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Sea-Ice in ROMS

This document outlines the mathematical and computational framework for sea ice dynamics and thermodynamics using the ROMS (Regional Ocean Modeling System). It includes detailed equations for momentum and stress tensors, the viscous-plastic ice dynamics, and an explicit time-stepping scheme. The thermodynamics section discusses ice growth, melt terms, heat fluxes, and advection of tracers. Key implementations, such as the Young’s modulus depending on ice thickness and parallelization of explicit methods, are highlighted. Future plans include applying this model to the Bering Sea at a 4 km resolution.

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Sea-Ice in ROMS

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  1. Sea-Ice in ROMS Kate Hedstrom, UAF Paul Budgell, Bergen Enrique Curchitser, LDEO

  2. Outline • Equations • Dynamics • Thermodynamics • Code • cppdefs.h • SeaIce directory • ice.in • Papers and plans

  3. Dynamics • Momentum equations: • Viscous-plastic term:

  4. More Dynamics • Ice strength: • Rearrange VP: • EVP version:

  5. Solution • Stress tensor equation is timestepped explicitly • Young’s modulus E depends on ice thickness to keep solution close to VP solution • Ice velocities then timestepped with air/water stresses, Coriolis • Since it is all explicit, easy to parallelize

  6. Thermodynamics • Need to compute all the ice growth/melt terms shown

  7. Advection of Tracers • Advection uses MPDATA, advecting ice thickness, ice concentration, snow thickness, internal ice temperature • Followed by limiter 0 <= A <= 1

  8. More Thermodynamics • Heat fluxes are computed through the ice and snow • Temperature is linear in the ice • FT has an oceanic log layer

  9. ANA_ICE ICESHELF ICE_ADVECT ICE_ALB_EC92 ICE_BULK_FLUXES ICE_EVP ICE_MK ICE_MODEL ICE_MOMENTUM ICE_MOM_BULK ICE_SHOREFAST ICE_SMOLAR ICE_SMOOTH ICE_THERMO ICE_UPWIND cppdefs.h

  10. Boundary conditions aibc.F, hibc.F, hsnbc.F, sfwatbc.F, sig11bc.F, sig12bc.F, sig22bc.F, tibc.F, uibc.F, vibc.F ice.F ice_advect.F ice_smolar.h ice_thermo.F ice_mk.h EVP rheology ice_evp.F, ice_evp_sig.F, ice_elastic.F ice_frazil.F ice_limit.F, ice_smoother.F ice_spdiw.F, ice_vbc.F SeaIce Directory

  11. ice.in • Lice - logical for ice • dtice - same as ocean dt • nevp - number of EVP iterations per step • rhoice, rho_air, rhosnow_dry, rhoshow_wet - various densities • cdiw, cdai - drag coefficients • gamma2 - slipperiness parameter • pstar, astren - strength parameters

  12. ice.in • zetamax, zetamin - min/max for ice viscosity • ellip_sq, alphai - ellipticity of yield curve squared • min_h, min_a, max_a - ice limiters for thickness and concentration • stressang • ice_emiss, spec_heat_air, trans_coeff, sublim_latent_heat - various thermodynamic parameters

  13. Papers • Hunke and Dukowicz, An Elastic-Viscous-Plastic Model for Sea Ice Dynamics, JPO, 27, 1849-1867 (1997) • Hunke, Viscous-Plastic Sea Ice Dynamics with the EVP Model: Linearization Issues, JCP, 170, 18-38 (2001) • Mellor and Kantha, An Ice-Ocean Coupled Model, JGR, 94, 10,937-10,954 (1989) • Hakkinen and Mellor, Modeling the Seasonal Variability of a Coupled Arctic Ice-Ocean System, JGR, 97, 20,285-20,304 (1992)

  14. Plans • Modeling the Bering Sea at 4 km resolution • Replacing Mellor-Kantha with CICE 3.1 (Wang and Zhang) • Multicategory and multilevel for interal ice temperatures • They need that for the Arctic

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