Meteorology and metrology are both sciences, as implied by the suffix -ology which means “the study of . . .” .
Meteorology is the science of weather, atmospheres, and climates.
Metrology is the science of measurement, especially of weights and units of measurement.
Meteorology is a well-known word in English. The weather-people on television news are meteorologists and meteor is the scientific name for what people call “shooting stars.”
Metrology, in contrast, is not an everyday word, though the prefix Metr-, meaning measure, does appear in many words, such as meter and metric.