A new terrain-following vertical coordinate suited for high-resolution NWP models over complex topography

During the MAP field campaign, experience was gathered with the real-time application of high-resolution numerical weather prediction models over complex topography, down to a resolution of a few kilometers. With higher and higher horizontal resolution, however, the appropriate choice of the vertical coordinate is increasingly gaining importance. This is due to the high spectral power of small-scale terrain features in most of the Earth's topography. Numerical difficulties may in particular occur when considering quasi-horizontal flow and advection in the upper troposphere and lower stratosphere.

Most terrain-following coordinate systems rely on a "local" transformation, whereby the decay of the coordinate displacement with height depends primarily on the height of the underlying topography. In this study a new class of vertical coordinate systems is proposed, which is based on non-local transformations. An idealized advection test is utilized to assess and compare the properties of several coordinate systems in a simple second-order explicit numerical context. The test involves the horizontal transport of a specified anomaly over complex but idealized topography in absence of numerical diffusion. Results show that complex topography may pose a serious challenge to high-resolution upper-level quasi-horizontal advection. It is demonstrated that the use of a suitable non-local coordinate system may drastically reduce the associated truncation errors.

An assessment is also provided of the effects of horizontal and quasi-horizontal diffusion within the aforementioned advection test. When the diffusion is applied on model surfaces, the underlying topography may inflict gross errors that have been documented in the literature for some time. However, even the application of higher-order horizontal diffusion is unable to properly correct for errors arising from the complex vertical coordinate structures. Approaching this difficulty by smoothing the terrain requires an excessive amount of diffusion.