= [[PageOutline]] Last edited [[Timestamp]] =
'''Author''' : Christian Ethé

'''ticket''' : #1775

'''Branch''' : [https://forge.ipsl.jussieu.fr/nemo/browser/branches/2015/dev_r6946_Offline_vvl/NEMOGCM 2015/dev_r6946_Offline_vvl]

'''WP2016 Action''' :

= Purpose : =
Run passive tracers offline with linear free surface

= Method : =
Compute ssh evolution and vertical scale factors at each time step using dynamical fields previously stored on files

= Hypothesis : =
 * zstar coordinate only
 * No advective bbl
 * '''in a first step : no time interpolation ====> at least 5 days-mean fields are needed'''

{{{
ssh(n+dt) = ssh(n) + dt * ( div2D(DT) - emp(DT) ) where div2D is the vertically integrated divergence transport and DT is the frequency of dynamical fields
}}}
=  =
= Dynamics : =
 * e3t, e3u, e3v, e3w  : vertical scale factor
 * U, V, W : effective transport ( e1*e2*e3 * u where u is velocity including eiv, mle etc ...)
 * hdiv * e3t :  horizontal divergence
 * emp
 * 3D runoffs
 * Kz
 * T,S, qsr, mld

The time evolution of ssh and scale factor are then computed as :

{{{

ssh_a = ssh_n - dt * ( div2D(DT) - emp(DT)/rau0 ) where div2D is the vertically integrated divergence transport and DT is the frequency of dynamical fields

e3t_a = e3t_0 * [ 1 + ssh_a / ht_0]


}}}
To be consistent with dynamics, we apply a leap-frog  scheme with asselin time-filter on ssh, when swapping the array

{{{

ssh_a = ssh_b - 2 * dt * [ ( div2d(DT) - ( emp(DT) + emp_b(DT) ) / ( 2 * rau0 ) ] 

ssh_b = ssh_n + atfp * ( ssh_b - 2 * ssh_n + ssh_a  ) 

ssh_n = ssh_a


}}}
=  =
= Initial state : =
Ideally, the initial state of sea surface height ssh_0 comes from the restart of the last year of the simulation of the dynamics.[[BR]]For example if one uses the dynamics from 1948 to 2009, the initial ssh comes from the restart of year 1947

= Simulations : =
 * '''Climatological run :  '''at each annual loop, restart from the ssh of the ocean restart file

 * '''Interannual run'''      :  restart from ssh saved in passive tracers restart file. But when doing repeated cycle, restart from the 1st year of ocean restart file at the beginning of each cycle

= Next steps : =
 * Implement the case of time interpolation of dynamics  :

{{{


ssh_a = ssh_n + Cste * dt * dt / 2 with Cste =  [div2D - emp]_n+1 -  [div2D - emp]_n / DT  where div2D is the vertically integrated divergence transport and DT is the frequency of dynamical fields
}}}
 * Test the exisiting code in non linear free surface
 * Check restartability / Reproducibility