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  

[Machine] The Prophet ﷺ said, "There has not been a year where it rained and the south wind blew, except that the valley of such and such flowed." This narration is reported with this chain of narrators and the authentic version is "stopped."  

قَالَ النَّبِيُّ ﷺ مَا عَامٌ بِأَمْطَرَ مِنْ عَامٍ وَلَا هَبَّتْ جَنُوبٌ إِلَّا سَالَ وَادِي كَذَا رُوِيَ مَرْفُوعًا بِهَذَا الْإِسْنَادِ وَالصَّحِيحُ مَوْقُوفٌ  

[Machine] "Abdullah, the son of Mas'oud, said: 'There is no year with more rain than another year, but rather, Allah directs it as He wills.'"  

قَالَ عَبْدُ اللهِ هُوَ ابْنُ مَسْعُودٍ مَا عَامٌ بِأَكْثَرَ مَطَرًا مِنْ عَامٍ وَلَكِنَّ اللهَ يُحَوِّلُهُ كَيْفَ يَشَاءُ  

[Machine] "Every year is not less rainy than the previous year, but rather Allah redirects it wherever He wills. Then recite this verse: 'And We have distributed it among them that they might be reminded, but most of the people refuse except disbelief.'" [Surah Al-Furqan, verse 50]  

مَا مِنْ عَامٍ بِأَقَلَّ مَطَرًا مِنْ عَامٍ وَلَكِنَّ اللهَ تَعَالَى يَصْرِفُهُ حَيْثُ يَشَاءُ ثُمَّ تَلَا هَذِهِ الْآيَةَ {وَلَقَدْ صَرَّفْنَاهُ بَيْنَهُمْ لِيَذَّكَّرُوا فَأَبَى أَكْثَرُ النَّاسِ إِلَّا كُفُورًا} [الفرقان 50]