* Firm cash differentials underpin expiring April contract * Nuclear outages still running above normal * Chilly weather to continue into early April * Coming up: Reuters natural gas storage poll Wednesday By Joe Silha NEW YORK, March 26 (Reuters) - U.S. natural gas futures ended sharply higher on Tuesday after four straight losing sessions, with chilly weather forecasts for the next week and strong cash premiums to paper driving the April contract to a strong expiration. Cold weather has put a huge dent in inventories and helped drive futures up about 25 percent since mid-February. Above-average nuclear plant outages have also increased demand for gas-fired replacement power and tightened the market. "Weather looks cold and is still playing a role. I think a lot of people have been underestimating the strength in this market, and that's caught some shorts by surprise," said Steve Platt, analyst at Archer Financial in Chicago. April gas futures on the New York Mercantile Exchange expired up 11.1 cents, or 2.9 percent, at $3.976 per million British thermal units after trading between $3.862 and $3.991. The front contract, which posted an 18-month high of $4.025 on Thursday, has risen for five straight weeks. Traders said strong heating demand this week from Texas to New York firmed cash differentials at Henry Hub, the benchmark supply point in Louisiana, to more than 10 cents per mmBtu over April futures, a premium that helped front-month paper outperform the rest of the complex before Tuesday's expiration. Other futures contracts settled 1 to 10 cents higher. Technical traders agreed the front contract seemed stalled here, noting prices have tested key $4 resistance several times over the last week but were unable to close above that level. With production still flowing at or near a record peak and milder spring weather likely to soon slow demand, many traders remain skeptical of further upside. They note that gas prices above $4 could curb demand by prompting some utilities to use more coal to generate power and increase supply by encouraging producers to turn on more wells. Commodity Weather Group still sees a cool six-to-10-day pattern for the Midwest and East, with cool weather continuing for the Central U.S. in the 11-to-15-day time frame. STRONG STORAGE DRAW EXPECTED U.S. Energy Information Administration data last week showed total gas inventories for the week ended March 15 fell by 62 billion cubic feet to 1.876 trillion cubic feet. The draw fell short of market expectations for the first time in five weeks. It did cut 36 bcf from the surplus versus the five-year average, but storage is 162 bcf, or 9 percent, above that benchmark. Most traders expect that surplus to shrink sharply in Thursday's inventory report. Withdrawal estimates range from 59 to 103 bcf, with most in the low-80s. Stocks rose 45 bcf in the same week last year. Storage normally gains 6 bcf that week. Stocks will likely end the heating season at just above the 1.73-tcf average for March 31. A Reuters poll in mid-January put the consensus end-winter inventory forecast at about 2 tcf. Total gas pulled from storage so far this winter is about 2.050 tcf, roughly 580 bcf, or 39 percent, more than the same time last year and nearly 5 percent above normal. RIGS CLIMB, OUTPUT NOT SLOWING MUCH Baker Hughes data on Friday showed the gas-directed drilling rig count fell last week for the third time in four weeks, dropping by 13 to 418. The count is hovering just above the 14-year low of 407 posted two weeks ago, but production has not slowed much, if at all, from the record high posted last year.