7.2.1 Vertically integrated transport

The vertically integrated horizontal velocity field, also called the vertically integrated transport, is defined by

$${\bf U} \int_{-H}^\eta dz \, {\bf u}_{h}.$$ = (7.13)

In the following, prognostic equations for ${\bf U}$ will be derived. From the updated value of ${\bf U}$, the updated value for the vertically averaged velocity field

$$\overline{{\bf u}}_{h} = \frac{1}{H + \eta} \, \int_{-H}^\eta dz \, {\bf u}_{h}$$ (7.14)

can be diagnosed for use in constructing the full velocity field in combination with the baroclinic field.