The board of supervisors in fixing the rate of assessment authorized by Section 35536 pursuant to Section 36608, or in levying such assessment pursuant to Section 37207, as the case may be, shall fix the rate or levy the assessment upon all lands within each zone sufficient to raise the amount stated in the estimate of the district board to be borne by such zone. Assessments made within such zones of benefit established pursuant to this chapter shall be levied on all lands within such zone of benefit on an ad valorem basis.