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  • View in gallery
    Fig. 1.

    (left) Tephigram and (right) hodograph of the control profile. The red and blue lines represent the temperature and dewpoint temperature of the environment, respectively, and the green line the temperature of a rising parcel of surface air. On the tephigram the units are hPa for pressure, g kg−1 for water vapor mixing ratio, and °C for all temperatures shown. Wind direction on the hodograph represents winds from that direction and the red numbers are pressure in hPa. Values above hodograph are calculated for near-surface air.

  • View in gallery
    Fig. 2.

    Hodographs for the diurnally varying profiles used. The profiles have been obtained by applying the average at (a) 0600, (b) 1200, (c) 1800, and (d) 0000 UTC (over July and August and with the overall average over those months deducted) to the control profile. As in Fig. 1 (right), wind direction on the hodograph represents winds from that direction and the red numbers are pressure in hPa.

  • View in gallery
    Fig. 3.

    Tephigrams for the diurnally varying profiles used. As in Fig. 1 (left).

  • View in gallery
    Fig. 4.

    Profiles of (a) CAPE, (b) CIN, (c) water vapor mixing ratio, and (d) zonal wind component at different heights. In (a) and (b) the profiles show the CAPE and CIN of idealized parcels ascents from the levels indicated. “Td” indicates the thermodynamic and “Winds” the wind profile from time of day stated.

  • View in gallery
    Fig. 5.

    Time evolution of (left) w¯max and (right) R¯, for Wind (dash–dotted), Thermodynamic (solid), and Combined (dashed) simulations. Vertical dashed lines indicate the analysis period. Error bars indicate the standard error of the mean.

  • View in gallery
    Fig. 6.

    Comparing Wind experiments. Time- and y-averaged profiles of vertical velocity (shaded contours). The cold pool depth is shown by a solid black line and is calculated relative to the environment 10 km in front of where B0 [Eq. (1)] is first negative working in the increasing x direction. The dashed yellow line indicates where B0 first becomes positive in each column. The dashed white line is drawn from the location of the maximum w¯ at the level of free convection of the initial profile to 11 km with white triangles indicating where the maximum of w¯ occurs at each height level. Gray thin lines indicate the total liquid and solid water content where above 0.01 g kg−1 (dashed) and precipitation where above 0.01 g kg−1 (solid). The black arrows represent ( u¯r,w¯), where u¯r is the system relative zonal wind component. The y-integrated domain is time integrated over the analysis period, and the x axis runs from 10 km in front of where B0 is first negative to 30 km behind.

  • View in gallery
    Fig. 7.

    Results from Wind experiments (W) averaged over the analysis period. (a) wll plotted against w¯max for heights of 4–11 km within the updraft with a correlation coefficient for the mean values of r = 0.91. (b) PRll plotted against R¯, with r = 0.90. (c) wll plotted against the total upward mass flux across the domain, with r = 0.94. Finally, (d) PRll plotted against Rtot, with r = 0.83; units: kg s−1106 where 1 kg m−2s−1 = 3600 mm h−1. The mean of the five repeated experiments for each environmental profile is marked with error bars that indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

  • View in gallery
    Fig. 8.

    Wind experiments. System-relative inflows of (a) mass, (b) water vapor, and (c) CAPE, calculated using the PS (as defined in section 2a) averaged over the analysis period.

  • View in gallery
    Fig. 9.

    As in Fig. 7, but for the Thermodynamic experiments (Td) with r values (a) −0.42, (b) −0.72, (c) 0.74, and (d) 0.53.

  • View in gallery
    Fig. 10.

    As Fig. 6, but for the Thermodynamic experiments.

  • View in gallery
    Fig. 11.

    Thermodynamic experiment (Td) results averaged over the analysis period with (a) PRll plotted against the rate of condensation (total over domain) and total cloud to precipitation rate vs (b) cloud evaporation rate and (c) rain evaporation rate. Error bars indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

  • View in gallery
    Fig. 12.

    Hovmöller diagrams for the 0600 and 1800 UTC Thermodynamic experiments. Potential temperature at 93 m (shaded contours) and surface rainfall in mm h−1 (black contours). The black dashed line shows the maximum theoretical cold pool speed cmax (Table 2) averaged over the analysis period.

  • View in gallery
    Fig. 13.

    Thermodynamic experiments (Td). System-relative inflows of (a) mass, (b) water vapor, and (c) CAPE, calculated using the propagation speed PS (as defined in section 2a) averaged over the analysis period. The θe (thick lines) and θes (thin lines) for the different profiles.

  • View in gallery
    Fig. 14.

    Results from the Combined (C), Thermodynamic (Td), and Wind (W) experiments over the analysis period including (a) index wll plotted against the in-cloud upward mass flux across the domain. Correlation coefficients for the mean values only, r, are 0.83 for Wind runs, 0.73 for Thermodynamic runs, 0.43 for Combined runs, and 0.54 when all runs are used together. (b) PRll plotted against Rtot, with r = 0.80 for Wind runs, 0.76 for Thermodynamic runs, 0.59 for Combined runs, and 0.43 when all runs are used together. The best-fit lines have been plotted for all cases (solid), Combined runs (dashed), Thermodynamic runs (dash–dotted), and Wind runs (dotted). Error bars indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

  • View in gallery
    Fig. 15.

    As in Fig. 8, but for the Combined experiments.

  • View in gallery
    Fig. 16.

    Combined (C), Thermodynamic (Td), and Wind experiments (W) including (a) ΔU vs mean rainfall with r = 0.72 and (b) changing propagation speed for Wind (dash–dotted), Thermodynamic (solid), and Combined (dashed) cases and its impact on wll. Vertical lines indicate the average PS of the front of the cold pool, over the analysis period, for the combined case at each time. Error bars in (a) indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

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The Influence of the Diurnal Cycle in Wind Shear and Thermodynamics on Squall Lines in the West African Monsoon

Megan BickleaCentre for Doctoral Training in Fluid Dynamics, University of Leeds, Leeds, United Kingdom

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John H. MarshambSchool of Earth and Environment, University of Leeds, Leeds, United Kingdom

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Stephen D. GriffithscDepartment of Applied Mathematics, University of Leeds, Leeds, United Kingdom

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Andrew N. RossbSchool of Earth and Environment, University of Leeds, Leeds, United Kingdom

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Julia CrookbSchool of Earth and Environment, University of Leeds, Leeds, United Kingdom

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Abstract

The West African monsoon has a clear diurnal cycle in boundary layer properties, synoptic flow, and moist convection. A nocturnal low-level jet (LLJ) brings cool, moist air into the continent and we hypothesize that it may support storms by providing vertical wind shear and a source of moisture. We use idealized simulations to investigate how the mean diurnal cycle in temperature and humidity compared with that of the wind shear impacts on mature squall lines. Thermodynamic diurnal changes dominate those of the winds, although when isolated the LLJ wind is favorable for more intense systems. Bulk characteristics of the storms, including in-cloud upward mass flux and—if precipitation evaporation is accounted for—total surface rain rates, correlate well with the system-relative inflow of convectively unstable air and moisture into the storms. Mean updraft speeds and mean rainfall rates over the storms do not correlate as well with system-relative inflows due to variations in storm morphology such as cold pool intensity. We note that storms tend to move near the speed of the African easterly jet and so maximize the inflow of convectively unstable air. Our results explain the observed diurnal cycle in organized moist convection, with the hours from 1800 to 0000 UTC being the most favorable. Storms are more likely to die after this, despite the LLJ supporting them, with the environment becoming more favorable again by midday.

Significance Statement

Large organized storms dominate rainfall in the West African Sahel, but models struggle to predict them at the correct time of day and the underlying mechanisms that control their timings are not well understood. Using idealized simulations, we show that the temperature and humidity of the late evening are favorable for such storms whereas inflow from the low-level jet supports storms overnight. Storm inflows of available energy and moisture predict upward mass transport and total rainfall rates, whereas the strength of the storm’s cold pool is important for storm structure and intensity. Our results demonstrate how the environmental wind profile (which varies throughout the day) interacts with internal storm dynamics, posing a major challenge to parameterized models.

© 2022 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: Megan Bickle, scmeb@leeds.ac.uk

Abstract

The West African monsoon has a clear diurnal cycle in boundary layer properties, synoptic flow, and moist convection. A nocturnal low-level jet (LLJ) brings cool, moist air into the continent and we hypothesize that it may support storms by providing vertical wind shear and a source of moisture. We use idealized simulations to investigate how the mean diurnal cycle in temperature and humidity compared with that of the wind shear impacts on mature squall lines. Thermodynamic diurnal changes dominate those of the winds, although when isolated the LLJ wind is favorable for more intense systems. Bulk characteristics of the storms, including in-cloud upward mass flux and—if precipitation evaporation is accounted for—total surface rain rates, correlate well with the system-relative inflow of convectively unstable air and moisture into the storms. Mean updraft speeds and mean rainfall rates over the storms do not correlate as well with system-relative inflows due to variations in storm morphology such as cold pool intensity. We note that storms tend to move near the speed of the African easterly jet and so maximize the inflow of convectively unstable air. Our results explain the observed diurnal cycle in organized moist convection, with the hours from 1800 to 0000 UTC being the most favorable. Storms are more likely to die after this, despite the LLJ supporting them, with the environment becoming more favorable again by midday.

Significance Statement

Large organized storms dominate rainfall in the West African Sahel, but models struggle to predict them at the correct time of day and the underlying mechanisms that control their timings are not well understood. Using idealized simulations, we show that the temperature and humidity of the late evening are favorable for such storms whereas inflow from the low-level jet supports storms overnight. Storm inflows of available energy and moisture predict upward mass transport and total rainfall rates, whereas the strength of the storm’s cold pool is important for storm structure and intensity. Our results demonstrate how the environmental wind profile (which varies throughout the day) interacts with internal storm dynamics, posing a major challenge to parameterized models.

© 2022 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: Megan Bickle, scmeb@leeds.ac.uk

1. Introduction

The West African monsoon (WAM) brings seasonal rainfall to the Sahel, one of the most densely populated areas on the African continent. The summer monsoon is dominated by mesoscale convective systems (MCSs) which contribute 90% of the annual rainfall in the Sahel (Mathon et al. 2002). During the monsoon period, most regions of West Africa have a single diurnal peak of rainfall either in the afternoon or night, with a minimum of rainfall in the morning (Zhang et al. 2016). Afternoon rainfall peaks are associated with locally initiated storms, some of which sustain into the night, developing into MCSs that propagate westward (Taylor et al. 2010) to give nocturnal rainfall peaks (Duvel 1989; Zhang et al. 2016).

Despite the drastic improvements in global numerical weather prediction over the last 50 years (Bauer et al. 2015), forecasts remain poor over northern Africa with weather models often struggling to provide any real skill for rainfall forecasts, even for lead times of less than a day (Vogel et al. 2018). A patchy observational network hampers successful forecasting (Kniffka et al. 2020), but even during the 2006 African Monsoon Multidisciplinary Analysis campaign (Parker et al. 2008) (when models were initialized with a larger and more consistent set of observations), the gain in skill was lost after 24 h of forecast time (Agustí-Panareda et al. 2010). Accurately capturing the diurnal cycle in numerical weather and climate models is important for correctly representing the entire monsoon system including pressure gradients, winds, and the water budget (Marsham et al. 2013; Birch et al. 2014). In this paper, we explore how aspects of this diurnal cycle support the decay or strengthening of mature squall lines.

The convection parameterizations used in global models struggle to capture MCSs leading to systematic errors in both global numerical weather prediction and climate models (Lee et al. 2007; Moncrieff 2013). Over land surfaces, convection parameterization schemes typically 1) trigger too easily, with rainfall peaks too early in the day, 2) produce rain that is both too weak and too widespread, and 3) lack any representation of organization (Dai et al. 1999; Yang and Slingo 2001; Collier and Bowman 2004; Stephens et al. 2010). This problem is particularly clear in the Sahel due to the dominance of organized convective systems (Peters et al. 2019; Kendon et al. 2019; Pante and Knippertz 2019; Fitzpatrick et al. 2020).

Sahelian storms in convection-permitting models have more intense rainfall, diurnal cycles and lifetimes that are more realistic, and improved propagation (Crook et al. 2019). Berthou et al. (2019a,b) compared convection-permitting climate models against those with parameterized convection on a pan-African domain with 4 km horizontal grid spacing. They found the former drastically improved the distribution of precipitation over the Sahel, particularly through simulating more short-lasting intense rainfall events linked to MCSs, which increases the mean precipitation and gives a better representation of wet and dry spells. This intensification of rainfall occurs in regions of both increased and decreased mean rainfall.

In the summer months, the differential sensible heating produces a low-level pressure gradient between the Saharan heat low and the cooler Gulf of Guinea (see Fig. 1 in Lafore et al. 2010). The resultant regional monsoon circulation (lower-tropospheric southwesterly winds) brings cool, humid air into the continent. This added moisture increases the low-level equivalent potential temperature (Parker et al. 2005b). The shallow monsoon layer undercuts the drier and hotter Saharan air layer, creating a transition zone associated with significant convective inhibition (CIN) and a buildup of convective available potential energy (CAPE). The lower-tropospheric temperature gradient from south to north (or baroclinicity) produces the midtropospheric African easterly jet (AEJ; see Fig. 10 in Parker et al. 2005a). To summarize, the WAM generates an environment with high CAPE and strong vertical wind shear between the low-level southwesterlies and the midlevel AEJ, while the large convective inhibition CIN barrier delays the triggering of convection.

Several studies have indicated how the diurnal cycle is intrinsic to the WAM. Throughout the night, radiative cooling of the surface results in the formation of a shallow, stable boundary layer such that air aloft is decoupled from the surface drag. Consequently, a nocturnal low-level jet (LLJ) forms via an inertial oscillation, which attains its peak intensity between 0500 and 0700 UTC, and is centered near 925 hPa. This southwesterly LLJ produces strong vertical shear with respect to the AEJ at around 600 hPa (Abdou et al. 2010). During the morning, strong solar heating of the ground causes dry boundary layer (BL) convection and erosion of the stably stratified layers formed overnight. Dry air is entrained from above into the BL, and there is downward mixing of momentum from the LLJ and strong near-surface gusts (Knippertz 2008). By midday, deep BL mixing has produced drag on this deep layer of air, and the vertical gradients of momentum and potential temperature are reduced. The LLJ and AEJ both weaken throughout the day, with the LLJ weakening rapidly after the morning and reaching a minimum in the late afternoon and early evening (Abdou et al. 2010). The AEJ has smaller diurnal variations, but weakens to a minimum around 1800 UTC on average (Kalapureddy et al. 2010). Thus, the diurnal cycles of the LLJ and AEJ combine to produce a diurnal minimum in vertical wind shear in the late afternoon (Parker et al. 2005b). The buildup of CAPE throughout the day, when combined with a daily minimum in the CIN barrier in the early evening, is conducive for the triggering of storms which then move westward overnight with the general direction of the midlevel AEJ (Zhang et al. 2016). Storms can be triggered through low-level convergence caused by orography, land surface gradients (e.g., from soil moisture differences), and African easterly waves.

It is well known that line-perpendicular vertical wind shear exerts a controlling influence on convective organization (Browning and Ludlam 1962; Ludlam 1963; Rotunno et al. 1988). However, it is still debated to what extent the ambient wind shear plays a dynamic role by counteracting the horizontal vorticity that is generated baroclinically at the cold pool’s outflow boundary (Weisman 1992; Fovell and Dailey 1995; Weisman and Rotunno 2004; Parker and Johnson 2004; Bryan et al. 2006), rather than a thermodynamic role by modulating the inflow of moisture and CAPE into the storm (Alfaro 2017). In the latter thermodynamic effect—the layer lifting model of convection (LLMC)—the composition of the air flowing into the storm is considered. A strong LLJ would favor the storms, by increasing the fraction of low-level high-θe air compared to the total system-relative inflow into the storm. Similarly, diurnal variations in vertical wind shear as well as changes in cold pool intensity can, according to Rotunno et al. (1988) or RKW theory, alter the structure of the storm including the tilt and intensity of updrafts.

Parker (2008) used idealized simulations to investigate the effects of low-level nocturnal cooling on mature surface-based convective systems, including on where inflowing parcels originate. He found that as the boundary layer cooled and convective systems transitioned from surface based to elevated (inflowing air comes from the lowest 500 m initially then from above that altitude), the mechanism responsible for lifting inflowing parcels evolved from a cold pool to a trapped internal gravity wave. Interestingly, another distinct behavior emerges as the cold pool temperature deficit decreases toward zero. As the system slows, it remains surface based, but produces more intense lifting. Parker (2008) attributes this to the vorticity at the outflow boundary being better balanced by the vertical wind shear, and so largely offsetting the increasing CIN and decreasing CAPE of the parcels that are being lifted. French and Parker (2010) expanded on this study to discuss the relative roles of shear and inflow in idealized MCS simulations with a nocturnal LLJ. They note that changes in the system relative inflow correlate well with changes in total upward mass flux, while changes in shear seem to better describe the changes in updraft intensity.

To summarize, there is a clear diurnal cycle to the WAM, including within the boundary layer flow. MCSs trigger in the evening and persist overnight, with an overall Sahel rainfall minimum in the late morning (Birch et al. 2014). Past studies have shown that the LLJ produces vertical wind shear with the AEJ, and we expect this shear to support the nocturnal squall-line MCSs which characterize much of the Sahel. The morning erosion of the LLJ is similarly expected to reduce shear, and we hypothesize that this provides a less favorable environment for MCSs.

In this study, we consider representative profiles of the Sahel at different times of the day, and use idealized simulations of propagating mature squall lines to study whether the diurnal cycle of shear alone is significant for MCSs and how this compares with the role of the diurnal cycle in temperature and humidity (thermodynamics). In this idealized framework we test 1) whether the nocturnal LLJ supports nocturnal storms and 2) whether the LLMC can be used to explain the modeled characteristics of the MCSs. Finally, we consider what insights these tools and analysis can give us into the actual diurnal cycle of the WAM, which includes both the wind and thermodynamic changes. It is important to note that the simulations used in this study are idealized, and so we do not consider the diurnal cycle of synoptically driven convergence, radiation, or mesoscale flows from inhomogeneous surfaces. Our experiments allow us to isolate the role of the diurnally changing environmental profiles from these factors.

In section 2, we describe our methods, including the control profile and how it is adapted to represent different times in the diurnal cycle and the numerical model that we use. In section 3, we outline how we determine the height, strength, and speed of the simulated cold pool, and introduce the LLMC theory that we will be testing. Numerical results are presented in section 4: results from varying wind profiles alone are in section 4a, results varying thermodynamics alone are in section 4b, and those from varying both wind profiles and thermodynamics together are in section 4c. Throughout we use these results to test the LLMC. We discuss our results and conclude in section 5.

2. Method

a. Numerical model: “Cloud Model 1”

Three-dimensional numerical simulations of idealized squall lines were performed with the Cloud Model 1, version 18 (Bryan and Fritsch 2002). The advection of velocities and scalars is integrated with fifth-order horizontal and vertical advection schemes with implicit diffusion, with a Klemp–Wilhelmson time-splitting, vertically implicit, horizontally explicit pressure solver. The domain extends 1600 km × 60 km in the horizontal (across-squall-line, x, and along-squall-line, y, directions, respectively) with 1 km grid spacing. Horizontal boundaries are open in the across-line (west to east) direction and periodic in the along-line direction. The Durran–Klemp formulation (Durran and Klemp 1983) is employed for the open-flow boundaries, and allows gravity waves to exit the computational domain with minimal reflection. The periodic boundary conditions in the along-line direction allow the squall line to extend across the entire domain in this direction. In the vertical, the domain is 23.4 km deep. The vertical grid stretches from 25 m spacing at the surface to 500 m at 8.4 km and above, resulting in 62 vertical levels. The lower boundary condition is set to a flat, rigid no-slip surface, while a free-slip boundary condition is applied to the top of the domain, with a Rayleigh damping sponge layer above 20 km. Microphysics processes are parameterized with a version of the Morrison double-moment scheme (Morrison et al. 2005), which predicts number concentrations and mixing ratios of cloud droplets, cloud ice, rain, snow, and hail. No radiation and surface heat and moisture fluxes are included in simulations shown here, which aids the isolation of the role of shear.

To trigger squall-line convection, a negative temperature perturbation ΔT(x, z) is applied locally around x = x0 = 912 km and z = z0 = 3 km, but extending uniformly across the entire y domain. We use a locally sinusoidal perturbation given by ΔT(x, z) = −ΔT(x, z)cos2(πβ/2) when β < 1, where β=(xx0)2/xr2+(zz0)2/zr2, with ΔTmax = 2 K, xr = 40 km, and zr = 3 km.

b. Environmental profiles

The model is initialized with vertical profiles of potential temperature, water vapor mixing ratio, and the horizontal wind components (i.e., θ, qυ, u, υ) created from 6-hourly radiosonde measurements made during the AMMA field campaign (Parker et al. 2008) in July–August 2006, at Niamey in Niger (location 13°29′N, 2°10′E). The control profile shown in Fig. 1 is a pre-storm composite profile (Bickle et al. 2020). To produce an atmospheric profile representative of those in which squall lines are observed to occur, only soundings from the evening, night, and early morning (1800, 0000, and 0600 UTC)1 are considered, since squall lines usually form in the evening and persist overnight. These profiles are then filtered to include only those within a 12-h period prior to the passing of a cold pool over Niamey, as identified by Provod et al. (2016). The control profile is a composite of the top 25% pre-storm profiles (13 in total) with the highest near-surface CAPE. The profile allows persistent MCSs in this idealized environment with no imposed large-scale convergence.

Fig. 1.
Fig. 1.

(left) Tephigram and (right) hodograph of the control profile. The red and blue lines represent the temperature and dewpoint temperature of the environment, respectively, and the green line the temperature of a rising parcel of surface air. On the tephigram the units are hPa for pressure, g kg−1 for water vapor mixing ratio, and °C for all temperatures shown. Wind direction on the hodograph represents winds from that direction and the red numbers are pressure in hPa. Values above hodograph are calculated for near-surface air.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

The control profile in Fig. 1 has a surface CAPE of 1862 J kg−1 and CIN barrier of −52 J kg−1. There is a decrease in humidity from 750 to 600 hPa indicating the Saharan air layer and the profile is almost dry adiabatic over these levels. The hodograph shows southwesterly winds above the surface, with the nocturnal LLJ spanning from 960 to 900 hPa with a peak in westerlies at 950 hPa. Above 900 hPa there is a continuous decrease in westerly winds, while southerly winds sustain around 3.8 m s−1 until 800 hPa when they start to weaken. The AEJ spans from 725 hPa to a maximum at 600 hPa. It is also worth noting the easterly winds above 250 hPa, as these control the spread of the cloud anvil. If compared to the overall mean July–August profile for Niamey, the pre-storm control profile has higher near-surface CAPE, a lower near-surface CIN barrier, and a stronger westerly component of the LLJ, but a weaker AEJ at 600 hPa. The simulation produced with this profile is discussed in Bickle et al. (2020).

Diurnal cycle from AMMA profiles

Radiosonde measurements at 0600, 1200, 1800, and 0000 UTC have been used to produce both an overall mean profile as well as mean profiles at each of the 6-hourly intervals to generate diurnal anomalies. The diurnal perturbations attained for each time were added to the pre-storm control profile (Fig. 1) to yield four new kinematic (Fig. 2) and thermodynamic (Figs. 3 and 4) environments. The diurnal variations in wind and thermodynamic profiles are shown in Figs. 24. This approach was selected as it provided a pre-storm profile to be used for the control, which allowed an MCS to be sustained in our simulations while producing unbiased anomalies of the mean diurnal cycle in wind and thermodynamics.

Fig. 2.
Fig. 2.

Hodographs for the diurnally varying profiles used. The profiles have been obtained by applying the average at (a) 0600, (b) 1200, (c) 1800, and (d) 0000 UTC (over July and August and with the overall average over those months deducted) to the control profile. As in Fig. 1 (right), wind direction on the hodograph represents winds from that direction and the red numbers are pressure in hPa.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Fig. 3.
Fig. 3.

Tephigrams for the diurnally varying profiles used. As in Fig. 1 (left).

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Fig. 4.
Fig. 4.

Profiles of (a) CAPE, (b) CIN, (c) water vapor mixing ratio, and (d) zonal wind component at different heights. In (a) and (b) the profiles show the CAPE and CIN of idealized parcels ascents from the levels indicated. “Td” indicates the thermodynamic and “Winds” the wind profile from time of day stated.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Nocturnal radiative cooling and the nocturnal LLJ result in near-surface air that is cool and moist at 0600 UTC (Fig. 3a), as well as a stable BL with both a maximum in the surface CIN barrier of −90 J kg−1 and a daily minimum in CAPE for air at all levels (Fig. 4a). The LLJ is at its sampled diurnal maximum of 10 m s−1 (Fig. 2a) and the vertical shear between the level of the LLJ and the AEJ is also at a maximum. By 1200 UTC, surface heating has increased temperatures at the surface to around 30°C, resulting in a well-mixed, turbulent convective BL (Fig. 3b). Additionally, CAPE values from the surface to 850 hPa have increased, while the CIN magnitudes have decreased from the surface to 925 hPa (Figs. 4a,b). Entrainment has deepened and dried the BL, and zonal wind speeds within the LLJ have decreased to less than 5 m s−1 but are at a maximum both near the surface and within the AEJ (Figs. 2b and 4d).

The BL continues to deepen throughout the day, such that there is a minimum CIN barrier at all heights at 1800 UTC, while CAPE values above 950 hPa are at a maximum (Figs. 4a,b). The decrease in BL humidity produces a higher lifting condensation level of 845 hPa and results in lower levels of surface CAPE than at 1200 and 0000 UTC (Figs. 3c and 4c). The LLJ has continued to weaken to a diurnal minimum, leading to a diurnal minimum in the vertical shear between the LLJ and the AEJ (Fig. 4d). After sunset, the surface cools again so that by 0000 UTC a stable nocturnal boundary layer has formed. The increased stratification allows the LLJ, which brings cool moist air to the region, to strengthen and so increase the near-surface qυ (Fig. 3d). The increased qυ and lower temperature of near-surface air results in a lower lifting condensation level at 923 hPa, and an increase in CAPE near the surface to a daily maximum of 2177 J kg−1 (Fig. 4). However, the stratified BL also results in large (around −70 J kg−1) CIN values.

c. Experiments

Three sets of simulations were run to isolate and explore the contributions of the diurnal cycle in the wind and thermodynamic profiles to the development of squall-line MCSs. These included 1) the “Wind experiments,” where the thermodynamic profile was kept constant (pre-storm control) while the wind profile was varied to represent the 6-hourly intervals of 0600, 1200, 1800, and 0000 UTC, 2) the “Thermodynamic experiments,” where the wind profile was constant (control) and the thermodynamic profile varied to represent the 6-hourly intervals, and 3) the “Combined experiments,” where both the thermodynamic and wind profiles were varied to represent each of the 6-hourly intervals. Each experiment was repeated five times with different random noise applied to the initial temperature perturbation, and the average across these five simulations was used in quantitative analysis.

3. Diagnostics

In this section, we describe how we will calculate the height, strength, and front of the simulated cold pool from the buoyancy difference. The LLMC is also introduced, along with the implied definitions of scalings for particular quantities linked to the storm, which will be tested throughout the rest of the paper by comparison with model output.

a. Cold pool

The buoyancy B of the fluid is defined (as in Bryan et al. 2006) as
B=g[θθ¯θ¯+0.61(qυqυ¯)+(qtqt¯)],
where θ is the potential temperature, g is the gravitational acceleration, qt is the total condensate mixing ratio (cloud, rain, snow, ice, graupel), and overbars denote values from a reference environment. In this study, we consider the buoyancy relative to two reference profiles, leading to 1) B0, the buoyancy relative to the original environmental sounding with which the model is initialized, and 2) B10km, the buoyancy relative to the profile 10 km to the front of where B0 is first negative. The latter represents the environment immediately in front of the system. We use this profile ahead of the system to calculate buoyancy in order to define cold pool depth, rather than the initial profile, as the initial profile is stably stratified at low levels. If the initial profile is used the ascent of environmental air ahead of the cold pool can lead to misidentification of lifted environmental air as cold pool air. The value of 10 km was chosen to ensure the profile was out of the cold pool, but included the ascent region ahead of the cold pool.
Cold pools are characterized by negative buoyancy and often take the form of density currents. We define the cold pool depth h as the height above the ground at which B10km is first observed to be 0 m s−2 using the pre–cold pool profile as a reference. The cold pool intensity c, which is the theoretical speed of a two-dimensional density current in an infinitely deep, unstratified quiescent environment (Benjamin 1968; Rotunno et al. 1988), can then be calculated for each grid column via
c2=20hB10kmdz.

In this study, the cold pool front is identified where the virtual θ perturbation from the original profile first becomes less than −0.1 K (working in the increasing x direction). The propagation speed (PS) of the system is defined as the speed of the cold pool front. This is consistent with Alfaro (2017); however, we consider the speed at 93 m, rather than at the surface. Due to the nocturnal stable boundary layer, there is a clearer signal-to-noise ratio at this height.

b. Layer-lifting model of convection

In this section, we describe the LLMC developed in Alfaro (2017). The LLMC provides a scaling for the strength of convective ascent and rainfall given initial (pre-storm) thermodynamic and dynamic conditions, and the squall-line propagation speed. We will explore whether such scalings, which are primarily based on an environmental profile ahead of a squall line, could be used to predict its relative intensity.

1) Vertical velocities

Integrated CAPE (ICAPE) measures the latent heating per unit area accomplished collectively by all unstable parcels as they ascend from their level of free convection to their level of neutral buoyancy:
ICAPE=0ztrρ(z)CAPE(z)dz,
where CAPE(z) represents the CAPE of a parcel originating at a given height, ztr marks the height of the tropopause, and ρ(z) is density. A layer-lifting index is then defined to measure the mean convective instability of the storm-relative inflowing tropospheric air by
CAPEll=[0ztrρ(z)|uenv(z)PS|CAPE(z)dz][0ztrρ(z)|uenv(z)PS|dz]1.
The environmental wind component normal to the squall line is defined as uenv. Equation (4) is calculated using the original pre-storm environment, and thus does not account for any changes to the CAPE profile due to the approaching squall line. Additionally, it assumes all CAPE is realized, as it does not consider CIN.
Alfaro (2017) defines an index for updraft strength as
wll=2CAPEll.
Alfaro (2017) and Bickle et al. (2020) showed that wll has a linear relationship with the maximum vertical velocity and the line-averaged maximum vertical velocity (averaged along the line of the storm), respectively, in simulated idealized mature squall lines. We will compare wll against 1) the line-averaged maximum vertical velocity, and 2) the upward mass flux across the storm. We will test both of these quantities to see if the scaling provides a good indication of 1) updraft or storm intensity, and 2) the bulk upward flow in the storm.

2) Precipitation

Alfaro and Khairoutdinov (2015) find that the precipitation rate is related to precipitable water. For constant lower-tropospheric wind shear, the rate of water vapor processed by a squall line is the main factor affecting precipitation rate. However, Alfaro and Khairoutdinov (2015) also discuss that precipitation efficiency decreases with weaker shear, drier midtropospheric conditions, and thus lower vertical velocities within the storm. To describe these processes, Alfaro (2017) introduced the diagnostic
PRll=(wllW)2Ly[0ztrρ(z)qυ(z)|uenv(z)PS|dz],
where PRll is the precipitation rate (in kg s−1), which depends on the water vapor inflow rate per unit length in the along-line direction (Ly). The constant (speed) W should be selected such that the term (wll/W)2 accounts for the efficiency of convection: the speed of upward-moving air, entrainment, and the fraction of precipitable water that falls as precipitation. We determined the value of W by fitting the mean control profile PRll to the total domain rainfall (see Table 2), and a value of 60.5 m s−1 was then used for all thermodynamic profiles.
Alfaro (2017) suggested that PRll is a good indicator of the total rainfall rate, while Bickle et al. (2020) found it correlated well with mean rainfall. Also note that we can substitute from Eqs. (4) and (5) to rewrite Eq. (6) as
PRll=2Ly[0ztrρ(z)|uenv(z)PS|qυ(z)dz][0ztrρ(z)|uenv(z)PS|CAPE(z)dz]W2[0ztrρ(z)|uenv(z)PS|dz].
In this form, PRll is proportional to the system relative inflow of moist air and CAPE divided by the system relative inflow of total air mass.

The LLMC calculates the inflow of moisture and air with CAPE into the squall line to produce scalings describing the intensity of an MCS. However, the LLMC does not predict the storm structure, area, differences in microphysics, or indeed the propagation speed (upon which all the LLMC scalings depend, via PS in the integrals). PRll will be compared against 1) the mean rainfall over the storm area and 2) the total rainfall across the domain.

4. Results

In section 4a we first detail experiments investigating how the diurnal wind cycle of the Sahel region can impact the severity and longevity of squall lines in the WAM. In section 4b, we consider the impact of the diurnal thermodynamic cycle alone, and finally in section 4c we consider the impact of the combined (wind plus thermodynamic) diurnal cycle. In each case, we consider whether the LLMC explains variations in storm updrafts and rainfall.

Line-averaged maximum updraft rates ( w¯max) and mean rain rates across the domain where raining ( R¯) from all simulations are shown in Fig. 5. See Table 1 for details of variables calculated from the initial profile and Table 2 for details of variables calculated from model output. All cases sustain gradually weakening convection after the initial “spinup” although the 0600 UTC thermodynamic case begins to die out after 6.25 h. We therefore only consider and compare the systems when they are steady between 3.5 and 6.25 h, which we call the analysis period. The PS of the system is defined as the average speed of the front edge of the cold pool during the analysis period.

Fig. 5.
Fig. 5.

Time evolution of (left) w¯max and (right) R¯, for Wind (dash–dotted), Thermodynamic (solid), and Combined (dashed) simulations. Vertical dashed lines indicate the analysis period. Error bars indicate the standard error of the mean.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Table 1

LLMC variables and ΔU calculated from the initial environmental profile of simulations.

Table 1

a. Effects of varying the wind profile with constant thermodynamic profile

Vertical cross sections of w¯ are shown in Fig. 6. The profiles have been time averaged over the analysis period over a domain that moves with the MCS. This has been achieved by averaging over a moving x domain, defined from 10 km ahead of the first x location where B0 is negative to 30 km behind this point at each time. The most upright and consistently strong updraft occurs in the simulations initialized with the 1200 UTC profile. In all cases there is an area of descent toward the rear of the squall line as well as rear-to-front system relative flow near the surface of the cold pool.

Fig. 6.
Fig. 6.

Comparing Wind experiments. Time- and y-averaged profiles of vertical velocity (shaded contours). The cold pool depth is shown by a solid black line and is calculated relative to the environment 10 km in front of where B0 [Eq. (1)] is first negative working in the increasing x direction. The dashed yellow line indicates where B0 first becomes positive in each column. The dashed white line is drawn from the location of the maximum w¯ at the level of free convection of the initial profile to 11 km with white triangles indicating where the maximum of w¯ occurs at each height level. Gray thin lines indicate the total liquid and solid water content where above 0.01 g kg−1 (dashed) and precipitation where above 0.01 g kg−1 (solid). The black arrows represent ( u¯r,w¯), where u¯r is the system relative zonal wind component. The y-integrated domain is time integrated over the analysis period, and the x axis runs from 10 km in front of where B0 is first negative to 30 km behind.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Layer lifting indices

The LLMC was tested by plotting wll against w¯max and the upward mass flux (Figs. 7a,c) for the wind profile experiments over the analysis period (Fig. 5). Similarly, PRll was plotted against R¯ and the domainwide surface rain rate Rtot (Figs. 7b,d). The values of PS, calculated using the method outlined in section 2a, are noted to be close to the AEJ speed in each case (Table 3). There is little variation in PS for the different wind profile cases with the cold pool initialized with the 1800 UTC profile moving slowest at 10.6 m s−1 and that initialized with the 1200 UTC profile traveling fastest at 11.1 m s−1 when the AEJ is also at its strongest (Table 3).

Fig. 7.
Fig. 7.

Results from Wind experiments (W) averaged over the analysis period. (a) wll plotted against w¯max for heights of 4–11 km within the updraft with a correlation coefficient for the mean values of r = 0.91. (b) PRll plotted against R¯, with r = 0.90. (c) wll plotted against the total upward mass flux across the domain, with r = 0.94. Finally, (d) PRll plotted against Rtot, with r = 0.83; units: kg s−1106 where 1 kg m−2s−1 = 3600 mm h−1. The mean of the five repeated experiments for each environmental profile is marked with error bars that indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Table 2

Diagnostics calculated from simulation results.

Table 2
Table 3

The maximum of the zonal component of the AEJ (m s−1), the zonal component of the LLJ (m s−1), and the zonal wind shear ΔU = UAEJULLJ (m s−1) for each environment. The average PS of squall lines (m s−1) as defined in section 2a, cmax (m s−1) the maximum of the theoretical cold pool speed as defined in Table 2 and the PS that maximizes wll [ PS(wllmax), m s−1] for each environment are also shown.

Table 3

The indices from Alfaro (2017) correlated well with w¯max and R¯ as well as bulk measures of in-cloud upward mass flux and Rtot with correlation coefficients of 0.83 to 0.94 for the mean values (Fig. 7). However, despite the cases initialized with the 0600 and 1200 UTC profiles having similarly high w¯max values, these do not produce equally high rain rates with the 0600 UTC case producing less (Fig. 7). Due to the strong winds near the surface, the inflow of CAPE at that level is higher for 1200 UTC (Fig. 8) which combined with the faster PS gives this profile high wll and PRll. When comparing the updrafts in Fig. 6 it can be seen that there is a broad area of ascent in the 1200 UTC case with consistent upward velocities over 0.35 m s−1 from 4 to 11 km. The 0600 UTC case has a higher peak value of w¯max but the area of ascent is narrower, explaining why despite the high w¯max value for 0600 UTC in Fig. 7 the in-cloud upward mass flux, R¯, and Rtot are lower than for the 1200 UTC case.

Fig. 8.
Fig. 8.

Wind experiments. System-relative inflows of (a) mass, (b) water vapor, and (c) CAPE, calculated using the PS (as defined in section 2a) averaged over the analysis period.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

b. Effects of varying the thermodynamic profile, with a constant wind profile

Simulations were run where the thermodynamic profile was varied with the wind profile held constant. In all cases, the storms were sustained, although the 1800 UTC case reintensifies from hour 5 to hour 6 and the 0600 UTC case begins to die out at 6.25 h (Fig. 5).

Layer lifting indices

The indices from the LLMC correlated with bulk measures, particularly in-cloud upward mass flux (r = 0.74, Fig. 9c) but also Rtot (r = 0.53, Fig. 9d), for all except the 1800 UTC initialized profile. However, the correlation was poorer than for the wind experiments (Fig. 7). When Fig. 9c was replotted for the total domain upward mass flux then the correlation improved (r = 0.88, not shown). This improved correlation is predominantly due to the simulations initialized with the 1800 UTC profile which produces strong upward velocities below the cloud base (Fig. 10c). Thus, Rtot appears to scale on the in-cloud upward mass flux, which is consistent with a quasi-steady system.

Fig. 9.
Fig. 9.

As in Fig. 7, but for the Thermodynamic experiments (Td) with r values (a) −0.42, (b) −0.72, (c) 0.74, and (d) 0.53.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Fig. 10.
Fig. 10.

As Fig. 6, but for the Thermodynamic experiments.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

The LLMC did not correlate well with w¯max (Fig. 9a) or R¯ (Fig. 9b). The main difference between the mean and bulk measures is that the rain or updraft area is important for the former which the LLMC does not account for. In the following discussion, we show that varying the thermodynamic profile varies these quantities, as well as affecting evaporation, causing a poorer fit for w¯max and R¯ than for runs when only winds were varied.

The 0600 UTC thermodynamic initialized ensemble mean has unexpectedly high w¯max and R¯ values compared to the calculated layer-lifting scalings of wll and PRll (Figs. 9a,b). The 0600 UTC case produces a more horizontally compact storm (cross sections in Fig. 10) such that R¯ is higher relative to Rtot as the former depends on the area of the storm (where raining). This lower value for Rtot correlates better with PRll (Fig. 9d).

The rate of rainfall evaporation in the 0600 UTC case is just above 80% of that of the other profiles (Fig. 11b) resulting in a warmer and so less dense cold pool. Furthermore, the 0600 UTC low-level environment is the coolest of the profiles with the potential temperature near the surface about 10°C lower than for the 1800 UTC case (Figs. 3 and 12). Thus, the cold pool produced with the 0600 UTC thermodynamic profile has a reduced buoyancy deficit compared to the other cases and is therefore slower (Fig. 12) and shallower. The near-surface stable layer that exists at 0600 UTC (Figs. 3 and 4) combined with the weak temperature deficit between the cold pool and its environment produces a system that acts differently to the other cases. These differences include the much smoother wave like shape of the 0600 UTC cold pool (Fig. 10a). Additionally, the ascent at the leading edge of the cold pool is weak, with a broad region of weak ascent feeding the main region of ascent above the yellow dashed line where B0 > 0 and so CAPE is realized.

Fig. 11.
Fig. 11.

Thermodynamic experiment (Td) results averaged over the analysis period with (a) PRll plotted against the rate of condensation (total over domain) and total cloud to precipitation rate vs (b) cloud evaporation rate and (c) rain evaporation rate. Error bars indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Fig. 12.
Fig. 12.

Hovmöller diagrams for the 0600 and 1800 UTC Thermodynamic experiments. Potential temperature at 93 m (shaded contours) and surface rainfall in mm h−1 (black contours). The black dashed line shows the maximum theoretical cold pool speed cmax (Table 2) averaged over the analysis period.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

For the simulations initialized with the 1200, 1800, and 0000 UTC profiles there is a weak system-relative rear-to-front flow near the surface of the cold pool in the 10 km behind the gust front (Figs. 10b–d) which follows the definition of a density current in Crook and Moncrieff (1988). There is also clear dynamical forcing of air at the edge of the cold pool front from levels beneath the yellow dashed line (where it is still negatively buoyant relative to the initial profile) that enables it to reach its level of free convection. For the simulation initialized with the 0600 UTC profile the cold pool is weaker and has a different structure. The system-relative flow is front to back and so has some resemblance to the definition of a gravity wave in Crook and Moncrieff (1988) and is similar to what is described in Parker (2008). Notably a temperature deficit still exists between the environment and the cold pool (Fig. 12a). To summarize, although the LLMC explains Rtot in its current form it does not predict storm structure nor storm area and thus cannot predict average ascent and rainfall rates across the storm. The 0600 UTC case, which has a cold pool with a weaker temperature deficit and a more stable environmental profile, gives more intense rain and ascent due to a narrower storm. The weaker cold pool is also structurally different appearing more wave based rather than density current based.

Even considering Rtot, the 1800 UTC case has lower rainfall than expected from its value of PRll. This profile also produces the fastest moving cold pool (Table 3). To gain insight into differences between the storms, we considered their condensation and evaporation rates and found that for the 1800 UTC case the total condensation of vapor to cloud (Fig. 11a) is around 1.5 × 106 kg s−1 lower than expected from PRll when compared to the other cases. The lifting condensation level of near-surface air is at its highest at this time of the day. Additionally, the rate of cloud which evaporates in the 1800 UTC case is around 50% of the rate at which cloud mass becomes precipitation while it is nearer 40% for the other cases (Fig. 11b). A larger fraction of this precipitation then evaporates in the 1800 UTC case, about 0.75 × 106 kg s−1 more than would be expected from the rate of conversion of cloud to precipitation (Fig. 11c). We conclude that the high rates of rain and cloud evaporation and low rate of condensation explain the low values of Rtot in the 1800 UTC case, compared to the value of PRll. The inflow from above 800 hPa is larger for this case (Fig. 13) and so although entrainment is not well resolved in these simulations more convectively stable and drier air is expected to enter the storm which explains the higher cloud evaporation.

Fig. 13.
Fig. 13.

Thermodynamic experiments (Td). System-relative inflows of (a) mass, (b) water vapor, and (c) CAPE, calculated using the propagation speed PS (as defined in section 2a) averaged over the analysis period. The θe (thick lines) and θes (thin lines) for the different profiles.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

To summarize, the LLMC correlates well with total upward mass flux while deviations from Rtot are explained by the LLMC not considering rain evaporation. The LLMC does not correlate well with average values across the storm, including w¯max and R¯, as it does not take the area or structure of the storm into account. The high w¯max value for 0600 UTC is due to a horizontally compact storm structure and a weaker cold pool.

We now consider what controls the variations in wll and PRll shown in Fig. 9. The 1800 and 0000 UTC thermodynamic cases have the greatest wll and upward mass flux (Fig. 9c) with the wll values explained by the high levels of CAPE in these profiles. The 0000 UTC case has the largest system-relative inflow of moisture (Fig. 13) which translates into high rainfall. Despite the 0600 UTC thermodynamic profile having enhanced moisture due to the presence of the LLJ overnight, the small values of PS (around 9.7 m s−1) ensure that the system-relative inflow of moisture is not as great as for other times.

c. Combined thermodynamic and wind experiments

Time-averaged properties for the three sets of ensemble-mean simulations (Wind, Thermodynamic, and Combined) are shown in Fig. 14. For both upward mass flux and rainfall, the thermodynamic change tends to dominate the wind change for the runs with the combined profile applied. The 1800, 0000, and 1200 UTC storms have greater upward mass flux and rainfall than the 0600 UTC storms (Fig. 14) and rainfall is at a maximum for the 1200 UTC case. The values of PS of the storms are similar to their thermodynamic experiment counterparts (Table 3).

Fig. 14.
Fig. 14.

Results from the Combined (C), Thermodynamic (Td), and Wind (W) experiments over the analysis period including (a) index wll plotted against the in-cloud upward mass flux across the domain. Correlation coefficients for the mean values only, r, are 0.83 for Wind runs, 0.73 for Thermodynamic runs, 0.43 for Combined runs, and 0.54 when all runs are used together. (b) PRll plotted against Rtot, with r = 0.80 for Wind runs, 0.76 for Thermodynamic runs, 0.59 for Combined runs, and 0.43 when all runs are used together. The best-fit lines have been plotted for all cases (solid), Combined runs (dashed), Thermodynamic runs (dash–dotted), and Wind runs (dotted). Error bars indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Layer lifting indices

The in-cloud upward mass flux correlates with wll (Fig. 14a) but not as well as if the total upward mass flux is considered (not shown but with correlations of 0.81 for Wind runs, 0.90 for Thermodynamic runs, 0.81 for Combined runs, and 0.82 when all runs are used together with consistent lines of best fit between the three sets of simulations). The Rtot results are accordant with the role of evaporation discussed in section 4b for cases initialized with the 1800 UTC thermodynamics (red triangles and circles in Fig. 14). Similarly to the thermodynamic experiments, it was found that the indices from Alfaro (2017) did not correlate well with w¯max or R¯ (not shown).

The 0600 UTC combined case has low values for wll despite the strong nocturnal jet. If the total inflow is considered it can be seen that although the inflow of moisture is high (Fig. 15b) the total inflow of mass (Fig. 15a) is also high compared to the other profiles. Thus, the minimum inflow of CAPE at 0600 UTC (Fig. 15c) produces a low value of wll as the fraction of convectively unstable air as a proportion of total inflow is smaller. The case also has low bulk measures of in-cloud upward mass flux and Rtot compared to the other storms (Fig. 14). This could be a result of the low equivalent potential temperatures (Fig. 13) and consequently the low CAPE values which occur despite the higher levels of qυ produced by the overnight advection of moisture.

Fig. 15.
Fig. 15.

As in Fig. 8, but for the Combined experiments.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

Recent observational studies have linked decadal trends in shear to decadal trends in extreme storm rainfall (Taylor et al. 2017). According to the LLMC it is not simply shear, but the system-relative inflows of mass, CAPE, and water vapor that determine the rainfall, which are themselves a function of shear. For the mean values of all runs, R¯ is better correlated with the maximum vertical difference in the zonal wind component from the LLJ to the AEJ (ΔU, r = 0.72, Fig. 16a) than PRll (r = 0.19, not shown). Future work should seek to understand these differing controls, but we note that variations in ΔU may change the structure of a storm, potentially resulting in higher values of R¯, for a given Rtot.

Fig. 16.
Fig. 16.

Combined (C), Thermodynamic (Td), and Wind experiments (W) including (a) ΔU vs mean rainfall with r = 0.72 and (b) changing propagation speed for Wind (dash–dotted), Thermodynamic (solid), and Combined (dashed) cases and its impact on wll. Vertical lines indicate the average PS of the front of the cold pool, over the analysis period, for the combined case at each time. Error bars in (a) indicate ±1.6 times the standard error of the mean, with a confidence interval of 90%.

Citation: Journal of the Atmospheric Sciences 79, 8; 10.1175/JAS-D-21-0025.1

The PS of storms is not predicted by the LLMC and the impact of varying PS on the scaling wll is explored in Fig. 16. The value of PS that maximizes wll appears mainly dependent on the wind profile and is generally slower but within 1 m s−1 of the speed of the AEJ (Table 3). Traveling close to the speed of the AEJ provides an enhanced inflow of low-level air compared to a minimum inflow from midlevels (i.e., the height of the AEJ). Any further increases in PS, i.e., greater than the AEJ, will increase the system-relative inflow into the front of the system of both moist low-level air with high CAPE and dry midlevel air with no CAPE. Thus, the optimum PS is close to the AEJ as further increases will cause a greater fraction of the total inflow to be from midlevels. From Fig. 16 and Table 3 it can be seen that storms do move within 2 m s−1 of this optimum PS but whether this is because the AEJ simply “steers” the storm or whether the storms tend toward this optimal speed is unclear and requires further study with more varied environmental profiles. Both the PS and the y-integrated maximum of the theoretical cold pool intensity cmax of the 0600 UTC combined case are closest to this optimal PS (Table 3).

5. Conclusions

Previous studies have shown that there are strong diurnal cycles in winds, vertical wind shear, and MCSs in the WAM. Idealized simulations were run with environmental profiles representative of different points in the day to isolate and study the effects of both combined and isolated diurnal variations in thermodynamics and shear. A particular motivation was to test whether the nocturnal LLJ supports MCSs overnight in the Sahel. Additionally, the LLMC and whether it provides useful indices for storm updraft speeds and rainfall was investigated.

We conclude that the LLJ winds do support nocturnal storms. Increasing the magnitude of the LLJ also increases the system-relative inflow of CAPE and water vapor. However, the variation in thermodynamics is large diurnally and so dominates when combined with that of the wind.

The LLMC was tested to see whether the relative inflow of moisture and convective instability could be used to explain rates of rainfall and updraft strength. The LLMC correlated well with bulk measures of total upward mass flux and the total condensation. However, as the LLMC neither predicts storm structure nor the area of the storm, LLMC indices correlated poorly with average ascent and rainfall rates averaged over the storm ( w¯max and R¯) unless only the wind profiles were varied. Our results are also in agreement with French and Parker (2010) where system-relative inflow correlated with upward mass flux and shear with updraft intensity.

Rtot is not particularly well correlated with PRll and our analysis shows that this can largely be explained by variations in thermodynamics affecting microphysical processes. The LLMC does not account for the rate of evaporation or the fraction of cloud that becomes rain. The simulations initialized with the 1800 UTC profile had a deep, dry, and warm BL and much greater fractional evaporation of rainfall, reducing Rtot and producing a strong and fast cold pool, which led to low condensation for its PRll. Despite the LLMC accounting for moisture moving into the storm this case shows that more consideration of the fraction that will condense and reach the surface as precipitation is needed.

Storms where the cold pool intensity was comparatively weak were more compact resulting in a more efficient storm with higher values of R¯ and this was not well explained by the LLMC. The weaker cold pool temperature deficit produced variations in the structure and form of the cold pool such that it was more wave based than density current based (Crook and Moncrieff 1988). Further investigation showed that by moving with the AEJ, storms maximize their system-relative inflow of CAPE. Whether there are mechanisms that create a tendency for storms to move at a speed that maximizes the system-relative inflow of CAPE, or whether this is simply because storms move with the AEJ and this maximizes the inflow is unclear and needs further research to investigate. Finally, shear alone was by far the best indicator of R¯ highlighting the need for further study.

We conclude that the LLMC does provide useful scalings for squall-line upward mass fluxes and rainfall, with results showing these properties are strongly controlled by shear. However, differences in microphysics and storm organization are not accounted for in the LLMC and this is particularly clear when the thermodynamic profile is varied, rather than the wind profile alone.

Our idealized simulations allow us to isolate how key features of the diurnal cycle in thermodynamics and wind shear can control the intensity of squall lines. However, they are artificially triggered storms which exist in an unchanging environment. In reality, storms tend to form in regions of synoptic and mesoscale convergence (Birch et al. 2014) which vary diurnally (Vizy and Cook 2018), as does radiation, which both interacts with clouds directly and produces the surface fluxes which drive BL circulations. Nevertheless, our simulations provide insight into the real world indicating that the most supportive profiles for convection are 1800 and 1200 UTC and then 0000 UTC. The 0600 UTC profile is the least favorable, consistent with observed storms dying through the late night and morning. This is explained by the maximum in surface CAPE and the minimum in the CIN barrier at 1800 UTC and the reverse at 0600 UTC.

Our 1200 UTC profile supports high rainfall due to environmental wind features which include strong surface winds and a maximum in the AEJ, the latter of which results in stronger shear despite the LLJ weakening as the surface heats up and the boundary layer increases. This is in apparent disagreement with the observed minimum in Sahel-wide rain at this time. However, analysis of observational data used in Crook et al. (2019) shows that there is a daily minimum of about 10% in the probability of an active storm dissipating at 1100–1200 UTC, compared with a probability of 22% from 0500 to 0700 UTC (not shown). Thus, our results are consistent with the observed decline in rainfall from 0000 to 1100 UTC, with storms triggering in the evening, persisting into the night, and dying out through the night and early morning, with the fraction of storms which die out at 1200 UTC being much lower than 0600 UTC.

We have also shown that the LLJ does help support storms overnight. Thus, for convection parameterization schemes to account for the diurnal cycle, a feature they currently struggle with, they must capture the shear effects. Future work should consider a temporally varying environment which would reveal how the life cycle of storms depends on different environments.

1

All times refer to UTC with sunrise and sunset in Niamey (where local time is UTC + 1 h) occurring at approximately 0530 and 1815 UTC, respectively.

Acknowledgments.

Thanks are due to Douglas Parker, whose advice and suggestions were invaluable. We thank George Bryan for making the CM1 model freely available (https://www2.mmm.ucar.edu/people/bryan/cm1/). This work also relied on efforts by others including the AMMA field campaign (Parker et al. 2008). This work was undertaken on ARC3, part of the High Performance Computing facilities at the University of Leeds, United Kingdom. We thank our funders who include EPSRC, University of Leeds CDT in Fluid Dynamics (EP/L01615X/1); Future Climate for Africa AMMA2050 and IMPALA projects (NE/M020126/1); GCRF African SWIFT (NE/P021077/1); National Centre for Atmospheric Science via the NERC/GCRF program, Atmospheric hazards in developing countries: risk assessment and early warning; NERC GENESIS and ParaCon programme (NE/N013840/1, NE/T003898/1). We thank the three anonymous reviewers, whose detailed and constructive comments have significantly improved the manuscript.

Data availability statement.

Radiosonde data used in this research were generated in Parker et al. (2008).

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