Nothing but the rain
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This appears to have originated from Galactica's earlier Cylon War-era commander, as Adama and Jaycie McGavin lightheartedly mimic the greeting during one of their sexual encounters (Razor Flashbacks, Episode 1).
Later while Starbuck defends Lee "Apollo" Adama's crippled Viper at the Ragnar Anchorage, William Adama uses their greeting over the wireless to draw Starbuck's attention and call her back to Galactica before making their escape FTL jump, with the sounds of debris deflecting off her cockpit adding some resonance to it (Miniseries, Night 2).
Before making an unauthorized jump to Cylon-occupied Caprica in a captured Raider, Thrace tells Adama that she is "bringing home the cat" after he questions her actions (Kobol's Last Gleaming, Part I).
In a deleted scene for the same episode, Adama again asks Starbuck what she hears when she is jogging through Galactica's hallways.
Over two years later, before her Viper is lost and she is presumed dead in "Maelstrom", a distracted Thrace walks past Admiral Adama and President Laura Roslin, oblivious to their presence, when Adama uses their greeting once more to get Thrace's attention. Adama again uses the greeting when he temporarily departs Galactica to wait for the missing President Roslin in "Sine Qua Non".
Adama and Thrace exchange the greeting one last time when they say their goodbyes in "Daybreak, Part II".
The greeting is generally consistent except for Thrace's last line, an acknowledgment which she tends to improvise: