图1 CMIP6模式预估的中国西北地区夏季降水量21世纪末期（2081—2100年）相比于历史时期（1995—2014年）相对变化的空间分布 注：图右上角数据表示区域平均的变化，图中加粗黑色实线为降水相对变化的零线。

Fig. 1 Spatial distribution of the relative change in summer precipitation over the Northwestern China predicted by CMIP6 models for the end of 21st century (2081-2100) compared to the historical period (1995-2014). (The data on the map represent the regional average changes, the bold black solid line in the figure represents the zero line of relative change in precipitation)

图2 中国西北地区夏季降水相对变化的模式间EOF分解(a)第一主模态，(b)第一主模态对应的各模式贡献序列与各模式的区域平均序列

Fig. 2 The first empirical orthogonal function (EOF) of the inter-model decomposition of relative changes in summer precipitation over Northwestern China. (a) The first mode, (b) the corresponding contribution sequences of each model and the regional average sequences of each model

图3 夏季西北地区区域平均降水分别与同期热带印度洋海温(a)以及700 hPa风场(b)的回归分布 注：(a)图中填色区域通过95%信度检验，框中区域为关键因子区域；(b)图中黑色加粗表示通过95%信度检验，框中区域为西北地区。

Fig. 3 Regression distribution of summer average precipitation over Northwestern China with contemporaneous sea surface temperatures in the tropical Indian Ocean (a) and the 700 hPa wind field (b), respectively. (The coloring area represent the 95% confidence level, the boxed area in (a) indicates the key factor region. The bold black lines represent areas passing the 95% confidence test, the boxed area in (b) indicates Northwestern China)

图4 夏季西北地区区域平均降水分别与东亚副热带200 hPa纬向风(a)，以及沿西北地区（74°~105°E）平均经向环流和纬向风(b)的回归 注：加点表示通过95%信度检验，框中区域为关键因子区域；红色阴影为西风异常增强，蓝色阴影为东风异常增强。

Fig. 4 Regression of summer average precipitation over Northwestern China with the East Asian subtropical 200 hPa zonal wind (a), and the zonal wind and meridional circulation along the Northwestern China region (74°-105°E) (b), respectively. (The dots represent areas passing the 95% confidence test, the boxed area indicates the key factor region. The red shading indicates west wind anomalies, while the blue shading indicates east wind anomalies)

图5 25个CMIP6模式模拟的热带印度洋海温(a)及东亚副热带200 hPa纬向风(b)与预估的夏季西北地区区域平均降雨量变化的散点图 注：红线表示观测到热带印度洋区域平均海温。

Fig. 5 Scatter plot of the tropical Indian Ocean sea surface temperature (a) and the East Asian subtropical 200 hPa zonal wind (b) simulated by 25 CMIP6 models and the estimated changes in summer average precipitation over Northwestern China. (The red line represents the observed region mean sea surface temperature over the tropical Indian Ocean)

图6 基于热带印度洋海温(a)和东亚副热带200 hPa纬向风(b)对夏季西北地区区域平均降水变化进行预估约束前后的散点图

Fig. 6 Scatter plot of the summer average precipitation over Northwestern China, constrained by the tropical Indian Ocean sea surface temperature (a) and East Asian subtropical 200 hPa zonal wind (b), showing the estimates after constraints versus unconstrained estimates

图7 不同变量下帕累托最优集合方案及基于该变量优选所得模式 (a)西北地区夏季降水与热带印度洋海温的帕累托最优集合（组合1)，(b)西北地区夏季降水与东亚副热带200 hPa纬向风的帕累托最优集合（组合2)，(c)基于西北地区夏季降水与热带印度洋海温以及东亚副热带200 hPa纬向风3个变量的帕累托最优集合（组合3） 注：图中每一个点即为一个模式，其中实心点为优选模式。

Fig. 7 Optimal models obtained from the Pareto-optimal ensemble schemes. (a) The Pareto-optimal ensemble of summer precipitation in the Northwest region and tropical Indian Ocean sea surface temperature, (b) the Pareto-optimal ensemble of summer precipitation in the Northwest region and East Asian subtropical 200 hPa zonal wind, (c) the Pareto-optimal ensemble based on three variables, namely, summer precipitation in the Northwest region, tropical Indian Ocean sea surface temperature, and East Asian subtropical 200 hPa zonal wind. (Each point in the graph represents a model, with filled legends indicating the optimal models)

图8 基于不同方案的未来21世纪末期（2081—2100年）夏季西北地区区域平均降水变化预估结果的箱须图 注：箱体的上下边界分别表示预估结果的75%和25%分位数，实线的上下边界分别表示90%和10%分位数，箱体内黑线为中位数。

Fig. 8 Boxplots of future summer precipitation estimates for the Northwest region at the end of the 21st century based on different schemes. (The upper and lower boundaries of the box represent the 75th and 25th percentiles of the estimated results, while the upper and lower limits of the box represent the 90th and 10th percentiles, the black line inside the box represents the median)

图9 基于三变量帕累托最优集合方案的 21世纪末期（2081—2100年）西北地区夏季降水相比于历史时期（1995—2014年）的相对变化(a)及其与未经约束预估的差值(b)

Fig. 9 Relative change in summer precipitation in the Northwest region at the end of the 21st century (2081-2100) compared to the historical period (1995-2014) based on the three-variable Pareto optimal ensemble scheme (a), along with the difference from the unconstrained estimate (b)