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The -cloud- system: In search of simplicity

Graham Feingold1 and Ilan Koren2

1 NOAA System Research Laboratory, Boulder, Colorado 2 Weizmann Instute, Rehovot, Israel

Acknowledgements: Hailong Wang, Huiwen Xue, Alan Brewer

Organizers of WCRP

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""! Mesoscale Cellular Convecon 500 km

MODIS image, South East Pacific ‐ Radiave forcing of the ‐cloud system ‐ Paerns and emergence in atmospheric systems Patterns and Synchronization in Flock of birds Natural Systems

Oscillatory behavior in Belousov‐Zhabonskii chemical reacons

Cloud fields

Mud pools

©Miki Meir‐Levi “Emergence”

System‐wide paerns emerge from local interacons between elements that make up the system

Implicaon: Complex problems with huge number of degrees of freedom may be amenable to soluon with much more simple set of equaons Rayleigh-Bénard Convecve regime: range of allowable scales a Rayleigh number R

Rc

kc wavenumber, k (scale) Controlled lab experiments with different scales: Paerns and preferred modes

Getling and Brausch, Phys. Rev. E 2003 Aerosol/ selects the state Albedo

Closed‐cell Albedo ~ 0.6 high aerosol (non‐ precipitang)

Onset of WRF Model drizzle + 2‐moment results in (i) Aerosol µphysics; “selects” the transion state of the system 60 km domain; to open‐cell (same ) Δx = Δy = 300 m convecon Δz = 30 m DYCOMS‐II (ii) The open state rearranges

Open‐cell low aerosol Albedo ~ 0.2 (precipitang)

Garay et al. 2004, MISR Wang and Feingold, 2009a Rearrangement of Open Cells

No advecon

Orange: Updras Feingold, Koren, Wang, Xue, Brewer (, 2010) Blue: Downdras/precipitaon Y‐shaped surface is region favoured for new convecon

Precipitaon is iniated

Downdras, opening of cell Y‐convergence Surface divergence  cloud   destroys buoyancy Rearrangement of Open Cells

No advecon

Orange: Updras Feingold, Koren, Wang, Xue, Brewer (Nature, 2010) Blue: Downdras/precipitaon Y‐shaped surface convergence zone is region favoured for new convecon

Precipitaon is iniated

Downdras, opening of cell Divergence Surface divergence Emergence due to interacon between oulows Synchronization: Oscillaons in Precipitaon

3 LES cases: DYCOMS ATEX VOCALS

Feingold, Koren, Wang, Xue, Brewer (Nature, 2010) Synchronization: Oscillaons in Rainrate

3 LES cases: Stability DYCOMS ATEX R R VOCALS

Stability How stable are the stable states? How readily does the system HovmullerHövmuller diagram transion from one state to another? Shi in rain “grid” Stable states A and B are stable Colored contours: rain and self‐sustaining Small Contours: updra perturbaons strengthen the resilience of the state Feingold, Koren, Wang, Xue, Brewer (Nature, 2010) Synchronization of Coupled Oscillators

Feingold, Koren, Wang, Xue, Brewer (2010) Are Oscillating Patterns Common? Large Eddy Simulaon of Aerosol‐Cloud‐Precipitaon

3‐D grid (~ 100 x 100 x 100)

Anclockwise loops in R; LWP phase

Koren and Feingold 2011, PNAS Similar paerns in trade cumulus simulaons (RICO)

Time, h

Jiang et al. 2010 Vercal Profile of Radar reflecvity (a proxy for Rainrate) from N. Atlanc (Porto Santo, 1992; ASTEX)

Rise in cloud depth H Heaviest Rain Decrease in H follows heavy rain Height

Time Data courtesy NOAA ESRL Radar Group Predator-Prey Model

Lotka‐Volterra Equaons (circa 1926)

x = prey Image courtesy of Wikipedia y = predator 4 parameters: a, b, g, d Predator-Prey Model

Clouds=Rabbits; Rain=Foxes

‐ Cloud builds up ‐ Rain follows some me behind ‐ Rain destroys cloud ‐ Cloud regenerates (met forcing, colliding oulows, etc)

and so on…

Many possible predator‐prey pairs:

Rain; Aerosol Convecon; Instability (Nober and Graf) Droplets; Supersaturaon ; (Bergeron‐Findeisin)

Koren and Feingold 2011, PNAS dN N NH d = 0 − d + N˙ (t cT1) 2 dt LWP =τ q(z)dzd = H 2 0 − 2 3 simple coupled Balance Equaons: !

dH ˙ H H Nd = 0 c2NdR ˙ Cloud depth = −− + Hr(t T ) dt τ1 −

αH3(t T ) R(t)= −3 1 RN= (αtH TN)− Rainrate d − d

dNd NdLWP0 Nd 2 1 ˙ (N +4= γτ −N H= )+2RNdN(t T ) conc. H = dtd dt1τ2 d 0− − d− 2γτ1

dH dH dLWP H˙ = N˙ == c N R r dtd −dLWP2 d dt

3 2 ˙ 1αH (t αTH!) HrR=(t)= R = − −c1HN (t −Tc1N) d d − ! 2 1

2 1 (N +4γτ N H ) 2 N H = d 1 d 0 − d 2γτ1

2 dNd N0 Nd = − + N˙ d(t T ) dt τ2 −

N˙ = c N R d − 2 d

3 αH (t T !) H c R(t)= − LWP = q(z)dz = 1 H2 N (t T ) 2 d − ! Steady!0 State Solution to Cloud Depth H

1 2 2 dH H0 H (Nd +4γτ1NdH0) Nd = − + H˙ r(t T )=0 H = − dt τ1 − 2γτ1

3 1 R = αH Nd−

dLWP = R dt dt − / 2 dCCN dH dH dLWP H˙ = = r dt dLWP dt

2 ˙ 1 αH Hr = R = ‐3 −c1H −c1Nd CCN, m 1 Baker and Charlson, 1990

Cloud Depth determined by H Cloud Depth determined by 0 drop concentraon Nd Koren and Feingold 2011, PNAS “Meteorological” cloud depth, H0 Aerosol Concentraon, N 0 W = LWP dH Koren H R dt H Strong dependence of ˙ H dN Higher ˙ r ( dt t r = = and Feingold 2011, PNAS = )= d = R ( dH R H = N d dt − ! ( LWP 0 α t d = N 0 2 dt N c N N Steady State Solutions Time-Dependent )= τ ˙ − H H 1 1 1 = +4 1 d o 0 H α d supports deeper clouds q H 3 = ( τ − H 1 ( d ( t R 2 α γτ z = t LWP N dH 3 − − N + H ) 2 − N = dz d 1 2 − c d 3 T N H ( γτ d 2 − T ˙ ( R t − + N ! = t d r 1 − ) 1 ! d ( H c − d α ) N t LWP 1 R c ˙ T H dt 0 2 N − 1 d T ) ! ( H 2 d ) 2 1 ! t T R ) − − 2 ) on N T

) d

H o

T τ 1 = τ = 10 min depleted Aerosol is condions; precipitang Strongly 2 2 = 60 min

Oscillating Solutions: No Steady State

H0 = 670 m ‐3 N0 = 515 cm

τ1 = 80 min τ2 = 84 min

T = 12.5 min

7 day simulaon

H; N H; R

Oscillaon around a steady state

Koren and Feingold 2011, PNAS Forcing at multiple timescales

dH H0 H ∆H = − + + H˙ i(t T ) dt τ1 τ2 −

∆H = H0! sin(2πt/τ2)

dN N0 N τ = 1 h (microphysics) = − + N˙ (t T ) 1dt τ3 −

τ2 = 24 h (largescale forcing) H; N αH3(t T ) R(t)= − H; R N(t T ) −

7 day simulaon

1 Robustness of the System How stable are the stable states?

Small perturbaons strengthen the resilience of the state

± 50% perturbaons to H0 and N0 every second: Soluons are robust Small perturbaons strengthen the resilience of the state; Large enough perturbaons will lead to collapse

Koren and Feingold 2011, PNAS Summary • Emergence – Local interacons result in system‐wide order – convergence of precipitang oulows

• Self‐organizaon – Aerosol/drizzle can select open/closed cellular state

• Synchronizaon – Local interacons: synchronized rain, oscillaons in open‐cell state

• The predator‐prey problem – Coupled oscillaons in Cloud‐Rain “Populaons” – Bifurcaon – Interacons at mulple mescales

• Can we exploit emergence to represent complex systems? – (E.g. Mapes 2011; Bretherton et al. 2010)