  Our comprehension of stellar evolution on the AGB still faces many
difficulties. To improve on this, a quantified understanding of large-amplitude
pulsator atmospheres and interpretation in terms of their fundamental stellar
parameters are essential. We wish to evaluate the effectiveness of the recently
released CODEX dynamical model atmospheres in representing M-type Mira
variables through a confrontation with the time-resolved spectro-photometric
and interferometric PTI data set of TU And. We calibrated the interferometric
K-band time series to high precision. This results in 50 nights of
observations, covering 8 subsequent pulsation cycles. At each phase, the flux
at 2.2$\mu$m is obtained, along with the spectral shape and visibility points
in 5 channels across the K-band. We compared the data set to the relevant
dynamical, self-excited CODEX models. Both spectrum and visibilities are
consistently reproduced at visual minimum phases. Near maximum, our
observations show that the current models predict a photosphere that is too
compact and hot, and we find that the extended atmosphere lacks H2O opacity.
Since coverage in model parameter space is currently poor, more models are
needed to make firm conclusions on the cause of the discrepancies. We argue
that for TU And, the discrepancy could be lifted by adopting a lower value of
the mixing length parameter combined with an increase in the stellar mass
and/or a decrease in metallicity, but this requires the release of an extended
model grid.
