Grell-Freitas scheme

Grell-Freitas descends from the Grell-Devenyi ensemble approach and adds the feature it is known for: scale awareness. The parameterised convective mass flux is scaled by the fraction of the grid cell a convective updraft would occupy, so as grid spacing decreases toward convection-permitting resolution, the scheme progressively hands responsibility to the resolved dynamics.

This addresses a genuine gap. Conventional cumulus parameterisations assume the grid cell is large compared with a convective cell, so that the sub-grid convective area is small and the cell contains many updrafts. At 12 km that assumption is defensible. At 4 km a single updraft may occupy a substantial fraction of the cell, and the scheme’s foundational assumption has quietly failed while the scheme keeps producing tendencies as though it had not.

The grey zone problem it targets

Between roughly 4 and 10 km, neither approach is correct. Parameterising convection violates the scale-separation assumption; resolving it is not possible at that spacing. The usual responses are to pick a side and accept the error, or to avoid the range entirely by jumping from 12 km to 3 km.

Grell-Freitas instead makes the parameterisation’s contribution a continuous function of resolution. At coarse spacing it behaves like a conventional mass-flux scheme; as spacing decreases, the parameterised flux is progressively reduced and the resolved flow takes over. In principle this gives a smooth transition rather than a discontinuity, which is exactly what a nested configuration spanning several resolutions needs — otherwise the same physics behaves inconsistently across domains, and differences between nests reflect the parameterisation switch as much as the resolution change.

Honest limits

The scaling function is a plausible construction, not a derived result. It assumes the resolved dynamics take up precisely the work the parameterisation gives up, and there is no guarantee the handover is clean — a partially resolved updraft plus a partially parameterised one is not obviously equivalent to either.

Scale awareness also does not make the grey zone a good place to run. It makes the scheme’s behaviour there defensible rather than arbitrary. The underlying difficulty, that convection is marginally resolved and the turbulence scheme is outside its own valid range at the same time, is untouched by anything the convection scheme does.

For nested setups spanning coarse to near-permitting resolutions I would use it. For a single-domain run comfortably in the parameterised regime, its advantage over a well-tested conventional scheme is small.

See also: Grell-Devenyi for the ensemble ancestor, convection-permitting modeling for the other side of the transition, cumulus convection schemes, and stochastically perturbed parameter schemes.