Interactions of Diabatic Heating in Convective Superbursts with Energy Conversion Processes in the Genesis of Cape Verde Hurricanes from African Easterly Waves

Robert S. Ross Earth, Ocean, and Atmospheric Science, The Florida State University, Tallahassee, Florida

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T. N. Krishnamurti Earth, Ocean, and Atmospheric Science, The Florida State University, Tallahassee, Florida

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S. Pattnaik Earth, Ocean, and Atmospheric Science, The Florida State University, Tallahassee, Florida

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Abstract

This paper defines a mechanism for the genesis of tropical cyclones from African easterly waves (AEWs) over the eastern Atlantic, the so-called Cape Verde storms. Convective “superbursts” produce strong diabatic heating, which then strengthens the African easterly jet (AEJ), leading to enhanced barotropic energy conversions, which occur at the critical developmental stages of the system.

Diabatic heating is calculated using the Ertel isentropic potential vorticity (IPV) equation, while energy conversions are determined using energy equations first derived by Lorenz. The genesis mechanism is developed from studying Hurricane Bill (2009), as well as Tropical Storm Debby, Hurricane Helene, and a nondeveloping AEW, all from the 2006 NASA African Monsoon Multidisciplinary Analysis (NAMMA) field experiment, using the NCEP Final (FNL) analyses and the Advanced Research Weather Research and Forecasting model (WRF-ARW) simulations.

A striking and singular maximum in the diabatic heating due to the convective superburst is shown to precede by 24–36 h a pronounced maximum in positive barotropic energy conversion, which is demonstrated to occur simultaneously with the strengthening of the AEJ. The maximum in barotropic energy conversion is documented to occur in the developmental stages of the system, typically in the depression or early storm stages.

A physical mechanism is developed to explain how a mesoscale convective superburst can lead subsequently to an enhanced synoptic-scale AEJ over the eastern Atlantic, an enhanced jet that is critical to the genesis mechanism.

The findings agree with cited idealized studies by other investigators who found that moist AEWs grow 3 times stronger than dry waves as a result of faster AEJ development and larger barotropic energy conversions.

Additional affiliation: Indian Institute of Tropical Meteorology, Pune, India.

Corresponding author address: Robert S. Ross, Earth, Ocean, and Atmospheric Science, The Florida State University, Tallahassee, FL 32306-4520. E-mail: rross@fsu.edu

Abstract

This paper defines a mechanism for the genesis of tropical cyclones from African easterly waves (AEWs) over the eastern Atlantic, the so-called Cape Verde storms. Convective “superbursts” produce strong diabatic heating, which then strengthens the African easterly jet (AEJ), leading to enhanced barotropic energy conversions, which occur at the critical developmental stages of the system.

Diabatic heating is calculated using the Ertel isentropic potential vorticity (IPV) equation, while energy conversions are determined using energy equations first derived by Lorenz. The genesis mechanism is developed from studying Hurricane Bill (2009), as well as Tropical Storm Debby, Hurricane Helene, and a nondeveloping AEW, all from the 2006 NASA African Monsoon Multidisciplinary Analysis (NAMMA) field experiment, using the NCEP Final (FNL) analyses and the Advanced Research Weather Research and Forecasting model (WRF-ARW) simulations.

A striking and singular maximum in the diabatic heating due to the convective superburst is shown to precede by 24–36 h a pronounced maximum in positive barotropic energy conversion, which is demonstrated to occur simultaneously with the strengthening of the AEJ. The maximum in barotropic energy conversion is documented to occur in the developmental stages of the system, typically in the depression or early storm stages.

A physical mechanism is developed to explain how a mesoscale convective superburst can lead subsequently to an enhanced synoptic-scale AEJ over the eastern Atlantic, an enhanced jet that is critical to the genesis mechanism.

The findings agree with cited idealized studies by other investigators who found that moist AEWs grow 3 times stronger than dry waves as a result of faster AEJ development and larger barotropic energy conversions.

Additional affiliation: Indian Institute of Tropical Meteorology, Pune, India.

Corresponding author address: Robert S. Ross, Earth, Ocean, and Atmospheric Science, The Florida State University, Tallahassee, FL 32306-4520. E-mail: rross@fsu.edu

1. Introduction

African easterly waves (AEWs) are responsible for the development of more than half of the tropical depressions in the Atlantic (Avila et al. 2000). However, only about 1 in 5 AEWs develops into a depression in a process known as genesis. There is considerable interest in identifying the processes that lead to genesis. This was a major scientific objective of the 2006 National Aeronautics and Space Administration (NASA) African Monsoon Multidisciplinary Analysis (NAMMA) field project conducted in the eastern Atlantic (Zipser et al. 2009). In 2010 NASA conducted the Genesis and Rapid Intensification Processes (GRIP) field experiment in the western Atlantic.

The genesis problem may be formulated by asking to what extent each of the following areas determines the development or nondevelopment of AEWs: 1) the large- scale environment surrounding the wave, 2) the synoptic-scale wave structure and dynamics, 3) the convective and mesoscale processes and their interactions, and 4) the cloud microphysics, including the impacts of cloud condensation nuclei (CCN). It should be noted that these four areas may interact in the genesis process. In fact, the central theme of this paper involves an interaction between convective processes (item 3) and synoptic scale wave dynamics (item 2).

The Saharan air layer (SAL) has been the most studied large-scale environmental influence on Atlantic tropical cyclogenesis in recent years. Dunion and Velden (2004) found that the SAL suppresses the development of tropical cyclones that it engulfs, but that tropical cyclones that escape from its influence can rapidly develop into strong hurricanes. Karyampudi and Pierce (2002) found that the SAL had a positive influence on the development of Ernesto (1994) and Luis (1995), but a negative influence on the development of Andrew (1992).

The relationship of synoptic-scale wave structure and dynamics to tropical cyclogenesis has been studied by many investigators. Thorncroft and Hodges (2001), Hopsch et al. (2007), Ross and Krishnamurti (2007), Chen et al. (2008), and others have documented two tracks for AEW disturbances, both of which may be involved in tropical cyclone formation. Ross et al. (2009) used analyzed fields to show that AEWs exhibiting both positive barotropic energy conversion and strong diabatic heating in organized convection were the waves that developed during the NAMMA field experiment. Cornforth et al. (2009) used an idealized model to study the African easterly jet–easterly wave (AEJ–AEW) system under moist versus dry conditions. In the moist case the wave growth rate increased as a result of larger barotropic conversions and faster AEJ development leading to AEWs that were 3 times stronger than their dry counterparts. The observational study of Ross et al. (2009) and the modeling study of Cornforth et al. (2009) show interesting parallels with regard to the importance of both barotropic and moist convective processes in the development of AEWs. Hopsch et al. (2010) used the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) and satellite brightness temperature to form composite structures of developing and nondeveloping AEWs between 1979 and 2001. Compared to nondeveloping waves, developing waves were found to have less dry air at mid- to upper levels just ahead of the AEW trough, among other differences. Dunkerton et al. (2009) defined the concept of a critical layer within the easterly wave where the wave phase speed matches the wind speed. Genesis can occur in this region because air parcels remain in the wave form where they are protected from potentially hostile environmental influences such as the dry air of the SAL. Note that this concept cannot specify whether development will occur, only where it may occur.

With regard to the role of convective and mesoscale processes in genesis, recently the focus has been on mesoscale convective vortices (MCVs) and their interaction with so-called vortical hot towers. MCVs that build upward from low to midlevels are thought to be the most effective in triggering genesis. Hendricks and Montgomery (2004) and Montgomery et al. (2006) have shown that convective-scale cumulonimbus hot towers that possess intense cyclonic rotation in their cores are the preferred structures for transforming MCVs into tropical depressions.

No clear consensus on the role of cloud microphysics in the genesis and subsequent intensification of tropical cyclones has been achieved. Zhang et al. (2007, 2009) used numerical simulations to study the impact of Saharan dust particles acting as cloud condensation nuclei (CCN) on tropical cyclone intensity and eyewall development. They found that simulated storm intensities differed by up to 22 hPa depending on CCN concentration; however, eyewall and rainband convection did not respond monotonically to CCN input because of nonlinear feedback on heating from a host of microphysical processes.

The current study stresses the importance of diabatic heating in convective superbursts, and positive barotropic energy conversion, in the genesis of cyclones from AEWs over the eastern Atlantic, the so-called Cape Verde storms. The primary system studied will be the AEW that developed into Hurricane Bill (2009). In addition, the AEWs that developed into Tropical Storm Debby and Hurricane Helene (2006), as well as a nondeveloping wave from that year, will be examined. The genesis mechanism will be developed through use of National Centers for Environmental Prediction (NCEP) Final (FNL) analyses on a 36-km grid, and the mechanism will be tested by using the Advanced Research Weather Research and Forecasting model (WRF-ARW) output also on a 36-km grid. Section 2 of the paper will outline the diagnostic and prognostic tools that will be employed. A brief synoptic history of Hurricane Bill (2009) will be presented in section 3. Section 4 will describe the initial genesis sequence of Bill from the wave stage to the vortex stage involving interactions of diabatic heating and barotropic/baroclinic energy conversions. Section 5 will develop evidence for a genesis mechanism for eastern Atlantic tropical cyclones by establishing a dynamical link between diabatic heating in convective superbursts and the subsequent strengthening of the AEJ, leading to enhanced barotropic energy conversions and storm genesis. Section 6 will present the conclusions.

2. Methodology

a. Energetics calculations

One approach to diagnosing the dynamical aspects of genesis from AEWs will be through the use of energetics calculations based on Norquist et al. (1977). The time rate of change of eddy kinetic energy KE is expressed as
e1
where CE is the conversion of eddy available potential energy to eddy kinetic energy (baroclinic process), CK is the conversion of zonal kinetic energy to eddy kinetic energy (barotropic process), BKE and BΦE are boundary fluxes of energy, and DE is frictional dissipation of eddy kinetic energy.
The barotropic energy conversion CK and the baroclinic energy conversion CE, respectively, are expressed as
e2
e3
The eddy kinetic energy KE is given by
e4
The two processes that contribute to the growth of the eddy kinetic energy of the waves through energy conversions, represented by Eqs. (2) and (3), will be computed. The boundary fluxes of energy and the frictional dissipation of eddy kinetic energy will not be calculated in this study. Since calculations are performed over a limited latitude range (5°–37°N) it is possible that energy fluxes and pressure–work interactions at the northern and southern boundaries contribute to wave energy. No attempt has been made to evaluate these effects. However, because of the centering of the computational grid on the region of wave fluctuations, and because of the close association of the waves with the AEJ, it was concluded that the wave energy results primarily from internal conversions rather than from energy transfers across the boundaries. This same conclusion was drawn by Norquist et al. (1977). In all cases, events near the boundaries were examined to see if they could sequentially influence the interior region where the genesis events occurred. The maps at these boundary regions appeared to be rather inconsequential for the interior. It should be noted that a complete energy budget was not the intention of this study; such a complete budget will be constructed in a future study.

In the above Eqs. (2), (3), and (4), [()] represents a zonal average of the quantity () and represents a meridional average of the zonal average (area mean). A prime indicates a deviation from a zonal average. For all calculations presented here, the zonal average was obtained over a longitudinal range of approximately 55° longitude. A positive value of CK represents an increase in eddy kinetic energy at the expense of the zonal kinetic energy that occurs when the eddy momentum flux is down the mean momentum gradient. When CE is positive this represents a gain of eddy kinetic energy at the expense of eddy available potential energy that occurs when warm air rises and/or cold air sinks.

When the vertical integrations and the area means in Eqs. (2), (3), and (4) are performed, one number is obtained from each equation representing the energy conversions [Eqs. (2) and Eq. (3)] and the eddy kinetic energy [Eq. (4)] over a large volume (in this case 5°–37°N, 15°E–40°W, and 1000–100 hPa). It is impossible to assess the energy conversions and the eddy kinetic energy at various levels, as well as spatially within the waves. Because it was important in the current study to be able to do just that, the vertical integrals were removed, as well as the area means. In addition, this study confirmed the finding of Norquist et al. (1977) that the first term in Eq. (2) was at least one order of magnitude larger than the remaining terms in that equation. Thus, only results from the calculation of this first term will be considered here. Following all of these assumptions and considerations, the expressions used to map the barotropic and baroclinic conversions and the eddy kinetic energy, respectively, become
e5
e6
e7

b. Diabatic calculations

Diabatic calculations are performed using the Ertel isentropic potential vorticity (IPV) equation as utilized by Krishnamurti et al. (2000). This equation has the following form:
e8
The IPV, ζpθ, is expressed as
e9
where ζaθ is the absolute vorticity on a θ surface.
The local rate of change of IPV, appearing on the left-hand side of Eq. (8), is due to the processes signified by the various terms on the right-hand side of the equation: horizontal advection, vertical advection, vertical differential of heating, horizontal differential of heating, and friction, in that order. All terms are calculated except friction. The total diabatic heating is considered to be the sum of terms 2–4 on the right-hand side of the equation (i.e., vertical advection, vertical differential of heating, and horizontal differential of heating). Vertical advection is included because a change in theta following the parcel represents a diabatic heating process (as well as vertical motion in the theta coordinate system). Because all variables from the FNL analyses were available on pressure surfaces (1000–100 hPa at an interval of 50 hPa), transform equations were used to convert Eqs. (8) and (9) from potential temperature to pressure coordinates. For example, Eq. (9) in pressure coordinates becomes
e10
Equation (8) was similarly transformed. It is important to note that the units for the terms on the right-hand side of Eq. (8) are not actual heating units. However, since terms 2–4 on the right-hand side of the equation represent processes that change the IPV through diabatic heating, these terms will be referred to as “diabatic heating” terms.

c. WRF-ARW model

The WRF-ARW dynamic solver version 3.2 was used in this study. Initial and boundary conditions are interpolated from NCEP FNL datasets available on a 1° latitude by 1° longitude grid. A single domain was used with a horizontal resolution of 36 km. The following are the physics schemes utilized: the rapid radiative transfer algorithm (Mlawer et al. 1997) for longwave radiation, the Dudhia scheme (Dudhia 1989) for shortwave radiation, the Monin–Obukhov and Janjic schemes (Monin and Obukhov 1954; Janjic 1996, 2002) for surface physics, the Mellor–Yamada–Janjic (MYJ) turbulent kinetic energy (TKE) PBL scheme (Janjic 1996, 2002) for the boundary layer parameterization, the Betts–Miller–Janjic scheme (Janjic 1994, 2000) for the convective parameterization, and the WRF Single-Moment 6-class (WSM6) scheme (Hong et al. 1998, 2004) for the microphysics.

3. Brief synoptic history of Hurricane Bill (2009)

Bill was the strongest hurricane of the 2009 season in the Atlantic, attaining category-4 status on the Saffir–Simpson Hurricane Scale. It formed from a “southern track” AEW (Ross and Krishnamurti 2007; Chen et al. 2008) that emerged from the west coast of Africa on 11 August. Based on inspection of earth-relative streamlines and storm-relative streamlines (westward motion of the wave subtracted out), the system became a vortex from the surface to 400 hPa near 12°N, 19°W by 0600 UTC 12 August, and this will be considered the location and time of initial genesis in this paper. The system maintained this vortex status until it was officially classified as a depression by NHC near 12°N, 31°W at 0600 UTC 15 August. Classification to storm strength occurred at 1800 UTC 15 August near 12°N, 34°W and to hurricane strength at 0600 UTC 17 August near 14°N, 43°W. The observed and forecast tracks of Bill are shown in Fig. 1. These tracks were determined subjectively by inspection of 700-hPa streamline and potential vorticity maps derived from gridded FNL analysis data (observed track) and from gridded model output data (forecast track).

Fig. 1.
Fig. 1.

Observed track (crisscrosses) and WRF model forecast track (open circles) for Bill (2009). Observed positions are for every 6 h beginning on 1200 UTC 10 Aug and ending on 1200 UTC 18 Aug with system classification indicated as: W (wave), V (vortex), D (depression), S (storm), and H (hurricane). Four positions with circled crosses highlight the initial genesis sequence from 1800 UTC 11 Aug to 1200 UTC 12 Aug. Forecast positions are for every 6 h beginning on 0000 UTC 14 Aug and ending on 0000 UTC 18 Aug.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

4. Initial genesis sequence

In this section of the paper the evolution of the AEW from a wave in the 900–400-hPa layer (1800 UTC 11 August) to a vortex at 900 hPa (0000 UTC 12 August) and finally to a vortex throughout the 900–400-hPa layer (0600 UTC 12 August and 1200 UTC 12 August), indicated by circled crosses in Fig. 1, will be examined through the use of FNL-based maps of sea level pressure and 700-hPa streamlines, as well as cross sections and maps of fields obtained from the energetics calculations (section 2a) and the diabatic calculations (section 2b). Infrared satellite imagery of the associated convection will also be examined. This will be our first look at the major convective burst, termed a superburst in this paper, its associated diabatic heating, and the barotropic energy conversions (and baroclinic energy conversions, to a lesser extent) that are the building blocks of the genesis mechanism that is developed in this paper.

Table 1 shows the status of the system from the surface to 400 hPa over the time frame of interest. The categories “closed low” at the surface and “vortex” aloft are highlighted in bold. The vortex status was seen in both earth-relative and storm-relative streamlines.

Table 1.

Classification of the Bill (2009) circulation at various levels during the period of initial genesis. The bold font signifies a closed circulation as opposed to an open wave.

Table 1.

a. Satellite imagery

The Meteosat infrared satellite imagery in Fig. 2 shows the impressive burst of convection that accompanied the initial genesis of this system. This convection initially formed over the West African continent (Figs. 2a,b) and then moved westward as the wave moved off the coast and intensified into a vortex (Figs. 2c,d). The scale of the convective feature is approximately 5° longitude. This burst of convection is “impressive” not so much because of its presentation in satellite imagery but because of the calculated diabatic heating accompanying this burst (see Fig. 13 to be discussed later). [In Fig. 13 the heating in the vortex stage is approximately 3 times larger than any subsequent heating in the studied life cycle of Bill, including the hurricane stage. Note that Figs. 14 and 15, to be discussed later, show additional cases (Debby and Helene from 2006, respectively) where a singular burst of convection in the wave stage has a calculated diabatic heating that is approximately 4–6 times greater than subsequent heating in the depression and storm stages.] This paper will deal with the dynamical impacts of such superbursts of convection and associated diabatic heating on the genesis of tropical cyclones from AEWs. These superbursts have been seen repeatedly in our work in both analyzed and forecast fields and are deemed to be of vital importance in the genesis sequence. A working definition of a superburst is a burst of convection with a scale of at least 5° longitude, as seen in infrared satellite imagery, and with a calculated diabatic heating rate that is 3–6 times greater than the heating rates typically seen in developing systems, even in the storm and hurricane stages.

Fig. 2.
Fig. 2.

Meteosat infrared satellite images of Bill (2009) during the period of initial genesis: (a) 1800 UTC 11 Aug, (b) 0000 UTC 12 Aug, (c) 0600 UTC 12 Aug, and (d) 1200 UTC 12 Aug. Longitude markers are for every 10°.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

b. Sea level pressure maps

Figure 3 shows the sea level pressure pattern accompanying the convective burst and associated system genesis, for the same times as in Fig. 2. Initially, there is a mesoscale high of 1013 hPa over the continent, associated with the burst of convection, and a weak trough of low pressure along the coast (Fig. 3a). As the wave moves off the coast and intensifies, an area of low pressure becomes increasingly better defined with one closed isobar at 0000 UTC 12 August (Fig. 3b) evolving into six closed isobars by 1200 UTC 12 August (Fig. 3d).

Fig. 3.
Fig. 3.

Observed sea level pressure at an interval of 0.5 hPa for Bill (2009) during the initial genesis period: (a) 1800 UTC 11 Aug, (b) 0000 UTC 12 Aug, (c) 0600 UTC 12 Aug, and (d) 1200 UTC 12 Aug.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

c. Streamline maps at 700 hPa

Streamline maps at 700 hPa for the same times as in Figs. 2 and 3 are presented in Fig. 4. At 1800 UTC 11 August (Fig. 4a) and 0000 UTC 12 August (Fig. 4b) the system is still clearly a wave. By the last two times, 0600 UTC 12 August and 1200 UTC 12 August (Figs. 4c,d), the system has become a vortex at 700 hPa for the first time in its synoptic history (see Table 1). The burst of convection, the development of a distinct low pressure center at the surface, and the evolution from a wave to a vortex from the low to the midtroposphere are viewed in this paper as indicative of tropical cyclone genesis.

Fig. 4.
Fig. 4.

Observed streamlines at 700 hPa for Bill (2009) during the period of initial genesis: (a) 1800 UTC 11 Aug, (b) 0000 UTC 12 Aug, (c) 0600 UTC 12 Aug, and (d) 1200 UTC 12 Aug. The trough line is indicated by a light solid line and the positions of the north–south cross sections discussed at length in the text are indicated by a bold solid line.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

d. Vertical cross sections of parameters from energetics and diabatic calculations

During genesis, significant characteristic changes in the system are defined by the calculation of energetic and diabatic properties, which can increase understanding of the genesis process from a dynamical perspective. First, we will examine these parameters and their changes from the viewpoint of vertical cross sections.

The cross sections are constructed for the times of the circled crosses in Fig. 1. The cross-section lines for these times are indicated in Fig. 4. For the first two times the system is still a wave at 700 hPa, but by the last two times the system has become a vortex at 700 hPa (and from the surface to 400 hPa), and this is one aspect of our definition of genesis.

1) Cross sections for 1800 UTC 11 August

The cross sections of energetics parameters for 1800 UTC 11 August along 18.2°W (see Fig. 4a) are depicted in Fig. 5. The cross-section line is placed near the trough axis at 700 hPa. The eddy kinetic energy (EKE) cross section (Fig. 5a) contains five maxima: 11°N at 650 hPa, 15°N at 750 hPa, 9°N at 450 hPa, 11.5°N at 300 hPa, and 9.5°N at 900 hPa. Two of these maxima are associated with the trough position at 700 hPa; the maximum at 11°N and 650 hPa is directly associated with the trough’s axis, while the maximum at 15°N and 750 hPa occurs with strong southeasterly flow to the east of that axis. Neither of these maxima is collocated with significant maxima in baroclinic (Fig. 5b) or barotropic (Fig. 5c) energy conversion. This is also the case for the EKE maximum at 9.5°N and 900 hPa, which occurs in localized northwesterly flow to the west of a vortex at 11°N, 16°W at that level, well to the east of the 700-hPa trough axis. The trough seen at 700 hPa extends into the upper troposphere where it is represented by two EKE maxima: 9°N at 450 hPa and 11.5°N at 300 hPa. The first of these EKE maxima is collocated with a positive maximum in barotropic conversion (BTCONV; Fig. 5c), which occurs to the south of an easterly jet maximum at that level where eddy momentum flux is directed down the mean momentum gradient {u′ > 0, υ′ > 0, ∂[u]/∂y < 0 in Eq. (5)}. The second of these EKE maxima is collocated with a very strong center of baroclinic conversion (BCCONV) resulting from strong rising motion in warm air [ω′ < 0, T′ > 0 in Eq. (6)].

Fig. 5.
Fig. 5.

Observed cross sections of energy conversion parameters for Bill (2009) at 1800 UTC 11 Aug along 18.2°W (see Fig. 4a) when the system was still a wave in the layer 900–400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

The corresponding cross sections of diabatic parameters shown in Fig. 6 confirm the well-developed nature of this system above 500 hPa. An impressive center of positive IPV is located at 10.5°N and 400 hPa (Fig. 6a) in proximity to the maximum in EKE in that region. This IPV center is evidently maintained by the collocated strong region of positive vertical differential of heating (VDH; Fig. 6b). The vertical advection (VA) positive–negative couplet (Fig. 6d) in the upper troposphere is consistent with the IPV center being imbedded in rising motion at that location. This rising motion fits with the previously diagnosed maximum in BCCONV in the same region (rising warm air), and the positive centers in VDH and VA are consistent with the production of the warm air by diabatic heating. It is very encouraging that the two methods of diagnosing the dynamics of genesis are consistent with each other. There is also a positive maximum in HDH at 9°N and 900 hPa (Fig. 6c). This is not generating an IPV maximum in the area, but it is interesting that this heating is approximately collocated with the EKE maximum in that region (Fig. 5a).

Fig. 6.
Fig. 6.

Observed cross sections of diabatic heating parameters for Bill (2009) at 1800 UTC 11 Aug along 18.2°W (see Fig. 4a) when the system was still a wave in the layer 900–400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

2) Cross sections for 0000 UTC 12 August

The cross sections of energetics parameters 6 h later at 0000 UTC 12 August along 19.2°W (see Fig. 4b) are shown in Fig. 7. This cross-section line is again placed near the trough axis at 700 hPa. The EKE cross section (Fig. 7a) contains the same five maxima as in Fig. 5 with only slight variations in location. The three maxima in the lower troposphere below 500 hPa are all produced in the same way as diagnosed in the previous energetics cross section except that the maximum in EKE at 10°N and 900 hPa now occurs in localized northeasterly flow (not northwesterly flow) to the west of the same vortex at 11°N, 16°W. The salient difference is that this maximum at 10°N and 900 hPa has strengthened significantly and now has a distinct maximum in BTCONV associated with it (Fig. 7c). The strong positive BTCONV is produced to the north of a westerly maximum in in the low-level monsoon flow (the localized flow is northeasterly but the zonally averaged flow is westerly and is consistent with monsoon flow at that level and latitude). With zonally averaged westerly flow decreasing sharply northward (∂[u]/∂y < 0), and with localized northeasterly flow (u′ < 0 and υ′ < 0), Eq. (5) is positive, with eddy momentum flux directed down the mean momentum gradient. The EKE maximum at 11°N and 650 hPa, located in the trough axis (Fig. 4b), also shows weak positive BTCONV (Fig. 7c) (stronger when cross section is placed just to the east, not shown) and a slightly stronger positive BCCONV (Fig. 7b). Thus, both barotropic and baroclinic energy conversions, although weak, are occurring with this wave in the vicinity of the midtropospheric AEJ. In the upper troposphere, the two previously mentioned EKE maxima and their associated energy conversions are still present. Comparing the EKE cross sections in Figs. 5 and 7 one gets the impression that the EKE center near 9°N and 400 hPa is becoming more connected with the EKE maximum near 11°N and 700 hPa, forming a downward- and northward-tilted region of EKE. Below this, the low-level EKE maximum around 900 hPa is strengthening and moving northward, and more underneath (more in phase with), the EKE region higher up, creating the possibility of a unified column of EKE extending throughout the troposphere.

Fig. 7.
Fig. 7.

Observed cross sections of energy conversion parameters for Bill (2009) at 0000 UTC 12 Aug along 19.2°W (see Fig. 4b) when the system was still a wave in the layer 800–400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

The corresponding cross sections of diabatic parameters are presented in Fig. 8. The prominent maximum in IPV in the upper troposphere (Fig. 8a) now extends downward to near 800 hPa forming a downward- and northward-tilted region of IPV much like the pattern seen in the EKE field. The positive VDH region also extends downward compared to 6 h earlier, with a center located near 550 hPa (previous center at 450 hPa). The VA positive–negative couplet in the upper troposphere (Fig. 8d) persists as a result of the IPV center still being imbedded in rising motion in that region. The HDH maximum at 900 hPa present 6 h earlier has weakened and a prominent maximum in VDH has developed in the same location. There is still no maximum in IPV at this level, but the VDH and HDH maxima are collocated with the maximum in EKE at that level (Fig. 7a).

Fig. 8.
Fig. 8.

Observed cross sections of diabatic heating parameters for Bill (2009) at 0000 UTC 12 Aug along 19.2°W (see Fig. 4b) when the system was still a wave in the layer 800–400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

3) Cross sections for 0600 UTC 12 August

Cross sections of energetics (Fig. 9) and diabatic (Fig. 10) characteristics at 0600 UTC 12 August define the structure of the vortex at the specified genesis time. The cross-section line runs along 19.3°W (see Fig. 4c) through the northernmost vortex at 700 hPa, which is viewed as the primary vortex, since it aligns with the developing low pressure center at the surface (Fig. 3c).

Fig. 9.
Fig. 9.

Observed cross sections of energy conversion parameters for Bill (2009) at 0600 UTC 12 Aug along 19.3°W (see Fig. 4c) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 10.
Fig. 10.

Observed cross sections of diabatic heating parameters for Bill (2009) at 0600 UTC 12 Aug along 19.3°W (see Fig. 4c) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Several major changes have occurred in the cross sections of energetics parameters (cf. Figs. 9 and 7). There has been a major strengthening of the EKE maximum at 900 hPa from 50 to 90 units, accompanied by a northward shift (10°–13°N) and a definite upward extension of this feature to approximately 500 hPa. This growth of EKE can be explained by the maximum in BTCONV, which likewise strengthens from 6 to 11 units as it shifts northward (cf. Figs. 9c and 7c). The strong positive BTCONV is produced to the north of a westerly maximum in in the low-level monsoon flow with eddy momentum flux directed down the mean momentum gradient, exactly as diagnosed in section 4d(2) for this feature. When one compares Figs. 5a, 7a, and 9a, it can reasonably be asked if this low-level EKE feature seen in Fig. 9 is the same one appearing in Figs. 5 and 7, since it appears to jump northward. Because the feature has been there for 18 h, and since it has already moved slightly northward from 1800 UTC 11 August (Fig. 5) to 0000 UTC 12 August (Fig. 7), and since it is associated with a center of positive BTCONV that has likewise moved northward from 0000 UTC 12 August (Fig. 7) to 0600 UTC 12 August (Fig. 9), and this is an energy conversion feature produced by identical properties of the flow pattern between those two figures, it is concluded that the low-level EKE maximum is, indeed, the same feature.

There has also been a strengthening of the EKE maximum near 10.5°N and 650 hPa from 20 to 40 units, as the associated BTCONV maximum has increased from 1 to 5 units while growing noticeably in size. The EKE maximum is associated with the primary vortex seen in Fig. 4c, and the BTCONV maximum occurs with eddy momentum flux directed down the mean momentum gradient, but this occurs to the south of the easterly jet (AEJ) in this instance {u′ > 0, υ′ > 0, ∂[u]/∂y > 0, Eq. (5) positive}. The positive energy conversion in the lower half of the troposphere is now dominated by the two significant BTCONV maxima, one occurring with a westerly jet and one with an easterly jet in the zonally averaged u wind component. In the upper troposphere the positive maximum in BCCONV at 400 hPa has increased from 20 to 70 units, compared to 6 h earlier, and has greatly expanded in size, extending downward to 600 hPa. This positive conversion, produced by rising warm air just to the east of the trough axis at 400 hPa, is likely aiding the upward extension of the EKE maximum seen near 13°N (Fig. 9a). From inspection of streamline maps (not shown), there is now a closed circulation extending from 900 to 400 hPa, whereas 6 h previously there was a closed circulation only at 900 hPa. Lifting of relatively cooler air in this circulation explains the region of negative BCCONV below 700 hPa and between 11.5° and 13.5°N, which acts as somewhat of a “brake” on the increase in EKE. The initial genesis of the system can be partially explained by the positive energy conversions just outlined: increased and upward extending BTCONV at 900 hPa, increased and expanded BTCONV at 650 hPa, and increased and expanded BCCONV at 400 hPa. The rest of the explanation of the initial genesis lies with the diabatic parameters.

The cross sections of diabatic parameters at 0600 UTC 12 August are shown in Fig. 10. Consistent with the genesis process, the prominent maximum in IPV in the upper troposphere (Fig. 10a) has increased in magnitude from 160 to 180 units and has continued to extend downward, now reaching nearly to the surface. These changes in IPV can be linked to an impressive increase in the VDH from 15 to 70 units (Fig. 10b), along with an equally impressive vertical expansion of the heating, with positive heating now extending from 450 hPa to the surface. A negative center of VDH (−50 units) has developed in the upper troposphere above the maximum in positive VDH, but this is offset by a strong positive center in VA of 120 units (Fig. 10d), which may also be interpreted as a diabatic heating mechanism. The positive VA (and the negative VA just below it) results from rising motion in the region of maximum IPV. There is a weaker center of positive horizontal differential of heating (HDH; Fig. 10c) located near 12.5°N and 900 hPa. Taken together, the maxima in VDH, VA, and HDH produce a vertical column of positive heating near 12.5°N extending from the surface to 300 hPa. This vertically aligned heating is a prominent cause of system genesis and is reflected in the deep column of positive IPV in the same location. And, as previously stated, genesis is also explained by the increased magnitudes of EKE centers and the increased and expanded BTCONV and BCCONV centers as diagnosed from Fig. 9.

At least one mystery remains. It is not clear why the vertical column of EKE in Fig. 9 is displaced northward compared to the vertical column of IPV in Fig. 10 (displacement of 1.5° latitude). These two measures of the genesis of the system do not line up exactly, and perhaps this reflects a type of tilt to the system that requires further study.

4) Cross sections for 1200 UTC 12 August

The cross sections of energetics and diabatic parameters, respectively, 6 h later at 1200 UTC 12 August along 20.5°W (see Fig. 4d), are depicted in Figs. 11 and 12. This cross-section line again runs through the northernmost vortex at 700 hPa. These cross sections are not qualitatively different from those at 0600 UTC 12 August, and for brevity only a few differences will be highlighted.

Fig. 11.
Fig. 11.

Observed cross sections of energy conversion parameters for Bill (2009) at 1200 UTC 12 Aug along 20.5°W (see Fig. 4d) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 12.
Fig. 12.

Observed cross sections of diabatic heating parameters for Bill (2009) at 1200 UTC 12 Aug along 20.5°W (see Fig. 4d) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

The energetics cross sections show that the EKE maxima (Fig. 11a) in the lower troposphere near 10.5°N and 700 hPa, and near 13.5°N and 900 hPa, have increased in magnitude. An EKE maximum of 80 units has now developed in the upper troposphere (400 hPa) approximately above the lower-tropospheric maximum near 13.5°N. This growth of EKE is consistent with the development of a very strong and vertically expansive region of positive BCCONV (Fig. 11b) centered at 13°N and 400 hPa with a magnitude of 250 units (warm air rising). Lifting of relatively cooler air in the vortex explains the region of negative BCCONV below 700 hPa and between 11.5° and 13.5°N (Fig. 11b), which acts as somewhat of a brake on the increase in EKE in the lower troposphere, as it did 6 h earlier (Fig. 9b). However, genesis is still being supported by two robust centers of positive BTCONV in the lower troposphere (Fig. 11c).

Between 0600 and 1200 UTC 12 August, a slight weakening occurred in the IPV structure of the vortex from 180 to 140 units (Fig. 12a). The pattern of VDH (Fig. 12b) is largely unchanged, but the peak positive heating values have increased from 70 to 140 units, indicating that the intense convective heating has increased. The negative maximum above the positive heating has increased in magnitude from −50 to −80 units. The positive maximum in VA (Fig. 12d) at 12.5°N and 400 hPa has increased from 120 to 200 units indicating an increase in the rising motion in this region. The HDH pattern (Fig. 12c) has become more chaotic, but there is a positive maximum in heating centered at 800 hPa and 13.5°N, which contributes to the heating of the vortex. Both the energetics and diabatic cross sections indicate that the genesis processes are still active in the system.

e. Summary of initial genesis mechanism

The initial genesis of this system resulted from an interaction of strong diabatic heating in a “superburst” of convection, with primarily barotropic energy conversions, that lead to a deep-tropospheric column of IPV and EKE. Barotropic energy conversions at low levels were defined by conversion of zonal kinetic energy (ZKE) to EKE in zonally averaged westerly monsoon flow. At midlevels, there was a ZKE to EKE conversion in zonally averaged easterly flow that defined the AEJ. Baroclinic energy conversion aided in the vertical extension of the EKE column into the upper troposphere. Maxima in VDH, VA, and HDH were the components of a strong and vertically aligned diabatic heating pattern extending from the surface to 300 hPa, leading to a deep column of positive IPV. The deep columns of EKE and IPV, together with their dynamical production mechanisms, constitute the genesis mechanism described here.

5. Evidence for a dynamical link between diabatic heating in convective superbursts and the subsequent growth of barotropic energy conversion in the genesis process

The previous section has described the near-simultaneous interplay of diabatic heating and energy conversion processes in the initial genesis of Bill (2009). The phenomenon to be described in this section of the paper is viewed as a vital aspect of genesis that operates over a more expansive time frame. A surprising result is described that has been noted in the observed development of three AEWs and one nondeveloping AEW in the eastern Atlantic, with results confirmed by WRF model simulations. The surprising result is that a singular maximum in diabatic heating, resulting from a superburst of convection in the predepression stage of the system, with diabatic heating rates 3–6 times greater than at any subsequent time in the life cycle of the system (even the storm and hurricane stages) is followed typically within 24–36 h (mean of 30 h) by a significant growth and enhancement of the positive barotropic energy conversion at 600–700 hPa in association with an increase in the zonally averaged easterly flow of the AEJ.

Figure 13 shows observed profiles of positive vertical differential of diabatic heating (the dominant heating term) and positive barotropic energy conversion as Bill develops from a wave to a hurricane (positions marked “×” in Fig. 1). Maximum barotropic energy conversion values apply to the location of the disturbance at each time and are based on calculations over a fixed domain (5°–37°N, 15°E–40°W for the period 1200 UTC 10 August–1200 UTC 14 August; 5°–37°N, 4°–60°W for the period 1200 UTC 14 August–1200 UTC 18 August). The prominent peak in diabatic heating associated with the superburst of convection at 1200 UTC 12 August is never equaled again and is followed by a gradual growth in the barotropic energy conversion, which has a relative peak at 1200 UTC 14 August (vortex stage) and an absolute peak at 0600 UTC 17 August (hurricane stage). Even the relative peak in positive barotropic energy conversion seen at 0600 UTC 12 August, which was a part of the discussion of initial genesis in section 4, occurs after a maximum in diabatic heating at 0600 UTC 11 August.

Fig. 13.
Fig. 13.

Profiles of observed maximum positive mean vertical differential of diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum positive barotropic energy conversion (W kg−1) at 700 hPa (dashed line) for Bill (2009) during the period 1200 UTC 10 Aug–1200 UTC 18 Aug. Vertical differential of diabatic heating is from term 3 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system is indicated at the top of the diagram as wave, vortex, depression, storm, and hurricane.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Figures 14, 15, and 16 depict the same phenomenon as just discussed for three NAMMA systems from 2006: Debby, Helene, and nondeveloping wavenumber 4, respectively. In all three cases a singular maximum in diabatic heating resulting from a superburst of convection, not equaled again in the sequence, is followed by a growth in the positive barotropic energy conversion. Just as in Fig. 13 the maximum barotropic energy conversion values apply to the location of the disturbance at each time and are based on calculations over a fixed domain of approximately 30° latitude by 55° longitude. Note that the nondeveloping wave (Fig. 16) has negative barotropic energy conversion throughout (part of the reason for nondevelopment), but this negative conversion decreases with time, representing a growth with time of a positive conversion. These results were previously reported in Ross et al. (2009).

Fig. 14.
Fig. 14.

Profiles of observed maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum positive barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for Debby (2006) during the period 0000 UTC 20 Aug–0000 UTC 24 Aug. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system is indicated at the top of the diagram as wave, depression, and storm.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 15.
Fig. 15.

Profiles of observed maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum positive barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system is indicated at the top of the diagram as wave, depression, and storm.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 16.
Fig. 16.

Profiles of observed maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum negative barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for NAMMA nondeveloping wave 4 during the period 1200 UTC 29 Aug–1200 UTC 2 Sep. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the system remained a wave throughout this time frame.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

The same relationship between a singular maximum in diabatic heating, not equaled again in the sequence, and the subsequent growth of barotropic energy conversion has been verified in WRF model simulations. Figure 17 shows this relationship for Bill 2009, which was initialized at 0000 UTC 14 August (observed vortex stage) and integrated to 0000 UTC 18 August (observed hurricane stage; positions marked with open circles in Fig. 1). The peaks in diabatic heating (in observed vortex stage) and positive barotropic energy conversion (in observed storm stage) are very prominent, with the latter lagging the former by 36 h. Figure 18 shows the relationship for the WRF model simulation of Helene 2006, which was initialized at 1200 UTC 10 September (observed wave stage) and integrated to 1200 UTC 14 September (observed storm stage), corresponding to the same times as in Fig. 15. Again, the peak diabatic heating is seen to precede the maximum in barotropic energy conversion, although the relationship is not as “clean” as for the simulation of Bill (2009; Fig. 17). But the simulated profiles in Fig. 18 are in rough agreement with the observed profiles in Fig. 15 with maximum diabatic heating occurring in the wave stage and maximum barotropic energy conversion occurring in the depression stage. For simulations of Bill (Fig. 17) and Helene (Fig. 18) the maximum barotropic energy conversion values apply to the location of the disturbance at each time and are based on calculations over a fixed domain of approximately 30° latitude by 55° longitude.

Fig. 17.
Fig. 17.

Profiles of WRF model forecast maximum positive mean vertical differential of diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and WRF model forecast maximum positive barotropic energy conversion (W kg−1) at 700 hPa (dashed line) for Bill (2009) during the period 0000 UTC 14 Aug–0000 UTC 18 Aug. Vertical differential of diabatic heating is from term 3 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system based on observation is shown at the top of the diagram as vortex, depression, storm, and hurricane.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 18.
Fig. 18.

Profiles of WRF model forecast maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and WRF model forecast maximum positive barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system based on observation is shown at the top of the diagram as wave, depression, and storm.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

A testable hypothesis was formed to explain the linkage between a singular maximum in diabatic heating, resulting from the convective superburst, and the subsequent growth of barotropic energy conversion in the zonally averaged easterly flow of the AEJ. The hypothesis is that the singular maximum in diabatic heating subsequently leads to an enhanced AEJ, one that is then more capable of producing a larger barotropic energy conversion. The hypothesis was tested using the following figures: Figs. 19 and 20 based on observations for Bill (2009) and Helene (2006), respectively; Figs. 21 and 22 based on WRF model simulations for Bill (2009) and Helene (2006), respectively. To construct each of these figures the maximum 650-hPa (or 700) u component of the wind to the north of the system center was determined, a mean of all the values was formed for the time series shown, and then the departure of each individual value from the time mean was determined and plotted. Bars oriented upward (downward) indicate a weaker (stronger) easterly u-wind component at each time. All figures show the time of the convective superburst and the classification of the system along the time line. In all cases, both observed and model simulated, the convective superburst is followed by a strengthening of the easterly wind maximum to the north of the system. For Bill (2009) the superburst occurs in the vortex stage, and in the wave stage for Helene (2006). For Bill the enhanced easterly jet occurs in the vortex/depression/storm stages, and for Helene this occurs in the depression stage. These figures are viewed as confirmation of the stated hypothesis: the singular maximum in diabatic heating resulting from the convective superburst occurs early in the life of the AEW and leads to an enhanced AEJ, which then allows for enhanced barotropic energy conversion in association with the jet, all this in the critical genesis stages of vortex, depression, and storm, prior to full hurricane development.

Fig. 19.
Fig. 19.

Time variation of the observed maximum 650-hPa easterly wind component (AEJ) in m s−1 to the north of Bill (2009) during the period 1200 UTC 10 Aug–1200 UTC 18 Aug. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the observed major convective burst (see most prominent peak in diabatic heating in Fig. 13) is indicated, as well as the observed classification of the system as wave, vortex, depression, storm, and hurricane.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 20.
Fig. 20.

Time variation of the observed maximum 650-hPa easterly wind component (AEJ) in m s−1 to the north of Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the observed major convective burst (see peak in diabatic heating in Fig. 15) is indicated, as well as the observed classification of the system as wave, depression, and storm.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 21.
Fig. 21.

Time variation of the WRF model forecast maximum 700-hPa easterly wind component (AEJ) in m s−1 to the north of Bill (2009) during the period 0000 UTC 14 Aug–0000 UTC 18 Aug. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the WRF model forecast major convective burst (see peak in diabatic heating in Fig. 17) is indicated, as well as the observed classification of the system as vortex, depression, storm, and hurricane.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 22.
Fig. 22.

Time variation of the WRF model forecast maximum 650-hPa easterly wind component (AEJ) in m s−1 to the north of Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the WRF model forecast major convective bursts (see twin prominent peaks in diabatic heating in Fig. 18) is indicated, as well as the observed classification of the system as wave, depression, and storm.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

The method of defining the strengthened AEJ in Figs. 1922 may be challenged. What if the maximum u component of the wind to the north of the system center is simply a part of the flow around the developing system and is not, therefore, representative of the jet? In all cases, inspection of the maps of streamlines and isotachs gave the subjective impression that the easterly wind maximum was separate from the immediate circulation around the system. Additional evidence that the recorded easterly wind maximum is not a measure of the flow around the system is that this wind maximum weakens in the storm stage (Helene) and hurricane stage (Bill) just when it should be strongest if it represented flow around the system.

Further evidence that it is the AEJ that strengthens after the singular maximum in diabatic heating produced by the convective superburst is provided for Bill (Fig. 23) and Helene (Fig. 24). In both figures the AEJ is defined by the observed 650-hPa zonally averaged u component of the wind {[u] in Eq. (5)}. In both cases the AEJ strengthens after the convective superburst, reaching a maximum in the storm stage for Bill and in the depression stage for Helene, and then weakens thereafter (hurricane stage for Bill and storm stage for Helene). This is identical to the pattern seen in Figs. 19 and 20, affirming that those figures were indeed defining observed changes in the strength of the AEJ with time.

Fig. 23.
Fig. 23.

Time variation in the observed maximum value of the 650-hPa zonally averaged u-wind component in m s−1 {[u] in Eq. (5)}, representing the AEJ associated with Bill (2009), during the period 1200 UTC 10 Aug–1200 UTC 18 Aug. Dates at 1200 UTC are indicated along the top of the diagram. The time span for the observed convective superburst (see the most prominent peak in diabatic heating in Fig. 13) is indicated, as well as the observed classification of the system as wave, vortex, depression, storm, and hurricane. The zonal average is constructed over the longitude range 15°E–40°W for the period 10–14 Aug, and over the range 5°–60°W for the period 14–18 Aug to account for the westward movement of the system. For all points plotted, the maximum value of [u] lies in the latitude range 13°–19°N, consistent with the observed location of the AEJ.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

Fig. 24.
Fig. 24.

Time variation in the observed maximum value of the 650-hPa zonally averaged u-wind component in m s−1 {[u] in Eq. (5)}, representing the AEJ associated with Helene (2006), during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Time and date are indicated along the top of the diagram. The time span for the observed convective superburst (see the most prominent peak in diabatic heating in Fig. 15) is indicated, as well as the observed classification of the system as wave, depression, and storm. The zonal average is constructed over the longitude range 10°E–45°W. For all points plotted, the maximum value of [u] lies in the latitude range 15°–16°N, consistent with the observed location of the AEJ.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

It is worth noting that preliminary investigations of category-4 Hurricane Julia from September 2010, to be reported in detail in a future publication, reveal the identical sequence discussed in this paper (i.e., convective superburst, followed by enhanced AEJ, followed by enhanced barotropic energy conversion and system genesis). Thus, evidence continues to mount in support of the claimed genesis mechanism for Cape Verde storms, and now includes observed studies of Debby and Helene and a nondeveloping wave from 2006, Bill (2009), and Julia (2010), in addition to WRF model simulations of Helene (2006) and Bill (2009), for a total to date of seven examples of the proposed mechanism. The chain of causality claimed in this paper (superburst to enhanced AEJ to enhanced barotropic energy conversion to genesis) can legitimately be challenged based on the methods used. However, the growing number of times that the chain of events has been observed lends credibility to the claim of causality. As stated, preliminary research on Julia (2010) has revealed a similar chain of events. Three additional category-4 Cape Verde storms from 2010 will be examined in the ongoing testing of our hypothesis: Danielle, Earl, and Igor.

An intriguing question is the following: what triggers the superbursts and why do they occur only once in the life cycle of a given system? The answer lies in the fact that the superbursts reported in this study occur in a very favorable geographical location. For Debby and Helene (2006), Bill (2009), and Julia (2010) the superbursts were all observed to occur along the West African coast just to the south of Dakar, as the AEW moved westward from the continent. In this region the low-level convergence is enhanced by confluence of the northeast trade winds with the southwest monsoonal flow. Additionally, the moist monsoonal flow is warmed by sea surface temperatures off the Guinea coast that are approximately 6°C warmer than farther to the north off the coast of western Sahara. The combination of low-level convergence and a warm and moist oceanic flow favors this region for superburst occurrence as the AEW translates westward.

Finally in this section, we will discuss a dynamical mechanism whereby a singular mesoscale superburst of convection can enhance the AEJ, producing a jet that is more capable of developing the barotropic energy conversions that have been shown in this paper to be associated with genesis. Recall that such a superburst may become mesoscale in dimensions (50–500 km), as was the case with Bill (2009; see Fig. 2), and that these superbursts typically have diabatic heating rates 3– 6 times greater than subsequent heating rates in the life cycle of the system, including the hurricane stage (see Fig. 13 for the Bill case). Such a large and intense convective burst might well be expected to alter the thermal properties of the atmosphere over a significant region, which would in turn be expected to alter the wind field. This has been observed in all the developing systems discussed in this paper (Bill, Debby, and Helene). The phenomenon will be illustrated only for the Helene case for brevity.

Figure 25 shows the temperature field at 700 hPa, the magnitude of the temperature gradient at 700 hPa, and the divergence field at 850 hPa for Helene (2006). Figures 25a–c are for 1200 UTC 10 September prior to the superburst of convection, while Figs. 25d–f are for 1200 UTC 11 September at the time of the superburst (see Figs. 15 and 20). The superburst of convection occurs as the wave reaches the West African coast near 12°N (Ross et al. 2009). Comparing Figs. 25a–c with Figs. 25d–f there are significant changes in all three fields as the superburst develops. The key change in all three fields is greater organization. A rather chaotic temperature field becomes much more organized (cf. Figs. 25a,d) with a large cool region forming where the convection develops centered on the coastline and located to the southeast of an elongated region of tightly packed isotherms running northeast to southwest and centered on the coastline. These changes in the temperature field are reflected in changes in the field of temperature gradient (cf. Figs. 25b,e), as an organized and elongated region of enhanced temperature gradient extending for about 1500 km runs from northeast to southwest straddling the coastline (denoted with a bold arrow in Fig. 25e) replacing a much more chaotic pattern of temperature gradient (Fig. 25b). The field of 850-hPa divergence has increased in intensity and organization (cf. Figs. 25c,f), and at the time of the convective superburst (Fig. 25f) a strong center of convergence is surrounded by a ring of divergence. This feature has a diameter of approximately 700 km and is indicative of a rising core of air in the convection which is surrounded by an organized ring of sinking air. Such an intense and organized pattern in the divergence field is consistent with the convective superburst and its associated peak in diabiatic heating (see Fig. 15). The strong convection located in the region of 850-hPa convergence generates the large cool region at 700 hPa (Fig. 25d). This cool region forms just to the south of the warm SAL yielding the enhanced temperature gradient (Fig. 25e). This gradient is likely further enhanced by sinking air on the north side of the convective superburst. Such an organized and horizontally expansive field of temperature gradient would be capable of strengthening the AEJ, and that jet would then be more able to produce the enhanced barotropic energy conversions that have been shown to accompany genesis. The process is initiated by a superburst of convection as defined in this paper. The linkage of convective burst (mesoscale) to enhanced AEJ (synoptic scale) occurs over a large horizontal extent as discussed here: divergence field with a diameter of 700 km and a field of enhanced temperature gradient with a length of 1500 km. It is proposed here that an elapsed time of 24–36 h between convective burst and peak barotropic energy conversion is required since the temperature field is first altered, followed by an alteration of the jet, followed by the increased energy conversion.

Fig. 25.
Fig. 25.

Thermal and divergence fields for Helene (2006): (a) temperature (K) at 700 hPa for 1200 UTC 10 Sep, (b) magnitude of temperature gradient [K (1000 km)−1] at 700 hPa for 1200 UTC 10 Sep, (c) divergence field (10−6 s−1) at 850 hPa for 1200 UTC 10 Sep. (d),(e),(f) As in (a)–(c), but for 1200 UTC 11 Sep. Divergence (convergence) in (c) and (f) is noted by solid (dashed) lines. A bold arrow in (e) points to the elongated region of enhanced temperature gradient.

Citation: Monthly Weather Review 140, 3; 10.1175/2011MWR3621.1

6. Conclusions

This paper develops evidence for a genesis mechanism for eastern Atlantic tropical cyclones by establishing a dynamical link between convective superbursts and storm genesis. A convective superburst is defined as a burst of convection with a scale of at least 5° longitude, as seen in infrared satellite imagery, and with a calculated diabatic heating rate that is 3–6 times greater than the heating rates typically seen in developing systems, even in the storm and hurricane stages.

Prior to fully developing the primary genesis mechanism it was important to illustrate with a detailed case study how two of the key intermediate processes in the genesis mechanism, diabatic heating and energy conversions, can act in concert. The initial genesis of Bill (2009) resulted from primarily barotropic energy conversions in the lower half of the troposphere, produced by conversions in both zonally averaged easterly and westerly flow, and leading to a vertical column of maximum EKE. Maxima in VDH, VA, and HDH were the components of a strong and deeply distributed diabatic heating pattern extending from the surface to 300 hPa, leading to a deep column of positive IPV. The deep columns of EKE and IPV, together with their dynamical production mechanisms, explained the initial genesis of Bill.

The primary genesis mechanism developed in this paper involves the following sequence: convective superburst → strong diabatic heating → enhanced AEJ → enhanced BTCONV → tropical cyclone genesis. Our work first revealed that a singular maximum in diabatic heating associated with a convective superburst was followed typically within 24–36 h by a pronounced maximum in positive BTCONV. Six examples of this occurrence were shown in this paper: Figs. 1316 from calculations based on observations (Bill, Debby, Helene, and a nondeveloping wave), and Figs. 17 and 18 from calculations based on WRF model simulations (Bill and Helene). It was hypothesized that the maxima in positive BTCONV would be produced by a strengthened AEJ. The increase in magnitude of the AEJ was, indeed, confirmed and demonstrated in this paper by Figs. 19 and 20 from observations (Bill and Helene) and by Figs. 21 and 22 from WRF model simulations (Bill and Helene). An alternate method of determining the magnitude of the AEJ further confirmed the increase in the jet based on observations of Bill (Fig. 23) and Helene (Fig. 24). In addition, the increase in the AEJ was shown to occur simultaneously with the peak in the positive BTCONV. Figures 19 and 23 show an increased jet in the vortex–depression–storm stages for the observed Bill case (peak BTCONV in storm–early hurricane stages from Fig. 13). Figures 20 and 24 show an increased jet in the depression stage for the observed Helene case (peak BTCONV in depression stage from Fig. 15). Figure 21 shows an increased jet in the depression–storm stages for the WRF forecast Bill case (peak BTCONV in the storm stage from Fig. 17). Figure 22 shows an increased jet in the depression state in the WRF forecast Helene case (peak BTCONV in the depression stage from Fig. 18). For the final element in the genesis mechanism sequence shown at the beginning of this paragraph, evidence has been presented in this paper to show that the enhanced BTCONV is, indeed, associated with genesis. Figures 13, 14, and 15, all for observation-based calculations, show that the peak in BTCONV occurs in the critical development stages prior to the hurricane stage: Fig. 13 has the peak in the storm stage–early hurricane stage for Bill, Fig. 14 has the peak in the depression stage for Debby, and Fig. 15 has the peak in the depression stage for Helene. The same pattern is seen in Figs. 17 and 18 for WRF-based calculations: Fig. 17 has the peak in the storm stage for Bill, and Fig. 18 has the peak in the depression stage for Helene.

A physical mechanism was developed to explain how a mesoscale convective superburst could lead subsequently to an enhanced synoptic-scale AEJ over the eastern Atlantic (see Fig. 25). In the Helene (2006) case, representative of the other storm cases studied here, the convective superburst was shown to have a horizontal extent of approximately 700 km based on the 850-hPa divergence field. Such a large, organized, and intense convective region was able to produce a comparably large cool pocket at 700 hPa, positioned just to the south of the warm SAL at that level. This led to a greatly enhanced thermal gradient oriented northeast to southwest and extending over a distance of 1500 km. Such an elongated region of tightened thermal gradient, essentially of synoptic-scale dimensions, would be expected with time to be able to enhance the AEJ, given that this jet is approximately in thermal wind balance. The time frame of 24–36 h between superburst and enhanced AEJ/BTCONV, developed in this paper, is evidently a required amount of time for the jet to grow. This may be related to dynamical adjustments between the pressure and wind fields and involving the divergent component of the wind associated with the convective superburst. In any event, superburst and enhancement of the AEJ did not appear in this study to be simultaneous processes.

The chain of causality claimed in this paper (superburst to enhanced AEJ to enhanced barotropic energy conversion to genesis) can legitimately be challenged based on the methods used. However, the growing number of times that the chain of events has been observed lends credibility to the claim of causality. In addition to all of the cases cited here, preliminary research on Julia (2010) has revealed a similar chain of events. Three additional category-4 Cape Verde storms from 2010 will be examined in the ongoing testing of our hypothesis.

It is worth noting that the primary thesis of the present study, developed through observation and supported by model simulations, generally agrees with a similar finding by Cornforth et al. (2009) based on idealized modeling studies. As mentioned in the introduction, that study showed that moist AEWs grew to be 3 times stronger than dry waves due to faster AEJ development and larger barotropic conversions. The agreement of that study and the present one adds greater credibility to both studies.

The apparent answer to the intriguing question of what triggers the superbursts and why they occur only once in the life cycle of a given system lies in the fact that the superbursts occur in a favored geographical location along the West African coast just to the south of Dakar. As discussed in section 5, the combination of enhanced low-level convergence and a warm and moist oceanic flow favors this region for superburst occurrence as the AEW translates westward from the continent into the Atlantic Ocean.

Acknowledgments

This research has been supported by NASA Grants NNX09AC37FG and NNX07AI94G.

REFERENCES

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    • Export Citation
  • Ross, R. S., and T. N. Krishnamurti, 2007: Low-level African easterly wave activity and its relation to Atlantic tropical cyclogenesis in 2001. Mon. Wea. Rev., 135, 39503964.

    • Search Google Scholar
    • Export Citation
  • Ross, R. S., T. N. Krishnamurti, S. Pattnaik, and A. Simon, 2009: Energy transformation and diabatic processes in developing and non-developing African easterly waves observed during the NAMMA project of 2006. Wea. Forecasting, 24, 15241548.

    • Search Google Scholar
    • Export Citation
  • Thorncroft, C. D., and K. Hodges, 2001: African easterly wave variability and its relationship to Atlantic tropical cyclone activity. J. Climate, 14, 11661179.

    • Search Google Scholar
    • Export Citation
  • Zhang, H., G. M. McFarquhar, S. M. Saleeby, and W. R. Cotton, 2007: Impacts of Saharan dust as CCN on the evolution of an idealized tropical cyclone. Geophys. Res. Lett., 34, L14812, doi:10.1029/2007GL029876.

    • Search Google Scholar
    • Export Citation
  • Zhang, H., G. M. McFarquhar, W. R. Cotton, and Y. Deng, 2009: Direct and indirect impacts of Saharan dust acting as cloud condensation nuclei on tropical cyclone eyewall development. Geophys. Res. Lett., 36, L06802, doi:10.1029/2009GL037276.

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., and Coauthors, 2009: The Saharan air layer and the fate of African easterly waves: NASA’s AMMA field study of tropical cyclogenesis. Bull. Amer. Meteor. Soc., 90, 11371156.

    • Search Google Scholar
    • Export Citation
Save
  • Avila, L. A., R. J. Pasch, and J. Jiing, 2000: Atlantic tropical systems of 1996 and 1997: Years of contrast. Mon. Wea. Rev., 128, 36953706.

    • Search Google Scholar
    • Export Citation
  • Chen, T. S., S. Y. Wang, and A. J. Clark, 2008: North Atlantic hurricanes contributed by African easterly waves north and south of the African easterly jet. J. Climate, 21, 67676776.

    • Search Google Scholar
    • Export Citation
  • Cornforth, R. J., B. J. Hoskins, and C. D. Thorncroft, 2009: The impact of moist processes on the African easterly jet-African easterly wave system. Quart. J. Roy. Meteor. Soc., 135, 894913.

    • Search Google Scholar
    • Export Citation
  • Dudhia, J., 1989: Numerical study of convection observed during the Winter Monsoon Experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 30773107.

    • Search Google Scholar
    • Export Citation
  • Dunion, J. P., and C. S. Velden, 2004: The impact of the Saharan air layer on Atlantic tropical cyclone activity. Bull. Amer. Meteor. Soc., 85, 353365.

    • Search Google Scholar
    • Export Citation
  • Dunkerton, T. J., M. T. Montgomery, and Z. Wang, 2009: Tropical cyclogenesis in a tropical wave critical layer: Easterly waves. Atmos. Chem. Phys., 9, 55875646.

    • Search Google Scholar
    • Export Citation
  • Hendricks, E. A., and M. T. Montgomery, 2004: The role of “vortical” hot towers in the formation of Tropical Cyclone Diana (1984). J. Atmos. Sci., 61, 12091232.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., H.-M. H. Juang, and Q. Zhao, 1998: Implementation of prognostic cloud scheme for a regional spectral model. Mon. Wea. Rev., 126, 26212639.

    • Search Google Scholar
    • Export Citation
  • Hong, S.-Y., J. Dudhia, and S.-H. Chen, 2004: A revised approach to ice microphysical processes for the bulk parameterization of clouds and precipitation. Mon. Wea. Rev., 132, 103120.

    • Search Google Scholar
    • Export Citation
  • Hopsch, S. B., C. D. Thorncroft, K. Hodges, and A. Aiyyer, 2007: West African storm tracks and their relationship to Atlantic tropical cyclones. J. Climate, 20, 24682483.

    • Search Google Scholar
    • Export Citation
  • Hopsch, S. B., C. D. Thorncroft, and K. R. Tyle, 2010: Analysis of African easterly wave structures and their role in influencing tropical cyclogenesis. Mon. Wea. Rev., 138, 13991419.

    • Search Google Scholar
    • Export Citation
  • Janjic, Z. I., 1994: The step-mountain Eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes. Mon. Wea. Rev., 122, 927945.

    • Search Google Scholar
    • Export Citation
  • Janjic, Z. I., 1996: The surface layer in the NCEP Eta Model. Preprints, 11th Conf. on Numerical Weather Prediction, Norfolk, VA, Amer. Meteor. Soc., 354–355.

    • Search Google Scholar
    • Export Citation
  • Janjic, Z. I., 2000: Comments on “Development and evaluation of a convection scheme for use in climate models.” J. Atmos. Sci., 57, 3686.

    • Search Google Scholar
    • Export Citation
  • Janjic, Z. I., 2002: Nonsingular implementation of the Mellor–Yamada level 2.5 scheme in the NCEP meso model. NCEP Office Note 437, 61 pp.

    • Search Google Scholar
    • Export Citation
  • Karyampudi, V. M., and H. F. Pierce, 2002: Synoptic-scale influence of the Saharan air layer on tropical cyclogenesis over the eastern Atlantic. Mon. Wea. Rev., 130, 31003128.

    • Search Google Scholar
    • Export Citation
  • Krishnamurti, T. N., J. Bhaskar, H. S. Bedi, and U. C. Mohanty, 2000: Diabatic effects on potential vorticity over the global tropics. J. Meteor. Soc. Japan, 78, 527542.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102 (D14), 16 66316 682.

    • Search Google Scholar
    • Export Citation
  • Monin, A. S., and A. M. Obukhov, 1954: Basic laws of turbulent mixing in the surface layer of the atmosphere (in Russian). Contrib. Geophys. Inst. Acad. Sci. USSR, 151, 163187.

    • Search Google Scholar
    • Export Citation
  • Montgomery, M. T., M. E. Nichols, T. A. Cram, and A. B. Saunders, 2006: A vortical hot tower route to tropical cyclogenesis. J. Atmos. Sci., 63, 355386.

    • Search Google Scholar
    • Export Citation
  • Norquist, D. C., E. E. Recker, and R. J. Reed, 1977: The energetics of African wave disturbances as observed during phase III of GATE. Mon. Wea. Rev., 105, 334342.

    • Search Google Scholar
    • Export Citation
  • Ross, R. S., and T. N. Krishnamurti, 2007: Low-level African easterly wave activity and its relation to Atlantic tropical cyclogenesis in 2001. Mon. Wea. Rev., 135, 39503964.

    • Search Google Scholar
    • Export Citation
  • Ross, R. S., T. N. Krishnamurti, S. Pattnaik, and A. Simon, 2009: Energy transformation and diabatic processes in developing and non-developing African easterly waves observed during the NAMMA project of 2006. Wea. Forecasting, 24, 15241548.

    • Search Google Scholar
    • Export Citation
  • Thorncroft, C. D., and K. Hodges, 2001: African easterly wave variability and its relationship to Atlantic tropical cyclone activity. J. Climate, 14, 11661179.

    • Search Google Scholar
    • Export Citation
  • Zhang, H., G. M. McFarquhar, S. M. Saleeby, and W. R. Cotton, 2007: Impacts of Saharan dust as CCN on the evolution of an idealized tropical cyclone. Geophys. Res. Lett., 34, L14812, doi:10.1029/2007GL029876.

    • Search Google Scholar
    • Export Citation
  • Zhang, H., G. M. McFarquhar, W. R. Cotton, and Y. Deng, 2009: Direct and indirect impacts of Saharan dust acting as cloud condensation nuclei on tropical cyclone eyewall development. Geophys. Res. Lett., 36, L06802, doi:10.1029/2009GL037276.

    • Search Google Scholar
    • Export Citation
  • Zipser, E. J., and Coauthors, 2009: The Saharan air layer and the fate of African easterly waves: NASA’s AMMA field study of tropical cyclogenesis. Bull. Amer. Meteor. Soc., 90, 11371156.

    • Search Google Scholar
    • Export Citation
  • Fig. 1.

    Observed track (crisscrosses) and WRF model forecast track (open circles) for Bill (2009). Observed positions are for every 6 h beginning on 1200 UTC 10 Aug and ending on 1200 UTC 18 Aug with system classification indicated as: W (wave), V (vortex), D (depression), S (storm), and H (hurricane). Four positions with circled crosses highlight the initial genesis sequence from 1800 UTC 11 Aug to 1200 UTC 12 Aug. Forecast positions are for every 6 h beginning on 0000 UTC 14 Aug and ending on 0000 UTC 18 Aug.

  • Fig. 2.

    Meteosat infrared satellite images of Bill (2009) during the period of initial genesis: (a) 1800 UTC 11 Aug, (b) 0000 UTC 12 Aug, (c) 0600 UTC 12 Aug, and (d) 1200 UTC 12 Aug. Longitude markers are for every 10°.

  • Fig. 3.

    Observed sea level pressure at an interval of 0.5 hPa for Bill (2009) during the initial genesis period: (a) 1800 UTC 11 Aug, (b) 0000 UTC 12 Aug, (c) 0600 UTC 12 Aug, and (d) 1200 UTC 12 Aug.

  • Fig. 4.

    Observed streamlines at 700 hPa for Bill (2009) during the period of initial genesis: (a) 1800 UTC 11 Aug, (b) 0000 UTC 12 Aug, (c) 0600 UTC 12 Aug, and (d) 1200 UTC 12 Aug. The trough line is indicated by a light solid line and the positions of the north–south cross sections discussed at length in the text are indicated by a bold solid line.

  • Fig. 5.

    Observed cross sections of energy conversion parameters for Bill (2009) at 1800 UTC 11 Aug along 18.2°W (see Fig. 4a) when the system was still a wave in the layer 900–400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 6.

    Observed cross sections of diabatic heating parameters for Bill (2009) at 1800 UTC 11 Aug along 18.2°W (see Fig. 4a) when the system was still a wave in the layer 900–400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 7.

    Observed cross sections of energy conversion parameters for Bill (2009) at 0000 UTC 12 Aug along 19.2°W (see Fig. 4b) when the system was still a wave in the layer 800–400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 8.

    Observed cross sections of diabatic heating parameters for Bill (2009) at 0000 UTC 12 Aug along 19.2°W (see Fig. 4b) when the system was still a wave in the layer 800–400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 9.

    Observed cross sections of energy conversion parameters for Bill (2009) at 0600 UTC 12 Aug along 19.3°W (see Fig. 4c) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 10.

    Observed cross sections of diabatic heating parameters for Bill (2009) at 0600 UTC 12 Aug along 19.3°W (see Fig. 4c) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 11.

    Observed cross sections of energy conversion parameters for Bill (2009) at 1200 UTC 12 Aug along 20.5°W (see Fig. 4d) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) EKE in m2 s−2 from Eq. (7), (b) baroclinic energy conversion in W kg−1 from Eq. (6), and (c) barotropic energy conversion in W kg−1 from Eq. (5). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 12.

    Observed cross sections of diabatic heating parameters for Bill (2009) at 1200 UTC 12 Aug along 20.5°W (see Fig. 4d) when the system has become a vortex from the surface to 400 hPa (see Table 1): (a) isentropic potential vorticity in kg−1 m2 s−1 K from Eq. (9), (b) vertical differential of heating in kg−1 m2 s−2 K from term 3 on the rhs of Eq. (8), (c) horizontal differential of heating in kg−1 m2 s−2 K from term 4 on the rhs of Eq. (8), and (d) vertical advection of isentropic potential vorticity in kg−1 m2 s−2 K from term 2 on the rhs of Eq. (8). Positive values are indicated with solid lines and negative values are indicated with dashed lines.

  • Fig. 13.

    Profiles of observed maximum positive mean vertical differential of diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum positive barotropic energy conversion (W kg−1) at 700 hPa (dashed line) for Bill (2009) during the period 1200 UTC 10 Aug–1200 UTC 18 Aug. Vertical differential of diabatic heating is from term 3 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system is indicated at the top of the diagram as wave, vortex, depression, storm, and hurricane.

  • Fig. 14.

    Profiles of observed maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum positive barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for Debby (2006) during the period 0000 UTC 20 Aug–0000 UTC 24 Aug. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system is indicated at the top of the diagram as wave, depression, and storm.

  • Fig. 15.

    Profiles of observed maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum positive barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system is indicated at the top of the diagram as wave, depression, and storm.

  • Fig. 16.

    Profiles of observed maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and observed maximum negative barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for NAMMA nondeveloping wave 4 during the period 1200 UTC 29 Aug–1200 UTC 2 Sep. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the system remained a wave throughout this time frame.

  • Fig. 17.

    Profiles of WRF model forecast maximum positive mean vertical differential of diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and WRF model forecast maximum positive barotropic energy conversion (W kg−1) at 700 hPa (dashed line) for Bill (2009) during the period 0000 UTC 14 Aug–0000 UTC 18 Aug. Vertical differential of diabatic heating is from term 3 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system based on observation is shown at the top of the diagram as vortex, depression, storm, and hurricane.

  • Fig. 18.

    Profiles of WRF model forecast maximum positive mean total diabatic heating (kg−1 m2 s−2 K) for the layer 800–400 hPa (solid line) and WRF model forecast maximum positive barotropic energy conversion (W kg−1) at 650 hPa (dashed line) for Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Total diabatic heating is from the sum of terms 2–4 on the rhs of Eq. (8) and barotropic energy conversion is from Eq. (5). Values are plotted every 6 h and the classification of the system based on observation is shown at the top of the diagram as wave, depression, and storm.

  • Fig. 19.

    Time variation of the observed maximum 650-hPa easterly wind component (AEJ) in m s−1 to the north of Bill (2009) during the period 1200 UTC 10 Aug–1200 UTC 18 Aug. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the observed major convective burst (see most prominent peak in diabatic heating in Fig. 13) is indicated, as well as the observed classification of the system as wave, vortex, depression, storm, and hurricane.

  • Fig. 20.

    Time variation of the observed maximum 650-hPa easterly wind component (AEJ) in m s−1 to the north of Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the observed major convective burst (see peak in diabatic heating in Fig. 15) is indicated, as well as the observed classification of the system as wave, depression, and storm.

  • Fig. 21.

    Time variation of the WRF model forecast maximum 700-hPa easterly wind component (AEJ) in m s−1 to the north of Bill (2009) during the period 0000 UTC 14 Aug–0000 UTC 18 Aug. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the WRF model forecast major convective burst (see peak in diabatic heating in Fig. 17) is indicated, as well as the observed classification of the system as vortex, depression, storm, and hurricane.

  • Fig. 22.

    Time variation of the WRF model forecast maximum 650-hPa easterly wind component (AEJ) in m s−1 to the north of Helene (2006) during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Each value is calculated as the departure of the individual u-wind component value from the series mean u-wind component value. Bars pointing upward (downward) indicate a weaker (stronger) easterly wind component value (AEJ). Values are plotted every 6 h. The time span of the WRF model forecast major convective bursts (see twin prominent peaks in diabatic heating in Fig. 18) is indicated, as well as the observed classification of the system as wave, depression, and storm.

  • Fig. 23.

    Time variation in the observed maximum value of the 650-hPa zonally averaged u-wind component in m s−1 {[u] in Eq. (5)}, representing the AEJ associated with Bill (2009), during the period 1200 UTC 10 Aug–1200 UTC 18 Aug. Dates at 1200 UTC are indicated along the top of the diagram. The time span for the observed convective superburst (see the most prominent peak in diabatic heating in Fig. 13) is indicated, as well as the observed classification of the system as wave, vortex, depression, storm, and hurricane. The zonal average is constructed over the longitude range 15°E–40°W for the period 10–14 Aug, and over the range 5°–60°W for the period 14–18 Aug to account for the westward movement of the system. For all points plotted, the maximum value of [u] lies in the latitude range 13°–19°N, consistent with the observed location of the AEJ.

  • Fig. 24.

    Time variation in the observed maximum value of the 650-hPa zonally averaged u-wind component in m s−1 {[u] in Eq. (5)}, representing the AEJ associated with Helene (2006), during the period 1200 UTC 10 Sep–1200 UTC 14 Sep. Time and date are indicated along the top of the diagram. The time span for the observed convective superburst (see the most prominent peak in diabatic heating in Fig. 15) is indicated, as well as the observed classification of the system as wave, depression, and storm. The zonal average is constructed over the longitude range 10°E–45°W. For all points plotted, the maximum value of [u] lies in the latitude range 15°–16°N, consistent with the observed location of the AEJ.

  • Fig. 25.

    Thermal and divergence fields for Helene (2006): (a) temperature (K) at 700 hPa for 1200 UTC 10 Sep, (b) magnitude of temperature gradient [K (1000 km)−1] at 700 hPa for 1200 UTC 10 Sep, (c) divergence field (10−6 s−1) at 850 hPa for 1200 UTC 10 Sep. (d),(e),(f) As in (a)–(c), but for 1200 UTC 11 Sep. Divergence (convergence) in (c) and (f) is noted by solid (dashed) lines. A bold arrow in (e) points to the elongated region of enhanced temperature gradient.