry case, consistent with the presence of
strong wave activity.
These simulations suggest that wave activity is associated more closely with intense
convection than with the African easterly jet. Additional evidence comes from the wet case, in
which wave activity becomes weak off the west coast of Africa in association with a rapid decay
18
of convection (not shown). On the other hand, stronger convection off the west coast and over
the tropical Atlantic in the dry case leads to more significant wave activity accompanying
reversed the IPV gradients over the tropical Atlantic (not shown).
5.2 Results of the synoptic mode simulations
In the synoptic simulation with NCEP soil moisture values (see section 3), the African
easterly jet is absent, and replaced by weak westerly flow in the mid-troposphere with weak
easterly flow below 650 hPa (Fig. 2f). Fig. 14a shows the mean zonal wind contours and wind
vectors at 625 hPa from this simulation. The complete elimination of the African easterly jet is a
consequence of the destruction of the meridional surface temperature gradient over West Africa
due to NCEP’s unrealistically wet conditions over the Sahara for 1988. We use this simulation
as an idealization, to understand whether or not wave activity can be generated in the absence of
the jet. It is compared with the synoptic simulation with Willmott et al. (1985) climatological
soil moisture values, which produces a reasonable African easterly jet at 625 hPa, as shown in
Fig. 14b.
Fig. 15a displays composite meridional wind contours of 3-5 day wave disturbances at
725 hPa for the synoptic case without the jet, using 12°N and 0°E as the reference point. Despite
the lack of an African easterly jet, easterly waves are still generated, but the 1100 km average
wavelength is smaller than the reported values of the previous studies (2000~4000 km). The
phase speed is approximately 6 m/s westward. Since the absence of the jet eliminates barotropic
conversions and the instability from the strong surface heating in the simulation, the waves are
being maintained by baroclinic energy conversions due to condensational heating. Some wave
disturbances may be triggered by finite amplitude perturbations in a neutral basic state. However,
19
without the condensational heating source, these finite amplitude disturbances in a neutral basic
state would eventually dissipate due to friction since they cannot obtain energy from a neutral
zonal flow.
The shorter wavelength of the waves embedded in a weak zonal flow can be explained by
considering a pressure perturbation due to a convective heating pulse, causing the flow to deviate
into the state of gradient motion, which is governed by
v
1 ∂φ
,
=−f +
r
v ∂r
(2)
where v is wind speed, φ is geopotential, r is radius of curvature. The gradient wind speed v can
be expressed as follow.
v=−
fr
±
2
∂φ
f 2r 2
+r
4
∂r
(3)
If the heating is very near the equator ( f ≈ 0 ), then r is approximately proportional to v2. If f is
relatively large (farther off the equator), e.g., with f and
1 ∂φ
of similar size, then r is proportional
v ∂r
to v. Therefore, the size of the generated vortex is approximately proportional to the scale
between v and v2, depending on the relative magnitudes of f and
1 ∂φ
. Thus, a smaller-scale
v ∂r
wave could be expected in weaker zonal flow. This suggests that the jet plays a role in setting
the scale of the waves, but the analysis shows that it is not directly involved in their generation.
The smaller wavelength response to weaker surface temperature gradient was also noted
by Chang (1993), who found that below the near-neutral layers over the Sahara the most unstable
range shifts toward shorter waves as meridional temperature gradient decrease.
The composite meridional wind pattern computed with reference point at 12˚N-0˚E in the
synoptic simulation with the jet (Fig. 15b) is obtained by averaging 206 snapshots,
20
approximately twice the number as in the synoptic case without the jet which suggests that
waves are more active in the synoptic case with the jet than in the simulation without the jet.
Wavelengths and phase speeds are more realistic, averaging 3300 km and 8 m/s, respectively.
Also, the wave axes tilt north and south of the jet (centered near 11°N), as in the realistic climate
mode simulation and the observations. Strong wave amplitudes over West Africa are associated
with the stronger ITCZ. The jet strength does not increase much over West Africa, as shown in
Fig.14b.
An examination of power spectral density distributions (not shown) for the two synoptic
simulations supports the results from the composite view of the waves in Figs. 15. Without the
jet, wave activity is present, but it is relatively weak and does not change much with longitude.
Wave activity in the synoptic case with the jet (Fig. 15b) is strong over West Africa and has both
realistic periods and wavelengths.
As reviewed above, simple model applications suggest that African easterly waves are
caused by barotropic instability associated with the jet (e.g. Simmons 1977, Kwon 1989). Some
observations, on the other hand, indicate that baroclinic conversions are more important over
land (e.g. Norquist et al. 1977). The viewpoints can be reconciled if the wave initiation is by
barotropic conversion, with the wave initiation perhaps missed by our current observing systems,
with baroclinic processes becoming dominant as the waves propagate to the west (e.g.
Thorncroft and Hoskins 1994a and b). Our results, however, do not support this idea. In the
simulation without a jet and, therefore, no barotropic conversions, waves are certainly initiated
over central Africa (Fig. 15a) and they are as strongly represented in this region as in the case
with a realistic jet.
21
Figs. 16a and b display the seasonal mean IPV and pressure distributions on isentropes
averaged between 10°E and 25°E for the synoptic simulations without and with the jet,
respectively. Shading indicates regions with reversed meridional IPV gradients. In the case with
no jet, there are two prominent IPV maxima, near the surface at 24°N and in the upper
troposphere at 6°N. There are no IPV gradient reversals in the mid-troposphere south of the
Sahara. As shown in Fig. 15a, the primary wave activity over Africa is located south of 18°N,
where the potential vorticity increases toward the north below the upper troposphere. Since the
Charney-Stern instability criterion is not met, eddy available potential energy generated by
condensational heating in the ITCZ is the only possible energy source for these waves.
In the synoptic simulation with the jet (Fig. 16b), there is a region of reversed IPV
gradient near 320K between 9°N and 15°N that coincides with the easterly jet, so both the
Charney-Stern and the Fjörtoft necessary conditions are satisfied in this region. The weaker IPV
anomaly is due to the weaker ITCZ convection over Central and East Africa, as noted in section
3. The mean variance maximum of meridional wind perturbations (not shown) is located
between10°N and 15°N near 315 K, which coincides with the unstable region suggested by the
IPV gradient reversal.
The 3-5-day easterly waves are generated in both synoptic simulations, despite the fact
that one does not have an African easterly jet and the Charney-Stern and Fjörtoft instability
criteria are not met. In this no-jet case, convective heating alone generates the waves. But the
waves are more realistic in the simulation with a jet, especially to the west of the initiation
region.
6. Summary and Conclusions
22
Regional model simulations are analyzed to explore the relationship between African
easterly waves and the basic state background climatology. The individual relationships of the
waves to the African easterly jet and the ITCZ are emphasized though they are not two
completely independent climatological features over Africa, as noted by Thorncroft and
Balckburn (1999).
The model is run in both climate- and synoptic-mode, with various
prescriptions of surface moisture used to modify, and even eliminate, the African easterly jet. In
climate mode, surface and lateral boundary conditions are taken from climatologies.
The
synoptic mode simulations are aimed at capturing a particular time and use boundary conditions
for the summer of 1988.
More insight into the wave generating mechanisms is sought by considering how the
background atmospheric state generates the meridional IPV gradient reversals required by the
Charney-Stern necessary (but not sufficient) instability criterion. The two possibilities are strong
wind shears near the jet, and very concentrated condensational heating aloft (in the ITCZ). The
former is associated with combined barotropic/ baroclinic energy conversions from the jet, and
the latter with induced barotropic and baroclinic conversions due to convection. (Cumulus
convection within the ITCZ not only induces baroclinic conversions due to vertical motion, but
also barotropic conversions as cyclonic relative vorticity is strengthened through vortex
stretching.) The positive IPV anomaly (IPV maximum) near 9˚N near the mid-troposphere
primarily results from moist convection south of the African easterly jet, while the IPV anomaly
(IPV minimum) north of the jet in the lower troposphere is caused by dry convection over the
Sahara.
In the climate-mode experiments, sign reversals of IPV gradients occur in all three cases,
even though no significant wave activity occurs over Africa in the dry case. Apparently, the
23
reversal of the IPV gradient does not necessarily lead to an unstable zonal flow since it is not a
sufficient condition.
Cyclonic IPV anomalies, caused by vortex stretching resulting from
cumulus convection, reverse the meridional IPV gradient on the poleward side of the ITCZ,
where the zonal flows are expected to be unstable.
Barotropic instability of the jet does not appear to be the key factor for the initiation of
the waves in the climate mode simulations, since no significant waves are generated over Africa
in the dry case with a strong jet. In contrast, stronger waves occur over Africa in the wet case
without a strong easterly flow.
In the synoptic simulation with no jet, the Charney-Stern
instability criterion is not met in the vicinity of the 3-5-day wave disturbances, again suggesting
that that these waves can be generated in the absence of shear instabilities. But without the
presence of the African easterly jet, the scale of the wave disturbances is smaller due, perhaps, to
a lack of interaction with the large-scale zonal flow.
Overall, these five simulations suggest that the Africa easterly jet is of less importance than
the convection associated with the ITCZ as a cause of wave activity. A detailed analysis of the
IPV budget, including associations with barotropic and baroclinic instability, is currently being
carried out to better understand how IPV gradient reversals are associated with the generation of
the waves.
Acknowledgements: The authors would like to thank Dr. Peter Gierasch for helpful discussions,
and Dr. Edward Vizy for his assistance with the regional modeling technique. The paper was
improved by the helpful comments of three anonymous referees. This research was supported by
NOAA’s CLIVAR Atlantic Program (Award NA16GP1568).
24
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30
Figure Captions
Figure 1. Domain and topography for the climate mode simulations. Topography over 500 m is
shaded, and shading interval is every 500 m.
Figure 2. Mean soil moisture availability (June 15th to September 14th) calculated from the soil
moisture climatologies of (a) Willmott et al. (1985) and (b) the NCEP reanalysis for 1988.
Contour interval is 0.1.
Figure 3. Latitude-pressure (hPa) cross-sections of the July-August mean zonal wind (solid
lines) and potential temperature (dashed lines), averaged from 10°W to 20°E, for the (a) realistic
climate-mode simulation, (b) NCEP/NCAR reanalysis climatology for 1949-2000, (c) ECMWF
reanalysis climatology for 1983-1992, (d) 1988 NCEP reanalysis, (e) 1988 synoptic simulation
with climatological soil moisture, and (f) 1988 synoptic simulation with NCEP reanalysis soil
moisture. The zonal wind contour interval is 2m/s, and the potential temperature contour interval
is 5K. Shading indicates easterly flow.
Figure 4. Zonal mean power spectral density of the 725 hPa meridional wind between 10˚W and
20˚E from the realistic climate mode simulation. The contour interval is 25 m2s-2 ∆ t, where
∆ t=day/8
indicates 8 samples each day. Power spectral density greater than 25 m2s-2 ∆ t is
shaded.
Figure 5. Response functions for band-passed filters with spectral windows in the 3-5 day range
(solid line) and the 6-9 day range (dashed line). Dotted lines indicate cut-off periods.
Figure 6. Composite streamlines and wind vectors at 725 hPa computed for the realistic climate
model simulation filtered to isolate (a) 3-5 day and (b) 6-9 day waves. Wind vectors with
magnitude greater than 0.5 m/s are displayed, and the vector scale is indicated in m/s.
31
Figure 7. Hovmöller diagrams of the meridional wind at 725 hPa filtered over (a) 3-5 and (b) 69-days. Solid contours represent positive correlations, and dashed contours represent negative
correlations. Contour interval is 0.2. Solid straight lines are used to compute wavelengths and
phase speeds (see text).
Figure 8. Seasonal mean zonal wind contours and wind vectors at 625 hPa from the climate
model simulations with (a) realistic soil moisture, (b) a uniformly dry surface, and (c) a
uniformly wet surface. The contour interval is 3 m/s, and the vector scale is indicated in m/s.
Dashed contours represent easterly zonal flow, and solid contours represent westerly zonal flow.
Figure 9. Composite streamlines and wind vectors at 725 hPa for 3-5 day waves for the climate
mode simulations with a (a) uniformly dry surface and (b) uniformly wet surface. Only wind
speeds greater than 0.5 m/s are displayed, and the vector scale is indicated in m/s.
Figure 10. Power spectral density of the 725 hPa meridional wind averaged between 10°N and
15°N for the climate mode simulations with (a) realistic soil moisture, (b) a uniformly dry
surface, and (c) a uniformly wet surface. Contour interval is 50 m2s-2 ∆ t, where ∆ t=day/8
indicates 8 samples each day.
Figure 11. Seasonal mean meridional cross sections averaged between 10˚E and 25˚E from the
realistic climate mode simulation of (a) IPV (solid lines) with a contour interval of 10-7 K m2 kg1 -1
s and isobars (dash-dot lines) with 50 hPa contour intervals, (b) meridional streamlines of (v,
10 × ω ), and (c) diabatic heating (W/kg). Shading in (a) indicates regions with negative IPV
gradients, and shading in (c) denotes diabatic cooling.
Figure 12. As in Fig.11 but from the uniformly-dry climate-mode simulation.
Figure 13. As in Fig.11 but from the uniformly-wet climate mode simulation.
32
Figure 14. Seasonal mean zonal wind contours and wind vectors at 625 hPa for (a) the synoptic
case with no jet using the 1988 NCEP soil moisture values, and (b) the synoptic case with the jet
using the observed soil moisture climatology from Willmott et al. (1985). Dashed contours
represent easterly zonal wind, and solid contours represent westerly zonal wind.
Contour
interval is 3 m/s, and the vector scale is indicated in m/s.
Figure 15. Composite meridional wind contours for 3-5 day waves at 725 hPa for the (a)
synoptic case with no jet and (b) synoptic case with the jet. Contour interval is 0.5 m/s.
Figure 16. Seasonal mean IPV (solid lines) and isobars (dash dot lines) averaged between 10°E
and 25°E for (a) the synoptic case without the jet and (b) the synoptic case with the jet. Contour
interval is 10-7 K m2 kg-1s-1. Shading indicates regions with negative meridional IPV gradient.
33
Figure 1. Domain and topography for the climate mode simulations. Topography over 500 m
is shaded, and shading interval is every 500 m.
34
Figure 2. Mean soil moisture availability (June 15th to September 14th) calculated from the soil
moisture climatologies of (a) Willmott et al. (1985) and (b) the NCEP reanalysis for 1988.
Contour interval is 0.1.
35
Figure 3. Latitude-pressure (hPa) cross-sections of the July-August mean zonal wind (solid
lines) and potential temperature (dashed lines), averaged from 10°W to 20°E, for the (a) realistic
climate-mode simulation, (b) NCEP/NCAR reanalysis climatology for 1949-2000, (c) ECMWF
reanalysis climatology for 1983-1992, (d) 1988 NCEP reanalysis, (e) 1988 synoptic simulation
with climatological soil moisture, and (f) 1988 synoptic simulation with NCEP reanalysis soil
moisture. The zonal wind contour interval is 2m/s, and the potential temperature contour interval
is 5K. Shading indicates easterly flow.
36
Figure 4. Zonal mean power spectral density of the 725 hPa meridional wind between 10˚W
and 20˚E from the realistic climate mode simulation. The contour interval is 25 m2s-2 ∆ t, where
2 -2
∆ t=day/8 indicates 8 samples each day. Power spectral density greater than 25 m s ∆ t is
shaded.
37
Figure 5. Response functions for band-passed filters with spectral windows in the 3-5 day
range (solid line) and the 6-9 day range (dashed line). Dotted lines indicate cut-off periods.
38
Figure 6. Composite streamlines and wind vectors at 725 hPa computed for the realistic
climate model simulation filtered to isolate (a) 3-5 day and (b) 6-9 day waves. Wind vectors
with magnitude greater than 0.5 m/s are displayed, and the vector scale is indicated in m/s.
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Figure 7. Hovmöller diagrams of the meridional wind at 725 hPa filtered over (a) 3-5 and (b)
6-9-days. Solid contours represent positive correlations, and dashed contours represent
negative correlations. Contour interval is 0.2. Solid straight lines are used to compute
wavelengths and phase speeds (see text).
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Figure 8. Seasonal mean zonal wind contours and wind vectors at 625 hPa from the climate
model simulations with (a) realistic soil moisture, (b) a uniformly dry surface, and (c) a
uniformly wet surface. The contour interval is 3 m/s, and the vector scale is indicated in m/s.
Dashed contours represent easterly zonal flow, and solid contours represent westerly zonal
flow.
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Figure 9. Composite streamlines and wind vectors at 725 hPa for 3-5 day waves for the climate
mode simulations with a (a) uniformly dry surface and (b) uniformly wet surface. Only wind
speeds greater than 0.5 m/s are displayed, and the vector scale is indicated in m/s.
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Figure 10. Power spectral density of the 725 hPa meridional wind averaged between 10°N and
15°N for the climate mode simulations with (a) realistic soil moisture, (b) a uniformly dry
surface, and (c) a uniformly wet surface. Contour interval is 50 m2s-2 ∆ t, where ∆ t=day/8
indicates 8 samples each day.
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Figure 11. Seasonal mean meridional cross sections averaged between 10˚E and 25˚E from the
realistic climate mode simulation of (a) IPV (solid lines) with a contour interval of 10-7 K m2
kg-1s-1 and isobars (dash-dot lines) with 50 hPa contour intervals, (b) meridional streamlines of
(v, 10 × ω ), and (c) diabatic heating (W/kg). Shading in (a) indicates regions with negative
IPV gradients, and shading in (c) denotes diabatic cooling.
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Figure 12. As in Fig.11 but from the uniformly-dry climate-mode simulation.
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Figure 13. As in Fig.11 but from the uniformly-wet climate mode simulation.
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Figure 14. Seasonal mean zonal wind contours and wind vectors at 625 hPa for (a) the synoptic
case with no jet using the 1988 NCEP soil moisture values, and (b) the synoptic case with the
jet using the observed soil moisture climatology from Willmott et al. (1985). Dashed contours
represent easterly zonal wind, and solid contours represent westerly zonal wind. Contour
interval is 3 m/s, and the vector scale is indicated in m/s.
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Figure 15. Composite meridional wind contours for 3-5 day waves at 725 hPa for the (a)
synoptic case with no jet and (b) synoptic case with the jet. Contour interval is 0.5 m/s.
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Figure 16. Seasonal mean IPV (solid lines) and isobars (dash dot lines) averaged between 10°E
and 25°E for (a) the synoptic case without the jet and (b) the synoptic case with the jet.
Contour interval is 10-7 K m2 kg-1s-1. Shading indicates regions with negative meridional IPV
gradient.
49