FLUXES AND GRADIENTS IN THE CONVECTIVE SURFACE LAYER AND THE POSSIBLE ROLE OF BOUNDARY-LAYER DEPTH AND ENTRAINMENT FLUX G. J. STEENEVELD*, A. A. M. HOLTSLAG and H. A. R. DEBRUIN Meteorology and Air Quality, Wageningen University, Duivendaal 2, 6701 AP Wageningen, The Netherlands (Received in final form 2 June 2004) Abstract. We study the relation between fluxes and gradients in the very unstable surface layer by comparing recent proposals in the literature with the well-known Businger–Dyer functions. The recent proposals include results from large-eddy simulation (LES), which account for entrainment effects and effects of the boundary-layer depth. A comparison of the relationships is made with experimental data. The LES-based gradient functions show the impact of entrainment in the surface layer, but the scatter in the field data is too large to confirm this. Therefore this result is preliminary and future tests against new observations are recom- mended. It appears that the Businger–Dyer relationship behaves differently to the alternatives, and that it deviates from observations for large stability. Keywords: Entrainment, Free convection, Similarity theory, Surface-layer gradient functions. 1. Introduction Businger et al. (1971) published their famous flux–profile relationships based on turbulent flux and vertical profile observations above prairie grassland over horizontal homogeneous terrain in Kansas, U.S.A. After some adap- tations, these relationships are now known as the Businger–Dyer relations (see Dyer, 1974; Businger, 1988; Ho¨gstro¨m, 1988, and for an heuristic deri- vation, Fleagle and Businger, 1980) that read as / h ¼ / 2 m ¼ 1  16 z L   1=2 ð1Þ in which / h and / m are dimensionless gradients of temperature and wind speed, z the height above the surface, and L the Obukhov length. The Kansas experiment in 1968 was set up to verify the Monin–Obukhov similarity theory (MOST), a theory that is based on the assumption that in the atmospheric surface layer (ASL) z and L are the only relevant turbulent length scales. Consequently, according to MOST, the height of the convective boundary layer (CBL), h, does not play a role in the ASL (e.g. Holtslag and Nieuwstadt, 1986). Moreover, the Kansas dataset was confined to conditions * E-mail: gert-jan.steeneveld@wur.nl Boundary-Layer Meteorology (2005) 116:237–252 Ó Springer 2005 DOI 10.1007/s10546-004-2730-7