The definitions provided here are taken from Wikipedia.

Metrology is simply defined as the science of measurement. Metrology is not to be confused with meteorology or metallurgy which are defined below:

  • Meteorology is defined as a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting.
  • Metallurgy is defined as a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are called alloys

However, it is intuitively obvious that metrology likely plays an important and essential role in both meteorology and metallurgy.