“…First-order closure is based on diagnostic flux gradient relations, i.e., the fluxes are represented by the downgradient approach, eventually semi-empirically corrected for countergradient flows. For the eddy diffusivity of scalars one can either use an ad hoc approach (e.g., O'Brien, 1970), diagnostic relations based on diagnostic flux equations (Holtslag and Moeng, 1991;Holtslag et al, 1995) or semi-empirical expressions based on the turbulence spectrum, such as proposed and evaluated, e.g., by Degrazia et al (1997aDegrazia et al ( ,b, 1998Degrazia et al ( , 2001 the flow characteristics, e.g., on atmospheric stability (see Subsection 5.1). However, the present approach opens a suitable way to investigate turbulence-related NPF.…”