The decay chain of most isotopes, accompanied by their respective probabilities are known, as well as the decay products of the given decay (which includes deca

The decay chain of most isotopes, accompanied by their respective probabilities are known, as well as the decay products of the given decay (which includes decay energy + mode - alpha, beta or gamma, see e.g. https://en.wikipedia.org/wiki/Radioactive_decay https://en.wikipedia.org/wiki/Radioactive_decay). Thus, for known radioactive isotope composites we can conclude which isotopes will be prevalent in which timeframe, and how much and which radioactive radiation will be emitted. As such it is possible to conclusively state how much radiation danger for living entities (see e.g. https://en.wikipedia.org/wiki/Gray_(unit) https://en.wikipedia.org/wiki/Gray_(unit)) will be emitted over a certain time frame. Since the composition of nuclear waste is usually known or verifiable, and applying the known decay chains, it is possible to derive the duration and amount of risk. I trust e.g. climate change and the scientists behind it; but their basis is, statistically, much weaker than the statistics and science behind nuclear decay (which is much easier to measure and to verify). Also, geologists are - if trusted - also able to predict the permeability of the composition of the underground over a given period. They are able to (to the best of our knowledge) deduce the age of sediments >40k years into the past.