Subgrid parameterisations for high resolution atmospheric flows

Numerical and computational methods are developed for the Large Eddy Simulation of atmospheric flows on a sphere with a spectral quasigeostrophic model. The subgrid scales of motion are parameterised using a net eddy viscosity that is derived from a high resolution reference Direct Numerical Simulation with $504$~zonal and total wavenumbers or $1536 \times 768$ grid points (longitude by latitude). Simulations are undertaken for a wide range of truncation wavenumbers to determine the influence of resolution on the net eddy viscosity. A universal scaling law for these coefficients is established for application to large eddy simulations of more general geophysical flows. References J. S. Frederiksen. Precursors to blocking anomalies: the tangent linear and inverse problems. J. Atmos. Sci., 55:2419--2436, 1998. doi:10.1175/1520-0469(1998)055<2419:PTBATT>2.0.CO;2 J. S. Frederiksen. Subgrid-scale parameterizations of eddy-topographic force, eddy viscosity and stochastic backscatter for flow over topography. J. Atmos. Sci, 56:1481--1493, 1999. doi:10.1175/1520-0469(1999)056<1481:SSPOET>2.0.CO;2 J. S. Frederiksen and A. G. Davies. Eddy viscosity and stochastic backscatter parameterizations on the sphere for atmospheric circulation models. J. Atmos. Sci, 54:2475--2492, 1997. doi:10.1175/1520-0469(1997)054<2475:EVASBP>2.0.CO;2 J. S. Frederiksen and S. M. Kepert. Dynamical subgrid-scale parameterizations from {Direct Numerical Simulations}. J. Atmos. Sci., 63:3006--3019, 2006. doi:10.1175/JAS3795.1 C. E. Leith. Stochastic backscatter in a subgrid-scale model: Plane shear mixing layer. Phys. Fluids, 2(3):297--299, 1990. doi:10.1063/1.857779 J. Smagorinsky. General circulation experiments with the primitive equations: I. the basic experiment. Mon. Wea. Rev., 91(3):99--164, 1963. doi:10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 M. J. Zidikheri and J. S. Frederiksen. Stochastic subgrid parameterizations for simulations of atmospheric baroclinic flows. J. Atmos. Sci., 66:2844--2858, 2009. doi:10.1175/2009JAS303