Ta'anis Chapter 3, Mishnah 1. The Mishnah opens: "Seder ta'aniyos eilu ha'amur birvi'ah rishonah" - the order of fasts that we learned about in the previous chapter: if no rain has fallen by a certain date, a series of fast days begins, growing progressively more stringent as it goes on. All of this refers to the first set of rains that is supposed to fall in the month of Marcheshvan, which is called the 'revi'ah'.
Two cases in which the alarm is sounded immediately:
"Avad tzemachim sheshanu" - plants that have already grown, but that have changed for the worse in a way that indicates a problem, and regarding them "matri'in aleihem miyad" - the alarm is sounded immediately. That is, we jump straight to the most severe form of the fast days, together with the blowing of the shofros (or trumpets) that is normally done only at the end of the process, because this is a severe and immediate problem.
"Vechein shepasku geshamim min geshem legeshem arba'im yom" - a gap of forty days between one rainfall and the next, in which case "matri'in aleihem miyad" - once again we immediately adopt the most severe form of the fast, "mipnei shehi makas batzores" - because it is a sign that famine is on the way.
In summary: two signs - plants changing for the worse, and a halt in the rains for forty days - take the community out of the gradual order of fasts and require an immediate alarm at the most severe level.