The present disclosure provides a roof ventilation system and method that provides ventilation for a roof while further providing simpler ventilation installation, prevention of ice dams, a non-slip surface to walk on, and a secondary membrane to prevent moisture intrusion into the living space or walls. The roof ventilation system provided by the invention includes vertical side walls having a top portion. A roof extends outwardly and beyond the vertical side walls. The roof has a top surface facing away from the vertical side walls. A web of extruded polymer monofilaments is secured to the top surface of the roof. The polymer monofilaments are heat welded at junctions to form a matrix of tangled monofilaments. The method for ventilating a roof of a building provided by the invention includes installing a web of extruded polymer monofilaments on a top surface of the roof.