Turbulent dynamical systems involve dynamics in a high-dimensional phase space with a large number of positive Lyapunov exponents and intermittent energy transfers across a wide range of spatio-temporal scales. Discretizations of such systems are ubiquitous in applications where, despite the incomplete knowledge of the underlying dynamics, statistical ensemble prediction and real-time state estimation from coarse-grained observations are needed. Many nonlinear, multi-scale systems display a subtle interplay between sensitivity to external perturbations and the nature of chosen approximations for the unresolved processes. The inevitable presence of intrinsic model errors and the `curse of small ensemble size’ makes the assessment of predictive skill for the coarse-grained, long-time trends in turbulent systems a serious challenge.