On May 2, 1998, at 1100 hours Pacific daylight time, a Luscombe 8E, N2435K, made a precautionary landing due to a rough running engine and came to rest inverted after striking a furrow in a wet grass field near Auburn, California. The aircraft sustained substantial damage. The private pilot/owner was not injured. Visual meteorological conditions existed for the personal local flight and no flight plan was filed. The pilot reported that while making a solo flight the engine "got rough." He turned on carburetor heat and the engine "cleared up then got rough again." The pilot stated that he knew of a grass field approximately 1 mile from his present position and decided to make a precautionary landing there. The pilot reported that on the landing roll, the wheels would not grab and slipped on the wet grass. He further stated that the field had been plowed and a furrow ran across the field. He stated that the aircraft struck the furrow and came to rest inverted. The pilot reported the ceiling as broken at 4,000 agl. Weather conditions reported at Beale Air Force Base, approximately 20 nmi northwest of Auburn were: 10 miles visibility; scattered clouds at 7,000, 10,000 and 25,000 broken; temperature 64 degrees; and dew point 55 degrees Fahrenheit. According to the carburetor ice probability chart, during cruise power there was a potential for moderate icing (see attachment). The Safety Board's meteorologist estimated that the freezing level in the Auburn area was approximately 8,500 feet mean sea level. In an interview with an airworthiness inspector from the Federal Aviation Administration, the pilot reported that he was flying approximately 500 to 800 feet below the clouds.