Previous reconstructions of summer temperatures from ice cores have relied on a statistical relationship between a melt layer and temperature observed at nearby stations. This study presents a novel method for reconstructing summer temperatures from melt layers in ice cores using an energy balance model that incorporates heat conduction and meltwater refreezing in the firn. We use the seasonal patterns in the ERA-Interim reanalysis data set for an ice core site to calculate the amounts of refreezing water within the firn under various summer mean temperature (SMT) and annual precipitation conditions, and prepared calibration tables containing these three variables. We then estimate the SMTs from the refreezing amount and annual accumulation, both of which can be obtained from an ice core. We apply this method to four ice cores that were recovered from sites with different climates: two sites on the Greenland Ice Sheet, one in Alaska, and one in Russian Altai. The reconstructed SMTs show comparable variations with those of observed temperatures at nearby stations. The nonlinear relationship between SMT and melt layer thickness differs between sites, indicating that a single linear approximation cannot be employed to estimate SMT. Sensitivity analyses suggest that the annual temperature range, amount of annual precipitation, and firn albedo (which is a time-invariant value in the model) significantly affect the relationship between SMT and melt layer thickness. This new method provides an alternative to existing approaches and yields an independent estimate of SMT from ice cores that have been affected by melting.

中文翻译：

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基于物理原理的冰芯融化层夏季温度重建

先前对冰芯夏季温度的重建依赖于融化层与附近站点观测到的温度之间的统计关系。本研究提出了一种使用能量平衡模型从冰芯中的融化层重建夏季温度的新方法，该模型结合了热传导和融水在冷杉中重新冻结。我们使用冰芯站点的 ERA-Interim 再分析数据集中的季节性模式来计算在各种夏季平均温度 (SMT) 和年降水条件下冷杉内再冻结的水量，并准备了包含这三个变量的校准表。然后我们根据再冻结量和年累积量估计 SMT，这两者都可以从冰芯中获得。我们将此方法应用于从不同气候地点回收的四个冰芯：两个地点在格陵兰冰盖上，一个在阿拉斯加，一个在俄罗斯阿尔泰。重建的 SMT 显示出与附近站点观测到的温度相当的变化。SMT 和熔体层厚度之间的非线性关系因站点而异，表明不能采用单一线性近似来估计 SMT。敏感性分析表明，年温差、年降水量和杉木反照率（模型中的时不变值）显着影响 SMT 与熔体层厚度之间的关系。这种新方法为现有方法提供了一种替代方法，并从受到融化影响的冰芯中产生了对 SMT 的独立估计。