On the role of roughness lengths in flux parameterizations of boundary-layer models

Flux-profile relationships based on surface-layer similarity theory are used to derive relationships between the Monin-Obukhov stability parameter = z/L and the bulk Richardson number Ri _b . In contrast to previous studies, the roughness length for heat, z _0h ,is assumed unequal to the roughness length for momentum, z _0m .For the stable case, an analytic expression of in terms of Ri _b can be derived and in the unstable case, the solution is obtained through a simple iterative process.Errors introduced from the simplification of z _0h = z _0m are evaluated and are shown to be very significant in most cases. Thus, this error in many practical applications may invalidate the intended solution.