Forced gravity waves and the tropospheric response to convection

Abstract

We present theoretical work directed toward improving our understanding of the mesoscale influence of deep convection on its tropospheric environment through forced gravity waves. From the linear, hydrostatic, non‐rotating, incompressible equations, we find a two‐dimensional analytical solution to prescribed heating in a stratified atmosphere, which is upwardly radiating from the troposphere when the domain lid is sufficiently high. We interrogate the spatial and temporal sensitivity of both the vertical velocity and potential temperature to different heating functions, considering both the near‐field and remote responses to steady and pulsed heating. We find that the mesoscale tropospheric response to convection is significantly dependent on the upward radiation characteristics of the gravity waves, which are in turn dependent upon the temporal and spatial structure of the source, and the assumed stratification. We find a 50% reduction in tropospherically averaged vertical velocity when moving from a trapped (i.e. low lid) to upwardly radiating (i.e. high lid) solution but, even with maximal upward radiation, we still observe significant tropospheric vertical velocities in the far‐field 4 h after heating ends. We quantify the errors associated with coarsening a 10 km‐wide heating to a 100 km grid (in the way a general circulation model (GCM) would), observing a 20% reduction in vertical velocity. The implications of these results for the parametrization of convection in low‐resolution numerical models are quantified, and it is shown that the smoothing of heating over a grid box leads to significant in‐grid‐box tendencies, due to the erroneous rate of transfer of compensating subsidence to neighbouring regions. Further, we explore a simple time‐dependent heating parametrization that minimizes error in a parent GCM grid box, albeit at the expense of increased error in the neighbourhood.

Environment of severe storm formations over West Africa on the 26‐28 June 2018

“…In an environment of sufficient moisture (as observed in Figure 2), the trapped wave acted to modify boundary layer processes to promote the initiation of severe convection and the growth and longevity of the thunderstorms on 26 June 2018, similar to findings by Howard (2013); Sachsperger et al (2015); Stephan et al (2021). The rear of the propagating gravity wave was a significant region for storm initiation (Figure 3), through the modification of tropospheric heating (Halliday et al, 2018). This heating can be envisaged in the higher than normal BLH and dissipation, occurring over the initiation zone.…”

“…The consequence is the initiation of intense MCSs south of the jet. This AEJ also has the potential to trap atmospheric gravity waves (Plougonven & Snyder, 2005), which releases significant energy to destabilize the lower troposphere and trigger secondary storms (Halliday et al, 2018; Parker & Diop‐Kane, 2017). According to Kafando et al (2008), the energy associated with the initiation of these waves in the region is twice higher in the wet than dry seasons and is highly correlated with cloudiness and rainfall in the wet season.…”

Upward and downward atmospheric Kelvin waves over the Indian Ocean

“…The plane wave view of tropical waves is sometimes used to explain phenomena like the downward propagation of zonal wind associated with the QBO (Baldwin et al, 2001), and fluctuations of tropopause height (Ryu et al, 2008). Other phenomena may be understood better assuming a radiative condition at the tropopause, for example Halliday et al (2018) conducted simulations for tropospheric gravity waves using the radiative condition by raising the upper boundary of the model; they found a decrease in the overall tropospheric response (in vertical wind), which might be more realistic than when the gravity waves are trapped in the troposphere. Chumakova et al (2013) constructed a hydrostatic, non-rotating model that simulates a leaky, a rigid, and a transparent tropopause.…”

“…Other phenomena may be understood better assuming a radiative condition at the tropopause, for example Halliday et al . (2018) conducted simulations for tropospheric gravity waves using the radiative condition by raising the upper boundary of the model; they found a decrease in the overall tropospheric response (in vertical wind), which might be more realistic than when the gravity waves are trapped in the troposphere. Chumakova et al .…”

On the Spectra of Gravity Waves Generated by Two Typical Convective Systems

“…Common sources that initiate gravity waves in the atmosphere include, but are not limited to, topography, convection, wind shear, jet-front systems, and wave-wave interactions [7,8]. Of these, moist convection is considered one of the most important sources of non-stationary gravity waves [9,10]. However, convection-induced waves are still not well understood.…”