Secondary ice production (SIP) is a crucial phenomenon for explaining the formation of ice crystal clouds, especially when addressing the discrepancies between observed ice crystal number concentrations and ice nucleating particles (INPs). In this study, we investigate parameterizations of three SIP processes (Hallett-Mossop, fragmentation of freezing drops, and fragmentation due to ice-ice collision) by simulating a deep convective cloud observed during the HAIC/HIWC campaign with the 3D bin microphysics scheme DESCAM (DEtailed SCAvening and Microphysics model). The simulated mean cloud properties, including particle size distributions and ice crystal number concentration are compared with in situ probe observations obtained during the campaign. Simulation excluding SIP show a large underestimation of small ice crystals ( < 1 mm diameter) for temperatures warmer than -30°C. In our results, incorporating Hallett-Mossop and fragmentation due to ice-ice collision processes leads to ice crystal number concentrations close to observed values, thereby reducing discrepancies by two orders of magnitude. Our simulations also indicates that fragmentation of freezing drops affect minimally the properties of the cloud at its mature stage. Furthermore, we investigate the impact of fragments sizes resulting from SIP processes and show that the size of fragments generated from fragmentation due to ice–ice collision significantly influences the shape of ice particle size distribution. Employing various parameterizations of the ice crystal sticking efficiency reveals a notable impact on cloud properties. This study shows that SIP mechanisms are important and have to be considered for cold and mixed-phase clouds. However their parameterization lack reliability, highlighting the need for better quantifying these mechanisms. The companion paper, investigates the effects of SIP processes on the formation and the evolution of the deep convective system.