## 1. Introduction

[2] The atmospheric boundary layer is the region of the atmosphere closest to the surface of the Earth and directly impacted by the surface fluxes of momentum, sensible heat, water vapor, and several gases of interest in air pollution and biogeochemical studies [*Brutsaert*, 1982; *Stull*, 1988; *Garratt*, 1994; *Seinfeld and Pandis*, 1998]. Therefore, the connection between the ABL features and the regional, or basin-wide, surface fluxes is evident: understanding the ABL is essential for identifying the relevant scales of most hydrological problems; to decide which processes to represent explicitly, and which to parameterize, and more generally for improving our hydrological models, as made clear by *Brutsaert* [1986].

[3] Most of the time, the ABL is turbulent, particularly in the case of the convective, daytime boundary layer, when the surface fluxes are largest. Then, prompted by the practical needs of hydrology, one is naturally drawn into studying ABL turbulence, a situation not unlike many other cases where engineering demands motivated the advancement of fluid mechanics. The archetypal flow is the turbulent boundary layer (originally studied for pipes and channels, see, e.g., *Darrigol* [2005]), which not only gives the name to the ABL but is the starting point for many concepts that prove fruitful also for atmospheric turbulence.

[4] As it happens with many researchers, the approaches used by Wilfried Brutsaert and his collaborators to a better understanding of atmospheric turbulence that we will be reviewing here follow many of the early paths taken by fluid dynamicists to study turbulent flows. At the same time, however, they added substantial improvements as these approaches needed adaptation to the particularities of the ABL: its inherent nonstationarity, the surface geometry imposed by nature, the surface spatial inhomogeneities, the effects of buoyancy, and many other facets, all required a concerted effort to adapt, and sometimes create, the concepts needed to model ABL turbulence.

[5] The focus of the present work is atmospheric turbulence itself. Thus, in section 2, we review the results derived from semi-emipircal, or K-theory, for the behavior of surfaces ranging from evaporating pans to natural lakes, as well as insights on the form of the turbulent diffusivity tensor itself. In section 3, we review contributions to the parameterization of scalar mass and heat-transfer coefficients with the identification of scalar roughnesses different from those for momentum. Section 4 gives a brief overview of results concerning the relative importance and direct dissipative effects of longwave radiation in ABL turbulence. Section 5 deals with results for the stable surface layer and section 6 with the important issue of how different the turbulent transport characteristics of two scalars are. In a sense, this is a development of the ideas started with the so-called Reynolds' analogy [*Reynolds*, 1900] to the study of turbulent transfer of different scalars. Section 7 then deals with results for the convective boundary layer and its interface with the top of the surface layer where local free convective conditions prevail. They are also related to drag, mass, and heat transfer equations for turbulent flow in pipes and channels, as well as by the matching techniques developed for the turbulent boundary layer, starting with *Milikan* [1938]. Some brief concluding remarks are given in section 8.