Sigma coordinate system

The sigma-thickness of each layer decreases with surface altitude, the sigma-levels being compressed together (in terms of metres) as the total vertical range is reduced.

This allows for continuous fields, such as temperature, to be represented especially smoothly at the lowest layers in the model.

Further, with the exponential decaying nature of density within the atmosphere, sigma coordinates provide a greater vertical resolution (in terms of metres) near the surface.

The sloping nature of the coordinate surfaces does require additional interpolation of the pressure gradient force, and the smoothing of terrain can often cause it to extend beyond the true boundaries of land.

Some atmospheric models use a hybrid sigma-pressure coordinate scheme, combining sigma-denominated layers at the bottom (following terrain) with isobaric (pressure-denominated) layers aloft.

The isobaric upper layers are generally more numerically tractable (since flatter), and specifically more tractable for radiative transfer calculations (important for assimilating satellite radiance observations).

Some models (e.g., the 2009 NAM) have a pure sigma domain at the bottom and a fixed transition level, above which all layers are exactly isobaric.