MODEL UNIFICATION my latest research excitement Akio Arakawa

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1 MODEL UNIFICATION my latest research excitement Akio Arakawa Department of Atmospheric and Oceanic Sciences, UCLA CMMAP, January 7, 24

2 Wayne Schubert ` 7 Cumulus/ L-S interaction David Randall Wayne Schubert Chin-Hoh Moeng David Randall Steven Krueger Chin-Hoh Moeng Kuan-Man Xu Steven Krueger Celal Kuan-Man Konor Xu Joon-Hee Celal Konor Jung Joon-Hee Jung 7 PBL/ L-S interaction 7 7 Cumulus/ L-S interaction PBL cloud srability stability 7 PBL/ L-S interaction 85 Cumulus/ PBL interaction 7 PBL cloud 85 Cumulus/ L-S interaction Cumulus/ PBL interaction Cumulus/ Frontogenesis L-S interaction (7) Frontogenesis (Stratosphere dynamics) (7) (Stratosphere dynamics) None of these students directly worked on GCM development because I wanted them to work on scientifically more focused problems. I am the one who benefitted the most from this policy!

3 HISTORY OF NUMERICAL MODELING OF THE ATMOSPHERE HISTORY OF NUMERICAL MODELING OF THE ATMOSPHERE I have been fortunate to witness and participate in the entire history of numerical modeling. I have been fortunate to witness and/or participate in the entire history of numerical modeling of the atmspgere FIRST PHASE SECOND PHASE THIRD PHASE

4 FIRST PHASE (5-) FIRST PHASE (5-) Introdcution of early NWP models with highly simplified dynamics Represented by early NWP models with highly simplified dynamics ALSO Recognition of the close relation between the dynamics of "cyclones" and that of "general circulation" Highlight: Phillips s (5) numerical experiment

5 MY FIRST RESEARCH EXCITEMENT (-) MY FIRST RESEARCH EXCITEMENT (-) Development of a cyclone-resolving model for global circulation Development of a model that unifies the dynamics Opening of general of circulation the SECOND and PHASE that of cyclones. Transition from Phase I to Phase II The primary interest was still in dynamics. The major problem was computational. My work on the finite-difference Jacobian was almost immediately recognized by the meteorological community, but it took years to convince the applied mathematicians.

6 SECOND PHASE (-2) The scope of general circulation modeling magnificently expanded MY FIRST MAJOR RESEARCH EXCITEMENT from single-process to multi-process modeling. Developmrnt of a model that unifies dynamics of general circulation and that of cyclones. The importance of cumulus convection was recognized Early NWP models almost immediately. Early GCMs The problem was mainly computational. My major concern was to find the logical basis for parameterizability

7 MY SECOND RESEARCH EXCITEMENT (7-74) HISTORY OF NUMERICAL MODELING OF THE ATMOSPHERE HISTORY OF NUMERICAL Arakawa-Schubert MODELING (74): OF THE ATMOSPHERE An attempt to find the logical basis for parameterizability Under the SECOND PHASE, the scope of general circulation modelig magnificently expanded FIRST PHASE It took time for this paper to be widely recognized SECOND PHASE because most people considered parameterization as a simpler engineering problem.

8 BASIC HYPOTHESES OF ARAKAWA-SCHUBERT BASIC Consider HYPOTHESES a horizontal OF area ARAKAWA-SCHUBERT large enough to contain an ensemble of cumulus clouds but small enough to Consider a horizontal area enough to contain cover only a fraction of a large-scale disturbance. an ensemble of cumulus clouds but small enough to cover only a fraction of a large-scale disturbance. The overall intensity of cumulus activity is determined by an approximate balance between destabilization by slow large-scale processes and stabilization by fast cumulus-convective processes. These are over-simplifications, but I didn t see how cumulus convection can be parameterized without them.

9 APPROACHING A PLATEAU? APPROACHING A PLATEAU? As the scope of numerical modeling expands, new modules were kept added, but As the scope of numerical modeling expands, there was people little tend effort to forget to improve the scientific the scientific aspects basis of modeling, for modeling. putting more emphasis on the engineering aspects. I was almost ready to fully retire around 2. But Dr. Tao asked me to give an invited talk at the Cumulus Parametrization Workshop at GSFC on December -5, 2

10 MAJOR CONCEPTUAL PROBLEMS IN EXISTING PARAMETERIZATIONS OF SUBGRID-SCALE PROCESSES EXISTING (An PARAMETERIZATIONS edited version of a slide shown OF SUBGRID-SCALE at the Workshop) PROCESSES. (An edited version of a slide shown at the Workshop) Different processes (e.g., radiation, cloud, turbulence, etc.) interact only through. Different grid-scale processes variables, (e.g., radiation, losing cloud, most of turbulence, their subgrid-scale etc.) Interact interactions. only through grid-scale variables, losing most of their subgrid-scale interactions. 2. A single non-physical scale - grid size - separates processes that can be explicitly simulated and those that can only be in quasi-equilibrium.. The resolution dependence of the required physics is left to blind tuning. At the same Workshop, David Randall presented early results of Super-Parameterization.

11 EVIDENCE FOR THE TRANSITION OF MODEL PHYSICS Jung and Arakawa (24) Budget analyses of CRM-simulated data applied to various space/time intervals Jung and Arakawa (24) with and without (a component of) model physics Budget analyses of CRM-simulated data applied to various space/time intervals Average Profiles with and of without "REQUIRED (a component Source of) for model Moist physics Static Energy Height (km) 5 5 (2 km, min) (2 km, 2 min) (K hour - ) GCM-type profile CRM-type profile

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13 MY LATEST RESEARCH EXCITEMENT (24-24) MY LATEST RESEARCH EXCITEMENT (24-24) Working toward unification of these families of models Working toward unifications of these families of models Thank you, CMMAP, for giving me this excitement!

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15 UNIFICATION OF THE ANELASTIC AND QUASI-HYDROSTATIC SYSTEMS OF EQUATIONS UNIFICATION OF THE ANELASTIC AND QUASI-HYDROSTATIC SYSTEMS OF EQUATIONS Arakawa and Konor. 2, MWR Arakawa and Konor. 2, MWR Refer to Celal Konor s presentation Refer to Celal Konor s presentation These systems are physically quite different. For example, the physical meaning of pressure is different as : Quasi-static system: A measure of the mass above Anelastic system: The potential of a force required to maintain anelasticity

16 As in the traditional model, unified models couple the host GCM with an ancillary model that provides collective effects of subgridscale with processes, an ancillary either model parameterized that provides or collective simulated. effects of As in the traditional model, unified models couple the host GCM subgrid-scale processes, either parameterized or simulated. If the ancillary model represents more than the subgrid-scale processes, double counting of the same process or spurious competition between the grid-scale and subgrid-scale processes may occur.

17 THE QUASI-D MULTISCALE MODELING FRAMEWORK THE QUASI-D MULTISCALE MODELING FRAMEWORK Jung and Arakawa. 25, MWR Jung and Arakawa. 2, 24, JAMES Jung and Arakawa. 25, MWR Refer Jung to and Joon-Hee Arakawa. Jung s 2, 24, presentation JAMES Refer to Joon-Hee Jung s presentation The CRM does not fully represent the cloud-scale D processes but recognizes GCM s D structure through the background field. A product of Joon-Hee s extraordinarily meticulous and patient work.

18 UNIFIED REPRESENTATION OF DEEP MOIST CONVECTION IN NUMERICAL MODELING OF THE ATMOSPHERE: PART I UNIFIED REPRESENTATION OF DEEP MOIST CONVECTION IN NUMERICAL MODELING Arakawa and OF Wu, THE 2, ATMOSPHERE: JAS PART I Arakawa and Wu, 2, JAS An attempt to eliminate these assumptions of AS. Consider a horizontal area large enough to contain an ensemble of cumulus clouds but small enough to cover only a fraction of a large-scale disturbance. The overall intensity of cumulus activity is determined by an approximate balance between destabilization by slow large-scale processes and stabilization by fast cumulus-convective processes.

19 THE KEY PARAMETER IN THE UNIFIED REPRESENTATION THE KEY PARAMETER IN THE UNIFIED REPRESENTATION : The fractional area in the grid cell covered by convective updrafts : The fractional area in the grid cell covered by convective updrafts When the area covered by individual updrafts is fixed, When is a the measure fractional of area the covered fractional by population individual updrafts of updrafts. is fixed, is a measure of the fractional population of updrafts.

20 UNIFIED PARAMETERIZATION UNIFIED PARAMETERIZATION The assumption of small is eliminated. The assumption of small is eliminated, where is the fractional area covered In the by limit updrafts. as, it reduces to a conventional cumulus parameterization with full adjustment to an equilibrium profile. For the transport, it formulates only the eddy transport. It includes the reduction of eddy transport as cell by updrafts. due to filling the grid is determined by the grid-scale destabilization rate normalized by the efficiency of eddy transport.

21 CRM SIMULATIONS USED FOR STATISTICAL ANALYSIS Model : The vorticity equation model of Jung and Arakawa (28) CRM SIMULATIONS USED FOR STATISTICAL ANALYSIS Horizontal domain size : 5 km Model : The vorticity equation model of Jung and Arakawa (28) Horizontal domain size : 5 km Horizontal grid size : 2km Snapshots of vertical velocity Horizontal w at grid km size height : 2km With Shear Without Shear

22 SUB-DOMAINS REPRESENTING DIFFERENT RESOLUTIONS To see the grid-size dependence of the statistics, the original CRM domain (5 km) is divided into sub-domains of same size. To see the grid-size dependence of the statistics, Examples the original CRM domain (5 km) is divided into sub-domains of same size. d = 5 km d = 25 km d = 8 km Examples d = 5 km d = 25 km d = 8 km d = 4 km d = 4 km d = 2 km d = 2 km d = km d = km The sub-domain size is interpreted as the GCM grid size.

23 RESOLUTION DEPENDENCE OF ENSEMBLE-AVERAGE The fractional number of grid points with w>.5 m/s in a sub-domain.8. < > : Average over an ensemble of cloud-containing (i.e., > ) sub-domains The fractional number of grid points with w>.5 m/s in a sub-domain < > < > : Average over an ensemble of cloud-containing (i.e., > ) sub-domains SHEAR CASE z= km.8. NON-SHEAR CASE z= km BIMODAL.2 BIMODAL Sub-domain size d (km) Sub-domain size d (km) The assumption of << is valid only for low resolutions.

24 RESOLUTION DEPENDENCE OF ENSEMBLE-AVERAGE VERTICAL TRANSPORT OF MOIST STATIC ENERGY m/s K 5 m/s K 5 ENSEMBLE-AVERAGE VERTICAL TRANSPORT OF MOIST STATIC ENERGY SHEAR CASE z = km 25 SHEAR CASE z = km total 2 total 2 transport transport < w h eddy < w h eddy sub-domain size d (km) < w h sub-domain size d (km) < < w h 8 < transport transport 8 < < h : Deviation of moist static energy from a reference state h : Deviation of moist static energy ( ) : from Average a reference over all state CRM grid points in the sub-domain ( ) : Average over all CRM grid points in the sub-domain ( ) : ( ) - ( ) ( ) : ( ) - ( ) Parameterization is supposed to produce the green curve NOT the red curve.

25 ENSEMBLE-AVERAGE VERTICAL TRANSPORT OF MOIST STATIC ENERGY THE DEPENDENCE OF ENSEMBLE-AVERAGE m/s K VERTICAL TRANSPORT OF MOIST STATIC ENERGY SHEAR CASE d = 8 km z = km d = 8 km z = km m/s K SHEAR CASE total transport.2 total transport.2 < w h < w h THE DEPENDENCE OF < < To be parameterized.4 transport eddy.4 eddy transport < w h < w h To be parameterized..8. Due to internal structure Due to internal of updrafts structure of clouds The relative importance of the component to be parameterized The relative importance of the component to be parameterized strongly depends on strongly depends on <..8. <

26 UNIFIED REPRESENTATION OF DEEP MOIST CONVECTION IN NUMERICAL MODELING OF THE ATMOSPHERE: PART II Arakawa and Wu, 24, submitted to JAS Analyses of the smulated data in ciew of the vertical transport of horizontal momentum and the depencence of physical sources

27 UNIFIED REPRESENTATION OF DEEP MOIST CONVECTION IN NUMERICAL MODELING OF THE ATMOSPHERE: PART II UNIFIED REPRESENTATION OF DEEP MOIST CONVECTION IN NUMERICAL MODELING OF THE ATMOSPHERE: PART II Wu and Arakawa, 24, submitted to JAS Arakawa and Wu, 24, submitted to JAS Analyses of the smulated data in view of the vertical Analyses transport of the smulated of horizontal data in view momentum of and the vertical the dependence transport of horizontal of physical momentum sources and the depencence of physical sources

28 RESOLUTION DEPENDENCE VERTICAL TRANSPORT OF HORIZONTAL MOMENTUM (a) TOTAL TRANSPORT * wu (b) TOTAL TRANSPORT THE VERTICAL TRANSPORT -.5OF HORIZONTAL MOMENTUM (a) TOTAL TRANSPORT.25 * wu Sub-domain size d (km) Sub-domain size d (km) (b) TOTAL TRANSPORT * wv 5 2 Sub-domain size d (km) * wv Sub-domain size d (km) The u-momentum and v-momentum transports have quite different vertical structures (and different dependence on d ).

29 RESOLUTION DEPENDENCE VERTICAL TRANSPORT OF HORIZONTAL MOMENTUM Mosty downgradient of u Mosty downgradient of u Sub-domain size d (km) 5 2 (a) TOTAL TRANSPORT * wu (b) TOTAL TRANSPORT THE VERTICAL TRANSPORT -.5 OF HORIZONTAL MOMENTUM -.25 (a) (a) TOTAL TRANSPORT.25 (a) Sub-domain size d (km) * wu HORIZONTAL VELOCITY (b) Sub-domain size d (km) height z height (km) z (km) HORIZONTAL VELOCITY (b) TOTAL TRANSPORT 5 2 Sub-domain size d (km) (b) * wv Sub-domain size d (km) * wv -2-4 Sub-domain size d (km) Mosty upgradient Mosty of v upgradient of v

30 RESOLUTION DEPENDENCE VERTICAL TRANSPORT OF HORIZONTAL MOMENTUM Similar to h-transport Similar to h-transport 5 (a) TOTAL TRANSPORT * wu (b) TOTAL TRANSPORT THE VERTICAL TRANSPORT -.5 OF HORIZONTAL MOMENTUM -.25 (a) TOTAL TRANSPORT Sub-domain size d (km) Sub-domain size d (km) (c) EDDY TRANSPORT 5 * w u (c) EDDY TRANSPORT * w u * wu height z height (km) z (km) 5 HORIZONTAL VELOCITY height z (km) 5 (b) TOTAL TRANSPORT * wv Sub-domain size d (km) EDDY VERTICAL TRANSPORT OF HORIZONTAL MOMENTUM * w v (d) EDDY TRANSPORT * w v * wv Sub-domain size d (km) (d) EDDY TRANSPORT Not Not similar to similar h-transport to h-transport

31 These results seem to be consistent wih what Mitchell Moncrieff has been emphasizing. All of these results seem to be consistent wih Dr. Moncrieff has been consistently emphasizing.

32 CLOUD-MICROPHYSICAL CONVERSIONS INCLUDED IN THE MODEL CLOUD-MICROPHYSICAL CONVERSIONS INCLUDED IN THE MODEL Water Vapor Water Vapor Cloud Water/Ice Cloud Water/Ice Rain Rain Snow/Graupel Snow/Graupel Solid lines: Conversions taking place primarily within updrafts Solid lines: Conversions taking place pimarily within updrafts Dashed lines: Conversions taking place primarily outside of updrafts Dashed lines: Conversions taking place pimarily outside of updrafts

33 HE NET CONVERSION FROM WATER VAPOR TO CLOUD WATER/ICE HE NET d = CONVERSION 8 KM FROM WATER VAPOR TO CLOUD WATER/ICE (a) d = 8 KM (a) (b) (b)

34 (a) 2 (b) (a) THE NET CONVERSION FROM CLOUD WATER/ICE TO RAIN d = 8 KM TO SNOW/GRAUPEL THE NET CONVERSION FROM WATER VAPOR TO RAIN d = 8 KM (c) TO SNOW/GRAUPEL (c) (d) 2 (b) (d)

35 THE NET CONVERSION FROM RAIN TO SNOW/GRAUPEL d = 8 KM THE NET CONVERSION FROM RAIN TO SNOW/GRAUPEL (a) d = 8 KM (a) 2 (b) 2 (b2) 2 (b) 2 (b2)

36 THE EVAPORATION OF RAIN AND SUBLIMATION OF SNOW/GRAUPEL FROM RAIN d = 8 KM FROM SNOW/GRAUPEL THE EVAPORATION OF RAIN AND SUBLIMATION OF SNOW/GRAUPEL (a) FROM RAIN d = 8 KM (c) FROM SNOW/GRAUPEL 5 (b) 5 (a) 8 (b) (c) (d) (d)

37 SUMMARY A generalized modeling framework, called unified parameterizaion, is presented. A generalized modeling framework, called unified parameterizaion, The is key presented. parameter in the framework is determined for each realization of grid-scale process. The eddy transport of moist static energy (and other thermodynamic variables) decreases as approaches. The traditional approach of parameterizing the vertical transport of horizontal momentum does not work for the line-normal component.. Cioud-microphysical conversions taking place within updrafts is roughly proportional to, while those taking place outside of updrafts are roughly proportional to -.

38 HISTORY OF NUMERICAL MODELING OF THE ATMOSPHERE HISTORY OF NUMERICAL MODELING LES OF Models THE ATMOSPHERE Early NWP models Early NWP models General Circulation Models Cloud Resolving LES Models Models Mesoscale Cloud models Resolving Models Global and Mesoscale Regional models NWP Models Global and Regional NWP Models General Circulation Models Unification Unification FIRST PHASE SECOND PHASE THIRD PHASE FIRST PHASE SECOND PHASE THIRD PHASE!!!!!!

39 THANK YOU, DAVE, AND ALL OF MY THANK EX-STUDENTS YOU, DAVE, AND COLLEAGUES AND FOR ALL GIVING TEAM ME MEMBERS THIS EXCITEMENT OF CMMAP! FOR THIS EXCITEMENT!