An aerial view of the coast of Sitkalidak Island where the Shell Drill Barge Kulluk ran aground. 8 Jan, 2013 © Greenpeace / Tim Aubry

President Obama is visiting Alaska today to put a spotlight on the realities of climate change and to forge his climate legacy. But less than two weeks ago, he granted Shell final approval to drill for oil in Alaska's Chukchi Sea.

We're as confused by that logic as you are.

That's not the only layer of irony here. The oil deep in Arctic waters is only accessible because of melting ice caused by climate change.

The fact that President Obama thinks he can forge a climate legacy while allowing Arctic drilling shows that he isn't in tune with the demands of people around the United States and the world to keep Arctic oil in the ground.

Whether simply ironic or downright hypocritical, what's clear is that President Obama's rhetoric on climate change is not matching up to his actions. You can write a letter to tell President Obama what true climate leadership looks like.

Here are four statements from President Obama himself that make it perfectly clear why climate leadership cannot include Arctic drilling:

President Barack Obama addresses the media at Coast Guard Station Grand Isle, La., concerning the ongoing, multi-agency response to the Deepwater Horizon incident, 28 May 2010. Coast Guard photo

"Alaskans are on the frontlines of one of the greatest challenges we face this century: climate change."

This much is true. Over the past 50 years, temperatures across Alaska have increased by an average of 3.4 degrees Fahrenheit (1.9 degrees Celsius), twice the average in the US.

The solution to climate change in Alaska — and everywhere else — obviously does not lie in extracting and burning more fossil fuels. In fact, a study published in the journal Nature earlier this year found that we cannot afford to burn any of the oil and gas reserves in the Arctic if we hope to avoid the worst impacts of climate change.

Allowing Shell to drill in the Arctic for "unburnable oil" will have devastating consequences for Alaskans already impacted by climate change.

Should global emissions continue to increase this century, temperatures will rise as much as 12 degrees Fahrenheit (6.6 degrees Celsius) in northern Alaska and 8 degrees Fahrenheit (4.4 degrees Celsius) in the rest of the state. This would greatly exacerbate ice melt, sea level rise, wildfire seasons and other threats already facing Alaskan communities.

"The hunting and fishing on which generations have depended for their way of life and their jobs is being threatened."

Once again, the President is right on with this one. And once again, drilling for oil in Alaskan waters is not going to help.

Indigenous Peoples in Alaska have spoken about how thinning sea and river ice is both threatening the habitats of traditional food sources and making hunting itself more dangerous. Rising temperatures and hotter, drier summers have already increased the strength and frequency of wildfires that decimate food and medicinal plant species and the habitats of food sources like caribou.

Of course, none of this gets better by extracting and burning more fossil fuels.

On top of that, the actual act of drilling poses a great threat to traditional hunting and fishing practices. There's a 75 percent chance of a major oil spill should Shell find oil — and that's by the government's own estimation.

For a sense of how such a spill would impact traditional ways of life, consider the case of the 1989 Exxon Valdez spill. That spill was so devastating for Native Alaskans that Chief Walter Meganack called it "the day the water died." More than 25 years later, communities are still recovering.

"Storm surges once held at bay now endanger entire villages."

Doesn't really sound like the kind of environment where you'd want to install massive, expensive oil infrastructure operated by a disaster-prone company, does it?

Cleaning up the likely event of an Arctic spill would be next to impossible, with the nearest Coast Guard station 1,000 miles away and harsh weather conditions complicating response. Shell has estimated it would take about six days for responders to reach the site of a spill, while oil would likely reach land — and coastal communities — within three days.

Shell's track record does little to inspire confidence in its ability to handle these conditions. Its 2012 attempt to drill in the Chukchi Sea ended in eight felony charges for its contractor Noble Drilling, a rig damaged beyond repair after running aground and a critical piece of spill response equipment "crushed like a beer can" during testing in the Puget Sound.

And just last month, a Shell icebreaker vessel tore a 39-inch gash in its hull while taking a shortcut, forcing it to undergo repairs and delaying Shell's entire operation. Clearly, this is not a company prepared to deal with harsh Arctic conditions only growing more extreme with our changing climate.

"What's happening in Alaska is … our wake up call. As long as I am president, America will lead the world to meet this threat before it's too late."

With this sentence — and indeed this entire trip — President Obama intends to cement his climate legacy. Unfortunately for him, opening the US Arctic to oil drilling for the first time in 20 years is hardly climate leadership.

In fact, it sends the exact wrong message to the rest of the world. As the current chair of the Arctic Council, US leadership must set the right tone for other Arctic nations. Already this year, Russia submitted a bid to claim more than 463,000 square miles of Arctic sea ice and Norway announced that it would expand Arctic drilling (parliamentary opposition has since delayed those plans).

Allowing Shell to drill in Alaska would open the floodgates for other nations to exploit Arctic resources, putting us further down a path towards climate disaster. If this is what "America lead[ing] the world" on climate change looks like, America is leading in the wrong direction.

Has President Obama been listening to his own words?

It's time to send him some of yours. Write a personal letter to President Obama and tell him why you think he should protect the Arctic and our climate.

Ryan Schleeter is an online content producer for Greenpeace USA.

A version of this blog was originally posted on Greenpeace USA's The Environmentalist.