[hakuseki]

That is not strictly true. The weather at time t0 may affect non-weather phenomena at time t1 (e.g. traffic), which in turn may affect weather at time t2.

Furthermore, a predictive model is not working with a complete picture of the weather, but rather some limited-resolution measurements. So, even ignoring non-weather, there may be local weather phenomena detected at time t0, escaping detection at time t1, but still affecting weather at time t2.