How do we know the δ2H and δ18O values of precipitation around the globe?

We don’t know the exact δ values for each spot of the globe. The Global Network of Isotopes in Precipitation (GNIP) was initiated by the International Atomic Energy Agency (IAEA) and World Meteorological Organisation (WMO). It is now managed and supported by the IAEA and compiles the data of hundreds of stations all around the world. The stations are mostly managed by the national weather services and voluntarily provide data to the Agency. The database contains data on monthly average temperature, amount and type of precipitation, stable isotope composition (δ2H and δ18O values) and tritium (3H) activity of precipitation.