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PBL Parameteriza-On Review PBL parameterizaon review Haroldo Fraga de Campos Velho E-mail: [email protected] Web-page: www.lac.inpe.br/~haroldo Research interest Haroldo F. de Campos Velho (LAC-INPE) Senior Researcher / Scientific computing RESEARCH FIELDS: • Scientific computing and Inverse problems • Data science and data assimilation: New method: based on neural network • Atmospheric turbulence parameterization: Some results: Taylor’s approach for turbulence in clouds New model for convective boundary layer growth Cosmological evolution as turbulent-like dynamics Scienfic compung Solving (integral and/or) partial differential equations by numerical methods COMPUTATIONAL FLUID DYNAMICS: • Cavity Flow Scienfic compung Cavity flow under fractal domain GENERATING PRE-FRACTAL WITH L-SYSTEM: 1. Start with a inital configuration 2. A rule to change de configuration 3. Iteration for Step 2. Koch square curve Postulate: F rules: F ==> F+F-F-FF+F+F-F θ = 90o Scienfic compung Cavity flow under fractal domain Koch square curve Postulate: F rules: F ==> F+F-F-FF+F+F-F θ = 90o Scienfic compung Cavity flow under fractal domain Scienfic compung Cavity flow under fractal domain Scienfic compung Cavity flow under fractal domain Scienfic compung Cavity flow under fractal domain (phase diagrams) Fractal: Level-zero Fractal: Level-two Inverse problems Damage in structural systems ISS: International Space Station Inverse problems Damage in structural systems ISS: International Space Station Inverse problems A.P. Calderon - Seminar on Inverse Problems and Applications LNCC, Rio de Janeiro (RJ), March-2006 Forecasts Scores ECMWF Inverse problems Atmospheric profiles from satellite data Inverse problems Atmospheric profiles from satellite data Inverse problems Atmospheric profiles from satellite data Causes Forward problem Effects Temperature Profile Radiance Inverse problem More important for Inverse problems numerical weather prediction Atmospheric profiles from satellite data 1 10 1 1 10 10 Radiossonde Radiossonde Radiossonde Neural Network Neural Network Neural Network Tikhonov-1 Tikhonov-1 Tikhonov-1 MaxEnt-2 MaxEnt-2 MaxEnt-2 2 2 2 10 10 10 Pressure Pressure (hPa) Pressure Pressure (hPa) Pressure Pressure (hPa) 3 3 3 10 10 10 180 200 220 240 260 280 300 320 180 200 220 240 260 280 300 320 180 200 220 240 260 280 300 320 Temperat ure (K) Temperat ure (K) Temperat ure (K) Retrievals using SDB1 Retrievals using TIGR Retrievals combining for training phase. for training phase. SDB1+TIGR. Inverse problems Inverse problems Calibration of models (parameter identification) Inverse problems Preparing the models: calibration (IBIS model) Inverse problems Preparing the models: calibration (IBIS model) Inverse problems Preparing the models: calibration (IBIS model) Calibraon: sensivy analysis (2) n Morris’ method ¨ SensiBvity analysis ¨ Trajectories in the search space (2D (a) / and 3D (b)) Numerical results (1) n IdenBfying faster to slower processes (Figure 1) Inverse problems Preparing the models: calibration (IBIS model) Data assimilaon Very important inverse problem Determining the initial condition Forecasts Scores ECMWF Data assimilaon Very important inverse problem Determining the initial condition 29 Data assimilaon Very important inverse problem Determining the initial condition 30 Data assimilaon § Data assimilation: data fusion 31 Impact with the exponential growth for the available data Numerical models with very high resolution Number of observation are increasing: different satellites with thousands of bands, sensor cost decreasing. Data assimilation: an essential issue § Temperature: ANN assimilation experiment LETKF neural network True Results from Rosangela Cintra PhD thesis (2011) Data assimilation: an essential issue § Moisture: 1 month assimilation experiment LETKF neural network True Results from Rosangela Cintra PhD thesis (2011) Numerical experiment: LEKF and ANN Execuon me LETKF method ANN method 04:20:39 00:02:53 hours : minutes : seconds Atmospheric general model circulaon (spectral model): 3D SPEEDY (Simplified Parameterizaons primiBvE Equaon DYnamics) Gaussian grid: 96 x 48 (horizontal) x 7 levels (verBcal) = T30L7 Total grid points: 32,256 Total variables in the model: 133,632 Observaons: (00, 06, 12, 18 UTC) – radiosonders “OMM staons” Observaons: 12035 (00 and 12 UTC) = 415 x 4 x 7 + 415 Observaons: 2075 (06 and 18 UTC) = 415 x 5 (only surface) Errors: (Kalman, Particles, Variational) x Neural Networks Atmospheric turbulence modeling Boundary Layer theory Why “boundary layer theory”? 1. The “happy world”: ideal fluid dynamics 2. The end of the “happy world”: the D’Alembert’s paradox 3. Solving the D’Alembert’s paradox: boundary layer 4. Boundary layer theory: a place to find turbulence Atmospheric turbulence modeling The “happy world”: ideal fluid dynamics Why “boundary layer theory”? 1. Ideal fluid (mechanical): incompressible 2. Ideal fluid (mechanical): constant density 3. Ideal fluid (mechanical): invisity Atmospheric turbulence modeling Ideal fluid dynamics: incompressible fluid Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: incompressible fluid Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: Rankine oval Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: Rankine oval Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: Rankine oval Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: Rankine oval Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: Rankine oval Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: Rankine oval Why “boundary layer theory”? Atmospheric turbulence modeling Ideal fluid dynamics: Rankine oval Why “boundary layer theory”? Atmospheric turbulence modeling The end of “happy world”: D’Alembert paradox Why “boundary layer theory”? “The drag force on a submerged body is zero!” Atmospheric turbulence modeling Solution for the paradox: Boundary layer theory Ludwig Prandtl (German physicist) suggested in 1904 that the effects of a thin viscous boundary layer could be the reason for the drag. Atmospheric turbulence modeling Boundary layer theory Theodore von Kármán (Hungarian): von Kármán vortex street Atmospheric turbulence modeling Boundary layer theory Theodore von Kármán (Hungarian): von Kármán vortex street Ocean: coast of Chile (near the islands Juan Fernandez) Atmospheric turbulence modeling • Leonardo da Vinci (~ 1510): ‘‘... thus the water has eddying motions, one part of which is due the principal current, the other to the random and reverse motion.’’ • Osborne Reynolds (1883): flow decomposition ! ! ! ⎧ v ( r , t ) = v(r,t) + v'(r,t) ⎨ ! ⎩v(r,t) : average flow (similar to laminar flow) • Lewis Fry Richardson (1922): - Cascade: ‘‘Big whirls have little whirls ...’’ - Universality: statistical behaviour is independent of external geometry, fluid nature, mecanism of injection of energy, ... • G.I. Taylor (1921): statistical theory Atmospheric turbulence modeling Old ideas on turbulence • Leonardo da Vinci (~ 1510): ‘’... thus the water has eddying motions, one part of which is due the principal current, the other to the random and reverse motion..” Atmospheric turbulence modeling Old ideas on turbulence • Osborne Reynolds (1883): flow decomposition Atmospheric turbulence modeling Old ideas on turbulence • Osborne Reynolds (1883): flow decomposition Atmospheric turbulence modeling Atmospheric turbulence modeling Old ideas on turbulence • Lewis Fry Richardson (1922): o Energy cascade: “Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity. Turbulence Universality: o - statístical properties do not depend on geometry - turbulence does not depend on fluid nature - mechanism of energy injection ... L. F. Richardson: English scientist, matematician, physisit, meteorologist, psicologist, and paece activist. Proponent of the numerical weather prediction and suggested similar approach for studying war causes for avoiting the war. Pionering in the fractal technics, linear equation solution, extrapolation method. Atmospheric turbulence modeling Old ideas on turbulence • Lewis Fry Richardson (1922): o Modern numerical weather prediction follows the Richardon’s scheme o Computers: Human beings to do the computation Atmospheric turbulence modeling Old ideas on turbulence • Lewis Fry Richardson: o Richardson’s Number (ratio between potential and kinetic energies): gh R = i u 2 o Richardson’s extrapolation: - Numerical analysis: a method for sequential speed-up - Aplications: (i) Romberg’s integration method (ii) Bulirsch–Stoer’s algorithm for EDO solution From the wikipedia Atmospheric turbulence modeling The (Geoffrey Ingram) Taylor’s theory • Associated phenomena with G. I. Taylor name * Taylor cone * Taylor dispersion * Taylor number * Taylor vortex * Taylor–Couette flow * Rayleigh–Taylor instability * Taylor-Proudman theorem * Taylor-Green vortex * Taylor microscale Atmospheric turbulence modeling Our challenge: representing Planetry Boundary Layer Introduction to the Taylor’s theory The (Geoffrey Ingram) Taylor’s theory Turbulence and Reynolds Hypothesis: The dynamical (turbulent) variable can be understood a sum of a mean stream and a deviation: ϕ = ϕ + ϕ ' ; being ϕ a mean stream (similar to laminar flow), and ϕ' a fluctuation (deviation) with zero mean: ϕ ' = 0 . Dealing with average process the Navie-Stokes and the diffusion equations become
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