The 'effective buoyancy' of an accelerating parcel is its Archimedean buoyancy B minus an offset, due to the parcel having to push some of the environmental fluid out of its way. This offset grows with parcel aspect ratio, so that wider parcels (at fixed height) accelerate less. Through a novel correspondence with the equations of magnetostatics, we find exact analytical expressions for this offset for idealized parcels with uniform B, and show that these expressions also apply to turbulent, heterogenous parcels (figure left). These expressions describe the `virtual mass' effect for fluid parcels, as well as the compensating subsidence in their environment. See Tarshish et al. (2018) for complete details.
An earlier approach to some of these questions, which emphasizes how this offset of B is enhanced when parcels are near the surface, can be found in Jeevanjee and Romps (2016). An application of these ideas to understanding how simulated convection depends on model grid spacing is given in "Vertical Velocity in the Gray Zone", Jeevanjee (2017), discussed below.
Vertical Velocity in the Gray Zone
Increasing computer power allows global atmospheric models to be run in a `gray zone' of horizontal resolution which permits but does not fully resolve convection. It is unclear where this gray zone ends, however, and how it is affected by the oft-employed hydrostatic approximation. We address these questions using GFDL's flagship FV3 dynamical core, running simulations across the gray zone both with and without the hydrostatic approximation. We find that horizontal resolutions of approximately 100 m are required for convective vertical velocities wc to converge, and that the hydrostatic approximation over-estimates wc at these resolutions by a factor of 2 - 3 (see figure right). These behaviors of wc can be described by simple analytical formulae, which also map out how wc behaves throughout the gray zone.
Climate Model Hierarchies
Inspired by the WCRP's recent Model Hierarchies Workshop, we attempted to survey and synthesize some of the current thinking on climate model hierarchies. We give a few formal descriptions of the hierarchy (see figure below), and survey its various uses. We also discuss some of the pitfalls of contemporary climate modeling, and to what extent the `elegance' advocated for by Held (2005) has been used to address them. See Jeevanjee et. al. (2017) for more.
Effective Buoyancy, Inertial Pressure, and Convective Triggering
The other force besides effective buoyancy acting on convecting parcels is the inertial (or dynamic) pressure force. In tropical deep convection, most new convection is generated on the edges of 'cold pools' of air produced by evaporation of rain from existing convection. (A large cold pool is visible in the B field in the figure to the right, and the triggered convection along its edge is visible in the w field). It had long been thought that inertial pressure was responsible for this triggering, but the results of Tompkins (2001) suggested that effective buoyancy might also contribute. We helped settle this question by numerically solving the Poisson equations for both effective buoyancy and inertial acceleration in a simulation of tropical convection, showing that indeed the inertial acceleration dominates (bottom row of figure).
See Jeevanjee and Romps (2015) for details.
Simulations of tropical convection can spontaneously develop large-scale circulations even in the absence of any large-scale forcing, in a phenomenon known as "self-aggregation". This large-scale circulation partitions the atmosphere into moist and dry regions, as can be seen in the individual panels to the left. Such self-aggregation had previously only been seen in simulations with a domain larger than ~ 300 km on a side, but by disabling cold pools in our simulation, we obtained aggregation at all domain sizes (see figure).
See Jeevanjee and Romps (2013) for details.