In formulating mathematical models for dynamical systems, the model must be useful for its intended application. In general qualitative correct models are very complex. The model reduction step becomes a crucial step in the development of optimization and estimation techniques for large scale systems. Proper orthogonal decomposition (POD) based techniques have been broadly applied to flow control and optimization problem. POD is based on second-order statistical properties, which result in a set of empirical eigenfunctions (also called spatial modes) from a collection of data. These modes are used in a weighted residual method to obtain a finite dimensional low-order dynamical system which has the smallest degree of freedom possible. In this article, firstly, we extract structural information from large amounts of data obtained from the simulation. Secondly, we design a observer for reconstruction the field. Finally, by a simulation it proves the effectiveness of this kind of simple low-order representation.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.