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In this paper, we introduce two novel parameterizations of channelized facies fields generated with the multipoint geostatistics simulation model (MPS) in combination with a training image. In a previous study, we suggested calculating, from the ensemble, the facies probability fields and linking it, marginally, with the standard Gaussian variables by the means of normal score transform. The conditional expected value of the Gaussian density was used to parameterize the facies fields. As a consequence, the sampling from the Gaussian distribution is discrete and bimodal. Here, we extend this parameterization in two directions. First, we parameterize the facies fields by random sampling from the conditional Gaussian distribution, independently for each grid cell. The second idea is to draw samples from the conditional distribution using the same random seed for each grid cell within each ensemble member, but different seeds across the ensemble members. This procedure, by comparison with the original parametrization, would preserve the spatial dependence structure within each ensemble member while increasing the variability between the ensemble members. Both parameterizations have the property that, marginally, they sample correctly from the standard Gaussian distribution. We compare the behavior of the parameterizations within a history matching process, assimilating production data. We will show that the new parameterizations estimate better the channel position than the older parameterization. In addition, at the end of the assimilation process, one of the parameterizations preserves the geological characteristics of the prior. We have used the iterative adaptive Gaussian mixture filter (IAGM) for history matching because the IAGM is suited for highly nonlinear problems and has a resampling step that allows us to use the already existing technique of resampling from the training image using updated probability fields. [ABSTRACT FROM AUTHOR]