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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.