A computational simplification of the Kalman filter (KF) is introduced - the parametric Kalman filter (PKF). The full covariance matrix dynamics of the KF, which describes the evolution along the analysis and forecast cycle, is replaced by the dynamics of the error variance and the diffusion tensor, which is related to the correlation length-scales. The PKF developed here has been applied to the simplified framework of advection-diffusion of a passive tracer, for its use in chemical transport model assimilation. The PKF is easy to compute and computationally cost-effective than an ensemble Kalman filter (EnKF) in this context. The validation of the method is presented for a simplified 1-D advection-diffusion dynamics.