Kain-Fritsch scheme

Kain-Fritsch is a mass-flux cumulus parameterisation and the most commonly used convection option in WRF. It represents sub-grid deep convection through an idealised updraft-downdraft pair with entrainment and detrainment, and closes the problem by requiring that convection remove most of the available CAPE over a specified adjustment period.

That closure is the scheme in a sentence: if CAPE exists and the trigger fires, convection runs until roughly 90% of the CAPE is consumed. Everything else follows from it.

What it computes

• Mixing ratios for cloud water, rain water, ice, and snow, which it passes to the microphysics and to radiation.
• Shallow convection as well as deep, which matters more than it sounds — shallow convection handles boundary-layer moistening that would otherwise be missing entirely.
• No momentum tendencies. Convective momentum transport is simply absent. For most regional applications this is acceptable; for anything where convective organisation feeds back on the flow, it is a real omission worth knowing about.

The cudt parameter sets the averaging timescale for the vertical velocity used in the trigger.

The trigger function, which is where the trouble lives

Kain-Fritsch initiates convection when a parcel lifted from the source layer, given a temperature perturbation derived from resolved grid-scale vertical velocity, reaches its level of free convection. This makes the trigger sensitive to resolved vertical motion — reasonable in principle, and the source of the scheme’s best-known bias in practice.

The scheme tends to fire too readily, consuming CIN earlier in the day than observations support. The result is the familiar error of rainfall peaking near local noon rather than late afternoon, with rain that falls too often and too weakly. This is not unique to Kain-Fritsch — it is close to universal among CAPE-closure schemes — but Kain-Fritsch is where most people meet it.

The diagnostic I find most reliable is the CAPE time series rather than the precipitation field. A scheme consuming CAPE as fast as the model generates it produces a suspiciously smooth diurnal CAPE curve with no afternoon build-up, and that shows up well before the rainfall bias becomes obvious.

When to use it, and when not

It remains a sound default for coarse regional configurations at 10 km and above, where convection is genuinely sub-grid and a well-tested mass-flux treatment is the right tool. Below roughly 10 km the assumptions weaken, since the scheme presumes the grid cell is large relative to a convective cell. In the 4-10 km grey zone neither parameterising nor resolving convection is defensible, and there is no clean answer. Below 4 km, switch it off and run convection-permitting.

If the diurnal timing matters for your application, check it against observations before trusting the run, and consider KF-CuP, which was developed specifically to address the trigger behaviour.

See also: cumulus convection schemes for the comparison table, KF-CuP for the modified variant, and the model physics map.