Typically, a water droplet on surfaces freezes with a tip singularity on the top in an experimental environment, and the magnitude of the singular tip is thought to be a constant of ∼ 131°. Interestingly, we observed that the tip magnitude can be variable from 131° to 180° (i.e., disappearing) under a ubiquitous convection environment. Especially, dependent on the competition between heat conduction (influenced by contact angle and substrate temperature) and convection, the traditional concave freezing front and a newly found convex freezing front were both observed during the freezing process, respectively corresponding to the emergence and disappearance of the singular tip. Additionally, an analytical model was proposed to clarify the variable mechanisms of tip singularity and the quantitative relationship between the magnitude of tip and the curvature of the ice-water interfaces during freezing. This study advances our understanding of freezing dynamics and ice crystal geometry. Simultaneously, the inhibition effect of convection on the singular ice crystals may provide a promising method for mitigating mechanical damage caused by sharp ice crystals during cryopreservation.