Medicanes are tropical-like cyclones that develop in the Mediterranean Sea. Due to their harmful potential, the study of medicanes has captured great attention from the scientific community. In the context of a changing climate, their future climatological characterization can only be achieved using climate model output. A frequently used method to characterize the thermal structure of medicanes is the cyclone phase space (CPS) described by Hart (2003). This requires geopotential data from 300 to 900 hPa every 50 hPa. However, in long, high-resolution climate simulations, model output requires very high storage space and only data from a few geopotential levels are saved. To overcome the lack of geopotential data at some levels, available data are vertically interpolated to obtain data for the 13 levels required. In this work, we use high horizontal resolution data from the ERA-5 reanalysis (1979-2018) to analyse the climatology of medicanes simulated using the 13 vertical levels required according to Hart (2003), as well as different combinations of geopotential data from a few selected levels. Our results allow us to propose, for the first time, a limited set of recommended geopotential levels required for an adequate climatological characterization of medicanes in the perspective of long climate change simulations, taking into account the associated limitations of output data storage.