A dual mass flux scheme for A dual mass flux scheme for shallow cumulus convectionshallow cumulus convection

Results for GCSS RICO Results for GCSS RICO

Roel Neggers, Martin Köhler, Anton Beljaars

ContentsThe DualM scheme

An extension to EDMF for shallow cumulus convection

A *VERY* short overview (more on Thursday) RICO results

Mean state

Equilibration

Updraft profiles & fluxes Variances

Cloudy state & precipitation

Experiments with an entrainment efficiency closure for cumulus

Eddy diffusivity - mass flux (EDMF) decomposition for turbulent transport

The current PBL scheme (cy30r1)

upupKK wawaw ´´´´´´ },{ tl q Siebesma et al. (Submitted to JAS)

Currently applied to dry PBL and stratocumulus topped PBL only

Goal: upgrade EDMF to enable representation of i) shallow cumulus convection ii) transitions What is needed?

KmoistupdraftK

dry updraft

zKwa

KK

´´ )(´´ upupup Mwa

The dual mass flux scheme – main EDMF upgrades

Moist updrafts

Flexible area partitioning

aup

Dry updrafts

K diffusion

a1up a2

up

h

z0

1 - aup

I. Multiple updrafts

N

i

upi

upi

upi

upup wawa1

)(´´

N=2: dry updrafts stopping at cloud base, moist updrafts continuing as cumulus clouds.

II. Flexible updraft area fractions

Closure as a function of model stateFacilitates representation of i) gradual regime transitions, ii) coupling of cumuli to mixed layer

III. Extension of EDMF partitioning into the statistical cloud scheme

A matching bimodal PDF (passive clouds and updraft clouds) Consistent treatment of PBL transport and cloudiness

IV. Top-entrainment efficiency closures for cumulus

V. … and many more …

Explicit treatment of transport across strong unresolved gradients ( cu inversion, transition layer)

Flexible updraft area fractions facilitate representation of gradual regime transitions

E

LCL

h

LCL

h

LCL E E

M2 M1

Stratocumulus Shallow cumulus Dry convection

M1

M2

a2

a1

Moist and dry updrafts can co-exist at any time

Closure of the flexible updraft area fractions

Explicit representation of the coupling between cumulus updrafts and mixed-layer

III. Vertical integration of updraft budgets then reconstructs the joint-PDF

I. First guess of cloud core fraction at cloud base, using local variance scaling

II. These fractions are subsequently used in surface initialization of updrafts

Knowledge of how many updrafts manage to reach LFC is `back-stitched` into the partitioning and initialization of the updrafts

This carries information on cloud base transition layer properties

RICO results – mean state

RICO results – cloudy state

DualM

cy30r1

RICO results - equilibration

waM

The flexibility of a and its closure introduce a valve mechanism in M, always acting to equilibrate the mixed layer budgets

Area fraction is retained in the updraft mass flux

Mwwth

LSe

RICO results - updrafts

Lateral entrainment closure makes differently initialized updrafts diverge with height.

w 1

RICO results - fluxes

LES

RICO results – variance IUsed in statistical cloud scheme

RICO results – variance II

qt

l

Updraft PDF

Diffusive PDF

Lewellen & Yoh (JAS,1993)

)( )(

222222 KKKupupup

KKupup

aa

aa

Extension of EDMF into the modelling of clouds – a bimodal distribution

Relations between moments

RICO results – variance II

Closure of updraft variance

RICO results – bimodal clouds

Passive clouds

Updraft clouds

RICO results - precipitation

RICO results - precipitationHow important is it?

RICO BOMEX

RICO results – entrainment efficiency experiments

RICO ATEX

Wyant et al. (1997)

All flux into cu inversion is explicitly modelled through the K-component of EDMF

Summary

A shallow cumulus extension is formulated for EDMFA shallow cumulus extension is formulated for EDMF

More complexity is added to the system of equations, in various new ways:More complexity is added to the system of equations, in various new ways: - multiple transporting updrafts - multiple transporting updrafts - flexible updraft area fractions - flexible updraft area fractions - EDMF partitioning is extended into the PBL cloud scheme (a bimodal PDF) - EDMF partitioning is extended into the PBL cloud scheme (a bimodal PDF)

Assuming flexible updraft area fractions facilitates representation of gradualAssuming flexible updraft area fractions facilitates representation of gradual regime transitions regime transitions

Closure of the updraft area fractions allows explicit representation of the couplingClosure of the updraft area fractions allows explicit representation of the coupling between cumuli and the mixed layer, introducing a valve mechanism in the between cumuli and the mixed layer, introducing a valve mechanism in the cumulus mass flux cumulus mass flux

The mean, turbulent and cloud structure of the RICO short composite case isThe mean, turbulent and cloud structure of the RICO short composite case is reproduced reproduced

Precipitation appears to be an important player in the SCM thermodynamic budgetsPrecipitation appears to be an important player in the SCM thermodynamic budgets

A more detailed discussion of model physics on Thursday…A more detailed discussion of model physics on Thursday…