Complex turbulent exchange coefficient in Akerblom–Ekman model

Abstract

Abstract The turbulent exchange in boundary layer models is usually characterized by a scalar eddy viscosity coefficient assumed to be a positive function of the vertical variable. We introduce a more general form for the turbulence exchange description, which includes two functions that describe the turbulence without any assumption about their positivity. We construct a model of the Akerblom–Ekman type, but with a complex coefficient of turbulent exchange. The basic quality criterion for these models and algorithms is the maximal agreement with meteorological observations. We optimize the agreement between the global meteorological archive of high-resolution wind observations that are provided by World Meteorological Organization (WMO) in Binary Universal Form for the Representation (BUFR). The main result of our work is that agreement between model solutions and observations will be much better if the turbulent exchange coefficient is optimized in the space of all complex-valued functions, and not limited to the cone of real positive functions.