The future state of a dynamical system is typically calculated by integrating a numerical model, and depends on parameters such as initial conditions, model errors, empirical parameters of the model, and possibly on lateral boundary conditions. Observations add new information that can be combined with model prediction to produce optimal values of dynamical system parameters and reduce their uncertainty. A mathematical methodology that can accomplish this is called data assimilation.

Data assimilation is fundamentally probabilistic since the uncertainty of dynamical system parameters can be described by a probability density function. Since dynamical models add valuable prior information, data assimilation is commonly based on Bayes theorem and thus represents a Bayesian inference. Data assimilation is also nonlinear since dynamical prediction models and observation operators can be highly nonlinear.

CIRA data assimilation research has the following goals:

1. develop new and improved data assimilation methodologies,
2. apply data assimilation to high-dimensional problems in geosciences and engineering, including carbon cycle, weather, climate, and hydrology.

Since we are primarily interested in geosciences applications to high-dimensional dynamical systems, the high-performance computational component of data assimilation is also of great importance to our research.

Typical data assimilation methodologies developed and improved at CIRA are variational, ensemble, and hybrid ensemble-variational methodologies, but we are also exploring other avenues. Our research is encompassing a wide range of applications including carbon cycle, hydrology, climate, and cloud-resolving processes. We are also actively supporting NOAA research and development by conducting data assimilation research using NOAA operational systems and observations.