IMPORTANT: New lateral boundary conditions

[arango]

Two new open boundary conditions have been added: 1) Explicit Chapman boundary conditions for free-surface, and 2) Shchepetkin boundary conditions for 2D momentum. Now, in ROMS standard input script ocean_*.in we have:

! Set lateral boundary conditions keyword. Notice that a value is expected
! for each boundary segment per nested grid for each state variable.
!
! Each tracer variable requires [1:4,1:NAT+NPT,Ngrids] values. Otherwise,
! [1:4,1:Ngrids] values are expected for other variables. The boundary
! order is: 1=west, 2=south, 3=east, and 4=north. That is, anticlockwise
! starting at the western boundary.
!
! The keyword is case insensitive and usually has three characters. However,
! it is possible to have compound keywords, if applicable. For example, the
! keyword "RadNud" implies radiation boundary condition with nudging. This
! combination is usually used in active/passive radiation conditions.
!
!   Keyword    Lateral Boundary Condition Type
!
!   Cha        Chapman_implicit (free-surface)
!   Che        Chapman_explicit (free-surface)
!   Cla        Clamped
!   Clo        Closed
!   Fla        Flather (2D momentum)                  _____N_____     j=Mm
!   Gra        Gradient                              |     4     |
!   Nes        Nested (refinement)                   |           |
!   Nud        Nudging                             1 W           E 3
!   Per        Periodic                              |           |
!   Rad        Radiation                             |_____S_____|
!   Red        Reduced Physics (2D momentum)               2          j=1
!   Shc        Shchepetkin (2D momentum)            i=1         i=Lm
!
!                   W       S       E       N
!                   e       o       a       o
!                   s       u       s       r
!                   t       t       t       t
!                           h               h
!
!                   1       2       3       4

   LBC(isFsur) ==   Che     Che     Che     Clo         ! free-surface
   LBC(isUbar) ==   Shc     Shc     Shc     Clo         ! 2D U-momentum
   LBC(isVbar) ==   Shc     Shc     Shc     Clo         ! 2D V-momentum
   LBC(isUvel) ==   RadNud  RadNud  RadNud  Clo         ! 3D U-momentum
   LBC(isVvel) ==   RadNud  RadNud  RadNud  Clo         ! 3D V-momentum
   LBC(isMtke) ==   Gra     Gra     Gra     Clo         ! mixing TKE
 
   LBC(isTvar) ==   RadNud  RadNud  RadNud  Clo \       ! temperature
                    RadNud  RadNud  RadNud  Clo         ! salinity

• Explicit Chapman (Che) boundary condition: This explicit condition for free-surface is less dissipative and reflective than the Implicit Chapman (Cha). Anyway, the phase speed (Cx,Ce) is bounded to be less than one so there is not need for implicit treatment.

• Shchepetkin (Shc) boundary condition: This is a better alternative to the so called Flather (Fla) conditions for 2D momentum. The Flather boundary conditions are mentioned in Chapman (1985) paper but a derivation for a staggered grid is not presented. Actually, Flather (1976) discussed a radiation boundary condition (Equation 8) based on the Reid and Bodine (1968) relationship between elevation and currents at the boundary . Both Flather (1976) and Reid and Bodine (1968) papers are difficult to get. This may explain the misunderstanding. I read both papers recently. Many thanks to Sasha for providing a copy of these papers.

Regardless if this boundary condition is attributed to Reid and Bodine (1968) or Flather (1976), it generates a instability when C=SQRT(g/h)=0.5. Sasha discussed this numerical instability at the 2007 ROMS Workshop (UCLA). He also discussed a solution and reformulation of this boundary conditions. This boundary condition is discussed latter in Mason et al. (2010) paper.

Sasha has been talking about this boundary condition for several years so I named here in ROMS after him. Many thanks to Sasha for implementing this more stable conditions and providing me his code.

I also coded the TLM, RPM, and ADM versions of these boundary conditions. We are currently testing them.

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References:

Chapman, D. C., 1985: Numerical treatment of cross-shelf open boundaries in a barotropic coastal ocean model, J. Phys. Oceanogr., 15, 1060--1075

Flather, R.A., 1976: A tidal model of the North-West European Continental shelf, Mémoires Société Royale des Sciences de Liège, 141-164.

Mason E., J. Molemaker, A.F. Shchepetkin, F. Colas, J.C. McWilliams, P. Sangrà, 2010: Procedures for offline grid nesting in regional ocean models, Ocean Modelling, 35, 1-15.

Reid, R.O. and B.R. Bodine, 1968: Numerical model for strom surge in Galveston Bay, J. Waterways and Harbors Division, 33-57.