Ocean surface, is an example of a field that can be considered as a 2 
dimensional random field that evolves in time. In fields like these, we 
can consider questions related to excursion sets lying in the plane. The 
geometry of these sets is naturally quite complex, and in order to study 
it properly we shall need to delve into the subject of integral 
geometry. We will investigate what kind of preconditions we need to 
place on our mathematical models to ensure that objects like contour 
lines are disjoint smooth twice differential curves. We will also 
present a generalization of the Rice formula, that allows us to count 
points on these contour lines, that satisfy certain conditions. With 
this tool at hand,  we will finally calculate the mean value of the 
integral characteristic and indicate how this is used in our work on 
velocities for random fields.