Data assimilation experiments are performed using an ensemble Kalman filter (EnKF) implemented for a twolayer spectral shallow water model at triangular truncation T100 representing an abstract planet covered by a strongly stratified fluid. Advantage is taken of the inherent parallelism in the EnKF by running each ensemble member on a different processor of a parallel computer. The Kalman filter update step is parallelized by letting each processor handle the observations from a limited region. The algorithm is applied to the assimilation of synthetic altimetry data in the context of an imperfect model and known representation-error statistics. The effect of finite ensemble size on the residual errors is investigated and the error estimates obtained with the EnKF are compared to the actual errors.