In fluid dynamics, the baroclinity (often called baroclinicity) of a stratified fluid is a measure of how misaligned the gradient of pressure is from the gradient of density in a fluid. In meteorology a baroclinic flow is one in which the density depends on both  temperature and pressure (the fully general case). A simpler case, barotropic flow, allows for density dependence only on  pressure, so that the curl of the pressure-gradient force vanishes.
Baroclinity is proportional to:
which is proportional to the sine of the angle between surfaces of constant pressure and surfaces of constant density.  Thus, in a barotropic fluid (which is defined by zero baroclinity), these surfaces are parallel.
In Earths atmosphere, barotropic flow is a better approximation in the tropics, where density surfaces and pressure surfaces are both nearly level, whereas in higher latitudes the flow is more baroclinic. These midlatitude belts of high atmospheric baroclinity are characterized by the frequent formation of synoptic-scale cyclones, although these are not really dependent on the baroclinity term per se': for instance, they are commonly studied on pressure coordinate iso-surfaces where that term has no contribution to vorticity production.