Retrieving the optical depth of the Martian clouds ($τ_\mathrm{cld}$) is a powerful way to monitor their spatial and temporal evolution. However, such retrievals from nadir imagery rely on several assumptions, including the vertical structure of the clouds in the atmosphere. Here we compare the results of cloud optical depth retrievals from the Emirates eXploration Imager (EXI) onboard the Emirates Mars Mission (EMM) "Hope" orbiter performed using an empirical cloud profile (typically used in similar studies) and using derived cloud profiles obtained from near-simultaneous Solar Occultation observations from the Middle-Infrared channel of the Atmospheric Chemistry Suite (ACS) instrument onboard the ESA Trace Gas Orbiter (TGO). We show that the latitudinal dependence of the cloud vertical profiles can have a strong impact on the nadir retrievals; neglecting it can lead to a significant underestimation of $τ_\mathrm{cld}$ in the polar regions (up to 25 %). We also discuss the impact of a vertically-dependent particle size profile, as previous studies have shown the presence of very small water ice particles at the top of the clouds. From this analysis, we provide recommendations for the improvement of water ice cloud parameterization in radiative transfer algorithms in nadir atmospheric retrievals.