1.兰州大学大气科学学院，兰州 730000;2.中国科学院东亚区域气候—环境重点实验室，中国科学院大气物理研究所，北京 100029;3.香港天文台，香港 999077;4.甘肃省天水市气象局，甘肃天水 741000
1.College of Atmospheric Sciences, Lanzhou University, Lanzhou 730000;2.Key Laboratory of Regional Climate-Environment for Temperate East Asia, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;3.Hong Kong Observatory, Hong Kong 999077;4.Tianshui Meteorology Office, Tianshui, Gansu Province 741000
National Natural Science Foundation of China Grants 41475075 and 41675087;National Key Research and Development Program of China Grant 2016YFA0600400National Natural Science Foundation of China (Grants 41475075 and 41675087), National Key Research and Development Program of China (Grant 2016YFA0600400)
借助英国气候研究所（Climate Research Unit, CRU）全球陆地格点分析数据集（CRU TS v4.0）月降水资料和24个国际耦合模式比较计划第五阶段（Coupled Model Intercomparison Project Phase 5, CMIP5）模式历史气候模拟及RCP4.5情景下的降水预估数据，设计了多种回归方案并对模式降水预估偏差进行订正。这些方案包括一元回归、一元对数回归、一元差分回归、一元对数差分回归、多元回归、多元对数回归、多元差分回归、多元对数差分回归和简单移除气候漂移等。2006～2015年中国大陆模式降水预估的订正结果表明，一元回归订正法普遍优于多元回归订正和扣除气候漂移订正法，其中一元对数回归法的效果最好，其降水距平同号率（Anomaly Rate, AR）和降水距平百分率相关系数（Anomaly Percentage Correlation Coefficient, APCC）最高，分别达到69%和0.5；而降水距平相关系数（Anomaly Correlation Coefficient, ACC）最高的是一元对数差分回归法。不同回归订正法所得预估结果的距平同号格点分布显示，一元对数回归法在北方优于南方，而一元差分（年际增量）或对数差分回归法在南方优于北方。这直接导致在中国南方区域（95°E以东，35°N以南）一元对数回归或多元对数回归订正结果的AR、ACC和APCC均低于对应的差分/对数差分回归法，在北方和西部地区则与此相反。因此，模式降水的回归订正方案具有区域性，这可能源于不同区域降水序列统计性质的差异。用区域组合回归订正法，即在南方用一元差分回归订正，其余地区用一元对数回归订正，其降水预估场的AR提高到72%，但ACC和APCC均略有下降，原因是差分回归订正增加了预估降水场的方差。对RCP4.5情景下2016～2045年24个模式集合平均降水预估的组合回归订正结果显示，相对于1976～2005年平均，未来30年降水异常大致呈南北少，中间多的格局，其中长江中下游、江南中西部、西南东北部、华南沿海和海南省等地降水偏少10%～20%，淮河流域、三江源区和台湾省降水偏多10%～40%，西北东部、华北和东北大部降水正常或略偏少。从降水百分率方差看，模式群的离散度（不确定度）呈现东部小，西部大的分布特征，说明模式预估的西北中部和青藏高原西部等降水偏少区的不确定性较大；而河套北部、华北南部和江南东部等地对应于2006～2015年检验期的“盲区”（模式与观测降水距平反号），其降水预估参考价值可能不大，需要引入他法加以改进。
Based on monthly precipitation data from CRU TS v4.0 (Climatic Research Unit Timeseries version 4.0), output of the CMIP5 (Coupled Model Intercomparison Project Phase 5) historical experiments and RCP4.5 (Representative Concentration Pathway 4.5) scenario from 24 models, a variety of simple and multiple regression methods were designed to bias-correct projected precipitation for China. These included simple regression (SR), simple regression with log-transformed rainfall (SR-Log), simple regression with year-to-year rainfall increment as predictand (SR-Increment), simple regression with year-to-year log-transformed rainfall increment as predictand (SR-Log-Increment), multiple regression (MR), multiple regression with log-transformed rainfall (MR-Log), multiple regression with year-to-year rainfall increment as predictand (MR-Increment), multiple regression with year-to-year log-transformed rainfall increment as predictand (MR-Log-Increment), and simple removal of climate drift (RCD). Bias-corrected results for projected precipitation over mainland China for 2006-2015 showed that univariate regression correction methods were generally better than multi-variate methods and simple RCD. SR-Log performed best, with rate of precipitation anomaly having the same sign with observation (AR) and precipitation anomaly percentage correlation coefficient (APCC) were the highest, reaching 69% and 0.5, respectively. On the other hand, SR-log-Increment obtained the highest correlation coefficient of precipitation anomaly (ACC) among the different methods. The distributions of precipitation anomaly with the same sign with respect to observation, using different bias-correction methods, showed that the SR-Log performed better in the north than in the south. To the contrary, SR-Increment and SR-Log-Increment performed better in the south than in the north. As a result, the AR, ACC and APCC of the SR-Log or MR-Log were lower than those of the SR-Log-Increment and MR-Log-Increment over southern China (east of 95°E and south of 35°N), while the opposite was true for northern and western China. Therefore, the best regression correction method for model precipitation was regional-dependent, possibly reflecting the differences in statistical properties of precipitation in different regions. Using synthesis of regional regression models, i.e., using SR-Increment in the southern region and SR-Log for the rest of China, the AR of projected precipitation for 2006-2015 improved to 72% while ACC and APCC declined slightly, as the increment regression method increased the variance of the projected precipitation. Projected precipitation for 2016-2045 was bias-corrected by the synthesis of regional regressions method. The results showed that, compared with the average of 1976-2005, the precipitation anomaly pattern for the next 30 years would display a “dry in the north and south, wet in the middle” pattern. Precipitation would decrease by 10%-20% in the middle and lower Yangtze River, middle and west of the regions south of the Yangtze River, the northeastern part of southwestern China, and the coastal regions of southern China and Hainan; precipitation would increase by 10%-40% in the Huai River basin, three rivers source regions, and Taiwan. Minimal changes, or slightly less precipitation was projected over the eastern part of northwestern China, northern China, and most of northeastern China. According to the variance of precipitation anomaly percentage, the spread (uncertainty) of the model group was smaller in the east and larger in the west. It indicated that the projected less precipitation areas were more uncertain such as in the central northwestern, and western Qinghai-Tibet Plateau. In addition, the northern part of the Hetao area, the southern part of northern China, and the eastern part of the south of the Yangtze River corresponded to the “obscured areas,” where the precipitation anomaly in the projections and observations showed opposite signs for the verification period 2006-2015. As such, the projected precipitation over these regions may not be of value. Consequently, alternative methods need to be developed in the future for further improvement.