Theoretical expressions for the ascent rate of moist deep convective thermals

The article of record as published may be found at http://dx.doi.org/10.1175/JAS-D-17-0295.1An approximate analytic expression is derived for the ratio, λ, of the ascent rate of moist deep convective thermals and the maximum vertical velocity within them. λ is characterized as a function of two non-dimensional buoyancy-dependent parameters y and h, and is used to express the thermal ascent rate as a function of the buoyancy field. The parameter y characterizes the vertical distribution of buoyancy within the thermal, and h is the ratio of the vertically integrated buoyancy from the surface to the thermal top and the vertical integral of buoyancy within the thermal. Theoretical λ values are calculated using values of y and h obtained from idealized numerical simulations of ascending moist updrafts and compared to λ computed directly from the simulations. The theoretical values of λ ≈ 0.4 to 0.8 are in reasonable agreement with the simulated λ (correlation coefficient of 0.86). These values are notably larger than the λ = 0.4 from Hill's (non-buoyant) analytic spherical vortex, which has been used previously as a framework for understanding the dynamics of moist convective thermals. The relatively large values of λ are a result of net positive buoyancy within the upper part of thermals that opposes the downward-directed dynamic pressure gradient force below the thermal top. These results suggest that non-zero buoyancy within moist convective thermals, relative to their environment, fundamentally alters the relationship between the maximum vertical velocity and the thermal top ascent rate compared to non-buoyant vortices. Implications for convection parameterizations and interpretation of the forces contributing to thermal drag are discussed