Kain-Fritsch cumulus potential scheme

KF-CuP is a modification of the Kain-Fritsch scheme that replaces the trigger function. Instead of deriving the parcel temperature perturbation from resolved grid-scale vertical velocity, it uses a probability density function of boundary-layer thermals — the cumulus potential approach — so that triggering depends on the turbulence statistics of the boundary layer the convection would actually rise out of.

The motivation is the failure mode standard Kain-Fritsch is known for. Basing the trigger on grid-scale vertical motion means convection fires when the resolved flow happens to be rising, which in practice is too early and too often. Boundary-layer thermals are what really initiate convection, and they are a sub-grid quantity that a PBL scheme already carries information about. KF-CuP uses it.

What changes as a result

Timing. Because the trigger now depends on boundary-layer development rather than resolved ascent, convection tends to initiate later and closer to observed timing. This is the main reason to choose it.

Cumulus cloud fraction. KF-CuP diagnoses a convective cloud fraction from the same distribution, with separate timescales for shallow and deep cumulus. Standard Kain-Fritsch leaves this to the host model, often crudely. Having a cloud fraction consistent with the scheme’s own convective activity means radiation sees something coherent with the convection producing it — which closes one of the more common sources of energy-budget inconsistency in WRF configurations.

Coupling to the PBL scheme. This is the trade-off. The trigger now depends on the boundary-layer scheme’s turbulence statistics, so KF-CuP inherits that scheme’s biases. It is no longer a self-contained convection choice, and swapping the PBL scheme changes convective behaviour through a path that is not obvious from either scheme’s documentation.

In practice

I would reach for it where the diurnal cycle of convective rainfall matters — which, for tropical and subtropical regional work, is most of the time — and where the shallow-cumulus cloud fraction is likely to affect the surface energy budget. The cost over standard Kain-Fritsch is minor.

The caveat is that it is less widely used and correspondingly less thoroughly tested across regions and configurations. Where standard Kain-Fritsch’s biases are at least well characterised and predictable, KF-CuP’s are less documented, and that is a real consideration for a long simulation you do not intend to revisit.

See also: the original scheme, cumulus convection schemes, convective cloud fraction, and PBL schemes it now depends on.