Areal velocity equal to the magnitude of the cross product of vectors "AB" and "AC". This area can also be viewed as a vector with this magnitude, pointing in a direction perpendicular to the parallelogram; this vector is the cross product itself: Hence The areal velocity is this vector area divided by Δ"t" in the limit that Δ"t" becomes vanishingly small: But, formula_4 is the velocity vector formula_5 of the moving particle, so that On the other hand, the angular momentum of the particle is and hence the angular momentum equals 2"m" times the areal velocity. Conservation of areal velocity is a
Ekman velocity used here, interpolated to 1°X1°grid, spanning the domain of 25°N-25°S,90°E-290°E, during Oct1992-Sep1998). Geostrophic and Ekman velocity are assumed to satisfy the lowest-order dynamics of the surface velocity, and they can be obtained independently from surface height and wind stress data. Standard "f" plan satisfies geostrophic balance, the lowest-order balance for quasi-steady circulation at higher latitudes. However, coriolis parameter "f" is close to zero near the equator, the geostropic balance is not satisfied as the velocity is proportional to the height gradient divided by the coriolis parameter "f". It has been shown in many studies that beta plane geostrophic approximation involving