The authority is composed of the territory that was contained in the city on January 1, 1981, as that territory may have been modified under:
(1) Subchapter J, Chapter 49, Water Code;
(2) Section 5, Chapter 12, Acts of the 57th Legislature, 3rd Called Session, 1962 (Article 8280-270, Vernon's Texas Civil Statutes);
(3) Section 9015.052; or
(4) other law.