The county engineer shall continue to act as a supervisor of a diking, drainage, or sewerage improvement district that is governed by a three-member board of supervisors until a replacement assumes office after being elected at the 1987 special district general election. At that election two supervisors shall be elected, with the person receiving the greatest number of votes being elected to a six-year term, and the person receiving the second greatest number of votes being elected to a four-year term. Thereafter, all supervisors shall be elected to six-year terms.