“From  Matsuno-­‐Gill  theory  to  dynamics  of  Madden-­‐Julian  Oscillation”  	  Bin	  WANG	  Department  of  Atmospheric  Sciences  and  Atmosphere-­‐Ocean  Research  Center  University  of  Hawaii  at  Manoa,  Honolulu  HI  96822  USA    The	   Madden-­‐Julian	   Oscillation	   (MJO)	   is	   a	   corner	   stone	   that	   bridges	   weather	   forecast	   and	  seasonal	   climate	   prediction.	   Understanding	   the	   origin	   and	   perpetuation	   of	   the	   MJO	   has	  eluded	   scientists	   for	   decades.	   In	   this	   presentation,	   I	   shall	   first	   discuss	   the	   fundamental	  features	  of	  MJO	  that	  request	  theoretical	  explanations.	  I	  shall	  then	  discuss	  essential	  physical	  processes	  that	  are	  involved	  in	  the	  MJO	  dynamics.	  	  From	   a	   dynamical	   standpoint,	   the	   MJO	   can	   be	   defined	   as	   a	   tropical	   planetary-­‐scale	  circulation	   system	   that	   is	   coupled	   with	   a	   multi-­‐scale	   convective	   complex	   and	   moves	  eastward	  slowly	  (~5	  m/s	  over	  the	  warm	  pool)	  with	  a	  rearward	  tilted	  upward	  motion	  and	  a	  mixed	   Kelvin-­‐Rossby	   wave	   structure.	   Why	   does	   the	   MJO	   possess	   a	   coupled	   Kelvin-­‐Rossby	  wave	   circulation	   structure?	   How	   can	   the	   circulation	   couple	   with	   convection	   and	   move	  eastward	   slowly,	   causing	   intraseasonal	   variability?	   What	   determines	   the	   MJO	   propagation	  speed	  and	  intensification	  rate?	  	  	  A	  general	  theoretical	  model	  framework	  is	  advanced	  in	  an	  attempt	  to	  unify	  the	  existing	  MJO	  theories	  and	  to	  address	  these	  fundamental	  issues	  of	  MJO	  dynamics.	  The	  model	  extends	  the	  Matsuno-­‐Gill	   theory	   by	   incorporating	   (a)	   full	   moisture	   feedback	   to	   precipitation	   heating	   and	  (b)	  a	  trio-­‐interaction	  among	  low-­‐frequency	  equatorial	  waves,	  boundary	  layer	  dynamics,	  and	  precipitation	   heating	   described	   by	   a	   simplified	   Betts-­‐Miller	   (B-­‐M)	   convective	  parameterization.	  	  The	   model	   can	   robustly	   produce	   essential	   large-­‐scale	   characteristics	   of	   the	   observed	   MJO:	  An	  equatorial	  planetary-­‐scale	  unstable	  system	  moving	  eastward	  slowly	  with	  coupled	  Kelvin-­‐Rossby	   wave	   structure	   and	   rearward	   tilted	   moisture	   and	   divergence	   anomaly.	   It	   is	   the	  boundary	   layer	   Frictional	   Convergence	   (FC)	   feedback	   that	   couples	   equatorial	   Kelvin	   and	  Rossby	  waves	  with	  convective	  heating	  and	  selects	  a	  preferred	  eastward	  propagation	  with	  a	  planetary	   zonal	   scale.	   In	   the	   presence	   of	   the	   FC	   feedback,	   the	   moisture	   feedback	   in	   the	   B-­‐M	  scheme	   can	   enhance	   Rossby	   wave	   response,	   thereby	   slowing	   down	   eastward	   propagation,	  and	   reinforce	   the	   Kelvin	   and	   Rossby	   wave	   coupling,	   resulting	   in	   a	   more	   realistic	   horizontal	  structure.	   The	   eastward	   propagation	   speed	   is	   inversely	   related	   to	   the	   relative	   intensity	   of	  the	   MJO	   westerly	   and	   the	   sea	   surface	   temperature	   (SST)	   that	   controls	   effective	   static	  stability	   through	   altering	   convective	   heating.	   The	   cumulus	   parameterization	   scheme	   may	  affect	  propagation	  speed	  through	  changing	  the	  MJO	  horizontal	  structure.	  The	  SST	  or	  basic-­‐
state	   moist	   static	   energy	   has	   a	   fundamental	   control	   on	   MJO	   intensification/decay.	   The	   FC	  feedback	   generates	   instability,	   while	   the	   moisture	   feedback	   tends	   to	   reduce	   the	   growth	  rate.	  	  	  A	   more	   general	   intermediate-­‐complexity	   model	   will	   be	   further	   formulated	   to	   explain	   the	  observed	  characteristics	  of	  boreal	  summer	  intraseasonal	  oscillation	  (BSISO)	  by	  including	  the	  impacts	  of	  boreal	  summer	  mean	  states.	  Using	  this	  intermediate	  model,	  I	  will	  further	  discuss	  how	   the	   boreal	   summer	   mean	   state	   affects	   BSISO,	   in	   particular,	   why	   the	   BSISO	   has	  maximum	  variability	  centers	  in	  the	  monsoon	  trough	  regions,	  and	  why	  the	  BSISO	  features	  a	  NW-­‐SE	  titled	  rainfall	  band	  and	  moves	  dominantly	  northward	  in	  the	  monsoon	  regions.	  
Ramifications	  of	  the	  model	  results	  to	  general	  circulation	  modeling	  are	  discussed.