parameterization of cumulus convection · 2018-07-16 · turbulent detrainment of cloud air...

COSMO-CLM-ART Training, Langen, Germany, 23 – 31 March 2015

Parameterization of

Cumulus Convection

Dmitrii V. Mironov

German Weather Service, Research and Development, FE14, Offenbach am Main, Germany

[email protected]

Outline

• Cumulus convection and the need for parameterizations

• Convection parameterization schemes

• Mass-flux schemes

• The COSMO-model convection parameterization scheme(s)

• Critical Issues

Phenomenology

P B L

Deep Cumulus(ITCZ)

Shallow Cumulus(Trade winds)

Stratus, stratocumulus(Sub-tropics)

A great variety of convective clouds

far and wide

Phenomenology (cont’d)

Stratus

Cumulus

Broken stratocumulus

Berlin-St. Petersburg, 28 August 2007.


Cumulus

Stratocumulus

Berlin-St. Petersburg, 28 August 2007.


Supercell near Alvo, Nebraska, USA, 13 June 2004. (http://www.extremeinstability.com)


Supercell off Burliegh, Australia, 31 December 2008. (http://www.sydneystormchasers.com)

The Need for a Parameterization

Convection is a sub-grid scale phenomenon. It cannot be explicitly computed (resolved) by an atmospheric model. Hence, it should be parameterized.

∆ y

∆ x

Recall ... what a convection parameterization shoul d do (it is not a mystery, it is just a model)

Transport equation for a generic quantity X

( )x

i

i

i

i Sx

Xu

x

Xu

t

X +∂

′′∂−=∂

∂+∂∂

...

SGS flux divergence

Source terms

Splitting of the SGS flux divergence and of the source term

( )otherxconvx

otheri

i

convi

i

i

i SSx

Xu

x

Xu

x

Xu

t

X ++∂

′′∂−∂

′′∂−=∂

∂+∂∂

...

What a convection parameterization should do (cont’ d)

Temperature and specific-humidity equations

Here, L is the specific heat of vaporization, e is the rate of evaporation, and c is the rate of condensation.

( )scalegridconv

radi

i

turbi

i

convi

i

i

i ecLecLx

R

x

Tu

x

Tu

x

Tu

t

T−

−+−+∂∂−

∂′′∂−

∂′′∂−=

∂∂+

∂∂

)()(

( )scalegridconv

turbi

i

convi

i

i

i cecex

qu

x

qu

x

qu

t

q−

−+−+∂

′′∂−∂

′′∂−=∂

∂+∂∂

)()(

Apart from mixing (redistribution of heat and moisture), convection produces precipitation

Convection Parameterization Schemes

• Moisture convergence schemes (e.g. Kuo 1965, 1974)

• Convective adjustment schemes (e.g. Betts 1986, Betts and Miller 1986)

• Mass-flux schemes (e.g. Arakawa and Schubert 1974; Bougeault 1985; Tiedtke 1989; Gregory and Rowntree 1990; Kain and Fritsch, 1990, 1993, Kain 2004; Emanuel 2001; Bechtold et al. 2001, 2004, 2013, 2014)

Mass-Flux Schemes. Basic Features

A triple top-hat decomposition

,1, =++++= edueedduu aaaXaXaXaX

“u”, “ d” and “e” refer to the updraught, downdraught and the environment, respectively, and a is the fractional area coverage.

In terms of the probabilities (δ is the Dirac delta function)

Vertical flux of a fluctuating quantity X

.)()()()(, eedduueedduu XXPXXPXXPXPXPXPXPX −′+−′+−′=′++= δδδ

),()()(

))(())(())((

XXMXXMXXM

XXwwaXXwwaXXwwaXw

eedduu

eeeddduuu

−+−+−=−−+−−+−−=′′ ρρρρ

is the updraught mass flux (similarly for downdraught and environment). )( wwaM uuu −= ρ

Mass-Flux Schemes. Basic Features (cont’d)

A top-hat representation of a fluctuating quantity

After M. Köhler (2005)

Updraught

Environment

Convection scheme only deals with the coherent top-hat part of the

signal

Mass-Flux Schemes. Basic Features (cont’d)

Assumption 1: a mean over the environment is equal to to a horizontal mean (over a grid box),

.11, <<<<= due aandaXX

Assumption 2: convection is in a quasi-steady state,

( ) .0,0 =

∂∂+

∂∂=

∂∂+

∂∂

uuu Xaz

wt

az

wt

Then, vertical flux of a fluctuating quantity X in mass-flux approximation is given by

[ ]XMMXMXMXw dudduu )(1 +−+=′′ρ

Mass-Flux Schemes. Basic Features (cont’d)The equations for convective updraughts

( )

( )

( ),

,

,

,

puuuuu

uuuuuu

uuuuuu

uuu

GclDz

lM

cqDqEz

qM

cLsDsEz

sM

DEz

M

ρρ

ρ

ρ

−+−=∂

∂

−−=∂

∂

+−=∂

∂

−=∂

∂

where s is the dry static energy, q is the specific humidity, l is the specific cloud condensate content, Eu

and Du are the rates of mass entrainment and detrainment per unit length, cu is the rate of condensation in the updraughts, and Gp is the rate of conversion from cloud condensate to precipitation.

The COSMO-Model Convection Parameterization Schemes

• Basic Namelist setting: lphys=.TRUE. , lconv=.TRUE.

• Namelist setting: itype_conv=0. Tiedtke (1989) mass-flux scheme, default in COSMO-EU (called every 4th time step, i.e. every 264 s).

• Namelist setting: itype_conv=2. The ECMWF-IFS scheme is implemented into COSMO (and is the default option in ICON); this option is available in COSMO-CLM; work is underway (c/o JochenFörstner) to implement the IFS scheme (Bechtold et al. 2014) into COSMO-NWP.

• Namelist setting: itype_conv=3. Shallow convection scheme [basically, a simplified Tiedtke (1989) scheme that treats shallow non-precipitation convection only and incorporates a number of rather crude assumptions, e.g. on the convection vertical extent], default in COSMO-DE (called every 10th time step, i.e. every 250 s).

The Tiedtke (1989) Mass-Flux Convection Scheme

• A set of ordinary differential equations (in z) for convective updraughts and downdraughts is solved (entraining-detraining plume model)

• Shallow, penetrative and mid-level convection are discriminated

• Turbulent and organised entrainment and detrainment are considered

• Turbulent entrainment and detrainment: Eu=εMu and Du= δMu , ε and δ being constants that are different for different types of convection (similarly for downdraughts)

• Organised entrainment is proportional to the large-scale moisture convergence (div of resolved scale moisture flux) and is applied in the lower part of convective cloud up to the level of strongest vertical ascent

• Organised detrainment is applied above the cloud top, where cloud condensate evaporates instantaneously (since July 2008, detrained cloud condensate is collected and passed to other COSMO-model routines for further processing)

• Convective cloud base and convective cloud top are determined using the parcel method, a test parcel perturbed with respect to its buoyancy originates near the surface

• Updraught mass flux at the cloud base Mb is linked to the sub-cloud layer moisture convergence (div of the SGS and resolved scale moisture fluxes integrated from the surface to the cloud base)

• Downdraught mass flux at the level of free sinking (where the downdraught originates) is proportional to Mb

• No mixed phase – cloud condensate is either water or ice depending on whether the temperature is above or below the freezing point (mixed phase is introduced in July 2008)

• Highly simplified microphysics: Gp∝l (the rate of conversion from cloud condensate to precipitation is proportional to the amount of cloud condensate)

• Evaporation of convective precipitation in the sub-cloud layer is considered

• Finally , convective tendencies in T, q, qc, u and v, and convective precipitation rate are computed

The Tiedtke (1989) Mass-Flux Convection Scheme (con t’d)

Moisture convergence in the sub-cloud layer

Turbulent detrainment of cloud air

Turbulent entrainment of environment air

Organized detrainment of cloud air

Evaporation of precipitation in the sub-cloud layer

Organized entrainment ofenvironment air due to moisture convergence

Conversion of cloud condensate

to precipitation

Assumptions of the T89 scheme are

many and varied!

Critical Issues

• Possible double-counting of energy-containing scales

• Diurnal cycle of convection

• Coupling of cumulus convection scheme with other physical parameterization schemes of the COSMO model

• Resolution issues (convection-resolving vs. convection-permitting, etc.)

• ...

Precipitation over Germany, mean over April 2006.

COSMO-EU(ca. 7 km mesh size) vs. observations.

Lines - total precipitation, hatched areas - convective precipitation.

Convective precipitation

Possible double-counting of energy-containing scale s

Convective precipitation:

modelvs. observations

Possible double counting due to the assumption au<<1

Precipitation over Germany, September 2007 through August 2008.COSMO-EU (ca. 7 km mesh size) vs. observations. Lines - total precipitation, hatched areas - convective precipitation. [Mixed-phase since July 2008.]

Possible double-counting of energy-containing scale s (cont’d)SON 2007 DJF 2007-2008

MAM 2008 JJA 2008Mixed phase introduced

Precipitation over Germany, September 2008 through August 2009.COSMO-EU (ca. 7 km mesh size) vs. observations. Lines - total precipitation, hatched areas - convective precipitation.

Possible double-counting of energy-containing scale s (cont’d)

JJA 2009

SON 2008 DJF 2008-2009

MAM 2009


Possible double-counting of energy-containing scale s (cont’d)DJF 2009-2010

JJA 2010

SON 2009

MAM 2010

Possible double-counting of energy-containing scale s (cont’d)DJF 2010-2011SON 2010

MAM 2011 JJA 2011


Possible double-counting of energy-containing scale s (cont’d)DJF 2011-2012SON 2011

MAM 2012 JJA 2012



MAM 2013 JJA 2013



JJA 2014MAM 2014


Possible double-counting of energy-containing scale s (cont’d)DJF 2014-2015

JJA 2015MAM 2015


SON 2014

Diurnal cycle of convection

Typical daily evolution of surface latent (thick solid line) and sensible (thin solid line) heat flux, and precipitation (dotted line) during a midlatitude or tropical summer day over reasonably humid land (from Bechtold 2013)

Surface latent heat flux

Precipitation

Surface sensible heat flux

Diurnal cycle of convection (cont’d)

Maximum of convective activity (precipitation) closely

follows surface fluxes and occurs too early, possibly due to dX/dt=0 (X being a quantity treated by convection scheme)

0 3 6 9 12 15 18 21 240

0.2

0.4

0.6

0.8

1

1.2

local time (h)

pre

cipi

tatio

n (m

m/h

)

Diurnal cycle of precipitation in the Rondônia area in February. GME forecasts vs. LBA 1999observational data (Silva Dias et al. 2002). The model curves show area-mean values,empirical curve shows point measurements. Both numerical and empirical curves representmonthly-mean values.

Observations

GME

Diurnal cycle of convection: an advance at ECMWFBechtold, P., N. Semane, P. Lopez, J.-P. Chaboureau, A. Beljaars, and N. Bormann, 2014: Representing equilibrium and nonequilibrium convection in large-scale models. J. Atmos. Sci., 71, 734–753. doi: http://dx.doi.org/10.1175/JAS-D-13-0163.1

NEW is much closer to observations

Divergence of SGS fluxes (mixing), fractional cloud cover using

statistical cloud scheme

Turbulence

Cumulus Convection

Divergence of SGS fluxes (mixing), convective precipitation,

fractional cover of convective clouds

SGS Cloud Cover Microphysics

Grid-Scale Saturation Adjustment

Evaporation/condensation using resolved scale quantities

Grid-scale precipitation,resolved scale amount of cloud condensate

No interaction between grid-scale precipitation

and convective precipitation

Fractional cloud cover using relative humidity scheme

Inconsistent treatment of fractional cloud cover, convective cloud cover

is insensitive to mixing rate

No (or inconsistent) interaction between

“turbulent” and “convective” mixing,

no resolution sensitivity of convective mixing

Coupling of convection scheme with other parameteri zation schemes

Although a feedback of evaporation/condensation

due to convection on the resolved scale amount of cloud condensate is now

introduced, a fully consistent treatment is

not yet achieved.

Resolution Issues

Deep convection is not resolved, parameterization is needed

Image © The COMET Program

∆x

∆xDeep convection is resolved, parameterization is not needed

Resolution Issues (cont’d)

Deep convection is “permitted”, do we need a parameterization scheme?

∆x

(i) Keep deep convection parameterization scheme but make it resolution dependent, i.e. the scheme should become less active as the mesh size decreases (e.g. Gerard and Geleyn 2005, Gerard et al. 2009, Gerard 2012, http://convection.zmaw.de for further references).

(ii) Switch off deep convection scheme but use shallow convection scheme (COSMO-DE solution).

(iii) Switch off deep convection scheme and use unified turbulence-shallow convection scheme formulated in the in the language of second-order closure (Machulskaya and Mironov 2013).

IMHO, (iii) is the way to go.

Resolution Issues (cont’d)

Shallow clouds and PBL turbulence are unresolved and should be parameterized.

∆x

PBL

Image http://en.wikipedia.org/wiki/Weather_lore

Outlook

• Existing convection schemes is difficult to improve ... however, a better coupling of cumulus convection scheme with other parameterization schemes should be attempted

• Careful consideration of the resolution issues is required

• Relax crucial assumptions of the existing mass-flux schemes, e.g. no time-rate-of-change terms, small area fraction of convective clouds (e.g. Grell and Freitas 2014, Lappen and Randall 2001)

• Achieve a unified description of shallow convection and turbulence (e.g. Mironov 2009, Machulskaya and Mironov 2013)

http://convection.zmaw.de (EU COST Action ES0905 “Basic Concepts for Convection Parameterization in Weather Forecast and Climate Models”)

References • Arakawa, A., 2004: The cumulus parameterization problem: past, present, and future. J. Climate, 17, 2493-2525.

• Bechtold, P., 2013: Atmospheric moist convection. ECMWF Lecture Notes, 82 pp. (http://www.ecmwf.int/newsevents/training/lecture_notes/pdf_files/PARAM/Moist_convection_v8_Bechtold.pdf)

• Bechtold, P., N. Semane, P. Lopez, J.-P. Chaboureau, A. Beljaars, and N. Bormann, 2014: Representing equilibrium and nonequilibrium convection in large-scale models. J. Atmos. Sci., 71, 734–753. doi: http://dx.doi.org/10.1175/JAS-D-13-0163.1

• Emanuel, K. A., 1994: Atmospheric Convection. Oxford Univ. Press, Oxford, 580 pp.

• Fedorovich, E., R. Rotunno, and B. Stevens (Eds.), 2004: Atmospheric Turbulence and Mesoscale Meteorology. Cambridge Univ. Press, Cambridge, 280 pp.

• Frank, W. M., 1983: The cumulus parameterization problem. Mon. Weather Rev., 111, 1859-1871.

• Houze, R. A., 1993: Cloud Dynamics. Academic Press, San Diego, etc., 573 pp.

• Mironov, D. V., 2009: Turbulence in the lower troposphere: second-order closure and mass-flux modelling frameworks. Interdisciplinary Aspects of Turbulence, Lect. Notes Phys., 756, W. Hillebrandt and F. Kupka, Eds., Springer-Verlag, Berlin, Heidelberg, 161-221.

• Plant, R. S., 2010: A review of the theoretical basis for bulk mass flux convective parameterization. Atmos. Chem. Phys., 10, 3529–3544.

• Smith, R. K., 2000: The role of cumulus convection in hurricanes and its representation in hurricane models. Rev. Geophys., 38, 465-489.

• Stensrud, D. J., 2007: Parameterization Schemes: Keys to Understanding Numerical Weather Prediction Models. Cambridge Univ. Press, Cambridge, 478 pp.

• Stevens, B., 2005: Atmospheric moist convection. Ann. Rev. Earth Planet. Sci., 33, 605-643.

• Tiedtke, M., 1988: The Parameterization of Moist Processes. Part 2: Parameterization of Cumulus Convection. Meteorological Training Course, Lecture Series, European Centre for Medium-Range Weather Forecasts, Reading, U.K., 78 pp.

References (cont’d)

• Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble withthe large-scale environment, Part I.J.Atmos. Sci., 31, 674-701.

• Bechtold, P., E. Bazile, F. Guichard, P. Mascart, and E. Richard, 2001: A mass-flux convection scheme for regional andglobal models.Quart. J. Roy. Meteorol. Soc., 127, 869-886.

• Bechtold, P., J.-P. Chaboureau, A. Beljaars, A. K. Betts, M. Köhler, M. Miller, and J.-L. Redelsperger, 2004: The simulationof the diurnal cycle of convective precipitation over land in a global model.Quart. J. Roy. Meteorol. Soc., 130, 3119-3137.

• Betts, A. K., 1986: A new convective adjustment scheme. Part I: Observational and theoretical basis. Non-precipitatingcumulus convection and its parameterization.Quart. J. Roy. Meteorol. Soc., 112, 677-691.

• Betts, A. K., and M. J. Miller, 1986: A new convective adjustment scheme. Part II: Single column tests using GATE wave,BOMEX, ATEX and arctic air-mass data sets.Quart. J. Roy. Meteorol. Soc., 112, 693-709.

• Bougeault, P., 1985: A simple parameterization of the large-scale effectsof cumulus convection.Mon. Weather Rev., 113,2108-2121.

• Emanuel, K. A., 2001: A scheme for representing cumulus convection in large-scale models.J. Atmos. Sci., 48, 2313-2335.

• Gregory, D., and P. R. Rowntree, 1990: A mass flux convection scheme with representation of cloud ensemble characteristicsand stability-dependent closure.Mon. Weather Rev., 118, 1483-1506.

• Kain, J. S., 2004: The Kain-Fritsch convection parameterization: an update.J. Appl. Meteorol., 43, 170-181.

• Kain, J. S., and J. M. Fritsch, 1990: A one-dimensional entraining/detraining plume model and its application in convectiveparameterization.J. Atmos. Sci., 47, 2784-2802.

• Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: the Kain-Fritsch scheme.TheRepresentation of Cumulus Convection in Numerical Models, Meteorol. Monogr. No. 24, Amer. Meteor. Soc., 165-170.

• Kuo, H. L., 1965: On formation and intensification of tropical cyclones throughlatent heat release by cumulus convection.J.Atmos. Sci., 22, 40-63.

• Kuo, H. L., 1974: Further studies of the parameterization of the influence of cumulus convection on large-scale flow.J.Atmos. Sci., 31, 1232-1240.

• Tiedtke, M., 1989: A comprehensive mass flux scheme for cumulus parameterization in large-scale models.Mon. WeatherRev., 117, 1779-1800.

Thanks for your attention!

COSMO-CLM-ART Training, Langen, Germany, 23 – 31 March 2015

UNUSED

Geändertes Tiedtke-Konvektionsschema

Wasser-Eis Mischung existiertim Temperaturbereich zwischen 0 C und -23 C

Detrained-Wolkenwasser und Detrained-Wolkeneis werden

als Tendenzen von q_c und q_i den anderen Parametrisierungsschemata

übergeben

Verbesserte Kopplung des Konvektionsschemas

mit den anderen Parametrisierungsschemata

Hochreichende Konvektionwird etwas gebremst



JJA 2007

SON 2006 DJF 2006-2007

MAM 2007

Precipitation over Germany, September 2008 through February 2009.COSMO-EU (ca. 7 km mesh size) vs. observations. Lines - total precipitation, hatched areas - convective precipitation.


SON 2008 DJF 2008-2009

Precipitation over Germany, JJA 2007 versus JJA 2008. COSMO-EU (ca. 7 km mesh size) vs. observations. Lines - total precipitation, hatched areas - convective precipitation.


JJA 2008JJA 2007

In JJA 2008 Mod < Obs?

(*) Changes were introduced into the T89 scheme in July 2008.

(*) Summer 2008 was dry.

parameterization of cumulus convection · 2018-07-16 · turbulent detrainment of cloud air...

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