Abstract
Abstract Two zero-order bulk models (ZOMs) are developed for the velocity, buoyancy, and moisture of a cloud-free barotropic convective boundary layer (CBL) that grows into a linearly stratified atmosphere. The models differ in the entrainment closure assumption: in the first one, termed the “energetics-based model,” the negative and positive areas of the buoyancy flux are assumed to match between the model and the actual CBL; in the second one, termed the “geometric-based model,” the modeled CBL depth is assumed to match different definitions of the actual CBL depth. Parameterizations for these properties derived from direct numerical simulation (DNS) are employed as entrainment closure equations. These parameterizations, and hence the resulting models, are free from the potential singularity at finite wind strength that has been a major limitation in previous bulk models. The proposed ZOMs are verified using the DNS data. Model results show that the CBL depths obtained from the energetics-based model and previous ZOMs correspond to the height that marks the transition from the lower to the upper entrainment-zone sublayer; this reference height is few hundred meters above the height of the minimum buoyancy flux. It is also argued that ZOMs, despite their simplicity compared to higher-order models, can accurately represent CBL bulk properties when the relevant features of the actual entrainment zone are considered in the entrainment closures. The vertical structure of the actual entrainment zone, if required, can be constructed a posteriori using the available relationships between the predicted zero-order CBL depth and various definitions of the actual CBL depth.
Highlights
Bulk, or integral, models of a convective boundary layer (CBL) have been developed over the last few decades to parameterize bulk properties such as the CBL depth, the inversion strength, and the entrainment fluxes in atmospheric models whose grid spacings are much larger than the dynamically relevant scales of CBLs (Haltiner and Williams 1980; Suarez et al 1983; Ayotte et al 1996)
The work presented here focuses on the entrainment closure and is motivated by challenges identified in previous work, namely, the lack of agreement on the minimum complexity of the bulk model that is necessary to accurately represent sheared CBLs (Pino et al 2006; Liu et al 2016) and a singularity in the entrainment closure that can appear at finite wind strength (Driedonks 1982; Conzemius and Fedorovich 2004; Liu et al 2018)
We show that the infinitesimal transition-layer representation of the zero-order bulk models (ZOMs) is sufficient to precisely reproduce bulk properties in the cloud-free sheared CBL, as long as the entrainment closure appropriately represents the local effects of wind shear on entrainment
Summary
Integral, models of a convective boundary layer (CBL) have been developed over the last few decades to parameterize bulk properties such as the CBL depth, the inversion strength, and the entrainment fluxes in atmospheric models whose grid spacings are much larger than the dynamically relevant scales of CBLs (Haltiner and Williams 1980; Suarez et al 1983; Ayotte et al 1996). Previous entrainment parameterizations suffer from a potential singularity at finite wind strength, which is a major long-standing limitation of previous zero-order and first-order models (Driedonks 1982; Conzemius and Fedorovich 2004; Liu et al 2018) This singularity arises when the entrainment parameterization is derived in the idealized framework of the bulk models and the CBL depth is used in the scaling of the shear production at the CBL top in the local TKE approach (see, e.g., Tennekes and Driedonks 1981), or is used in the scaling of the integral of the negative buoyancy flux in the integral TKE approach (see, e.g., Boers et al 1984).
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