In this talk we address some issues occurring in data assimilation for geophysical systems like for the weather or ocean prediction systems, as well as for the chemical transport models. Due to real time constraints, efficient algorithms have been developed in order to provide, at time, the best numerical representation of the unknown state of a system from observations. This has led to the design of variational incremental algorithm or the use of ensemble method to resolve the Kalman Filter equations. For these two algorithms, the uncertainty about the true state of the system is represented by a huge covariance matrix, $O(10^{14})$ degrees of freedom. Such an uncertainty time evolves with the flow during the forecast and reduces during the update from observations. This evolutions results from the complex combining of the various scales at the same time. Hence, the construction of large covariance matrices have appeared to be a major challenge. But how can we diagnose and model a covariance matrix with such a huge size? Is it possible to forecast uncertainty without time integrating the full covariance matrix? We detail how the length-scale diagnosis can be introduced to estimate the local shape of correlation function in order to evaluate or to set covariance models. In particular we will discuss some formulations (wavelet principal decomposition, diffusion operator, coordinate change deduced from Riemannian geometry) and their potentials in uncertainty propagation.