A Joint Probability Density–Based Decomposition of Turbulence in the Atmospheric Boundary Layer

Abstract

In convective flows, vertical turbulent fluxes, covariances between vertical velocity and scalar thermodynamic variables, include contributions from local mixing and large-scale coherent motions, such as updrafts and downdrafts. The relative contribution of these motions to the covariance is important in turbulence parameterizations. However, the flux partition is challenging, especially in regions without convective cloud. A method to decompose the vertical flux based on the corresponding joint probability density function (JPD) is introduced. The JPD-based method partitions the full JPD into a joint Gaussian part and the complement, which represent the local mixing and the large-scale coherent motions, respectively. The coherent part can be further divided into updraft and downdraft parts based on the sign of vertical velocity. The flow decomposition is independent of water condensate (cloud) and can be applied in cloud-free convection, the subcloud layer, and stratiform cloud regions. The method is applied to large-eddy simulation model data of three boundary layers. The results are compared with traditional cloud and cloud-core decompositions and a decaying scalar conditional sampling method. The JPD-based method includes a single free parameter and sensitivity tests show weak dependence on the parameter values. The results of the JPD-based method are somewhat similar to the cloud-core and conditional sampling methods. However, differences in the relative magnitude of the flux decomposition terms suggest that an objective definition of the flow regions is subtle and diagnosed flow properties like updraft characteristics depend on the sampling method. Moreover, the flux decomposition depends on the thermodynamic variable and convection characteristics.

Object‐Oriented Identification of Coherent Structures in Large Eddy Simulations: Importance of Downdrafts in Stratocumulus

“…This study focuses on the diurnal cycle of marine stratocumulus using the FIRE framework (Duynkerke et al, ) in an LES run by the Meso‐NH model. At nighttime, we confirm the importance of downdrafts in carrying heat and moisture within the boundary layer (Davini et al, ; Chinita et al, ). At daytime, solar heating and boundary layer decoupling strengthen updraft transport and weaken cloud top entrainment.…”

“…The object contribution to domain‐averaged moisture vertical fluxes is important at both daytime and nighttime, and the relative updraft/downdraft contributions are maximum below/above 350 m, respectively. Nighttime vertical relative coverage of coherent structures and its flux partitioning between updraft and downdraft are in agreement with Chinita et al ().…”

“…However, identifying these structures is often case specific and based on statistical clustering (Raupach, 1981) related to vertical velocity (e.g., Nicholls, 1989;Schumann & Moeng, 1991), conservative variables (e.g., Berg & Stull, 2004), and/or passive tracers (e.g., Couvreux et al, 2010;Park et al, 2016). Recently, some studies analyzed these structures in stratocumulus simulations using various classifications (e.g., Yamaguchi & Randall, 2012;Chinita et al, 2018). Specifically, the octant classification used in Davini et al (2017) highlights that updrafts, downdrafts, and cloud top entrainment contribute significantly to the stratocumulus-topped boundary layer turbulent transport of mass, heat, and moisture.…”

Turbulence Structure in a Stratocumulus Cloud

“…Kopec et al [35] compare the sign of mean and median of www and conclude that strong but narrow updrafts are present in the cloud. The profiles of updraft and downdraft area fractions and the decomposition of covariances for the present case are discussed in [36].…”

“…The joint probability density functions (JPD) of the two conserved thermodynamic variables and θ v , i.e., the buoyancy variable, versus vertical velocity are used to gain a fuller picture of the flow. Moreover, probability density functions are often used in modeling, e.g., [36,[51][52][53][54][55]. [36] using data from all grid cells at the corresponding model level.…”