A stochastic framework for modeling the population dynamics of convective clouds

Transcription

1 A stochastc framework for modelng the populaton dynamcs of convectve clouds SAMSON HAGOS, ZHE FENG, BOB PLANT, ROBERT HOUZE, HENG XIAO Acknowledgement: Alan Protat and hs team at the Australan BOM 1

2 Introducton Populatons of convectve clouds cover a spectrum of szes and lfetmes and are often transtonng. Questons: I What are the processes the govern the evoluton of the populaton of convectve cells? II How can these processes be modelled and represented n global models? 2

3 Background Effort at representng cloud populatons and ther dynamcs General energy cycle (Arakawa and Schubert 1974) da dt dk N MBj F AM B j1 dt d K Bulk, devaton from quas-equlbrum (Pan and Randall 1998) (Yano and Plant 2010) 2 K M B K M B Spectral varatons about quas-equlbrum (Crag and Plant 2008) (Wagner and Graf 2010) Stochastc Populaton dynamcs Non-equlbrum cloud populaton model (Plant 2012) 3

4 Objectves Informed by analyss of radar observatons, cloud permttng model smulatons and theory, develop a probablstc model of non-equlbrum dynamcs of cloud populatons for: Testng hypotheses regardng the roles of varous physcal processes and Parameterzng the spectrum of convectve clouds (from solated to MCSs) n a unfed framework. 4

5 Descrpton of observaton and CPM smulaton C-Pol observaton at Darwn 3 wnters of C-Pol radar scans are used to dentfy convectve cells. The varablty n sze and number of the convectve cells are used n the analyss. CPM smulaton 2.5 km grd spacng Two months long smulaton Jan-Feb No cumulus parameterzaton. 5

6 The General Framework A Master equaton representaton of populaton dynamcs dn dt j W n W n j j j Transton to sze a Transton from sze a Defntons Cell sze a a 1 Area fracton af A na doman pa A 1 doman Cloud base mass flux per cell area mb w Cloud base mass flux of a cell M m a B b

7 Cell sze dstrbuton Assumpton Dscretzaton Cloud work functon A ma da dt N j1 M F Bj M dp 1 ; dt a1m b1 B F The equaton gves us dp but what we are lookng for s the new { n } The problem For a gven area fracton, what s the sze dstrbuton of the cells? How s the sze dstrbuton related to the mass G flux? We need a probablty of growth vector for >0 f ( envronment, n, a...) Such that the probablty of new cell formaton s G 0 1 G 0 7

8 Ths framework s hereafter referred to as STOchastc framework for Modellng Populaton dynamcs of convectve cells (STOMP). 8

9 (a) A unform probablty model Assumpton: dp convectve pxels land on the doman randomly wth unform probablty Forcng: Addng dp pxels one at a tme: Growth of cells New cell formaton G 0 G0 1af Adoman n1 n11 1 n 11 n na Dampng: Removng dp pxels one at a tme: P n n n 1 na N j1 na n n n 1 1 n 11 Mass flux s assumed to be lnear functon of cell area M m a B b mb 0.78 / 2 kg m s 9

10 (a) A unform probablty model (STOMP-UP) Sze dstrbuton STOMP-UP CPM smulaton C-Pol radar X Unform probablty results n too many small cells and too few large cells. Chance does not explan the exstence of large convectve cells. 10

11 Mean number of cells Mean sze of cells Durnal cycle of cell count and mean cell sze STOMP-UP CPM smulaton C-Pol radar In the unform probablty model they are n phase. In both the observatons and the CPM the mean cell sze lags behnd cell count. 11

12 (b) Aggregaton probablty model (STOMP-AP) Probablty of growth vector Probablty that favors growth Through detranment of mosture by exstng convecton for example (Mack and Crag 2015) We defne an aggregaton parameter Hgher probablty of growth Lower probablty of new cell formaton G na 0 G0 max(1 af,0) Adoman 12

13 (b) Aggregaton probablty model (STOMP-AP) Aggregaton wth delta=30.0 ntroduces the observed lag of mean cell sze behnd the cell count. It suggest n ths case, growth of exstng cells s about 30 tmes more lkely than formaton of new cells. 13

14 Mass flux and convectve cell szes Why do we care about cell sze dstrbuton anyway? CPM cloudbase massflux CPM 10DBZ echo-top heght C-Pol 10DBZ echo-top heght Larger cells carry more than ther share of mass flux. 14

15 Closure: Dependence of mass flux on cell area M n a m b b N ) Lnear: mb 0.78 / 2 kg m s ) Non-lnear m b ( a a ) ( ) kg / m s a 500km a1 m b ( a a ) ( ) kg / m s a 500km a1 15

16 Response to constant forcng Non-lnearty ntroduces a stochastc recharge-dscharge behavor. The length of the suppressed recharge perod ncreases wth the adjustment tme-scale. 16

17 Response to durnal forcng Because of convectve dampng the mass flux lags behnd the forcng. The non-lnear relatonshp between cell sze and mass flux per cell area further delays the mass flux durnal cycle. 17

18 Cell sze dstrbuton STOMP-AP (Lnear) STOMP-AP (Non-lnear) CPM C-Pol Aggregaton probablty model wth non-lnear mass flux produces the desred frequency of large cells. 18

19 Summary A framework for stochastc modelng populaton dynamcs of convectve clouds s developed. A specfc model n ths framework s defned by the representaton of a growth probablty vector (G) and decay vector (D) or more generally by a transton rate martrx. If convectve plumes prefer to form near exstng cells and f mass flux s an non-lnear functon of cell area: Under steady forcng: A recharge-dscharge response s obtaned. Under durnally varyng forcng: Peak mass flux s delayed. 19

20 Future work A more general transton rate matrx W that represents, lfecycle of convecton and formaton of cold pools and stratform area wll be derved from observatons and cloud permttng model smulatons. Ths modellng framework wll be mplemented nto a clmate model 20