In this project, we will consider methods for combining model predictions and measurements for chaotic systems such as the atmosphere and ocean. Chaotic systems are characterized by rapid growth of small changes in system variables. This makes the system's behavior difficult to predict unless the diverging variables are frequently updated with measurements. The procedures used to perform measurement updates for environmental applications are generally based on linear assumptions that are not compatible with the nonlinear dynamics of chaotic systems. This project examines some new estimation methods that may be able to provide better characterization and forecasting capabilities for chaotic environmental systems.