History's more memorable monarchies are often those that confronted adversity with uncommon fortitude and vigor. After battling a range of noteworthy adversaries from cheap natural gas to China's notorious deceleration, the king of coal has returned to its rightful throne as the world's most powerful force within the powerful world of coal.

Peabody Energy (BTU) is the ruler in question, and the miner's stellar third-quarter performance in the face of daunting challenges set its loyal subjects to cheering. The stock rocketed higher by as much as 15% on Monday after Peabody reported adjusted earnings of $0.51 per share on revenue of $2.1 billion. 

The competitive advantage of Peabody's concentrated U.S. portfolio of Powder River Basin and Illinois Basin coals -- which I outlined here back in 2010 -- was revealed in all its splendor. In contrast to the 40% decline year-to-date in coal-fueled electricity generation using coals from the once-dominant central Appalachian region, generation using coals from the remaining U.S. basins suffered only a 10% decline. On the strength of this "ongoing shift in demand from Appalachia to Midwestern and Western regions," Peabody recorded a slight increase in western U.S. shipments at a time when competitors Arch Coal (NYSE: ACI), Alpha Natural Resources (NYSE: ANR), and CONSOL Energy (NYSE: CNX) were each maneuvering to curtail production in the eastern basins. More impressively, Peabody achieved an 8% expansion of its operating margin on U.S. coal operations, as cost-containment activities combined with slightly higher realized prices.

Although higher natural gas prices are pointing to recovering domestic demand for western and Midwestern coals during 2013, Peabody remains keenly focused on how important the seaborne coal trade is to securing its long-term growth outlook. Toward this end, Peabody made agreements with Kinder Morgan Energy Partners (NYSE: KMP) and Union Pacific (UNP -0.31%) back in July to secure its share of bottlenecked export capacity, while continuing to grow production from its exciting portfolio of Australian operations. Peabody's remarkable 39% increase in Australian production -- bolstered substantially by last year's Macarthur Coal acquisition -- positioned the miner to easily absorb a 13% dip in realized prices over the prior-year period.

Looking ahead, the king's reign looks poised for considerable longevity. Even during one of the worst years for the coal market in recent memory, Peabody expects worldwide seaborne demand for thermal coal to grow 12.5% to reach 900 million tons -- with further gains to follow next year -- and corresponding demand for metallurgical coal to rise between 10% and 15% during 2013. China's net coal imports alone are up by 60 million tons year-to-date, and India's imports are poised to mark a fresh record after a 15% increase year-to-date. Even on the debt-distressed European continent, coal-fueled generation has increased 14% so far in 2012.

With strong indications from diversified commodity producers Rio Tinto (NYSE: RIO) and BHP Billiton (BHP -1.36%) that China's deceleration may be stabilizing with well-timed infrastructure investments adding fuel to the fire, and this observable strength in both domestic and seaborne demand for U.S. coals in those basins where Peabody reigns as king, I believe the long-term outlook for Peabody's shares remains resiliently bullish following the trailing period of weakness. I am delighted by my prior decision to add additional shares of Peabody Energy when the share valuation grew more insane than King George III, and I have every confidence that -- particularly as Peabody moves forward with an impressive $100 million in potential annual cost savings -- my still-underwater CAPScall on the stock will ultimately give way to coal-fired gains.