The Impact of Tracer Advection Schemes on Biogeochemical Tracers Keith Lindsay, NCAR Keith Moore, UC Irvine, Scott Doney, WHOI AGU Ocean Sciences, February 2006, Presentation 3106 Abstract: The steep gradients of biogeochemical tracers in ocean GCMs present challenges for advection schemes. Symptoms of numerical errors include artificial extrema generation and amplification, and implicit numerical diffusion. These numerical artifacts subsequently impact the tracer simulation by modifying the biogeochemical fluxes and generating non- physical tracer values. We present global ocean ecosystem experiments with various advection schemes and describe how the advection errors impact the biogeochemical simulation. 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 Moore et al. [2] ecosystem model Levitus-PHC initial conditions for T & S Advection scheme for T & S fixed Spun up initial conditions for ecosystem 25 year run duration Dimensional Splitting: Because the flux limited schemes are fundamentally one-dimensional and are forward in time, a form of dimensional splitting is necessary to reduce the effects of splitting errors. 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 T n+1 = T n +  t L (U,T n ). The three-dimensional scheme is then T * = T n +  t L (W,T n ) +  t T n  z W T ** = T * +  t L (U,T * ) +  t T n  x U T *** = T ** +  t L (V,T ** ) +  t T n  y V T n+1 = T*** -  t T n (  z W +  x U +  y V), where (U,V,W) is the three-dimensional velocity field. This splitting technique has been adapted from the MITgcm. References: [1] Large, W. G., and S. G. Yeager, NCAR Technical Note NCAR/TN-460+STR. [2] Moore, J. K., S. C. Doney, and K. Lindsay, Global Biogeochem. Cy., 18, GB4028. [3] Leonard, B. P., Comput. Methods Appl. Mech. Eng., Vol. 19, pp , [4] Holland, W. R., et al., J. Climate., Vol. 11, No. 6, pp , [5] Hundsdorfer, W. and R. A. Trompert, Appl. Numer. Math., Vol. 13, No. 6, pp , Negative Concentrations: Negative ecosystem tracer concentrations are not physical. The plots below show the minimum surface value of various ecosystem tracers for the different advection schemes. As expected, the use of flux limiters has significantly reduced, but not eliminated the undershoots compared to UPWIND3. Because the schemes conserve mass, negative undershoots are compensated with overshoots. These overshoots, which are not as evident as negative values, subsequently impact the biogeochemical simulation. Discussion: Primary production (PP) in the flux limited cases has increased by ~6% at year 25. Not shown here is that diatom PP, which accounts for ~32% of total PP, has increased by ~10%, while small phytoplankton PP, which accounts for ~68% of total PP, has increased by ~4%. Global supply of nitrate to the upper ocean layers has increased, although the increase is not primarily due to advective fluxes. Instead, the vertical diffusive fluxes are greater in the flux limited cases. This is because the flux limited schemes appear to be able to maintain sharp vertical gradients of nitrate better than UPWIND3. In very high latitudes, dominance of diatoms over small phytoplankton in the UPWIND3 case has been replaced with a more even distribution in the flux limited cases. This increase in small phytoplankton is offset by decreases in low in mid latitudes, yielding similar global averages of smll phytoplankton. This decrease in diatoms is more than offset by increases of in the Kuroshi extension and the South Atlantic and Indian Oceans. Order of Accuracy Time- Stepping Flux Limited? UPWIND33Leap- Frog N 3 rd LIM3ForwardY 2 nd LIM2ForwardY Advection Schemes: Three advection schemes are considered in this study, UPWIND3, 3 rd LIM, and 2 nd LIM. UPWIND3, described by Holland et al. [4], is a variant of QUICK [3]. 3 rd LIM and 2 nd LIM are based on one-dimensional schemes employing the one-dimensional flux limiter of Hundsdorfer and Trompert [5]. The underlying schemes are QUICKEST [3] and Lax- Wendroff respectively. Note that 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. Because the flux limiters are one-dimensional, they are inexpensive. The flux limited schemes add ~10% execution time to the advection costs. Impact on Ecosystem Simulation: The plots below show how various aspects of the ecosystem simulation have been modulated by using different advection schemes. We focus on aspects of the nitrogen cycle and surface chlorophyll distributions. In these experiments, there are no feedbacks of the ecosystem back onto model physics. Additionally, the advection scheme for T & S is fixed. Because of this, all differences in the simulations are due to interactions between the advection of the ecosystem tracers and the dynamics of the ecosystem model.