MM5 similarity surface layer scheme

The MM5 similarity scheme computes surface exchange coefficients for momentum, heat, and moisture in WRF. It is inherited from the MM5 model and remains the most widely used surface-layer option, largely because it is well tested and because most PBL schemes were developed against it.

It is a fairly direct implementation of Monin-Obukhov similarity theory, using standard stability functions to relate near-surface gradients to fluxes, with separate roughness lengths for momentum and for scalars.

Why the pairing constraint exists

Surface-layer and PBL schemes are not freely interchangeable in WRF, and the reason is not arbitrary. The PBL scheme consumes surface fluxes and expects them computed with particular conventions — the same friction velocity definition, compatible stability functions, consistent treatment of the lowest model level. The YSU scheme was developed against MM5 similarity and pairs with it as standard.

Using an unsupported combination does not usually produce an error. It produces subtly wrong fluxes, which is worse, because there is nothing to notice.

Where it struggles

The failure modes are inherited from the underlying theory rather than introduced by the implementation, but two are worth naming as practical matters:

Stable conditions. Under strong stability the similarity functions drive exchange coefficients toward zero, which would decouple the surface entirely and let surface temperature fall without limit. The scheme imposes minimum values to prevent this. Those limits are tuning constants, not derived quantities, and they are a substantial part of why nocturnal near-surface temperature bias is among the more persistent errors in regional simulations.

Roughness length for heat. The scheme derives the scalar roughness length from the momentum roughness length through a relation that is empirical and poorly constrained. It has a large effect on surface temperature and is effectively a tuning parameter that is rarely acknowledged as one.

Worth remembering that the 2 m temperature and 10 m wind most people actually use are diagnosed here, interpolated using these same similarity relations. A model can have a reasonable boundary layer and still report poor near-surface values through the diagnostic alone — which makes this the first place I look for a near-surface bias, not the last.

See also: Monin-Obukhov similarity, surface schemes, YSU, and Noah LSM beneath it.