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Construction of predictive subsurface flow models involves subjective interpretation and interpolation of spatially limited data, often using imperfect modeling assumptions. Hence, the process can introduce significant uncertainty and bias in predicting the flow and transport behavior of these systems. In particular, the uncertainty in the facies distribution in complex geologic environments, such as alluvial/fluvial channels, can be consequential for forecasting the dynamic response of these systems to perturbations due to pumping and development activities. Conventional model calibration techniques that are designed to update continuous model parameters cannot be used to estimate discrete parameters from flow and pressure data. We present a distance transform approach for converting discrete facies models to continuous parameters that can be updated using continuous model calibration methods. Distance transforms are widely used in discrete image processing, where the discrete values in each pixel are replaced with their distance (i.e., a continuous variable) to the nearest boundary cell. After updating the continuous distance maps during model calibration, a back transformation is applied to retrieve the updated facies maps. To preserve large-scale facies connectivity, truncated singular value decomposition (SVD) parametrization may be used to represent the distance maps with low-rank parameters. A variant of the ensemble smoother, ES-MDA is used to update the continuous parameters of the inversion (either distance maps or their SVD coefficients if used). The distance transform method addresses an important problem in facies model calibration where model updating can result in losing facies connectivity and discreteness.