1. Introduction
African easterly waves (AEWs) are wavelike disturbances over West Africa characterized by wavelengths of 3000–5000 km, periods of 3–5 days, and a maximum amplitude near 3000 m altitude (e.g., Erickson 1963; Burpee 1972; Reed et al. 1977). Erickson (1963), then Carlson (1969a) hypothesized that some Atlantic tropical cyclones originated from such AEWs. Carlson (1969b) suggested that the energetic growth of AEWs over West Africa partly comes from convective processes, but could not find any evident correlation between the intensity of an AEW leaving the West African coast and cyclogenetic evolution over the tropical Atlantic Ocean. Systematic operational tracking of AEWs has been done since and it is now recognized that a large proportion of Atlantic and even eastern Pacific Ocean hurricanes develop from AEWs, although the majority of AEWs does not develop (e.g., Avila and Clark 1989).
There is some evidence that midlatitude mesoscale convective systems (MCSs) create long-lived mesoscale convective vortices (MCVs) at midlevels in their stratiform region, and that these MCVs intensify and develop downward during successive convective events, as a consequence of a reduced local Rossby radius (Menard and Fritsch 1989; Chen and Frank 1993). These authors claimed that such processes might play a role in tropical cyclogenesis. However, as pointed out by Fritsch et al. (1994), MCSs are generally characterized by a mesohigh at low levels, induced by cooling due to melting and evaporation of precipitation in the stratiform region. In consequence, these authors hypothesized that the development of the initial cyclonic disturbance at the surface requires inflow at low levels provided by the large-scale environment and warming by oceanic sensible heat fluxes to replace the mesohigh. In a midlatitude case study, Rogers and Fritsch (2001) argued that persistent diabatic warming embedded in a midlevel vortex can generate a negative pressure perturbation at low levels, such that it could offset the effect of the surface layer of anomalously cold air and create low-level cyclonic vorticity.
The production of cyclonic vorticity by MCSs during tropical cyclogenesis events has been addressed in various case studies in the western equatorial Pacific. Keenan and Rutledge (1993) found a production of cyclonic vorticity at midlevels by stretching, and attributed it to the thermodynamically induced convergence in a MCS. Vertical advection also contributed to increase cyclonic vorticity at low and midlevels due to up- and downward motions induced by convective processes. Moreover, the interaction between the MCS and the surrounding monsoon trough resulted in positive horizontal advection of cyclonic vorticity in the MCS at low levels, but the production of cyclonic vorticity was slowed down by a negative tilting term at low and midlevels. Trier et al. (1997) studied an earlier stage of cyclonic vorticity generation in such an MCS. Like midlatitude cases (e.g., Brandes 1990; Chen and Frank 1993; Rogers and Fritsch 2001; Knievel and Johnson 2003), they found that midlevel cyclonic vorticity was originally produced by tilting of horizontal vorticity due to the horizontal wind shear, then later amplified by stretching. Bousquet and Chong (2000) found that the production of cyclonic vorticity at mid- and upper levels in a western equatorial Pacific MCS was mainly due to stretching of preexisting cyclonic vorticity, while horizontal advection and tilting of horizontal vorticity had a negative effect. Therefore, it seems that stretching and horizontal advection, as well as tilting and vertical advection, are anticorrelated at all levels. Alternatively, tropical cyclogenesis can also be seen as resulting from progressive segregation, merging, and axisymetrization of small-scale vortices and low-level convergence, induced by convective hot towers in a large-scale rotating environment (e.g., Van Sang et al. 2008).
Lin et al. (2005) studied the AEW that spawned Hurricane Alberto (2000) and identified three successive convective genesis and lysis periods before the final cyclogenesis evolution occurred off the Guinean coast. For the same case study, Berry and Thorncroft (2005) suggested that the large-scale cyclonic vorticity structure of this AEW merged with small-scale cyclonic vortices of convective origin over the Guinean Highlands, thus resulting in its intensification. This disturbance left the West African coast the following day and quickly spawned Hurricane Alberto (2000). Arnault and Roux (2009) hypothesized that the intensification of the pre-Helene (2006) disturbance observed during the National Aeronautics and Space Administration African Monsoon Multidisciplinary Analysis (NAMMA), 15 August–14 September 2006 (Zipser et al. 2009) in the Cape Verde Islands area was the consequence of a “geostrophic adjustment” following the pressure decrease observed as the system crossed the West African coast, in conjunction with deep convective events. For the same case study, Schwendike and Jones (2009, manuscript submitted to Quart. J. Roy. Meteor. Soc., hereinafter SJ) compared Ertel potential vorticity (EPV) production of continental and oceanic MCSs embedded in the developing AEW. In both locations, they observed an increase of low-level EPV by diabatic processes. In a case study of a nondeveloping AEW, referred to as “perturbation D,” which occurred during the third Special Observing Period of AMMA (AMMA/SOP-3 during 15–29 September 2006; Redelsperger et al. 2006). Arnault and Roux (2010, hereinafter ArRo) showed that anticyclonic flow associated with the ridge east of the disturbance was enhanced by midlevel Saharan anticyclonic air and a midlatitude upper-level trough. This anticyclonic circulation stretched the cyclonic vorticity structure of perturbation D. The associated cloud disturbance was then embedded in a region of relatively high pressure compared to the case of Helene (2006), and could not further develop.
All these studies assume that convective systems embedded in an AEW trough contribute to intensify the cyclonic vorticity at low and midlevels. However, the synoptic environment also plays a role through the presence of large-scale convergence, cyclonic vorticity, and wind shear. To further investigate the respective contributions of these synoptic and convective processes, we simulated the developing pre-Helene disturbance and the nondeveloping perturbation D with Méso-NH (Lafore et al. 1998) using explicit convection, and quantified the evolution of the associated absolute vertical vorticity (ζa) budgets. Details of these simulations are given in section 2, vorticity budget analysis is explained in section 3, and results are discussed in section 4. Conclusions are given in section 5.
2. Simulations with Méso-NH
a. Pre-Helene disturbance
Arnault and Roux (2009) conducted a 4-day Méso-NH simulation of the pre-Helene (2006) West African disturbance, starting on 0000 UTC 9 September 2006, with a horizontal resolution of 24 km and parameterized convection. The boundaries of the simulated domain were 8°S–34°N, 37°W–7°E. The vertical grid had 66 levels from the surface to 28 km with a grid spacing of 60 m near the surface up to 600 m at the tropopause level, and the orography was taken into account with the Gal-Chen and Sommerville (1975) vertical coordinate. This simulation has been complemented for the same period with an additional inner model of boundaries 9°–17°N, 24°W–3°E and the same 66 vertical levels as model 1, using one-way grid nesting. The inner model is large enough to contain the synoptic disturbance during the simulation period so it explicitly resolves the interaction between synoptic and convective processes and there is no need to use two-way grid nesting. This second model has a horizontal resolution of 4 km and it does not use parameterized convection. The outer model is updated with the European Centre for Medium-Range Weather Forecasts (ECMWF) operational analyses every 6 h at the boundaries. Very similar results were later obtained with the AMMA reanalyses from ECMWF (Agusti-Panareda et al. 2009), as few additional radiosounding measurements have been included in the AMMA reanalyzing process for the considered period. In the inner model, microphysics is parameterized with a one-moment mixed scheme with six classes of liquid and ice hydrometeors (Pinty and Jabouille 1998), turbulence is parameterized with the 1D scheme with a 1.5-order closure proposed by Bougeault and Lacarrère (1989), and radiative processes with the scheme used at ECMWF (Gregory et al. 2000). The inner model outputs are saved every 30 min. The diagnosed data contain the dynamic and thermodynamic variables as well as the model-derived brightness temperature in the 6.85–7.85-μm water vapor channel of the Meteorological Satellite-9 (Meteosat-9; Chaboureau and Lafore 2002; Saunders et al. 2005). The three-dimensional variables are interpolated from the Méso-NH original grid to constant altitude levels, to compute the budgets discussed in section 3.
b. Perturbation D
ArRo conducted a 5-day Méso-NH simulation of perturbation D, starting at 0000 UTC 24 September 2006, with a horizontal resolution of 24 km and parameterized convection. The boundaries of this simulated domain were 6°S–36°N, 35°W–9°E. Like the Helene case study, this simulation has been complemented during the same period with an additional inner model, using one-way grid nesting. This second model has a horizontal resolution of 4 km, its boundaries are 8°–18°N, 4°–26°W and it does not use parameterized convection. The simulation is updated every 6 h at the boundaries of the outer domain with the AMMA reanalyses from ECMWF, which led to more realistic results compared to those with operational analyses. This is probably related to a more realistic synoptic environment provided by additional AMMA radiosondes and, especially, SOP-3 dropsonde data (Agusti-Panareda et al. 2009). Other details of this simulation are similar to those for Helene.
3. Budget analyses
a. General description of the method
The aim of this work is to analyze the different processes involved in the evolution of absolute vertical vorticity (ζa) in the pre-Helene disturbance and perturbation D. Budgets of ζa are computed in relatively large boxes encompassing the simulated disturbances during periods of 12–32 h, in order to compare the simulated developing and nondeveloping disturbances at different stages of their evolution.
The simulated pre-Helene disturbance moved relatively fast at a nearly constant latitude during the period of interest (see section 4), so the vorticity budgets are computed within domains of 3.5° in latitude and 11° in longitude. The simulated perturbation D moved more slowly and somewhat northward during the periods of interest (see section 4), so for this case the considered domains are 5° in latitude and 8° in longitude. For both cases, domains have comparable horizontal areas and they extend vertically from 1 to 18 km as we are interested in the processes occurring in the whole troposphere.
For each budget, the tendency of vorticity is approximated by the difference between two consecutive model outputs at 30-min intervals, and the vorticity source/sink and advective terms are computed as the mean of terms calculated for each of these two outputs. We verified that very similar results are obtained when vorticity source/sink and advective terms are computed with the mean dynamic and thermodynamic variables from these two outputs. The main difficulty with this method is that the computed vorticity source/sink and advective terms are representative of processes at temporal scales comparable to the time step used in the Méso-NH simulation (4 s), whereas the time resolution for the tendency term is much larger (30 min). Consequently, the budget is not exactly balanced at each grid point. However, averaging the tendency, source/sink, and advective terms over the relatively large horizontal domains result in nearly balanced mean vorticity budgets.
The large box for the vorticity budgets makes the separation between synoptic and convective scales difficult. However, using a smaller box would not allow us to analyze synoptic-scale processes. A complementary analysis would be to compute horizontal and vertical cross sections of the terms in the budget for the large box in order to precisely localize and separate the processes quantified by the budget. However, this would require balanced budgets at each grid point, which is not the case here owing to the long interval (30 min) between the successive model outputs.
b. Budget of absolute vertical vorticity
4. Results
a. Pre-Helene disturbance
The pre-Helene disturbance was associated with a well-defined AEW and a growing MCS on 9 September 2006 northwest of Burkina Faso (Fig. 3 in Arnault and Roux 2009). Successive convective developments associated with the AEW occurred during the two following days. On 12 September, the offshore convective redevelopment south of the Cape Verde Islands spawned a tropical depression that became Hurricane Helene 4 days later. Following SJ, we quantify the evolution of vorticity at two different stages from the results of the inner model at 4-km resolution of the Méso-NH simulation: 1) when it was over the West African continent from 0600 UTC 10 September 2006 until 0000 UTC 11 September 2006 and 2) when it crossed the West African coast from 1200 UTC 11 September 2006 to 18 UTC 12 September 2006.
1) “Continental” stage
During the period from 0600 UTC 10 September 2006 to 0000 UTC 11 September 2006, the simulated pre-Helene disturbance was located in the horizontal domain 12°–15.5°N, 2°–13°W, referred to as H1, which is used for the vorticity budget during the “continental” stage. During the morning of 10 September, the observed pre-Helene disturbance was associated with a large and intense MCS centered on 13.5°N, 7°W, which moved westward while decaying during the day (Figs. 2a–d). The simulated evolution is slightly different (Figs. 2e–h). The simulated MCS in the morning of 10 September was less intense, but it did not decay while propagating westward during the day and reached its maximum intensity during the night of 10–11 September. These differences between modeling results and observations are similar to those described by Arnault and Roux (2009) with Méso-NH at a resolution of 24 km, and by SJ with their Consortium for Small-Scale Modeling (COSMO) model at a resolution of 2.8 km. Despite these differences, we believe that the analysis of the simulated evolution can shed some light on the physical processes associated with the evolution of vorticity in this AEW.
The simulated disturbance was associated with a well-defined cyclonic circulation at 3000 m (Fig. 3). The simulated MCS on the morning of 10 September was located 4° west of the cyclonic vorticity center of an AEW trough and moved toward the downstream ridge (Figs. 2e–h, 3e–h). This MCS displayed small-scale cyclonic and anticyclonic vorticity structures (Fig. 4) that could play a role in the synoptic-scale vorticity intensification (e.g., Van Sang et al. 2008). The horizontally averaged vertical velocity within domain H1 was positive between 1 and 15 km during the continental stage of the simulated pre-Helene disturbance (Fig. 5a), with a maximum near 11 000 m. Slightly stronger values between 0700 and 0900, 1100 and 1300, 1500 and 1800, and after 2100 UTC, were associated with convective bursts in the simulated MCS (Figs. 2e–h). Accordingly, the airflow was convergent below 2 km and divergent between 11 and 16 km (Fig. 5b). Convergence was observed up to 9 km during the two intense convective phases between 1500 and 1800, and after 2100 UTC. Otherwise, divergence occurred between 3 and 5 km until 1500 UTC, probably associated with the anticyclonic circulation of the AEW ridge downstream of the propagating system (Figs. 3e,f).
(i) Budget of absolute vorticity in the morning of 10 September
The production of ζa between 3 and 9 km from 0900 to 1300 UTC 10 September (Fig. 6h) was the result of a positive budget from positive horizontal and vertical advection (Figs. 6a,b), and negative stretching and tilting (Figs. 6c,d). An opposite situation was observed below 3-km altitude. The stretching (tilting) term and horizontal (vertical) advection were clearly anticorrelated, as observed in many previous studies. This anticorrelation between tilting and vertical advection is consistent with the vertical profile of vertical vorticity (Fig. 5c), according to the schematical view proposed in section 3b and Fig. 1. As seen in Fig. 5b, on the morning of 10 September, the airflow was convergent below 2 km (divergent between 2 and 5 km), which is consistent with the positive (negative) stretching and negative (positive) horizontal advection observed at these heights during that period. The positive tendency of ζa between 3 and 9 km on 0900–1300 UTC 10 September resulted mainly from a positive imbalance between horizontal advection and stretching (Fig. 6e), with vertical advection and tilting being approximately balanced (Fig. 6f).
Vertical vorticity was probably produced in the low levels through stretching and tilting (e.g., Trier et al. 1997), transported upward through vertical advection (e.g., Keenan and Rutledge 1993; Bousquet and Chong 2000), then outward through horizontal advection. Convectively induced low-level convergence and vertical velocities are certainly the main cause of low-level positive stretching and tilting and midlevel positive vertical advection. The midlevel positive horizontal advection is probably caused by synoptic-scale divergence associated the AEW ridge downstream, which spreads the convectively induced small-scale vorticity structures outward (Fig. 4), thus increasing large-scale cyclonic vorticity. The similarity between the sum of the source terms (Fig. 5g) and the tendency term (Fig. 5h) during the period 0600–1300 UTC 10 September gives us confidence in this result.
(ii) Budget of absolute vorticity in the afternoon of 10 September
The small decrease of ζa between 1 and 5 km from 1600 to 2300 UTC 10 September (Fig. 6h) was the result of a negative budget from negative horizontal advection and positive stretching between 1 and 4–5 km (Figs. 6a,c), negative vertical advection and positive tilting below 2 to 5 km (Figs. 6b,d), and positive vertical advection and negative tilting above. This anticorrelation between tilting and vertical advection is still consistent with the vertical profile of vertical vorticity. After 1600 UTC, the sum of vertical advection and tilting became negative above 3 km, close to 0 below. Meanwhile, the airflow was convergent from 1 to 9–10 km except between 3 and 5 km between 2000 and 2200 UTC (Fig. 5b), which is consistent with the positive stretching and negative horizontal advection observed at these heights. The fact that midlevel convergence prevailed after 1600 UTC means that the downstream AEW ridge did not have much influence in the domain (Figs. 3g,h).
The simulated intensification of the southwesterly monsoon flow during the afternoon (Fig. 3) certainly contributed to the intensification of the low-level positive stretching and negative horizontal advection, since such a monsoon surge is associated with increased low-level convergence. However, absolute vertical vorticity at the synoptic scale was relatively weak and positive stretching was dominated by negative horizontal advection between 1 and 5 km (Fig. 6e). Hence, the observed decrease of ζa from 1300 to 2100 UTC 10 September below 6 km was caused by the sign change between the anticorrelated stretching term and horizontal advection at 1300 UTC, resulting from deeper convergence induced by convection in the low levels and by the enhanced AEW trough in the midlevels. Above 3 km, vorticity decreased owing to a negative imbalance between positive vertical advection and negative tilting (Fig. 6f). As vertical advection and tilting are explicitly related to convectively induced vertical velocities, this negative imbalance was probably a consequence of convective processes. This result is plausible since, during the period from 1300 to 2100 UTC 10 September and below 6 km, the sum of the source terms (Fig. 6g) is comparable to, though slightly more intense than the tendency term (Fig. 6h).
2) “Oceanic transition” stage
During the period from 1200 UTC 11 September 2006 to 1800 UTC 12 September 2006, the simulated pre-Helene disturbance propagated from the West African continent to the tropical eastern Atlantic. Mean values and the vorticity budget relative to this stage have been calculated within domain H2: 12.5°–16°N, 12°–23°W. The MCS observed during the morning of 11 September decayed during the afternoon (Figs. 7a–c), an oceanic MCS developed in the morning of 12 September near 12°–14°N, 22°W and moved out of the considered horizontal domain during the afternoon (Figs. 7d–f). It spawned tropical depression Helene in the afternoon of 12 September near 12°N, 22°W. In the Méso-NH simulation, a MCS developed near 14°N, 15°W during the morning of 11 September, did not dissipate but intensified continuously while moving westward (Figs. 7g–l). During the afternoon of 12 September, this MCS was located near 15°N, 21°W and it showed some evidence of tropical cyclogenesis (e.g., organized convection, cyclonically rotating cloud bands). As stated above, despite these differences, some information on the cyclogenetic evolution off the West African coast can probably be derived from the simulated results.
The simulated perturbation was associated with a well-defined and intensifying cyclonic circulation at 3000 m associated with the AEW trough (Figs. 8g–l). The simulated MCS of 11 September developed west of the cyclonic vorticity center, propagated westward more slowly, and it was close to the vorticity center in the morning of 12 September. The associated small-scale cyclonic and anticyclonic vorticity structures (Fig. 9) organized and resulted in an intense large-scale cyclonic vorticity structure in the morning of 12 September. Intensification of the cyclonic circulation at midlevels occurred simultaneously with the organization and intensification of cyclonic vorticity at low levels (Figs. 8a–f).
The horizontally averaged vertical velocity in domain H2 was positive between 1 and 16 km (Fig. 10a), and it increased in the mid- and upper levels (7–14 km) during the considered period, with maximum values between 1500 and 2100 UTC 11 September, 0000 and 0300 UTC 12 September, and 0900 and 1500 UTC 12 September. These are the signatures of the successive convective bursts in the developing MCS. Accordingly, horizontal convergence expanded upward from 2 to 9 km, while upper-level divergence intensified between 12 and 16 km (Fig. 10b). However, between 1200 and 1800 UTC 11 September, then between 2100 UTC 11 September and 0300 UTC 12 September, divergence prevailed between 3 and 9 km, probably in relation with the anticyclonic circulation of the AEW ridge downstream of the propagating system (Figs. 8g–i). The profile of horizontally averaged relative vorticity was cyclonic in the low- to midlevels (1–11 km) and anticyclonic above, with an increase of cyclonic vorticity between 1 and 9 km from 1800 to 2400 UTC 11 September, followed by a decrease from 0900 to 1500 UTC 12 September (Fig. 10c). Compared with the continental stage (Fig. 5c), the “oceanic transition” stage was characterized by a downward extension of large cyclonic vorticity values to the surface. The profile of horizontally averaged geostrophic vorticity had similar features although with significantly stronger amplitude and it did not decrease during the morning of 12 September (Fig. 10d). So during the oceanic transition stage, the flow was still not geostrophically balanced. Like the continental stage, this evolution probably resulted from a pressure decrease caused by deep convective developments, followed by a slower increase of cyclonic vorticity as a consequence of geostrophic adjustment. Positive vertical velocity, horizontal convergence, cyclonic relative vorticity, and positive geostrophic vertical vorticity were stronger below 2 km during the oceanic transition than during the continental stage (Fig. 5 versus Fig. 10), leading to the cyclogenetic evolution of the simulated pre-Helene disturbance.
(i) Budget of absolute vorticity in the afternoon of 11 September
The production of ζa between 1200 UTC 11 September and 0000 UTC 12 September (Fig. 11h) resulted from a positive budget between positive stretching and negative horizontal advection below 2 km and an opposite situation above (Figs. 11a,c), positive vertical advection and negative tilting below 2 km and between 4 and 10 km, and an opposite situation between 2 and 4 km (Figs. 11b,d). The observed anticorrelation between tilting and vertical advection at 2–10 km is again consistent with the vertical profile of vertical vorticity at these heights. Between 1200 UTC 11 September and 0000 UTC 12 September, the airflow was convergent below 2 km and mainly divergent above, which is consistent with the positive, then negative stretching, and negative, then positive horizontal advection at these heights. As observed during the beginning of the continental stage, the positive tendency of ζa between 1 and 9 km on the afternoon of 11 September mainly resulted from positive imbalance between horizontal advection and stretching (Fig. 11e), with vertical advection and tilting being approximately balanced (Fig. 11f). As it happened during the beginning of the continental stage, convection was probably the main contributor in the production of vertical vorticity through stretching in the low levels, tilting in the midlevels, and upward transport through vertical advection. The synoptic-scale divergence related to the downstream AEW ridge was probably more important for the outward transport of vertical vorticity in the midlevels by horizontal advection. During the period from 1200 UTC 11 September to 0000 UTC 12 September, between 1 and 12 km, the sum of the source terms (Fig. 11g) was comparable, though slightly more intense than, the tendency term (Fig. 11h).
(ii) Budget of absolute vorticity on 12 September
The decrease of ζa between 1 and 6 km on 12 September between 0300 and 1800 UTC (Fig. 11h) was the result of a negative budget between negative horizontal advection and tilting (Figs. 11a,d), positive stretching, and vertical advection (Figs. 11c,b). The flow was convergent below 2 km (Fig. 10b). After 1800 UTC 11 September the convergence extended upward, except between 2 and 4 km, which is consistent with the positive stretching and negative horizontal advection observed between 1 and 6 km, as happened during the continental stage. The observed decrease of ζa at midlevels during the afternoon resulted from a sign change between the anticorrelated stretching term and horizontal advection (cf. Figs. 11e,f,h). This means that the cyclogenetic evolution of simulated pre-Helene disturbance was largely controlled by the sign of horizontal divergence, which mainly resulted from large-scale forcing. In other words, the organization of small-scale cyclonic and anticyclonic vorticity structures associated with the simulated MCS of 11 September (Fig. 9), resulting in a large-scale cyclonic structure on the morning of 12 September (Figs. 8i–j), was associated with the midlevel horizontal divergence induced by the downstream AEW ridge.
(iii) Concluding remarks on pre-Helene
The main difference between the vorticity budgets during the continental and oceanic transition stages is the low-level increase of ζa which can be attributed to the stretching term. Low-level convergence and cyclonic vorticity in the central part of the pre-Helene disturbance were then strong enough for the stretching to dominate the negative effect of horizontal advection. This last term actually depends on the radial gradient of ζa, and a large area of enhanced cyclonic vorticity would minimize it (Fig. 9a).
b. Perturbation D
Perturbation D during AMMA/SOP-3 was also associated with an AEW and a series of convective developments (Fig. 1 in ArRo). More precisely, a MCS was initiated by a surge of southwesterly moist air from the Gulf of Guinea over Ghana in the afternoon of 22 September. It propagated westward and dissipated during the night of 23–24 September. Several convective systems developed, especially near the Guinean highlands during 25–26 September, in association with an increasing cyclonic curvature of the AEW. However, on 26 September, an anticyclonic southeasterly flow coming from Sahara stretched this cyclonic vorticity structure, preventing it from further intensification over the ocean (ArRo). Using the inner model at 4-km resolution of the Méso-NH simulation of perturbation D, we quantify the associated evolution of vorticity at two different stages: 1) when it was over the West African continent, from 1200 UTC 24 September 2006 to 0000 UTC 25 September 2006; and 2) when it crossed the West African coast, from 1200 UTC 25 September 2006 to 1800 UTC 26 September 2006.
1) “Continental” stage
During the afternoon and evening of 24 September 2006, the simulated perturbation D was located within 8.5°–13.5°N, 7°–15°W, referred to as domain D1. During the afternoon of 24 September, both Méso-NH and Meteosat-9 showed scattered convection in the region 11°–13°N, 10°–13°W (Fig. 12). These convective clouds decayed during the evening, but they spawned a larger and more organized MCS which developed and propagated in the region 11°–13°N, 12°–15°W during the night of 24–25 September. The better resemblance between modeling results and observations than for pre-Helene probably resulted from a more realistic synoptic environment provided by the ECMWF AMMA reanalyses used as boundary conditions for this simulation (Agusti-Panareda et al. 2009).
The simulated disturbance was associated with a well-defined cyclonic curvature of the AEW at 3000 m (Figs. 13d–f). The simulated MCS on the afternoon of 24 September grew ahead of the trough, moved more slowly than the AEW, and it was located north of the trough at midnight. As obtained for the pre-Helene disturbance (Fig. 4), small-scale cyclonic and anticyclonic vorticity structures embedded in a MCS merged at low and midlevels and contributed to increase the large-scale cyclonic circulation (not shown). Moreover, the growth of the simulated MCS during the afternoon of 24 September was associated with an intensification of the southwesterly monsoon flow (Figs. 13b,c), as also occurred during the continental stage of the pre-Helene disturbance.
On 1200–1600 UTC 24 September, the horizontally averaged vertical velocity within domain D1 was positive between 1 and 6 km, in association with scattered convection, and negative above (Fig. 14a). After 1600 UTC, vertical velocity increased substantially and became positive throughout the troposphere, as the simulated MCS was developing. On 24 September, the airflow was convergent below 2 km and mostly divergent above (Fig. 14b). In association with convective bursts occurring during the late afternoon, the flow became progressively convergent up to 8 km and strongly divergent at upper levels (11–16 km). The horizontally averaged relative vorticity (Fig. 14c) was cyclonic in the low to midlevels (1–9 km), with some increase below 7 km between 1500 and 1800 UTC in association with the developing MCS, and anticyclonic above. Horizontally averaged geostrophic vorticity had similar features although with stronger amplitude (Fig. 14d), especially between 1500 and 1800 UTC during the convective burst. Like the simulated pre-Helene disturbance, this could have resulted from a pressure decrease (geostrophic vorticity increase) in relation to deep convective developments, followed by cyclonic vorticity increasing more slowly through the geostrophic adjustment. It is interesting to note that low to midlevel mean vertical velocity was stronger in perturbation D than that associated with to the pre-Helene disturbance during its continental stage (cf. Figs. 5a and 14a), but the mean vertical vorticity at these heights was weaker (Fig. 5c versus Fig. 14c). This difference can be attributed to the fact that the mean vertical vorticity of the pre-Helene disturbance was stronger at the beginning of its continental stage, while the larger MCS on 10 September was associated with more efficient vorticity production than scattered convection occurring on 24 September afternoon.
(i) Budget of absolute vorticity in the afternoon of 24 September
The production of ζa between 1 and 6 km on 1200–1800 UTC 24 September (Fig. 15h) was the result of a positive budget between positive vertical advection and stretching (Figs. 15b,c), and negative horizontal advection and tilting (Figs. 15a,d). This result seems coherent since, during the period 1200–1800 UTC 24 September between 1 and 6 km, the sum of the source terms (Fig. 15g) is comparable to the tendency term (Fig. 15h), although more intense. The schematic view of section 3b does not explain the respective signs of vertical advection and tilting in the presence of a positive vertical gradient of vertical vorticity below 3 km. The positive vertical advection and negative tilting at low levels could have resulted from convective downdrafts, although they were not strong enough to produce a negative mean vertical velocity (Fig. 14a). On 1200–1800 UTC 24 September, the horizontally averaged divergence profile was convergent between 1 and 3 km, and divergent between 3 and 6 km, which partly explains the negative horizontal advection and positive stretching between 1 and 6 km. However, compared to Helene in its continental stage, simulated perturbation D was not associated with a closed cyclonic circulation (e.g., Fig. 13e versus Fig. 3g), so the schematical view of section 3b does not apply exactly. The positive tendency of ζa resulted from a positive imbalance between stretching and horizontal advection below 2 km, from a positive imbalance between horizontal advection and stretching between 2 and 4 km from 1200 to 1500 UTC, from a positive imbalance between vertical advection and tilting between 2 and 6 km from 1500 to 1900 UTC (cf. Figs. 15e,f,h).
The relative importance of vertical advection and tilting during the continental stage of perturbation D suggests that convection had a major impact on the production of area-averaged vorticity through locally enhanced vertical motions. Convection may also have contributed significantly to the low and midlevel vorticity production by stretching through enhanced low- to midlevel convergence, thus dominating the negative horizontal advection term.
2) “Oceanic transition” stage
During the period from 1200 UTC 25 September 2006 to 1800 UTC 26 September 2006, the simulated perturbation D was near the West African coast in the horizontal domain 9.5°–14.5°N, 13°–21°W, referred to as D2. On the afternoon of 25 September, small but relatively intense convective systems near the coast lead to the formation of a large MCS during the night, which resulted offshore in a relatively large zone of rather stratiform clouds on 26 September (Figs. 16a–f). The simulated convective activity during the afternoon and the evening of 25 September was relatively weaker, but the simulation and observations were rather similar on 26 September. As noted above, this simulation is closer to the observations than the pre-Helene disturbance.
On 25 September, the simulated perturbation D was associated with the well-defined cyclonic circulation of the AEW trough at 3000 m, though not as intense as the simulated pre-Helene disturbance during its oceanic transition stage (cf. Figs. 8 and 17). Likewise, the monsoon flow and associated low-level cyclonic vorticity were weaker on 25 September. Small-scale cyclonic and anticyclonic vorticity structures embedded in a MCS merged at midlevels and resulted in a large northwest–southeast-oriented band of cyclonic vorticity (Fig. 18). On 26 September, the cyclonic vorticity of the AEW trough was stretched by a southeasterly flow associated with the enhanced AEW ridge to the east, in connection with a strong Saharan anticyclone at midlevels (ArRo). An intensification of the southwesterly monsoon flow, though weaker than on 12 September (Figs. 8c–f), was simulated on the afternoon of the 25 September, but it quickly weakened during the night.
The horizontally averaged vertical velocity within domain D2 was positive between 3 and 14 km (Fig. 19a), with two maxima in the mid- and upper levels (5–14 km) on 1200–1800 UTC 25 September and 0600–1500 UTC 26 September. These are the signatures of convective developments associated with growing and decaying MCSs during these 2 days. Below 3 km, vertical velocity was weak and even negative at the end of the considered period. Accordingly, the airflow was convergent between 3 and 10 km, and strongly divergent between 11 and 15 km (Fig. 19b), while during the night of 25–26 September, it was mostly divergent through the troposphere. The horizontally averaged relative vorticity was cyclonic at low and midlevels (1–9 km), anticyclonic above, and it remained relatively constant (Fig. 19c). Cyclonic vorticity extended to a slightly higher level than during the continental phase. The profile of horizontally averaged geostrophic vorticity (Fig. 19d) had similar characteristics, although with more complex evolution, and stronger cyclonic maxima associated with convective developments. The maxima were however weaker than those during the continental stage of perturbation D, due to short-lived and moderately intense convective systems simulated with Méso-NH (Figs. 16g–l). In other words, the geostrophic adjustment following the pressure decrease of convective origin was not very efficient in intensifying cyclonic vorticity for this case.
(i) Budget of absolute vorticity on 26 September
On 26 September, the relatively constant ζa at low and midlevels was the result of a mostly balanced budget between positive vertical advection and stretching, negative horizontal advection, and tilting (Fig. 20). Compared with the oceanic transition stage of pre-Helene (Fig. 11), perturbation D was associated with significantly weaker tilting, stretching, horizontal, and vertical advection, which resulted from less efficient production and transport by convection and from less favorable synoptic conditions (weaker downstream/westward and stronger upstream/eastward anticyclonic circulations) for the outward transport of cyclonic vorticity (lack of midlevel divergence).
5. Conclusions
Two case studies of developing and nondeveloping AEWs, respectively NAMMA/pre-Helene disturbance (9–12 September 2006) and AMMA/SOP-3/perturbation D (24–28 September 2006), have been simulated with Méso-NH using explicit convection. Both simulated disturbances were associated with growing and decaying convective systems over West Africa and the tropical Atlantic Ocean close to the coast, although only the first one developed into a tropical cyclone offshore. Budgets of absolute vertical vorticity ζa have been computed at two different stages of these simulated perturbations to investigate and quantify the associated physical processes.
Convective-scale processes are associated with low- to midlevel positive stretching and negative horizontal advection through convectively induced low- to midlevel convergence, and with enhanced low- to midlevel tilting and vertical advection through convective upward motions, the sign of these terms depending on the sign of vertical wind shear. Synoptic-scale processes are associated with enhanced stretching and horizontal advection associated with the monsoon flow in the low levels and with cyclonic and anticyclonic circulations associated with AEW troughs and ridges in the midlevels. The synoptic-scale contribution on tilting and vertical advection is through environmental wind shear, but strong vertical motions associated with convective processes are necessary for these terms to become significant. However, the scale separation in the budget of ζa is not straightforward.
As in many previous studies, we found that stretching and horizontal advection, tilting, and vertical advection are globally anticorrelated. The respective signs of these terms can be explained in the idealized case of a large-scale cyclonic circulation with upward motion in its central part. In such a situation, tilting is expected to be positive (negative) when tangential winds associated with the cyclonic circulation increase (decrease) with height. Likewise, vertical advection is expected to be negative (positive) when cyclonic vorticity increases (decreases) with height. Assuming this large-scale cyclonic circulation is characterized by a maximum of vorticity in the central region, hence a horizontal gradient of cyclonic vorticity directed toward the center, the respective signs of stretching and horizontal advection depend on the large-scale divergence of the horizontal flow. A convergent (divergent) flow is associated with negative (positive) horizontal advection, since it is upgradient (downgradient). Likewise, a convergent (divergent) flow is associated with positive (negative) stretching. With these theoretical considerations in mind, budgets of ζa have been computed for the “continental” and “oceanic transition” stages of the simulated pre-Helene disturbance and perturbation D, which were associated with cyclonic circulations and convective developments.
During the first part of the continental stage of the pre-Helene disturbance (0600–1500 UTC 10 September), cyclonic vorticity increased in the mid- to upper levels mainly as a result of a positive imbalance between positive horizontal advection and negative stretching (“horizontal” terms), with positive vertical advection and negative tilting (“vertical” terms) being approximately equilibrated. More precisely, a MCS simulated west of the AEW trough enhanced low-level convergence and low- to midlevel upward velocities, thus producing cyclonic vorticity through tilting and stretching in the low levels (as in, e.g., Trier et al. 1997) and transporting it upward through vertical advection (as in, e.g., Keenan and Rutledge 1993; Bousquet and Chong 2000). Then, the downstream (westward) AEW ridge induced midlevel divergence in the MCS region, resulting in an outward transport of cyclonic vorticity through horizontal advection.
The continental phase of perturbation D was slightly different. In particular, cyclonic vorticity increased in the low to midlevels. There was no interaction with the downstream AEW ridge inducing synoptic-scale divergence and midlevel horizontal advection was negative. Positive stretching dominated the negative horizontal advection in the low to midlevels, in conjunction with stronger convection and deeper convergence. Moreover, there was no low-level cyclonic vorticity production through tilting in the low levels due to a vertical profile of vorticity with maximum values in the lowest levels, but positive vertical advection dominated negative tilting and contributed to the production of cyclonic vorticity in the low to midlevels.
For the developing pre-Helene disturbance, low-level cyclonic vorticity intensified during the first half of the oceanic transition stage in the afternoon and evening of 11 September. The low-level increase below 3 km was attributed to a positive imbalance between positive stretching and negative horizontal advection, with the sum of positive vertical advection and negative tilting being weakly negative. Since the environmental vorticity was relatively strong over a large area, the resulting weaker radial gradient led to weak horizontal advection largely compensated by strong positive stretching. An opposite situation prevailed between 3 and 12 km with positive horizontal advection and negative stretching. As observed during the continental stage, a MCS west of the AEW trough enhanced low-level convergence and low- to midlevel upward velocities, thus producing cyclonic vorticity through stretching in the low levels, tilting in the midlevels, and transporting it upward through vertical advection. Then, the downstream (westward) AEW ridge induced midlevel divergence in the MCS region, resulting in an outward transport of cyclonic vorticity through horizontal advection. On 12 September, horizontal convergence extended upward in association with the intensifying convection, so did negative horizontal advection and positive stretching, but the large-scale vorticity above 3 km was relatively weak and the sum of the horizontal terms was then negative, except in the lowest levels. Meanwhile, tilting decreased, then became negative as the strongest swirling winds migrated downward and the vertical wind shear became mostly negative. But this term was almost exactly balanced by vertical advection.
For perturbation D the horizontal term (i.e., the sum of horizontal advection and stretching) was comparatively smaller during its oceanic transition stage. In this case, the large-scale cyclonic circulation was less intense and, at the altitudes where convergence prevailed, negative horizontal advection compensated positive stretching. Absolute vorticity was also produced by tilting between 2 and 6 km, then transported upward and horizontally advected outward between 6 and 9 km, but this was almost compensated by negative stretching and did not lead to significant change in the mean vorticity. Compared with the oceanic transition stage of pre-Helene disturbance, low- to midlevel cyclonic vorticity production through stretching and tilting, and vertical transport were smaller because of weaker convective activity. Moreover, there was little outward transport through horizontal advection as there was little midlevel divergence induced by the downstream AEW ridge in this case. In other words, there were fewer small-scale vorticity structures associated with convection and the synoptic environment was less favorable for upscale organization.
These results show that, for cyclogenesis to occur off the West African coast, MCSs developing west of an AEW trough and a midlevel divergent environment in connection with the downstream (westward) AEW ridge are needed. For Helene, the well-defined AEW trough, the downstream ridge and the series of convective developments represented favorable conditions. For perturbation D, the lack of interaction with the downstream (westward) ridge, the enhanced AEW ridge upstream (eastward), as well as too weak convective developments, prohibited a cyclogenetic evolution during the oceanic transition stage.
Acknowledgments
The present work is part of the first author’s Ph.D. thesis in Université Paul Sabatier Toulouse 3, France. Based on a French initiative, AMMA was built by an international scientific group and is currently funded by a large number of agencies, especially from France, the United Kingdom, the United States, and Africa. It has been the beneficiary of a major financial contribution from the European Community’s Sixth Framework Research Programme. (Detailed in formation on scientific coordination and funding is available online on the AMMA International Web site http://www.amma-international.org.) Numerical simulations were conducted on CNRS/IDRIS computers under Grants 070591 and 080591. We thank Didier Gazen and Juan Escobar for the technical support in Méso-NH, Dr. Jean-Pierre Chaboureau for the scientific support in Méso-NH, and Dr. Jean-Pierre Cammas for valuable discussions about the vorticity budget. We also thank the anonymous reviewers for valuable comments, which helped to substantially improve the manuscript.
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Vertical cross sections of a large-scale closed cyclonic circulation in the presence of convective upward motions close to its center, with axial symmetry around vertical axis z. Radial coordinate of point M is r. Crossed and dotted ellipses represent tangential velocity associated with the cyclonic circulation. Vertical arrows represent vertical velocity. Tubes represent tilted horizontal vorticity. Symbol C (A) stands for cyclonic (anticyclonic) vorticity. Tangential velocity (a) increases and (b) decreases with height so tilting is expected to be positive and negative, respectively, and vertical advection to be negative and positive, respectively.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
Vertical cross sections of a large-scale closed cyclonic circulation in the presence of convective upward motions close to its center, with axial symmetry around vertical axis z. Radial coordinate of point M is r. Crossed and dotted ellipses represent tangential velocity associated with the cyclonic circulation. Vertical arrows represent vertical velocity. Tubes represent tilted horizontal vorticity. Symbol C (A) stands for cyclonic (anticyclonic) vorticity. Tangential velocity (a) increases and (b) decreases with height so tilting is expected to be positive and negative, respectively, and vertical advection to be negative and positive, respectively.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
Vertical cross sections of a large-scale closed cyclonic circulation in the presence of convective upward motions close to its center, with axial symmetry around vertical axis z. Radial coordinate of point M is r. Crossed and dotted ellipses represent tangential velocity associated with the cyclonic circulation. Vertical arrows represent vertical velocity. Tubes represent tilted horizontal vorticity. Symbol C (A) stands for cyclonic (anticyclonic) vorticity. Tangential velocity (a) increases and (b) decreases with height so tilting is expected to be positive and negative, respectively, and vertical advection to be negative and positive, respectively.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a)–(d) Brightness temperature (°C) in the water vapor channel (7.3 μm) derived from Meteosat-9 for the period from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006 in the horizontal domain 12°–15.5°N, 2°–13°W. (e)–(h) As in (a)–(d), but for brightness temperatures derived from the inner model at 4-km resolution of the Méso-NH simulation of pre-Helene disturbance. The scale is given by the gray shaded bar on the bottom right of (h). These maps are limited to the horizontal domain used for the vorticity budget quantifying the evolution of simulated pre-Helene disturbance during its continental stage.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a)–(d) Brightness temperature (°C) in the water vapor channel (7.3 μm) derived from Meteosat-9 for the period from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006 in the horizontal domain 12°–15.5°N, 2°–13°W. (e)–(h) As in (a)–(d), but for brightness temperatures derived from the inner model at 4-km resolution of the Méso-NH simulation of pre-Helene disturbance. The scale is given by the gray shaded bar on the bottom right of (h). These maps are limited to the horizontal domain used for the vorticity budget quantifying the evolution of simulated pre-Helene disturbance during its continental stage.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a)–(d) Brightness temperature (°C) in the water vapor channel (7.3 μm) derived from Meteosat-9 for the period from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006 in the horizontal domain 12°–15.5°N, 2°–13°W. (e)–(h) As in (a)–(d), but for brightness temperatures derived from the inner model at 4-km resolution of the Méso-NH simulation of pre-Helene disturbance. The scale is given by the gray shaded bar on the bottom right of (h). These maps are limited to the horizontal domain used for the vorticity budget quantifying the evolution of simulated pre-Helene disturbance during its continental stage.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a)–(d) As in Figs. 2a–d, but for horizontal cross sections of horizontal wind at 1000 m derived from the inner model at 4-km resolution of the Méso-NH simulation of the pre-Helene disturbance. (e)–(h) As in (a)–(d), but for the horizontal wind at 3000 m. The scale for horizontal velocity is represented on the bottom right of (a)–(h).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a)–(d) As in Figs. 2a–d, but for horizontal cross sections of horizontal wind at 1000 m derived from the inner model at 4-km resolution of the Méso-NH simulation of the pre-Helene disturbance. (e)–(h) As in (a)–(d), but for the horizontal wind at 3000 m. The scale for horizontal velocity is represented on the bottom right of (a)–(h).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a)–(d) As in Figs. 2a–d, but for horizontal cross sections of horizontal wind at 1000 m derived from the inner model at 4-km resolution of the Méso-NH simulation of the pre-Helene disturbance. (e)–(h) As in (a)–(d), but for the horizontal wind at 3000 m. The scale for horizontal velocity is represented on the bottom right of (a)–(h).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a) Horizontal cross section of relative vorticity (s−1) at 3000 m on 1800 UTC 10 Sep 2006 derived from the inner model at 4-km resolution of the Méso-NH simulation of the pre-Helene disturbance. The vorticity scale is given by the gray shaded bar on the right of (a) and horizontal velocity is represented by arrows with the scale indicated on the bottom right of (a). (b) As in (a), but for model derived brightness temperature. The temperature scale is given by the gray shaded bar on the bottom right of (b).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a) Horizontal cross section of relative vorticity (s−1) at 3000 m on 1800 UTC 10 Sep 2006 derived from the inner model at 4-km resolution of the Méso-NH simulation of the pre-Helene disturbance. The vorticity scale is given by the gray shaded bar on the right of (a) and horizontal velocity is represented by arrows with the scale indicated on the bottom right of (a). (b) As in (a), but for model derived brightness temperature. The temperature scale is given by the gray shaded bar on the bottom right of (b).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
(a) Horizontal cross section of relative vorticity (s−1) at 3000 m on 1800 UTC 10 Sep 2006 derived from the inner model at 4-km resolution of the Méso-NH simulation of the pre-Helene disturbance. The vorticity scale is given by the gray shaded bar on the right of (a) and horizontal velocity is represented by arrows with the scale indicated on the bottom right of (a). (b) As in (a), but for model derived brightness temperature. The temperature scale is given by the gray shaded bar on the bottom right of (b).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
Time–altitude plot of mean values in the horizontal domain 12°–15.5°N, 2°–13°W derived from the inner model at 4-km resolution of the Méso-NH simulation of pre-Helene disturbance. The horizontal axis gives the time in days from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006, with a graduation every 3 h. The vertical axis gives the altitude in meters. The gray color scale is indicated in the right of (a)–(d). (a) Vertical velocity (m s−1), (b) horizontal divergence (s−1), (c) relative vorticity (s−1), and (d) geostrophic vorticity (s−1).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
Time–altitude plot of mean values in the horizontal domain 12°–15.5°N, 2°–13°W derived from the inner model at 4-km resolution of the Méso-NH simulation of pre-Helene disturbance. The horizontal axis gives the time in days from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006, with a graduation every 3 h. The vertical axis gives the altitude in meters. The gray color scale is indicated in the right of (a)–(d). (a) Vertical velocity (m s−1), (b) horizontal divergence (s−1), (c) relative vorticity (s−1), and (d) geostrophic vorticity (s−1).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
Time–altitude plot of mean values in the horizontal domain 12°–15.5°N, 2°–13°W derived from the inner model at 4-km resolution of the Méso-NH simulation of pre-Helene disturbance. The horizontal axis gives the time in days from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006, with a graduation every 3 h. The vertical axis gives the altitude in meters. The gray color scale is indicated in the right of (a)–(d). (a) Vertical velocity (m s−1), (b) horizontal divergence (s−1), (c) relative vorticity (s−1), and (d) geostrophic vorticity (s−1).
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for the different terms of the budget of ζa applied to simulated pre-Helene disturbance during its continental stage from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006 in the horizontal domain 12°–15.5°N, 2°–13°W: (a) horizontal advection; (b) vertical advection; (c) stretching of preexisting vorticity; (d) tilting of horizontal vorticity; (e) sum of horizontal advection and stretching; (f) sum of vertical advection and tilting; (g) sum of horizontal advection, stretching, vertical advection, and tilting; and (h) Eulerian tendency of ζa. These terms are in inverse seconds squared, and the gray color scale is indicated in the bottom right.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for the different terms of the budget of ζa applied to simulated pre-Helene disturbance during its continental stage from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006 in the horizontal domain 12°–15.5°N, 2°–13°W: (a) horizontal advection; (b) vertical advection; (c) stretching of preexisting vorticity; (d) tilting of horizontal vorticity; (e) sum of horizontal advection and stretching; (f) sum of vertical advection and tilting; (g) sum of horizontal advection, stretching, vertical advection, and tilting; and (h) Eulerian tendency of ζa. These terms are in inverse seconds squared, and the gray color scale is indicated in the bottom right.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for the different terms of the budget of ζa applied to simulated pre-Helene disturbance during its continental stage from 0600 UTC 10 Sep 2006 to 0000 UTC 11 Sep 2006 in the horizontal domain 12°–15.5°N, 2°–13°W: (a) horizontal advection; (b) vertical advection; (c) stretching of preexisting vorticity; (d) tilting of horizontal vorticity; (e) sum of horizontal advection and stretching; (f) sum of vertical advection and tilting; (g) sum of horizontal advection, stretching, vertical advection, and tilting; and (h) Eulerian tendency of ζa. These terms are in inverse seconds squared, and the gray color scale is indicated in the bottom right.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006 in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006 in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006 in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006 in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006 in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006 in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 4, but at 0000 UTC 12 Sep 2006.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 4, but at 0000 UTC 12 Sep 2006.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 4, but at 0000 UTC 12 Sep 2006.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006, in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006, in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for the period from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006, in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for the budget of ζa applied to simulated pre-Helene disturbance during its oceanic transition stage from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006, in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for the budget of ζa applied to simulated pre-Helene disturbance during its oceanic transition stage from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006, in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for the budget of ζa applied to simulated pre-Helene disturbance during its oceanic transition stage from 1200 UTC 11 Sep 2006 to 1800 UTC 12 Sep 2006, in the horizontal domain 12.5°–16°N, 12°–23°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 8.5°–13.5°N, 7°–15°W. (left) Black rectangles correspond to the area below the model terrain elevation.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 8.5°–13.5°N, 7°–15°W. (left) Black rectangles correspond to the area below the model terrain elevation.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 8.5°–13.5°N, 7°–15°W. (left) Black rectangles correspond to the area below the model terrain elevation.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for simulated perturbation D from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for simulated perturbation D from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for simulated perturbation D from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for simulated perturbation D during its continental stage from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for simulated perturbation D during its continental stage from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for simulated perturbation D during its continental stage from 1200 UTC 24 Sep 2006 to 0000 UTC 25 Sep 2006 in the horizontal domain 8.5°–13.5°N, 7°–15°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 2, but for the period from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 3, but for the period from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 4, but from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D at 1800 UTC 26 Sep 2006.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 4, but from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D at 1800 UTC 26 Sep 2006.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 4, but from the inner model at 4-km resolution of the Méso-NH simulation of perturbation D at 1800 UTC 26 Sep 2006.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for simulated perturbation D from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for simulated perturbation D from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 5, but for simulated perturbation D from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for simulated perturbation D during its oceanic transition stage from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for simulated perturbation D during its oceanic transition stage from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
As in Fig. 6, but for simulated perturbation D during its oceanic transition stage from 1200 UTC 25 Sep 2006 to 1800 UTC 26 Sep 2006 in the horizontal domain 9.5°–14.5°N, 13°–21°W.
Citation: Monthly Weather Review 138, 4; 10.1175/2009MWR3120.1
