统计与数据科学学院知识库

近百年来全球气候正经历以全球变暖为主要特征的显著变化，我国气温变化和全球大体一致，但不同区域略有不同。兰州地处我国西北，其气温变化趋势如何值得研究。气温是天气预报的基础指标，提高气温预报精度对人类生活至关重要。

利用局部多项式拟合分析兰州市年、季、月平均最低气温、平均最高气温、平均温差变化的长期趋势，利用PB断点检验分析兰州市气温变化的间断点，并以突变点为分割计算不同阶段兰州市年、季、月平均最低气温、平均最高气温、平均温差变化速率以揭示兰州市气温变化规律，得出以下结论：(1)兰州市气温呈显著的波动增加趋势，且在80年代升温最快。(2)兰州市高温、低温变化具有明显的非对称性。具体表现在最高气温波动性强，上升幅度较小，最低气温变化相对单一，上升幅度较大。(3)兰州市气温变化没有明显的周期性。具体表现气温突变年份在1960年、1970年、1983年、2000年左右，且不同阶段气温变化速度不一致。(4)不同季节、月份兰州市气温变化速度不同。相较于其他季节，兰州市冬季变暖趋势更加明显；相较于其他月份，一月、二月、十二月温度升高幅度更大。

目前气温预测研究多将气温序列作为一个整体进行预测，没有实现长期趋势、周期性和剩余残差项的分离，难以满足预测精度的要求。本文利用B-样条函数拟合气温演变长期趋势，傅里叶级数展开拟合气温序列中的周期性分量，QAR模型拟合原始序列中剔除长期趋势和周期性分量后的零均值残差序列，构建基于B-Spline-Fourier-QAR的气温组合预测模型对气温进行预测。通过分析不同预测步长下气温预测得精度，发现基于B-Spline-Fourier-QAR的气温组合预测精度较高。

In the past 100 years, the global climate is undergoing significant changes characterized by global warming. The temperature change in China is generally consistent with that in the world, but slightly different in different regions. Lanzhou is located in the northwest of China. Temperature is the basic index of weather forecasting, and improving the accuracy of temperature forecasting is very important for human life.

By using local polynomial fitting analysis in lanzhou city, quarterly, monthly mean minimum temperature, mean maximum temperature, average temperature change of long-term trend, using PB breakpoint test analysis lanzhou discontinuity point temperature changes, and with a separation method at different stages of mutations in lanzhou city, quarterly, monthly mean minimum temperature, mean maximum temperature, average temperature changing rate to reveal lanzhou city air temperature change rule, the following conclusions: (1) The lanzhou city temperatures were significantly increased volatility trend, and heat up the fastest in the 80 s. (2) The changes of high temperature and low temperature in lanzhou have obvious asymmetry. The specific performance is that the highest temperature has a strong fluctuation and a small increase, while the lowest temperature has a relatively single change and a large increase. (3) There is no obvious periodicity of temperature change in lanzhou. Specifically, the abrupt temperature change years were around 1960, 1970, 1983 and 2000, and the temperature change rate in different stages was not consistent. (4) The temperature changes in lanzhou are different in different seasons and months. Compared with other seasons, lanzhou's winter warming trend is more obvious. Temperatures rose more in January, February and December than in any other month.At present, temperature series are mostly used as a whole in temperature prediction research, and the separation of long-term trend, periodicity and residual residual term is not realized, which is difficult to meet the requirement of prediction accuracy. In this paper, b-spline function is used to fit the long-term trend of temperature evolution, Fourier series is developed to fit the periodic components in the temperature sequence, and QAR model is used to fit the zero mean residual sequence after removing the long-term trend and periodic components in the original sequence, and a combined temperature prediction model based on b-spline-fourier -QAR is constructed to predict the temperature. By analyzing the precision of temperature prediction under different prediction steps, it is found that the temperature combination prediction precision based on b-spline-fourier -QAR is higher.