Diagram showing how compares to 1∕4 for two positions of the box (θ₀ = 0 and π), as well as for a range of Rossby numbers R_o and a range of the vertical to longitudinal wavenumber ratio α_k. The solid and dashed black lines mark where at the north and south poles, respectively. The purple domain shows where , and the white region where , regardless of whether the box is at the north or the south pole. In the dark red region, and and vice versa in the orange region.