中文摘要：

区域优化平均法是一种有效的过去温度重建方法.它具有使用较少的数据达到较高重建精度的优点,能较好地解决过去温度重建过程中数据分布稀疏的问题.然而,区域优化平均法只能重建局部区域内的平均温度,无法重建较大范围的平均温度.为克服该缺陷,本文引入球谐分析法改进现有方法,使区域优化平均法可以计算全球或半球的平均温度.本文使用Climatic Research Unit（CRU）的年平均温度数据计算1951～2013年全球年平均温度序列,以验证该方法的可靠性.在此基础上重建了过去1400年北半球夏季平均温度序列.结果表明,改进的区域优化平均法可以较好地重建过去温度序列.

英文摘要：

Optimal Regional Averaging Method is an effective method to reconstruct temperature variations of the past. It has the advantage of obtaining a reliable regional-scale temperature reconstruction using a limited dataset. This method has been successfully applied in reconstructing average temperature on a given target area in the recent years. However, it should be noted that this method only can calculate average temperature over a local area, and there is still no continental-or hemispheric-scale temperature reconstructions reported. In this paper, we use spherical harmonic function to improve this method. To validate reliability of this method, we calculate average temperature series over the Northern Hemisphere during the period 1951-2013 using temperature data from Climatic Research Unit （CRU）, and compare it with the result derived from the simple average method. The results show that the improved method is better than the simple digital method while using the same dataset, and it can calculate global average temperature series in the case of discontinuous data. We also use 15 regional Maximum Latewood Density （MXD） series from Schneider et al. （2015） to reconstruct summer temperature during the past 1400 years using the improved Optimal Regional Averaging Method. The reconstruction results show that there are obvious warm period in the Medieval Period （800- 1100A.D.）, low temperatures during the Little Ice Age （ 1700- 1900A.D.） , and the warming trend in the 20 century. These results support that the improved Optimal Regional Averaging Method is an effective method to reconstruct temperature variations of the past.