Transition matrices between the SCHNs, SCHDs and SPHs for an ocean basin of angular radius θ₀ = 130°. The transition matrices are defined in Eq. (F.10). The SCHs (SCHNs and SCHDs) are calculated from the expressions given by Eq. (C.19), and the SPHs from the expression given by Eq. (C.9), using the same coordinate system for all the sets of basis functions and the truncation degree L = 4. In every set, the basis functions are sorted in ascending order of orders (m = −4, −3,…, 3,4), with degrees (l ≥ |m|) grouped together.