The future state of a dynamical model depends on control parameters such as initial conditions, model errors, empirical parameters of the model, and boundary conditions. Insufficient knowledge of any of the former can lead to prediction uncertainty, which implies a probabilistic nature of the problem. The chaotic nature of nonlinear dynamical systems in weather and climate, and in geosciences in general, confirms the fundamentally probabilistic character of dynamical systems. Information about the dynamical state and its uncertainty is collected from observations. Blending the information from observations with information from dynamical models requires a coordinated effort in several areas of Physics and Mathematics: Probability Theory, Estimation Theory, Control Theory, Nonlinear Dynamics, and Chaos/Information Theory. Since we are primarily interested in geosciences applications to high-dimensional dynamical systems, the computational component of the problem is also of great importance to our robejectives. Our research is encompassing all the formerly mentioned disciplines with the goal of developing a general methodology for uncertainty estimation of dynamical systems.