  Rapidly diminishing Arctic summer sea ice is a strong signal of the pace of
global climate change. We provide point, interval, and density forecasts for
four measures of Arctic sea ice: area, extent, thickness, and volume.
Importantly, we enforce the joint constraint that these measures must
simultaneously arrive at an ice-free Arctic. We apply this constrained joint
forecast procedure to models relating sea ice to atmospheric carbon dioxide
concentration and models relating sea ice directly to time. The resulting
"carbon-trend" and "time-trend" projections are mutually consistent and predict
a nearly ice-free summer Arctic Ocean by the mid-2030s with an 80% probability.
Moreover, the carbon-trend projections show that global adoption of a lower
carbon path would likely delay the arrival of a seasonally ice-free Arctic by
only a few years.
