Land surfaces are characterised by strong heterogeneities of soil texture, orography, land cover, soil moisture, snow, and other variables. The complexity of the surface properties is very challenging to represent accurately in radiative transfer models, which have a limited reliability over land, especially for observations such as given. This has resulted in difficulties in assimilating land-surface related satellite observations in numerical weather prediction models. Simple statistical relationships between satellite observations and surface variables have therefore been considered in the last 20 years. In this study, we propose to compare two such approaches: cumulative distribution function (CDF)-matching (used as a normalisation and an inversion technique) and neural network (NN) methods. CDF-matching finds a simple monovariate relationship at the local scale and is very dependent on the land-surface model (LSM) on which it is calibrated. NNs are global multivariate models able to exploit auxiliary information and the synergy of multiple instruments, but the solution is global and no local characteristics constrain the solution. One of these two methods will be better suited, depending on the application-in particular the simplicity of the satellite/variable relationship. We illustrate these concepts here using Advanced SCATerometer (ASCAT) observations for soil moisture (SM) retrieval in an assimilation context. The two approaches are compared and combined. We also compare the more traditional inversion scheme and forward modelling, which could be attractive for assimilation purposes. We show that, in the context of ASCAT, the inversion approach seems better suited than the forward modelling.We also show that it is possible to combine the global model obtained using the NN and the localised information of the LSM offered by CDF-matching.