Surface Schemes

A surface-layer scheme computes the turbulent fluxes of heat, moisture, and momentum between the surface and the lowest model level. It sits between the land-surface model, which knows the state of the ground, and the boundary-layer scheme, which mixes whatever the surface delivers through the depth above it.

Almost all such schemes rest on Monin-Obukhov similarity theory, which states that in the surface layer, non-dimensionalised gradients of wind and temperature are universal functions of a single stability parameter. That reduces the flux calculation to evaluating empirical stability functions and a pair of roughness lengths. It is a compact and remarkably durable piece of theory.

Where the assumptions bite

Monin-Obukhov similarity assumes horizontal homogeneity, stationarity, and a well-defined constant-flux layer. Real surfaces frequently violate all three, and the violations are not evenly distributed:

• Stable conditions. At night, particularly over snow or in light winds, turbulence becomes intermittent and may decouple from the surface entirely. Similarity theory has no representation for this, and stability functions have to be limited artificially to stop fluxes collapsing to zero. Nocturnal near-surface temperature errors in regional models very often originate here rather than in the land surface.
• Heterogeneous surfaces. A grid cell containing forest, field, and lake has no single roughness length or surface temperature. Schemes either use effective parameters or tile the surface and average the fluxes — and the two give different answers, because the flux relationships are nonlinear.
• Roughness lengths. Momentum and heat roughness lengths differ, often by an order of magnitude, and their ratio is poorly constrained. This is one of the more consequential tuning knobs in a model and is rarely discussed as such.

Why the small scheme matters disproportionately

The variables people actually consume — 2 m temperature, 10 m wind, near-surface humidity — are not prognostic. They are diagnosed by the surface-layer scheme, interpolating between the surface and the lowest model level using the same similarity functions. A model can have a defensible boundary layer and still report a poor 2 m temperature, purely through the diagnostic relation.

This is worth knowing before attributing a near-surface bias to the land surface or the boundary layer. In my WRF work the surface-layer scheme has more often been implicated in nocturnal near-surface errors than either of the components it sits between, and it is the last place people look.

See also: Monin-Obukhov similarity for the theory, land-surface models for what supplies the surface state, PBL schemes for what consumes the fluxes, and the model physics map.