Improving the atmospheric component of hydrological models is beneficial for applications such as water resources assessment and hydropower operations. Within this goal, precise characterization of rain microphysics is key for climate and weather modeling, and thus for hydrometeorological applications. Such characterization can be achieved by analyzing the evolution in time of the particle size distribution (PSD) of hydrometeors, which can be measured at ground using disdrometers for validation. The estimation, however, depends on the choice of the PSD form (the shape) and on the parameters to define the exact shape. In the case of modeling rain microphysics, two approaches compete: the use of the number concentration of drops decoupled from the shape of the distribution (the [N-T, E(D), E(D-2)] and the {N-T, E(D), E[log(D)]} models), and the (N-0, , ) model that embeds in N-0 both the shape of the distribution and the number concentration of drops. Here we use a comprehensive dataset of disdrometer measurements to show that the N-T-based approaches allow a more precise characterization of the drop size distribution (DSD) and also a physically based modeling of the microphysical processes of rain since N-T is analytically independent of the shape of the DSD {parameterized by E(D), and E(D-2) or E[log(D)]}. The implication is that numerical models would benefit from decoupling the number of drops from the shape of distribution in their modules of precipitation microphysics in order to improve outputs that eventually feed hydrological models.