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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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