Direct Solution of Various Micrometeorological Problems via the Lambert-W Function

Abstract

For a family of relatively common problems in micrometeorology, whose forms previously required iterative or indirect treatment, analytical solution is possible via the Lambert-W function. Use of this function reduces computational time and the need for approximations, while offering a clearer view of the character and solution of such problems. This note provides a generalized form for such problems, and demonstrates its use for three applications: internal boundary-layer growth due to a change in surface roughness; flow displacement over a canopy; and determination of friction velocity and roughness length over the sea.