Army Corps of Engineers Communications Accountability Act of 2013 - Requires the Chief of Engineers: (1) to notify the public within seven days after determining that runoff conditions in the Missouri River System are likely to reach the upper quartile or upper decile scenarios specified for a year in an annual operating plan for such System; and (2) to meet with a state, local, or tribal government with jurisdiction over an area that will be affected by a flood occurring in the System within seven days after such government requests such a consultation regarding such an upper decile determination. Authorizes the Chief to provide in such consultation information regarding expected water levels, advice regarding preparedness actions, and technical assistance.