In both Matthew (12:38-41; 16:1-4) and Luke (11:29-32) Jesus speaks of the “sign of Jonah.” In Matthew Jesus correlates Jonah’s three days and nights in the fish with his own “three days and nights in the heart of the earth.” Luke is not so specific, but (contrary to some interpreters) likely has the same meaning. Thus, just as Jonah suffered a judgment akin to death and then experienced a kind of resurrection so that others could be saved, the same would be true of Jesus. However, Jesus is clear that he is greater than Jonah. This is true in many ways, but here it is worth noting that Jesus willingly left the Father’s presence to come to earth in order to carry out the mission of salvation entrusted to him. He greatly desired the salvation of those he ministered to, even when they rejected him.
Also worth noting, Jesus’s ability to calm storms matched God’s ability to do so in Jonah 1. This testifies to the deity of Christ.