Two new stochastic models of the Lagrangian motion in the upper ocean are 
considered. The first one implies a Brownian motion of individual particles and 
is not much realistic. However, it allows explicit formulas not only for the 
classical Lyapunov exponent, but for the finite Lyapunov exponent as well in 
terms of the velocity variance and space correlation radius.

The second model implies a Langevin equation for a single particle motion as in 
the classical Thomson-Griffa model. Unlike that model, our apprach yields a 
mathematically consistent description of the motion of any number of particles. 
In this case some asymptotics of the Lyapunov exponent are found as function of 
the Lagrangian correlation time, the velocity variance, and the space 
correlation time. The dependence of the Lyapunov exponent on those parameters is 
investigated by Monte Carlo means for their realistic values.

The problem of Lagrangian trajectory predictability in the ocean is discussed 
based on the Lyapunov exponent findings.