Global Modeling with NASA Supercomputing Technology: When Sandy Meets Lorenz Bo-Wen Shen, Ph

Global Modeling with NASA Supercomputing Technology: When Sandy Meets Lorenz Bo-Wen Shen, Ph. D. [email protected] Department of Mathematics and Statistics Center for Climate and Sustainability Studies Computational Science Research Center San Diego State University

GMCS 214 SDiSttUiitSan Diego State University 21 November 2014

When Sandy Meets Lorenz 1 San Diego State Univ. Nov 21, 2014 Outline

1. ItIntrod ucti on 2. Navier-Stokes Equations, High-resolution Global Model, and Multiscale Modeling Framework (MMF) 3. Supercomputing and Visualization Technology 4. Simulations of Hurricanes Sandy and Others 5. Nonlinear Processes in Modified Lorenz Models 6. SdFtTkSummary and Future Tasks

When Sandy Meets Lorenz 3 San Diego State Univ. Nov 21, 2014 Sandy: Tropical Cyclones with Multiscale Interactions

Hurricane France Hurricane Howard Tropical Storm Phoebe Super typhoon Sonda

When Sandy Meets Lorenz 4 San Diego State Univ. Nov 21, 2014 Lorenz: Chaos Theory with Butterfly Effect

• The butterfly effect of first kind: sensitive dependence on initial conditions. • The butterfly effect of second kind: a metaphor for indicating that small perturbations can alter large-scale structure. • Lorenz’s studies suggested finite predictability and nonlinearity as the source of chaos.

The studies by Lorenz (1963, 1972) laid the foundation for chaos theory, which was viewed as the third scientific revolution of the 20th century after relativity and quantum mechanics (e.g. Gleick, 1987; Anthes 2011).

When Sandy Meets Lorenz 5 San Diego State Univ. Nov 21, 2014 When Sandy Meets Lorenz

Sandy Lorenz Hurricane Dynamics Chaos Dynamics Earth Science Mathematics Complex Model Theoretical Model Real-world Model Idealized Model PDE ODE Complexities in Modeling Complexities in Mathematics Multiscale Processes Butterfly Effect Sandy (2012) Lorenz (1963) Can Sandy's ego be retained?

(San Diego)

When Sandy Meets Lorenz 6 San Diego State Univ. Nov 21, 2014 High-impact Tropical Weather: Hurricanes

Each year tropical cyclones (TCs) cause tremendous economic losses and many fatalities throughout the world. Exampp()les include Hurricanes Katrina (2005) and Sandy (2012) .

Hurricane Katrina (2005) (Shen et al., 2006b; 2013a) • Cat 5, 902 hPa, with two stages of rapid intensification • The sixth-strongest Atlantic hurricane ever recorded. • The third-strongest landfalling U.S. hurricane ever recorded. • The costliest Atlantic hurricane in history! ($100+ billion)

Hurricane Sandy (2012) (Shen et al., 2013c) • The deadliest and the most destructive TC of 2012 Atlantic hurricane season • The second-costliest hurricane in United States history ($50 or 75$ billion) • The largest Atlantic hurricane on record

When Sandy Meets Lorenz 7 San Diego State Univ. Nov 21, 2014 My Journey with Computational Science

08. 02. 2004 – Initial Columbia Promising

When Sandy Meets Lorenz 8 San Diego State Univ. Nov 21, 2014 Computational Science

July, 2004 June, 2005 Dec., 2007

• Computational Science (CS) is defined as an inter-disciplinary field with the goal s of und erst andi ng and so lv ing comp lex pro blems us ing hig h-end computing facilities. • CS is identified as one of the most important fields of the 21st century to contribute to the scientific , economic , social and national security goals of USA by the President’s Information Technology Advisory Committee (PITAC).

When Sandy Meets Lorenz 9 San Diego State Univ. Nov 21, 2014 Supercomputers @Top 500.org

1: Roadrunner Japan Earth 2: Jugar Simulator 3: NASA Pleiades (06/2002) (11/2008) (38.86 Tflops)

1: IBM/DOE BG/L Beta (70.72 Tflops) 2: NASA Columbia (51.87 Tflops) 3: Japan ES (38.86 Tflops) (11/2004)

When Sandy Meets Lorenz 11 San Diego State Univ. Nov 21, 2014 NASA Supercomputing and Visualization Systems

Pleiades Supercomputer (as June 2013) • one of a few petascale supercomputers

•Rmax of 1,240 teraflops (LINPACK); Rpeak of 2 ,880 tera flops • 162,496 cores in total; Intel Xeon processors, Nehalem, Westmere,Sandy Bridgg,e, Ivyyg, Bridge, • 417 TB memory • 3.1 PB disk space • Largest InfiniBand network. • Large-scale visualization system – 8x16 LCD tiled panel display – 245 million pixels • 128 nodes – 1024 cores, 128 GPUs • InfiniBand (IB) interconnect to Pleiades – 2D torus topology – High-bandwidth

When Sandy Meets Lorenz 12 San Diego State Univ. Nov 21, 2014 My Journey with Computational Science

1. Ten (Five) awards from UMCP, SAIC and NASA/GSFC Since 2001 (2006). 2. Research results featured by Dr. Jack• Two Kaye major (Associate supercomputers: Director at Earth NASA/HQs) at the Interdepartmental Hurricane ConferencesSimulator and in 2012, NASA 2013, Columbia and 2014. 3. Researc h resu lts fea ture d in a recen• t Three Pres id modeling en t's C orner teams: arti c onel e o f from UCAR Magazine by Dr. Rick Anthes in 2011.NASA The article and two is entitled from Japan ``Turning the Tables on Chaos: Is the atmosphere more predictable than we assume?’’ 4. Research results featured in NASA News Stories (()07/2010 and 11/2010). It was also translated in Chinese by Science and Technology Division, Taipei Economic and Cultural Representative Office in the United States (駐美國台北經濟文化代表處科技組). 5. Research results appeared in news medias, such as MSNBC, PhysOrg. com, National Geographic--Indonesia, ScienceDaily, EurekAlert, Yahoo News, TechNews Daily, Scientific Computing, HPCwire, etc. (2010) 6. Research projects selected as one of top 4 demonstrations at NASA Booth for Supercomputing Conferences (SC) in 2004, 2008, 2009, and 2010. 7.7. Selected Selected as as Journal Journal Highlights Highlights by by American American Geophysical Geophysical Union Union (07/2006) (07/2006) 8.8. Research Research results results featured featured in in Science Science magazine magazine (08/2006) (08/2006) “Is new science being produced or just really cool pictures?” which was raised by Mahlman and others who have reservations

When Sandy Meets Lorenz 13 San Diego State Univ. Nov 21, 2014 Inspirational Comments

When Sandy Meets Lorenz 14 San Diego State Univ. Nov 21, 2014 Inspirational Comments

When Sandy Meets Lorenz 15 San Diego State Univ. Nov 21, 2014 Mathematical Models (math151) • The mathematical model often takes the form of a differential equation. • A differential equation is an equation that contains a unknown function and some of its derivatives. • An ordinary differential equation (ODE) is an equation containing a function of one independent variable and its derivatives. • A partial differential equation (PDE)differential equation that contains unknown multivariable functions and their partial derivatives. • Climate models use qu antitative methods to sim u late the interactions of the atmosphere, oceans, land surface, and ice. • A general circulation model (GCM), a type of climate model, is a mathema tica l mo de l o f the genera l c ircu la tion o f a p lane tary atmosphere or ocean and based on the Navier–Stokes equations on a rotating sphere with thermodynamic terms for various energy sources (radiation, latent heat). PDEs Æ GCM; PDEs –> ODEs (Lorenz model)

When Sandy Meets Lorenz 16 San Diego State Univ. Nov 21, 2014 Navier-Stokes Equations

The Navier–Stokes equations are strictly a statement of the conservation of momentum.

Viscosity, 2v gravitational force, g

When Sandy Meets Lorenz 17 San Diego State Univ. Nov 21, 2014 Navier-Stokes Equations + Other Equations

• They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing. • The Navier–Stokes equations in their full and simplified forms help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things. •Couppqyled with Maxwell's equations they can be used to model and study magnetohydrodynamics. To fully describe fluid flow, more information is needed. This additional information may include boundary data (e.g., no-slip), conservation of mass, conservation of energy, and/or an equation of state. ∂ρ + ∇ • ()ρv = 0 continuity equation, conservation of mass ∂t p = ρRT an equation of state

• hydrostatic? ( dw/dt~0); incompressible? (d/dt ~0). • Source: Wikipedia

When Sandy Meets Lorenz 18 San Diego State Univ. Nov 21, 2014 Idealized Equations for a Rotating Flow

Coriolis Force

d θ = 0 Thermodynamic equation Shen (1992, 1998) dt

When Sandy Meets Lorenz 19 San Diego State Univ. Nov 21, 2014 Governing Equations (NCAR CAM 5.0)

the momentum Eq.

the hydrostatic Eq. π =p/ is the pseudo- density with eq. 3.1; is the general vertical coordinate

the continuity Eq. The conservation of total air mass using π

the thermodynamic Eq. virtual potential temperature

the mass conservation q, water vapor law for tracer species

When Sandy Meets Lorenz 20 San Diego State Univ. Nov 21, 2014 Parameterizations

• Parametrization is the process of deciding and defining the parameters necessary for a complete or relevant specification of a model • Non-uniqueness: Parametrizations are not generally unique. • Dimensionality: the minimum number of parameters required to describe a model or geometric object is equal to its dimension, and the scope of the parameters—within their allowed ranges—is the parameter space. • Parameterization in a weather or climate model within numerical weather prediction refers to the method of replacing processes that are too small-scale or complex to be physically represented in the model (i.e., the so-called unresolved processes) by a simplified process (that can emulate the impact of unresolved processes) . • Associated with these parameterizations are various parameters used in the simplified processes.

Parameterization are used to emulate the impact of unresolved processes.

When Sandy Meets Lorenz 21 San Diego State Univ. Nov 21, 2014 NCAR CAM 5.0

dyypnamical processes, resolved ppyhysical processes , unresolved

No direct interactions among different parameterizations!

When Sandy Meets Lorenz 22 San Diego State Univ. Nov 21, 2014 Early Efforts with NCAR CAM

March 1999 – September 2003

NCAR Community Atmosphere Model (CAM)

• Unix System and Network Programming: Unix curses, device control (serial I/O), file system control, inter-process communication (pipes, 1992-1994 semaphore, shared memory, TCP/IP sockets), process control, signal handling. • Supercomputing (Parallel/Distributed/Cluster Computing): MPI (Message Passing Interface), MPI-2 remote memory access, MLP (Multi- 1999-2003 Level Parallelism), OpenMP, ESMF (Earth Science Modeling Framework), POSIX Threads, and JAVA Threads. Knowledge of Gird computing. • Software: Fortran (F77/F90/F95), OOP (Object Oriented Programming), C/C++, JAVA, Basic, Pascal, UNIX Shells, UNIX m4 script, PERL, Python, PHP, HTML, XML, XHTML, CGI, AWK. CVS (Concurrent Version System), GNU Make, gdb, LaTex, MATLAB, VMWARE, Secure Shell, MS-Office, VIS5D, AVS, GrADS, NCAR Graphics, GEMPAK.

When Sandy Meets Lorenz 23 San Diego State Univ. Nov 21, 2014 Global Mesoscale Modeling on NASA Supercomputers

A B

D C Frances

F E

5-day forecasts of total precipitable water initialized at 0000 UTC 1 September, 2004 with the 1/12o fvGCM

F: Madden-Julian Oscillation (MJO) D: Asian Mei-Yu Front A: Atlantic Hurricanes B: Catalina Eddy G: African Easterly Wave (AEW) E: Twin Tropical Cyclones C: Hawaiian Lee Wakes The Global Mesoscale Model

1. Model Dynamics and Physics:

• The finite-volume dynamical core (Lin 2004); • The NCAR physical parameterizations, and NCEP SAS as an alternative cumulus parameterization scheme • The NCAR land surface model ((,CLM2, Dai et al. 2003)

2. Computational design, scalability and performance (suitable for running on clusters or multi-core systems)

Shen,B.-W., R. Atlas, O. Oreale, S.-J Lin, J.-D. Chern, J. Chang, C. Henze,and J.-L. Li, 2006b: HiHurricane Forecas ts w ithGlblMith a Global Mesosca le-RliMdlPliiRltithHiResolving Model: Preliminary Results with Hurricane Katrina(2005). Geophys. Res. Lett., L13813, doi:10.1029/2006GL026143. (This has been selected as an AGU Journal Highlight, and has also been highlighted in Science, 25 August, 2006)

Shen,B.-W., R. Atlas, J.-D. Chern, O. Reale, S.-J. Lin, T. Lee, and J.Change 2006a: The 0.125 degree Finite Volume General Mesoscale Circulation Model:Preliminary simulations of mesoscale vortices. Geophys. Res. Lett., 33, L05801, doi:10.1029/2005GL024594.

When Sandy Meets Lorenz 25 San Diego State Univ. Nov 21, 2014 Physics Parameterizations

• Moist physics: -Deep convections: Zhang and McFarlane (1995); Pan and Wu (1995, aka NCEP/SAS) -Shallow convection: Hack (1994) -large-scale condensation (Sundqvist 1988) -rain evaporation • Boundary Layer - first order closure scheme - local and non-local transport (Holtslag and Boville 1992) • Surface Exchange - Bryan et al. (1996)

Paa,n, H.-L.,,a and W.-S. W u, 1995 : Imp le me nt ing a mass fl ux conv ecti on par am eteriz ati on package for the NMC medium-range forecast model. NMC office note, No. 409, 40pp. [Available from NCEP].

When Sandy Meets Lorenz 26 San Diego State Univ. Nov 21, 2014 General Issues in Global Modeling

• Hydrostatic vs. non-hydrostatic (resolved scale ~ 10km, Pielke 2002, Shen 1992) • Cumulus Parameterizations (validity at a mesoscale resolution? Validity for TC formation?) • (Additional) Required Physical Processes (e.g., surface flux exchange for TC formation and intensification)? • Added skill in weather simulations?

When Sandy Meets Lorenz 27 San Diego State Univ. Nov 21, 2014 Grid Cells vs. Grid Spacing

Resolution x y Grid cells 1o (~110km) 288 181 52 K 0.5o (~55km) 576 361 208 K 0.25o (~28km) 1000 721 721 K 0.125o (~14km) 2880 1441 4.15 M 0.08o (~9km) 4500 2251 10.13 M 2005 2009- MMF (2D CRM) 144x64 90 829 K 2010

The 1/12 degree model with 48 vertical levels has 480 M grid points. In comparison, the hyperwall-2 is able to display 245 M pixels. 1/8 degree, 02:39:51/5day using 1440 cores. 1/4 degree, 35 minutes/ 5 day run using 240 cores.

When Sandy Meets Lorenz 33 San Diego State Univ. Nov 21, 2014 The Catalina Eddy

The Catalina eddy is a localized weather phenomenon that occurs in the mostly convex portion of the Southern California coast running from Point Conception to San Diego. We showed that model can simulate the formation of the Catalina eddies and Hawaiian lee vortices, which are generated by the interaction of the synoptic-scale flow with surface forcing, and have never been reproduced in a GCM before (Shen et al., 2006a).

SfSurface wi idnds an d ver tiltical vorticiti es valida te d a t 0000 UTC 4 S ept emb er 2004 . (a) NCEP T384 GFS analysis, and (b) 72 h simulation. (Shen et al., 2006a)

When Sandy Meets Lorenz 34 San Diego State Univ. Nov 21, 2014 Concurrent Visualization: Why and How?

1. Large time-varying simulations generate more data than can be saved – Problem gets worse as processing power increases – Models increase spatial and temporal-resolution 2. Saving data to mass storage consumes a significant portion of runtime 3. Only a small fraction of timesteps are typically saved and important dynamics may be missed process huge data efficiently

1. Extract data directly from running simulation for asynchronous processing • Add instrumentation to the simulation code, usually quite minimal 2. Simultaneously produce a series of visualizations • Many fields; • Multiple views 3. Generate and store images, movies, and “extracts” 4. Send visualizations of current simulation state almost anyygwhere, including web • Images of current state kept up-to-date in web browser • Stream progressively growing movies to remote systems 5. Use hyperwall-2 for parallel rendering and asynchronous I/O generate visualizations while model is still running

When Sandy Meets Lorenz 35 San Diego State Univ. Nov 21, 2014 Concurrent Visualizations: GMM

Green, B., C. Henze, B.-W. Shen, 2010: Development of a scalable concurrent visualization approach for high temporal- and spatial-resolution models. Eos Trans. AGU, 91(26), West. Pac. Geophys. Meet. Suppl., Abstract A23B-142. AGU 2010 Western Pacific Geophysics Meeting, Taipei, Taiwan, June 22-25, 2010. Shen, B.-W., B. Nelson, W.-K. Tao, and Y.-L. Lin, 2013a, "Advanced Visualizations of Scale Interactions of Tropical Cyclone Formation and Tropical Waves," Computing in Science and Engineering, vol. 15, no. 2, pp. 47-59, March-April 2013, doi:10.1109/MCSE.2012.64

When Sandy Meets Lorenz 36 San Diego State Univ. Nov 21, 2014 Concurrent Visualizations: WRF

Vis Support: NASA AIST CAMVis Project (PI: Shen) (Visualizations by David E. of NASA/Ames) Model Development: MAP Project (PI: Tao)

When Sandy Meets Lorenz 37 San Diego State Univ. Nov 21, 2014 A Personal Note on the History of Numerical Modeling

GCE Columbia fvGCM MMF ARPS (parallel) (Goddard)

1985 1990 1995 2000 2005

WRFv2 Lin et al (1983) MM4-NH MM5v1 ARPSv5

MM5v2 Earth Simulator

When Sandy Meets Lorenz 38 San Diego State Univ. Nov 21, 2014 Training and Stabilizer Wheels

• Heavy Duty BMX Training Wheels for 20-Inch BMX Wheel Bicycles, bilfboys or girls frame In the (regional) models, the • Heavy-Duty Steel Tubing to Support over 200lbs! Do not settle for interaction is one way. unsafe universal axle mounted training wheels

When Sandy Meets Lorenz 39 San Diego State Univ. Nov 21, 2014 Multi-Scale Modeling Framework (MMF): Super-parameterization

• fvGCM + embedded Goddard Cumulus Ensemble (GCE) cloud model – Global coverage + sophisticated microphysical processes • GCEs embedded at every grid point – Replaces Cumulus Parameterization (CP) at one grid point • Current configuration – 2x2. 5 degree fvGCM – 13,104 2D GCEs, at 4km resolution currently (using 99% of time) Æ viewed as a super component: meta-global GCE (mgGCE) – 3D GCEs are needed to improve simulations different parallelism in the fvGCM and mgGCE

When Sandy Meets Lorenz 40 San Diego State Univ. Nov 21, 2014 fvGCM vs. GCE grids

fvGCM grid (x-y-z) “2D “ GCE grid (x-z)

(0,2) Z’ (1~32) Z’ 2) 33 (0, 1) Z’ (1~ Z’

(0,0) (1,0) (2,0) (3,0)

X (1~144) X’ (1~64) dx~250km; dy~200km dx~4km (x, y, z) is (longitude, latitude, altitude). T, q at the center point; U, V, W at the edge point. Tao, W.-K., J. Chern, R. Atlas, D. Randall, X. Lin, M. Khairoutdinov, J._L. Li, D. E. Waliser, A. Hou, C. Peters-Lidard, W. Lau, and J. Simpson, 2009: Multi-scale modeling system: Development, applications and critical issues, Bull. Amer. Meteor. Soc. 90, 4, p. 515 Shen, B.-W., W.-K. Tao, J.-D. Chern, and R. Atlas, 2009: Scalability Improvements in the NASA Goddard Multiscale Multicomponent Modeling Framework for Tropical Cyclone Climate Studies. International Conference for High-Performance Computing in ASIA-Pacific Reggg,pion 2009. Proceedings, p249-256. Kaohsiung, Taiwan , March 2-5, 2009. Shen, B.-W., B. Nelson, S. Cheung, and W.-K. Tao, 2013b: Improving the NASA Multiscale Modeling Framework's Performance for Tropical Cyclone Climate Study. Computing in Science and Engineering, IEEE computer Society Digital Library. IEEE Computer Society, no. 5, pp. 56-67, Sep./Oct. 2013

When Sandy Meets Lorenz 41 San Diego State Univ. Nov 21, 2014 Revised Parallel Implementation: Domain Decomposition

Daemon Processes (driven by the input data from fvGCM tasks)

In the new version, a second level of Inter-communicator parallelism is implemented, decomposing a single row into individual columns. Each fvGCM task has an associated set of In the original 1-D decomposition, mgGCE tasks that compute the GCE's for each fvGCM task gets three or more a row in parallel. latitudes (rows), and computes the GCE's for eac h long itu de (co lumn ) [This second level is only for the GCE within a row. computation, not all of fvGCM.]

When Sandy Meets Lorenz 42 San Diego State Univ. Nov 21, 2014 Flow Charts of Parallel Implementation

Other column-based mmf_gce2d_task_ init() parameterizations P (~23) Q (()~3312) Master Slave mpi_comm_split() Creation of two groups fvGCM progresses GCE processes of processes

mpi_intercomm_create()

Process mapping gce2d_ task_ main ( ) mmf_gce2d_task_ (daemon, between two groups assignment() data-driven)

Inputs Dynamical mmf_call_gce2d(); distribution of Inputs mmf_invoke_gce2d() gce2d( ) outputs Shen, B.-W., B. Nelson, S. Cheung, and W.-K. Tao, 2013b: Improving the NASA Multiscale Modeling Framework's Performance for Tropical Cyclone Climate Study. Computing in Science and Engineering, IEEE computer Society Digital Library. IEEE Computer Society, no. 5, pp. 56-67, Sep./Oct. 2013

When Sandy Meets Lorenz 43 San Diego State Univ. Nov 21, 2014 Performance of fvMMF 2.0 on Pleiades (the first climate model implemented with MPI inter- and intra- communications)

120 Process Hierarchy: intra- and inter- fvMMF 2.0 100 communication Linear Speedup MMF consists of one 79.8 80 fvGCM and 13,104 (91x144) copies of GCE. 60 CtlCurrently, fGCMfvGCM is 50.2 running at a 2.5 degree 40 resolution, and GCEs 38.5 are at a 4km resolution.

20 The benchmark is 19.5 based on 5-day runs

0 with standard modeling 30 530 1030 1530 2030 2530 3030 configurations for MjMajor Feat ures: climate simulations . 1. Scalable with two-level parallelism on Pleiades (distributed memory) supercomputer; 2. A speedup of 79.8 with 3335 cores, which allows to finish a 30-day run within 41 minutes; 3. Bit-by-bit identical results with different CPU configurations; 4. Enablinggg high-resolutions and higher-dimensions for Goddard Cumulus Ensemble (()GCE) model Shen, Bo-Wen, B. Nelson, S. Cheung, W.-K. Tao, 2013b: Scalability Improvement of the NASA Multiscale Modeling Framework for Tropical Cyclone Climate Study. (accepted by IEEE CiSE; to appear in Sep/Oct 2013)

When Sandy Meets Lorenz 45 San Diego State Univ. Nov 21, 2014 Architecture of the CAMVis v1.0 (the Coupled Advanced Multiscale modeling and concurrent Visualization systems; Shen e al. 2011)

Multi-scale Modeling with “M” nodes Current Visualization with “N” nodes Real-time Display GMM

Large Scale

Intra-communication Parallel I/O Search for RDMA the MMF Coupler predictability Inter-communication•data regridding; •data input and output limits

Intra-communication

Cloud Scale

mgGCE comparison SimulationSimulation ParallelExtraction Transfer VisualizationVisualization withMPEG satellite generationDiscovery

When Sandy Meets Lorenz 46 San Diego State Univ. Nov 21, 2014 Progress of Hurricane Forecasts (National Hurricane Center) Track Errors (1989-2012) Intensity Errors (1990-2012)

bttbetter During the past twenty years, track forecasts have been steadily imppgroving ((pleft panel ), but Intensity forecasts have lagged behind until recently (e.g., 2012) (right panel).

``… the general problem of tropical cyclogenesis remains in large

measure,Shen, Bo-Wen, Bron one Nelson, o W.-K.fthf th Tao,e greaand Y.-L.t Lin,es 2013a:t mysAdvancedt eri es Visualizations of fth th eof Scalet rop Interactionsi cal a oft mospTropical Cycloneh ere. Formation’’ – and Tropical Waves. Computing in Science and Engineering, vol. 15, no. 2, pp. 47-59, March-April 2013, doi:10.1109/MCSE.2012.64 Kerryhttp://www.nhc.noaa.gov/verification/verify5.shtml Emanuel of MIT, The Divine Wind (2005).

When Sandy Meets Lorenz 47 San Diego State Univ. Nov 21, 2014 Formation of Hurricane Helene (2006)

• Simulations from Day 20 to Day 30 in a run initialized at 00Z Aug 22, 2006. http://goo.gl/arWSZ • Upper-level winds in red; middle-level winds in green; low-level winds in blue • Low-llCC(liili)Ulevel CC (cyclonic circulation); Upper-llAC(level AC (antiliicycloniccili)irculation) • Shen, B.-W. W.-K. Tao and M.-L. Wu, 2010b: African Easterly Waves in 30-day High- resolution Global Simulations: A Case Study during the 2006 NAMMA Period. GRL., L18803

When Sandy Meets Lorenz 48 San Diego State Univ. Nov 21, 2014 Simulations of Helene (2006) between Day 22-30 (Helene: 12-24 September, 2006)

Track Forecast Intensity Forecast

OBS model

to what extent can large-scale flows (e.g., an AEW) determine the mo vement and intensification of H urricane Helene?

Shen, B.-W., W.-K. Tao, and M.-L. Wu, 2010b: African Easterly Waves and African Easterly Jet in 30-day High-resolution Global Simulations. A Case Study during the 2006 NAMMA period. Geophys. Res. Lett., L18803, doi:10.1029/2010GL044355.

When Sandy Meets Lorenz 49 San Diego State Univ. Nov 21, 2014 Predicting Genesis of Six TCs in May 2002

``Although some aspects of the transformation of atmospheric disturbances into tropical cyclones are relatively well understood, the general problem of tropical cyclogenesis remains in large measure, one of the greatest mysteries of the tropical atmosphere.’’ – Kerry Emanuel, The Divine Wind (2005) Init at Init at 05/01 05/06 TC01A TC02B (May 6-10) (May 10-12) simu la tion, 2007 ; v isua liza tion, 2008; paper su bm itte d 2007,an d pu blis he d 2012, 28pp Errol May May May May May May (May 9-14) Kesiny 1 6 11 16 21 26 (May 3-11) Kesiny

01A Init at Init at 05/11 Errol 02B 05/22 Typhoon Hurricane Hagibis Hagibis Alma (May 24- June 1) (May 15-21) Alma

Best tracks (observations) indicated by blue lines:

When Sandy Meets Lorenz 50 San Diego State Univ. Nov 21, 2014 Hurricane Sandy (2012)

Remarkable simulations of TC formation and different tropical waves include: • TC Nargis (2008) and an Equatorial Rossby (ER) Wave (Shen et al., 2010a) • Hurricane Helene (()2006) and an African Easterl y Wave (AEW;;,) Shen et al., 2010b) • Twin TCs (2002) and a mixed Rossby Gravity (MRG) Wave (Shen et al., 2012)

The W all Street J ournal AGUGAGU Geop hys ica lRl Researc hLh Le tter October 28, 2012 September 19, 2013

When Sandy Meets Lorenz 51 San Diego State Univ. Nov 21, 2014 7-day Simulation and Visualization of Sandy

Collaboration with Dr. David Ellsworth of NASA/ARC/NAS

Shen, B.-WBNlW., B. Nelson, W.-KTK. Tao, and dY Y.-L. Lin, 2013a: Advance d Visua liza tions o f Sca le In terac tions o f Tropical Cyclone Formation and Tropical Waves. IEEE Computing in Science and Engineering, vol. 15, no. 2, pp. 47-59, March-April 2013, doi:10.1109/MCSE.2012.64.

When Sandy Meets Lorenz 52 San Diego State Univ. Nov 21, 2014 Multiscale Processes associated with Sandy

(a) (b) L T T

S S

Figure 7: 4D visualizations of Hurricane Sandy (2012) at 00Z Oct. 23 (a), 12Z Oct. 25 (b), 12Z Oct. 27 (c), and 12Z Oct. 28 (d). During the period, Sandy (labeled in a pink ‘S’) moved northward under the influence of the sub-tropical middle- and upper-level trough (to Sandy’s northwest) (a) , interacted with the trough that was deepening (b), increased its spatial extent (c), and encountered a pair of high-and-low blocking pattern over the North Atlantic, which prevent Sandy moving eastward further (d).

When Sandy Meets Lorenz 53 San Diego State Univ. Nov 21, 2014 Questions

• From a modeling perspective, why high-resolution global models have skills?

• From a perspective of hurricane dynamics, if and how the lead time of hurricane predictions can be extended? Æ a conceptual model with a focus on multiscale processes and approaches

• From a perspective of chaos (nonlinear) dynamics, are the simulations of TC formation consistent with chaos theory? (e.g., sensitive dependence on initial conditions?) Æ high-order Lorenz models (Shen 2014a,b)

When Sandy Meets Lorenz 54 San Diego State Univ. Nov 21, 2014 Scientific Goals

Tropical smallsmall-- Tropical ??? Cyclone ??? scale Waves Formation processes

Large scales Medium/Meso scales Small scales 1. to what extent can large-scale flows determine the timing and location of Tropical Cyclone (TC) genesis? (e. g., downscaling ) 2. to what extent can resolved small-scale processes impact solutions’ stability (or predictability)? (e.g., upscaling)

When Sandy Meets Lorenz 55 San Diego State Univ. Nov 21, 2014 Scientific Goals

Tropical MAP smallsmall-- Tropical MAP with??? Cyclone wi???th scale Waves PEEMD Formation SAT processes

MAP: Multiscale Analysis Package PEEMD: Parallel Ensemble Empirical Mode Decomposition SAT: Stability Analysis Tool

When Sandy Meets Lorenz 56 San Diego State Univ. Nov 21, 2014 Data and Model Analysis with the MAP

MAP Tropical MAP small- Tropical with Cyclone with scale Waves PEEMD Formation SAT processes

Data Analysis Model Analysis

When Sandy Meets Lorenz 58 San Diego State Univ. Nov 21, 2014 Empirical Mode Decomposition (EMD)

1. HHT (Hilbert Huang Transform, Huang et al., 1998) consists of Empirical mode decomposition (EMD) and Hilbert Transform. 2. The data-driven EMD method is Complete, Orthogonal, Local, and Adaptive (COLA), which is ideal for the local and nonlinear analysis. 3. EMD generates a set of intrinsic mode functions (IMFs), each of which has features with comparable scales (Wu and Huang 2009, and references therein). 4. EMD performs like a filter bank (e.g., a dyadic filter); the unique feature suggests a potential for hierarchical multiscale analysis.

When Sandy Meets Lorenz 59 San Diego State Univ. Nov 21, 2014 PEEMD: Scaling of 5000 Cores

MRG Case, Grid:1000x1000 (400MB), Ivy Bridge Processors 4-Level Parallelization SGI MPT library is used 10000 Grid DELayout Speed

(secs) I J Ens OMP Total Time ( secs.) Up 5 6 2 60 6543.56 1.0

Time 10 10 2 200 1983.25 3.3 10 10 4 400 1021.10 6.4 1000 20 20 2 800 531.36 12.3 20 20 4 1600 289.42 22.6 25 40 2 2000 231.69 28.2 25 20 2 2 2000 251.21 26.0 25 25 4 2500 200.60 32.6 25 25 4 2 5000 129.68 50.4 50 50 2 5000 123.85 52.8 100 10 100 1000 Parallel efficiency: 2000 cores , 28.2 /(2000/60)= 84.6% Total processors used 5000 cores, 52.8/(5000/60)=63.4%

When Sandy Meets Lorenz 61 San Diego State Univ. Nov 21, 2014 Analyzing Real-world Cases with the PEEMD

Multiscale analyygsis of the following case is discussed:

• Hurricane Sandy (2014) and tropical waves (e.g., MRG and ER)

1. to what extent can large -scale flows determine the timing and location of TC genesis? (e.g., downscaling)

When Sandy Meets Lorenz 62 San Diego State Univ. Nov 21, 2014 Decompositions of V winds with the PEEMD

Time

When Sandy Meets Lorenz 63 San Diego State Univ. Nov 21, 2014 Characteristics of Wave-like Disturbances (200-hPa V winds)

Time IMF 4 MRG Wave ER Wave

MRG

• A dispersion relation describes the relationship between the wavelength and period of a specific wave. • A mixed Rossby gravity (MRG) wave is indicated by dashed lines. • An Equatorial Rossby (ER) wave is indicated by white lines. • X indicates the location of Sandy. (Shen et al., 2013c, GRL; Shen et al., 2013e, IEEE Earthzine).

When Sandy Meets Lorenz 64 San Diego State Univ. Nov 21, 2014 Data and Model Analysis with the MAP

MAP Tropical MAP small- Tropical with Cyclone with scale Waves PEEMD Formation SAT processes

Data Analysis Model Analysis

When Sandy Meets Lorenz 65 San Diego State Univ. Nov 21, 2014 Scientific Goals

2. to what extent can resolved small-scale processes impact solutions’ stability (or predictability)? (e.g., upscaling)

• Increase or decrease complexities of the Lorenz model (3DLM) by deriving high-order Lorenz models (5DLM and 6DLM) or non- dissipative Lorenz model (NLM) • Apply the SAT to examine the stability of the above modified Lorenz models with the aim of understanding the impact of increased degree of nonlinearity, dissipation or heating terms on solutions’ stability (Un ders tandi ng th e ro le o f non linear ity i n ch aoti c responses ) • Investigate the possibility of applying the SAT (e.g., the calculations of eLE) to determining the predictability of global models

When Sandy Meets Lorenz 66 San Diego State Univ. Nov 21, 2014 Nonlinearity and Forcing Terms Rayleigh-Benard Convection

By assuming 2D (x,z), incompressible and Boussinesq flow, the following equations were used in Lorenz (1963)

This does not appear explicitly in the Lorenz model .

Non-linear terms

Boundary Forcing, which is represented by ‘r’.

• Navier-Stokes equation with constant viscosity • Heat transfer equation with constant thermal conductivity

When Sandy Meets Lorenz 67 San Diego State Univ. Nov 21, 2014 Lorenz Models

D, H, and N refer to as the dissipative terms, the heating term, and nonlinear terms

associated with the primary modes (low wavenumber modes), respectively. Ds, Hs, and Ns refer to as the dissipative terms, the heating term, and nonlinear terms associated with the secon dar y m odes (hi gh w av en um ber m odes), r espectiv el y. NLM r ef er s t o th e n on- dissipative Lorenz mode.

DHNDs Hs Ns Critical points rc Remarks for (X,Y) Linearzied V V “1” Unstable as r>1 3DLM

= = ± − 3DLM V V V X c Yc b(r 1) 24.74

= ± σ conservative 3D-NLM V V ( X c ,Yc ) ( 2 r ,0)

5DLM V V V V V= ± − 42.9 = = ± + X c Yc ~ 2b(r 1) X c Yc b(Zc 2Z1c ) 6DLM V V V V V V 41.1

Shen, B.-W., 2014a: Nonlinear Feedback in a Five-dimensional Lorenz Model. J. of Atmos. Sci. 71, 1701–1723. doi: http://dx.doi.org/10.1175/JAS-D-13-0223.1 Shen, B.-W., 2014b: On the Nonlinear Feedback Looppgyy and Energy Cycle of the Non-dissipative Lorenz Model. Nonlin. Processes Geophys. Discuss., 1, 519-541, 2014. www.nonlin-processes-geophys-discuss.net/1/519/2014/ Shen, B.-W., 2014c: Nonlinear Feedback in a Six-dimensional Lorenz Model. Impact of an Additional Heating Term. (to be submitted to JAS)

When Sandy Meets Lorenz 68 San Diego State Univ. Nov 21, 2014 3DLM vs. 5DLM

• The butterfly effect of first kind: sensitive dependence on initial conditions. • The butterfly effect of second kind: a metaphor (or symbol ) that small perturbations can alter large-scale structure. • Lorenz’s studies suggested finite predictability and nonlinearity as the source of chaos. • Increased degree of nonlinearity (e.g., multiscale interactions) can stabilize solutions and thus improve simulations (Shen et al., 2014a, b). r=25 Lorenz Model High-order Lorenz Model

Lorenz (1963) Shen, B.-W., 2014a

Negative Nonlinear Feedback The studies by Lorenz (1963, 1972) laid the foundation for chaos theory, which was viewed as the third scientific revolution of the 20th century after relativity and quantum mechanics (e.g. Gleick, 1987; Anthes 2011).

When Sandy Meets Lorenz 69 San Diego State Univ. Nov 21, 2014 Major Results with the 5DLM

• Generalized LMs: We derived the generalized 5D and 6D LMs to investigate the impact of three higher-wavenumber modes on the numerical predictability. • Unique Features of the 5DLM: The 5DLM is the lowest order generalized LM with improved system stability. The analytical solutions of the critical points in the 5DLM and its mathematical simplicity make it easier to identify the major feedback process and its role in the solutions' stability of the generalized LMs; and perform stability analysis near the critical points over a wide range of values in parameters (σ, r). • Nonlinear Feedback Loop: Just as Lorenz demonstrated the association of the nonlinearity with the existence of the non-trivial critical ppgoints and strange attractors in the 3DLM, we emphasized the importance of the nonlinearity in both producing new modes and enabling subsequent negative feedback to improve solution stability. M2 M3 M3 M5

• Degree of Nonlinearity: Inclusion of the M5 and M6 modes can extend the existing feedback loop and enable the subsequent negative feedback that stabilize the solution

When Sandy Meets Lorenz 70 San Diego State Univ. Nov 21, 2014 Track Forecasts of Sandy (2012) by different models

Oct 23 Oct 24 • Observation in white • ECMWF in coral • GFS in cyan • GFS ensem ble in ye llow • TVCA model consensus in red

Lead time: 6 days

Lead time: 4 days

Model forecast tracks for Sandy at 0000 UTC 23 Oct 25 Oct 26 October (a), 0000 UTC 24 October (b), 0000 UTC October 25 (c), and 0000 UTC 26 October (d). Solid color lines are the forecasts through 72 h, while dashed lines are from 72-120 h, and dotted lines represent the 120-168 h forecasts (top panels only). The ECMWF is in coral, the GFS ensemble in yellow, the GFS is in cyan, and the TVCA model consensus is in red.

Blake, E. S., T. B. Kimberlain, R. J. Berg, J. P. Cangialosi and J. L. Beven II, 2013: Tropical Cyclone Report: Hurricane Sandy, Rep. AL182012. Natl. Hurricane Cent., Miami, Fla.

When Sandy Meets Lorenz 73 San Diego State Univ. Nov 21, 2014 Questions

• What are the controlling factors in determining the eastward or westward movement of Hurricane Sandy in the mo de ls ? • What are the characteristics of solutions near a saddle point? What are the factors in determining the accuracy of solutions near the saddle point? • Is nonlinearity a source of chaos? (if so, is it good to idl’lti?)increase a model’s resolution?) (additi ona l fixe d po in ts ?) Nonlinearity can lead to H diverged trajectories at a finite time in a non- S dissipative Loren model wihith r= 0 or r≠0.

When Sandy Meets Lorenz 75 San Diego State Univ. Nov 21, 2014 The 3D non-dissipative Lorenz Model (3D-NLM)

To examine the role of the nonlinearity in the original 3DLM, our approach is to go back to simplify the original governing equations (for 2D Rayygleigh-Benard convection))y by dropp ppging the dissi pative terms , leading to

which contain two kinds of “forcing” terms, nonlinearity and heating.

Shen, B.-W., 2014b: On the Nonlinear Feedback Loop and Energy Cycle of the Non- dissipative Lorenz Model. Nonlin. Processes Geophys. Discuss., 1, 519-541, 2014 www.nonlin-processes-geophys-discuss.net/1/519/2014/ doi:10.5194/npgd-1-519-2014 (also being reviewed by the journal NPG; Sep. 17, 2014)

When Sandy Meets Lorenz 76 San Diego State Univ. Nov 21, 2014 3D-NLM vs. 3DLM

3D-NLM 3DLM

3D-NLM: 3D non-dissipative Lorenz model 3DLM: 3D Lorenz model

When Sandy Meets Lorenz 77 San Diego State Univ. Nov 21, 2014 Energy Conservation Laws

When Sandy Meets Lorenz 78 San Diego State Univ. Nov 21, 2014 Closed-form Solutions with the Trigonometric and Elliptic functions r=0 Trigonometric Elliptic function function

While waiting at the SFO airport

• It is nonlinear, forced and non-dissipative. • It is conservative for KE+PE and KE+APE, here KE, PE and APE are referred to as kinetic energy, potential energy, and available potential energy. • Numerical solutions of energy conservative quantities (KE+PE and KE+APE) show dependence on time intervals and/or forcing parameters.

When Sandy Meets Lorenz 79 San Diego State Univ. Nov 21, 2014 Butterflies in the Lorenz Models

Nonlinear Oscillatory Solutions

(0,0) is a stable critical point.

When Sandy Meets Lorenz 80 San Diego State Univ. Nov 21, 2014 Diverged Trajectories

Nonlinearity may Yic=1 cause a frequency shift in the solutions of the Yic=1+0.001 control and perturbation runs.

The continuous frequency shifts lead to diverged trajectories.

When Sandy Meets Lorenz 81 San Diego State Univ. Nov 21, 2014 Diverged Trajectories caused by Phase Shift

r=0

σ 2 = φ Xφ 2Yic sin( ) τ = Xdτ ∫ 0

When Sandy Meets Lorenz 83 San Diego State Univ. Nov 21, 2014 Ensemble Lyapunov Exponents (eLEs)

r=0 r=5

•∆=0.0001, • N=10,000,000 (time steps), giving the total =1,000. • En=10,000 ensemble runs with Gaussian white noise as ICs

When Sandy Meets Lorenz 84 San Diego State Univ. Nov 21, 2014 Butterflies in the Lorenz Models

3D-NLM (r=25)

Sa ddle point

When Sandy Meets Lorenz 85 San Diego State Univ. Nov 21, 2014 Glasswinged Butterfly in the 3D-NLM

3D-NLM (r=25) The wing pattern of a glasswinged butterfly

When Sandy Meets Lorenz 86 San Diego State Univ. Nov 21, 2014 Energy Cycle in the 3D-NLM

Linear Nonlinear ≥ APE ≤ APE APEY APE z Y z Half of a big cycle

( X c ,Yc ) = ± σ + 2 ( 2 r X 0 ,0)

CiConservative Nonlinear oscillatory solutions

When Sandy Meets Lorenz 87 San Diego State Univ. Nov 21, 2014 Nonlinear Oscillatory Solutions

Linear Nonlinear Nonlinear A saddle point at (0,0) and nonlinearity

( X c ,Yc ) = ± σ + 2 ( 2 r X 0 ,0)

Linear

When Sandy Meets Lorenz 88 San Diego State Univ. Nov 21, 2014 A Summary of Shen (2014b)

5. Based on the energy analysis, an energy cycle with four different

regimes is identified with the following four points: A(X,Y)=(0,0), B=(Xt, Yt), C=(Xm,Ym), D=(Xt, -Yt). (Xt, Yt)=( 2 σ r ,r) , (Xm,Ym)=( 2 σ r , 0). 6. The conservative 3D-NLM can be analytically reduced into a 2D system, which is not chaotic (at infinite time). 7. A small but positive ensemble Lyapunov exponent over a total time period of (=1,000) indicates the presence of diverged trajectories over a long but finite period of time in the 3D-NLM with r=0 and r≠0. Æ This suggests thfHilihhe appearance of Hamiltonian chaos. 8. The following factors may cause diverged trajectories: (1) nonlinearity alone (i.e., nonlinear feedback loop), which may continuously change the p hase o f the so lu tion an d (2) th e i ncl usi on of a h eati ng term th at could introduce a saddle point and interact with the nonlinear terms.

When Sandy Meets Lorenz 90 San Diego State Univ. Nov 21, 2014 Lessons Learned from the Studies of Hurricane Sandy and Lorenz models • Accurate representations of environmental flows near a saddle point are crucial for capturing the northwestward movement of Hurricane Sandyyp prior to its landfall. • Nonlinearity and the appearance of a saddle point can lead to chaotic responses in a non-dissipative Lorenz model, which is a conservative and has nonlinear oscillatory solutions. • High (spatial) resolution can improve the representation of environmental flows near a saddle point where the gradient of wind directions is large. • A lat-lon grid system, which non-uniform, may have advantage of simulating Hurricane Sandy as its grid spacing decreases when Sandy moved northward? • Factors in determining the phase speed of systems (e.g., an upper trough and/or vortex itself) may determine the eastward or westward movement of Sandy near the saddle point; these factors include grid spacing, initial conditions and physics parameterizations etc, (some of which may have cumulative impacts).

When Sandy Meets Lorenz 91 San Diego State Univ. Nov 21, 2014 AIST11

data transfer

Global Multiscale Supercomputing Modeling & Visualization

Satellite Data

NASA AIST CAMVis - Multiscale MAP(PI: Shen): $1,107K, 05/2012–08/2015, Analysis Integration of the NASA CAMVis and Multiscale Scalable framework for global EMD, ensemble EMD Analysis Package (CAMVis- Scalableand, multi-dimensional Multiscale ensemble Analysis EMD P ackage MAP) for Tropical Cyclone Climate Study.

When Sandy Meets Lorenz 92 San Diego State Univ. Nov 21, 2014 AIST14 (pending)

NASA AIST Project (PI: Shen): $957.8K, 05/2015-04/2017 (pending) Integration of Concurrent Ensemble Hierarchical Modeling and Fusion- Based Multivariate Data Visualization into the NASA CAMVis for Improving Climate Simulations

When Sandy Meets Lorenz 93 San Diego State Univ. Nov 21, 2014 Acknowledgements

• SDSU: Sam Shen and Ricardo Carretero • NASA/GSFC: Wei-Kuo Tao, William K. Lau, Jiundar Chern, Chung-Li Shie, Zhong Liu • UCAR: Richard Anthes • CU: Roger Pielke Sr. • NC A&T State U.: Yuh-Lang Lin • NASA/JPL: Frank Li, Peggy Li • Navy Research Lab: Jin Yi • NOAA/AOML: Robert Atlas • NOAA/NCEP/NHC, Mark DeMaria • UAH: Yu-Ling Wu • NASA/ARC: Piyush Mehrotra, Samson Cheung, David Kao, Bron Nelson, Johnny Chang, Chris Henze, Bryan Green, David Ellsworth, control-room • Funding Sources: SDSU College of Sciences, NASA ESTO (Earth Science Technology Office) AIST (Advanced Information System Technology) Program; NASA Compu tati ona l Mo de ling Algor ithms an d CbifttCyberinfrastructure (CMAC) program;

When Sandy Meets Lorenz 94 San Diego State Univ. Nov 21, 2014 Published Articles since 2010

Journal Articles: 1. Shen, B.-W., 2014a: Nonlinear Feedback in a Five-dimensional Lorenz Model. J. of Atmos. Sci. 71, 1701–1723. doi: http://dx.doi.org/10.1175/JAS-D-13-0223.1 2. Shen, B.-W., M. DeMaria, J.-L. F. Li and S. Cheung, 2013c: Genesis of Hurricane Sandy (2012) simulated with a global mesoscale model, Geophys. Res. Lett., 40, 4944–4950, doi:10.1002/grl.50934. 3. Shen, B.-W., B. Nelson, S. Cheung, W.-K. Tao, 2013b: Improving NASA’s Multiscale Modeling Framework for Tropical Cyclone Climate Study. IEEE Computing in Science and Engineering, vol. 15, no 5, pp 56-67. Sep/Oct 2013. 4. Shen, B.-W., B. Nelson, W.-K. Tao, and Y.-L. Lin, 2013a: Advanced Visualizations of Scale Interactions of Tropical Cyclone Formation and Tropical Waves. IEEE Computing in Science and Engineering, vol. 15, no. 2, pp. 47-59, March-April 2013, doi:10.1109/MCSE.2012.64. 5. Shen, B.-W., W.-K. Tao, and Y.-L. Lin, and A. Laing, 2012: Genesis of Twin Tropical Cyclones as Revealed by a Global Mesoscale Model: The Role of Mixed Rossby Gravity Waves. J. Geophys. Res. 117, D13114, doi:10.1029/2012JD017450. 28pp 6. Shen, B.-W., W.-K. Tao, and B. Green, 2011: Coupling Advanced Modeling and Visualization to Improve High-Impact Tropical Weather Prediction (CAMVis). IEEE Computing in Science and Engineering (CiSE), vol. 13, no. 5, pp. 56-67, Sep./Oct. 2011, doi:10.1109/MCSE.2010.141. 7. Shen, B .-W., W.-K. Tao , and M.-LWuL. Wu, 2010b: African Easterly Waves in 30 -day High resolution Global Simulations: A Case Study during the 2006 NAMMA Period. Geophys. Res. Lett., 37, L18803, doi:10.1029/2010GL044355. 8. Shen, B.-W., W.-K. Tao, W. K. Lau, R. Atlas, 2010a: Predicting Tropical Cyclogenesis with a Global Mesoscale Model: Hierarchical Multiscale Interactions During the Formation of Tropical Cyclone Nargis (2008) . J. Geophys. Res.,115, D14102, doi:10.1029/2009JD013140. Magazine Articles: 9. Shen, B.-W., S. Cheung, J.-L. F. Li, and Y.-L. Wu, 2013e: Analyzing Tropical Waves using the Parallel Ensemble Empirical Model Decomposition (PEEMD) Method: Preliminary Results with Hurricane Sandy (2012), NASA ESTO Showcase . IEEE Earthzine. 10. Shen, B.-W., 2013f: Simulations and Visualizations of Hurricane Sandy (2012) as Revealed by the NASA CAMVis. NASA ESTO Showcase. IEEE Earthzine. posted December 2, 2013. Papers under review/preparation: 11. Shen, B.-W., 2014b: On the Nonlinear Feedback Loop and Energy Cycle of the Non-dissipative Lorenz Model. (accepted, NPGD) 12. Shen, B.-W., 2014c: Nonlinear Feedback in a Six-dimensional Lorenz Model. Impact of an Additional Heating Term. (to be submitted)

When Sandy Meets Lorenz 95 San Diego State Univ. Nov 21, 2014 Back up Slid es

When Sandy Meets Lorenz 97 San Diego State Univ. Nov 21, 2014 (Global) Lyapunov Exponent (e.g., Shen, 2014a)

(Global) Lyapunov Exponent (e.g., climate scale) Finit e-Time L yapunov Exponen t (e.g., weather scale)

Trajectory (n)

Variational equation (n2)

δ = s(0) d0 unperturbed trajectory

When Sandy Meets Lorenz 98 San Diego State Univ. Nov 21, 2014 Ensemble Lyapunov Exponent (eLE)

• the trajectory separation (TS or orbit separation) method ∆=10-9 , an initial displacement in the TS scheme (e.g., Sprott, 2003, http://sprott.physics.wisc.edu/chaos/lyapexp.htm) • the Gram-Schmidt reorthonormalization (GSR) procedure (e.g. Wolf et al., 1985; Christiansen and Rugh, 1997) To minimize the dependence on ICs, 10,000 ensemble runs with the same model con fifigura tions bu t differen t IC s were perf ormed and an ensembl e averaged LE (eLE) was obtained from the average of the 10,000 LEs. •∆=0.0001, • N=10, 000,000 (time steps) , giving the total =1,000 . • En=10,000 ensemble runs with Gaussian white noise as ICs

When Sandy Meets Lorenz 99 San Diego State Univ. Nov 21, 2014 LEs of the 3DLM and 5DLM

When Sandy Meets Lorenz 100 San Diego State Univ. Nov 21, 2014