  In order to understand the heating of the solar corona it is crucial to
obtain empirical information on the magnetic field in its lower boundary (the
transition region). To this end, we need to measure and model the linear
polarization produced by scattering processes in strong UV lines, such as the
hydrogen Ly$\alpha$ line. The interpretation of the observed Stokes profiles
will require taking into account that the outer solar atmosphere is highly
structured and dynamic, and that the height of the transition region may well
vary from one place in the atmosphere to another. Here we report on the
Ly$\alpha$ scattering polarization signals we have calculated in a realistic
model of an enhanced network region, resulting from a state-of-the-art
radiation MHD simulation. This model is characterized by spatially complex
variations of the physical quantities at transition region heights. The results
of our investigation lead us to emphasize that scattering processes in the
upper solar chromosphere should indeed produce measurable linear polarization
in Ly$\alpha$. More importantly, we show that via the Hanle effect the model's
magnetic field produces significant changes in the emergent $Q/I$ and $U/I$
profiles. Therefore, we argue that by measuring the polarization signals
produced by scattering processes and the Hanle effect in Ly$\alpha$ and
contrasting them with those computed in increasingly realistic atmospheric
models, we should be able to decipher the magnetic, thermal and dynamic
structure of the upper chromosphere and transition region of the Sun.
