Integral Scales for the Nocturnal Boundary Layer. Part 1: Empirical Depth Relationships

Abstract

The stable-layer thickness h and near-surface potential temperature strength ??s, of the nocturnal boundary layer (NBL) are shown to have a ?background? square-root of time dependence. Superimposed upon this background are other time variations caused by changes in bulk turbulence parameter B and average surface heat flux Q?H: h = 5(?Q?HtB)&frac12 and &minus??s = (?Q?HtB?1)&frac12). As an intentionally different approach to the NBL problem B is modeled in terms of forcings external to the NBL rather than in terms of internal variables such as friction velocity or Obukhov length. Nocturnal boundary layer observations from the Wangara and Koorin field experiments in Australia are used to guide some dimensional arguments to yield B ? (?GUG?1)(|fUG|Zs)3/2/(?QHg), where UG is the geostrophic wind vector, f the Coriolis parameter, g the acceleration due to gravity, Zs is a site and wind-direction-dependent empirical parameter and the overbear indicates time-average since transition (near sunset). Apparently, Zs is a measure of the influence of terrain features such as roughness and slope on NBL development. The resulting model is shown to be adaptable to frost-warning and air-quality applications.