区域优化平均法的改进及其在计算平均温度中的应用

气候重建研究中,重建数据有限的特点对研究造成很大影响。对于解决这个问题,区域优化平均法是一个很有效的重建方法。区域优化平均法可以通过最优权值和有限的温度数据计算目标区域平均温度的一种方法。应用区域优化平均法时,首先利用均方差最小化的优化加权机制和拉格朗日乘子法计算得到最优权值,然后最优权值结合温度数据计算得到区域平均温度。现阶段的区域优化平均在计算大范围区域的平均温度时有其自身弱点。为克服这一弱点,使其可以计算大范围区域的平均温度,例如北半球平均温度,本文对区域优化平均法做如下改进：不再使用网格划分求和的方式求解协方差模式,利用Haar小波函数和矩阵算子求得协方差模式;利用全选主元高斯消去法求解线性代数方程组得到最优权值。结果表明,Haar小波函数和矩阵算子用于计算中,使协方差模式的计算结果更精确。计算所用数据源于气候研究中心（CRU）,CRU被认为是最权威的数据来源之一。以计算北半球1961~1990年平均温度为例,发现改进后的区域优化平均法的计算所得结果与CRU已有结果的相关性较改进之前有所提高。因此,针对古气候重建过程中代用数据记录有限的问题,改进后的区域优化平均法提供了一个更为合理可行的计算方法。

Improvement of Optimal Regional Averaging Method and Its Application in Average Temperature Calculation

In the palaeoclimatic reconstruction research, the characteristics of proxy data are limited in number, which has a great deal to do with the influence of research. The optimal regional averaging method is a far more effective approach to slove this problem. The optimal regional averaging method is a method that can obtain the average temperature of target area by means of optimal weights using limited temperature data in target areas. In the application of this method, first optimal weighting mechanism based on minimum mean squqre error and Lagrange multiplier method are applied to get optimal weight, and then Optimal weights and temperature data are joined together to obtained regional average temperature. This existing optimal regional averaging method has weakness in the regional average temperature calculation of large target area. To overcome the weakness and make this method can calculate the average temperature of the large region, such as the Northern Hemisphere (NH) average temperature, the optimal regional averaging method is improved in this article. 1) Haar wavelet function and matrix operator are used to replace mesh summation method in process of solving covariance pattern. 2) Optimal weights are got through applying all principal component gauss elimination method to solve the linear algebraic equations. The result shows that the covariance pattern solved is more accurate because of the application of Haar wavelet function and matrix operator in the calculation. The temperature data used in the calculation derived from Climatic Research Unit (CRU), which is considered among the most authoritative sources on reconstruction research. After adopting the above mentioned improvement, taking calculation of the Northern Hemisphere (NH) average temperature in 1961-1990 as an example, it is found that the correlation coefficient between the NH temperature series obtained by the improved optimal regional averaging method and the published result from CRU is higher than the result obtained by this method before the above improvement. Thus the improved the optimal regional averaging method provides a reasonable approach for palaeoclimatic reconstruction in case that proxy data are limited and scarce in spatial distribution.