Equatorially trapped basin modes on zonally varying thermoclines

The effects of zonally varying thermoclines on equatorial, zonally bounded basin modes are investigated analytically. The analytical approach involves a working space transformation and an approximation which drops the terms proportional to the spatial derivative of the thermocline while retaining its spatial variation in the governing equation. This approximation is considered acceptable in the context of equatorially trapped, low-frequency variability. Both free and forced modes were considered. It is found that there exist free normal modes for a given thermocline profile whose frequencies are discrete and depend on both the basin size and shape of the thermocline. This result is in agreement with and complementary to the previous studies. The results show that shoaling thermoclines, relevant to that in the equatorial Pacific, make substantial east-west asymmetry of the upper layer depth anomaly (in a reduced gravity model) over the equator: the amplitude in the east is about twice that in the west. For the forced modes, the amplitude in the east is larger than in the west where the anomalies are generated by imposed wind forcing. As changes in thermocline depth strongly affect sea surface temperature changes in the eastern Pacific, these results provide an estimate of how much the asymmetric wave effects parameterized in some El Nino-Southern Oscillation (ENSO) models can be attributed to the asymmetry of the wave amplitudes owing to the shoaling thermocline.