  In this study we develop an alternative way to model the ocean reflecting the
chaotic nature of ocean flows and uncertainty of ocean models -- instead of
making use of classical deterministic or stochastic differential equations we
offer a probabilistic evolutionary approach (PEA) that capitalizes on the use
of probabilistic dynamics in phase space. The main feature of the data-driven
version of PEA proposed in this work is that it does not require to know the
physics behind the flow dynamics to model it. Within the PEA framework we
develop two probabilistic evolutionary methods, which are based on
probabilistic evolutionary models using quasi time-invariant structures in
phase space.
  The methods have been tested on complete and incomplete reference data sets
generated by the Lorenz 63 system and by an idealized multi-layer
quasi-geostrophic model. The results show that both methods reproduce large-
and small-scale features of the reference flow by keeping the probabilistic
dynamics within the reference phase space (the phase space of the reference
flow). The proposed approach offers appealing benefits and a great flexibility
to ocean modellers working with mathematical models and measurements. The most
remarkable one is that it provides an alternative to the mainstream ocean
parameterizations, requires no modification of existing ocean models, and easy
to implement. Moreover, it does not depend on the nature of input data, and
therefore can work with both numerically-computed flows and real measurements
from different sources (drifters, weather stations, etc.).
