The famine would not break out because of drought, but there would be famine despite heavy rainfall as nothing would grow from the earth. (Using translation from Muslim 2904)
أَنَّ رَسُولَ اللهِ ﷺ قَالَ لَيْسَتِ السَّنَةُ بِأَنْ لَا تُمْطَرُوا وَلَكِنِ السَّنَةُ بِأَنْ تُمْطَرُوا وَتُمْطَرُوا وَلَا تُنْبِتُ الْأَرْضُ شَيْئًا