Why does Sauron’s darkness over Gondor disperse before the set time?

Question

In The Lord of the Rings, before his assault on Gondor (with the siege of Minas Tirith), Sauron sends a darkness from Mordor which cuts out the daylight. At the end of the Chapter 4, The Siege of Gondor, a cock crows “welcoming only the morning that in the sky far above the shadows of death was coming with the dawn”, and and the start of Chapter 6, we read that “The darkness was breaking too soon, before the date that his” (the Lord of the Nazgul’s) “Master had set for it”.

Is there any explanation why the darkness broke early?

Other mentions of the breaking of the darkness, without explanations, are:

• Towards the end of Chapter 5, The Ride of the Rohirrim, it is predicted by Wídfara, one of the Rohirrim: “Already the wind is turning. … Above the reek it will be dawn when you pass the wall”. When they reach the Pelennor Fields, we read “Merry felt it at last, beyond doubt, a change. Wind was in his face! Light was glimmering. Far, far away, in the South the clouds could be dimly seen …, morning lay beyond them” and “For morning came, morning and a wind from the sea; and darkness was removed”.
• In Book VI, Chapter 2, The Land of Shadow, after excaping from Cirith Ungol, Frodo and Sam observe it breaking: “‘Look at it, Mr. Frodo!’ said Sam. ‘Look at it! The wind’s changed’”.

_{N.B. All quotes are from the first edition.}

Answer 1

This is never explained

Interestingly, an early draft of the chapter is less definitive on the subject, raising (though not confirming) the possibility that the darkness was breaking up according to Sauron's schedule:

But it was no orc-chief or brigand that led the assault on Gondor. Who knows whether his Master himself had set a date to the darkness, designing the fall of the City for that very hour and needing light for the hunting of those that fled, or fortune had betrayed him and the world turned against him? None can tell.

^{History of Middle-earth VIII The War of the Ring Part 3: "Minas Tirith" Chapter IX: "The Battle of the Pelennor Fields"}

Scanning through all of my books, this is the closest thing to an explanation I can find. In Reader's Companion, Wayne Hammond and Christina Scull note the possible connection to Manwë, noted by Jonah in a comment on the question:

The wind from the south is blowing away the darkness that flowed out of Mordor, and speeding the Haradrim ships captured by Aragorn up the Anduin. Some readers have speculated that this is due to the unseen intervention of Manwë, chief of the Valar, whose province is the winds and breezes and regions of the air

^{The Lord of the Rings: A Reader's Companion Book 5 Chapter 6: "The Battle of the Pelennor Fields"}

They go on to note a similarity to two other instances of wind blowing away Evil, which are also normally attributed to Manwë and the Valar (though without confirmation from Tolkien):

• [A]s the Captains gazed south to the Land of Mordor, it seemed to them that, black against the pall of cloud, there rose a huge shape of shadow, impenetrable, lightning-crowned, filling all the sky. Enormous it reared above the world, and stretched out towards them a vast threatening hand, terrible but impotent: for even as it leaned over them, a great wind took it, and it was all blown away, and passed

  ^{Return of the King Book VI Chapter 4: "The Field of Cormallen"}

• To the dismay of those that stood by, about the body of Saruman a grey mist gathered, and rising slowly to a great height like smoke from a fire, as a pale shrouded figure it loomed over the Hill. For a moment it wavered, looking to the West; but out of the West came a cold wind, and it bent away, and with a sigh dissolved into nothing.

  ^{Return of the King Book VI Chapter 4: "The Field of Cormallen"}