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.
Highlights
“gregarious” nature of mesoscale tropical convection cells is Cloud Scheme), but these are principally used to interact with thought to be driven by a low-level rising mode the radiation scheme and do not feed back on to the dynamic, in the vicinity of a convecting storm, which increases the depth thermodynamic and cloud fields at present
Of moisture at low-levels, making conditions more favourable In summary, while current convection schemes hold some for new convective events (Mapes 1993; Fovell et al 1992). information about the subgrid cloud field, they do not use any Momentum and temperature changes, communicated through the subgrid cloud information in the excitation of gravity waves: propagation of convectively generated gravity waves may waves are only forced by the grid-resolved tendencies imposed condition the remote troposphere to convection triggering or by the convection scheme
In current General Circulation Models (GCMs) deep convection is represented as a sub-grid process, and so a theoretical understanding of the way in which convective heating gives rise to tropospheric adjustment is essential
Summary
To obtain quantitative predictions of w and b (and θ) a horizontal variation X(x) and a vertical variation Z(z) must be chosen. The choice of Z(z) is informed by observed heating profiles, which peak in the mid troposphere. With this assumed form for X, the vertical velocity may be determined straightforwardly from (9) and (16). The simplest possible representation of the tropospheric and stratospheric stratification is cn =. We seek the corresponding free modes φn(z) and wavespeeds cn from (7), which yields a solution. The solutions (25) and (26) must be matched at the tropopause, z = Ht, by applying continuity of φn and dφn/dz, yielding an equation for cn: kn kn′.
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