No person shall kindle, build, maintain, or in any way light a fire in any public park in the City except in fireplaces provided, or in self-supporting barbecue grills or stoves in places designated as picnic areas, or by special written permit from the City Administrator after a determination that such fire creates no hazards to the park or to persons in the immediate vicinity. No fire shall be built within ten feet of any tree or building or beneath the branches of any tree or in any underbrush unless such fire is enclosed within a stove, oven, or fireplace provided on the premises by the City for use in picnic cooking. Any fire shall be continuously under the care and control of a competent person, from the time it is kindled until it is extinguished.