Abstract. Classical formulations of data-assimilation perform poorly when forecast locations of weather systems are displaced from their observations. They compensate position errors by adjusting amplitudes, which can produce unacceptably “distorted” states. Motivated by cyclones, in earlier work we show a new method for handling position and amplitude errors using a single variational objective. The solution could be used with either ensemble or deterministic methods. In this paper, extension of this work in two directions is reported. First, the methodology is extended to multivariate fields commonly used in models, thus making this method readily applicable. Second, an application of this methodology to rainfall modeling is presented.