Machine learning-based influencing factors analysis and estimation of winter temperature anomalies in China
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摘要: 使用1951—2021年160个中国国家级气象观测站冬季平均气温及多项大气环流及海温等指数，用机器学习方法研究影响中国冬季气温异常的大气环流及海温等外强迫因子，并建立估算拟合模型，评价筛选出的影响因子组合对中国冬季气温异常分布的贡献。使用最小绝对收缩和选择算子（Lasso）算法提取与冬季气温异常相关的影响因子。为体现特征因子之间非线性关系，使用泰勒公式对筛选后的特征进行多项式增广。使用最小二乘梯度提升决策树（LS-GBDT）算法对筛选出的特征因子与冬季气温异常之间的非线性关系进行估算拟合。结果表明，机器学习方法能够对影响冬季气温异常的特征因子进行合理筛选与重要性分析，建立的估算模型在一定程度上体现了气候系统特征因子与冬季气温异常变化之间的非线性联系。本研究为了解中国冬季气温异常分布的影响因素及其模拟与估算提供了新方法和途径。Abstract: In the study, the mean winter temperature collected at 160 stations in China from 1951 to 2021 and a number of atmospheric circulation and sea temperature indices are used to investigate the relationship between the distribution of winter temperature anomalies and the atmospheric circulation and external forcing factors. A model of fitting is also established by using machine learning methods. In this way, we can understand to what extent the screened combination of influencing factors can explain the distribution of winter temperature anomalies in China. The Least Absolute Shrinkage and Selection Operator (Lasso) algorithm is used to extract the influencing factors related to winter temperature anomalies. In addition, to reflect the nonlinear relationship between these factors, the original features are augmented to polynomial features using Taylor's formula. To further study the nonlinear relationship between the selected factors, the least squares gradient boosting decision tree (LS-GBDT) algorithm is used to estimate and fit winter temperature. Experiments are conducted on the training samples and test samples respectively and have achieved good results. The result verifies that machine learning can be used to screen and analyze the importance of factors affecting winter temperature anomalies more reasonably, and the estimation model established can to a certain extent reflects the nonlinear relationship between the factors influencing the climate system and winter temperature. This work provides a new way to simulate and estimate distribution of the winter tmperature anomalies in China.
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Key words:
- Winter temperature /
- Machine learning /
- Lasso /
- LS-GBDT /
- Climate prediction
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图 1 经验正交函数分解中国冬季平均气温距平的前4个空间模态 （a1—d1） 及其对应的时间系数 （a2—d2）
Figure 1. Empirical orthogonal function （EOF） decomposition of the first four spatial modes （a1—d1） and their corresponding time coefficients （a2—d2） of China's winter mean temperature anomalies
图 2 Lasso拟合系数轨迹 （df代表自由度；绿色虚线：最小拟合均方误差对应的Lambda；蓝色虚线：在不大于最小拟合均方误差的1个标准差内对应的最大Lambda；彩色实线：随Lambda变化而变化的不同特征因子的拟合系数）
Figure 2. Trajectory plot of fitting coefficient on Lasso （df：degrees of freedom；green dotted line：Lambda corresponding to the minimum fitting root mean square error；blue dashed line：the corresponding maximum Lambda no greater than one standard deviation of the minimum fitting root mean square error；solid colored line: different features，the fitting coefficients of which vary with the change of Lambda）
图 4 1956/1957年中国冬季平均气温距平实况 （a）、基于Lasso+LS-GBDT再代入 （b） 和Lasso+LS-GBDT+泰勒多项式特征再代入 （c） 结果 （单位：℃）
Figure 4. Spatial distributions of （a） China's winter mean temperature anomalies，（b） re-substitution based on Lasso+LS-GBDT and （c） re-substitution based on the characteristics of Lasso+LS-GBDT+Taylor polynomials features in 1956/1957 （unit：℃）
图 5 1998/1999年中国冬季平均气温距平实况 （a）、基于Lasso+LS-GBDT的再代入（b）和Lasso+LS-GBDT+泰勒多项式特征的再代入 （c） 结果 （单位：℃）
Figure 5. Spatial distributions of （a） China's winter mean temperature anomalies，（b） re-substitution based on Lasso+LS-GBDT and （c） re-substitution based on the characteristics of Lasso+LS-GBDT+Taylor polynomials features in 1998/1999 （unit：℃）
图 6 2012/2013年中国冬季平均气温距平实况 （a）、基于Lasso+LS-GBDT的拟合 （b） 和Lasso+LS-GBDT +泰勒多项式特征的拟合 （c） 结果 （单位：℃）
Figure 6. Spatial distributions of （a） China's winter mean temperature anomalies，（b） forecast based on Lasso+LS-GBDT and （c） forecast based on the characteristics of Lasso+LS-GBDT+Taylor polynomials features in 2012/2013 （unit：℃）
图 7 2017/2018年中国冬季平均气温距平实况 （a）、基于Lasso+LS-GBDT的拟合 （b） 和Lasso+LS-GBDT +泰勒多项式特征的拟合 （c） 结果 （单位：℃）
Figure 7. The map of （a） China's winter mean temperature anomalies，（b） the forecast map based on Lasso + LS-GBDT tree and （c）the forecast map based on the characteristics of Lasso + LS-GBDT tree + Taylor polynomials features in 2017/2018 （unit：℃）
表 1 特征因子分类
Table 1. Classification of features
类别 筛选气候系统指标集合 极涡 （1）北半球极涡中心纬向位置指数
（2）亚洲区极涡强度指数；亚洲区极涡面积指数；大西洋欧洲区极涡强度指数；大西洋欧洲区极涡面积指数；太平洋区极涡强度指数；太平洋区极涡面积指数；北半球极涡强度指数；北半球极涡面积指数；北美区极涡面积指数副热带高压 南海副高脊线位置指数（10°—60°N﹑100°—120°E）；北非副高脊线位置指数（10°—60°N﹑20°W—60°E） 大尺度环流 （1）亚洲纬向环流指数；亚洲经向环流指数
（2）南极涛动；北大西洋涛动
（3）东大西洋-西俄罗斯遥相关型；斯堪的纳维亚遥相关型；西大西洋遥相关型；极地-欧亚遥相关型；北太平洋遥相关型海温 NINO W区海表温度距平指数；热带南大西洋海温指数；西太平洋暖池面积指数；大西洋多年代际振荡指数 高空槽 西藏高原-2指数；印缅槽强度指数 纬向风场 850 hPa东太平洋信风指数 
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表 2 距平符号一致率和空间距平相关系数 （相关系数通过样本量为160的
$ \alpha $ =0.001显著性检验）Table 2. Anomaly sign rate and spatial anomaly correlation coefficient （correlation coefficients are tested by the significance level of
$ \alpha $ =0.001 with a sample size of 160）试验名称 平均距平符号一致率 平均空间距平相关系数 统计机器学习 统计机器学习+泰勒 统计机器学习 统计机器学习+泰勒 训练样本 86.0% 86.8% 0.72 0.74 独立样本 73.1% 73.8% 0.30 0.39
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