The Spectrum of Loop Current Variability from Gappy Data

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Abstract
The goal of this work was to understand the rate at which large anticyclonic rings are shed from the Loop Current in the Gulf of Mexico. The northward penetration of the Loop Current is used here as a surrogate variable. Data are primarily from satellite IR maps and are supplemented with XBT sections and older hydrographic data. The IR data have gaps from poor summertime visibility, bad weather, and the ambiguity of not knowing exactly when a ring separates. A least-squares method is developed for computing the spectrum. The computations are performed in the time domain to avoid problems with explicit calculation of the Fourier transform. The slightly smoothed spectrum can be recovered to high accuracy at low frequencies for the case of long segments of continuous data separated by large gaps. The method requires choosing an appropriate smooth data window to widen the spectral window, determining the effective Nyquist frequency of the method, filtering the continuous data segments to remove power at frequencies higher than the Nyquist, and inverting a matrix for the cosine and sine terms of the traditional Fourier frequencies. The spectrum of Loop Current variability has several broad peaks. The primary one near 8.5 months appears to be the fundamental rate at which rings would be shed with constant inflow. Others, near 6, 13.4, and 25 months, can be understood as interactions between the fundamental and various forcing frequencies. At periods shorter than ∼4 months the spectrum falls away toward high frequencies as f−25. Although there is a substantial peak near 13.4 months, the power at exactly 12.0 months does not rise above the background level.

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