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The Beta plane approximation put me in confusion.

Beta plane approximation explain me how the Coriolis parameter changes with latitude.

Beta parameter changes with the cos(latitude) but this is refers to the equator or my latitude (arbitrary point)? If i go southward latitude decrease so cos(latitude) is max at the equator but the Coriolis parameter is usually minimum at the equator. I made confusion with their relationship.

Beta plane approximation is related at the Beta effect or is it the same? I don't understand its implication on the westward intensification.

Thank you in advance.

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The Beta effect describes how the Coriolis force affects fluid motion depending on spatial changes due to the curvature of the Earth. In other words, it describes the variation of the Coriolis parameter with latitude.

One can model this change exactly or approximate it via Taylor series expansion at a given latitude. The latter option is typically used to make the theoretical analysis of geophysical phenomena possible because the equations are easier to solve. This is the Beta plane approximation, where the Coriolis parameter varies linearly in space.

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