Parameterisation of
Cumulus Convection
COSMO-CLM Training Course, Langen, Germany, 14 -17 February 2012
Dmitrii V. Mironov
German Weather Service, Research and Development, FE14, Offenbach am Main, Germany
dmitrii.mironov@dwd.de
Outline
•
Cumulus convection and the need for
parameterisations
•
Convection parameterisation schemes
•
Mass-flux schemes
•
The COSMO-model convection parameterisation
scheme(s)
Phenomenology
P B L
Deep Cumulus (ITCZ) Shallow Cumulus (Trade winds) Stratus, stratocumulus (Sub-tropics)A great variety
of convective clouds
Phenomenology (cont’d)
StratusCumulus Broken stratocumulus
Phenomenology (cont’d)
Cumulus Stratocumulus
Phenomenology (cont’d)
Phenomenology (cont’d)
The Need for a Parameterisation
Convection is a sub-grid scale phenomenon.
It cannot be explicitly computed (resolved)
by an atmospheric model. Hence, it should be
parameterised.
∆
y
∆
x
Recall ... what a convection parameterisation should do
(it is not a mystery, it is just a model)
Transport equation for a generic quantity X
( )
x
i
i
i
i
S
x
X
u
x
X
u
t
X
+
∂
′
′
∂
−
=
∂
∂
+
∂
∂
...
SGS flux divergence Source termsSplitting of the SGS flux divergence and of the source term
( )
other
x
conv
x
other
i
i
conv
i
i
i
i
S
S
x
X
u
x
X
u
x
X
u
t
X
+
+
∂
′
′
∂
−
∂
′
′
∂
−
=
∂
∂
+
∂
∂
...
What a convection parameterisation should do (cont’d)
Temperature and specific-humidity equations
Here, L is the specific heat of vaporisation, e is the rate of evaporation,
and c is the rate of condensation.
( )
scale grid conv rad i i turb i i conv i i i iL
c
e
L
c
e
x
R
x
T
u
x
T
u
x
T
u
t
T
−−
+
−
+
∂
∂
−
∂
′
′
∂
−
∂
′
′
∂
−
=
∂
∂
+
∂
∂
)
(
)
(
( )
scale grid conv turb i i conv i i i ie
c
e
c
x
q
u
x
q
u
x
q
u
t
q
−−
+
−
+
∂
′
′
∂
−
∂
′
′
∂
−
=
∂
∂
+
∂
∂
)
(
)
(
Apart from mixing (redistribution of heat and moisture),
convection produces precipitation
Convection Parameterisation 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;
Mass-Flux Schemes. Basic Features
A triple top-hat decomposition
,
1
,
+
+
=
+
+
=
a
u
X
u
a
d
X
d
a
e
X
e
a
u
a
d
a
e
X
“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
.
)
(
)
(
)
(
)
(
,
u u d d e e e e d d u uX
P
X
P
X
P
X
P
X
X
P
X
X
P
X
X
P
X
=
+
+
′
=
δ
′
−
+
δ
′
−
+
δ
′
−
),
(
)
(
)
(
)
)(
(
)
)(
(
)
)(
(
X
X
M
X
X
M
X
X
M
X
X
w
w
a
X
X
w
w
a
X
X
w
w
a
X
w
e e d d u u e e e d d d u u u−
+
−
+
−
=
−
−
+
−
−
+
−
−
=
′
′
ρ
ρ
ρ
ρ
is the updraught mass flux (similarly for the downdraught and for the environment).
)
(
w
w
a
Mass-Flux Schemes. Basic Features (cont’d)
A top-hat representation of a fluctuating quantity
After M. Köhler (2005) Updraught Environment Only coherent top-hat part of the signal is accounted for
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),
.
1
1
,
<<
<<
=
u d eX
a
and
a
X
Assumption 2: convection is in a quasi-steady state,
(
)
0
.
,
0
=
∂
∂
+
∂
∂
=
∂
∂
+
∂
∂
u u ua
X
z
w
t
a
z
w
t
Then, vertical flux of a fluctuating quantity X in mass-flux approximation is given by
[
M
X
M
X
M
M
X
]
X
w
′
′
=
1
u u+
d d−
(
u+
d)
Mass-Flux Schemes. Basic Features (cont’d)
The equations for convective updraughts
(
)
(
)
(
)
,
,
,
,
p u u u u u u u u u u u u u u u u u u u uG
c
l
D
z
l
M
c
q
D
q
E
z
q
M
c
L
s
D
s
E
z
s
M
D
E
z
M
ρ
ρ
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 Parameterisation 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=1.
Kain and Fritsch (1990) mass-flux scheme,
optional in COSMO-EU.
•
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 ECMWF-IFS scheme (Bechtold 2010) is implemented into GME (c/o Kristina
Fröhlich); this option (
itype_conv=2
) is not yet available in the COSMO model
(Peter Brockhaus et al., Ulrich Schättler).
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 , εand δbeing 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
The Tiedtke (1989) Mass-Flux Convection Scheme (cont’d)
Moisture convergence in the sub-cloud layer
Turbulent detrainment of cloud air Turbulent entrainment of environment air
Organised detrainment of cloud air
Evaporation of precipitation in the sub-cloud layer Organised entrainment of
environment 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 parameterisation schemes of the
COSMO model
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 scales
Convective precipitation:
model vs. observations
Possible double counting due
to the assumption a
u<<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 scales (cont’d)
SON 2007 DJF 2007-2008
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 scales (cont’d)
JJA 2009
SON 2008 DJF 2008-2009
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 scales (cont’d)
DJF 2009-2010
JJA 2010 SON 2009
Possible double-counting of energy-containing scales (cont’d)
DJF 2010-2011 SON 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.
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 2010)
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 24 0 0.2 0.4 0.6 0.8 1 1.2
local time (h)
p
re
c
ip
it
a
ti
o
n
(
m
m
/h
)
Diurnal cycle of precipitation in the Rondônia area in February. GME forecasts vs. LBA 1999 observational data (Silva Dias et al. 2002). The model curves show area-mean values, empirical curve shows point measurements. Both numerical and empirical curves represent monthly-mean values.
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 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 interaction between “turbulent” and “convective” mixing, no resolution sensitivity
of convective mixing
Coupling of convection scheme with other parameterisation 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
Outlook
•
Existing convection schemes is difficult to improve ... However, a
better coupling of cumulus convection scheme with other
parameterisation schemes of the COSMO model should be attempted
Longer term prospects
•
Relax crucial assumptions of the existing mass-flux schemes (no
time-rate-of-change terms, small area fraction of convective clouds);
the model of Lappen and Randall (2001) holds promise
•
Achieve a unified description of shallow-convection and turbulence
(see Mironov 2009, for discussion)
•
EU COST Action ES0905 “Basic Concepts for Convection
Parameterization in Weather Forecast and Climate Models”
(http://convection.zmaw.de)
References
•
Arakawa, A., 2004: The cumulus parameterization problem: past, present, and future. J. Climate, 17, 2493-2525.•
Bechtold, P., 2010: Atmospheric moist convection. ECMWF Lecture Notes, 77 pp. (http://www.ecmwf.int/newsevents/training/lecture_notes/LN_PA.html)•
Emanuel, K. A., 1994: Atmospheric Convection. Oxford Univ. Press, Oxford, 580 pp.•
Fedorovich, E., R. Rotunno, and B. Stevens (Eds.), 2004: Atmospheric Turbulence and MesoscaleMeteorology. 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 WeatherPrediction 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 CumulusConvection. Meteorological Training Course, Lecture Series, European Centre for Medium-Range
References (cont’d)
• Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the 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 and global 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 simulation of 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-precipitating cumulus 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 effects of 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 characteristics and 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 convective parameterization. J. Atmos. Sci., 47, 2784-2802.
• Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for mesoscale models: the Kain-Fritsch scheme. The
Representation 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 through latent 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. Weather
COSMO-CLM Training Course, Langen, Germany, 14 -17 February 2012
Geändertes Tiedtke-Konvektionsschema
Wasser-Eis Mischung existiert im 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 Konvektion wird 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 scales (cont’d)
JJA 2007
SON 2006 DJF 2006-2007
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 scales (cont’d)
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 scales (cont’d)
JJA 2008 JJA 2007
In JJA 2008
Mod
<
Obs
?
(*) Changes were introduced into the T89 scheme in July 2008. (*) Summer 2008 was dry.
