The loss of water from Mars to space is thought to result from the transport of water to the upper atmosphere, where it is dissociated to hydrogen and escapes the planet. Recent observations have suggested large, rapid seasonal intrusions of water into the upper atmosphere, boosting the hydrogen abundance. We use the Atmospheric Chemistry Suite on the ExoMars Trace Gas Orbiter to characterize the water distribution by altitude. Water profiles during the 2018-2019 southern spring and summer stormy seasons show that high-altitude water is preferentially supplied close to perihelion, and supersaturation occurs even when clouds are present. This implies that the potential for water to escape from Mars is higher than previously thought.