A Mechanical Energy Budget and Evaluation of an Eddying Global
Transcript of A Mechanical Energy Budget and Evaluation of an Eddying Global
![Page 1: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/1.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
A Mechanical Energy Budget andEvaluation of an Eddying Global Ocean
Model with a Wave Drag Parameterization
David Trossman1 Brian Arbic1 Steve Garner2
John Goff3 Steven Jayne4 E. Joseph Metzger5
Alan Wallcraft5
1University of Michigan-Ann Arbor, Dept Earth & Environmental Sciences2NOAA/Geophysical Fluid Dynamics Laboratory
3University of Texas-Austin, Institute for Geophysics4Woods Hole Oceanographic Institution, Physical Oceanography Department5Naval Research Laboratory-Stennis Space Center, Oceanography Division
LOM Meeting, 2013
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Outline
1 IntroductionMotivation and what wave drag isThe model and observations for comparison
2 Putting wave drag into an ocean modelWave drag scheme choices
3 Energy budgetMechanical energy budget from the continuity andmomentum equations
4 Model evaluationTaylor diagrams of all five diagnostics
![Page 3: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/3.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
Outline
1 IntroductionMotivation and what wave drag isThe model and observations for comparison
2 Putting wave drag into an ocean modelWave drag scheme choices
3 Energy budgetMechanical energy budget from the continuity andmomentum equations
4 Model evaluationTaylor diagrams of all five diagnostics
![Page 4: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/4.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
A truncated history of topographic wave drag studies
Previous studiesAtmospheric general circulation models improved withwave drag (e.g., Palmer et al., 1986)
∃ ample observational evidence that vertical diffusivity isenhanced in regions with rough topography (e.g., Polzin etal., 1997; ...; St. Laurent et al., 2012)Wave drag boosts vertical diffusivity (e.g., St. Laurent etal., 2002) and improves all considered tidal constituentamplitudes (e.g., Jayne and St. Laurent, 2001) inbarotropic tidal modelsOffline estimates suggest wave drag dissipates energy at0.2− 0.49 TW in abyssal hill regions (e.g., Nikurashin andFerrari, 2011; Scott et al., 2011)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
A truncated history of topographic wave drag studies
Previous studiesAtmospheric general circulation models improved withwave drag (e.g., Palmer et al., 1986)∃ ample observational evidence that vertical diffusivity isenhanced in regions with rough topography (e.g., Polzin etal., 1997; ...; St. Laurent et al., 2012)
Wave drag boosts vertical diffusivity (e.g., St. Laurent etal., 2002) and improves all considered tidal constituentamplitudes (e.g., Jayne and St. Laurent, 2001) inbarotropic tidal modelsOffline estimates suggest wave drag dissipates energy at0.2− 0.49 TW in abyssal hill regions (e.g., Nikurashin andFerrari, 2011; Scott et al., 2011)
![Page 6: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/6.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
A truncated history of topographic wave drag studies
Previous studiesAtmospheric general circulation models improved withwave drag (e.g., Palmer et al., 1986)∃ ample observational evidence that vertical diffusivity isenhanced in regions with rough topography (e.g., Polzin etal., 1997; ...; St. Laurent et al., 2012)Wave drag boosts vertical diffusivity (e.g., St. Laurent etal., 2002) and improves all considered tidal constituentamplitudes (e.g., Jayne and St. Laurent, 2001) inbarotropic tidal models
Offline estimates suggest wave drag dissipates energy at0.2− 0.49 TW in abyssal hill regions (e.g., Nikurashin andFerrari, 2011; Scott et al., 2011)
![Page 7: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/7.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
A truncated history of topographic wave drag studies
Previous studiesAtmospheric general circulation models improved withwave drag (e.g., Palmer et al., 1986)∃ ample observational evidence that vertical diffusivity isenhanced in regions with rough topography (e.g., Polzin etal., 1997; ...; St. Laurent et al., 2012)Wave drag boosts vertical diffusivity (e.g., St. Laurent etal., 2002) and improves all considered tidal constituentamplitudes (e.g., Jayne and St. Laurent, 2001) inbarotropic tidal modelsOffline estimates suggest wave drag dissipates energy at0.2− 0.49 TW in abyssal hill regions (e.g., Nikurashin andFerrari, 2011; Scott et al., 2011)
![Page 8: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/8.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
A history of topographic wave drag improving models (contd...)
Our goalsHow do we insert wave drag into an eddying global oceanmodel (without tides)?
How does wave drag impact the stratification, kineticenergy, and the input and output terms in the kineticenergy equation?Are general circulation ocean models forced only by windsand air-sea fluxes improved when wave drag is included?
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
A history of topographic wave drag improving models (contd...)
Our goalsHow do we insert wave drag into an eddying global oceanmodel (without tides)?How does wave drag impact the stratification, kineticenergy, and the input and output terms in the kineticenergy equation?
Are general circulation ocean models forced only by windsand air-sea fluxes improved when wave drag is included?
![Page 10: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/10.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
A history of topographic wave drag improving models (contd...)
Our goalsHow do we insert wave drag into an eddying global oceanmodel (without tides)?How does wave drag impact the stratification, kineticenergy, and the input and output terms in the kineticenergy equation?Are general circulation ocean models forced only by windsand air-sea fluxes improved when wave drag is included?
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Motivation and what wave drag is
What is topographic wave drag? (Froude number= U/NH)
Minimum Froude number needed to go over
Maximum Froude number limit
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Outline
1 IntroductionMotivation and what wave drag isThe model and observations for comparison
2 Putting wave drag into an ocean modelWave drag scheme choices
3 Energy budgetMechanical energy budget from the continuity andmomentum equations
4 Model evaluationTaylor diagrams of all five diagnostics
![Page 13: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/13.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Our models
HYbrid Coordinate Ocean Model (HYCOM)32 hybrid layers1/12.5o, 1/25o resolutions
Parallel Ocean Program (POP) component of theCommunity Earth System Model (CESM) 1.1
62 z-layers1/10o resolution
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Our models
HYbrid Coordinate Ocean Model (HYCOM)32 hybrid layers1/12.5o, 1/25o resolutions
Parallel Ocean Program (POP) component of theCommunity Earth System Model (CESM) 1.1
62 z-layers1/10o resolution
![Page 15: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/15.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Energy Inputs and Outputs
Inputs
Air-sea fluxes - monthly mean ECMWF Re-Analysis (ERA-40; Kallberg et al.,2004) for HYCOM, Coordinate Ocean Reference Experiment (CORE 2.0; Largeand Yeager, 2009) for POP
Winds - monthly mean ERA-40 supplemented with 6-hourly 2003 fields of theNavy Operational Global Atmospheric Prediction System (NOGAPS; Rosmondet al., 2002) for HYCOM, CORE 2.0 for POP
Dissipators
Horizontal viscosity - (∼ 102 − 103 m2 s−1) includes the maximum of aLaplacian and a Smagorinsky (1993) parameterization with an additionalbiharmonic term for HYCOM, biharmonic term for POP
Vertical viscosity - (∼ 10−4 − 10−3 m2 s−1) multiply the vertical diffusivitiesfrom KPP (Large et al., 1994) by a Prandtl number (ten)
Bottom drag - quadratic in the momentum equations with coefficient,Cd = 2.5× 10−3 for HYCOM, 10−3 for POP (Taylor, 1919; ...; Arbic et al., 2009)
Wave drag - Garner (2005) scheme is used (see later)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Energy Inputs and Outputs
Inputs
Air-sea fluxes - monthly mean ECMWF Re-Analysis (ERA-40; Kallberg et al.,2004) for HYCOM, Coordinate Ocean Reference Experiment (CORE 2.0; Largeand Yeager, 2009) for POP
Winds - monthly mean ERA-40 supplemented with 6-hourly 2003 fields of theNavy Operational Global Atmospheric Prediction System (NOGAPS; Rosmondet al., 2002) for HYCOM, CORE 2.0 for POP
Dissipators
Horizontal viscosity - (∼ 102 − 103 m2 s−1) includes the maximum of aLaplacian and a Smagorinsky (1993) parameterization with an additionalbiharmonic term for HYCOM, biharmonic term for POP
Vertical viscosity - (∼ 10−4 − 10−3 m2 s−1) multiply the vertical diffusivitiesfrom KPP (Large et al., 1994) by a Prandtl number (ten)
Bottom drag - quadratic in the momentum equations with coefficient,Cd = 2.5× 10−3 for HYCOM, 10−3 for POP (Taylor, 1919; ...; Arbic et al., 2009)
Wave drag - Garner (2005) scheme is used (see later)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Energy Inputs and Outputs
Inputs
Air-sea fluxes - monthly mean ECMWF Re-Analysis (ERA-40; Kallberg et al.,2004) for HYCOM, Coordinate Ocean Reference Experiment (CORE 2.0; Largeand Yeager, 2009) for POP
Winds - monthly mean ERA-40 supplemented with 6-hourly 2003 fields of theNavy Operational Global Atmospheric Prediction System (NOGAPS; Rosmondet al., 2002) for HYCOM, CORE 2.0 for POP
Dissipators
Horizontal viscosity - (∼ 102 − 103 m2 s−1) includes the maximum of aLaplacian and a Smagorinsky (1993) parameterization with an additionalbiharmonic term for HYCOM, biharmonic term for POP
Vertical viscosity - (∼ 10−4 − 10−3 m2 s−1) multiply the vertical diffusivitiesfrom KPP (Large et al., 1994) by a Prandtl number (ten)
Bottom drag - quadratic in the momentum equations with coefficient,Cd = 2.5× 10−3 for HYCOM, 10−3 for POP (Taylor, 1919; ...; Arbic et al., 2009)
Wave drag - Garner (2005) scheme is used (see later)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Energy Inputs and Outputs
Inputs
Air-sea fluxes - monthly mean ECMWF Re-Analysis (ERA-40; Kallberg et al.,2004) for HYCOM, Coordinate Ocean Reference Experiment (CORE 2.0; Largeand Yeager, 2009) for POP
Winds - monthly mean ERA-40 supplemented with 6-hourly 2003 fields of theNavy Operational Global Atmospheric Prediction System (NOGAPS; Rosmondet al., 2002) for HYCOM, CORE 2.0 for POP
Dissipators
Horizontal viscosity - (∼ 102 − 103 m2 s−1) includes the maximum of aLaplacian and a Smagorinsky (1993) parameterization with an additionalbiharmonic term for HYCOM, biharmonic term for POP
Vertical viscosity - (∼ 10−4 − 10−3 m2 s−1) multiply the vertical diffusivitiesfrom KPP (Large et al., 1994) by a Prandtl number (ten)
Bottom drag - quadratic in the momentum equations with coefficient,Cd = 2.5× 10−3 for HYCOM, 10−3 for POP (Taylor, 1919; ...; Arbic et al., 2009)
Wave drag - Garner (2005) scheme is used (see later)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Energy Inputs and Outputs
Inputs
Air-sea fluxes - monthly mean ECMWF Re-Analysis (ERA-40; Kallberg et al.,2004) for HYCOM, Coordinate Ocean Reference Experiment (CORE 2.0; Largeand Yeager, 2009) for POP
Winds - monthly mean ERA-40 supplemented with 6-hourly 2003 fields of theNavy Operational Global Atmospheric Prediction System (NOGAPS; Rosmondet al., 2002) for HYCOM, CORE 2.0 for POP
Dissipators
Horizontal viscosity - (∼ 102 − 103 m2 s−1) includes the maximum of aLaplacian and a Smagorinsky (1993) parameterization with an additionalbiharmonic term for HYCOM, biharmonic term for POP
Vertical viscosity - (∼ 10−4 − 10−3 m2 s−1) multiply the vertical diffusivitiesfrom KPP (Large et al., 1994) by a Prandtl number (ten)
Bottom drag - quadratic in the momentum equations with coefficient,Cd = 2.5× 10−3 for HYCOM, 10−3 for POP (Taylor, 1919; ...; Arbic et al., 2009)
Wave drag - Garner (2005) scheme is used (see later)
![Page 20: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/20.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Energy Inputs and Outputs
Inputs
Air-sea fluxes - monthly mean ECMWF Re-Analysis (ERA-40; Kallberg et al.,2004) for HYCOM, Coordinate Ocean Reference Experiment (CORE 2.0; Largeand Yeager, 2009) for POP
Winds - monthly mean ERA-40 supplemented with 6-hourly 2003 fields of theNavy Operational Global Atmospheric Prediction System (NOGAPS; Rosmondet al., 2002) for HYCOM, CORE 2.0 for POP
Dissipators
Horizontal viscosity - (∼ 102 − 103 m2 s−1) includes the maximum of aLaplacian and a Smagorinsky (1993) parameterization with an additionalbiharmonic term for HYCOM, biharmonic term for POP
Vertical viscosity - (∼ 10−4 − 10−3 m2 s−1) multiply the vertical diffusivitiesfrom KPP (Large et al., 1994) by a Prandtl number (ten)
Bottom drag - quadratic in the momentum equations with coefficient,Cd = 2.5× 10−3 for HYCOM, 10−3 for POP (Taylor, 1919; ...; Arbic et al., 2009)
Wave drag - Garner (2005) scheme is used (see later)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Diagnostics informed by observations and compared with modeloutput
Current meters (Global Multi-Archive Current MeterDatabase;http://stockage.univ-brest.fr/s̃cott/GMACMD/updates.html)
Mean vertical structure of kinetic energy
Satellite altimetry (Archiving, Validation and Interpretationof Satellite Oceanographic;http://www.aviso.oceanobs.com/es/data/index.html)
Surface kinetic energyEddy length scales (inverse first centroid of kinetic energypower spectrum)Sea surface height varianceIntensified jet positions (via Kelly et al., 2007)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
The model and observations for comparison
Diagnostics informed by observations and compared with modeloutput
Current meters (Global Multi-Archive Current MeterDatabase;http://stockage.univ-brest.fr/s̃cott/GMACMD/updates.html)
Mean vertical structure of kinetic energy
Satellite altimetry (Archiving, Validation and Interpretationof Satellite Oceanographic;http://www.aviso.oceanobs.com/es/data/index.html)
Surface kinetic energyEddy length scales (inverse first centroid of kinetic energypower spectrum)Sea surface height varianceIntensified jet positions (via Kelly et al., 2007)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
Outline
1 IntroductionMotivation and what wave drag isThe model and observations for comparison
2 Putting wave drag into an ocean modelWave drag scheme choices
3 Energy budgetMechanical energy budget from the continuity andmomentum equations
4 Model evaluationTaylor diagrams of all five diagnostics
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
1) What is the range of wavenumbers over which the internalwaves are not evanescant?
f/U ∼ 10−4m−1 < |~k | < N/U ∼ 10−1m−1. (1)
Here,f is the Coriolis parameterN is the buoyancy frequencyU is the velocity near the seafloor|~k | is the wavenumber of the internal wave
Scott et al. (2011) used a range that went down to f/U ∼ 10−6
m−1.
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
2) Which wave drag parameterizations are there to choose from?
Using a momentum sink:Implement in wavenumber space; e.g., Bell (1975)Implement in physical space; e.g., Garner (2005)
Features of Garner (2005) vs those of Bell (1975)Garner (2005) - allows for topographic blocking, but doesnot depend on CoriolisBell (1975) - does not allow for topographic blocking, butdoes depend on CoriolisBoth schemes - depend on stratification, velocity, andunderlying topographic features and assume f � N
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
2) Which wave drag parameterizations are there to choose from?
Using a momentum sink:Implement in wavenumber space; e.g., Bell (1975)Implement in physical space; e.g., Garner (2005)
Features of Garner (2005) vs those of Bell (1975)Garner (2005) - allows for topographic blocking, but doesnot depend on CoriolisBell (1975) - does not allow for topographic blocking, butdoes depend on CoriolisBoth schemes - depend on stratification, velocity, andunderlying topographic features and assume f � N
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
2) (cont...) Comparison of the Bell (1975) and Garner (2005)schemes
We choose to use the Garner (2005) scheme, but the Bell(1975) scheme yields similar results (offline)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
3) Where do we apply wave drag?
Is the model numerically stable when wave drag is appliedeverywhere?Is it possible and does it make sense to apply wave drageverywhere?
Interpolate over topographic slopes that are supercritical?Apply wave drag only in abyssal hill regions? Apply wave dragonly in regions deeper than 500 meters? . . .
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
4) Estimate the input parameters for the wave drag scheme of yourchoice
Integrate Goff and Jordan (1988) abyssal hill power spectrum, weighted bywavenumbers from (1)parameters for power spectrum from Goff and Arbic (2010) and Goff (2010) inabyssal hill regionsuse a machine learning algorithm (Wood, 2006) to fill in the non-abyssal hillregions
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Wave drag scheme choices
5) How should the momentum be deposited vertically?
Is there observational evidence for enhanced turbulence, ifnot lee wave drag, in the bottom, say, 500 meters? (seeNaveira-Garabato et al., 2012)Is there evidence that there needs to be adepth-dependent vertical deposition of momentum?(Polzin (2009) suggests that there is and the Garner(2005) scheme is capable of doing this)Are there locations where a non-trivial vertical depositionof momentum is important? (will not be addressed here)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Outline
1 IntroductionMotivation and what wave drag isThe model and observations for comparison
2 Putting wave drag into an ocean modelWave drag scheme choices
3 Energy budgetMechanical energy budget from the continuity andmomentum equations
4 Model evaluationTaylor diagrams of all five diagnostics
![Page 32: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/32.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Momentum equations→ kinetic energy equation
∂~u∂t
+ (~u · ~∇)~u +1ρ~∇p + f k̂ × ~u + gk̂ = (2)
δs
ρ
~τwind
Hs− δb,HBD
Cd
HBD|~u|~u − δb,HWD
|rdrag |HWD
~u
− ∂
∂z(νz
∂
∂z~uH)− ~∇ · (νh,2~∇~uH + νh,4~∇∇2~uH)
Multiply the momentum equations by ρ and take a dot productwith velocity, ~u; then integrate over the globe
PEK time + PEK advection = Ppressure + Pinput − Poutput + CEK→EP (3)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Momentum equations→ kinetic energy equation
∂~u∂t
+ (~u · ~∇)~u +1ρ~∇p + f k̂ × ~u + gk̂ = (2)
δs
ρ
~τwind
Hs− δb,HBD
Cd
HBD|~u|~u − δb,HWD
|rdrag |HWD
~u
− ∂
∂z(νz
∂
∂z~uH)− ~∇ · (νh,2~∇~uH + νh,4~∇∇2~uH)
Multiply the momentum equations by ρ and take a dot productwith velocity, ~u; then integrate over the globe
PEK time + PEK advection = Ppressure + Pinput − Poutput + CEK→EP (3)
![Page 34: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/34.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Momentum equations→ kinetic energy equation
∂~u∂t
+ (~u · ~∇)~u +1ρ~∇p + f k̂ × ~u + gk̂ = (2)
δs
ρ
~τwind
Hs− δb,HBD
Cd
HBD|~u|~u − δb,HWD
|rdrag |HWD
~u
− ∂
∂z(νz
∂
∂z~uH)− ~∇ · (νh,2~∇~uH + νh,4~∇∇2~uH)
Multiply the momentum equations by ρ and take a dot productwith velocity, ~u; then integrate over the globe
PEK time + PEK advection = Ppressure + Pinput − Poutput + CEK→EP (3)
![Page 35: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/35.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Bottom and wave drag
c) Wave drag percent difference (offline-inline)
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Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Global Integrals of Input/Output Terms in TW= 1012W
PEK time + PEK advection = CEK→EP + Ppressure (4)+PWind − PBD − PWD − PVV − PHV
WD? Wind Buoy BD WD VV HVno 0.87 0.066 0.31 N/A 0.29 0.29yes 0.87 0.066 0.14 0.40 0.28 0.26
Inputs vs Outputs:5% imbalance (outputs less than inputs) without wave drag15% imbalance (inputs less than outputs) with wave drag
![Page 37: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/37.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Mass conservation equation→ potential energy equation
∫dV
d(ρgz)dt
=
∫dV[∂(ρgz)∂t
+ ~u · ~∇(ρgz)]
(5)
∫dV
d(ρgz)dt
=
∫dV[ρ
d(gz)dt
+dρdt
(gz)]
(6)
=
∫dV [ρgw ] +
∫dx∫
dy[gηκ
∂ρ
∂z
]−∫
dV[gκ
∂ρ
∂z
]
PEP time + PEPadvection = Pdiffusive + CEP→EK + CEI→EP (7)
![Page 38: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/38.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Mass conservation equation→ potential energy equation
∫dV
d(ρgz)dt
=
∫dV[∂(ρgz)∂t
+ ~u · ~∇(ρgz)]
(5)
∫dV
d(ρgz)dt
=
∫dV[ρ
d(gz)dt
+dρdt
(gz)]
(6)
=
∫dV [ρgw ] +
∫dx∫
dy[gηκ
∂ρ
∂z
]−∫
dV[gκ
∂ρ
∂z
]
PEP time + PEPadvection = Pdiffusive + CEP→EK + CEI→EP (7)
![Page 39: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/39.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Mass conservation equation→ potential energy equation
∫dV
d(ρgz)dt
=
∫dV[∂(ρgz)∂t
+ ~u · ~∇(ρgz)]
(5)
∫dV
d(ρgz)dt
=
∫dV[ρ
d(gz)dt
+dρdt
(gz)]
(6)
=
∫dV [ρgw ] +
∫dx∫
dy[gηκ
∂ρ
∂z
]−∫
dV[gκ
∂ρ
∂z
]
PEP time + PEPadvection = Pdiffusive + CEP→EK + CEI→EP (7)
![Page 40: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/40.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Mechanical energy budget from the continuity and momentum equations
Global Integrals of Mechanical Energy Budget Terms inTW= 1012W
PEK time + PEP time + PEK advection + PEPadvection = (8)Ppressure + Pdiffusive + Pinput − Poutput + CEI→EP
KEadv . PEadv . press. diffuse EI → EP input output-.00284 .174 < .001 .00309 .0865 .868 1.06
7% imbalance of mechanical energy budget we ignore:partial time derivatives of KE and PEalong-isopycnal contributions to power associated withbuoyancy diffusioncompressibility
![Page 41: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/41.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Taylor diagrams of all five diagnostics
Outline
1 IntroductionMotivation and what wave drag isThe model and observations for comparison
2 Putting wave drag into an ocean modelWave drag scheme choices
3 Energy budgetMechanical energy budget from the continuity andmomentum equations
4 Model evaluationTaylor diagrams of all five diagnostics
![Page 42: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/42.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Taylor diagrams of all five diagnostics
Does wave drag ever make the model simulations in worseagreement with diagnostics informed by observations?
Observations, 1/12o HYCOM without wave drag, 1/12o HYCOM with wave drag, 1/25o HYCOM without wavedrag, 1/25o HYCOM with wave drag, 1/10o POP without wave drag (Taylor, 2001)
![Page 43: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/43.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several details that could use some work whenputting wave drag into a model like:
what’s the best way to specify the range of relevantwavenumbers for the internal waves to not be evanescent?
are internal lee waves are generated by bottom flow-topographyinteractions in non-abyssal hill regions?physical derivation of wave drag parameters in non-abyssal hillregions?what’s the more appropriate wave drag scheme to use and inwhat context?use of the full wave drag tensor that Garner (2005) formulated?use of a depth-dependent momentum deposition procedure thatGarner (2005) formulated?use of an alternative, non-local momentum depositionprocedure?
![Page 44: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/44.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several details that could use some work whenputting wave drag into a model like:
what’s the best way to specify the range of relevantwavenumbers for the internal waves to not be evanescent?are internal lee waves are generated by bottom flow-topographyinteractions in non-abyssal hill regions?
physical derivation of wave drag parameters in non-abyssal hillregions?what’s the more appropriate wave drag scheme to use and inwhat context?use of the full wave drag tensor that Garner (2005) formulated?use of a depth-dependent momentum deposition procedure thatGarner (2005) formulated?use of an alternative, non-local momentum depositionprocedure?
![Page 45: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/45.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several details that could use some work whenputting wave drag into a model like:
what’s the best way to specify the range of relevantwavenumbers for the internal waves to not be evanescent?are internal lee waves are generated by bottom flow-topographyinteractions in non-abyssal hill regions?physical derivation of wave drag parameters in non-abyssal hillregions?
what’s the more appropriate wave drag scheme to use and inwhat context?use of the full wave drag tensor that Garner (2005) formulated?use of a depth-dependent momentum deposition procedure thatGarner (2005) formulated?use of an alternative, non-local momentum depositionprocedure?
![Page 46: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/46.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several details that could use some work whenputting wave drag into a model like:
what’s the best way to specify the range of relevantwavenumbers for the internal waves to not be evanescent?are internal lee waves are generated by bottom flow-topographyinteractions in non-abyssal hill regions?physical derivation of wave drag parameters in non-abyssal hillregions?what’s the more appropriate wave drag scheme to use and inwhat context?
use of the full wave drag tensor that Garner (2005) formulated?use of a depth-dependent momentum deposition procedure thatGarner (2005) formulated?use of an alternative, non-local momentum depositionprocedure?
![Page 47: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/47.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several details that could use some work whenputting wave drag into a model like:
what’s the best way to specify the range of relevantwavenumbers for the internal waves to not be evanescent?are internal lee waves are generated by bottom flow-topographyinteractions in non-abyssal hill regions?physical derivation of wave drag parameters in non-abyssal hillregions?what’s the more appropriate wave drag scheme to use and inwhat context?use of the full wave drag tensor that Garner (2005) formulated?
use of a depth-dependent momentum deposition procedure thatGarner (2005) formulated?use of an alternative, non-local momentum depositionprocedure?
![Page 48: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/48.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several details that could use some work whenputting wave drag into a model like:
what’s the best way to specify the range of relevantwavenumbers for the internal waves to not be evanescent?are internal lee waves are generated by bottom flow-topographyinteractions in non-abyssal hill regions?physical derivation of wave drag parameters in non-abyssal hillregions?what’s the more appropriate wave drag scheme to use and inwhat context?use of the full wave drag tensor that Garner (2005) formulated?use of a depth-dependent momentum deposition procedure thatGarner (2005) formulated?
use of an alternative, non-local momentum depositionprocedure?
![Page 49: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/49.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several details that could use some work whenputting wave drag into a model like:
what’s the best way to specify the range of relevantwavenumbers for the internal waves to not be evanescent?are internal lee waves are generated by bottom flow-topographyinteractions in non-abyssal hill regions?physical derivation of wave drag parameters in non-abyssal hillregions?what’s the more appropriate wave drag scheme to use and inwhat context?use of the full wave drag tensor that Garner (2005) formulated?use of a depth-dependent momentum deposition procedure thatGarner (2005) formulated?use of an alternative, non-local momentum depositionprocedure?
![Page 50: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/50.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several ways wave drag impacts the modelactive feedback on velocities and stratification
diapycnal diffusivity is generally enhanced all the way up tothe surfacesubstantially less bottom drag dissipation with wave drag,and wave drag cannot be substituted for by boostingbottom dragall other mechanical energy budget terms are spatiallyaltered, but changed by little in their global integralswave drag either improves the model or does not make themodel worse
![Page 51: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/51.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several ways wave drag impacts the modelactive feedback on velocities and stratificationdiapycnal diffusivity is generally enhanced all the way up tothe surface
substantially less bottom drag dissipation with wave drag,and wave drag cannot be substituted for by boostingbottom dragall other mechanical energy budget terms are spatiallyaltered, but changed by little in their global integralswave drag either improves the model or does not make themodel worse
![Page 52: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/52.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several ways wave drag impacts the modelactive feedback on velocities and stratificationdiapycnal diffusivity is generally enhanced all the way up tothe surfacesubstantially less bottom drag dissipation with wave drag,and wave drag cannot be substituted for by boostingbottom drag
all other mechanical energy budget terms are spatiallyaltered, but changed by little in their global integralswave drag either improves the model or does not make themodel worse
![Page 53: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/53.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several ways wave drag impacts the modelactive feedback on velocities and stratificationdiapycnal diffusivity is generally enhanced all the way up tothe surfacesubstantially less bottom drag dissipation with wave drag,and wave drag cannot be substituted for by boostingbottom dragall other mechanical energy budget terms are spatiallyaltered, but changed by little in their global integrals
wave drag either improves the model or does not make themodel worse
![Page 54: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/54.jpg)
Introduction Putting wave drag into an ocean model Energy budget Model evaluation Summary
Summary
There are several ways wave drag impacts the modelactive feedback on velocities and stratificationdiapycnal diffusivity is generally enhanced all the way up tothe surfacesubstantially less bottom drag dissipation with wave drag,and wave drag cannot be substituted for by boostingbottom dragall other mechanical energy budget terms are spatiallyaltered, but changed by little in their global integralswave drag either improves the model or does not make themodel worse
![Page 55: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/55.jpg)
Non-input/output mechanical energy budget terms
![Page 56: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/56.jpg)
SST bias
![Page 57: A Mechanical Energy Budget and Evaluation of an Eddying Global](https://reader031.fdocuments.net/reader031/viewer/2022020704/61fb6b002e268c58cd5deebd/html5/thumbnails/57.jpg)
SSH variance