Any 1 or more intercounty drains or any portion thereof, now or hereafter existing, may be cleaned out, relocated, widened, deepened, straightened, extended, tiled, interconnected or otherwise improved, or branches added or connected thereto, when necessary for the public health, in the same manner as an intercounty drain may be located, established and constructed under this chapter, with such variations in the proceedings as may be necessary to make the same applicable, and also the cost thereof may be financed in like manner. A project to improve intercounty drains may include backfilling and leveling any portion thereof no longer needed after the improvements.