It shall be the duty of the county assessor of any county embracing the whole or a part of any irrigation district, to assess and enter upon his tax rolls each year, the name of the owner, if known, and the description and area of each tract of land in said district in his said county, subject to assessment and taxation under this act, and upon receipt by such assessor of the notice from the county commissioner of the levies to be made as hereinafter provided, he shall extend the same upon his tax roll to be collected in the same manner as other taxes.