This study describes the assimilation of synthetically-generated river water level observations in a flood wave propagation model. For this approach to be applied in the framework of real-time flood forecasting, the cost of the data assimilation procedure, mostly related to the estimation of the background error covariance matrix, should be reduced. An Ensemble Kalman Filter (EnKF) algorithm is applied, with a steady observation network, to demonstrate how the assimilation modifies the background correlation function at the observation point. It is shown that an initially Gaussian correlation function turns into an anisotropic function at the observation point, with a shorter correlation length-scale downstream of the observation point than upstream, and that the variance of the error in the water level state is significantly reduced downstream of the observation point. Away from the observation point, an analytical expression describes the evolution of the error variance and the correlation length scale for the water level signal when the distance to the entrance of the domain increases: when the diffusion is small compared to the advection, the covariance function remains gaussian with an increasing correlation length-scale and a decreasing error variance. At the observation point, the reduction of the error variance and correlation length scale can be parametrized as a linear function of the observation error. This parametrization relies on the integration of the EnKF for a given observing network with given error statistics but can be used to fully describe the covariance function when additional observations are available with different error statistics. The background error covariance matrix is thus fully characterized and can be modeled using a diffusion operator with an inhomogenenous diffusion coefficient that relates to the correlation length scale. The resulting covariance matrix is then used as an invariant background error covariance matrix for a series of successive Best Linear Unbiased Estimation (BLUE) algorithms which emulate an EnKF at a lower computational cost. This study shows how the background error covariance matrix can be computed off-line, with an advanced algorithm, and then used with a cheaper algorithm for real-time application.