* Front-month futures score biggest one-day gain in 4 months * Milder U.S. weather next week expected to slow gas use * Nuclear plant outages slip back below normal By Joe Silha NEW YORK, April 5 (Reuters) - U.S. natural gas futures ended up sharply on Friday, with the front-month contract driven to a 20-month high by bullish weekly storage data and stronger price expectations this year after a chilly winter helped whittle down record high inventories. Traders agreed Thursday's 94 billion cubic feet weekly inventory draw was bullish, noting that it came in above the Reuters poll estimate of 91 bcf and that stocks usually build slightly that week. Inventory draws have exceeded market expectations in six of the last seven weeks. It was the first time since September 2011 that stocks dropped below the five-year average, a supportive sign particularly with another draw expected next week. Cold late-winter weather and above-average nuclear plant outages have helped put a huge dent in inventories and drive futures prices up about 30 percent since mid-February. "I was expecting a pullback once the forecasts turned warmer, but it might be over already. Storage is well below last year, but we'll have to see how prices react next week once warmer weather arrives," said Steve Mosley at The SMC Report. Traders said upward revisions by some prominent price forecasters also backed some of the buying. Goldman Sachs on Thursday raised its 2013 U.S. natural gas price forecast by 17 percent to $4.40 per mmBtu due to cold weather in March that helped tighten the market. Front-month gas futures on the New York Mercantile Exchange ended up 17.8 cents, or 4.5 percent, at $4.125 per million British thermal units after climbing late to $4.135, its highest since August 2011. It was the biggest one-day gain for the nearby contract in four months. Despite modest losses early in the week, the front contract ended the week up 2.5 percent, the seventh straight weekly rise. Volume was heavy, with the official tally to be posted on Monday likely to top the high so far this year of 758,506 hit on March 14. But many traders still expect milder spring weather to soon slow gas use and pressure prices, noting production was still high and there were plenty of new longs in the market that may rush to cash out quickly when more moderate weather moves in. In its 11-to-15-day outlook, forecaster MDA Weather Services expects above- to much-above-normal temperatures to stretch from Texas to the Northeast and parts of the Midwest. ANOTHER STRONG STORAGE DRAW U.S. Energy Information Administration data on Thursday showed total domestic gas inventories fell last week to 1.687 trillion cubic feet, 779 bcf, or 32 percent below last year's record highs at that time and 37 bcf, or 2 percent, below the five-year average. Early withdrawal estimates for next week's EIA report range from 20 to 36 bcf versus an 11-bcf build during the same week last year and a five-year average rise for that week of 15 bcf. Stocks peaked last year at a record high 3.929 tcf in early November but will likely end the heating season about 33 percent below last winter's record high finish of 2.48 tcf and 4 percent below average for that time. OUTPUT STARTS TO SLOW? Baker Hughes data on Friday showed the gas-directed drilling rig count fell this week for the fifth time in six weeks, dropping by 14 to a 14-year low of 375. Despite near steady rig declines over the last 18 months, output has not slowed much from the record high hit last year. EIA data last week showed gross natural gas production in January fell for the second straight month and dropped below year-ago levels for the first time since February 2010. But it is still unclear if recent monthly output declines were due to well freeze-offs from the cold or producers curbing dry gas flows because prices were not that attractive.