Shallow Moist Convection
•Basic Moist Thermodynamics
•Remarkable Features of Moist Convection
•Shallow Cumulus
•(Stratocumulus)
Courtesy: Dave Stevens
Basic Moist Thermodynamics
Large scaleLarge scale
advectionadvection
Large scaleLarge scale
subsidencesubsidence
VerticalturbulenttransportVerticalturbulenttransport
NetCondensationRateNetCondensationRate
Grid Averaged Budget Equations
Schematically:
Objectives
•Understand Moist Convection….
•Design Models…..
•But ultimately design parameterizations of:
qv:Specific Humidity (g/kg)
Condensation occurs if qv exceeds the saturation value qs(T,p)
Usually through rising motion
ql:Liquid Water (g/kg)
Moist Conserved Variables
qt = qv + ql :Total water specific humidity
(Conserved for phase changes!!)
•Potential Temperature
•Conserved for dry adiabatic changes
•Virtual Potential Temperature
•Directly proportional to the density
•Measure for buoyancy
•Liquid Water Potential Temperature
•Conserved for moist adiabatic changes
Used Temperature Variables
Energy equivalent:
•Liquid Water Static Energy
Grid averaged equations for moist conserved variables:
Parametrization issue reduced to aconvective mixing problem!
A Unique Feature of Moist Convection
Moist Adiabatic Lapse Rate
A saturated ascending parcel will conserve hl :
Leads to a moist adiabatic lapse rate :
•Example: T=290K,p=1000mb
•Temperature decrease less than for dry parcels
•Difference between and becomes progressively smaller for lower temperatures
Remarks:
z
(K)
T(K)
z
Absolute Instability
•Lift a (un)saturated parcel from a sounding at z0 by dz
•Check on buoyancy with respect to a mean profile:
Tv(K)
z
zo
sounding
Unstable for saturated and unsaturated parcels
Example 1:
Absolute Unstable
Absolute Stability
•Lift a (un)saturated parcel from a sounding at z0 by dz
•Check on buoyancy with respect to the sounding:
Stable for saturated and unsaturated parcels
Example 2:
Tv(K)
zo
sounding
Absolute stable
Conditional Instability
•Lift a (un)saturated parcel from a sounding at z0 by dz
•Check on buoyancy with respect to the sounding:
Stable for unsaturated parcels
Unstable for saturated parcels
Example 2:
Conditionally Unstable!!!
Tv(K)
z
zo
sounding
Lifting condensation level (LCL)
Level of free convection (LFC)
Level of neutral buoyancy (LNB)
“Level of zero kinetic energy”
Mean profile
height
well mixed layer
Inversion
conditionally
unstable
layer
The Miraculous Consequences of conditional Instability
or: the “Cinderalla Effect” (Bjorn Stevens)
CIN
Non-local integrated stability funcions: CAPE, CINNon-local integrated stability funcions: CAPE, CIN
CAPE = Convective Available Potential Energy.
CAPE
z0
LNB
z1
Define a work function:
Positive part:
CIN = Convection Inhibition
Negative part:
CIN allows the accumulation of CAPE
CAPE and CIN: An Analogue with ChemistryCAPE and CIN: An Analogue with Chemistry
Free
Energy
Surf Flux
Mixed Layer
CAPE
CIN
Activation (triggering)
LS-forcing
LS-forcing
RAD
LFC
LNB
Parcel Height
1) Large ScaleForcing:
• Horizontal Advection
• Vertical Advection(subs)
• Radiation
2) Large ScaleForcing:
slowly builds up CAPE
3) CAPE
•Consumed by moistconvection
• Transformed in KineticEnergy
•Heating due to latentheat release (asmeasured by theprecipitation)
•Fast Process!!
Free after Brian Mapes
Quasi-EquilibriumQuasi-Equilibrium
au
wu
Mb=au wu Amount of convective vertical motion at cloud base (in an ensemble sense)
The convective process that stabilizesenvironment
LS-Forcing that slowly builds up slowly
Quasi-equilibrium: near-balance is maintained even when F isvarying with time, i.e. cloud ensemble follows the Forcing.
Forfilled if :adj << F
Used convection closure (explicit or implicit) JMb ~ CAPE/ adj
adj : hours to a day.
Quasi-Equilibrium: An Earthly AnalogueQuasi-Equilibrium: An Earthly Analogue
•Think of CAPE as the length of the grass
•Forcing as an irrigation system
•Convective clouds as sheep
•Quasi-equilibrium: Sheep eat grass nomatter how quickly it grows, so the grass isallways short.
•Precipitation………..
Free after Dave Randall:
Typical Tradewind Cumulus
Strong horizontal variability !
Mean profile
height
Horizontal Variability and Correlation
•Schematic picture of cumulus moist convection:
Cumulus convection:
1.more intermittant
2.more organized
than
Dry Convection.
a
wc
a
a
Mass flux concept: tomorrow more!!
Photo courtesy Bjorn Stevens
Shallow Cumulus Convection
Observational Characteristics : Trade wind shallow Cu
non well-mixed cloud layer
Surface heat-flux: ~10W/m^2
Surface Latent heat flux : 150~200W/m^2
Data provided by: S. Rodts, Delft University, thesis availablefrom:http://www.phys.uu.nl/~www.imau/ShalCumDyn/Rodts.html
Mixing between Clouds and Environment
(SCMS Florida 1995)
adiabat
Due to entraiment!
Liquid water potential temperature
Total water (ql+qv)
Entrainment Influences:
1.Vertical transport
2.Cloud top height
adiabat
The simplest Cloud MixingModel
Typical Tradewind Cumulus Case (BOMEX)
Data from LES: Pseudo Observations
Diagnose
through conditional sampling:
Trade wind cumulus: BOMEX
LES
Observations
Cumulus over Florida: SCMS
Siebesma JAS 2003
Horizontal or vertical mixing?
Lateral
mixing
Adopted in cloud parameterizations:
Cloud-top
mixing
Observations
(e.g. Jensen 1985)
However: cloud top mixing needssubstantial adiabatic cores within the clouds.
adiabat
(SCMS Florida 1995)
No substantial adiabaticcores (>100m) foundduring SCMS except nearcloud base. (Gerber)
Does not completelyjustify the entrainingplume model but………
It does disqualify asubstantial number ofother cloud mixing models.
May 16, 2007
Backtracing particles in LES: where does the air inthe cloud come from?
Entrance level
Cloudtop
Cloudbase
Cloudtop
Measurement level
Lateral entrainment
Cloudtop entrainment
Inflow from subcloud
Courtesy Thijs Heus
May 16, 2007
Height vs. Source level
Virtually all cloudy air comes from below theobservational level!!
5.Dynamics, Fluxes and otherstuff that can’t be measuredaccurately
BOMEX ship array (1969)
•No observations of turbulent fluxes.
•Use Large Eddy Simulation (LES)
based on observations
•No observations of turbulent fluxes.
•Use Large Eddy Simulation (LES)
based on observations
observed
observed
To be modeled by LES
•10 different LES models
•Initial profiles
•Large scale forcings prescribed
•6 hours of simulation
•10 different LES models
•Initial profiles
•Large scale forcings prescribed
•6 hours of simulation
Is LES capable ofreproducing the steady state?
Is LES capable ofreproducing the steady state?
•Large Scale Forcings
•Large Scale Forcings
•Mean profiles after 6 hours
•Mean profiles after 6 hours
•Use the last 4 simulation hours for analysis of …….
•Use the last 4 simulation hours for analysis of …….
To do analyses of the dynamics using theLES results
How is the steady state achieved?
c-e
c-e
turb
turb
forcing
forcing
rad
How is the steady state achieved?
•Cloud cover
•Cloud cover
•Turbulent Fluxes of and
•Turbulent Fluxes of and
Subcloud layer looks similar than dry PBL!!
•Turbulent Fluxes of the conservedvariables qt and l
•Turbulent Fluxes of the conservedvariables qt and l
Cloud layer looks like a enormous entrainment layer!!
Dry PBL velocity variance profile
Vertical Velocity in the cloud and the total vertical velocity variance
Conditional Sampling of:
•Total water qt
•Liquid water potential temperature l
Conditional Sampling of:
•Total water qt
•Liquid water potential temperature l
Shallow Cumulus Growth, (an idealized view)
Extension from the dry PBL growth, but now…..
Adding Moisture
Bjorn Stevens accepted for JAS
Non-precipating cumulus
dry
cloudy
Temporal Evolution
Temporal Evolution
dry pbl growth
cloud base height
cloud top height
condensation
evaporation
Energetics
Stabilisation of Cloud Base (1)
Mass flux
Growth through dry top-entrainment
Negative in the presense of subsidence
Mass leaking out of PBL through clouds
Stabilisation of Cloud Base height (2)
Pbl-height
cloud top height
Bjorn Stevens (accepted JAS)
Many Parameterization of Shallow Cu still give poor results
Role of Precipitation
Mesoscale-Organisation
Momentum Transport