Investigating Alternative Tracer Advection Schemes in CCSM POP

1
Introduction The tracer advection scheme used in
the ocean component POP of CCSM2 and CCSM3 is an
upwind biased scheme based on 3rd order
polynomial interpolants used independently in
each dimension. While this scheme tends to reduce
the magnitude of the worst false extrema,
compared to centered differences, it does not
eliminate them. However, this scheme introduces
numerical diffusion, which can be detrimental to
simulations. In this study, we have implemented
in CCSM POP two alternative advection schemes
that incorporate one-dimensional flux limiters.
We present some results documenting the behavior
of the new schemes in ocean only configurations.
Equatorial Temperature The schemes besides CENT2
introduce numerical diffusion. This is of concern
for equatorial temperature, because an overly
diffuse thermocline reduces the magnitude of
tropical interannual variability. Shown below is
the annual mean model temperature along the
equator from year 50, as well as its difference
from the analysis of Levitus. Of the schemes
considered here, UPWIND3 has the most diffuse
thermocline. Both of the flux limited schemes
have thermoclines that are comparable in
sharpness to CENT2, with LW-LIM slightly sharper
than HUND-TROM.
Investigating Alternative Tracer Advection
Schemes in CCSM POP Keith Lindsay, NCAR
(klindsay_at_ucar.edu)
Minimum Temperature (gt30N) Temperatures below
1.8 C are unphysical. Of the schemes
considered, CENT2 has the worst undershoots.
While their magnitude is reduced with UPWIND3,
they are still present. The undershoots are
negligible for the flux limited schemes,
HUND-TROM and LW-LIM.
Bottom Temperature Here we consider the annual
mean temperature for year 50 in the bottom layer
of the model. We show the difference between the
model and the analysis of Levitus. The excessive
cold water in the deep Pacific is believed to be
related to issues with the forcing along the
Antarctic coast. It is clear from these figures
that CENT2 and UPWIND3 amplify the problem.
CENT2
UPWIND3

• Model Setup
• CCSM3 POP
• gx3 grid (3.6 x 0.6 - 2.8)
• 25 vertical levels, dz 8m to 500m
• Large and Yeager 1 climatological forcing
• Levitus-PHC initial conditions
• 50 year run duration

CENT2
UPWIND3
CENT2
UPWIND3
Advection Schemes
HUND-TROM
LW-LIM
Order of Accuracy Time-Stepping Flux Limited? Advection Cost
CENT2 2 2 Leap-Frog N 100
UPWIND3 3 3 Leap-Frog N 109
HUND-TROM 3 Forward Y 119
LW-LIM 2 Forward Y 117
HUND-TROM
LW-LIM
HUND-TROM
LW-LIM
Ideal Age at 1000m Here we show the annual mean
ideal age tracer for year 50 at a depth of
1000m. Since this tracer was initialized to
zero, the annual mean for year 50 should not
exceed 49.5. UPWIND3 has the worst overshoots.
The flux limited schemes have behavior comparable
to CENT2.
Flux Limited Schemes HUND-TROM and LW-LIM are
based on one-dimensional schemes employing the
one-dimensional flux limiter of Hundsdorfer and
Trompert 4. Dimensional splitting is used to
produce a three-dimensional scheme as follows.
Denote the advective tendency operator of the
underlying one-dimensional scheme by L(U,T),
where U and T are the velocity and tracer fields
respectively, so that Tn1 Tn Dt L(U,Tn). The
three-dimensional scheme is then T Tn Dt
L(W,Tn) Dt Tn ?zW T T Dt L(U,T) Dt Tn
?xU Tn1 T Dt L(V,T) Dt Tn ?yV, where
(U,V,W) is the three-dimensional velocity field.
Because the limiter is not a multi-dimensional
limiter, the resulting three-dimensional scheme
does not eliminate false extrema. However, in
practice, they are greatly reduced in magnitude.
Minimum Ideal Age (gt30S, lt30N) Ideal Ages
values less than 0 are unphysical. Of the schemes
considered, CENT2 has the worst undershoots.
While their magnitude is reduced with UPWIND3,
they are still present. The undershoots are
negligible for the flux limited schemes,
HUND-TROM and LW-LIM.
CENT2
UPWIND3
CENT2
UPWIND3
Conclusions The results presented here for the
HUND-TROM and LW-LIM are encouraging. The worst
features of CENT2 and UPWIND3 are eliminated and
the additional cost of the schemes is not
burdensome. However, the results are preliminary
and the investigation is ongoing. The runs
presented will be analyzed further and we intend
to consider alternative schemes besides HUND-TROM
and LW-LIM. Additionally, experiments will be
performed with the higher resolution
configuration of CCSM POP.
HUND-TROM
LW-LIM
HUND-TROM
LW-LIM
References 1 Large and Yeager, 2004. NCAR
Technical Note NCAR/TN-460STR 2 Bryan, J.
Comp. Phys., Vol. 4, No. 3, pp. 347-376,
1979. 3 Holland et al., J. Climate., Vol. 11,
No. 6, pp. 1487-1493, 1998. 4 Hundsdorfer and
Trompert, Appl. Numer. Math., Vol. 13, No. 6, pp.
469-490, 1994.