I am sometimes asked about the appropriate channels for author-reviewer interaction. In a word: GEMS.
The reviewer, who knows the author’s identity, should only contact the authors through emails by way of AGU/GEMS. Reviews should be uploaded to GEMS and any additional correspondence should be sent to the editorial office. The AGU staff will forward the email on to the Editor and perhaps, if appropriate, on the reviewer. Never contact authors directly; that’s a breach of reviewer guidelines and ethics.
The reviewer has the right to reveal their identity to the authors. This is no longer done in the Acknowledgments of the published paper, by the way. AGU stopped that practice just a few months ago. You’ll notice that very recent papers no longer include the extra sentence in the Acknowledgments, “The Editor thanks…” It was decided that this wasn’t really serving a good purpose, and most times it just said “two anonymous reviewers” rather than names. Really, the only appropriate way for a referee to reveal their identity is to sign the review. The Editor will not delete this signature and the authors will see the referee’s name in the review text.
Similar to the reviewer-initiated correspondence, the author should not contact the reviewer directly but only via the editorial office. This ensures that there is a permanent record of all correspondence, protecting both author and reviewer in case of a later dispute.
Really, the only acceptable time for direct author-reviewer interaction about a manuscript is after publication (or rejection). When you submit a manuscript to a journal and when you accept a reviewing assignment from a journal, you are agreeing to abide by the rules of formal interaction about this manuscript until final decision.