全球气候变化是当代人类社会面临的挑战之一。常用的气候变化预估工具全球气候模式（Global Climate Model，GCM）输出的模拟结果空间分辨率较低，很难反映区域内的精确气候特点和差异。因此，本研究基于逐步聚类分析方法和Vine Copula理论，开发了一套逐步聚类Copula集合降尺度（Stepwise-Clustered Vine Copula Downscaling，SCVCD）方法，希望通过该模型建立多模型大尺度预报因子与局部地表变量间的统计关系，在GCM输出的基础上获取高分辨率的气候要素模拟结果。
本研究首先基于逐步聚类分析方法建立了基于逐步聚类分析的多因变量降尺度（Stepwise-Clustered Multivariate Downscaling，SCMD）模型，该模型能够反映多个区域变量与大尺度气候因素的关系。使用华北平原地区历史气候再分析数据和观测数据对模型进行验证和评价。接着，基于Vine Copula方法对SCMD模型输出进行集合偏差修正，开发SCVCD方法，并利用华北平原地区历史气候观测数据和GCM历史模拟数据对模型进行验证和评价。最后，利用已验证的模型对两种共享社会经济路径SSP2-4.5、SSP5-8.5情景下华北平原地区2015–2099年间的日平均温度、日最低温度、日最高温度进行预估，并对华北平原地区未来时期年平均温度、季节温度、热量资源变化趋势进行分析。
研究结果表明：
（1）    SCMD模型在验证期（2000–2010年）的日尺度温度预估上表现良好，对于研究区域的17个气候站点，验证期内SCMD对日平均温度的降尺度结果R2≥0.88；对于日最低气温，降尺度结果R2≥0.81；对于日最高气温，R2≥0.80；日平均温度降尺度结果的均方根误差（RMSE）为1.5~3.6℃，日最低气温为2.6~4.5℃，日最高气温为2.3~4.3℃。降尺度结果标准差与观测数据接近。将SCMD模型的性能与基于逐步聚类分析方法的单个因变量降尺度方法（SDM）进行比较，发现当某个因变量与其他变量相比模拟效果较差时，SCMD对该变量的模拟效果明显优于SDM。在研究选取的4个GCM中，整体上，NorESM2-LM降尺度结果对华北平原地区17个站点的模拟效果最好，CanESM5降尺度结果较差。
（2）    SCVCD模型在验证期对日最低温度、日平均温度、日最高温度均有良好的降尺度效果，其中，对日最低温度、日平均温度的降尺度效果相对更好。对于日最低温度、日平均温度月平均值，SCVCD模拟数据R2≥0.95，日最高温度月平均值SCVCD模拟数据R2≥0.91。在RMSE方面，对于日最低温度，各站点的月平均值日平均温度的月平均值RMSE在1.5~2.0℃间，日最高温度的月平均值RMSE在1.9~2.8℃间。在MAE方面，对于日最低温度，各站点的月平均值MAE在1.3~1.7℃间，日平均温度的月平均值MAE在1.2~1.6℃间，日最高温度的月平均值MAE在1.6~2.2℃间。模型表现优于常用偏差修正方法Qmap方法、常用集合方法集合平均，且对输入数据质量要求低。
（3）    基于SCVCD方法SSP2-4.5、SSP5-8.5情景下华北平原地区2015–2099年间的日平均温度、日最低温度、日最高温度进行预估，分析结果表明：①年际温度变化方面，至2071–2090年，SSP2-4.5情景下各站点的日平均温度上升1.4~2.0℃；SSP5-8.5情景下各站点的日平均温度上升2.6~3.2℃。日最高温度升温幅度大于日平均温度和日最低温度。SSP2-4.5情景下，日最低温度、日平均温度、日最高温度在2021–2040年和2041–2060年期间上升幅度较大，到2061–2090年，其上升幅度均降低；SSP5-8.5情景下，在2021–2040年、2041–2060年以及2061–2090年三个阶段内，日最低温度、日平均温度上升幅度基本不变，日最高温度在2061–2090年上升幅度进一步增大。②年内各月份、各季节温度变化方面，各月份中，7月、8月的温度上升幅度最低，甚至在某些站点出现下降的情况，1月、10~12月温度上升幅度较高。在四个季节中，冬季的温度增长幅度最高，夏季温度增长幅度最低。至2071–2090年，SSP2-4.5情景下，各站点冬季温度增长1.9~2.9℃，夏季温度增长0.2~1.6℃；SSP5-8.5情景下，各站点冬季温度增长3.2~4.4℃，夏季温度增长0.6~2.5℃。③热量资源方面，未来时期华北平原地区暖温带区域缩小，北亚热带区域扩大。在SSP5-8.5情景下，到2071–2090年，华北平原地区北部、中部11个站点属于北亚热带区域，南部5个站点划分至中亚热带区域。
本研究开发的SCVCD方法能够作为气候因素多模式集合降尺度的有效工具，应用到各类相关领域研究中。而华北平原未来温度的高分辨率预估结果将为华北平原地区气候相关领域研究和政府部门的决策制定提供科学依据。

Global Climate change is a big challenge faced by human society. Global climate models (GCMs) are currently widely used for future climate projection under different scenarios. However, the relatively coarse resolution makes them unreliable when it comes to a regional or site-specific scale study. Therefore, a stepwise-clustered vine Copula downscaling (SCVCD) approach is developed on the basis of stepwise cluster analysis (SCA) method and vine Copula theory in this study. The model can project a finer resolution of multiple local-scale atmospheric variables based on multiple GCMs.
First, a stepwise-clustered multivariate downscaling (SCMD) model is developed on the basis of stepwise cluster analysis. The historical reanalysis data and observed data in the North China Plain has been used for model construction and validation. Second, the output data from SCMD is ensembled and corrected based on vine Copula, and the SCVCD method is developed. The historical GCM output data and observed data has been used for model construction and validation. Finally, future temperature changes over the North China Plain under the SSP2-4.5 and SSP5-8.5 scenarios are projected through SCVCD. The variation trend of annual, seasonal and monthly average temperature, as well as heat resources in the North China Plain in the future has been analyzed.
The results of the research indicate that:
(1) the SCMD model performs well on daily-scale temperature predictions for the validation period (2000–2010), with downscaled results of R2≥ 0.81 for daily minimum temperatures, R2≥ 0.88 for daily mean temperatures, and R2≥ 0.80 for daily maximum temperatures for the 17 climate stations in the study area. The daily RMSE of the downscaled results for daily minimum temperature ranged from 2.6 to 4.5°C, for daily mean temperature from 1.5 to 3.6°C, and for daily maximum temperature from 2.3 to 4.3°C. The standard deviation of the downscaled results was close to the observed data. Comparing the performance of the SCMD model with the SCA-based downscaling method (SDM) for a single dependent variable, it was found that when a dependent variable was poorly simulated compared to other variables, SCMD simulated that variable significantly better than SDM. Among the four GCMs selected for the study, overall, the Nor downscaling results are the best for the 17 stations in the North China Plain region, followed by the MPI downscaling results and the INM downscaling results, and the Can downscaling results are poor.
(2) The SCVCD model has good downscaling effects on daily minimum temperature, daily average temperature, and daily maximum temperature during the validation period, among which the downscaling effects on daily minimum temperature and daily average temperature are relatively better. For the monthly average of daily minimum temperature and daily average temperature, R2≥ 0.95; and for the monthly average of daily maximum temperature the R2≥ 0.91. In terms of RMSE, for the daily minimum temperature, the monthly average RMSE of each site is between 1.5 and 2.1°C, the monthly average RMSE of daily average temperature is between 1.5 and 2.0°C, and the monthly average RMSE of daily maximum ranged from 1.9 to 2.8°C. In terms of MAE, for the daily minimum temperature, the monthly mean MAE at each site ranged from 1.3 to 1.7°C, the monthly mean MAE for the daily average temperature ranged from 1.2 to 1.6°C, and the monthly mean MAE for the daily maximum temperature ranged from 1.6 to 2.2°C. The model performs better than the commonly used bias correction method Qmap method, and the commonly used ensemble method ensemble average. The model shows better robustness when the quality of input data is rather low.
(3) In the future period, the daily average temperature in the North China Plain region increases by 1.4~2.0℃ under the SSP2-4.5 scenario, and by 2.4~3.2℃ under the SSP5-8.5 scenario by 2071–2090. Under the SSP2-4.5 scenario, the daily minimum temperature, daily mean temperature, and daily maximum temperature rise more during 2021-2040 and 2041-2060, and their rise decreases by 2061-2090; under the SSP5-8.5 scenario, the 2021-2040, 2041-2060, and 2061-2090, the daily minimum and daily mean temperature increases are basically unchanged, and the daily maximum temperature increases further in 2061-2090. During the annual cycle, the lowest temperature increases and even decreases at some sites were observed in July and August, and higher temperature increases were observed in January and October to December. Among the four seasons, the highest temperature increase was observed in winter, with 1.9~2.9°C increase in winter temperature at each site under the SSP2-4.5 scenario and 3.2~4.4°C increase in winter temperature at each site under the SSP5-8.5 scenario to 2071-2090. and its difference with the annual temperature increase continues to increase over time. Summer temperature increases are the lowest, ranging from 0.2 to 1.6°C at each site for the SSP2-4.5 scenario and 0.6 to 2.5°C for the SSP5-8.5 scenario to 2071-2090. The warm-temperate zone in the North China Plain region shrinks and the northern subtropical zone expands in the future period. Under the SSP5-8.5 scenario, by 2071–2090, 11 stations in the northern and central parts of the North China Plain region belong to the North Subtropical Region, and 5 stations in the south are classified to the Central Subtropical Region.
The SCVCD method developed in this research can be applied as an effective tool for multimodal ensemble downscaling of climate factors in various related field studies. The results of the high-resolution prediction of the future temperature in the North China Plain will provide a scientific basis for the research and decision making of government departments in the climate related fields in the North China Plain.