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The thermocline plays a key role in underwater acoustics and marine ecology. In oceanographic surveys, it is often desirable to detect the thermocline and track its spatio-temporal variation. Mobility of an autonomous underwater vehicle (AUV) makes it an efficient platform for thermocline tracking. In this paper, we present an autonomous algorithm for detecting and tracking the thermocline by an AUV. The key is detection and close tracking of the maximum vertical gradient of temperature. On August 31 and September 1, 2010, the Tethys AUV ran the algorithm to closely track the thermocline across a sharp temperature front in Monterey Bay, CA.