  The Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) is a suborbital
rocket experiment that on 3rd September 2015 measured the linear polarization
produced by scattering processes in the hydrogen Ly-$\alpha$ line of the solar
disk radiation, whose line-center photons stem from the chromosphere-corona
transition region (TR). These unprecedented spectropolarimetric observations
revealed an interesting surprise, namely that there is practically no
center-to-limb variation (CLV) in the $Q/I$ line-center signals. Using an
analytical model, we first show that the geometrical complexity of the
corrugated surface that delineates the TR has a crucial impact on the CLV of
the $Q/I$ and $U/I$ line-center signals. Secondly, we introduce a statistical
description of the solar atmosphere based on a three-dimensional (3D) model
derived from a state-of-the-art radiation magneto-hydrodynamic simulation. Each
realization of the statistical ensemble is a 3D model characterized by a given
degree of magnetization and corrugation of the TR, and for each such
realization we solve the full 3D radiative transfer problem taking into account
the impact of the CLASP instrument degradation on the calculated polarization
signals. Finally, we apply the statistical inference method presented in a
previous paper to show that the TR of the 3D model that produces the best
agreement with the CLASP observations has a relatively weak magnetic field and
a relatively high degree of corrugation. We emphasize that a suitable way to
validate or refute numerical models of the upper solar chromosphere is by
confronting calculations and observations of the scattering polarization in
ultraviolet lines sensitive to the Hanle effect.
