Mu Mu F.F.Zhou,H.L.Wang and X.G.Wu

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Some New Progresses in the Applications of Conditional Nonlinear Optimal Perturbations. Mu Mu F.F.Zhou,H.L.Wang and X.G.Wu State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), - PowerPoint PPT Presentation

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  • Mu Mu F.F.Zhou,H.L.Wang and X.G.WuState Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics (IAP),Chinese Academy of Sciences (CAS)mumu@lasg.iap.ac.cn

    http://web.lasg.ac.cn/staff/mumu/ Some New Progresses in the Applications of Conditional Nonlinear Optimal Perturbations

  • Outline1. Concept of conditional nonlinear optimal perturbation (CNOP) and the difference between CNOP and LSV2.Adaptive observations (MM5 model)

    3.The sensitivity of oceans thermohaline circulation (THC) to the finite amplitude initial perturbations

  • 1. Conditional Nonlinear Optimal Perturbation(1)

  • Conditional Nonlinear Optimal Perturbation(CNOP)Constraint condition

  • The initial error which has largest effect on the uncertainty at prediction time. 2. The initial anomaly mode which will evolve into certain climate event most probably (ENSO)3. The most unstable (or sensitive ) initial mode of nonlinear model with the given finite time periodPhysical meaning of CNOP

  • : (linear) propagator of (1)where(2)

  • [1] Mu Mu, Duan Wansuo, Wang Bin, 2003, Nonlinear Processes in Geophysics, 10, 493-501.

    [2] Duan Wansuo, Mu Mu, Wang Bin, 2004,. JGR Atmosphere, 109, D23105, doi:10.1029/2004JD004756.

    [3] Mu Mu, Sun Liang, D.A. Henk, 2004, J. Phys. Oceanogr., 34, 2305-2315.

    [4] Sun Liang, Mu Mu, Sun Dejun, Yin Xieyuan, 2005, JGR-Oceans, 110, C07025,doi: 10.1029/2005JC002897.

    [5] Mu Mu and Zhiyue Zhang,2006,J.Atmos.Sci..

    [6] Mu Mu ,Hui Xu and Wansuo Dun(2007),GRL

    [7] Mu Mu ,Wansuo Duan and Bin Wang (2007),JGR

    [8] Mu Mu and Wang Bo,2007, Nonlinear Processes in Geophysics[9]Olivier Riviere et al,2008,JASReference

  • When nonlinearity is of importance , there exist distinct difference between CNOP and LSV represented by two facts:a. The initial patterns are different Note: LSV stands for the optimal growing direction , but CNOP the patternb. Linear and nonlinear evolutions of CNOP and LSV are different.Mu Mu and Zhiyue Zhang,2006.J.Atmos.Sci.

  • 2. Adaptive ObservationFASTEX (Snyder 1996)NORPEX (Langland et al.1999)WSR (Szunyogh et al. 2000,2002)DOTSTAR (Wu et al.2005)NATReC (Petersen et al. 2006 )THORPEX (in process)

  • Methods used in Adaptive ObservationsSV (Palmer et al.1998)Adjoint Sensitivity (Ancell and Mass 2006) ET (Bishop and Toth 1999)EKF (Hamill and Snyder 2002) ETKF (Bishop et al. 2001) Quasi-inverse Linear Method (Pu et al.1997)ADSSV (Wu et al. 2007)

  • The sensitive areas identified by different methods may differ much. Which one is better is still in discussion (Majumdar et al.2006).

    Conditional nonlinear optimal perturbation (CNOP), which is a natural extension of linear singular vector (SV) into the nonlinear regime, is in the advantage of considering nonlinearity (Mu et al, 2003; Mu and Zhang,2006).

  • Applications of CNOP to Adaptive Observations Rainstorms Tropical cyclones

  • RainstormsCase A: Rainfall during 0000 UTC 4 July~ 0000 UTC 5 July, 2003 on the Jianghuai drainage basin in China

    Case B: Rainfall during 0000 UTC 5 Aug~ 0000 UTC 6 Aug, 1996 on the Huabei plain in China

  • optimization algorithm SPG2(Spectral projected gradient, Birgin etal,2001)Characters: box or ball constraints linearity convergence high dimensions The constraint in this study is The optimization time interval is 24 hours.

  • Experimental designModel: MM5 and its Adjoint Grid number: 51*61*10 Grid distance: 120kmTop level: 100hPaPhysical parameterizations: dry-convective adjustment grid-resolved large scale precipitation high resolution PBL scheme Anthes-Kuo cumulus parameterization scheme

    Data: NCEP analysis ECMWF reanalysis routine observations

  • Total dry energy is chosen as a metricwhere,The integration extends the full horizontal domain D and the vertical direction .

  • Figure1.The temperature (shaded, unit:K) and wind (vector, unit: m/s) components of CNOP(a,b), FSV (c,d) and loc CNOP (e,f) on levelat 0000 UTC 4 July (a,c,e) and their nonlinear evolutions at 0000 UTC 5 July (b,d,f).

    Case Ac (FSV)b(CNOP)a (CNOP)d (FSV)e (loc CNOP)f (loc CNOP) Nonlinear evolutions

  • Figure 2. Case AThe evolution of the total dry energy on targeting area during the optimization time interval. CNOP (solid), local CNOP(dashed), FSV (dot) and -FSV (dashdotted). The TE showed is divided by the initial. Table 1.Case A: The maxima (minima) of temperature (unit: K), zonal and meridional wind (unit: m/s) on level time type0000 UTC 4 July, 20030000 UTC 5 July, 2003

  • Figure 3. Same as Fig.1(a,b,c,d), but for case B at 0000 UTC 5 Aug, 1996 (a,c) and at 0000 UTC 6 Aug, 1996 (b,d)a (CNOP)b (CNOP)c (FSV)d (FSV)Nonlinear evolutions

  • Table 2. Same as table 1, but for case B Figure 4Same as Fig.2, but for case B 0000 UTC 5 Aug, 19960000 UTC 6 Aug, 1996time type

  • Sensitivity experimentsCase ACase BFigure 5. the variations of the cost function due to the reductions of CNOP (solid) or FSV (dashed) during the optimization time interval for case A and case B.

  • Tropical Cyclones Case C: Mindulle, North-West Pacific Tropical cyclones 0000 UTC 28 Jun ~ 0000 UTC 29 Jun, 2004 Case D: Matsa, North-West Pacific Tropical cyclones 0000 UTC 5 Aug ~ 0000 UTC 6 Aug , 2005

  • optimization algorithm SPG2(Spectral projected gradient, Birgin etal,2001)The constraints are for case C,and for case D.The optimization time intervals for these two casesare still 24 hours.

  • Experimental designModel: MM5 and its Adjoint Grid number: 41*51*11(case C), 55*55*11(case D) Grid distance: 60kmTop level: 100hPaPhysical parameterizations: dry-convective adjustment grid-resolved large scale precipitation high resolution PBL scheme Anthes-Kuo cumulus parameterization scheme

    Data: NCEP reanalysis

  • Metricstotal dry energydynamic energywhere,The integration extends the full horizontal domain D and the vertical direction .

  • Simulation of case C (Mindulle)aba: model domainb: target areaFigure 6.Simulation track from MM5 (red)and the observation track (blue) from CMA

  • ab

    a: model domainb: target areaFigure 7.Simulation track from MM5 (red)and the observation track (blue) from CMA Simulation of case D (Matsa)ab

  • ResultsMindulledynamic energy, 24-hNonlinear evolutions CNOPat 0000 UTC 28 Junat 0000 UTC 29 JunFSVCNOPFSV

  • Mindulledry energy, 24-hat 0000 UTC 28 Junat 0000 UTC 29 JunNonlinear evolutionsCNOPFSVCNOPFSV

  • Case C (Mindulle)The evolutions of the dynamic energies (KE) and total dry energies (TE) of CNOP (blue) and FSV (red) on targeting area during the optimization time interval. Unit: J/kg

    Chart1

    16.2717.479

    9561734.17

    2088.518241.971

    9215.3343862.78

    36823.87674259.65

    21207.97953330.92

    14474.631293.195

    31586.96925839.203

    80881.4326518.69

    CNOP

    FSV

    time(h)

    TE(J/kg)

    24h nonlinear development (TE)

    Sheet1

    16.2717.47911.8372.0430

    9561734.17854.411602.1763

    2088.518241.9711928.137651.5766

    9215.3343862.788786.2641740.999

    36823.87674259.6536174.23772375.4712

    21207.97953330.9220689.3451137.115

    14474.631293.19513743.229284.01418

    31586.96925839.20330501.4724669.4721

    80881.4326518.6978741.2525395.4124

    te-CNOP-4ps160kmwhl-cnop-24hte-FSV4ps160kmwhl-lsv-24hcnop-kelsv-ke

    21.058.9232

    336.8584.81

    1413.672283.6

    7354.52914500.1

    28286.630459.576

    23810.0727039.443

    11933.7218691.8703

    21980.118526.316

    64608.67928568.59

    ke-4ps160kmwhl-cnop-24hke-4ps160km-lsv-24h

    Sheet1

    CNOP

    FSV

    CNOP-KE

    FSV-KE

    24h nonlinear development

    Sheet2

    CNOP

    FSV

    24h nonlinear development (KE)

    Sheet3

    CNOP

    FSV

    time(h)

    TE(J/kg)

    24h nonlinear development (TE)

    Chart1

    21.058.9232

    336.8584.81

    1413.672283.6

    7354.52914500.1

    28286.630459.576

    23810.0727039.443

    11933.7218691.8703

    21980.118526.316

    64608.67928568.59

    CNOP

    FSV

    time(h)

    KE(J/kg)

    24h nonlinear development (KE)

    Sheet1

    16.2717.47911.8372.0430

    9561734.17854.411602.1763

    2088.518241.9711928.137651.5766

    9215.3343862.788786.2641740.999

    36823.87674259.6536174.23772375.4712

    21207.97953330.9220689.3451137.115

    14474.631293.19513743.229284.01418

    31586.96925839.20330501.4724669.4721

    80881.4326518.6978741.2525395.4124

    te-CNOP-4ps160kmwhl-cnop-24hte-FSV4ps160kmwhl-lsv-24hcnop-kelsv-ke

    21.058.9232

    336.8584.81

    1413.672283.6

    7354.52914500.1

    28286.630459.576

    23810.0727039.443

    11933.7218691.8703

    21980.118526.316

    64608.67928568.59

    ke-4ps160kmwhl-cnop-24hke-4ps160km-lsv-24h

    Sheet1

    CNOP

    FSV

    CNOP-KE

    FSV-KE

    24h nonlinear development

    Sheet2

    CNOP

    FSV

    time(h)

    TE(J/kg)

    24h nonlinear development (TE)

    Sheet3

    CNOP

    FSV

    time(h)

    KE(J/kg)

    24h nonlinear development (KE)

  • Matsadynamic energy, 24-hat 0000 UTC 5 Augat 0000 UTC 6 AugNonlinea

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