Abstract
We use dimensional analysis and direct numerical simulations to characterize specific humidity statistics in the equilibrium (quasi‐steady) entrainment regime of cloud‐free convective boundary layers that grow into linearly stratified free atmospheres. The first three moments and the mean vertical flux are studied for arbitrary combinations of free‐atmosphere lapse‐rates and surface fluxes of buoyancy and specific humidity. First, we find the combination of these parameters that distinguishes between the entrainment‐drying regime and the surface‐moistening regime. We also provide a zero‐order model describing both regimes. Second, we parametrize the variances in the mixed layer and in the entrainment zone separately, based on convective and entrainment‐zone scales, respectively. We show that the large variances in the entrainment zone are not only due to large production rates, but also due to low dissipation rates. Third, we provide the skewness for any regime between the pure drying limit and the pure moistening limit. The variation of the skewness indicates that knowing the sign of the skewness near the surface is often insufficient to distinguish between drying and moistening regimes, in contrast to previous conjectures. In a more general context, this paper further supports the applicability of direct numerical simulations to investigate the atmospheric boundary layer, as inferred from the degree of Reynolds number similarity observed in the results and from the consistency of the derived parametrizations with field measurements.
Highlights
Surface processes and cloud formation critically depend on the moisture field in the planetary boundary layer
We have learned to distinguish between drying and moistening regimes depending on the ratio between entrainment and surface fluxes, we have learned that the variance of the specific humidity peaks in the entrainment zone, and we have learned that dry air from the free atmosphere can penetrate deep into the boundary layer, which favours a negative skewness of the specific humidity in most of the mixed layer (e.g. Deardorff, 1974; Mahrt, 1991; Couvreux et al, 2007; Turner et al, 2014; Wulfmeyer et al, 2016, and references therein)
This paper provides these parametrizations for one regime of the planetary boundary layer, namely, the equilibrium entrainment regime of a free convective boundary layer (CBL) that grows into a linearly stratified atmosphere (Fedorovich et al, 2004)
Summary
Surface processes and cloud formation critically depend on the moisture field in the planetary boundary layer. That previous work is mainly based on single-case studies, i.e. particular combinations of surface fluxes and free-atmosphere lapse-rates, and we are still missing the parametrizations that allow us to extrapolate those results, quantitatively, to different meteorological conditions This paper provides these parametrizations for one regime of the planetary boundary layer, namely, the equilibrium (quasi-steady) entrainment regime of a free convective boundary layer (CBL) that grows into a linearly stratified atmosphere (Fedorovich et al, 2004). A complete characterization of the moisture skewness for arbitrary meteorological conditions is still missing We provide it here for a shear-free CBL penetrating into a linearly stratified atmosphere as a function of the surface fluxes and free-atmosphere lapse-rates.
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