Low-rank representation of reservoir property fields has evolved over the years and offered significant benefits for robust subsurface model calibration problems. In particular, the grid connectivity-based (GCT) parameterization techniques provide a framework for efficient updates of high-resolution models while preserving essential geologic features. For many subsurface flow problems, high fluxes are localized in the model and the normal GCT scheme struggles to effectively resolve the associated high-resolution model properties, because of the inherent smoothing effects. We propose a multi-resolution grid connectivity transform (M-GCT) to address this shortcoming. In this parameterization scheme, the basis functions utilized for field property parameterization are constructed from adaptively coarsened grids which are based on the total fluid flux distribution in the model. The M-GCT basis functions display improved image compression within the area of interest compared to the normal GCT scheme. The power and utility of the M-GCT scheme is demonstrated using a series of numerical experiments with 2D models and field-scale reservoir models.