Approximate solutions for the Obukhov length and the surface fluxes in terms of bulk Richardson numbers

Simple analytic approximate solutions are presented for the set of equations that follows from the Monin-Obukhov flux-profile relationships using the stability functions of Dyer (unstable case) and Beljaars-Holtslag (stable case). Several publications are devoted to the same subject, however the current approach contains some new features, namely: (a) it appears to be more accurate for unstable situations and (b) it applies also to the general case where wind speed (u) and potential temperature (theta) are given at different levels. In order to illustrate the accuracy of the approach a comparison with the actual solutions is presented for some selected combinations of theta and u levels typical for various practical applications.