T

qsat(T)

qt .(T,qt)

Statistical cloud scheme

•Determine cloud cover and liquid water using the sub-grid variability:

Go over to one variable:

s

satt qqtQ

For a certain PDF, cloud cover and liquid water can be written as a function of just one variable:

Main Problem: How to determine s?

(for simplicity: )2'2

ts q

s

satt Tpqqt

),(

sqt-qsat(p,T)

How to parameterize variance?

Link it to convection/turbulence schemes using a variance budget:

21t

tt q

z

qqw

2*)( tcloud

cut

tcut q

l

w

z

qqqM

z

ql

w

qqMq t

cloudcut

cut

t

*

2 )(

Production Dissipation

Lenderink& Siebesma 2000

2't

turb

ttturb q

l

e

z

q

z

qel

Variance due to convection2

22'

z

qlq tturbt

Variance due to turbulence

Variance due to/coupled with turbulence:

2

22'

z

qlq tturbt

Very simple: • = (0.02qs)2 (Lenderink)

Simple: •lturb=40 (Siebesma) •lturb=0.2z for z<900 and 180 for z> 900m (Chaboureau & Bechtold)

Less simple (stability dependent):•lturb from moist CBR (implementation Colin Jones)

Even without convective or turbulent activity (free atmosphere)some variance is needed!

2'tq

Project: Statistical cloud scheme(from simple to complex)

First 1D tests cases (start with BOMEX):

1. Use cloud cover (ac) diagnostically

2. Use ac and ql prognostically

Subsequently 3D

1. Test cases

2. Long time verification

Problems with Hirlam KF convection:

•Intermittent behavior

•Negative buoyant cloud (TV_UPDRAFT < TV_ENVIRONMENT)

•Artificially looking closure for shallow convection

•Mass flux does not decrease (enough) with height

•Results for Bomex are disappointing

•Fundamental problems? (Sander Jonker)

•Code is complex, hard to understand (and slow)

q profile BOMEX with standard Hirlam KF

Some of the adaptations to KF:

•Fractional entrainment/detrainment according to Siebesma (2003)

•Vertical velocity equation (Gregory, 2001)

•More simple and physically appealing closure (Grant, 2001)

Good results with convection and statistical cloud scheme for Bomex

q profile BOMEX with adaptations

Variance BOMEX

LES Hirlam (40 lvls) with modified KF

Cloud cover Bomex

LES Hirlam with modified KF

Our conclusion: It is not appealing to build further developments on the current Hirlam KF code.

Two alternatives:1. KF from Meso-NH2. Latest ECMWF IFS convection code

Peter Bechtold coded 1 and currently works on 2.His advice: Use 2 (performance, speed, use of AROME iscompatible with 2, synergy, etc.)

=> Implement 2 in Hirlam(1D)

Provisional results: Hirlam 1d with new ECMWF convection,old Sundqvist condensation and moist CBR (Colin Jones)