Spectral-timing techniques have proven valuable in studying the interplay between the X-ray corona and the accretion disc in variable active galactic nuclei (AGNs). Under certain conditions, photoionized 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 not only for the determination of their role in the AGN environment but also for 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.
