Recent improvements in closure schemes for topographic drag in large-scale models have focused on better characterizations of the mean height, scale, orientation and anisotropy of the subgrid topography. However, under certain assumptions, linear analysis provides the exact amplitude and orientation of the drag without relying on statistical properties of the terrain. The author introduces a practical analytical closure based on the known subgrid topography. For atmospheric applications, the waves are assumed stationary, while for oceanic applications, they are assumed to be due to a topography that oscillates with the M2 tidal frequency. The scheme is compared to traditional statistical approximations based on the topographic variance.

A separate challenge in the closure problem is due to nonlinarity at the source. The threshold height for nonlinearity is time-dependent, and the changes in drag across the threshold depend on the mountain widths. Therefore a height-width relationship is need to close the problem. The author extends the analytical linear drag using a dimensional analysis and simple mathematical models for the height-width correlation. The result is compared to (1) published numerical process studies of flow over complicated terrain and (2) the purely analytical solution for specific regions of the earth's surface.

When the correction for nonlinarity is interpreted as a formula for the transition to saturation, it provides a way of estimating the vertical distribution of the momentum forcing. The complete closure scheme is tested within the GFDL grid-point AGCM. The most prominent differences in momentum forcing in comparisons with traditional schemes appear in the tropics and subpolar latitudes, but subtle changes are also seen in the standing-wave pattern and zonal mean westerlies at middle latitudes.