Source: TW
Invocation of nAga-s for rain-inducing rituals is common in the bauddha world & in early shaiva rituals like that preserved in the jayadrathayAmala. However, later it became muted or entirely lost in the H world while continuing in the saugatan sphere.
One of the earliest surviving nAga rites for rain-making in the bauddha world is that deploying a mantra known as the mUlamantra. The ritual is said to involve pratiShTha of an image of a nAga followed by the ritual performed by a vidyAdhara for weather control - rain or its modulation in case of an excess.
The roots of the rain-making ritual are mysterious but we posit that they originate from the “water” incantations to ahi budhnya mentioned in the RV itself & also metaphorically but indicated in the taittirIya saMhitA.
nU rodasI ahinA budhnyena
stuvIta devI apyebhir iShTaiH |
samudraM na saMcharaNe saniShyavo
gharmasvaraso nadyo apa vran ||
e.g., from vAmadeva gautama’s incantation. The “sAgaragambhIre svAhA |” in the tAthAgatan mUlamantra is likely a memory of the serpent in the depths of the ocean ~ ahi budhnya.
As an aside the boast of the sAkhya overwhelming the vaidika v1 urubilva jaTila kAshyapa involves the former suppressing a nAga in the firehouse of the latter. It could be an allusion to ahi budhnya installed at the gArhapatya upon upasthAna.