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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
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.
Phenomenology (cont’d)
Cumulus
Stratocumulus
Berlin-St. Petersburg, 28 August 2007.
Phenomenology (cont’d)
Supercell near Alvo, Nebraska, USA, 13 June 2004. (http://www.extremeinstability.com)
Phenomenology (cont’d)
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
Precipitation over Germany, September 2009 through August 2010.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)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
Precipitation over Germany, September 2010 through August 2011.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)DJF 2011-2012SON 2011
MAM 2012 JJA 2012
Precipitation over Germany, September 2011 through August 2012.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)SON 2012 DJF 2012-2013
MAM 2013 JJA 2013
Precipitation over Germany, September 2012 through August 2013.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)SON 2013 DJF 2013-2014
JJA 2014MAM 2014
Precipitation over Germany, September 2013 through August 2014.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)DJF 2014-2015
JJA 2015MAM 2015
Precipitation over Germany, September 2014 through August 2015.COSMO-EU (ca. 7 km mesh size) vs. observations. Lines - total precipitation, hatched areas - convective precipitation.
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
Precipitation over Germany, September 2006 through August 2007.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 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.
Possible double-counting of energy-containing scale s (cont’d)
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.
Possible double-counting of energy-containing scale s (cont’d)
JJA 2008JJA 2007
In JJA 2008 Mod < Obs?
(*) Changes were introduced into the T89 scheme in July 2008.
(*) Summer 2008 was dry.