* Front month up for second day after last week's losses
* Warm weather on tap for consuming regions
* Inventory data, production data both supportive
* Coming Up: API oil data Tuesday, EIA oil data Wednesday
By Eileen Houlihan
NEW YORK, June 5 (Reuters) - U.S. natural gas futures rose about 2 percent early Tuesday, up for a second straight session on forecasts for warmer weather that should boost demand to power air conditioners.
Another drop in gas drilling rigs last week and a slowdown in March gas production were also cited.
Front-month July natural gas futures on the New York Mercantile Exchange were at $2.465 per million British thermal units in early trade, up 5 cents, or about 2 percent.
The nearby contract rose about 4 percent on Monday, after losing more than 9 percent last week.
Futures hit a 3-1/2-month high of $2.759 in mid-May, which most traders said removed gas from favor over coal for power generation.
But since posting a 10-year low of $1.902 twice in late April, nearby futures are up 29 percent on signs that record production was finally slowing and demand picking up as more electric utilities switched from coal to gas.
DESPITE LIGHTER BUILDS, STORAGE STILL BLOATED
Weekly gas storage data, while in line with Reuters poll estimates, was well below average for the seventh time in eight weeks.
Data last week from the U.S. Energy Information Administration showed U.S. natural gas inventories rose 71 billion cubic feet, in line with Reuters estimates for a 70-bcf gain, but well below the year-ago adjusted build of 89 bcf and the five-year average build for that week of 100 bcf.
Total domestic gas inventories rose to 2.815 trillion cubic feet, still 35 percent above last year and also 35 percent above the five-year average.
(Storage graphic: link.reuters.com/mup44s)
The surplus to last year has dropped 17 percent from late-March peaks, but stocks remained at record highs for this time of year. There are concerns the glut will drive prices lower this summer as storage caverns fill.
The storage surplus to last year will have to be cut by at least another 480 bcf to avoid breaching the government's 4.1-tcf estimate of capacity. Stocks peaked last year in November at a record 3.852 tcf.
Early estimates for this week's EIA report range from 45 bcf to 80 bcf versus an 81-bcf adjusted increase a year earlier and a five-year average gain for that week of 99 bcf.
PRODUCTION FALLING FROM RECORD
EIA data last week also showed gas production was finally dropping from January's record high, with two straight monthly declines.
The EIA said U.S. natural gas production fell 0.4 percent in March to 71.76 bcf as producers continued to scale back drilling in the face of low prices. It was a second monthly decline after a revised 1 percent fall in February.
In addition, Baker Hughes data on Friday showed the gas-directed rig count fell by six to a 12-1/2 year low of 588. The 37 percent drop in dry gas drilling -- since peaking at 936 in October -- has stirred talk producers were finally getting serious about stemming the flood of supplies.
But the shift away from dry gas to higher-value shale oil and shale gas liquid plays still produces plenty of associated gas that ends up in the market after processing. That has slowed the overall drop in dry gas output.
(Rig graphic: r.reuters.com/dyb62s)
Colorado State University researchers last week raised their forecast for the 2012 Atlantic hurricane season to 13 tropical storms, with five hurricanes and two 'major' hurricanes.
The National Weather Service's six- to 10-day outlook issued on Monday again called for above-normal readings for much of the nation, with below-normal readings in Florida and in the West.
Nuclear power plant outages were running at about 16,500 megawatts, or 16 percent, on Tuesday, down from about 17,000 MW out a year ago but up from a five-year outage rate of about 10,900 MW. (Reporting by Eileen Houlihan)