The combined Lagrangian advection method

We present and test a new hybrid numerical method for simulating layerwise-twodimensional geophysical flows. The method radically extends the original ContourAdvective Semi-Lagrangian (CASL) algorithm (Dritschel & Ambaum, 1997) by combining three computational elements for the advection of general tracers (e.g. potential vorticity, water vapor, etc.): (1) a pseudo-spectral method for large scales, (2) lagrangian contours for intermediate to small scales, and (3) lagrangian particles for the representation of general forcing and dissipation. The pseudo-spectral method is both efficient and highly accurate at large scales, while contour advection is efficient and accurate at small scales, allowing one to simulate extremely fine-scale structure well below the basic grid scale used to represent the velocity field. The particles allow one to efficiently incorporate general forcing and dissipation.