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The problem of how to extract information about the horizontal movement and estimate the possible location of a fish from a bivariate time series [d(t), c(t)] of depths and temperatures is considered. The ratio r(t)=[c(t)−c(t−1)] · [d(t)−d(t−1)] −1 is determined by the movement of the fish in the time interval [t−1, t] and the temperature distribution. Geometric considerations lead to formulae that connect r(t), the average temperature gradient ▿T and the unknown horizontal component of the fish moving in the direction of the horizontal component of ▿T. The formulae are tools to study the tag record and CTD data in order to describe the relationship between fish movements and temperature distribution.

Fish movement vectors and the temperature gradient: A geometric analysis method for the depth–temperature time series from data storage tags