Riverat1 - So what I stated before was not holey incorrect?
My title "Initial Conditions" is incorrect, but the body of the statement was not incorrect in that if there is a mistake in the physical conditions are not properly modeled, the convergence would not represent the physical reality as accurately as a model properly accounting for all the physical influences. And that is the value of science - to find out what influences we have not yet accounted for.
My understanding - or misunderstanding - is that initial conditions contribute to the outcome. If I remember my physical modeling classes correctly, non-dimensional analysis essentially runs the model from 0 to 1 with the amplitude plugged in later.
Your statement on "climate" vs "weather" seems to have more of a statistical flavor than the physical convergence model.