cblast: coupled boundary layers and air-sea transfer

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John Wilkin [email protected] John Wilkin [email protected] s.edu Modeling the Heat Budget of Modeling the Heat Budget of Southeast Southeast New England Shelf Waters New England Shelf Waters for CBLAST-Low for CBLAST-Low John Wilkin John Wilkin H. Arango, K. Fennel, L. Lanerolle, J. Levin H. Arango, K. Fennel, L. Lanerolle, J. Levin Institute of Marine and Coastal Sciences Institute of Marine and Coastal Sciences Rutgers, The State University of New Jersey Rutgers, The State University of New Jersey NSF CoOP Buoyancy driven flow (LATTE) NSF CoOP Buoyancy driven flow (LATTE) Northeast Observing System (NEOS) Northeast Observing System (NEOS) Northeast North American shelf (NENA) Northeast North American shelf (NENA) North Atlantic Basin (NATL) North Atlantic Basin (NATL)

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Page 1: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Modeling the Heat Budget of Southeast Modeling the Heat Budget of Southeast New England Shelf Waters New England Shelf Waters

for CBLAST-Lowfor CBLAST-Low

John WilkinJohn Wilkin

H. Arango, K. Fennel, L. Lanerolle, J. LevinH. Arango, K. Fennel, L. Lanerolle, J. Levin Institute of Marine and Coastal SciencesInstitute of Marine and Coastal Sciences

Rutgers, The State University of New Jersey Rutgers, The State University of New Jersey

NSF CoOP Buoyancy driven flow (LATTE)NSF CoOP Buoyancy driven flow (LATTE)Northeast Observing System (NEOS)Northeast Observing System (NEOS)

Northeast North American shelf (NENA)Northeast North American shelf (NENA)North Atlantic Basin (NATL) North Atlantic Basin (NATL)

Page 2: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

• Precise observations of air-sea fluxes and turbulent mixing from Precise observations of air-sea fluxes and turbulent mixing from CBLAST are ideal for evaluating the suite of ocean model vertical CBLAST are ideal for evaluating the suite of ocean model vertical turbulence closure schemes implemented in ROMS.turbulence closure schemes implemented in ROMS.

• This comparison will be possible provided the model captures the This comparison will be possible provided the model captures the essential features of the ocean heat budget on diurnal to several essential features of the ocean heat budget on diurnal to several day time-scales, and spatial scales of order 1 km.day time-scales, and spatial scales of order 1 km.

• Modeling complements the interpretation of the field observations Modeling complements the interpretation of the field observations by quantifying unobserved lateral transport and mixing of heat.by quantifying unobserved lateral transport and mixing of heat.

CBLAST: CBLAST: Coupled Boundary Layers and Air-Sea TransferCoupled Boundary Layers and Air-Sea Transfer

The ONR CBLAST-Low program focuses on air-sea interaction and The ONR CBLAST-Low program focuses on air-sea interaction and coupled atmosphere/ocean boundary layer dynamics at low wind coupled atmosphere/ocean boundary layer dynamics at low wind

speeds where processes are strongly modulated by thermal forcing.speeds where processes are strongly modulated by thermal forcing.

Page 3: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

LowWinds

Improve Flux ParameterizationsImprove Flux Parameterizations

= = C CDD UU22

Research Research Question:Question:What physical What physical processes are processes are responsible for responsible for thisthisenhancement?enhancement?

Page 4: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Irradiance

Irradiance

23m

15m

U, T, QU, T, Q Heat, mass & Heat, mass &

mom. flux, mom. flux, εεWavesWaves

WavesWaves T, ST, S

Heat, mass Heat, mass mom. flux, mom. flux, εε

Solar, IR, rain, Solar, IR, rain, U, T, QU, T, Q Heat, mass & Heat, mass & momentum flux, momentum flux, εε

Page 5: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

MVCOMVCO

K

ASITASIT

CBLAST-Low Observing System 2002:CBLAST-Low Observing System 2002:

Nantucket Nantucket SODARSODAR

IR AircraftIR Aircraft

3-D mooring3-D mooring

Flux AircraftFlux Aircraft

RemoteRemoteSensingSensing

ASIMET ASIMET mooringsmooringswith ocean with ocean T(z) T(z) and ADCP and ADCP

Page 6: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

The Regional Ocean Modeling System (ROMS/TOMS) has been The Regional Ocean Modeling System (ROMS/TOMS) has been configured for a region of the southeastern New England shelf configured for a region of the southeastern New England shelf encompassing the CBLAST observation areaencompassing the CBLAST observation area

Purpose:Purpose:

Obtain model hind-cast of summertime ocean conditions Obtain model hind-cast of summertime ocean conditions that captures the essential features of the ocean heat that captures the essential features of the ocean heat budget on diurnal to several day time-scales, and spatial budget on diurnal to several day time-scales, and spatial scales of order 1 kmscales of order 1 km

Page 7: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

The Regional Ocean Modeling System (ROMS/TOMS) has been The Regional Ocean Modeling System (ROMS/TOMS) has been configured for a region of the southeastern New England shelf configured for a region of the southeastern New England shelf encompassing the CBLAST observation areaencompassing the CBLAST observation area

Motivation (1)Motivation (1)

Model evaluation: Model evaluation:

Compare model heat budget to observations:Compare model heat budget to observations:

• Evaluate heat budget sensitivity to vertical Evaluate heat budget sensitivity to vertical turbulent closures in ROMSturbulent closures in ROMS

• Evaluate heat budget sensitivity to air-sea flux Evaluate heat budget sensitivity to air-sea flux bulk formulae bulk formulae

• Evaluate contribution to hind-cast skill of Evaluate contribution to hind-cast skill of meteorological model (COAMPS) compared to meteorological model (COAMPS) compared to using observed marine boundary layer conditionsusing observed marine boundary layer conditions

Page 8: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Motivation (2)Motivation (2)

Observational data analysis: Observational data analysis:

Horizontal mixing and advection are largely Horizontal mixing and advection are largely unobserved by the CBLAST field instrumentation. unobserved by the CBLAST field instrumentation. This affects closure of the observed heat budget, This affects closure of the observed heat budget, especially:especially:

• Advection of vertically mixed waters originating on Advection of vertically mixed waters originating on the Nantucket Shoalsthe Nantucket Shoals

• Advection past the CBLAST tower of tidally Advection past the CBLAST tower of tidally generated eddies transporting Vineyard Sound generated eddies transporting Vineyard Sound water through Muskeget channelwater through Muskeget channel

To what extent does wind-driven upwelling maintain To what extent does wind-driven upwelling maintain stratification, and contribute to local heat budgets?stratification, and contribute to local heat budgets?

Page 9: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

ROMS CBLAST domain

1 km grid 1 km grid resolutionresolution

20 vertical levels 20 vertical levels (stretched)(stretched)

Surface forcing:Surface forcing:

• Observed Observed ASIT/MVCO and ASIT/MVCO and modeled (COAMPS) modeled (COAMPS) mairne boundary mairne boundary conditionsconditions

Initial and Initial and inflow/outflow inflow/outflow boundary boundary conditions from bi-conditions from bi-monthly monthly climatologyclimatology

TidesTides

Page 10: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

COAMPS CBLAST, 3km, 91x91

9 km

27 km, 151x121x30

Surface forcing:Surface forcing:

Heat and momentum Heat and momentum fluxes from bulk fluxes from bulk formulaeformulae

• model SSTmodel SST

• TTairair, p, pairair, rel. humidity, , rel. humidity,

UU1010, V, V1010, and short-, and short-

wave radiation from wave radiation from 3km resolution nested 3km resolution nested COAMPS 6--72 hr COAMPS 6--72 hr forecastforecast

• observed downward observed downward long-wave at MVCO or long-wave at MVCO or net long-wave from net long-wave from COAMPSCOAMPS

Courtesy S. Wang and Q. Courtesy S. Wang and Q. Wang, NRLWang, NRL

Page 11: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Split-explicit, free-surface, hydrostatic, primitive equation Split-explicit, free-surface, hydrostatic, primitive equation modelmodel

Generalized, terrain-following vertical coordinatesGeneralized, terrain-following vertical coordinates

Orthogonal curvilinear, horizontal coordinates, Arakawa C-Orthogonal curvilinear, horizontal coordinates, Arakawa C-gridgrid

33rdrd- and 4- and 4thth-order advection and time-stepping; weighted -order advection and time-stepping; weighted temporal averaging; reduced pressure gradient and mode-temporal averaging; reduced pressure gradient and mode-splitting errorsplitting error

Simultaneous conservation and constancy preservation for Simultaneous conservation and constancy preservation for tracer equations in combination with evolving coordinate tracer equations in combination with evolving coordinate system due to free-surfacesystem due to free-surface

Continuous, monotonic reconstruction of vertical gradients Continuous, monotonic reconstruction of vertical gradients to maintain high-order accuracyto maintain high-order accuracy

ROMS/TOMS MPI shared and distributed memory f90 codeROMS/TOMS MPI shared and distributed memory f90 code

netCDF I/OnetCDF I/O

ROMS model attributesROMS model attributes

Split-explicit, free-surface, hydrostatic, primitive equation Split-explicit, free-surface, hydrostatic, primitive equation modelmodel

Generalized, terrain-following vertical coordinatesGeneralized, terrain-following vertical coordinates

Orthogonal curvilinear, horizontal coordinates, Arakawa Orthogonal curvilinear, horizontal coordinates, Arakawa C-gridC-grid

33rdrd- and 4- and 4thth-order advection and time-stepping; weighted -order advection and time-stepping; weighted temporal averaging; reduced pressure gradient and temporal averaging; reduced pressure gradient and mode-splitting errormode-splitting error

Simultaneous conservation and constancy preservation Simultaneous conservation and constancy preservation for tracer equations in combination with evolving for tracer equations in combination with evolving coordinate system due to free-surfacecoordinate system due to free-surface

Continuous, monotonic reconstruction of vertical Continuous, monotonic reconstruction of vertical gradients to maintain high-order accuracygradients to maintain high-order accuracy

ROMS/TOMS MPI shared and distributed memory f90 ROMS/TOMS MPI shared and distributed memory f90 codecode

netCDF I/OnetCDF I/O

Page 12: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

• Mellor-Yamada level 2.5Mellor-Yamada level 2.5

• Non-local, k-profile parameterization (KPP) surface and Non-local, k-profile parameterization (KPP) surface and bottom bottom closure scheme closure scheme

• surface boundary layer (KPP; Large et al., 1994)surface boundary layer (KPP; Large et al., 1994)

• bottom boundary layer (inverted KPP; Durski et al., bottom boundary layer (inverted KPP; Durski et al., 2001)2001)

• Generalized Ocean Turbulence ModelGeneralized Ocean Turbulence Model http://www.gotm.net

• Eddy viscosity and diffusivity product of a non-Eddy viscosity and diffusivity product of a non-dimensional stability function, normalized TKE, and dimensional stability function, normalized TKE, and macro length scalemacro length scale

• The stability functions are the result of various second-The stability functions are the result of various second-moment closures. TKE and the length scales are moment closures. TKE and the length scales are calculated by dynamic equations (as in k-epsilon or calculated by dynamic equations (as in k-epsilon or Mellor-Yamada models) or algebraic formulations.Mellor-Yamada models) or algebraic formulations.

ROMS Vertical Turbulence Closure optionsROMS Vertical Turbulence Closure options

Umlauf, L. and H. Burchard. A generic length-scale equation for geophysical Umlauf, L. and H. Burchard. A generic length-scale equation for geophysical turbulence modelsturbulence modelsJ. Mar. Res., 2003 J. Mar. Res., 2003

Warner, J.C., Sherwood, C.R., Butman, B., Arango, H.G., and Signell, R.P., Warner, J.C., Sherwood, C.R., Butman, B., Arango, H.G., and Signell, R.P., Implementation of a generic length scale turbulence closure in a 3D oceanographic Implementation of a generic length scale turbulence closure in a 3D oceanographic model." Ocean Modeling, 2003.model." Ocean Modeling, 2003.

Page 14: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Circulation around Nantucket Shoals is augmented by tidal rectified anti-Circulation around Nantucket Shoals is augmented by tidal rectified anti-cyclonic flow that carries water into Vineyard Sound through Muskeget Channelcyclonic flow that carries water into Vineyard Sound through Muskeget Channel

Page 15: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Circulation around the Circulation around the Nantucket Shoals is augmented Nantucket Shoals is augmented by strong tidal rectified cyclonic by strong tidal rectified cyclonic flow that carries water flow that carries water northward into Vineyard Sound northward into Vineyard Sound through Muskegat Channel through Muskegat Channel (between Nantucket and the (between Nantucket and the Vineyard). Vineyard).

Mean circulation and heat budgetMean circulation and heat budget

The open boundary climatology imposes a The open boundary climatology imposes a south and westward flow from the Gulf of south and westward flow from the Gulf of Maine, through Great South Channel and Maine, through Great South Channel and around Nantucket Shoals.around Nantucket Shoals.

Southwest of Martha’s Vineyard, and within Southwest of Martha’s Vineyard, and within Vineyard Sound, winds drive eastward depth Vineyard Sound, winds drive eastward depth averaged flow.averaged flow.

July 2002 mean

Page 16: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Tidal mixing generates a region of perpetually cold SST on the eastern flank of the Nantucket Shoals

3-day composite SST for 30-Aug-2002

Page 17: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Air-sea flux (QAir-sea flux (Qnetnet) is greatest east of Vineyard Sound where SST is ) is greatest east of Vineyard Sound where SST is

cold, but is largely balanced by divergence due to tidal mixing. cold, but is largely balanced by divergence due to tidal mixing.

Ocean temperature increase (storage) is largest south of The Islands, Ocean temperature increase (storage) is largest south of The Islands, primarily due to surface heating. primarily due to surface heating.

Horizontal divergence is small in the region of the Horizontal divergence is small in the region of the B-CB-C ASIMET ASIMET moorings - indicating a region of approximate 1-D vertical heat balance moorings - indicating a region of approximate 1-D vertical heat balance suited to evaluating ROMS vertical turbulence closures. suited to evaluating ROMS vertical turbulence closures.

July 2002

Page 18: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

MVCO

The time mean advection The time mean advection cools the box at, on cools the box at, on average, 200 W/maverage, 200 W/m22. The . The net “eddy” divergence net “eddy” divergence ((u’T’u’T’) warms the MVCO ) warms the MVCO region at about 50 W/mregion at about 50 W/m22. .

Episodic positive Episodic positive divergence (cooling) divergence (cooling) events briefly arrest the events briefly arrest the warming trend. warming trend.

Time series of the heat budget in a box near Time series of the heat budget in a box near MVCO shows half the air-sea flux goes to MVCO shows half the air-sea flux goes to warming the water column, and half is warming the water column, and half is removed by lateral divergence. removed by lateral divergence.

Page 19: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

CTD temperature section between ASIT and mooring-A, late July 2001.

Observed Modeled

Qualitative comparison to subsurface validation data (below) shows realistic Qualitative comparison to subsurface validation data (below) shows realistic vertical stratification and mixed layer depths. In 2003, an array of 5 subsurface vertical stratification and mixed layer depths. In 2003, an array of 5 subsurface moorings between ASIT and ASIMET mooring-moorings between ASIT and ASIMET mooring-AA will enable validation of the will enable validation of the modeled evolution of the diurnal mixed layer. modeled evolution of the diurnal mixed layer.

Page 21: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

COAMPS 72-hour forecast was generated every COAMPS 72-hour forecast was generated every 12 hours at ARL.HPC.mil and transferred to 12 hours at ARL.HPC.mil and transferred to IMCS where ROMS ran for the same forecast IMCS where ROMS ran for the same forecast cycle.cycle.

Operational forecasts were generated forOperational forecasts were generated forJuly 21 through September 3, 2003July 21 through September 3, 2003

Page 22: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer
Page 23: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer
Page 30: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Raw CTD data acquired via Raw CTD data acquired via Iridium from a Slocum Glider Iridium from a Slocum Glider transiting between ASIT and transiting between ASIT and ASIMET mooring-ASIMET mooring-A.A.

Page 31: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Long-range Long-range CODAR at CODAR at ’Siasconset ’Siasconset NantucketNantucket

Page 32: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

CBLAST:CBLAST:

Lessons for ocean modeling:Lessons for ocean modeling:

• Differing vertical turbulence parameterizations lead to differentDiffering vertical turbulence parameterizations lead to different3-dimensional coastal mesoscale flows 3-dimensional coastal mesoscale flows

• CBLAST data suited to turbulence closure evaluation:CBLAST data suited to turbulence closure evaluation:

– Combination of direct air-sea flux and vertical turbulence Combination of direct air-sea flux and vertical turbulence observations, and in situ oceanic conditions for validationobservations, and in situ oceanic conditions for validation

• Spatially variable atmospheric forcing (COAMPS) is importantSpatially variable atmospheric forcing (COAMPS) is important

• Heat budget requires further analysis of horizontal/vertical circulations: Heat budget requires further analysis of horizontal/vertical circulations: overturning/upwelling vs. depth-average flow contributions, especially overturning/upwelling vs. depth-average flow contributions, especially at moorings and ASIT at moorings and ASIT

Page 33: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

CBLAST:CBLAST:

Lessons for data analysis:Lessons for data analysis:

• Tides affect the circulation and heat budget through residual mean currents and vertical Tides affect the circulation and heat budget through residual mean currents and vertical mixing mixing

• Wind-driven upwelling circulation contributes to the heat budget southwest of Martha’s Wind-driven upwelling circulation contributes to the heat budget southwest of Martha’s Vineyard Vineyard

• Lateral heat transport is large in much of the region, including near MVCO, and will need Lateral heat transport is large in much of the region, including near MVCO, and will need to be considered in the analysis of ASIT heat budgets to be considered in the analysis of ASIT heat budgets

• Vineyard Sound, Nantucket Shoals, MVCO, shows differing heat balances in July mean Vineyard Sound, Nantucket Shoals, MVCO, shows differing heat balances in July mean

• Modeling shows a 1-D heat balance occurs near the B-A-C ASIMET mooring sites, which Modeling shows a 1-D heat balance occurs near the B-A-C ASIMET mooring sites, which suggests vertical turbulence closures can be evaluated locally theresuggests vertical turbulence closures can be evaluated locally there

Page 34: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

12

3

5

4

12

3

6

5

4

Nested GridsNested Grids

1) NENA1) NENA2) NEOS2) NEOS3) CBLAST3) CBLAST4) LATTE4) LATTE5) NY/NJ Bight5) NY/NJ Bight6) Caribbean6) Caribbean

Page 35: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

North AtlanticNorth Atlantic

Climatological Climatological heat/freshwatheat/freshwatererfluxesfluxes

3-day average3-day averageNCEP windsNCEP winds

Page 36: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

Northeast North Atlantic (NENA) embedded in NATLNortheast North Atlantic (NENA) embedded in NATL

3-day average open boundary values from NATL3-day average open boundary values from NATL10-component NPZD ecosystem: NO10-component NPZD ecosystem: NO3,3,NH4, chl-a, phytoplankton, NH4, chl-a, phytoplankton,

zooplankton, small/large detritus, TIC, alkalinity, oxygenzooplankton, small/large detritus, TIC, alkalinity, oxygen

TemperaturTemperaturee

ChlorophyllChlorophyll

Page 37: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

CO

2 flu

x (m

ol m

-2 yr

-1)

Day of year

Air-sea CO2-flux:

- simulated (above and top right)

- observed (bottom right; Boehme et al., Mar. Chem. 1998)

Page 38: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

NEOS

NENA

SalinitySalinityat 20 mat 20 m

Initialized Initialized 01-Jan-199301-Jan-1993

Northeast Observing System (NEOS)Northeast Observing System (NEOS)

Page 39: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

• Assimilate Assimilate regional CODAR regional CODAR with 4D-with 4D-variational variational methodmethod

• Develop AUV Develop AUV deployment deployment strategies; strategies; tangent linear tangent linear and adjoint give and adjoint give singular vectors singular vectors of model showing of model showing regions of most regions of most rapid perturbation rapid perturbation growth growth

• Multiple-scale Multiple-scale nesting in support nesting in support of sub-region of sub-region studies (LaTTE, studies (LaTTE, CBLAST)CBLAST)

Northeast Observing System (NEOS)Northeast Observing System (NEOS)

Page 40: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

LaTTE: Lagrangian Transport LaTTE: Lagrangian Transport and Transformation Experimentand Transformation Experiment

• Dye release in Hudson River plumeDye release in Hudson River plume

• 4D-var assimilation with ROMS4D-var assimilation with ROMS

• Coupled bio-optical modeling with EcoSimCoupled bio-optical modeling with EcoSim

Page 41: CBLAST:  Coupled Boundary Layers and Air-Sea Transfer

John [email protected] [email protected]

• Hierarchy of integrated observational/modeling studies from basin to Hierarchy of integrated observational/modeling studies from basin to coastal using ROMS/TOMS tools coastal using ROMS/TOMS tools

• Processes: coastal bio-optics, sediment transport, COProcesses: coastal bio-optics, sediment transport, CO22 cycling, cycling,

buoyancy-driven flow, wind-driven upwelling, air-sea interaction buoyancy-driven flow, wind-driven upwelling, air-sea interaction

• Adjoint, tangent linear, variational assimilation codes feature in projectsAdjoint, tangent linear, variational assimilation codes feature in projects

• Objectives (2004-2005) for coastal prediction system development:Objectives (2004-2005) for coastal prediction system development:

• turbulence closure: evaluate with CBLAST-Low dataturbulence closure: evaluate with CBLAST-Low data

• air-sea fluxes, coupling to atmospheric models (COAMPS, WRF)air-sea fluxes, coupling to atmospheric models (COAMPS, WRF)

• 4D-variational assimilation 4D-variational assimilation

• new observing system technologies (CODAR, gliders)new observing system technologies (CODAR, gliders)

• use adjoint for sampling design and predictability studiesuse adjoint for sampling design and predictability studies

SummarySummary