toward accurate coastal ocean modelingchu/web_paper/conference/01/accurate_pred.pdf · •pro –...
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Toward Accurate Coastal Ocean Modeling
Peter C. ChuNaval Postgraduate SchoolMonterey, CA 93943, USA
Email: [email protected]://www.oc.nps.navy.mil/~chu
International Council for Sciences, Scientific Committee for Oceanic Research (SCOR)-, Miami, FL,
April 5-7, 2001.
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Coastal Model
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Lynch et al. (Oceanography 2001)
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Major Problems in Coastal Modeling
• (1) Discretization• (2) Sigma Error• (3) Difference Schemes• (4) POM Capability • (5) Air-Ocean Coupling• (6) Severe Weather Effect • (7) Velocity Data Assimilation • (8) Turbulence/Wave Effects
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(1) Discretization
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Diversity in Discretization
• Finite Differences– Z – coordinate (MOM, …)– σ - coordinate (POM, COHERENS, etc…)– s- coordinate (SCRUM, ROMS …)– Layered/Isopycnal coordinates (NLOM,
MICOM, …)• Finite Elements
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Z-Coordiante
• Note “staircase” topography representation, normally with no-slip conditions
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Problems of the “Staircase Presentation”
• Difficult in simulating coastal flow.
• Example: Japan/East Sea (JES) Simulation (Kim and Yoon, 1998 JO)
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JES Circulation Model Using MOM(Kim & Yoon, 1998)
• 1/6 deg resolution• 19 vertical level• Monthly mean wind
stress (Na et al. 1992)• Monthly mean heat
flux (Haney type)
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Problem in Simulating Coastal Currents
• Model Observation
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Layered/Isopycnal Coordinates• Pro
– Horizontal mixing is exactly along the surfaces of constant potential density
– Avoids inconsistencies between vertical and horizontal transport terms
• Con– It requires an evident
layered structure (not suitable for shelf circulation
– Some difficulty in modeling detrainment of ocean mixed layer
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Layered/Isopycnal Coordinates
• (Metzger and Hurlburt1996, JGR)
• 1/8o, 6 layer with realistic bottom topography
• Not applicable to simulating shelf circulation
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Sigma Coordinate Models
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Sigma Coordinates
• Pro– Realistic Bottom
Topography
– Applicable to Shelf and Estuarine Circulation
• Con– Horizontal Pressure
gradient Error– High Vertical
Resolution in Shallow Water (Shelf) and Low Resolution in Deep Water
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Horizontal Diffusion
• The second and fourth terms in the righthand side are neglected.
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(2) Sigma Error
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Pressure Gradient Error
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Pressure Gradient Error
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Seamount Test Case
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Two Kinds of Sigma Errors(Mellor et al. 1998, JTECH)
• First Kind (SEFK):Horizontal Density GradientOscillatory Decaying
• Second Kind (SESF)– Vorticity Error
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Reduction of Sigma Error
• Smoothing topography• Subtracting horizontally averaged density
field• Using generalized topography-following
coordinate system (e.g., S-coordinates in ROMS)
• Using high-order difference schemes
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S-CoordinateGeneralized Topography-Following
Coordinates (Song & Haidvogel, 1994)
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Error Analysis (S-Coordinate)
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Error Evolution (S-coordinate)
• Radius of Seamount: r1 = 40 km, r2 =80 km
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High-Order Schemes• Ordinary Five-Point Sixth-Order Scheme (Chu and Fan,
1997 JPO)• Three-Point Sixth-Order Combined Compact Difference
(CCD) Scheme (Chu and Fan, 1998 JCP)• Three-Point Sixth-Order Nonuniform CCD Scheme (Chu
and Fan, 1999, JCP)• Three-Point Sixth-Order Staggered CCD Scheme (Chu
and Fan, 2000, Math. & Comp. Modeling)• Accuracy Progressive Sixth-Order Scheme (Chu and
Fan, 2001, JTECH)
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(3) Difference Schemes
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Why do we need high-order schemes?
• (1) Most ocean circulation models are hydrostatic.
• (2) If keeping the same physics, the grid space (∆x) should be larger than certain criterion such that the aspect ratio
δ = H/ ∆x << 1
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A Hidden Problem in Second Order Central Difference Scheme
• Both Φ’ and Φ’’ are not continuous at each grid point. This may cause some problems.
• Local HermitianPolynomials
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Three-Point Sixth-Order Scheme
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Three-Point Sixth Order CCD Schemes
• Existence of Global Hermitian Polynomials• First Derivative Continuous
• Second Derivative Continuous
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Error Reduction Using CCD Schemes (Seamount)
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Rotating Cone for Testing Various Schemes
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Accuracy Comparison
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(4) POM Capability
Chu et al 2001, JTECH
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Evaluation of POM Using the South China Sea Monsoon Experiment (SCSMEX) Data
• IOP (April – June 1998)
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T-S Diagram from SCSMEX Observations
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Two Step Initialization of POM• (1) Spin-up
– Initial conditions: annual mean (T,S) + zero velocity– Climatological annual mean winds + Restoring type
thermohaline flux (2 years)• (2) Climatological Forcing
– Monthly mean winds + thermohaline fluxes from COADS (3 years) to 1 April
• (3) The final state of the previous step is the initial state of the following step
• (4) Synoptic Forcing– NCEP Winds and Fluxes: April 1 to June 30, 1998 (3 Months)
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Two Types of Model Integration
• (1) MD1: – Without Data Assimilation – Hindcast Period: April-June 1998 (3 Months)
• (2) MD2: – With Daily SCSMEX-CTD Data Assimilation – Hindcast Period:
• May 1998: No data Assimilation in May • June 1998: No data Assimilation in June
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Skill-Score
• Model-Data Difference
•• Mean Square Error
• Skill-Score (SS)
• SS > 0, Model has capability
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Scatter Diagrams Between Model and Observation (MD1)
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Histograms of (Model – Obs) for MD1
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RMS Error for MD1 (No Assimilation)
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Bias for MD1 (No Assimilation)
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Skill-Score for MD1 (No Assimilation)
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Scatter Diagrams for MD2 (with Assimilation)
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RMS Error for MD2 (with Assimilation)
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Bias for MD2 (with Assimilation)
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Skill-Score for MD2 (with Assimilation)
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Comments
• (1) POM-SCS has synoptic flux forcing.• (2) Without data assimilation, it has
capability to predict temperature, but not salinity.
• (3) With data assimilation, it has capability to predict salinity.
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(5) Air-Ocean Coupling
• Coastal Atmosphere-Ocean Coupled System (CAOCS) for East Asian Marginal Sea (EAMS) Prediction
• Chu et al. (1999, JO)
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Necessity for Air-Ocean Coupling
• (1) Sparse Meteorological Observation over Ocean
• (2) Uncertain Surface Fluxes
• (3) Nowcast/Forecast
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Uncertain Atmospheric Forcing
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RMS Difference Between NSCAT and NCEP Winds
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Temporally Varying RMS Difference Between POM Model Results Under the Two Wind Forcing
(Chu et al. 1998, JGR)• Surface elevation
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Temporally Varying RMS Difference Between POM Model Results Under the Two Wind Forcing
(Chu et al. 1998, JGR)• Velocity
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Temporally Varying RMS Difference Between POM Model Results Under the Two Wind Forcing
(Chu et al. 1998, JGR)• Temperature
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CAOCS Components
• Atmosphere: MM5-V3.4
• Ocean: POM
• Land Surface: BATS
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CAOCS for East Asian Marginal Sea Prediction
Chu et al. (1999, 2000)
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East Asian Circulation System
• Nitani (1972) Beardsley et al. (1983)
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Area for Atmospheric Model
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Distribution of Vegetation
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Area for Ocean Model
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Ocean Bottom
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CAOCS Numerics• MM5V3.4
– Resolution• Horizontal: 30 km• Vertical: 16 Pressure Levels
– Time step: 2 min• POM
– Resolution• Horizontal: 1/6o × 1/6o
• Vertical: 23 σ levels– Time Steps: 25 s, 15 min
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Ocean-Atmospheric Coupling
• Surface fluxes (excluding solar radiation) are of opposite signs and applied synchronously to MM5 and POM
• MM5 and POM Update fluxes every 15 min
• SST for MM5 is obtained from POM • Ocean wave effects (ongoing)
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Lateral Boundary Conditions
• MM5: ECMWF T42
• POM: Lateral Transport at 142oE
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MM5 Initialization
• Initialized from: 30 April 1998 (ECMWF T42)
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Three-Step Initialization of POM• (1) Spin-up
– Initial conditions: annual mean (T,S) + zero velocity– Climatological annual mean winds + Restoring type
thermohaline flux (2 years)• (2) Climatological Forcing
– Monthly mean winds + thermohaline fluxes from COADS (3 years)
• (3) Synoptic Forcing– Winds and thermohaline fluxes from NCEP (1/1/96 – 4/30/98)
• (4) The final state of the previous step is the initial state of the following step
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Simulated Surface Air Temperature, May 98
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Volume Transport (Sv) Through Taiwan Strait
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Volume Transport (Sv) Through Korean/Tsushima Strait
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(6) Severe Weather Effect
• Response of the South China Sea to tropical cyclone Ernie 1996
• Chu et al. 2000 (JGR)
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Tropical Cyclone Ernie 1996
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Tropical Cyclone Wind Profile Model (Carr & Elsberry 1997, MWR)
• r ~ horizontal distance to the storm center• (uc, vc ) ~ radial and tangential velocities• γ ~ wind inflow angle to storm center• a = r/Rm , scaling factor • X ~ parameter
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Surface Wind Field
• Vc ~ Wind field relative to the storm center (from the wind profile model)
• Vt ~ Strom translation velocity• Vbg ~ Back ground wind field
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Computed Wind Field
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NSCAT Winds
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Time series of velocity and power density at 13oN and 119.5oE from
November 2 to 18, 1996
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Comments
• Pom has a capability to simulate response of coastal water to tropical cyclones.
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(7) Velocity Data Assimilation
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Can we get the velocity signal from sparse and noisy data?
• Black Sea
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Reconstruction of Velocity Field in Open Domain
Chu (2000)Chu and Ivanov (2001a,b)
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Flow Decomposition
• 2 D Flow (Helmholtz)
• 3D Flow (Toroidal & Poloidal): Very popular in astrophysics
•
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3D Incompressible Flow
•• When •u = 0• We have
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Flow Decomposition
• 2 Ψ = - ζ, ζ is relative vorticity• 2Φ = - w
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Boundary Conditions
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Basis Functions
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Flow Reconstruction
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Reconstructed Circulation
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Several Comments
• Reconstruction is a useful tool for processing real-time velocity data with short duration and limited-area sampling.
• The scheme can handle highly noisy data.• The scheme is model independent.• The scheme can be used for assimilating s
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(8) Turbulence/Wave Effects
(a) Wave Momentum Flux in the Ocean (especially near the bottom)(b) Surface Roughness Length
(c) Wave Effect on TKE
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Turbulence Parameterizations
• Bulk Mixed Layer Models – Garwood (1977), Price et al. (1986), Chu et al.
(1990), Chu and Garwood (1991), Chu (1993)
• Diffusion Models – Mellor and Yamada (1982)– Kantha and Clayson (1994)
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Flow Decomposition
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Momentum Flux
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Turbulence/Wave Effects
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Wave Stress in the Interior
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Bottom Boundary Layer
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Wave Effect on Surface Roughness Length
• TKΕ Dissipation in Air and Ocean are Functions of Wave Variables
• ε = f(h, λ, uph)
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Wave Breaking & Turbulent Dissipation
• TKE Equation:
• D TKE/DT = S + WB ± B – D
– S: Shear Production– WB: Wave Breaking Effect– B: Buoyancy Production or Damping– D: Dissipation
• WB = γ (uphh)3/ λ4