Pyongyang-watchers have long dismissed the possibility of US military action against North Korea’s nuclear weapons programme as “unthinkable”. But after Kim Jong-un’s rogue regime last week test fired a ballistic missile that could potentially target the US state of Alaska, a pre-emptive strike no longer looks so inconceivable.

An armed response would strain America’s conventional military resources to their utmost, and the risks entailed would be horrendous. But for US policymakers, the time may soon be approaching when the risk of continuing to pursue a peaceful solution becomes greater than the dangers of military action.

Although Kim has successfully tested both explosive nuclear devices and long-range missiles, his development programme is not yet sophisticated enough to fit a miniature warhead on a missile to create a viable nuclear weapon.

This gives the US a window of opportunity in which to pursue a diplomatic solution. But the chances that Washington can achieve its stated aim of denuclearising the Korean peninsular by diplomatic means are slight at most.

As North Korea’s neighbour and biggest economic partner, China would like to see a multilateral deal under which Kim would agree to halt his weapons programme. In return, the US would discontinue military exercises with South Korea, end economic sanctions, open diplomatic relations with Pyongyang and eventually withdraw its armed forces from the Korean peninsular.

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The chances are negligible. US President Donald Trump has roundly condemned 2015’s similar deal with Iran. And given Pyongyang’s long record of reneging on its previous agreements, there is little enthusiasm among North Korea’s other near-neighbours for striking another bargain. Moreover, there is small chance that Kim would voluntarily give up his weapons programme. The lesson of recent history in Iraq and Libya has taught him that rogue regimes which cannot boast a substantial weapons capability are likely to get toppled by conventional force.

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If a negotiated solution is not on the table, the US can do little in the near term but tighten sanctions in an attempt to force Kim’s regime to abandon its development of nuclear weaponry by bringing the North Korean economy to its knees.

But to succeed, a course of economic isolation would require the wholehearted participation of China.

And China has repeatedly shown it has no appetite for enforcing sanctions so strict that they could precipitate the complete collapse of North Korea’s economy. That would merely threaten chaos, and a flood of millions of refugees across the Yalu river into China’s depressed North Eastern provinces.

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Nor does the Chinese leadership feel inclined to cooperate with the US administration in imposing additional sanctions, given Washington’s recent attempts to apply pressure on Beijing with naval patrols in the South China Sea and an agreement to sell sophisticated arms to Taiwan.

As a result, there is little chance that stepped-up sanctions will achieve the outcome Washington wants. That means at some point in the next year or two, US policymakers may find themselves contemplating the likelihood that North Korea will soon deploy viable nuclear missiles that could strike US territory.

US Secretary of State Rex Tillerson has declared this is something Washington cannot allow.

Attacking North Korea would be no small undertaking. Any pre-emptive strike would have to destroy Kim’s nuclear programme and degrade his ability to retaliate with conventional or chemical weapons against either South Korea or Japan.

There is no chance the US would cross the 38th parallel with ground forces. Instead it would launch a synchronised, three-pronged air assault. First, the US Air Force’s stealth bombers would attempt to take out North Korea’s underground nuclear facilities with their new “massive ordnance penetrators”. Similar in principle to the earthquake bombs that were used to great effect against Germany in the last year of the second world war – only much larger – these are designed to destroy targets deep underground with seismic shock waves.

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At the same time, US forces would launch an assault against North Korea’s command centres, communications and air defences, very likely using submarine-launched cruise missiles with conventional warheads. Finally, a third assault consisting of both cruise missiles and the remainder of the USAF’s strategic bomber force, including its venerable B-52 aircraft, would target the massed ranks of North Korea’s artillery positioned along its southern border to threaten Seoul.

Whether such an attack could work is questionable. Even with excellent intelligence and faultless targeting, mounting an assault would require the full force of the USAF’s 150-strong strategic bomber fleet, and the majority of the US Navy’s attack submarines, which together can bear some 2,000 cruise missiles.

The logistical challenges would be immense. The planning, training and rehearsing would take months. And the odds that a force of such magnitude could be concentrated in secret without alerting either North Korea or China are surely far-fetched.

Nevertheless, if both diplomatic efforts and sanctions fail to produce results, and if tensions worsen further, US policymakers could find themselves facing the danger that Anchorage in Alaska, a city of 300,000, might soon be struck by a nuclear missile should they fail to act. If they judge the threat to be genuine, US military action against North Korea will no longer be “unthinkable”. It will be highly likely.

Tom Holland is a former SCMP staffer who has been writing about Asian affairs for more than 20 years