No lessee shall commence any operation upon lands covered by the lease until such lessee has provided for compensation to owners of private rights therein according to law, or in lieu thereof, filed a surety bond with the department in an amount sufficient in the opinion of the commissioner to cover such compensation until the amount of compensation is determined by agreement, arbitration, or judicial decision and has provided for compensation to the state of Washington for damage to the surface rights of the state in accordance with the rules adopted by the department.