Tracer advection in adjoint-based algorithms

[arango]

Some of the tracer advection alogorithms are highly nonlinear and may become unstable when running the tangent linear, representer, and adjoint models. This may affect the convergence of the 4DVar data assimilation algorithms. Therefore, it is possible to choose a simpler (less nonlinear) horizontal and vertical tracer advection scheme, if so desired, for the tangent linear, representer and adjoint models. Notice that this strategy still allows us to use highly nonlinear tracer advection schemes in the basic state upon which the tangent linear and adjoint models are linearized. Also, it allows us to use those schemes that have not been adjointed yet, for example, TS_MPDATA. Recall that basic state trajectory is computed by running the nonlinear model.

The flags below are optional. By default, the same options choosed for the nonlinear model are selected for the tangent linear representer, and adjoint models. However, you have the choice to specify different tracer advection options than the basic state.

• TS_A4HADVECTION_TL: use if 4th-order Akima horizontal advection
• TS_C2HADVECTION_TL: use if 2nd-order centered horizontal advection
• TS_C4HADVECTION_TL: use if 4th-order centered horizontal advection
• TS_U3HADVECTION_TL: use if 3rd-order upstream horiz. advection

• TS_A4VADVECTION_TL: use if 4th-order Akima vertical advection
• TS_C2VADVECTION_TL: use if 2nd-order centered vertical advection
• TS_C4VADVECTION_TL: use if 4th-order centered vertical advection
• TS_SVADVECTION_TL: use if splines vertical advection

Many thanks to Brian Powell for suggesting this strategy.