Evaluation of the HYbrid Coordinate Ocean Model (HYCOM) Using Atlantic Ocean Simulations

George Halliwell, Rainer Bleck, Eric Chassignet, Linda Smith
This slide show describes several Atlantic Ocean simulations performed using HYCOM with different vertical mixing schemes and with both hybrid and isopycnic vertical coordinates. Properties of HYCOM are outlined first. Model performance is then evaluated by comparing simulated fields to each other, to observed fields (Levitus climatology), and to fields simulated by the Miami Isopycnic Coordinate Ocean Model (MICOM).

OUTLINE
Press button to jump forward to each section:
I. The Model
2. Model Simulations
3. Surface/Mixed Layer Thermodynamical Fields
4. Surface/Mixed Layer Dynamical Fields
5. Cross-Sections
6. Model Censuses
7. Meridional Overturning Circulation and Heat Flux
8. Regional Differences in Upper Ocean Variability
9. Regional Mixed Layer Profiles
10. Summary
11. Referencess

The Model (1)
History
Developed from MICOM version 2.8
See Bleck (1998) for a description of MICOM
Hybrid coordinate scheme used in HYCOM
Model equations written in generalized vertical coordinates
Originally used in the Bleck and Boudra (1981) quasi-isopycnic model
Numerical schemes could not handle zero thickness layers
Minimum layer thickness was enforced
The vertical coordinate became non-isopycnic in regions where the layers became too thin
A hybrid (isentropic-sigma) vertical coordinate was used in the atmospheric model of Bleck and Benjamin (1993)
The HYCOM isopycnic-level-sigma vertical coordinate scheme is an adaptation and extension of the Bleck/Benjamin algorithm

The Model (2)
Major changes from MICOM
New vertical coordinate scheme
Multiple mixed layer models, including non-slab models
Interior convection due to static instability (two layers exchange fluid when the upper one is more dense)
Hydrostatic and momentum equations modified to handle non-isopycnic densities and horizontal density gradients
Choice of temperature-salinity, temperature-density, or salinity-density advection

The Model (3)
Vertical Coordinates
Hybrid coordinates
Nearsurface: z-coordinates
Shallow water: sigma (terrain-following) coordinates
Coordinates are isopycnic in the bulk of the ocean interior
Isopycnic coordinates (MICOM mode)
Hybrid Vertical Coordinate Scheme (part 1)
In the open ocean, the coordinates are isopycnic except year the surface where minimum coordinate separation is enforced. The minimum separation differs for each layer, giving the user great flexibility to set the vertical coordinate structure in the z-coordinate domain.
A cushion function described in Bleck and Benjamin (1993) provides a smooth transition between the isopycnic and z-coordinate domains.
To activate the sigma coordinate domain, the user specifies the number of sigma coordinates n and the coordinate separation d. Vertical coordinates become terrain-following where bottom depth is less than n*d. In extremely shallow water, the coordinates revert to level coordinates.

The Model (4)
Hybrid Vertical Coordinate Scheme (part 2)
In the deep ocean, the isopycnic-level coordinate transition is performed as follows:
If the density of a given layer does not equal the isopycnic reference density, the interfaces bounding the layer are adjusted to return the density to its reference value
If the layer is too light, the interface below is moved downward so that the entrained denser water returns the density to its reference value
If the layer is too dense, the interface above is moved upward in the same manner
If minimum coordinate separation is violated near the ocean surface, the cushion function is used to re-calculate the vertical coordinate location, prohibiting the restoration of isopycnic conditions.
Two of the thermodynamical variables T, S, and density are mixed across the moving interfaces (user selectable), with the third calculated from the equation of state. If T and S are mixed, exact isopycnal density is not restored, but repeated application keeps the error small.

The Model (5)
Horizontal Advection
Two of the thermodynamical variables T, S, and density are advected (user selectable), with the third calculated from the equation of state.
If HYCOM is run in MICOM mode, advection is performed as in MICOM 2.8, with T and S advected in layer 1 (the mixed layer) and S only advected in the isopycnic layers.

The Model (6)
Mixing Schemes
K-Profile Parameterization
Kraus-Turner Mixed Layer Model
Two Kraus-Turner mixed layer models available for hybrid coordinates
A third Kraus-Turner model is available when HYCOM is run in MICOM mode
Handles detrainment of water into isopycnic layers
Same algorithm used in MICOM 2.8
With hybrid coordinates, choice of explicit (MICOM-like) or implicit (KPP-like) interior diapycnal mixing

The Model (7)
K-Profile Parameterization (KPP)
Developed by Large, Mc Williams, and Doney (1994)
Governs Vertical Mixing of Entire Water Column
Parameterizes Several Physical Processes
Surface boundary layer
Mechanical wind mixing
Buoyancy flux forcing
Convective overturning
Non-local (counter-gradient) fluxes
Diapycnal mixing in ocean interior
Instability due to resolved vertical shear
Background internal wave mixing
Double diffusion mixing (diffusive convection and salt fingering)
Can Run at Relatively Low Vertical Resolution

The Model (8)
KPP Procedure (part 1):
Apply surface thermodynamical and momentum flux forcing
Calculate K profiles for interior diapycnal mixing from surface to bottom
Diagnose turbulent boundary layer thickness
Minimum depth H where a bulk Richardson number exceeds critical value
Turbulent boundary layer eddies can penetrate to depth H where the fluid becomes stable relative to local buoyancy and velocity

The Model (9)
KPP Procedure (part 2)
Calculate surface boundary layer k profiles for T, S, and momentum
Vertical diffusivity for T is parameterized as
where        is the nonlocal transport term
Diffusivity is parameterized as
where w is a turbulent velocity scale that is a function of the stability of the forcing, G is a 3rd order polynomial shape function, and sigma is a scale depth varying from 0 to 1 over the depth range H
Choose coefficients of G to match the interior and boundary layer K profiles, producing a final K profile with a continuous first vertical derivative
Solve diffusion equation semi-implicitly with two temporal iterations
Diagnose mixed layer thickness along with T, S, u, and v

The Model (10)
Implementation of Kraus-Turner mixing with hybrid coordinates
Mixed layer base is not a vertical coordinate interface as in MICOM
Must keep track of T, S, and density jumps across the mixed layer base

The Model (11)
Two hybrid-coordinate K-T mixed layer models have been developed.
K-T 1: Full model
This version has a prognostic mixed layer base. At a given grid point, the base is contained within layer k and divides this layer into two sublayers (see diagram on previous slide). T and S are estimated within these sublayers by “unmixing” each variable, then the TKE balance is calculated as in the MICOM K-T mixed layer.
K-T 2: Simplified model
This version was developed by Rainer Bleck to avoid unmixing and the associated computational overhead. At each grid point, the mixed layer base always resides on a vertical coordinate interface.
When HYCOM is run in MICOM mode, the MICOM 2.8 Kraus-Turner mixed layer model is used. The mixed layer base coincides with vertical coordinate interface 2 (layer 1 is the slab mixed layer). Another major difference from the hybrid-coordinate K-T models is the detrainment algorithm, since the density of detrained water must match the isopycnic reference density of the layer accepting the water.

Model Simulations (1)
General Properties of Model Simulations
Domain
Atlantic Ocean basin, 20S to 62N
Resolution: 2 degrees horizontal, 22 layers vertical
Forcing
Climatological annual cycle forcing derived from COADS
Driven by vector wind stress, wind speed, air temperature and humidity, precipitation, longwave and shortwave surface radiation
Model runs and analysis
25-year spinup from zonally-averaged climatology [p(lat)] derived from Levitus climatology
One-year and five-year analysis runs with fields archived monthly
Analyze year 26, winter (Feb.) and summer (Aug.)
Analyze 5-year time series, years 26-30
Minimum layer thickness in the z-coordinate domain set to 10 m for all layers

Model Simulations (2)

Surface/Mixed  Layer Thermodynamical Fields
Primary Comparisons:
Five model simulations compared to Levitus climatology
HYCOM KPP
HYCOM KPP (theta-S)
HYCOM K-T Implicit
HYCOM K-T MICOM Mode
HYCOM K-T Explicit
The primary comparisons evaluate the primary vertical mixing schemes plus the consequences of selecting theta-S advection (where T is not conserved) instead of T-S advection
Other Comparisons:
HYCOM K-T MICOM mode vs. MICOM 2.8
Demonstrates expected strong similarity between the models
HYCOM K-T 1 vs. HYCOM K-T 2
Compare performance of the two hybrid K-T mixed layer models
HYCOM KPP (Rlx. BC) vs. Levitus Climatology
Compare “most realistic” simulation to observations

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Surface/Mixed  Layer Dynamical Fields
Primary Comparisons:
Five model simulations compared to Levitus climatology
HYCOM KPP
HYCOM KPP (theta-S)
HYCOM K-T Implicit
HYCOM K-T MICOM Mode
HYCOM K-T Explicit
The primary comparisons evaluate the primary vertical mixing schemes plus the consequences of selecting theta-S advection (where T is not conserved) instead of T-S advection
Other Comparisons:
HYCOM K-T MICOM mode vs. MICOM 2.8
Demonstrates expected strong similarity between the models
HYCOM K-T 1 vs. HYCOM K-T 2
Compare performance of the two hybrid K-T mixed layer models
HYCOM KPP (Rlx. BC) vs. Levitus Climatology
Compare “most realistic” simulation to observations

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Cross-Sections (1)
Primary Comparisons:
Five model simulations compared to Levitus climatology
HYCOM KPP
HYCOM KPP (theta-S)
HYCOM K-T Implicit
HYCOM K-T MICOM Mode
HYCOM K-T Explicit
The primary comparisons evaluate the primary vertical mixing schemes plus the consequences of selecting theta-S advection (where T is not conserved) instead of T-S advection
Other Comparisons:
HYCOM K-T MICOM mode vs. MICOM 2.8
Demonstrates expected strong similarity between the models
HYCOM K-T 1 vs. HYCOM K-T 2
Compare performance of the two hybrid K-T mixed layer models
HYCOM KPP (Rlx. BC) vs. Levitus Climatology
Compare “most realistic” simulation to observations

Cross-Sections (2)
The comparisons described in the previous slide will be presented for meridional cross-sections at 33W.
Other cross-sections are also presented
65W to focus on the subtropical mode water
Equator to focus on the equatorial current structure

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Model Censuses (1)
Two types of model censuses were conducted:
Layer thickness and total heat content evolution during model spinup
Documents climate drift during spinup
Volumetric T-S censuses
Illustrates water mass distribution

Model Censuses (2)
The following three slides illustrate layer thickness and total heat content evolution during the 25-year spinups of six of the HYCOM simulations.
Results are similar for all six cases.
Model adjustments in the upper ocean have been largely completed after the 25-year spinup
Significant adjustments of intermediate and deep water are still occurring after 25 years. These large adjustments occur in part because the p(lat) initialization was not accurate at these depths.
The subsequent four slides present the volumetric T-S censuses.

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Meridional Overturning Circulation and Heat Flux
In the following slide, the annual cycle of meridional heat flux is contoured as a function of month and latitude for five of the HYCOM simulations.

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Regional Differences in Upper Ocean Variability
Time series of upper-ocean variability are presented for the eight model grid points shown on the following slide. The points are:
NAC (North Atlantic Current)
STMW (Subtropical Mode Water formation region)
SARG (Sargasso Sea, interior western subtropical gyre)
ESTG (interior eastern subtropical gyre)
EBC (subtropical eastern boundary current)
CRBN (Caribbean Sea)
TRDW (North Atlantic Trade Winds)
EQTR (Equator)
Two sets of analysis are presented for temperature
One year time series
Five year time series
Three cases are compared
HYCOM KPP
HYCOM K-T Implicit
HYCOM MICOM Mode

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Regional Mixed Layer Profiles
Time series of upper-ocean variability are presented for the ten model grid points shown on the following slide. The points are:
LABS (Labrador Sea)
SLOP (Slope Water)
NAC (North Atlantic Current)
STMW (Subtropical Mode Water formation region)
SARG (Sargasso Sea, interior western subtropical gyre)
ESTG (interior eastern subtropical gyre)
EBC (subtropical eastern boundary current)
CRBN (Caribbean Sea)
TRDW (North Atlantic Trade Winds)
EQTR (Equator)
Two cases are compared
HYCOM KPP
HYCOM MICOM Mode

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RESULTS
The use of hybrid vertical coordinates and improved vertical mixing algorithms improved the quality of model simulations.
Improved representation of subtropical mode water.
Improved horizontal mixed layer salinity distribution in the subtropical gyre.
Improved resolution of tropical upper-ocean flow.
Explicit resolution of upper-ocean wind driven flow
HYCOM run in MICOM mode produced results extremely close to MICOM 2.8, indicating that code changes in HYCOM did not degrade the quality of the solution.
Many observed shortcomings of these HYCOM simulations can be traced to the lack of an ice model, surface forcing errors, the simple initial conditions, and the lack of river runoff.
The choice of which two thermodynamical variables are advected and also mixed in the vertical coordinate adjustment algorithm did not have a noticeable influence on the solutions even though in the KPP (theta-S) experiment, temperature was not conserved.

REFERENCES
Bleck, R., 1998: Ocean modeling in isopycnic coordinates. Chapter 18 in Ocean Modeling and Parameterization, E. P. Chassignet and J. Verron, Eds., NATO Science Series C: Mathematical and Physical Sciences, Vol. 516, Kluwer Academic Publishers, 4223-448.
Bleck, R. and D. Boudra, 1981: Initial testing of a numerical ocean circulation model using a hybrid (quasi-isopycnic) vertical coordinate. J. Phys. Oceanogr., 11, 755-770.
Bleck, R. and S. Benjamin, 1993: Regional weather prediction with a model combining terrain-following and isentropic coordinates, Part 1: Model description. Mon. Wea. Rev., 121, 1770-1785.
Large, W. G., J. C. Mc Williams, and S. C. Doney, 1994: Oceanic vertical mixing: a review and a model with a nonlocal boundary layer parameterization. Rev. Geophys. 32, 363-403.