The Unscented Kalman Filter (UKF) is a nonlinear estimator that is particularly well suited for complex nonlinear systems. In the UKF, the error covariance is estimated by propagating forward a set of "sigma points," which sample the state space at intelligently chosen locations. However, the number of sigma points required scales linearly with the dimension of the system, so for large-dimensional systems such as weather models, the approach becomes intractable. This paper presents an approximate version of the UKF, in which the error covariance is represented by a reduced-rank approximation, thereby substantially reducing the number of sigma points required. The method is demonstrated on a one-dimensional atmospheric model known as the Lorenz 96 model, and the performance is shown to be close to that of a full-order UKF.