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  • View in gallery
    Fig. 1.

    Lag–longitude composite Hovmöller of 650-hPa 2–10-day easterly filtered PKE (shading) averaged 5°–15°N for (a) CPEW, (b) SPEW, and (c) CPEW − SPEW cases over the base point at 650 hPa, 10°N, 15°W. Black (stripes) dots represent values that are 95% statistically significantly higher (lower) from climatology. Contours are 200-hPa unfiltered velocity potential anomalies averaged over 5°–15°N. Dashed (solid) contours represent convective (suppressed) phase of the KW. Outer dashed contour in (a) and (c) is −2 × 106 m2 s−1 and in (b) is 2 × 106 m2 s−1. Contours in (a) and (c) are drawn with an interval of −2 × 106 m2 s−1 and in (b) with an interval of 2 × 106 m2 s−1. The thin vertical and horizontal gray line marks the longitudinal base point and day 0 in the composite analysis.

  • View in gallery
    Fig. 2.

    Lag–longitude composite Hovmöller of 900-hPa 2–10-day easterly filtered PKE (shading) averaged 5°–15°N for (a) CPEW, (b) SPEW, and (c) CPEW − SPEW cases over the base point at 900 hPa, 20°N, 10°W. Black (blue) stripes represent values that are 95% statistically significantly higher (lower) from climatology. Contours are 200-hPa unfiltered velocity potential anomalies averaged over 15°–25°N. Dashed (solid) contours represent convective (suppressed) phase of the KW. The outer dashed contour in (a) and (c) is −2 × 106 m2 s−1 and in (b) is 2 × 106 m2 s−1. Contours in (a) and (c) are drawn with interval of −2 × 106 m2 s−1 and in (b) with an interval of 2 × 106 m2 s−1. The thin vertical and horizontal gray line marks the longitudinal base point and day 0 in the composite analysis.

  • View in gallery
    Fig. 3.

    (top) Day 0 composite map and (bottom) zonally averaged (0°–30°W) vertical cross section of 10-day low-pass-filtered zonal wind (thick contours) and its meridional gradient (du¯/dy; shading) for (a),(b) CPEW and (c),(d) CPEW − SPEW cases. Light contours in (a) and (b) are 200-hPa unfiltered velocity potential anomalies where dashed (solid) light contours represent the convective (suppressed) phase of the KW. The dots in (c) and (d) represent values that are 95% significant. The thin vertical and horizontal gray line marks the pressure level and latitudinal base point.

  • View in gallery
    Fig. 4.

    (top) Day +1 composite pressure–latitude cross section of zonally averaged (0°–30°W) 10-day low-pass-filtered temperature (thick contours) and its meridional gradient (dT¯/dy; shading) for (a) CPEW and (c) CPEW − SPEW cases. (bottom) Day 0 composite pressure–latitude cross section of zonally averaged (0°–30°W) 10-day low-pass-filtered zonal wind (thick contours) and its vertical gradient (du¯/dp; shading) for (b) CPEW and (d) CPEW − SPEW cases. The stripes in (c) and (d) represent values that are 95% significant. The thin vertical and horizontal gray line marks the pressure level and latitudinal base point.

  • View in gallery
    Fig. 5.

    Lag–longitude Hovmöller of vertically integrated PKE and PAPE budget terms for the southern AEW track composited over each lag of the CPEW and averaged 5°–15°N. (a) Barotropic energy conversion BT (shaded), (b) baroclinic overturning Cpk (shaded), (c) generation of PAPE by diabatic heating QT (shaded), and (d) baroclinic energy conversion BC (shaded). Solid and dashed contours represent 2–10-day easterly filtered 650-hPa PKE positive and negative anomalies. Outer solid and dashed contour in all panels is 0.5 and −0.5 m2 s−2, respectively. Contour interval is 0.5 m2 s−2. The thin vertical and horizontal gray line marks the longitudinal base point (15°W) and day 0 in the composite analysis. Black stripes represent values that are 95% statistically significantly higher from climatology, while blue stripes represent values that are 95% statistically significantly lower from climatology.

  • View in gallery
    Fig. 6.

    As in Fig. 5, but composited over each lag of SPEW cases.

  • View in gallery
    Fig. 7.

    As in Fig. 5, but for a difference composite (CPEW − SPEW). Black stripes represent values that are statistically significant at 95% confidence.

  • View in gallery
    Fig. 8.

    Lag–longitude Hovmöller of vertically integrated PKE and PAPE budget terms for the northern AEW track composited over each lag of the CPEW and averaged 15°–25°N. (a) Barotropic energy conversion BT (shaded), (b) baroclinic overturning Cpk (shaded), (c) generation of PAPE by diabatic heating QT (shaded), and (d) baroclinic energy conversion BC (shaded). Solid and dashed contours represent 2–10-day easterly filtered 900-hPa PKE positive and negative anomalies. The outer solid and dashed contour in all panels is 1 and −1 m2 s−2, respectively. The contour interval is 0.5 m2 s−2. The thin vertical and horizontal gray line marks the longitudinal base point (10°W) and day 0 in the composite analysis. Black stripes represent values that are 95% statistically significantly higher from climatology, while blue stripes represent values that are 95% statistically significantly lower from climatology.

  • View in gallery
    Fig. 9.

    As in Fig. 8, but composited over each lag of SPEW cases.

  • View in gallery
    Fig. 10.

    As in Fig. 8, but for a difference composite (CPEW − SPEW). Black stripes represent values that are statistically significant at 95% confidence.

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Energetics of Interactions between African Easterly Waves and Convectively Coupled Kelvin Waves

Rama Sesha Sridhar MantripragadaaDepartment of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina

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C. J. Schreck IIIaDepartment of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina
bNorth Carolina Institute for Climate Studies, North Carolina State University, Asheville, North Carolina

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Anantha AiyyeraDepartment of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina

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Abstract

Perturbation kinetic and available energy budgets are used to explore how convectively coupled equatorial Kelvin waves (KWs) impact African easterly wave (AEW) activity. The convective phase of the Kelvin wave increases the African easterly jet’s meridional shear, thus enhancing the barotropic energy conversions, leading to intensification of southern track AEWs perturbation kinetic energy. In contrast, the barotropic energy conversion is reduced in the suppressed phase of KW. Baroclinic energy conversion of the southern track AEWs is not significantly different between Kelvin waves’ convective and suppressed phases. AEWs in the convective phase of a Kelvin wave have stronger perturbation available potential energy generation by diabatic heating and stronger baroclinic overturning circulations than in the suppressed phase of a Kelvin wave. These differences suggest that southern track AEWs within the convective phase of Kelvin waves have more vigorous convection than in the suppressed phase of Kelvin waves. Barotropic energy conversion of the northern track AEWs is not significantly different between Kelvin waves’ convective and suppressed phases. The convective phase of the Kelvin wave increases the lower-tropospheric meridional temperature gradient north of the African easterly jet, thus enhancing the baroclinic energy conversion, leading to intensification of northern track AEWs perturbation kinetic energy. In contrast, the baroclinic energy conversion is reduced in the suppressed phase of KW. These results provide a physical basis for the modulation of AEWs by Kelvin waves arriving from upstream.

Mantripragada’s current affiliation: Department of Atmospheric, Oceanic, and Earth Sciences, George Mason University, Fairfax, Virginia.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: R. S. S. Mantripragada, rmantrip@gmu.edu

Abstract

Perturbation kinetic and available energy budgets are used to explore how convectively coupled equatorial Kelvin waves (KWs) impact African easterly wave (AEW) activity. The convective phase of the Kelvin wave increases the African easterly jet’s meridional shear, thus enhancing the barotropic energy conversions, leading to intensification of southern track AEWs perturbation kinetic energy. In contrast, the barotropic energy conversion is reduced in the suppressed phase of KW. Baroclinic energy conversion of the southern track AEWs is not significantly different between Kelvin waves’ convective and suppressed phases. AEWs in the convective phase of a Kelvin wave have stronger perturbation available potential energy generation by diabatic heating and stronger baroclinic overturning circulations than in the suppressed phase of a Kelvin wave. These differences suggest that southern track AEWs within the convective phase of Kelvin waves have more vigorous convection than in the suppressed phase of Kelvin waves. Barotropic energy conversion of the northern track AEWs is not significantly different between Kelvin waves’ convective and suppressed phases. The convective phase of the Kelvin wave increases the lower-tropospheric meridional temperature gradient north of the African easterly jet, thus enhancing the baroclinic energy conversion, leading to intensification of northern track AEWs perturbation kinetic energy. In contrast, the baroclinic energy conversion is reduced in the suppressed phase of KW. These results provide a physical basis for the modulation of AEWs by Kelvin waves arriving from upstream.

Mantripragada’s current affiliation: Department of Atmospheric, Oceanic, and Earth Sciences, George Mason University, Fairfax, Virginia.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: R. S. S. Mantripragada, rmantrip@gmu.edu

1. Introduction

African easterly waves (AEWs) are synoptic-scale westward-moving systems that form during the West Africa monsoon season. These have periods of 2.5–6 days and wavelengths of 2000–4000 km (e.g., Burpee 1972; Reed et al. 1977; Kiladis et al. 2006). AEWs have two circulation centers—one around 900 hPa north of the African easterly jet (AEJ) and the other around 650 hPa south of the AEJ (e.g., Pytharoulis and Thorncroft 1999; Chen 2006). These are typically referred to as the northern and southern AEW tracks, respectively.

Barotropic instability associated with the potential vorticity gradient reversal at the jet level as well as feedback with moist convection (e.g., Norquist et al. 1977; Hsieh and Cook 2005; Berry and Thorncroft 2012; Mekonnen et al. 2006; Tomassini et al. 2017; Russell and Aiyyer 2020; Russell et al. 2020) are related to the origin and maintenance of the southern AEW track. In comparison, the northern track AEWs grow through baroclinic energy conversions over West Africa in the low static stability atmosphere along the intertropical discontinuity (~20°N; Chang 1993).

Mesoscale convective systems such as squall lines are the primary rain-producing systems over West Africa during boreal summer (e.g., Laing et al. 1999; Mathon and Laurent 2001), and more than 60% of squall lines initiate or intensify in association with the AEWs (Fink and Reiner 2003). It is well documented that AEWs seed Atlantic and eastern Pacific tropical cyclones (e.g., Frank 1970; Avila and Pasch 1992; Landsea et al. 1998; Hopsch et al. 2007; Russell et al. 2017). Given the importance of AEW to rainfall variability during the West African monsoon and their role in tropical cyclone formation, it is important to understand the sources of their variability.

Equatorially trapped, convectively coupled Kelvin waves (KWs) are ubiquitous in the tropical atmosphere. Kelvin waves propagate eastward with speeds of 10–22 m s−1 and have periods ranging from 2.5 to 20 days and wavelengths of 3000–7000 km (Straub and Kiladis 2002). Kelvin waves coupled with convection have two distinct phases convective and suppressed. The former is associated with lower-tropospheric westerlies and the latter with easterlies. Kelvin waves modulate rainfall over West Africa from subdaily (Schlueter et al. 2019) to synoptic and intraseasonal time scales (e.g., Mekonnen et al. 2008; Nguyen and Duvel 2008). Previous studies have shown that KW activity over Africa is responsible for intense and more frequent mesoscale convective systems (e.g., Nguyen and Duvel 2008; Laing et al. 2011). Kelvin waves also increase the potential for tropical cyclogenesis over the eastern Atlantic Ocean (Schreck 2015).

Leroux et al. (2010) suggested that the intraseasonal variability of AEW activity is modulated by the MJO and convectively coupled Kelvin waves over West Africa. This relationship was confirmed by Ventrice et al. (2011) and Alaka and Maloney (2012) who showed that these eastward propagating modes modulate the AEJ shear and convection near the AEJ entrance region. Alaka and Maloney (2014) used energy budgets to show that, over East Africa, periods of increased intraseasonal variability of AEW activity are associated with enhanced baroclinic energy conversions. Mekonnen et al. (2008) showed that strong convectively coupled Kelvin waves initiated a series of AEWs over tropical Africa. Ventrice and Thorncroft (2013) showed that AEW initiation over East Africa is associated with enhanced low-level vertical wind shear within the convective phase of Kelvin Wave.

While the studies mentioned above have clarified several aspects of AEW–KW interactions, some issues remain. Past studies have suggested that the convective phase of KW enhances the AEW growth via baroclinic overturning circulations. However, these studies did not focus on the sources of the baroclinic overturning circulation—specifically, the relative importance of baroclinic energy conversions and PAPE generation by diabatic heating within the AEWs. Further, past studies have focused on the impact of Kelvin waves on the southern AEW track but not on the northern AEW track. The motivation for this study is the hypothesis of Ventrice and Thorncroft (2013) that Kelvin waves modulate AEW activity through mixed barotropic–baroclinic conversions. We examine the relative role of energy conversions in the intensification of preexisting southern and northern AEW track in the background environment influenced by the convective and suppressed phase of Kelvin waves. We diagnose the AEW growth and decay on KW time scales using the perturbation kinetic energy and perturbation available potential energy budgets.

2. Data and methods

a. Data

We use the 6-hourly European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim; Dee et al. 2011). The data are on 0.702° latitude × 0.703° longitude grids at 27 pressure levels (1000–200 hPa). We focus on the months June–September over 1999–2018. Kelvin waves and AEWs are diagnosed based on wavenumber–frequency techniques as discussed in Hayashi (1982) implemented in Wheeler and Kiladis (1999). The KW filter is bounded by periods of 2.5–20 days, with eastward propagating zonal wavenumbers 1–14, and constrained by the shallow-water dispersion curves for equivalent depths of 8–90 m (Straub and Kiladis 2002). Instances of 200-hPa KW velocity potential that are one standard deviation below the mean at any grid point are deemed as its convective phase, and conversely the suppressed phase is defined as one standard deviation above the mean. The easterly wave filter is bounded by periods of 2–10 days, with westward-propagating zonal wavenumbers 26–6 (approximately 1500–6500 km). To identify AEW activity, we use the peak northerlies that are one standard deviation below the mean in the AEW filtered data.

b. Energy budgets

We diagnose the impact of the Kelvin waves on the growth and maintenance of the southern and northern AEWs through vertically integrated perturbation kinetic energy (PKE) and perturbation available potential energy (PAPE) budget. PKE and PAPE are defined as (e.g., Leroux et al. 2010; Ventrice and Thorncroft 2013; Alaka and Maloney 2014):
k=(u2+υ22)¯,
p=cpγT2¯2T¯.
Here all terms with primes denote AEW-scale eddies that are calculated using the wavenumber–frequency filter described earlier. The terms with overbars denote the slowly varying background state and are calculated using a 10-day low-pass filter. The terms u′ and υ′ are eddy zonal and meridional winds, cp is the specific heat at constant pressure, and T′ and T¯ are eddy temperature and mean temperature, respectively. The term γ is inverted static stability:
γ=ΓdΓdΓ,
where Γd is the dry adiabatic lapse rate (g/cp) and Γ is the environmental lapse rate (T¯/z). To avoid values of observed lapse rates close to dry adiabatic lapse rates and p′ being ill-defined, γ magnitudes less than 50 are omitted similar to that in Rydbeck and Maloney’s (2014) study.
Following Alaka and Maloney (2014), we write the vertically integrated local PKE and PAPE budgets as follows:
tk=AM+AP+BT+ϕFC+Cpk+D,
tp=QT+BCCpk+Re.
In Eq. (4), the term ∂tk′ represents the PKE tendency. The terms AM and AP represent the advection of PKE by mean and eddy flow, respectively:
AM=u¯kxυ¯kyω¯kp,
AP=ukx¯υky¯ωkp¯,
where ω′ and ω¯ are eddy and mean vertical pressure velocity, respectively. The barotropic energy conversion BT represents the conversion of mean to perturbation kinetic energy through the mean zonal and meridional wind shears:
BT=uu¯u¯xuυ¯u¯yuω¯u¯pυu¯v¯xυυ¯υ¯yυω¯υ¯p.
The fourth term, on the right-hand side of Eq. (4), represents the rearrangement of PKE by perturbation geopotential flux convergence, which is expressed as follows:
ϕFC=(uϕ¯)x(υϕ¯)y(ωϕ¯)p.
Term Cpk is the baroclinic energy conversion of PAPE to PKE due to vertical overturning and defined as follows:
Cpk=RpωT¯,
where p is pressure and R is the specific gas constant for dry air. The last term, D, is the dissipation of PKE by friction, and it is included in the residual, which is calculated as the difference of the left-hand side and the sum of the first five terms in the right-hand side of Eq. (4). Other sources that can contribute to the residual is through the data assimilation process, parameterization schemes, and due to using finite difference schemes in calculating budget terms (Diaz and Aiyyer 2013b). The residual will be largely negative in the direction of friction and of the same order of magnitude as the PKE growth terms (Diaz and Aiyyer 2013b; Alaka and Maloney 2014).
In Eq. (5), the term on the left-hand side, ∂tp′, represents PAPE tendency. On the right-hand side, QT is the generation of PAPE due to diabatic heating when the perturbation heat source and temperature covary. A positive value of QT results from heating in positively anomalous temperature (warm) regions or cooling in the negatively anomalous temperature (cold) regions. Term QT is defined as follows:
QT=γT¯TQ¯,
where Q′ is the perturbation heat source approximated by (Rydbeck and Maloney 2014):
Q=cpTtcp[ωσ¯(uT¯x+υT¯y)],
where σ¯ is the static stability given by
σ¯=RT¯cppT¯p.
The term BC represents the conversion of mean available potential energy to PAPE via extraction of energy from the mean temperature gradient by eddy heat fluxes:
BC=γcpT¯(uT¯T¯x+υT¯T¯y).

Term Cpk in Eq. (4) acts as a sink of PAPE and as a source of PKE in Eq. (5). Finally, the residual (Re) includes errors due to parameterization of subgrid-scale processes not resolved by ERAI and errors from using centered difference schemes in calculating the budget terms (Alaka and Maloney 2014).

c. Composite analysis

We examine both northern and southern AEW tracks using a composite average over a large number of samples. The calculations are based on the following definitions:

  • Peak AEW activity: From the time series of AEW-filtered meridional wind (υ′) at any location, peak AEW activity is defined as any instance when the magnitude of northerly wind exceeds one standard deviation above zero.

  • KW phase: The phase of the KW is based on the 200-hPa velocity potential anomalies. At any location, the convective (suppressed) phase of the KW is defined as values that at least are one standard deviation below (above) zero.

We define the following categories of AEW–KW interactions for the southern and northern tracks:

  • CPEW: When the peak AEW is located within the convective phase of the KW.

  • SPEW: When the peak AEW is located within the suppressed phase of the KW.

For the southern storm track, we use the base point of 10°N, 15°W (similar to Ventrice and Thorncroft 2013) and the 650-hPa AEW-filtered wind. A total of 63 CPEW and 63 SPEW cases were identified for this storm track. For the northern storm track, we use the base point of 20°N, 10°W and the 950-hPa AEW-filtered wind. A total of 63 CPEW and 62 SPEW cases were identified for this storm track. These basepoints are chosen where the AEW activity is at, or near, its peak as noted from seasonal mean PKE maps (not shown).

d. Statistical significance testing

Statistical significance for the composite fields and their differences are calculated using a resampling method employed in Schreck et al. (2013). For the difference fields, the null hypothesis is that there is no difference in the means of two composites (e.g., CPEW and SPEW). For each composite, a synthetic composite is generated by randomly selecting with replacement from the cases within that composite. This process is repeated 1000 times, and each time the means of both synthetic composites are compared. Using a two-tailed test, the difference of the original two composite fields is considered statistically significant at the 95% if either sample is greater than the other 975 times.

For the statistical significance testing of a composite field, the null hypothesis is that the random variability leads to the composite values. This hypothesis is verified by creating 1000 null composites. Each of these composites are obtained by drawing the samples that have same month and day but different year of the original composite sample. Using two-tailed test, these 1000 null composites then compared with the original composite and considered significant at the 95% level and different from climatology, if for 975 times, the original composite is greater or less than the random composite.

3. Results

a. Impact of the Kelvin waves on AEWs

1) Southern AEW track

The CPEW and SPEW composites are prepared considering the preexisting AEW interacting with KW on day 0. It is clear from Fig. 1a that the convective phase of KW (dashed contours) increases the AEW associated 650-hPa EKE (shading) during their interaction over the west coast of Africa on day −3. The AEW activity is amplified further as it moves westward in the envelope of the convective phase of KW and peaks on day +2. However, in Fig. 1b, the preexisting AEW associated PKE decreases in magnitude as it interacts with the suppressed phase of KW (solid contours) near the west coast of Africa after day −2.

Fig. 1.
Fig. 1.

Lag–longitude composite Hovmöller of 650-hPa 2–10-day easterly filtered PKE (shading) averaged 5°–15°N for (a) CPEW, (b) SPEW, and (c) CPEW − SPEW cases over the base point at 650 hPa, 10°N, 15°W. Black (stripes) dots represent values that are 95% statistically significantly higher (lower) from climatology. Contours are 200-hPa unfiltered velocity potential anomalies averaged over 5°–15°N. Dashed (solid) contours represent convective (suppressed) phase of the KW. Outer dashed contour in (a) and (c) is −2 × 106 m2 s−1 and in (b) is 2 × 106 m2 s−1. Contours in (a) and (c) are drawn with an interval of −2 × 106 m2 s−1 and in (b) with an interval of 2 × 106 m2 s−1. The thin vertical and horizontal gray line marks the longitudinal base point and day 0 in the composite analysis.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

This distinction is more apparent in the composite difference of PKE, as shown in Fig. 1c. The PKE differences after day 0 are positive, indicating that the convective phase of the KW promotes more PKE growth than the suppressed phase. As expected, given the imposed periodicity, the PKE differences are reversed before day 0. This distinction implies that AEW growth is inhibited after the passage of the suppressed phase of the KW.

The enhancement and suppression of AEW activity in the envelope of the convective and suppressed phase of KW are consistent with Mekonnen et al. (2008) and Ventrice and Thorncroft (2013). The mechanism through which it influences the AEW activity is discussed further in sections 3 and 4. In brief, the KW modifies the background environment in which AEWs extract the energy through baroclinic and barotropic energy conversions.

2) Northern AEW track

Figure 2a displays the Hovmöller of AEW 900-hPa PKE (shading) composited over each lag of the CPEW. The PKE significantly increases on day −2 at 10°W coinciding with the passage of the leading edge of the convective phase of KW. The PKE values increase further as the AEW moves westward in the envelope of the convective phase of KW and peak (PKE > 11 m2 s−2) on day +1. Figure 2b depicts the northern AEW track evolution during the passage of the suppressed phase of KW. The AEW grows in the envelope of suppressed phase. However, the PKE and its increase within the suppressed phase are smaller than in the convective phase of KW. Moreover, the AEW growth is halted in the eastern Atlantic after day +1.

Fig. 2.
Fig. 2.

Lag–longitude composite Hovmöller of 900-hPa 2–10-day easterly filtered PKE (shading) averaged 5°–15°N for (a) CPEW, (b) SPEW, and (c) CPEW − SPEW cases over the base point at 900 hPa, 20°N, 10°W. Black (blue) stripes represent values that are 95% statistically significantly higher (lower) from climatology. Contours are 200-hPa unfiltered velocity potential anomalies averaged over 15°–25°N. Dashed (solid) contours represent convective (suppressed) phase of the KW. The outer dashed contour in (a) and (c) is −2 × 106 m2 s−1 and in (b) is 2 × 106 m2 s−1. Contours in (a) and (c) are drawn with interval of −2 × 106 m2 s−1 and in (b) with an interval of 2 × 106 m2 s−1. The thin vertical and horizontal gray line marks the longitudinal base point and day 0 in the composite analysis.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

This distinction is apparent in the composite difference of PKE (Fig. 2c). The PKE differences after day 0 are significantly positive over West Africa and the eastern Atlantic, implying more AEW growth in the convective phase of KW than the suppressed phase. It will be shown later that KW modifies the baroclinic energy conversions through which AEWs northern track growth is either amplified or muted. The above results for both the AEW southern and northern track also suggest that stronger AEWs are favored in the low-level westerly phase of the Kelvin wave phase than in the low-level easterly phase of the Kelvin wave.

b. Impact of the Kelvin waves on mean environment

The previous section showed that the AEW growth is either amplified or halted depending on whether it interacts with the convective or suppressed phase of KW. Understanding the impact of Kelvin waves on the background environment can give clues about the potential pathway for KW and AEW interactions. Top row and bottom row of Fig. 3 displays the day 0 composite map and zonally averaged (0°–30°W) vertical cross section of 10-day low-pass-filtered zonal winds (thick contours) and its meridional gradient (du¯/dy, shading) based on CPEW cases. The thin dashed contours in the composite map (top row) indicate the KW-convective phase (unfiltered 200-hPa VP). In Fig. 3a, the AEJ (−11 m s−1 contour) centered around 15°N near the west coast of Africa (~15°W) shifts slightly southward to 12°N inland (~5°E). The meridional gradient of zonal wind (shading) changes sign at 15°N near the west coast of Africa and 12°N over central Africa(~20°E). The spatial pattern of mean zonal wind and its meridional gradient in Fig. 3a looks similar in the day 0 composite based on SPEW case (not shown).

Fig. 3.
Fig. 3.

(top) Day 0 composite map and (bottom) zonally averaged (0°–30°W) vertical cross section of 10-day low-pass-filtered zonal wind (thick contours) and its meridional gradient (du¯/dy; shading) for (a),(b) CPEW and (c),(d) CPEW − SPEW cases. Light contours in (a) and (b) are 200-hPa unfiltered velocity potential anomalies where dashed (solid) light contours represent the convective (suppressed) phase of the KW. The dots in (c) and (d) represent values that are 95% significant. The thin vertical and horizontal gray line marks the pressure level and latitudinal base point.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

However, the magnitudes of mean zonal wind and its meridional gradient over eastern Atlantic and West Africa significantly differ between the convective and suppressed phase of the KW. The convective phase of KW is associated with the lower troposphere westerly anomalies to the west of the convective center (Straub and Kiladis 2003; Ventrice et al. 2012), and when added to the background easterlies, results in a decrease of easterlies south of the AEJ. For example, in Fig. 3c, at 20°W and 10°N, a positive difference of 1.8 m s−1 indicates that easterlies are weaker during the convective phase than during the suppressed phase of KW. In Fig. 3c, the closer isotachs south of the AEJ during the convective phase of KW indicates enhanced magnitudes of zonal wind meridional gradients indicated by an elongated strip of significant negative zonal wind from 5°E to 45°W over 8°–14°N.

Figure 3b displays the latitude–pressure cross section of mean zonal wind (contours) and its meridional gradient (shading) averaged over 0°–30°W. The AEJ maximum is centered around 600 hPa at 15°N, while monsoon westerlies are located below 800 hPa at 8°N and become shallower to the north. The AEJ is flanked to its north by positive zonal wind meridional gradients and to its south by negative zonal meridional gradients. The zero contours at the surface around 18°N marks the location of intertropical discontinuity, where southwesterly monsoon and northeasterly Harmattan winds intersect. The spatial pattern of mean zonal wind and its meridional gradient in Fig. 3c look similar to the day 0 SPEW composite (not shown).

In the difference composite shown in Fig. 3d, the significant negative difference values between 550 and 750 hPa from 10° to 15°N implies enhanced mean zonal wind meridional gradients to the south of the AEJ during the convective phase compared to the suppressed phase. The convective phase of KW weakens the easterlies south of the AEJ as indicated by the positive difference zonal wind values (contours) of ~1 m s−1 at 650 hPa and 11°N. In contrast, the convective phase of KW intensifies westerlies below 850 hPa at 10°N indicated by the positive difference zonal wind values (contours) of ~1 m s−1. The preceding results indicate that Kelvin waves modulate the background shear south of the AEJ. Previous studies have highlighted the importance of background shear at the AEJ level to the growth of the AEW southern track. In the next section, the mechanisms through which the AEW extract energy and grow is discussed using energetics framework.

Previous studies highlighted the importance of the background temperature gradients for the AEW growth. Now the analysis will focus on how KW modifies the background temperatures north of the AEJ. Figure 4a represents the day +1 vertical cross section of zonally averaged (0°–30°W) 10-day low-pass-filtered temperature (thick contours) and its meridional gradient (dT¯/dy, shading) composite based on CPEW for the AEW northern track. The mean temperature contours below 750 hPa between 0° and 23°N slope upward in the presence of heat low to the north of 20°N and ocean to the south of 5°N. The positive meridional temperature gradients peak between 800 and 925 hPa from 15° to 20°N. The observed spatial distribution of zonally averaged temperature looks similar in the composites based on the suppressed phase of the KW (not shown).

Fig. 4.
Fig. 4.

(top) Day +1 composite pressure–latitude cross section of zonally averaged (0°–30°W) 10-day low-pass-filtered temperature (thick contours) and its meridional gradient (dT¯/dy; shading) for (a) CPEW and (c) CPEW − SPEW cases. (bottom) Day 0 composite pressure–latitude cross section of zonally averaged (0°–30°W) 10-day low-pass-filtered zonal wind (thick contours) and its vertical gradient (du¯/dp; shading) for (b) CPEW and (d) CPEW − SPEW cases. The stripes in (c) and (d) represent values that are 95% significant. The thin vertical and horizontal gray line marks the pressure level and latitudinal base point.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

As shown in Fig. 4c, the negative difference temperature values (dashed contours) greater than 0.1 K are observed below 650 hPa to the south of 19°N. Positive temperature difference anomalies (solid contours) north of 19°N imply mean temperatures higher in the convective phase than in the suppressed phase of KW. The cooling to the south of the AEJ is due to the convective phase of KW associated negative temperature anomalies in the lower troposphere (Straub and Kiladis 2003; Ventrice et al. 2012) adding to the mean temperatures. Both negative and positive temperature anomalies south and north of 19°N increases meridional temperature gradients. As a consequence of thermal wind relation, the greater meridional temperature gradient below 650 hPa between 17° and 21°N increases the vertical shear of the zonal wind, which is shown in Fig. 4d as positive values below the AEJ.

Figure 4b displays the day +1 vertical cross section of zonally averaged (0°–30°W) zonal wind and its vertical gradient (du¯/dp, shading). The AEJ is flanked above and below by negative zonal wind vertical gradients and positive zonal wind vertical gradients. The peak positive zonal wind vertical gradients are observed around 15°N at 800 hPa. These patterns are broadly similar in the day +1 SPEW composite (not shown). The difference composite of zonally averaged zonal wind in Fig. 4d shows enhanced vertical shear of the zonal wind between 750 and 925 hPa from 15° to 20°N, which is consistent with the enhanced meridional temperature gradient (Fig. 4c) via thermal wind balance. The above result implies more mean available potential energy during the convective phase than the suppressed phase of KW, which gives a clue about the potential pathway through which the AEW northern track can grow.

c. Energetics

The diagnosis presented here focuses on how Kelvin waves modulate the growth of the southern and northern AEW track through energy conversions that are crucial for PKE generation: barotropic energy conversion BT, baroclinic overturning Cpk, diabatic generation of PAPE QT, and baroclinic energy conversion BC.

1) Southern AEW track

The following discussion will compare each energy conversion terms between the CPEW, SPEW, and CPEW − SPEW composites. To make it more reader friendly and consistent, the discussion will be in the following order: BT (Figs. 5a, 6a, and 7a), BC (Figs. 5d, 6d, and 7d), QT (Figs. 5c, 6c, and 7c), and Cpk (Figs. 5b, 6b, and 7b).

Fig. 5.
Fig. 5.

Lag–longitude Hovmöller of vertically integrated PKE and PAPE budget terms for the southern AEW track composited over each lag of the CPEW and averaged 5°–15°N. (a) Barotropic energy conversion BT (shaded), (b) baroclinic overturning Cpk (shaded), (c) generation of PAPE by diabatic heating QT (shaded), and (d) baroclinic energy conversion BC (shaded). Solid and dashed contours represent 2–10-day easterly filtered 650-hPa PKE positive and negative anomalies. Outer solid and dashed contour in all panels is 0.5 and −0.5 m2 s−2, respectively. Contour interval is 0.5 m2 s−2. The thin vertical and horizontal gray line marks the longitudinal base point (15°W) and day 0 in the composite analysis. Black stripes represent values that are 95% statistically significantly higher from climatology, while blue stripes represent values that are 95% statistically significantly lower from climatology.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

Fig. 6.
Fig. 6.

As in Fig. 5, but composited over each lag of SPEW cases.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

Fig. 7.
Fig. 7.

As in Fig. 5, but for a difference composite (CPEW − SPEW). Black stripes represent values that are statistically significant at 95% confidence.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

In Fig. 5a, the AEW associated positive barotropic energy conversion BT values increase on day −3 at 20°W and peaks on day 0 at 25°W. To the east of 15°W, there is no significant increase in the positive BT values. In contrast, in Fig. 6a, the positive BT values decrease in the envelope of the suppressed phase of Kelvin wave over the eastern Atlantic between day −2 and day +2. The decrease in positive BT values is also evident to the east of 0°. In the difference composite (Fig. 7a), the positive difference anomalies over the eastern Atlantic (20°–45°W) between day −2 and day +5 indicate an enhancement of positive BT values in the convective (westerly) phase than in the suppressed (easterly) phase of the Kelvin wave.

The total barotropic energy conversion is composed of six components, as shown in Eq. (8). The second term contributes most to the total BT (not shown). As discussed in section 3b and shown in Fig. 3c, the meridional gradient of mean zonal wind du¯/dy is greater in the convective phase than in the suppressed phase of KW. The most significant increase is between 20° and 25°W, which then explains the greatest increase seen in Fig. 7a at the same location on day 0.

In Fig. 5d, the AEW associated baroclinic energy conversions increase between day −2 and day +2 near 15°W, while increase at 0° is statistically insignificant, and to the west of 15°W, no indication of an increase in the positive BC values. This is also true in the SPEW composite (Fig. 6d). The difference composite (Fig. 7d) indicates near-zero difference BC values over eastern Atlantic and West Africa and after day −2. This result implies neither increase nor decrease of BC in the convective and suppressed phase of Kelvin wave relative to each other. However, this does not hold for the AEW northern track growth, which will be shown in section 3c(2).

Figure 5c indicates a significant increase in the generation of PAPE (positive values) by diabatic heating within AEWs to the east of 15°E and between day −2 and day +3. In addition, the positive QT values significantly increase over the eastern Atlantic after the passage of the convective phase of KW. In comparison, as indicated in Fig. 6c, the PAPE is destroyed (negative values) by diabatic heating within AEWs over the eastern Atlantic and West Africa between day −2 and day +2 in the suppressed phase of KW. However, to the east of 15°E between day −2 and day +3, there exists a statistically insignificant positive QT value. The difference composite (Fig. 7c) indicates a significant positive difference in QT values to the east of 15°E between day −1 and day +2. Also evident is an elongated strip of significant positive difference values over the eastern Atlantic after day 0. The above result implies PAPE is generated by diabatic heating within AEWs over the eastern Atlantic and West Africa when the convective phase of KW modulates the background environment. In contrast, PAPE is destroyed by diabatic heating within AEWs when the suppressed phase of KW modulates the background environment.

The PAPE created by QT and BC within AEWs during the convective phase of KW is then converted to PKE through baroclinic overturning circulations (Cpk) as shown in Fig. 5b. The significant increase in the positive Cpk values is located to the east of 15°E between day −2 and day +4, and this is also the region where the positive QT values peak. In addition, the significant positive Cpk values, which peak near 15°W between day −1 and day +1, coincide with the region where positive BC values are statistically significant though smaller in magnitude. In contrast, as indicated in Fig. 6b, the positive Cpk values start to decrease after day −2 to the east of 15°E as the background environment is modified by the suppressed (easterly) phase of the Kelvin wave. Whereas the positive Cpk values start to increase after day +4 when the suppressed phase of KW exits the region. The difference composite shows the positive Cpk values near 15°E between day 0 and day +3 and over the eastern Atlantic (30°–40°W) after day 0 are greater in magnitude in the convective than in the suppressed phase of KW.

Based on the above observations, it appears that the baroclinic overturning circulations (via QT and BC) are more critical for AEW southern storm track initiation (east of 15°E), while barotropic energy conversions are more important for the AEW southern storm track intensification near the west coast of Africa and in the eastern Atlantic. Moreover, the barotropic energy conversions and baroclinic overturning circulations (via QT) are amplified more in the convective phase than in the suppressed phase of KW.

2) Northern AEW track

Likewise for the AEW southern track energetics, the discussion will be in the following order: BT (Figs. 8a, 9a, and 10a), BC (Figs. 8d, 9d, and 10d), QT (Figs. 8c, 9c, and 10c), and Cpk (Figs. 8b, 9b, and 10b).

Fig. 8.
Fig. 8.

Lag–longitude Hovmöller of vertically integrated PKE and PAPE budget terms for the northern AEW track composited over each lag of the CPEW and averaged 15°–25°N. (a) Barotropic energy conversion BT (shaded), (b) baroclinic overturning Cpk (shaded), (c) generation of PAPE by diabatic heating QT (shaded), and (d) baroclinic energy conversion BC (shaded). Solid and dashed contours represent 2–10-day easterly filtered 900-hPa PKE positive and negative anomalies. The outer solid and dashed contour in all panels is 1 and −1 m2 s−2, respectively. The contour interval is 0.5 m2 s−2. The thin vertical and horizontal gray line marks the longitudinal base point (10°W) and day 0 in the composite analysis. Black stripes represent values that are 95% statistically significantly higher from climatology, while blue stripes represent values that are 95% statistically significantly lower from climatology.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

Fig. 9.
Fig. 9.

As in Fig. 8, but composited over each lag of SPEW cases.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

Fig. 10.
Fig. 10.

As in Fig. 8, but for a difference composite (CPEW − SPEW). Black stripes represent values that are statistically significant at 95% confidence.

Citation: Monthly Weather Review 149, 11; 10.1175/MWR-D-21-0003.1

Figures 8a and 9a displays the Hovmöller of vertically integrated barotropic energy conversions composited over each lag of the CPEW and SPEW. In both the composites, the magnitudes of barotropic energy conversions are small than the baroclinic energy conversions (Figs. 8d and 9d). This observation implies that the AEW northern track growth is not primarily through barotropic energy conversions. Furthermore, the difference composite indicates neither significant increase nor decrease in BT relative to each other, which implies neither convective nor suppressed phase of KW enhances the barotropic energy conversions.

Figures 8d and 9d displays the Hovmöller of vertically integrated baroclinic energy conversions composited over each lag of the CPEW and SPEW. The positive BC values in Fig. 8d start to increase just ahead of day 0 to the east of 10°E and peak on day +1. In contrast, the positive BC values shown in Fig. 9d start to decrease after day 0 around 10°E. The difference composite indicates significant positive difference anomalies after day 0 around 10°E, which implies enhanced baroclinic energy conversions in the convective phase than in the suppressed phase of KW. Also, the negative difference values to the east of 0 after day +2 imply enhanced baroclinic energy conversions in the suppressed phase than in the convective phase of KW.

The total baroclinic energy conversion is composed of two components, as shown in Eq. (14). The second term contributes most to the total BC (not shown). As discussed in section 3b and shown in Fig. 4c, the meridional gradient of mean temperature dT¯/dy is greater in the convective phase than in the suppressed phase of KW. The greatest increase is below 800 hPa between 17° and 23°N, which then explains the greatest increase seen in Fig. 10a between 5° and 15°W after day +1.

The PAPE generation by diabatic heating within AEWs in both composites (Figs. 8c and 9c) are significantly smaller in magnitude than the baroclinic energy conversions. In fact, in both the composites, the PAPE is destroyed (negative) within the AEWs after day −3 between 10°E and 15°W. However, the negative difference values between 10° and 20°W and positive difference values between 0° and 10°E after day +1 in the difference composite (Figs. 10c) imply PAPE destruction is more in the convective phase of KW over 10°–20°W, while PAPE destruction is more in the suppressed phase of KW over 0°–10°E.

The PAPE created by QT and BC within AEWs is then converted to PKE through baroclinic overturning circulations (Cpk) as shown in Fig. 5b. The significant increase in the positive Cpk values is seen between day 0 and day +3 around 10°W, and this is also the region where the positive BC values peak. In contrast, as indicated in Fig. 9b, the positive Cpk values start to decrease after day −1 to the east of 10°E as the background environment is modified by the suppressed (easterly) phase of the Kelvin wave. Whereas the positive Cpk values start to increase after day +4 when the suppressed phase of KW exits the region. The difference composite shows the positive Cpk values around 10°E between day −3 and day +3, which imply enhanced baroclinic overturning circulations in the convective than in the suppressed phase of KW.

Based on the above observations, it appears that the baroclinic energy conversions are more critical for AEW northern track growth (around 10°E), whereas barotropic energy conversions are insignificant for the AEW northern track growth over West Africa. Moreover, the baroclinic overturning circulations (via BC) are amplified more in the convective phase than in the suppressed phase of KW.

4. Summary and conclusions

Using ERA-I reanalysis data, we investigate the impact of the Kelvin waves on the growth and maintenance of the northern and southern tracks of AEWs over the eastern Atlantic and West Africa. AEW activity is diagnosed via PKE. As in Mekonnen et al. (2008) and Ventrice and Thorncroft (2013), the convective phase of the KW enhances southern AEW track, and the suppressed phase of the KW inhibits them. This study uniquely performed PKE budget analysis on these interactions and also explored a similar modulation of the northern track AEWs.

Contrasting the AEW energetics between the convective and suppressed KW phases illustrates how KW modulates AEW activity. The convective phase of KW enhances the barotropic energy conversions over the eastern Atlantic. The KW westerly zonal wind anomalies are strongest over the ocean, so the KW are particularly effective at enhancing the meridional gradient of zonal wind south of the AEJ (Figs. 3c,d). These downstream enhancements may invigorate the AEWs over West Africa through their eastward group velocity (Diaz and Aiyyer 2013a).

Baroclinic energy conversion in the southern AEW track is not significantly different between the convective and suppressed KW phases (Fig. 7d). However, AEWs over West Africa during the convective phase of KW generated more PAPE by diabatic heating within AEWs (Fig. 7c) and had stronger baroclinic overturning circulations (Fig. 7d). In contrast, in the suppressed phase of the KW, destruction of PAPE by diabatic heating within AEWs acts as a sink of PAPE. Consequently, the net available PAPE for conversion to PKE through baroclinic overturning is reduced (Fig. 6b). Our analysis has relied on the parameterized convection in the ERA interim data. High resolution convection-permitting simulations are needed to verify these budgets.

In contrast, the Kelvin waves primarily modulate the northern AEW growth through baroclinic energy conversions. The convective phase of KW brings cold anomalies, enhancing the north–south gradients of mean temperatures below 850 hPa, thereby increasing the baroclinicity (Fig. 4c). This is also reflected as an increase in the mean vertical zonal wind gradient to the north of the AEJ between 750 and 900 hPa (Fig. 4d). The enhanced baroclinic energy conversion during the convective phase occurs via strengthened heat fluxes acting on the enhanced mean temperature meridional gradients. We observe no significant differences in the barotropic energy conversions in the convective and suppressed phase (Fig. 10a). The PAPE is destroyed by diabatic heating within AEWs in both the convective and suppressed phase of KW. However, the PAPE destruction is greatest in the suppressed phase of KW over West Africa, and PAPE destruction is greatest in the convective phase of KW over the eastern Atlantic (Fig. 10c).

The northern track modulations are particularly intriguing because KW circulations are generally confined to 10°–15° of the equator (Straub and Kiladis 2003), but the northern track AEWs are strongest at 15°–25°N. Straub and Kiladis (2003) noted that Kelvin waves move eastward at the same speed and scale as extratropical Rossby waves. It is possible that the northern track variability is caused by extratropical variability that projects onto the KW filter band. Alternatively, the northern track variability may be associated with interactions between the Kelvin waves and extratropical Rossby waves, similar to those described by Straub and Kiladis (2003). More analysis is needed to explore these relationships.

The increase of AEW PKE over the Atlantic—especially in the main development region (MDR)—after the passage of the convective phase of the KW can lead to tropical cyclogenesis. Recent studies (Ventrice et al. 2012; Schreck 2015) have shown that tropical cyclogenesis over the Atlantic is favored in the three days after the passage of a convective phase of the KW and inhibited in the three days before the passage of a convective phase of the KW. It is possible that the growth of AEWs following the convective phase of the KW may provide the additional push toward TC genesis.

Acknowledgments

This work was supported by NASA through Awards NNX16AE33G and NNX17AH61G and by the National Science Foundation through Award 1433763. We thank ECMWF and NCAR for access to the ERA-Interim reanalysis (obtained from: https://rda.ucar.edu/datasets/ds627.0/). There are no conflicts of interest. Data and codes are available upon request.

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