Sampling the Structure of Convective Turbulence and Implications for Grey-Zone Parametrizations

Abstract

The grey zone of dry convection is the range of scales in which boundary-layer thermals are partly explicitly resolved by numerical weather prediction (NWP) models and partly parametrized. We seek to determine how thermals are divided into subgrid and resolved scales in the grey zone of convective boundary-layer thermals. Reference data for grid-scale and subgrid-scale fields at these resolutions are constructed by filtering 62.5-m large-eddy simulation data. A conditional sampling is adapted to detect subgrid thermals, and is used to characterize the subgrid thermals at several grid spacings in the grey zone. A mass-flux parametrization used in NWP models is compared with the subgrid thermal field. The analysis demonstrates that, although the mass-flux framework is suitable in the grey zone, some assumptions of the mass-flux schemes, usually used at the mesoscale, cannot be made in the grey zone. In particular, the thermal fraction is not small, the resolved vertical velocity is not negligible, the entrainment and detrainment rates depend on the horizontal resolution, the triggering and the closure at the surface are moreover random.

Appendix 1 Notations used in this article

${\mathbb {D}}$	Domain size
${\mathbb {J}}$	LES domain of one ${\varDelta }x$-grid cell
${\varDelta }x$	Horizontal grid spacing
z	Altitude
h	Boundary-layer height
$L_{O}$	Obukhov lenght
${h}_{c}$	Depth of the cloud layer
sv	Tracer concentration
w	Vertical velocity
q	Total water mixing ratio
$\theta _v$	Virtual potential temperature
$\theta _l$	Liquid potential temperature
g	Standard gravitational acceleration
$\rho$	Volumic mass of the air
${\alpha }$	Fraction of a grid cell covered by convective thermal, LES field not depending on ${\varDelta }x$
i	LES-grid cell number
j	${\varDelta }x$-Grid cell number
$\phi$	A thermodynamical variable
${\phi _i}$	$\phi$ of the $\text {i}\text {th}$ cell of a LES grid
${\phi _j}$	$\phi$ of the $\text {j}\text {th}$ cell of ${\varDelta }x$ grid spacing
${\alpha _u}_i$	Grid cell covered by convective subgrid thermal, LES field depending on ${\varDelta }x$
${{\phi _u}_i}$	$\alpha _u\times \phi$ of the $\text {i}\mathrm{th}$ cell of the LES
$<\phi >$	Average value of $\phi$ over the whole horizontal domain
$\overline{\phi }$	Average value of $\phi$ (reference resolved value of $\phi$) over a cell of ${\varDelta }x$ Grid spacing
N	Number of LES cell at one level
$N_j$	Number of LES cell in a ${\mathbb {J}}$ domain
${N_u}_j$	Number of LES cell occupied by a subgrid thermal in a cell of ${\varDelta }x$ Horizontal resolution
$M_u$	Mass Flux
$B_u$	Buoyancy inside the updraft
E	Entrainment term
D	Detrainment term
$\epsilon$	Entrainment rate
$\delta$	Detrainment rate
$\textit{H}_{\textit{0}v}$	Averaged surface buoyancy flux
$\textit{E}_{\textit{0}}$	Averaged surface humidity flux
$w_{*}$	Averaged convective velocity scale computed at ground level
$u_{*}$	Averaged friction velocity computed at ground level