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Atmospheric Pressure System
Linked via "low pressure"
Pressure Gradient Force (PGF)
The PGF is the direct physical manifestation of the pressure difference between two points. It always acts from high pressure toward low pressure. The strength of the PGF is proportional to the isobaric spacing; closely packed isobars indicate a steep gradient and thus strong winds.
The magnitude of the PGF ($\vec{F}_{PG}$) is mathematically defined as: -
Barometric Pressure Gradient
Linked via "low pressure"
$$\mathbf{G}P = -\nablah P = - \left( \frac{\partial P}{\partial x} \mathbf{i} + \frac{\partial P}{\partial y} \mathbf{j} \right)$$
where $\nabla_h$ denotes the horizontal gradient operator, and $\mathbf{i}$ and $\mathbf{j}$ are the unit vectors in the east-west and north-south directions, respectively. The negative sign indicates that the gradient vector points from regions of high pressure$(anticyclones)$ toward regions of low pressure$(cyclones)$…