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Has the Catholic Church drawn a parallel between the sleep of Jonah on board the ship and that of Jesus in the boat?
St. Cyril of Jerusalem does so.
Calming of the storm of Jonas, has been paralleled to the Gospel story by a least on Church Father. The circumstances surrounding the storm that hit the ship bound for Tarshish bears striking similarities to the account of the calming of the storm in the gospels (Matthew 8, Luke 8, and Mark 4). In both cases, the protagonist is sleeping during the storm (Jonah in the Old Testament, Jesus in the New). Both protagonists have to be woken as their shipmates plead them to take action to calm the storm. And both end up doing just that, albeit in different ways: Jonah is thrown overboard while Christ rebukes the winds. St. Cyril of Jerusalem elaborates on the parallels and the important contrasts between the two stories in the following manner:
And when we examine the story of Jonah, great is the force of the resemblance. Jesus was sent to preach repentance; Jonah also was sent: but whereas the one fled, not knowing what should come to pass; the other came willingly, to give repentance unto salvation. Jonah was asleep in the ship, and snoring amidst the stormy sea; while Jesus also slept, the sea, according to God’s providence, began to rise, to show in the sequel the might of Him who slept. To the one they said, “Why are you sleeping? Arise, call you’re your God, that God may save us;” but in the other case they say unto the Master, “Lord, save us.” Then they said, Call upon thy God; here they say, save Thou. But the one says, Take me, and cast me into the sea; so shall the sea be calm unto you; the other, Himself rebuked the winds and the sea, and there was a great calm. The one was cast into a whale’s belly: but the other of His own accord went down, where the invisible whale of death is. And He went down of His own accord, that death might cast up those whom he had devoured, according to that which is written, I will ransom them from the power of the grave; and from the hand of death I will redeem them.
Saint Cyril of Jerusalem
Caveat: Although taken from an Orthodox website, St. Cyril of Jerusalem is a recognized saint and Church Father in both Churches.