Shallow Moist Convection • Basic Moist Thermodynamics • Remarkable Features of Moist Convection • Shallow Cumulus • (Stratocumulus) Courtesy: Dave Stevens
Large scale advection Large scale subsidence Vertical turbulent transport Net Condensation Rate Grid Averaged Budget Equations
Schematically: • Objectives • Understand Moist Convection…. • Design Models….. • But ultimately design parameterizations of:
Moist Conserved Variables qv:Specific Humidity (g/kg) Condensation occurs if qvexceeds the saturation value qs(T,p) Usually through rising motion ql:Liquid Water (g/kg) qt = qv + ql :Total water specific humidity (Conserved for phase changes!!)
Used Temperature Variables • Potential Temperature • Conserved for dry adiabatic changes • Liquid Water Potential Temperature • Conserved for moist adiabatic changes Energy equivalent: • Liquid Water Static Energy • Virtual Potential Temperature • Directly proportional to the density • Measure for buoyancy
Grid averaged equations for moist conserved variables: Parametrization issue reduced to a convective mixing problem!
z z T(K) A saturated ascending parcel will conserve hl : Moist Adiabatic Lapse Rate Leads to a moist adiabatic lapse rate : Remarks: • Example: T=290K,p=1000mb • Temperature decrease less than for dry parcels • Difference between and becomes progressively smaller for lower temperatures Q (K)
sounding z zo Tv(K) Absolute Instability • Lift a (un)saturated parcel from a sounding at z0 by dz • Check on buoyancy with respect to a mean profile: Example 1: Unstable for saturated and unsaturated parcels Absolute Unstable
sounding zo Tv(K) Absolute Stability • Lift a (un)saturated parcel from a sounding at z0 by dz • Check on buoyancy with respect to the sounding: Example 2: Stable for saturated and unsaturated parcels Absolute stable
sounding z zo Tv(K) Conditional Instability • Lift a (un)saturated parcel from a sounding at z0 by dz • Check on buoyancy with respect to the sounding: Example 2: Stable for unsaturated parcels Unstable for saturated parcels Conditionally Unstable!!!
Mean profile “Level of zero kinetic energy” Inversion Level of neutral buoyancy (LNB) conditionally unstable layer height Level of free convection (LFC) Lifting condensation level (LCL) well mixed layer The Miraculous Consequences of conditional Instability or: the “Cinderalla Effect” (Bjorn Stevens)
CIN Non-local integrated stability funcions: CAPE, CIN Define a work function: LNB CAPE Positive part: CAPE = Convective Available Potential Energy. z1 Negative part: z0 CIN = Convection Inhibition CIN allows the accumulation of CAPE
CAPE and CIN: An Analogue with Chemistry • 1) Large Scale Forcing: • Horizontal Advection • Vertical Advection (subs) • Radiation Activation (triggering) LS-forcing Surf Flux CIN 2) Large Scale Forcing: slowly builds up CAPE CAPE Free Energy • 3) CAPE • Consumed by moist convection • Transformed in Kinetic Energy • Heating due to latent heat release (as measured by the precipitation) • Fast Process!! RAD LS-forcing Mixed Layer LFC LNB Parcel Height Free after Brian Mapes
Quasi-Equilibrium LS-Forcing that slowly builds up slowly The convective process that stabilizes environment Quasi-equilibrium: near-balance is maintained even when F is varying with time, i.e. cloud ensemble follows the Forcing. Forfilled if : tadj << tF Used convection closure (explicit or implicit) JMb ~ CAPE/ tadj tadj : hours to a day. wu au Mb=au wur :Amount of convective vertical motion at cloud base (in an ensemble sense)
Quasi-Equilibrium: An Earthly Analogue Free after Dave Randall: • Think of CAPE as the length of the grass • Forcing as an irrigation system • Convective clouds as sheep • Quasi-equilibrium: Sheep eat grass no matter how quickly it grows, so the grass is allways short. • Precipitation………..
Typical Tradewind Cumulus Strong horizontal variability !
Horizontal Variability and Correlation Mean profile height
Schematic picture of cumulus moist convection: • Cumulus convection: • more intermittant • more organized • than • Dry Convection.
a a a Mass flux concept: tomorrow more!! wc
Shallow Cumulus Convection Photo courtesy Bjorn Stevens
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
adiabat Mixing between Clouds and Environment (SCMS Florida 1995) Due to entraiment! Data provided by: S. Rodts, Delft University, thesis available from:http://www.phys.uu.nl/~www.imau/ShalCumDyn/Rodts.html
adiabat Liquid water potential temperature Total water (ql+qv) • Entrainment Influences: • Vertical transport • Cloud top height
hc 4.1 lateral mixing bulkmodel Fractional entrainment rate
Diagnose through conditional sampling: Typical Tradewind Cumulus Case (BOMEX) Data from LES: Pseudo Observations
Trade wind cumulus: BOMEX LES Observations Cumulus over Florida: SCMS Siebesma JAS 2003
Adopted in cloud parameterizations: Lateral mixing Horizontal or vertical mixing? Cloud-top mixing Observations (e.g. Jensen 1985) However: cloud top mixing needs substantial adiabatic cores within the clouds.
adiabat (SCMS Florida 1995) No substantial adiabatic cores (>100m) found during SCMS except near cloud base. (Gerber) Does not completely justify the entraining plume model but……… It does disqualify a substantial number of other cloud mixing models.
Cloudtop Cloudtop entrainment Entrance level Lateral entrainment Inflow from subcloud Measurement level Cloudbase Cloudtop Backtracing particles in LES: where does the air in the cloud come from? Courtesy Thijs Heus
Height vs. Source level Virtually all cloudy air comes from below the observational level!!
No observations of turbulent fluxes. • Use Large Eddy Simulation (LES) • based on observations BOMEX ship array (1969) observed observed To be modeled by LES
10 different LES models • Initial profiles • Large scale forcings prescribed • 6 hours of simulation Is LES capable of reproducing the steady state?
Mean profiles after 6 hours • Use the last 4 simulation hours for analysis of …….
How is the steady state achieved? forcing forcing rad turb turb c-e c-e
Turbulent Fluxes of and Subcloud layer looks similar than dry PBL!!
Turbulent Fluxes of the conserved variables qt and ql Cloud layer looks like a enormous entrainment layer!!
Vertical Velocity in the cloud and the total vertical velocity variance Dry PBL velocity variance profile
Conditional Sampling of: • Total water qt • Liquid water potential temperature ql
Bjorn Stevens accepted for JAS Non-precipating cumulus Shallow Cumulus Growth, (an idealized view) Extension from the dry PBL growth, but now….. Adding Moisture dry cloudy