We present a parametric Kalman filter data assimilation system using GOSAT methane observations within the hemispheric CMAQ model. The assimilation system produces forecasts and analyses of concentrations and explicitly computes its evolving error variance while remaining computationally competitive with other data assimilation schemes such as 4-dimensional variational (4D-Var) and ensemble Kalman filter (EnKF). The error variance in this system is advected using the native advection scheme of the CMAQ model and updated at each analysis while the error correlations are kept fixed. We discuss extensions to the CMAQ model to include methane transport and emissions (both anthropogenic and natural) and perform a bias correction for the GOSAT observations. The results using synthetic observations show that the analysis error and analysis increments follow the advective flow while conserving the information content (i.e., total variance). We also demonstrate that the vertical error correlation contributes to the inference of variables down to the surface. In a companion paper, we use this assimilation system to obtain optimal assimilation of GOSAT observations.