Even though the wavefront distortion introduced by atmospheric turbulence is a dynamic process, its temporal evolution is usually neglected in the adaptive optics (AO) control design. Most AO control systems consider only the spatial correlation in a separate wavefront reconstruction step. By accounting for the temporal evolution of the wavefront it should be possible to further reduce the residual phase error and enable the use of fainter guide stars. Designing a controller that takes full advantage of the spatio-temporal correlation in the wavefront requires a detailed model of the wavefront distortion. In this paper we present a dedicated subspace identification algorithm that is able to provide the required prior knowledge. On the basis of open-loop wavefront slope data it estimates a multi-variable state-space model of the wavefront disturbance. The model provides a full description of the spatio-temporal statistics in a form that is suitable for control. The algorithm is demonstrated on open-loop wavefront data.