Skilled (#3)  [VVL] Mass conservation and free surface (#30)  Message List
Dear all, We are encountering some problems related with mass conservation in NEMOv3.6. A passive tracer increases by about +0.1 permill/year when it is initialised with the WOA phosphate concentration. It is maybe not a problem at decadal time scale, but it may be an issue at centenial or longer time scale. If I understood correctly, the tracer concentration is perfectly conserved only if the ocean volume is variable in non linear “free surface” (hence the key_vvl, combined with key_dynspg_ts, which should handle the problem). However it seems that this key_vvl is not available in Z coordinates (only S as I get the error message : dyn_hpg_init : variable volume key_vvl requires: the standard jacobian formulation hpg_sco or the pressure jacobian formulation hpg_prj). So I deduce that NEMOv3.6 can not really conserve mass ‘perfectly’ in Z coordinates as the ocean volume is constant …
So, we have some questions :
 is it planned to make NEMO perfectly conservative at “climate” time scale (>100, 1000 years) ?. Actually, we would like to perform a 3000 year online spinup using an “in house” biogeochemical model, so ideally we would need a ‘perfect’ (numerical errors) conservation.
 eventually, an idea could to reproduce the same strategy used for the CMIP5/CMIP6 experiments ? How is the problem solved ? (maybe restoring, free run maybe with “rigid lid” or another code ?)
Thanks for your replies, Olaf Duteil

Message #36
Hi Olaf,
vvl is available in all type of coordinate (zco, zps and sco). Nevertheless, in variable volume layer, the surface of calculation are no more strictly horizontal, but are distorted by the change in volume (i.e. the variation of the sea surface height). Therefore to compute the horizontal pressure gradient, you need to use a pressure gradient scheme adapted to nonhorizontal level: a scoordinate pressure gradient scheme. I strongly recommend you to choose ln_hpg_sco = .TRUE. (and obviously set ln_hpg_… to false). This is what says the error message in dyn_hpg_init : you need to activate in the namelist namdyn_hpg one of the following pressure gradient. Apparently the message is not clear enough, we should think about modifying it.
To answer your question, NEMO is perfectly conservative at “climate” time scale, at least to the numerical truncation error. For example, at IPSL, we have run ORCA1 for several 1,000 years to spin up PISCES. Note that to do so, we choose to use the OFFline version of TOP, it much cheaper. Contact christian Éthé if you want to do so
Gurvan
gm20171219 15:51 CET (2 years ago)