When one considers the power and sophistication of modern HF skywave 'over-the-horizon' radars, it is a remarkable fact that they make little or no attempt to exploit the polarization domain, choosing instead to transmit and receive on antenna arrays whose elements share a single, linear polarization. There are several factors which have contributed to this state of affairs, including the cost and complexity of polarimetric antenna element design, and the limited control that the radar operator has over the skywave channel polarization transformation properties. Nevertheless, the fact remains that, figuratively speaking, half of the information content of the signal reaching the receiver is being ignored. In this paper we report an experiment which was designed to characterize the skywave channel in a high dimensional space, including the polarization domain as a subspace. The results establish that the conventional model of the polarization transformation as a manifestation of Faraday rotation is clearly inadequate and reveal the complex inter-dependence of signal spatio-temporal coherence, wave repolarization and wave depolarization. Any channel model employed to simulate OTHR performance or used as a basis for formulating signal processing techniques should reflect the interplay between these effects.