The department of water resources shall have power:
(1) To exercise the rights, powers and duties vested by law in the state engineer [department of water resources].
(2) To exercise the rights, powers and duties vested by law in the state board of land commissioners so far as their duties relate to the administration of the Carey Act. Through this provision the department has authority to convey to equitable claimants, their heirs, successors or assigns, title to lands retained in state ownership which were patented to the state under the Carey Act prior to July 1, 1931, provided that the director determines that equitable claims to such lands have accrued prior to July 1, 1982, and are based upon the cultivation or improvement of such lands, or the payment of property taxes thereon. Title to any such lands for which the director determines that an equitable claim has not accrued shall be conveyed to the state board of land commissioners for retention or disposal in accordance with applicable state law.