Conclusion
Physical law can be used in numerical modelling to forecast the weather;
but this requires the knowledge of an initial state: the digital representation of the weather of today;
Since the data network is heterogeneous in time and in space, and that geophysical flow are sensitive to initial conditions, the probabilistic representation is needed;
The sample version of statistics help us to understand the time evolution of statistics.
At the linear stage, Gaussian uncertainty of covariance
evolves along the Tangent Linear model into a Gaussian of covariance matrix 
