Study on Statistical–Dynamical Downscaling for Precipitation in the Heihe River Basin
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摘要: 依据区域气候模式RIEMS2.0输出的3 km高分辨率数据和站点降水记录分析了中国西北黑河流域降水的动力降尺度和统计—动力降尺度问题，检验了多种因子组合下多元线性回归（MLR）和贝叶斯模式平均（BMA）降尺度模型，评估了降尺度降水的均方根误差、相关系数、方差百分率及“负降水”偏差率等方面的统计特征。结果表明，动力降尺度降水相关系数最高，误差也最大，降水方差达到观测值的1.5～2倍；除相关系数外，统计—动力降尺度模型的几个统计特征均最优，纯统计模型次之。检验表明，仅用700 hPa位势高度场、经向风和比湿等构建的统计降尺度模型估计的站点降水相关系数较低，均方根误差也较大。当在统计降尺度模型中引入模式降水因子后站点降水的估计得到明显改善，其中MLR类模型的降水相关系数和方差百分率均明显高于BMA类模型，均方根误差二者相当，但前者“负降水”出现频次明显大于后者，“负降水”偏差主要出现在降水稀少的冬半年及黑河中、下游干旱或极端干旱区，上游出现频率较低，其中MLR类模型“负降水”出现频次明显高于BMA类模型，后者仅出现在黑河中、下游地区。包含模式降水因子的统计—动力降尺度模型能减少“负降水”出现的频次。此外，降尺度模型估计降水的统计特征随季节变化，其中7种降尺度模型估计的站点降水误差与站点气候降水量成比例，但相对误差与之相反。这些评估结果表明，即使用高分辨率动力降尺度估计干旱区站点降水也存在明显偏差，需要结合统计降尺度模型进一步降低站点降水估计的不确定性。Abstract: This paper focuses on the dynamic and statistical–dynamical downscaling techniques for estimating the precipitation at the stations in the Heihe River basin of Northwest China based on local observations at 14 sites and the outputs from RIEMS2.0 (Regional Climate Model) with a grid resolution of 3×3 km. The precipitation estimated further using MLR (multiple linear regression) and BMA (Bayesian Model Average) with different factor combinations is tested on the assessment indices as RMSE (Root Mean Square Error), correlation coefficient, variance percent, and “negative precipitation bias” with observation. Results show that the precipitation produced by the dynamic model has the largest RMSE, the most significant coherence, and a considerably larger variance than the observation by a factor of 1.5–2. Except for correlation coefficients, the statistical–dynamical downscaling models are optimal, and the statistical models are between statistical–dynamical models and dynamic model. The test shows that the correlation coefficient of the statistical downscaling models constructed with 700-hPa geopotential height field, meridional wind, and specific humidity is lower, and the RMSE is larger. The statistic indices were improved when the precipitation factor was introduced into the statistically downscaling models. The correlation coefficient and variance percentage of MLR models are considerably higher than BMA models, the RMSE of the two types of models is close in value, but the bias of negative precipitation of the former is significantly higher than that of the latter. The negative precipitation produced by the statistically downscaling models appears mainly in the cold season or dry and arid lands, such as the lower reaches of the river, of which the “negative precipitation” frequency decreases if the model precipitation is added as a factor in the downscaling models. Moreover, the statistical assessment of the monthly precipitation estimated from the downscaling models reveals that the four indices would evolve with season, in which the errors of dynamical downscaling are also the largest among the downscaling models, and their relative errors are smaller in summer and larger in winter, particularly in lower reaches of the river. This implies that precipitation downscaling in the dry land or dry season is still difficult for climate study. These results show a significant bias in dynamic downscaling, even for the high-resolution regional climate model. Therefore, the regional model must be combined with statistic downscaling to form a statistical–dynamical model for decreasing the precipitation uncertainties estimated in the river basin.
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图 1 黑河流域14个气象站点的分布。数字1～14分别表示14个气象站点（额济纳旗、拐子湖、玉门镇、鼎新、金塔、酒泉、高台沟、阿拉善右旗、托勒、野牛沟、张掖、祁连、山丹、永昌）
Figure 1. Distribution of 14 meteorological observatories in the Heihe River basin. Numbers 1–14 represent 14 meteorological observatories (Eji’ naqi, Guaizihu, Yumenzhen, Dingxin, Jinta, Jiuquan, Gaotaigou, Alashanyouqi, Tuole, Yeniugou, Zhangye, Qilian, Shandan, Yongchang)
图 2 1980～2012年模式模拟与观测的黑河流域站点年降水量均方根误差（单位：mm）：（a）上游；（b）中游；（c）下游；（d）区域站点平均
Figure 2. RMSE (root mean square error, units: mm) of the annual precipitation between simulated and observed at the stations in the Heihe River basin during 1980–2012: (a) Upper reaches; (b) middle reaches; (c) lower reaches; (d) average over the regional stations
图 3 1980～2012年降尺度模型估计与观测的黑河流域站点年降水量的相关系数：（a）上游；（b）中游；（c）下游；（d）区域站点平均
Figure 3. Correlation coefficients between the precipitation estimated by downscaling models and the observation at the stations in the Heihe River basin during 1980–2012: (a) Upper reaches; (b) middle reaches; (c) lower reaches; (d) average over regional stations
图 4 1980～2012年降尺度模型估计的与观测的黑河流域站点年降水量方差百分率：（a）上游；（b）中游；（c）下游；（d）区域站点平均
Figure 4. Percentage of the precipitation variance between estimated by downscaling models and observed at the stations in the Heihe River basin during 1980–2012: (a) Upper reaches; (b) middle reaches; (c) lower reaches; (d) average over regional stations
图 5 1980～2012年降尺度模型估计的与观测的黑河流域月降水量均方根误差（左）、相对均方根误差（右）：（a、b）上游；（c、d）中游；（e、f）下游
Figure 5. RMSE (left) and relative RMSE (right) of monthly precipitation between estimated by downscaling models and observed at the stations in the Heihe River basin during 1980–2012: (a, b) Upper reaches; (c, d) middle reaches; (e, f) lower reaches
图 6 1980～2012年降尺度模型估计的与观测的黑河流域月降水量相关系数：（a）上游；（b）中游；（c）下游
Figure 6. Correlation coefficients of the monthly precipitation between estimated by downscaling models and observed at the stations in the Heihe River basin during 1980–2012: (a) Upper reaches; (b) middle reaches; (c) lower reaches
图 7 1980～2012年降尺度模型估计的与观测的黑河流域月降水量方差百分率：（a）上游；（b）中游；（c）下游
Figure 7. Percentage of monthly precipitation variance estimated by downscaling models and observed in the Heihe River basin during 1980–2012: (a) Upper reaches; (b) middle reaches; (c) lower reaches
图 8 1980～2012年降尺度模型估计的黑河流域站点平均月降水量“负降水”次数：（a）上游；（b）中游；（c）为下游
Figure 8. Negative monthly precipitation number estimated by downscaling models averaged in the Heihe River basin during 1980–2012: (a) Upper reaches; (b) middle reaches; (c) lower reaches
表 1 黑河流域气象观测站点信息
Table 1. Information of meteorological stations in the Heihe River basin
序号 站点编号 站点名称 站点位置 海拔高度/m 年平均降水量/mm 1 52267 额济纳旗 （101.0°N，42.0°E） 940.5 31.8 2 52378 拐子湖 （102.3°N，41.4°E） 960.0 39.9 3 52436 玉门镇 （97.0°N，40.3°E） 1526.0 66.7 4 52446 鼎新 （99.5°N，40.3°E） 1177.4 53.3 5 52447 金塔 （98.9°N，40°E） 1270.5 62.1 6 52533 酒泉 （98.5°N，39.8°E） 1477.2 87.8 7 52546 高台沟 （99.8°N，39.4°E） 1332.2 110.4 8 52576 阿拉善右旗 （101.7°N，39.2°E） 1510.1 115.4 9 52633 托勒 （98.4°N，39.0°E） 3367.0 292.9 10 52645 野牛沟 （99.6°N，38.4°E） 3320.0 412.5 11 52652 张掖 （100.4°N，38.9°E） 1482.7 130.5 12 52657 祁连 （100.3°N，38.2°E） 2787.4 406.8 13 52661 山丹 （101.1°N，38.8°E） 1764.6 199.4 14 52674 永昌 （102.0°N，38.2°E） 1976.9 201.7 
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表 2 统计和动力降尺度模型的基本信息
Table 2. Information of statistical–dynamical downscaling models
序号 模型名称 方法 因子 1 BMA1 BMA h700 (3PCs)、v700、q700 2 MLR1 MLR h700 (3PCs)、v700、q700 3 BMA2 BMA 模式降水(3PCs)、h700 (3PCs)、v700、q700 4 MLR2 MLR 模式降水(3PCs)、h700 (3PCs)、v700、q700 5 BMA3 BMA 模式站点降水、h700 (3PCs)、v700、q700 6 MLR3 MLR 模式站点降水、h700 (3PCs)、v700、q700 7 RIEMS 动力降尺度 模式站点降水（双线性插值获得） 注： h700 (3PCs)和模式降水（3PCs）分别表示站点周围49个格点模式700 hPa位势高度场的前3个主分量和站点周围49个格点模式降水的前3个主成分。v700和q700分别表示模式700 hPa站点上空格点四个角平均值的经向风和比湿。
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