  Spectral-timing techniques have proven valuable in studying the interplay
between the X-ray corona and the accretion disc in variable active galactic
nuclei (AGN). Under certain conditions, photo-ionized outflows emerging from
central AGN regions also play a role in the observable spectral-timing
properties of the nuclear components. The variable ionizing flux causes the
intervening gas to ionize or recombine, resulting in a time-dependent
absorption spectrum. Understanding the spectral-timing properties of these
outflows is critical for the determination of their role in the AGN
environment, but also the correct interpretation of timing signatures of other
AGN components. In this paper, we test the capabilities of the Athena X-IFU
instrument in studying the spectral and spectral-timing properties of a black
hole system displaying a variable outflow. We take the narrow-line Seyfert 1
IRAS 13224-3809 as a test case. Our findings show that while the non-linear
response of the absorbing medium can result in complex behaviour of time lags,
the resulting decrease in the coherence can be used to constrain gas density
and distance to the central source. Ultimately, modelling the coherence spectra
of AGN outflows may constitute a valuable tool in studying the physical
properties of the outflowing gas.
