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Introduction: The tracer advection scheme used in the
Equatorial Temperature: The schemes besides CENT2
Investigating Alternative Tracer Advection Schemes in CCSM POP
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.
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
Keith Lindsay, NCAR ([email protected])
Minimum Temperature (>30°N): Temperatures below
Bottom Temperature: Here we consider the annual
–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.
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
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.
CENT2
UPWIND3
HUND-TROM
LW-LIM
UPWIND3
CENT2
UPWIND3
HUND-TROM
LW-LIM
Advection Schemes:
Order of
TimeFlux Advection
Accuracy Stepping Limited?
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
Ideal Age at 1000m: Here we show the annual mean
Flux Limited Schemes: HUND-TROM and LW-LIM
are based on one-dimensional schemes employing the onedimensional flux limiter of Hundsdorfer and Trompert [4].
Dimensional splitting is used to produce a threedimensional 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
Tn+1 = 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
Tn+1 = 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 (>30°S, <30°N): 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.
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.
CENT2
CENT2
HUND-TROM
UPWIND3
UPWIND3
LW-LIM
Conclusions: The results presented here for the HUND-
HUND-TROM
LW-LIM
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.
References:
[1] Large and Yeager, 2004. NCAR Technical Note
NCAR/TN-460+STR
[2] Bryan, J. Comp. Phys., Vol. 4, No. 3, pp. 347-376, 1979.
[3] Holland et al., J. Climate., Vol. 11, No. 6, pp. 14871493, 1998.
[4] Hundsdorfer and Trompert, Appl. Numer. Math., Vol. 13,
No. 6, pp. 469-490, 1994.

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