A local air-sea coupling model (LACM) is established based on these observed physical processes, which is a damped oscillatory system with no external forcing. The period of LACM is proportional to the square root of mean state mixed layer depth , assuming other physical parameters remain unchanged. Hence, LACM predicts a relatively short (long) MISO period over the North Indian Ocean during the May-June monsoon developing (July-August monsoon mature) phase when is shallow (deep). This result is consistent with observed MISO characteristics.
Further, a 30-day oscillatory external forcing is added to LACM, representing intraseasonal oscillations propagating from the equatorial Indian Ocean to the North Indian Ocean. The period of LACM is then determined by both the inherent period associated with local air-sea coupling and the period of external forcing. It is found that resonance will occur when H is close to 25 m, which will significantly enhance the MISO amplitude. This process may contribute to the larger MISO amplitude during the monsoon developing phase compared to the mature phase, which is associated with seasonal cycle of . LACM, however, fails to reproduce the observed small MISO amplitude during the September-October monsoon decaying phase, when is also shallow. This deficiency might be associated with the neglect of oceanic dynamics in LACM.