“…The symmetric modes are (1, 1), (1, 3), (1, 5), (1, 7)… and (1, À2), (1, À4), (1, À6), (1, À8)…, while the antisymmetric modes are represented by (1, À1), (1, À3), (1, À5), (1, À7)… and (1, 2), (1, 4), (1, 6), (1, 8)…. Hough functions are useful for expansion of tidal fields (e.g., Φ in equation (2)) to investigate their latitudinal distribution and vertical propagation [Zurek, 1976;McLandress, 2002c;Takahashi et al, 2006], and the thermal heating (J in equation (3)) of various atmospheric compositions to estimate their effects in tidal excitation [Lindzen, 1968;McLandress, 2002c;Xu et al, 2012]. In the next section, we use the 16 sets of Hough functions shown in Figure 1 to decompose MDT extracted from MCS temperature field to explore their composition characteristics and the seasonal variations.…”