Water Resources Research Amendments Act of 2013 - Amends the Water Resources Research Act of 1984 to: (1) declare that additional research is required into increasing the effectiveness and efficiency of new and existing treatment works through alternative approaches, including non-structural alternatives, decentralized approaches, energy use efficiency, water use efficiency, and actions to extract energy from wastewater; (2) require each water resources research and technology institute to arrange for research that fosters the exploration of new ideas that expand understanding of water resources (currently, of water-related phenomena); (3) direct the Secretary of the Interior to report to specified congressional committees annually on each institute's compliance with matching fund requirements and provisions permitting the use of funds only to reimburse direct cost expenditures incurred for the conduct of the water resources research program; and (4) authorize appropriations for such institutes through FY2018.