1 Dry Convection Phenomenology, Simulation and Parameterization of Atmospheric Convection Pier Siebesma Yesterday: “Dry” Atmospheric Convection Today: “Moist” Convection and (shallow cumulus) clouds

2 Dry Convection 1.Motivation 2. Equations 3.Moist Thermodynamics Concepts 4.LES of shallow cumulus convection 5.Parameterization of cumulus convection 6.Geometry of Cumulus Clouds 7.(PDF cloud schemes)

Subsidence ~0.5 cm /s 10 m/s inversion Cloud base ~500m Tropopause 10km Stratocumulus Interaction with radiation Shallow Convective Clouds Little precipitation Vertical turbulent transport No net latent heat production Fuel Supply Hadley Circulation Deep Convective Clouds Precipitation Vertical turbulent transport Net latent heat production Engine Hadley Circulation

EUROCS intercomparison project on cloud representation in GCM’s in the Eastern Pacific Large Scale Models tend to overestimate Tradewind cumulus cloudiness and underestimate Stratocumulus Siebesma et al. (2005, QJRMS) scu Shallow cu Deep cu

5 Dry Convection 1.Motivation 2. Equations 3.Moist Thermodynamics Concepts 4.LES of shallow cumulus convection 5.Parameterization of cumulus convection 6.Geometry of Clouds 7.(PDF cloud schemes)

Large scale advection subsidence turbulent transport Net Condensation Rate Grid Averaged Equations of thermodynamic variables

Introduce moist conserved variables! Liquid water potential Temperature Total water specific humidity What happened with the clouds?

Buoyancy is the primary source for the vertical velocity With: Typical numbers:  = 0.5K  q v = 1~5 g/kg  q l = 0~3 g/kg So we need to go back to “down to earth” variables:

{ { Cloud Scheme in LES: All or Nothing In Climate models we have partial cloud cover so we need a parameterization.

10 Dry Convection 1.Motivation 2. Equations 3.Moist Thermodynamics Concepts 4.LES of shallow cumulus convection 5.Parameterization of cumulus convection 6.Geometry of Clouds 7.(PDF cloud schemes)

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 Conditionally Unstable!!! z vv profile stable unstable 5.4K/km

CIN Introductory Concepts 1: CAPE CAPE = Convective Available Potential Energy. CIN = Convection Inhibition CAPE CAPE and CIN unique properties of moist convection Primary Reason why moist convection is so intermittant

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

Introductory Concepts 3: 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. (Arakawa and Schubert JAS 1974)

Introductory Concepts 4: 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 and no matter how quickly it grows, the grass is allways short. Precipitation……….. Free after Dave Randall:

16 Dry Convection 1.Motivation 2. Equations 3.Moist Thermodynamics Concepts 4.LES of shallow cumulus convection 5.Parameterization of cumulus convection 6.Geometry of Clouds 7.(PDF cloud schemes)

History of LES of cumulus topped PBL 1.Sommeria, G. (1976) J. Atm Sci. 33, Sommeria, G and Lemone, M.A (1978) J. Atm Sci. 35, Beniston, M.G. and Sommeria G (1981) J. Atm Sci. 38, Bougeault, Ph (1981) J. Atm Sci. 38, Nicholls, L, Lemone, M.A. and Sommeria, G. (1982) QJRMS 108, Cuijpers J,W,M and Duynkerke, P.G, (1993) J. Atm Sci. 50, Siebesma and Cuijpers J,W,M (1995) J. Atm Sci. 52, GCSS; LES intercomparison studies of shallow cumulus: 2006 Precipitating trade wind cu RICO 2000 Diurnal Cycle Cumulus ARM 1998 Trade wind cu topped with Scu ATEX 1997 Steady state Trade wind cu BOMEX yearCaseExperiment Siebesma et al. JAS 2003 Stevens et al. JAS 2001 Brown et al. QJRMS 2002 Van Zanten et al. in preperation

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 Nitta and Esbensen 1974 JAS

11 different LES models Initial profiles Large scale forcings prescribed 6 hours of simulation 11 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 …….

Turbulent Fluxes of the conserved variables qt and  l Cloud layer looks like a enormous entrainment layer!!

LES: “clouds in silico” mass flux = cloud core fraction * core velocity Convective Mass flux decreasing with height x x = Siebesma et al JAS 2003

Updraft mass flux = updraft fraction * updraft velocity clouds “in vivo” Recently validated for “Clouds in vivo” (Zhang, Klein and Kollias 2009) ARM mm-cloud radar

Conditional Sampling of: Total water qt Liquid water potential temperature  l Conditional Sampling of: Total water qt Liquid water potential temperature  l Lateral Mixing between clouds and environment

26 Dry Convection 1.Motivation 2. Equations 3.Moist Thermodynamics Concepts 4.LES of shallow cumulus convection 5.Parameterization of cumulus convection 6.Geometry of Clouds 7.(PDF cloud schemes)

Mass Flux decomposition a M M-fluxenv. fluxsub-core flux Courtesy : Martin Kohler (ECMWF) Siebesma and Cuijpers JAS (1995)

Cloud ensemble: approximated by 1 effective cloud: In general: bulk approach:

M   The old working horse: Entraining plume model: Plus boundary conditions at cloud base. How to estimate updraft fields and mass flux? Betts 1974 JAS Arakawa&Schubert 1974 JAS Tiedtke 1988 MWR Gregory & Rowntree1990 MWR Kain & Fritsch1990 JAS And many more……..

Different tendency to form cumulus anvils is caused by differences in the vertical structure of model mass flux: MM , values fixed Mixing; Flexible structure Tiedtke (1989) in IFS EDMF-DualM Siebesma et al 2007 (JAS) Neggers et al 2009 (JAS)

Double counting of processes Problems with transitions between different regimes: dry pbl  shallow cu scu  shallow cu shallow cu  deep cu This unwanted situation has led to: Standard (schizophrenic) parameterization approach:

Deterministic versus Stochastic Convection (1) ~500 km Traditionally convection parameterizations are deterministic: Instantaneous large scale Forcing and mean state is taken as input and convective response is deterministic One to one correspondency between sub-grid state and resolved state assumed. Conceptually assumes that spatial average is a good proxy for the ensemble mean.

Deterministic versus Stochastic Convection (2) However: Cloud Resolving Models (CRM’s) indicate that operational resolutions show considerable fluctuations of convective response around the ensemble mean. This suggests that a deterministic (micro-canonical) approach might be too restricitive for most operational resolutions. Mass Flux pdf Plant and Craig 2006 JAS

More Sophisticated Parameterization (2) (Plant and Craig 2007) Parameterization: Select N cloud updrafts stochastically according to the pdf Calculate impact for each updraft by using a cloud updraft model Note : N is a function of the resolution Only tested in 1D setting

35 Dry Convection 1.Motivation 2. Equations 3.Moist Thermodynamics Concepts 4.LES of shallow cumulus convection 5.Parameterization of cumulus convection 6.Geometry of Clouds 7.(PDF cloud schemes)

Is this a Cloud?? ….and, how to answer this question?

“Shapes, which are not fractal, are the exception. I love Euclidean geometry, but it is quite clear that it does not give a reasonable presentation of the world. Mountains are not cones, clouds are not spheres, trees are not cylinders, neither does lightning travel in a straight line. Almost everything around us is non- Euclidean”. Fractal Geometry Benoit Mandelbrot Instead of

Area-Perimeter analyses of cloud patterns (1) Procedure: Measure the projected cloud area A p and the perimeter L p of each cloud Define a linear size through Perimeter dimension define through: Slope: D p = 1 For “ordinary” Euclidean objects:

Pioneered by Lovejoy (Science 1982) Area-perimeter analyses of projected cloud patterns using satellite and radar data Suggest a perimeter dimension Dp=4/3 of projected clouds!!!!! Confirmed in many other studies since then… Area-Perimeter analyses of cloud patterns (2) Instead of Consequences: Cloud perimeter is fractal and hence self-similar in a non-trivial way. Makes it possible to ascribe a (quantitative) number that characterizes the structure Provides a critical test for the realism of the geometrical shape of the LES simulated clouds!!!! Slope 4/3

Similar analysis with LES clouds Measure Surface As and linear size of each cloud Plot in a log-log plot Assuming isotropy, observations would suggest Ds=Dp+1=7/3 Siebesma and Jonker Phys. Rev Letters (2000)

Result of one cloud field

Repeat over 6000 clouds

Some Direct Consequences Surface area can be written as a function of resolution (measuring stick) l : Euclidian area SL underestimates true cloud surface area S(l=  ) by a factor LES model resolution of l=50m underestimates cloud surface area still by a factor 5!!! Does this have consequences for the mixing between clouds and the environment??? With L=outer scale (i.e. diameter of the cloud) and the normalizing area if measured with L.

Transport = Contact area x Flux turbulence diffusive flux Resolution dependence for transport over cloud boundary (1) resolved advection Subgrid diffusion

Consequences for transport over cloud boundary (2) (Richardson Law) No resolution dependancy for Ds=7/3!!

Is this shear luck ???? Not really: Repeat the previous arguments for Boundary flux T only Reynolds independent if which completes a heuristic “proof” why clouds are fractal with a surface dimension of 7/3.

47 Dry Convection Gradient Percolation A stronger underlying mechanism ? (Peters et al JAS 2009) Dp=4/3

Scale Hierarchy High Low low high Direct Numerical Simulati on Conceptual models Statistical Mechanics Self-Organised Criticality Level of “understanding ” or conceptualisation Large Eddy Simulations Global Climate Simulations Laboratory experiments Atmospheric Profiling stations Field campaigns Satellite data Observations Models/Parameterizations resolution Mixed layer models Interface & microphysical models