Report

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.