section_path: Formation/Droplet size distribution
section_name: Droplet size distribution
paragraph_text: Droplet size distribution
  
  The final droplet size distribution is an exponential distribution. The number of droplets with diameter between d {\displaystyle d} and D + d D {\displaystyle D+dD} per unit volume of space is n (d) = n 0 e − d / ⟨ d ⟩ d D {\displaystyle n(d)=n_{0}e^{-d/\langle d\rangle }dD}. This is commonly referred to as the Marshall–Palmer law after the researchers who first characterized it. The parameters are somewhat temperature-dependent, and the slope also scales with the rate of rainfall ⟨ d ⟩ − 1 = 41 R − 0.21 {\displaystyle \langle d\rangle ^{-1}=41R^{-0.21}} (d in centimeters and R in millimeters per hour).
  
  Deviations can occur for small droplets and during different rainfall conditions. The distribution tends to fit averaged rainfall, while instantaneous size spectra often deviate and have been modeled as gamma distributions. The distribution has an upper limit due to droplet fragmentation.