Where all or any portion of the costs are to be assessed against the abutting property, an assessment roll shall be prepared by the proper city official or by the city council which shall to the extent necessary be based on benefits and which shall describe the property assessed, the name of the owner, if known, otherwise stating that the owner is unknown and fixing the amount of the assessment. The assessment roll shall be filed with the city clerk, and when so filed the council shall by resolution fix a date for hearing thereon and direct the clerk to give notice of the hearing and the time and place thereof. The notice of hearing shall be mailed to the person whose name appears on the county treasurer's tax roll as the owner or reputed owner of the property, at the address shown thereon, and shall be published before the date fixed for the hearing for two consecutive weeks in the official newspaper or regular official publication of the city. The notice shall be mailed and first publication made at least ten days before the hearing date. Proof of mailing and publication shall be made by affidavit and shall be filed with the city clerk before the date fixed for the hearing. Following the hearing the city council shall by ordinance affirm, modify, or reject or order recasting of the assessment roll. An appeal may be taken to the superior court from the ordinance confirming the assessment roll in the same manner as is provided for appeals from the assessment roll by chapters 35.43 to 35.54 RCW, inclusive, as now or hereafter amended.