The aerosol-cloud-precipitation system: In search of simplicity Graham Feingold1 and Ilan Koren2 1 NOAA Earth System Research Laboratory, Boulder, Colorado 2 Weizmann Instute, Rehovot, Israel Acknowledgements: Hailong Wang, Huiwen Xue, Alan Brewer Organizers of WCRP WCRP October 2011 A complex system: Aerosol‐Cloud‐Dynamics‐Radiaon‐Land Surface‐… !"#$%&'()*+,-.%"(#,/(%(0)+',1!-/2, , 30450).,6787, -+*(4+(,049,:)$;)0#,:<04, ! Complexity!! Complexity!! Complexity!! Complexity!! ! !"#$%&'(From DOE/ASR Science and Program Pla#! $%&'()*+,-.!(/(%+&!0+)-.%-'1!(*'2-13!4!(56(+%!'7!%*+!4%&'()*+,-.!),'.+((+(!%*4%!&5(%!6+!n 510+,(%''0!410!4..5,4%+8/!,+),+(+1%+0!-1!.8-&4%+!&'0+8(#!!9*-(!7-35,+!(.*+&4%-.488/!0-()84/(! ‐ Complexity at a huge range of spaotemporal scales ':+,4,.*-13!%*+&+(!;-1!488!.4)-%48!8+%%+,(<!410!4!,+),+(+1%4%-:+=!65%!1'%!+>*45(%-:+=!(+%!'7! 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Mesoscale Cellular Convecon 500 km MODIS image, South East Pacific ‐ Radiave forcing of the ocean‐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 Convection 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/drizzle selects the state Albedo 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 meteorology) 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 (Nature, 2010) Blue: Downdras/precipitaon Y‐shaped surface convergence zone is region favoured for new convecon Precipitaon is iniated Downdras, opening of cell Y‐convergence Surface divergence Buoyancy cloud rain 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 space 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 Ice; Water (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 ) Drop 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 H c LWP = Time-Dependentq(z)dz = 1 H2 2 !0Steady State Solutions Strongly dH H0 H precipitang 0 = − + H˙ r(t T ) dt τ1 − condions; Aerosol is depleted 3 1 R = αH Nd− 3 αH (t T !) R(t)= − dLWPNd(t T !) =− R Strong dependence of dt − R on Ho dH dH dLWP “Meteorological” cloud depth, H H˙ = = r dt dLWP dt dNd N0 Nd = − + N˙ d(t T ) dt τ2 − 2 ˙ 1 αH HHigher r = No supports deeper clouds R = −c1H −c1Nd N˙ d = c2NdR 1 − τ1 = τ2 = 60 min T = 10 min Aerosol Concentraon, N0 Koren and Feingold 2011, PNAS 3 αH (t T !) R(t)= − N (t T ) d − ! 2 1 (N +4γτ N H ) 2 N H = d 1 d 0 − d 2γτ1 2 1 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) .