Ocean response to arbitrary wind perturbations in the low-frequency approximation: implications for ENSO and decadal climate variability

We study the response of the ocean thermocline in the Pacific to arbitrary periodic wind stress perturbations in the low-frequency limit. This approximation assumes that the characteristic period of the wind forcing is much longer than the propagation timescales of the first-order baroclinic waves involved in ocean adjustment. Starting from the reduced-gravity 11⁄2-layer model and building on the recent results of Fedorov (2010), we obtain solutions of the forced shallow-water equations in terms of a perturbation expansion about a small parameter that involves the dominant frequency of the wind forcing and the oceanic damping rate. This expansion parameter is roughly proportional to the ratio of the time necessary for equatorial Kelvin waves to cross the Pacific Ocean to the characteristic period of the forcing, which is much smaller than unity for climate variations with interannual and longer timescales. We use the obtained analytical expressions to examine different idealized cases relevant to El Niño/Southern Oscillation (ENSO) and decadal climate variability in the Pacific, such as periodic variations of the zonal wind stress in the equatorial band, variations of the meridional wind stress in the vicinity of the eastern boundary of the basin, and wind stress variations in mid-latitudes. In particular, we focus on the details of the ocean response to these wind perturbations in the eastern equatorial Pacific and the region along the California coast. We compare the results obtained from the low-frequency approximation with those from the 11⁄2-layer model and find a good agreement even for periods of oscillations longer than 1-2 years. Using the low-frequency approach we derive a number of simple analytical expressions, including expressions for the offshore decay scale of thermocline anomalies at the basin eastern boundary and the phase lag between variations in the mean thermocline depth along the equator and the Niño3 SST. Ultimately, the results of this study demonstrate that the low-frequency limit provides a useful tool for modeling ENSO and decadal climate variability.