The state treasurer, on behalf of the department, must distribute to counties for all lands acquired from private landowners for the purposes of this chapter an amount in lieu of real property taxes equal to the amount of tax that would be due if the land were taxable as open space land under chapter 84.34 RCW except taxes levied for any state purpose, plus an additional amount equal to the amount of weed control assessment that would be due if such lands were privately owned. The county assessor and county legislative authority shall assist in determining the appropriate calculation of the amount of tax that would be due. The county shall distribute the amount received under this section in lieu of real property taxes to all property taxing districts except the state in appropriate tax code areas the same way it would distribute local property taxes from private property. The county shall distribute the amount received under this section for weed control to the appropriate weed district.