Avalokiteśvara and the bīja sa

Doug wrote recently to ask about the association of the bīja sa (left) with the Bodhisattva Avalokiteśvara. He had taken a photo of a Tendai altar dedicated to Avalokiteśvara which showed a Siddhaṃ sa. I should mention that in the Tibetan tradition, and on the Visiblemantra.org Avalokiteśvara page the bīja is hrīḥ.

I looked around for more info on this, but couldn't find much. Shingon sources all seem to make the association, but it's not clear why. I did find this in Lokesh Candra's Dictionary of Buddhist Iconography:

Sa, for all forms of Kwannon specially for Shō-Kwannon (ie Ārya Avalokiteśvara). Sa means 1. to see the spiritual lotus in sentient beings; 2. purity of the spiritual lotus; 3. attainment of nirvāṇa. The source of this remark is cited as the Asaba-shō by Shōchō (AD 1205-1282). [v.2, p.463]

This doesn't really explain why sa. Often the syllable relates to the Bodhisattva's name, or a prominent quality, but sa doesn't seem to fit this pattern. If anyone has any thoughts please either leave a comment or email Jayarava.