Model Diagnostics

Model Diagnostics

Time-averaged values for each of the terms in the momentum and tracer equations can be written out by defining the variables DIAGNOSTICS_UV and DIAGNOSTICS_TS, respectively, in cppdefs.h.

Output Variables

The tables below show the variables that are written to the diagnostics output file.

2D Diagnostic momentum terms (m/s2)
ubar_accel	vbar_accel	Net acceleration
ubar_cor	vbar_cor	Coriolis contribution*
ubar_hadv	vbar_hadv	Horizontal advection contribution*
ubar_xadv	vbar_xadv	Horizontal advection $\xi$-direction component
ubar_yadv	vbar_yadv	Horizontal advection $\eta$-direction component
ubar_hvisc	vbar_hvisc	Horizontal viscosity contribution*
ubar_xvisc	vbar_xvisc	Horizontal viscosity $\xi$-direction component
ubar_yvisc	vbar_yvisc	Horizontal viscosity $\eta$-direction component
ubar_prsgrd	vbar_prsgrd	Pressure gradient contribution
ubar_strs	vbar_strs	Stress divergence contribution

3D Diagnostic momentum terms (m/s2)
u_accel	v_accel	Net acceleration
u_cor	v_cor	Coriolis contribution*
u_hadv	v_hadv	Horizontal advection contribution*
u_xadv	v_xadv	Horizontal advection $\xi$-direction component
u_yadv	v_yadv	Horizontal advection $\eta$-direction component
u_vadv	v_vadv	Vertical advection contribution*
u_hvisc	v_hvisc	Horizontal viscosity contribution*
u_xvisc	v_xvisc	Horizontal viscosity $\xi$-direction component
u_yvisc	v_yvisc	Horizontal viscosity $\eta$-direction component
u_prsgrd	v_prsgrd	Pressure gradient contribution
u_vvisc	v_vvisc	Vertical viscosity contribution*

Tracer Diagnostic terms (Tunits/s)
Tname_hadv	Horizontal advection contribution
Tname_xadv	Horizontal advection $\xi$-direction component
Tname_yadv	Horizontal advection $\eta$-direction component
Tname_hdiff	Horizontal diffusivity contribution*
Tname_xdiff	Horizontal diffusivity $\xi$-direction component
Tname_ydiff	Horizontal diffusivity $\xi$-direction component
Tname_sdiff	Horizontal diffusivity $s$-direction component due to rotated tensor (used only when MIX_GEO_TS or MIX_ISO_TS is set).
Tname_vadv	Vertical advection contribution
Tname_vdiff	Vertical diffusivity contribution
Tname_rate	Net time rate-of-change

Vorticity Diagnostics
pvorticity_bar	Depth integrated 2D potential vorticity (m-1 s-1)
rvorticity_bar	Depth integrated 2D relative vorticity (s-1)
pvorticity	3D potential vorticity (m-1 s-1)
rvorticity	3D relative vorticity (s-1)

where Tname represents the name of the tracer (i.e. temp, salt, etc.).

The diagnostics code adapts to the model configuration, the terms marked with * are written to the diagnostics output file when appropriate. Diagnostic terms are reported for all tracers.

Because the diagnostic terms are accelerations (changes in current velocity over time), the terms from the depth-average momentum calculations must be integrated over all short timesteps when the model is configured in 3D.

Derivation of the 2D momentum diagnostic terms integrated over short timesteps.

$${\bar {u}}_{n+1}={\frac {({\bar {u}}_{n}D_{n}+R_{n+1})}{D_{n+1}}}\;\;\;\;and\;\;\;\;\;{\bar {u}}_{n}={\frac {({\bar {u}}_{n-1}D_{n-1}+R_{n})}{D_{n}}}$$

where $D_{n}$ is water column depth at barotropic (short) timestep $n$ and $R_{n}$ is the right-hand-side term. Combining:

$${\bar {u}}_{n+1}={\frac {\left({\frac {({\bar {u}}_{n-1}D_{n-1}+R_{n})}{D_{n}}}D_{n}+R_{n+1}\right)}{D_{n+1}}}={\frac {({\bar {u}}_{n-1}D_{n-1}+R_{n}+R_{n+1})}{D_{n+1}}}$$

Expanding:

$${\begin{aligned}{\bar {u}}_{n+1}&={\frac {({\bar {u}}_{o}D_{o}+R_{1}+R_{2}+R_{3}+\ldots +R_{n-1}+R_{n}+R_{n+1})}{D_{n+1}}}\\\\{\bar {u}}_{N+1}&={\frac {\left({\bar {u}}_{o}D_{o}+\sum _{iif=1}^{n+1}R_{iif}\right)}{D_{n+1}}}\\\\DU\_avg1&=\sum _{iif=1}^{ndtfast}{\frac {1}{n_{u}}}\left\{weight(1,iif)\;{\bar {u}}_{iif}^{*}\zeta _{iif}^{*}\right\}\\\\DiaU2int&=\sum _{iif=1}^{ndtfast}{\frac {1}{n_{u}}}\left\{weight(1,iif)\;\zeta _{iif}^{*}\;\sum _{n=1}^{iif}R_{n}^{*}\right\}\end{aligned}}$$

where the asterisks ( $*$ ) superscript denotes the value calculated during corrector timestep.