A Theory for Buoyancy and Velocity Scales in Deep Moist Convection

Abstract

Buoyancy and velocity scales for dry convection in statistical equilibrium were derived in the early twentieth century by Prandtl, but the scaling of convective velocity and buoyancy, as well as the fractional area coverage of convective clouds, is still unresolved for moist convection.In this paper, high-resolution simulations of an atmosphere in radiative-convective equilibrium are performed using the Weather Research and Forecasting (WRF) model, a three-dimensional, nonhydrostatic, convection-resolving, limited-area model. The velocity and buoyancy scales for moist convection in statistical equilibrium are characterized by prescribing different constant cooling rates to the system.It is shown that the spatiotemporal properties of deep moist convection and buoyancy and velocity scales at equilibrium depend on the terminal velocity of raindrops and a hypothesis is developed to explain this behavior. This hypothesis is evaluated and discussed in the context of the numerical results provided by the WRF model. The influence of domain size on radiative-convective equilibrium statistics is also assessed. The dependence of finescale spatiotemporal properties of convective structures on numerical and physical details is investigated.

Increases in moist‐convective updraught velocities with warming in radiative‐convective equilibrium

“…The sensitivity to fall speed is largest at the highest SST; the 99.99th percentile of vertical velocity increases from roughly 10 to 12 m s −1 at pressure levels near 600 hPa (∼ 5 km) as the fall speed is increased from 1 to 8 m s −1 . This sensitivity to fall speed is smaller than found in the simulations of Parodi and Emanuel (2009). Preliminary investigations indicate that a larger effect of hydrometeor fall speed is found when a simpler, warm-rain microphysics scheme is employed, as was the case in Parodi and Emanuel (2009), and this may be the cause of the discrepancy.…”

“…This sensitivity to fall speed is smaller than found in the simulations of Parodi and Emanuel (2009). Preliminary investigations indicate that a larger effect of hydrometeor fall speed is found when a simpler, warm-rain microphysics scheme is employed, as was the case in Parodi and Emanuel (2009), and this may be the cause of the discrepancy.…”

“…This insensitivity to fall speeds is in contrast to the results of Parodi and Emanuel (2009), possibly because here we focus on the effect of changes in temperature and because the microphysics scheme we use includes frozen species.…”

“…However, Parodi and Emanuel (2009) found that the fall speed of hydrometeors plays a large role in determining updraft velocities in simulations of RCE. We investigate the effect of hydrometeor fall speed on updraft velocities by conducting additional RCE simulations in which we fix the fall speed of all hydrometeors to a constant value regardless of their size or type.…”

Large‐scale length and time‐scales for use with stochastic convective parametrization

“…Various CRM studies (e.g. Robe and Emanuel, 1996;Shutts and Gray, 1999;Cohen, 2001;Parodi and Emanuel, 2009) have shown that the strength of the forcing seems to have only a weak effect on the mean mass flux of individual clouds: rather, a change in forcing is associated mainly with a change in the mean number of clouds N . A recent CRM investigation by Davies and Jakob (2011, pers.…”