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.

翻译：急剧减少的北极夏季海冰是全球气候变化速度的强烈信号。我们针对北极海冰的四个衡量指标——面积、范围、厚度和体积——提供了点预测、区间预测和密度预测。重要的是，我们强制施加了这些指标须同时达到无冰北极状态的联合约束。我们将这一约束性联合预测方法应用于两类模型：一类是联系海冰与大气二氧化碳浓度的模型，另一类是直接联系海冰与时间的模型。由此产生的“碳趋势”和“时间趋势”预测相互一致，并预测到21世纪30年代中期，北冰洋夏季几乎无冰的概率为80%。此外，碳趋势预测表明，全球采纳低碳路径可能仅会将季节性无冰北极的到来推迟数年。