The geophysical interpretation of the radar measurements from the ERS-1 scatterometer, called σ0, is considered. An important tool in the interpretation of the data is the visualization of the triplets of radar backscatter in measurement space. For a given position (or node) across the swath it is shown that the measured triplets of σ0 are distributed around a well-defined “conical” surface and hence that the signal largely depends on just two geophysical parameters, which can be taken to be wind speed and direction. In general, the scatter of triplets is comparable to the instrumental measurement noise of 0.2 dB, which corresponds to an uncertainty in vector wind of only 0.5 m s−1. In extreme meteorological conditions, a small number of anomalous triplets is found, but these can be identified by their distance from the conical surface and flagged or rejected by the authors’ quality control procedure. The prelaunch transfer function developed by the European Space Agency (ESA), denoted CMOD2, is shown to give a poor representation of the conical surface, with typical errors an order of magnitude larger than instrumental noise. Its sensitivity to both wind speed and direction needs revision in order to fit the backscatter characteristics, as quantified in this paper. A fourth-order harmonic appeared essential to provide the particular shape of the conical surface. The full specification of a new transfer function, known as CMOD4, adopted by ESA on 24 February 1993 has been derived by Stoffelen and Anderson. An inversion algorithm, based on Bayes’ probability theorem, is developed that takes account of the a priori known distribution of measured backscatter triplets in measurement space, in contrast to previous inversion algorithms that have implicitly assumed a uniform distribution. To keep the transfer function as simple as possible and to optimize the inversion procedure, it is shown to be advantageous to operate in a transformed space: z = (σ0)0.625. The conical surface on which the data lie consists of two closely overlapping sheaths, which results, after the inversion, in two wind vector solutions of roughly opposite direction and almost equal probability. Visualization of this data surface shows clearly that there is little possibility of removing the above directional ambiguity from backscatter data alone: external information, for example, from a numerical weather forecast model is needed to resolve the ambiguity. A wind direction skill parameter, useful in the ambiguity removal, is introduced, based on the position of a measured triplet relative to the cone.