Frodo's dream of the Elf Tower, in Crickhollow

Eventually [Frodo] fell into a vague dream, in which he seemed to be looking out of a high window over a dark sea of tangled trees. Down below among the roots there was the sound of creatures crawling and snuffling. He felt sure they would smell him out sooner or later. Then he heard a noise in the distance. At first he thought it was a great wind coming over the leaves of the forest. Then he knew that it was not the leaves, but the sound of the Sea far-off; a sound he had never heard in waking life, though it had often troubled his dreams. Suddenly he found he was out in the open. There were no trees after all. He was on a dark heath, and there was a strange salt smell in the air. Looking up he saw before him a tall white tower, standing alone on a high ridge. A great desire came over to him to climb the tower and see the Sea. He started to struggle up the ridge towards the tower: but suddenly a light came in the sky, and there was a noise of thunder.

Frodo's dream in the house at Crickhollow, the third night of the quest; from A Conspiracy Unmasked in The Fellowship of the Ring. 

**

For long I was puzzled by the above dream, because it does not correspond to anything that happens in The Lord of the Rings. 

A partial answer was provided by the analysis of Frodo's dreams in Verlyn Flieger's A Question of Time. 

From studying The Treason of Isengard volume in The History of Middle Earth; it turns-out that Frodo's Crickhollow dream is a revised version of a dream that, in an earlier draft, accurately and literally referred to Gandalf being besieged by the Black Riders in one of the three Elf Towers that lie to the west of The Shire; from the tops of which Shire hobbits believe that the sea can be seen. 

Later revisions leading to the published dream in The Fellowship of the Ring, had Gandalf held captive by Saruman on the tower of Orthanc (i.e. not an Elf Tower). And, during the night following the Crickhollow dream (the first sleep in the House of Tom Bombadil) Frodo accurately saw Gandalf's rescue from Orthanc by Gwaihir the eagle - a correct vision of an event remote in space, and also in time; since the rescue had happened some eight nights earlier than this dream. 

But why did Tolkien retain this dream for the published text, after plot revisions had made it obsolete and without reference to real events of the story? And why was Frodo's accurate clairvoyance delayed by more than a week? 

There are two possible kinds of question and answer to why: the first asks what was Tolkien's actual and conscious motivation and suggests a possible answer; while the second is to ask what makes inferential sense in terms of the logic of the story - even though Tolkien might not have been aware of it at the time of writing. 

Flieger's explanation refers to the first of these questions - it is a speculation as to why Tolkein might consciously have preserved the Elf Tower dream. She says the published dream functions mainly as an effective "mood piece", characteristic of Frodo, and one that establishes him as A Dreamer - often previsionary, or able to see other times and places - within the rest of the story. 

But I believe that more can be said. Frodo only becomes A Dreamer after Gildor named him Elf Friend. 

This naming can be seen to have had a lasting and transformative effect on Frodo - giving him elvish qualities and attributes that were immediately apparent; first to Goldberry, then to others able to discern such things in the later story.   

However, it can further be suggested that the elvish ("magical") transformation was something that built-up over a period of time. 

Thus the first night after being named Elf Friend, Frodo dreamed the Elf Tower dream - which was a real things, but an event that never happened. 

The second night's dream (in the house of Tom Bombadil) was an impressively accurate dream, but several days late. 

The third night's dream - which happened during the second night at Tom Bombadil's - was again accurate, but even more impressive; because it was a prevision of Frodo's arrival in the undying lands some time after the narrative of The Lord of the Rings has ended - presumably at Elvenhome (the Lonely Isle of Eressea).  

Therefore, my suggestion as to Tolkien's unconscious (not deliberately-intended), but perhaps implicit, reason for including the inaccurate Elf Tower dream; could be understood as depicting stages en route to Frodo becoming a full Elf Friend, and a fully-fledged Dreamer.