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99 Subaru bucking and touchy braking following mountain descent

99 Subaru Legacy 154,000 miles. Descent mountain from Idyllwild Ca at 5,000 ft to Hemet Ca at 2,000 feet across 16 miles. Steepest initially, slope lessens and is essentially flat for some distance before the first stop light. Some braking during first 2,000 ft of descent. Perhaps less or no braking during last 1000 feet of descent. Intermittent problem, may not occur for 6 months or may occur several times in a row when this trip is taken. Symptoms have not been reported in any other circumstances. At first stop light with the light touch of the brake the brakes grab, the car bucks and the tackometer goes from 2000 rpm to 3000 rpm while stopping. Problem occurs across various seasons and weather conditions and has been going on for 3 years. If no braking is needed at the first stoplight (green light) problem does not seem to occur braking at stoplights further into Hemet. Question. What is the diagnosis and then how do I repair this annoying and scarry behavior of the car?