hsieh and cook article

Generation of African Easterly Wave Disturbances: Relationship to theAfrican Easterly Jet

JEN-SHAN HSIEH AND KERRY H. COOK

Department of Earth and Atmospheric Sciences, Cornell University, Ithaca, New York

(Manuscript received 19 March 2004, in final form 8 October 2004)

ABSTRACT

The relationship between African easterly waves and the background climatology in which they form isstudied using a regional climate model. The surface and lateral boundary conditions in the model aremanipulated to modify the background climatology, especially the African easterly jet and the ITCZ, andthe 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 aweak jet and a strong ITCZ. In these simulations, the presence of wave activity is more closely associatedwith the concentration of the ITCZ than the strength of the African easterly jet. In particular, the simulationwith a strong jet accompanied by a weak ITCZ does not produce significant wave activity, but a weak jetwith a strong ITCZ has realistic wave disturbances. Both the Charney–Stern and the Fjörtoft necessaryconditions are satisfied in all three simulations, suggesting that combined barotropic and baroclinic insta-bility contributes to the generation of waves. Near the origin of the waves, meridional gradient reversals ofisentropic potential vorticity result from potential vorticity anomalies generated by convective heatingwithin the ITCZ, implying that the unstable zonal flow may be caused by cumulus convection within theITCZ and not by shear instability associated with the jet.

Two additional simulations with 1988 lateral boundary conditions demonstrate that 3–5-day wave dis-turbances can be generated in the absence of the African easterly jet, but with unrealistically small wave-lengths. These results suggest that African easterly waves are initiated by cumulus convection within theITCZ, and not by barotropic instability associated with the jet.

1. Introduction

African easterly waves are an important synoptic fea-ture of the summer climate in West Africa and thetropical Atlantic. Observations during the Global At-mospheric Research Program (GARP) Atlantic Tropi-cal Experiment (GATE) revealed synoptic-scale distur-bances with periods of 3–5 days and wavelengths of2000–4000 km propagating to the west across West Af-rica and the tropical Atlantic with phase speeds of 6–8m s�1 (Carlson 1969; Burpee 1972; Reed et al. 1977).The waves regularly traverse the Atlantic to reach theCentral and North American coasts and are associatedwith the formation of tropical cyclones in the westernAtlantic Ocean and Caribbean Sea (Riehl 1954; Thorn-croft and Hodges 2001). Frank (1970) showed thatabout half of the tropical cyclone formation in the At-lantic is related to African easterly waves. Avila and

Pasch (1992) investigated Atlantic tropical systems dur-ing the 1991 hurricane season and found that nearly allof the eastern Pacific tropical cyclones were associatedwith African waves.

Diedhiou et al. (1998) distinguish similar periods inthe National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalyses and find that 3–5-day waves haveaverage wavelengths of 2500 km and phase speedsaround 8 m s�1. They note two preferred tracks, one tothe north and one to the south of the African easterlyjet, and suggest that these tracks tend to merge over theAtlantic. The 6–9-day waves originate farther norththan 3–5-day waves, have longer wavelengths of about5500 km, and move westward at a lower phase speed ofapproximately 6 m s�1.

Numerous studies address the causes and dynamicsof African easterly waves, but outstanding questionsremain. Many investigations focus on the hydrody-namic stability of the zonal flow since African easterlywave activity occurs in the vicinity of the African east-erly jet. This midtropospheric feature is centered near15°N in summer and is a consequence of the strongpositive meridional temperature and geopotential

Corresponding author address: Jen-Shan Hsieh, Dept. of Earthand Atmospheric Sciences, 3152 Snee Hall, Cornell University,Ithaca, NY 14850.E-mail: [email protected]

MAY 2005 H S I E H A N D C O O K 1311

© 2005 American Meteorological Society

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height gradients that develop over Sahelian Africa(Thorncroft and Blackburn 1999; Cook 1999).

The relationship between the jet and the waves isinvestigated here in a series of synoptic and climate-mode simulations with a regional climate model. Acompanion paper (Hsieh and Cook 2004b, manuscriptsubmitted to J. Atmos. Sci.) presents a thorough ener-getics analysis of the model output. Central to the be-lievability of both investigations is the quality of theAfrican easterly wave simulation in the model. After areview of the pertinent literature in section 2, the modelis described (section 3) and shown to produce an excel-lent reproduction of the African easterly wave clima-tology in section 4. In section 5, the modeling results areanalyzed to investigate the relationship between the jetand the waves. Section 6 is the summary and conclu-sions.

2. Background

Much of the theoretical work concerned with thegeneration of these waves focuses on the African east-erly waves as an expression of hydrodynamic instabilityassociated with meridional gradient reversal of isen-tropic potential vorticity (IPV). Fjörtoft (1950) appliedRayleigh theory to atmospheric flows and obtained anecessary condition for barotropic instability, which re-quires that the zonal velocity be positively correlatedwith the meridional gradient of potential vorticity.Charney and Stern (1962) generalized the instabilityproblem to three dimensions and applied it to an inter-nal jet by including horizontal and vertical wind shearin a stratified atmosphere. They showed that the insta-bility of such a jet requires a sign reversal of the me-ridional IPV gradient; that is, a disturbance cannotgrow in zonal flow that has a positive meridional IPVgradient everywhere in the domain (Eliassen 1983).

Burpee (1972) used the Charney–Stern necessarycondition to explain the existence of African easterlywaves, even though the African easterly jet cannot bestrictly classified as an internal jet. His study suggestedthat the generation of African easterly waves is directlyrelated to the African easterly jet since the Charney–Stern necessary condition is satisfied near the jet. Thetheory relating the waves and the jet was further devel-oped in the modeling studies of Rennick (1976) andSimmons (1977), who considered confined zonal flowsand suggested that the waves grow at the expense of thezonal kinetic energy of the jet without large influencesfrom latent heat releases.

Thorncroft and Hoskins (1994a,b) and Thorncroft(1995) used the primitive equations with the hydrostaticcondition to study the linear and nonlinear behavior ofeasterly waves near the easterly jet. Their studies indi-cate that initial wave generation occurs through baro-tropic conversion but that later growth is supported bybaroclinic conversion in a nonlinear process. They con-

cur that African easterly waves grow by combinedbarotropic and baroclinic instabilities associated withthe jet, but note that the role of latent heating is im-portant in increasing the baroclinic conversion and de-termining the synoptic structure of the waves.

Other investigations emphasize the role of diabaticheating in generating wave disturbances. Holton (1971)suggested that latent heat released in convection drivenby frictional moisture convergence is of primary impor-tance for waves that form along the ITCZ. Mass (1979)studied African waves using a linear model and foundthat convective heating dramatically increases the per-turbations in the lower and upper troposphere, inagreement with observations (Burpee 1974; Reed et al.1977). Schubert et al. (1991) investigated the potentialvorticity characteristics of the ITCZ using a simple zon-ally symmetric balanced inviscid model. They foundthat concentrated convective heating can cause largeIPV gradient reversals and suggested that the existenceof the African easterly jet is not necessary for the wavesto occur. Ferreira and Schubert (1997) used a nonlinearshallow water model on the sphere to simulate theITCZ breakdown and found that ITCZ convectionplays an important role in the origin of the unstablemean flow in which easterly waves form.

Finally, whether the waves are associated with Char-ney–Stern instability (the reversal of IPV gradient) isalso studied. Chang (1993) studied the unstable wavesunder the near-neutral conditions over the Sahara andfound that waves in this region occur through baroclinicenergy conversions where the Charney–Stern necessarycondition is not satisfied.

3. Model and simulation description

Considering some limitations of simpler models, forexample, the hydrostatic assumption and simple param-eterizations of latent heat release, a nonhydrostaticmodel with the ability to realistically capture the clima-tology of northern Africa and the tropical Atlantic mayoffer an alternative modeling approach for studying therelationship between African easterly waves and thejet. In this study, climate-mode simulations with a re-gional model are performed to study the relationshipbetween the background climatology and wave activityin the absence of interannual variability. In addition,synoptic-mode experiments are conducted to simulatethe summer of 1988. According to Avila and Clark(1989), the African easterly waves of 1988 were vigor-ous during the entire summer, with 62 tropical waves,19 tropical depressions, and 12 tropical storms.

The fifth-generation Pennsylvania State University(PSU)–NCAR Mesoscale Model (MM5; version 3.4)(Grell et al. 1994) is used. MM5 is a regional modelbased on finite differencing in both space and time. Itsnonhydrostatic dynamics, with 24 vertical sigma levels,allows the model to be valid for mesoscale simulations.

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Here, large domains are used to position the lateralboundaries far from the area in which the waves occurand eliminate the possibility that disturbances arepropagating into the domain rather than being gener-ated by the model physics.

Three climate-mode simulations are presented. Eachis 124 days in length, and a horizontal resolution of 80km is used across the domain, shown in Fig. 1. Themodel is initialized at 0000 UTC on 15 May using cli-matological May conditions from the NCEP–NCAR re-analysis (Kalnay et al. 1996) and run through themiddle of September. The first 17 days are discardedfor model spinup. Lateral boundary conditions forwinds, temperature, and moisture at each vertical levelare also taken from the NCEP–NCAR reanalysis, up-dated every 12 h based on a linear interpolation be-tween monthly means as in Vizy and Cook (2002).Thus, the lateral boundary conditions include the influ-ence of the seasonal cycle, but not the diurnal cycle. Seasurface temperatures are prescribed and also updatedevery 12 h using linear interpolation of the monthlySST climatology of Shea et al. (1992).

Considerable testing and validation were performedto choose a set of lateral boundary locations, surfaceand lateral boundary conditions, and physical param-eterizations that produce a good simulation of WestAfrica and the adjacent Atlantic Ocean (Vizy and Cook2002, 2003). The radiation parameterization used is theRapid Radiative Transfer Model (RRTM) longwavescheme (Mlawer et al. 1997). This scheme combineswith the cloud-radiation shortwave scheme and thesimple ice explicit moisture scheme (Dudhia 1989) todetermine shortwave fluxes and cloud ice. The RRTMradiation scheme was chosen because it produces amuch more realistic surface radiation budget in oursimulation compared to the other radiation parameter-ization options in the model. The Community ClimateModel Version 2 (CCM2) scheme, for example, consis-tently produces far too little solar radiation incident atthe ground because of its strong interaction with lowclouds. Other parameterizations chosen are the Kain–Fritsch (1993) cumulus scheme, the high-resolutionBlackadar (1979) planetary boundary layer scheme(Zhang and Anthes 1982), and shallow cumulus param-eterization (Grell et al. 1994). The parameterizationchoices are based on the work of Vizy and Cook (2002,2003) in their simulations of Africa and the tropicalAtlantic.

In the three climate-mode simulations, changes insoil moisture availability are used to manipulate thestrength of the African easterly jet and then examinechanges in the waves. Soil moisture availability, a di-mensionless fraction, is used in the model as a multi-plier in the surface moisture flux equation. Empiricalconversion formulas in the soil bucket model are usedto convert the observed or the NCEP soil moisture (inunits of millimeters) to soil moisture availability,though no soil model is used in the present study.

Therefore, moisture availability is not exactly equiva-lent to the degree of saturation on the ground, but it isrelated to it. Effects of vertical soil moisture distribu-tions are not included. One simulation has realistic soilmoisture availability, which is updated every 12 h bylinear interpolation based on the monthly soil moistureclimatology of Willmott et al. (1985). Across northernAfrica, the soil moisture availability ranges from about0.6 over the West African rain forests to 0.02 over theSahara, as shown in Fig. 2a. This range motivates twoidealized soil moisture experiments, in which the soilmoisture availability is uniform at values of 0.02 and0.06, respectively. A land surface model is not used, andthe soil moisture is prescribed and indifferent to thestate of the atmosphere.

For the two synoptic-mode simulations, 120-km hori-zontal grid spacing is used on an even larger domainthan in the climate-mode simulations, covering 14°S to51°N in latitude and 125°W to 70°E in longitude (notshown). The same 24 vertical � levels are used. Thephysical parameterizations for the synoptic experi-ments are those used in the climate-mode simulations,except the CCM2 scheme is used to parameterize ra-diation (see below) and the Grell scheme for cumulusconvection.

Lateral boundary conditions for wind, temperature,and moisture are taken from the 1988 NCEP reanalysis.The 12-hourly time series is linearly interpolated togenerate boundary conditions for each model time stepof 3 min. Both of the 124-day synoptic simulations areinitialized at 0000 UTC on 15 May using the May 1988NCEP reanalysis conditions and run through themiddle of September 1988. As in the climate-mode in-tegrations, the first 17 days are discarded for modelspinup.

Druyan and Fulakeza (2000) and Druyan et al.(2001) have also used a mesoscale model for synopticsimulations of African easterly waves, but on a smallerdomain. They find that the simulated waves are sensi-tive to the treatment of initial moisture field and soilmoisture in the model. In the synoptic simulations pre-sented here, we needed 12-hourly soil moisture values

FIG. 1. Domain and topography for the climate-mode simula-tions. Topography over 500 m is shaded, and shading interval isevery 500 m.


for that particular year (1988). The only available“data” are from the NCEP reanalysis, even thoughthese values are largely unvalidated and derived solelyfrom the model fields forced by the data assimilation.Since the 1988 NCEP soil moisture on distribution doesnot look very realistic, as shown in Fig. 2b, anothersynoptic-mode simulation using observed soil moistureclimatology (Willmott et al. 1985) was carried out. Thesmall meridional gradient of soil moisture in the 1988NCEP values produce a simulation with no jet, consis-tent with the results of Cook (1999).

Two modifications are made to compensate for thestrong radiation interaction with low clouds that occurswhen the CCM2 scheme is used. (The need for thesemodifications motivated our change to the RRTM ra-diation parameterization for the climate-mode simula-tions.) The first, similar to Giorgi et al. (1993), Vizy andCook (2002), and Cook et al. (2003), is to specify cloudsbelow 850 hPa transparent to incoming solar radiation.The second modification is to remove excessive mois-ture from the upper troposphere by fixing mixing ratiovalues in the top six � levels (above 300 hPa) to theirinitial conditions, as in Vizy and Cook (2002) and simi-lar to Horel et al. (1994). (The need for these modifi-cations disappears with the use of the RRTM scheme.)

4. Model validation

Since the focus of this paper is the relationship be-tween African easterly waves and a feature of the back-ground climatology, namely, the African easterly jet,the model validation begins with an examination of thebasic state in which the waves occur.

Latitude–pressure distributions of the July–Augustaverage zonal wind and potential temperature from theclimate-mode simulation with realistic soil moistureand the NCEP reanalysis are displayed in Figs. 3a and3b, respectively. Both are averaged from 20°E to 10°Wlongitude. Although reanalyses cannot be treated aspure observations, some fields like wind velocity andair temperature used for validation are strongly con-strained by observed data (Kalnay et al. 1996), and theyprovide a validation opportunity in data-sparse regionssuch as West Africa. To compare with the NCEP re-analysis, the model variables are interpolated onto thecoarser grid of the NCEP reanalysis, which is 2.5° by2.5° for the horizontal resolution and has 17 verticallevels.

A more consistent comparison with the NCEP clima-tology would result from an ensemble average of thesimulations for each year, but that is not practical. Themagnitude of the simulated African easterly jet is 14m s�1, somewhat stronger than the 10 m s�1 jet in theNCEP reanalysis, but well placed at 600 hPa and 13°N.The low-level westerly monsoon flow below the jet isalso stronger in the model, so vertical and meridionalwind shears are larger. The average magnitude of thejet in the climatology of the 1983–92 European Centrefor Medium-Range Weather Forecasts (ECMWF) re-analysis is 8 m s�1, and the low-level westerly flow isonly 2 m s�1, as shown in Fig. 3c. Some of the differ-ences between the ECMWF and NCEP reanalyses maybe related to the different averaging periods. The simu-lated isentropes are quite similar to those in the re-analyses. All show large deflections toward the groundnorth of 15°N, suggesting strong baroclinicity in asso-ciation with strong sensible heating over the Sahara.

Figures 3d and 3e show the July–August mean zonalwind and potential temperature from the 1988 NCEPreanalysis and the synoptic-mode simulation with Will-mott et al. (1985) soil moisture distributions, respec-tively. The 1988 jet is weaker than the climatological jet(Fig. 3b). (The 1988 jet in the ECMWF climatology issimilar to that in the NCEP reanalysis, but the low-levelwesterly flow is weaker.) The 1988 simulated Africaneasterly jet is broader and stronger than in the reanaly-ses.

Figure 3f displays the 1988 synoptic-mode simulationwith NCEP soil moisture prescribed. The African east-erly jet and the low-level westerlies are absent in thissimulation. These differences are related to the use of adifferent soil moisture distribution, since the soil mois-ture’s control on the surface temperature is an impor-

FIG. 2. Mean soil moisture availability (15 Jun to 14 Sep) cal-culated from the soil moisture climatologies of (a) Willmott et al.(1985) and (b) the NCEP reanalysis for 1988. Contour interval is0.1.


tant factor determining the jet location and strength(Cook 1999).

The model produces realistic summer rainfall distribu-tions over Africa and the tropical Atlantic. Vizy and Cook

(2002) compared model results with various observationaland satellite-gauge estimates and concluded that themodel captures the summer rainfall over this region.

Figure 4 displays the zonal mean power spectral den-

FIG. 3. Latitude–pressure (hPa) cross sections of the Jul–Aug mean zonal wind (solid lines) and potentialtemperature (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 1983–92, (d) 1988 NCEPreanalysis, (e) 1988 synoptic simulation with climatological soil moisture, and (f) 1988 synoptic simulation withNCEP reanalysis soil moisture. The zonal wind contour interval is 2 m s�1, and the potential temperature contourinterval is 5 K. Shading indicates easterly flow.


sity averaged from 10°W to 20°E from the realistic cli-mate-mode simulation, computed from the time seriesof the meridional wind at 725 hPa from mid-June tomid-September. The maximum at a period of about 4.5days between 10° and 15°N indicates the presence of3–5-day African easterly waves, in agreement with thespectral analyses of previous studies (Burpee 1974;Diedhiou et al. 1998, 1999). North of about 25°N, thereis strong wave activity between 4.5–7 days and 8–10days, consistent with the 6–9-day African easterlywaves identified in the reanalyses.

To further validate the modeled waves with the vari-ous easterly wave types distinguished by Viltard et al.(1997) and Diedhiou et al. (1998), bandpass filters areused to separate wave disturbances with 3–5-day peri-ods from the 6–9-day waves. Figure 5 shows the re-sponse functions of the two bandpass filters used, whichoffer steep rolloff characteristics for the spectral win-dows. The two filtered time series are used to formcomposite waves as in Diedhiou et al. (1998) by select-ing and averaging the 725-hPa filtered wind fields withfiltered meridional wind speed magnitudes at 18°N and0° greater than 1 m s�1 (northward). The compositewaves reflect an average picture of the significantly per-turbed fields based on the reference point (18°N, 0°).

The 3–5-day composite waves are shown in Fig. 6a.They tilt from southeast to northwest north of the jet(between 10° and 15°N), and from northeast to south-west south of the jet, as noted in Diedhiou et al. (1998).The wave trains merge over the Atlantic, similar toReed et al.’s (1988) findings from the ECMWF reanaly-sis. The axis of the cyclonic circulation at 25°N between10° and 0° tilts from the southwest to the northeast,leading to negative barotropic conversions (Ck � ��p/g[u��]�[u]/�y) since [u��] � 0 in westerly shears, that is,�[u]/�y � 0 (u is zonal wind, � is the meridional wind,and p is pressure). In contrast to the positive barotropicconversions near the two sides of the jet, this cycloniccirculation cannot be obtaining eddy kinetic energyfrom the African easterly jet.

The vertical structure of the composite 3–5-day wave(not shown) is also in agreement with previous investi-gations (Burpee 1974, 1975; Reed et al. 1977). The wavetrough axis tilts eastward with increasing height belowthe jet, and westward above the jet. This structure im-plies that energy is being converted from zonal mean toeddy available potential energy.

Figure 6b displays 6–9-day composite waves. Thesewave patterns are located farther north, in agreementwith observations. Diedhiou et al. (1998) suggested thatthe 6–9-day waves originate from the Libyan and theAzores areas, and this is consistent with the modeledwaves since the first anticyclonic circulation is centeredaround 25°N, 20°E (Libyan area), and the first cycloniccirculation is centered farther north around 35°N, 30°W(near the Azores). The 6–9-day wind perturbations areweak south of 5°N and stronger between 10° and 15°N.

Figure 7a shows Hovmöller correlation diagrams ofthe 3–5-day filtered meridional wind at 725 hPa, com-puted by correlating the time series of the filtered me-ridional wind at 15°N, 0° with that of each grid pointalong 15°N in different time lags (Liebmann and Hen-don 1990). The slope of the contours indicates the west-ward propagation of the African easterly waves. At15°N, the wavelength increases from 2400 km at 20°Eto 3500 km at 10°W. The modeled wavelength also in-creases toward the equator, similar to the observationalstudy by Diedhiou et al. (1999). The slope of the cor-relation isopleths in Fig. 7a gives the waves’ average

FIG. 4. Zonal mean power spectral density of the 725-hPa me-ridional wind between 10°W and 20°E from the realistic climate-mode simulation. The contour interval is 25 m2 s�2�t, where �t �day/8 indicates eight samples each day. Power spectral densitiesgreater than 25 m2 s�2�t are shaded.

FIG. 5. Response functions for bandpassed filters with spectralwindows in the 3–5-day range (solid line) and the 6–9-day range(dashed line). Dotted lines indicate cutoff periods.


phase speed, which is about 8.3 m s�1 at 0°. At 15°N, itincreases from 6 m s�1 at 20°E to 10 m s�1 at 10°W,similar to those of previous investigations (Reed et al.1977; Diedhiou et al. 1998).

Figure 7b shows a Hovmöller correlation diagram for6–9-day waves with the reference point at 22°N, 0°. Thedistortion of the correlation isopleths near 10°E is dueto the Tahat Mountains (see Fig. 1). However, since the6–9-day waves occur east of the Tahat Mountains, theyare clearly not caused by the interaction of the flowwith topography. The average wavelength is around5300 km, the local phase speed is 6 m s�1. The wave-length and phase speed estimated by Diedhiou et al.(1998) are 5500 km and 6 m s�1, respectively.

5. Results

a. The climate-mode simulations

The relationship between the African easterly jet andthe waves in the three climate-mode experiments is ex-amined. As described in section 3, the “realistic case”has soil moisture availability prescribed based on ob-servations, and two idealized cases have uniform soilmoisture availability of 0.02 and 0.06, the “dry” and“wet” cases, respectively.

Figures 8a–c show horizontal wind vectors and con-tours of the zonal wind at 625 hPa, averaged from 15June to 14 September for the realistic, dry, and wetcases, respectively. In the realistic and dry cases, the

FIG. 6. Composite streamlines and wind vectors at 725 hPa computed for the realistic climate model simulationfiltered to isolate (a) 3–5- and (b) 6–9-day waves. Wind vectors with magnitude greater than 0.5 m s�1 aredisplayed, and the vector scale is indicated in m s�1.


African easterly jet extends to about 30°E and hasmaximum wind speeds of 15 m s�1 near the west coast,similar to the observations. The jet is a little weakerover West Africa in the dry case than in the realisticcase in association with a slight decrease of the meridi-onal 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�1 over Cen-tral Africa. This jet structure is associated with a de-crease in meridional geopotential height gradients overWest Africa. Strong evaporative cooling over the Sa-hara due to the unrealistically wetland surface cools thisregion and reduces the magnitude of the (positive) sur-

face and, thereby, lower-tropospheric temperature gra-dient.

Composite 3–5-day waves at 725 hPa for the dry case,computed using 57 snapshots, are shown in Fig. 9a. Thesame reference point at 18°N, 0°, as in the realistic case,is used for the composite waves of both the dry and wetcases. The 3–5-day wave disturbances are active off thewest coast of Africa, similar to the realistic case, butthere is no robust wave structure over the African con-tinent except, perhaps, within the ITCZ near 5°N. Thus,the presence of a realistic African easterly jet in thissimulation (Fig. 8b) and, with it, the possibility of baro-tropic energy conversions to initiate African waves overthe land surface, does not produce significant wave ac-tivity.

Figure 9b displays composite 3–5-day waves for thewet case. Despite the absence of a well-defined jet inthe west, the waves are quite active. The fact that 204snapshots exceed the 1 m s�1 threshold velocity alsoindicates that the wave activity is stronger than in thedry case. A realistic tilt of the wave axes is present (cf.with Fig. 6a), and the phase speed and wavelength ofthe wave disturbances are around 10 m s�1 and 3700km, respectively, within the ranges reported in previousinvestigations (Burpee 1974; Diedhiou et al. 2001).

Figures 10a–c display the seasonal mean power spec-tral density averaged between 10° and 15°N of the 725-hPa meridional wind for the realistic, dry, and wetcases, respectively. (The coast is near 17°W.) In therealistic case, 3–5-day wave activity occurs as far east as20°E, with a local maximum between 4 and 5 days near7°E, and modes with periods between 3 and 4 daysappear near the Greenwich meridian and over the east-ern Atlantic. The 3–5-day wave activity is confined westof the Greenwich meridian in the dry case (Fig. 10b),consistent with the composite analysis (Fig. 9a), withstrong activity centered at 11°W. The wet case, withouta strong jet over West Africa, has the strongest waveactivity, centered at about 2°E and a period of 4.5 days.

Strong waves may weaken the jet temporally throughbarotropic conversions, as noted by the previous simplemodeling results. However, as long as the strong sur-face temperature gradient exists, the jet will restore itsstrength through a thermally direct ageostrophic me-ridional circulation (Cook 1999). Therefore, the weakjet in the wet case is not the result of strong waves butof a weaker surface temperature gradient.

As discussed in section 2, the Charney–Stern andFjörtoft necessary conditions for instability have beenassociated with the generation of African easterlywaves. To evaluate this association in the climate-modesimulations, Ertel IPV is computed. As given in Moli-nari et al. (1997),

IPV � �g��

�p�� f � � g��1�� f �, 1�

where � � ��p/�� is the mass density, � is potentialtemperature, � is the vertical component of relative

FIG. 7. Hovmöller diagrams of the meridional wind at 725 hPafiltered over (a) 3–5 and (b) 6–9 days. Solid contours representpositive correlations, and dashed contours represent negative cor-relations. Contour interval is 0.2. Solid straight lines are used tocompute wavelengths and phase speeds (see text).


FIG. 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 3m s�1, and the vector scale is indicated in m s�1. Dashed contours represent easterly zonal flow, and solid contoursrepresent westerly zonal flow.


vorticity computed on isentropic surfaces, g is gravita-tional acceleration, p is pressure, and f � 2� sin ø is theCoriolis parameter. Equation (1) indicates that the IPVanomaly is associated with both an absolute vorticityanomaly and with a mass density anomaly. Note thatthey are not independent. The former is related to baro-tropic instability, and the latter to baroclinic instability.

Figure 11a shows contours of the seasonal mean po-tential vorticity (solid line) and pressure distribution(dashed–dotted lines) averaged between 10° and 25°Eon isentropic surfaces for the realistic climate-modesimulation. This averaging region is chosen to empha-size the wave generation region and to explore the ideathat the initial or early wave growth associated with theIPV gradient reversals is related to the jet’s wind

shears. Over West Africa, strong convection effect maydominate over the effect of wind shears. The blank areadenotes regions in which the isentropes dip underground in the Sahara (Fig. 3a) some time during thesummer analysis period. IPV is at a maximum at 9°Nnear the 320-K isentrope on the southern side of theAfrican easterly jet, which is located near the 318-Kisentrope between 10° and 15°N (Fig. 3a). The meridi-onal IPV gradient is larger on the southern side of thisIPV anomaly than on the northern side due to thelarger planetary vorticity gradient (df/dy) on the south-ern side. A second IPV maximum appears in the uppertroposphere near the tropical easterly jet, which is lo-cated around 7°N near the 345-K isentrope, as noted inprevious studies (Diedhiou et al. 2002).

FIG. 9. Composite streamlines and wind vectors at 725 hPa for 3–5-day waves for the climate-mode simulationswith a (a) uniformly dry surface and (b) uniformly wet surface. Only wind speeds greater than 0.5 m s�1 aredisplayed, and the vector scale is indicated in m s�1.


Shading in Fig. 11a indicates areas with negative IPVgradients. In the region of negative meridional gradientof IPV between 9° and 15°N, the Fjörtoft necessarycondition is also satisfied since the flow is easterly (seeFig. 3a). Note that this negative IPV gradient regionextends from the lower troposphere to the tropopause,where the IPV increases dramatically as a result of thesmallness of mass density, �. This structure suggeststhat the horizontal and vertical shears of the meanzonal wind (i.e., the African easterly jet) are not theprimary cause of the negative IPV gradients becausethese shears are confined below the 500-hPa (325 K)level (Fig. 3a). Thorncroft and Hoskins (1994a) reex-amined the analytically defined jet flow (centered at

15°N) by Simmons (1977) and found that the negativeIPV gradient is located between 10° and 20°N below400 hPa. The negative IPV gradient north of 12°N be-low 600 hPa (not clearly shown in Fig. 11a because ofthe deflection of the isentropes over the Sahara) resultsfrom the IPV minimum north of 12°N in the lowertroposphere in association with dry convection over

FIG. 10. Power spectral density of the 725-hPa meridional windaveraged between 10° and 15°N for the climate-mode simulationswith (a) realistic soil moisture, (b) a uniformly dry surface, and (c)a uniformly wet surface. Contour interval is 50 m2 s�2�t , where�t � day/8 indicates eight samples each day.

FIG. 11. Seasonal mean meridional cross sections averaged be-tween 10° 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 (�, 10 � � ), and (c) diabatic heating (Wkg�1). Shading in (a) indicates regions with negative IPV gradi-ents, and shading in (c) denotes diabatic cooling.


the Sahara, as noted by Thorncroft and Blackburn(1999).

Figures 11b and 11c show cross sections of seasonalmean streamlines and diabatic heating, respectively, av-eraged between 10° and 25°E. The zonal mean conflu-ent streamlines tilt southward with increasing height to7°N as the warm dry air from the Sahara is lifted overcooler humid air from the south. Convection in theITCZ reaches up to the 340-K isentrope (about 300hPa), with two condensational heating maxima that areapproximately proportional to the vertical p velocity �(not shown). The modeled precipitation maximum near6°N is consistent with the observation (Nieuwolt 1977)that most of the rainfall within the ITCZ over Africafalls to the south of the surface convergence zone(18°N; not shown in isentropic coordinate) since theuplifting air condenses near and above the midtropo-sphere. Air north of the confluence zone tends to bewarm and dry. Because of the smaller inertial stability(smaller f ) and larger moisture supply on the equator-ward side of the ITCZ, there is stronger condensationalheating.

Schubert et al. (1991) found that reversed IPV gra-dients can occur when concentrated regions of convec-tion produce IPV maxima. Such a reversal would beproduced on the poleward side of the ITCZ at lowlevels and on the equatorward side of the ITCZ at up-per levels. In the simulation, a positive IPV anomalyoccurs to the north of the convergent center near 7°N(Fig. 11a). A detailed analysis of the IPV budget (Hsiehand Cook 2004a, manuscript submitted to J. Atmos.Sci.) shows that this IPV anomaly is a result of IPVstretching and tilting caused by ITCZ convection,which suggests that the negative IPV gradient near themidtroposphere is primarily caused by ITCZ convec-tion. IPV compression, associated with divergence near345 K, induces anticyclonic vorticity and leads to thelocal minimum of IPV near the tropopause. These con-vective IPV sources in the midtroposphere (near 320 K)accompanied by sinking aloft produce the negative IPVgradient to the north of the ITCZ near middle levels (9°and 15°N) and to the south at upper levels (4° and 7°N).

The spatial and temporal scales of the convective sys-tem are close to the scales of synoptic-scale wave dis-turbances over West Africa because of the interactionsbetween the convective-scale and the large-scale flow.For the seasonal mean climatology, synoptic-scale con-vective systems along the ITCZ can produce an IPVanomaly with a magnitude of about 3 � 4 � 10�7 K m2

kg�1 s�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 inthe midtroposphere are both smaller than in the real-istic case, suggesting a smaller unstable region in thevicinity of the jet (centered at 12°N near the 318-Kisentrope). The strength of the African easterly jet iscomparable to that of the realistic case, which indicatesthat comparable zonal mean kinetic and available po-

tential energy is present. However, there is no signifi-cant 3–5-day wave activity over Africa despite the IPVgradient reversal. Dickinson and Molinari (2000) ob-tained a similar result over northern Australia. Theyfound little evidence for 2–10-day wave disturbances inthe region and suggested that this may be because theunstable region is not long enough to support waves.

According to Figs. 12b and 12c, convection between6° and 9°N in the dry case is much more shallow andweaker than in the realistic case (Figs. 11b and 11c).Figure 12c displays the diabatic heating distribution for

FIG. 12. As in Fig. 11, but from the uniformly dry climate-modesimulation.


the dry case. This result is similar to that of the obser-vational analysis of Taylor et al. (2003), who suggestthat soil moisture plays an important role in determin-ing the stability of the atmosphere. The weakening ofthe ITCZ leads to a weaker IPV anomaly south of theAfrican easterly jet, causing a smaller region of IPVgradient reversal between 9° and 13°N than in the re-alistic case.

Figure 13 is the same format as Fig. 11, but for thewet case. The IPV maximum near 12°N is comparablein extent to that in the realistic case, but slightly weaker

and located about 2° of latitude farther north. As in therealistic case, IPV gradient reversals occur on the pole-ward side of the convergence maximum at lower levelsnear 9°N, and on the equatorward side aloft between 6°and 9°N. The total condensational heating is somewhatlarger than that in the realistic case and nearly doublethe magnitude in the dry case, consistent with the pres-ence of strong wave activity.

These simulations suggest that wave activity is asso-ciated more closely with intense convection than withthe African easterly jet. Additional evidence comesfrom the wet case, in which wave activity becomes weakoff the west coast of Africa in association with a rapiddecay of convection (not shown). On the other hand,stronger convection off the west coast and over thetropical Atlantic in the dry case leads to more signifi-cant wave activity accompanying reversed the IPV gra-dients over the tropical Atlantic (not shown).

b. Results of the synoptic-mode simulations

In the synoptic simulation with NCEP soil moisturevalues (see section 3), the African easterly jet is absentand is replaced by weak westerly flow in the midtropo-sphere with weak easterly flow below 650 hPa (Fig. 3f).Figure 14a shows the mean zonal wind contours andwind vectors at 625 hPa from this simulation. The com-plete elimination of the African easterly jet is a conse-quence of the destruction of the meridional surfacetemperature gradient over West Africa due to NCEP’s

FIG. 13. As in Fig. 11, but from the uniformly wet climate-modesimulation.

FIG. 14. Seasonal mean zonal wind contours and wind vectors at625 hPa for (a) the synoptic case with no jet using the 1988 NCEPsoil moisture values, and (b) the synoptic case with the jet usingthe observed soil moisture climatology from Willmott et al.(1985). Dashed contours represent easterly zonal wind, and solidcontours represent westerly zonal wind. Contour interval is 3m s�1, and the vector scale is indicated in m s�1.


unrealistically wet conditions over the Sahara for 1988.We use this simulation as an idealization, to understandwhether or not wave activity can be generated in theabsence of the jet. It is compared with the synopticsimulation with Willmott et al. (1985) climatologicalsoil moisture values, which produces a reasonable Af-rican easterly jet at 625 hPa, as shown in Fig. 14b.

Figure 15a displays composite meridional wind con-tours of 3–5-day wave disturbances at 725 hPa for thesynoptic case without the jet, using 12°N, 0° as the ref-erence point. Despite the lack of an African easterly jet,easterly waves are still generated, but the 1100-km av-erage wavelength is smaller than the reported values ofthe previous studies (2000�4000 km). The phase speedis approximately 6 m s�1 westward. Since the absenceof the jet eliminates barotropic conversions and the in-stability from the strong surface heating in the simula-tion, the waves are being maintained by baroclinic en-ergy conversions due to condensational heating. Somewave disturbances may be triggered by finite-amplitudeperturbations in a neutral basic state. However, withoutthe condensational heating source, these finite-ampli-tude disturbances in a neutral basic state would even-tually dissipate due to friction since they cannot obtainenergy from a neutral zonal flow.

The shorter wavelength of the waves embedded in aweak zonal flow can be explained by considering a pres-sure perturbation due to a convective heating pulse,causing the flow to deviate into the state of gradientmotion, which is governed by

�

r� �f

1�

��

�r, 2�

where � is wind speed, � is geopotential, and r is radiusof curvature. The gradient wind speed � can be ex-pressed as follows:

� � �fr

2��f2r2

4 r

��

�r. 3�

If the heating is very near the equator ( f � 0), then r isapproximately proportional to �2. If f is relatively large(farther off the equator), for example, with f and 1/�(��/�r) of similar size, then r is proportional to �. There-fore, the size of the generated vortex is approximatelyproportional to the scale between � and �2, dependingon the relative magnitudes of f and 1/� (�� /�r). Thus, asmaller-scale wave could be expected in weaker zonalflow. This suggests that the jet plays a role in setting thescale of the waves, but the analysis shows that it is notdirectly involved in their generation.

The smaller wavelength response to weaker surfacetemperature gradient was also noted by Chang (1993),who found that below the near-neutral layers over theSahara the most unstable range shifts toward shorterwaves as meridional temperature gradient decrease.

The composite meridional wind pattern computedwith the reference point at 12°N, 0° in the synoptic

simulation with the jet (Fig. 15b) is obtained by aver-aging 206 snapshots, approximately twice the numberas in the synoptic case without the jet, which suggeststhat waves are more active in the synoptic case with thejet than in the simulation without the jet. Wavelengthsand phase speeds are more realistic, averaging 3300 kmand 8 m s�1, respectively. Also, the wave axes tilt northand south of the jet (centered near 11°N), as in therealistic climate-mode simulation and the observations.Strong wave amplitudes over West Africa are associ-ated with the stronger ITCZ. The jet strength does notincrease much over West Africa, as shown in Fig. 14b.

An examination of power spectral density distribu-tions (not shown) for the two synoptic simulations sup-ports the results from the composite view of the wavesin Figs. 15. Without the jet, wave activity is present, butit is relatively weak and does not change much withlongitude. Wave activity in the synoptic case with thejet (Fig. 15b) is strong over West Africa and has bothrealistic periods and wavelengths.

As reviewed above, simple model applications sug-gest that African easterly waves are caused by barotro-pic instability associated with the jet (e.g., Simmons1977; Kwon 1989). Some observations, on the otherhand, indicate that baroclinic conversions are more im-portant over land (e.g., Norquist et al. 1977). The view-points can be reconciled if the wave initiation is bybarotropic conversion, with the wave initiation perhapsmissed by our current observing systems, with baro-clinic processes becoming dominant as the wavespropagate to the west (e.g., Thorncroft and Hoskins1994a,b). Our results, however, do not support thisidea. In the simulation without a jet and, therefore, nobarotropic conversions, waves are certainly initiated

FIG. 15. Composite meridional wind contours for 3–5-day wavesat 725 hPa for the (a) synoptic case with no jet and (b) synopticcase with the jet. Contour interval is 0.5 m s�1.


over central Africa (Fig. 15a), and they are as stronglyrepresented in this region as in the case with a realisticjet.

Figures 16a and 16b display the seasonal mean IPVand pressure distributions on isentropes averaged be-tween 10° and 25°E for the synoptic simulations with-out and with the jet, respectively. Shading indicates re-gions with reversed meridional IPV gradients. In thecase with no jet, there are two prominent IPV maxima,near the surface at 24°N and in the upper troposphereat 6°N. There are no IPV gradient reversals in themidtroposphere south of the Sahara. As shown in Fig.15a, the primary wave activity over Africa is locatedsouth of 18°N, where the potential vorticity increasestoward the north below the upper troposphere. Sincethe Charney–Stern instability criterion is not met; eddyavailable potential energy generated by condensationalheating in the ITCZ is the only possible energy sourcefor these waves.

In the synoptic simulation with the jet (Fig. 16b),there is a region of reversed IPV gradient near 320 Kbetween 9° and 15°N that coincides with the easterlyjet, so both the Charney–Stern and the Fjörtoft neces-

sary conditions are satisfied in this region. The weakerIPV anomaly is due to the weaker ITCZ convectionover central and East Africa, as noted in section 3. Themean variance maximum of meridional wind perturba-tions (not shown) is located between 10° and 15°N near315 K, which coincides with the unstable region sug-gested by the IPV gradient reversal.

The 3–5-day easterly waves are generated in bothsynoptic simulations, despite the fact that one does nothave an African easterly jet and the Charney–Stern andFjörtoft instability criteria are not met. In this no-jetcase, convective heating alone generates the waves. Butthe waves are more realistic in the simulation with a jet,especially to the west of the initiation region.

6. Summary and conclusions

Regional model simulations are analyzed to explorethe relationship between African easterly waves andthe basic-state background climatology. The individualrelationships of the waves to the African easterly jetand the ITCZ are emphasized, though they are not twocompletely independent climatological features overAfrica, as noted by Thorncroft and Blackburn (1999).The model is run in both climate and synoptic mode,with various prescriptions of surface moisture used tomodify, and even eliminate, the African easterly jet. Inclimate mode, surface and lateral boundary conditionsare taken from climatologies. The synoptic-mode simu-lations are aimed at capturing a particular time and useboundary conditions for the summer of 1988.

More insight into the wave-generating mechanisms issought by considering how the background atmosphericstate generates the meridional IPV gradient reversalsrequired by the Charney–Stern necessary (but not suf-ficient) instability criterion. The two possibilities arestrong wind shears near the jet, and very concentratedcondensational heating aloft (in the ITCZ). The formeris associated with combined barotropic/baroclinic en-ergy conversions from the jet, and the latter with in-duced barotropic and baroclinic conversions due toconvection. (Cumulus convection within the ITCZ notonly induces baroclinic conversions due to vertical mo-tion, but also barotropic conversions as cyclonic rela-tive vorticity is strengthened through vortex stretch-ing.) The positive IPV anomaly (IPV maximum) at 9°Nnear the midtroposphere primarily results from moistconvection south of the African easterly jet, while theIPV anomaly (IPV minimum) north of the jet in thelower troposphere is caused by dry convection over theSahara.

In the climate-mode experiments, sign reversals ofIPV gradients occur in all three cases, even though nosignificant wave activity occurs over Africa in the drycase. Apparently, the reversal of the IPV gradient doesnot necessarily lead to an unstable zonal flow since it isnot a sufficient condition. Cyclonic IPV anomalies,

FIG. 16. Seasonal mean IPV (solid lines) and isobars (dash dotlines) averaged between 10° and 25°E for (a) the synoptic casewithout the jet and (b) the synoptic case with the jet. Contourinterval is 10�7 K m2 kg�1s�1. Shading indicates regions withnegative meridional IPV gradient.


caused by vortex stretching resulting from cumulus con-vection, reverse the meridional IPV gradient on thepoleward side of the ITCZ, where the zonal flows areexpected to be unstable.

Barotropic instability of the jet does not appear to bethe key factor for the initiation of the waves in theclimate-mode simulations, since no significant wavesare generated over Africa in the dry case with a strongjet. In contrast, stronger waves occur over Africa in thewet case without a strong easterly flow. In the synopticsimulation with no jet, the Charney–Stern instabilitycriterion is not met in the vicinity of the 3–5-day wavedisturbances, again suggesting that that these waves canbe generated in the absence of shear instabilities. Butwithout the presence of the African easterly jet, thescale 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 Afri-can easterly jet is of less importance than the convec-tion associated with the ITCZ as a cause of wave ac-tivity. A detailed analysis of the IPV budget, includingassociations with barotropic and baroclinic instability,is currently being carried out to better understand howIPV gradient reversals are associated with the genera-tion of the waves.

Acknowledgments. The authors thank Dr. Peter Gi-erasch for helpful discussions, and Dr. Edward Vizy forhis assistance with the regional modeling technique.The paper was improved by the helpful comments ofthree anonymous referees. This research was supportedby NOAA’s CLIVAR Atlantic Program (AwardNA16GP1568).

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