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PBL schemes for ICON: CGILS test Martin Köhler (DWD)
• Transport (prognostic) equations for TKE and variances of scalars (<’2> and (<qt’2>) including third-order transport.
• Algebraic (diagnostic) formulations for scalar fluxes, Reynolds-stress components, and turbulence length scale (for speed).
• Statistical SGS cloud scheme, either Gaussian (e.g. Sommeria and Deardorff 1977), or with exponential tail to account for the effect of cumulus clouds (e.g. Bechtold et al. 1995).
• Optionally, prognostic equations for scalar skewness (mass-flux ideas recast in terms of ensemble-mean quantities).
Treatment of Scalar Variances
TKE equation:
22
2
1
2
1wzz
wt
pwuwz
wg
z
vvw
z
uuw
t
ei2
2
1
Scalar-variance equation:
Convection/stable stratification = Potential Energy Kinetic Energy
No reason to prefer one form of energy over the other!
Comparison with One-Equation Models(Draft Horses of Geophysical Turbulence Modelling)
Scalar variance equation:
22
2
1
2
1wzz
wt
Production = Dissipation
Flux equation:
No counter-gradient term
2
gC
zeCw bg
EDMF schemes
EDMF at ECMWFConvective Boundary Layer
dry EDMF theory & SCM
Pier Siebesma & Joao Teixeira 2000, 2007
stratocumulus EDMF & unified implementation
Martin Köhler 2005, 2010
stratocumulus inversion entrainment numerics
Martin Köhler 2008
shallow cumulus DUALM EDMF
Roel Neggers & Martin Köhler 2007-2010
ECMWF operational
EDMF at ECMWF:Stratocumulus
• sl, qt conserved variables
• M surface driven
• cloud top down diffusion
• cloud top entrainment
• cloud scheme: conversion (Beta distr.)
• stability criteria allowing strcu
lqtq
preVOCA: VOCALS at Oct 2006 – Low Cloud
EDMF at ECMWF:Shallow Cumulus DUALM
Neggers, Köhler, Beljaars 2009
Concepts: • multiple updrafts
• mass-flux closure
• entrainment pre-moistening
• bimodal statistical cloud scheme
• cloud overlap
Brian Mapes (~1995 GCSS meeting):Postulates that convection selects favourable environment.
Peter Bechtold (2008):Moist environments yield less entrainment.
Convective premoistening
Brown, Zhang 1997
RH during TOGA/COARE
Moist low levels (~800hPa) favour deep convection
PDF
RH (%)
Derbyshire et al 2004MetO CRM CNRM CRM
MetOffice SCMIFS SCM
Environment RH
RH (%)
mass flux mass flux
• small ε to get high cloud top
• large ε to get large RH sensitivity
Jarecka, Grabowski, Pawlowska, 2009
cloud fraction (grid box)
box
env
RH
RHenvironment
Entrained air is premoistened.
BOMEX LES runentrainment
regime
BOMEX LES cloud blobs
x
t
cloud blob time scalecloud
dt
cloud blob identification from LWP boundaries
WVP
x
y
BOMEX LES cloud blobs
blobs size 1000: (250m)2 · 300s
Time, lagged around blob center, normalized by blob time scale
166 blobs size 1000-10000
shifte
d b
lob m
ean W
VP [
g/m
2]
/ cloudt
100g/m2
40g/m2
2890g/mWVP
prognostic total water variance equation
most moist environment favours shallow convection
decay time-scale outside BL
3 hours
DUALM convective preconditioningMartin Köhler & Olaf Stiller & Thijs Heus