Suggestions of mobile alternatives to a horizontal multiple dropdown filter system

I am currently working on mobile/responsive facelift to an old static website.

The original site uses a number of drop down menus arranged in a horizontal bar to allow the selection of multiple filters at the same time. Below the filters is a product grid that shows/hides products based on the selected filters.

A wireframe of the current implementation

Can anyone suggest any good mobile-friendly alternative strategies for multi-filtering on smart phone?