A function defined as the size truncation function is introduced to quantify the effect of truncating the cloud droplet size distribution on the autoconversion rate. It is shown that the size truncation function can be used as a threshold function to represent the threshold behavior associated with the autoconversion process, providing a physical basis for the threshold function. Comparisons of the new threshold function with those ad hoc threshold functions associated with existing Kessler-type and Sundqvist-type parameterizations reveals the degree of approximations of the two empirical parameterizations. Application of the new threshold function leads to a new type of autoconversion parameterization that is fully analytical, physics-based, and removes the ad hoc nature of threshold representation in existing autoconversion parameterizations.