Shallow Moist Convection Basic Moist Thermodynamics Remarkable Features of Moist Convection Shallow Cumulus (Stratocumulus) Courtesy: Dave Stevens

Basic Moist Thermodynamics

Large scale advection subsidence Vertical turbulent transport Net Condensation Rate Grid Averaged Budget Equations

Schematically: Objectives Understand Moist Convection…. Design Models….. But ultimately design parameterizations of:

q v :Specific Humidity (g/kg) Condensation occurs if q v exceeds the saturation value q s (T,p) Usually through rising motion q l :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 a convective mixing problem !

A Unique Feature of Moist Convection

Moist Adiabatic Lapse Rate A saturated ascending parcel will conserve h l : 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: T v (K) z zozo 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: T v (K) zozo 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!!! T v (K) z zozo 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, CIN CAPE = Convective Available Potential Energy. CAPE z0z0 LNB z1z1 Define a work function : Positive part: CIN = Convection Inhibition Negative part: CIN allows the accumulation of CAPE

CAPE and CIN: An Analogue with Chemistry Free Energy Surf Flux Mixed Layer CAPE CIN Activation (triggering) LS-forcing RAD LFCLNB Parcel Height 1) Large Scale Forcing: Horizontal Advection Vertical Advection (subs) Radiation 2) Large Scale Forcing: slowly builds up CAPE 3) CAPE Consumed by moist convection Transformed in Kinetic Energy Heating due to latent heat release (as measured by the precipitation) Fast Process!! Free after Brian Mapes

Quasi-Equilibrium auau wuwu M b =a u w u  Amount of convective vertical motion at cloud base (in an ensemble sense) The convective process that stabilizes environment LS-Forcing that slowly builds up slowly Quasi-equilibrium: near-balance is maintained even when F is varying with time, i.e. cloud ensemble follows the Forcing. Forfilled if :  adj <<  F Used convection closure (explicit or implicit) JM b ~ CAPE/  adj  adj : hours to a day.

Quasi-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 no matter how quickly it grows, so the grass is allways 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 wcwc 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 available from: 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 adiab at

The simplest Cloud Mixing Model

4.1 lateral mixing bulk modelbulk hchc Fractional entrainment rate

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 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.

May 16, 2007 Backtracing particles in LES: where does the air in the 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 the observational level!!

5.Dynamics, Fluxes and other stuff that can’t be measured accurately

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 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 of reproducing the steady state?

Large Scale Forcings

Mean profiles after 6 hours Use the last 4 simulation hours for analysis of …….

To do analyses of the dynamics using the LES results

How is the steady state achieved? c-e turb forcing rad

How is the steady state achieved?

Cloud cover

Turbulent Fluxes of and Subcloud layer looks similar than dry PBL!!

Turbulent Fluxes of the conserved variables 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

Virtual potential temperature:  v

Cloud Liquid water

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

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