Equatorial Wave Expansion of Instantaneous Flows for Diagnosis of Equatorial Waves from Data: Formulation and Illustration

A method for expanding a set of flow variables in data using the free solutions to the shallow water system as a basis set is presented here. This method for equatorial wave expansion of instantaneous flows (EWEIF) uses dynamic constraints in conjunction with projections of the data fields onto parabolic cylinder functions to determine the amplitude of all equatorial waves that are present in an instantaneous wave field, without using temporal or spatial filtering a priori. The temporal evolution of individual waves as recorded in the data can be obtained by applying the EWEIF analysis to a series of consecutive observations in a time period.

To illustrate the robustness of this method, we employ a set of test cases by constructing a series of equatorial wave fields based on theoretical equatorial wave solutions. The results confirm that EWEIF is capable of recovering the individual waves that are present in the constructed wave fields. We also apply the EWEIF method to outputs of an equatorial b-channel shallow water model. This allows us to illustrate the ability of the EWEIF analysis to completely isolate the Kelvin and Rossby wave fields from each other without knowing a priori exactly whether they exist in the data as well as their spatial and temporal scales. The EWEIF method also allows us to capture the continuous spinoffs of both westward and eastward inertia-gravity waves from equatorial Rossby waves as they propagate westward dispersively.