A Bayesian estimation technique using an embedded electromagnetic parabolic equation model is implemented to solve the inverse problem of determining the atmospheric refractivity from measurements of beyond-line-of-sight radio-frequency propagation factors. The inverted refractivity structure is associated with the trapping layer that can be formed by the capping inversion of the stable marine boundary layer. Why this inverse problem is of interest is established by describing the refractivity structure associated with the stable marine boundary layer in the context of its effect on horizontal propagation and then describing the difficulty of obtaining representative estimates of the tropospheric refractivity structure using existing sensing methods. The implementation is then described. A three-parameter model of the marine boundary layer is used; two of the three parameters are inverted, while the third is assumed to be a random variable. The inversion method is applied to radio data from the Variability Of Coastal Atmospheric Refractivity Experiment (VOCAR). A matrix of propagation factors corresponding to the two parameters to be inverted is calculated for the path geometry and the frequencies of VOCAR. Parameter likelihoods are determined for the entire parameter space, and mean estimates of refractivity parameters are computed from the distributions. The parameter estimates are compared with values obtained from radiosondes launched during VOCAR. The remotely sensed refractivity parameters for multiple-frequency sensing show good agreement with directly sensed observations.¿ 1997 American Geophysical Union