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

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.