because we have the technologies you have mentioned there we are able to predict weather, because we have a good understanding of processes that happen in the atmosphere.
We now use fore casts from computer models, which get inputs from ground level, buoys at the sea, satellites and so on. We can also measure windspeed and rainfall using radar and other smart technologies.
The model (which is a very smart computer programme really) then collects all of this information and puts in into equations about how density and pressure behave. These can then predict the future state of the atmosphere!
But because processes in the atmosphere can be fairly chaotic, it can be difficult to predict weather with high success or accuracy!
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