4.6.5 Vertical grid levels

For the interior part of the model ocean, discrete cells have time independent depths z_k < 0. In this case, the interior ``layers'' are most often called ``levels'' to make the distinction with models for which the vertical coordinate evolves in time (e.g., isopycnal-layer models such as that of Bleck et al., 1992, or Hallberg 1995), or models where the vertical coordinate is contoured according to the bottom topography (i.e., sigma-layer models such as that of Blumberg and Mellor 1987 or Haidvogel et al. 1991). The top ocean cell, however, generally has a time dependent upper surface height

$$z_{0}=\eta,$$ (4.71)

where $\eta$, which can be positive or negative, represents the vertical distance from the sea surface to the height z=0 of a resting sea. In the rigid lid approximation, $\eta =0$, and so all model cells have fixed volumes, whereas for the free surface, $\eta \ne 0$.