﻿ 基于RegCM4模式的中国区域日尺度降水模拟误差订正 基于RegCM4模式的中国区域日尺度降水模拟误差订正
 大气科学  2017, Vol. 41 Issue (6): 1156-1166 PDF

1 中国气象科学研究院, 北京 100081
2 中国气象局国家气候中心, 北京 100081
3 中国科学院大气物理研究所气候变化研究中心, 北京 100029
4 中国科学院大学, 北京 100049
5 盖州市气象局, 盖州 115200

Bias Correction of Daily Precipitation Simulated by RegCM4 Model over China
TONG Yao1,2,5, GAO Xuejie3,4, HAN Zhenyu2, XU Ying2
1 Chinese Academy of Meteorological Science, Beijing 100081
2 National Climate Center, China Meteorological Administration, Beijing 100081
3 Climate Change Research Center, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
4 University of Chinese Academy of Sciences, Beijing 100049
5 Gaizhou Meteorological Bureau, Gaizhou 115200
Abstract: There are biases in climate model simulations compared to the observations, which makes it hard to directly use model simulations to drive the impact models. In the present study, the authors try to correct biases in daily precipitation simulated by a regional climate model (RegCM4.4) based on probability distribution (Quantile-Mapping) over China. Transfer functions are established from the reference period 1991-2000, and then applied to the period 2001-2010 to validate the performance of the method. Six different methods using parametric or nonparametric transformations are employed and compared to observations. Results show that all the six methods can effectively reduce the biases of the precipitation simulated, the RQUANT (Non-parametric quantile mapping using robust empirical quantiles) is found to perform better than other methods. Further analysis shows that RQUANT can significantly improve the simulation of the mean precipitation and the interannual variability and extreme events.
Key words: Regional climate model      Daily precipitation      Bias correction      Transfer function
1 引言

2 模式、数据与方法 2.1 模式和数据

2.2 分位数订正方法及传递函数的建立和选取

 ${x_{{\rm{bc}}}} = F({x_{\rm{m}}}),$ (1)

（1）参数传递函数PTFe。在参照时段中利用公式：

 ${P_{\rm{o}}} = (a + b{P_{{\rm{m1}}}})\left[ {1 - \exp (- {P_{{\rm{m1}}}}/\tau)} \right]$ (2)

 ${P_{{\rm{bc}}}} = (a + b{P_{{\rm{m2}}}})\left[ {1 - {\rm{exp}}(- {P_{{\rm{m2}}}}/\tau)} \right],$ (3)

（2）参数传递函数PTFl。与方法（1）类似，但利用下述公式计算系数：

 ${P_{\rm{o}}} = a + b{P_{{\rm{m1}}}}.$ (4)

（3）参数传递函数PTFp。与方法（1）类似，但利用下述公式计算系数：

 ${P_{\rm{o}}} = bP_{{\rm{m1}}}^{\rm{c}}.$ (5)

（4）非参数转换QUANT。在参照时段中使原始输出数据的经验累积概率分布函数尽可能与观测相近，即：

 ${F_{{\rm{cdfm}}1}}({x_{m1}}) = {F_{{\rm{cdfo}}}}({x_o}).$ (6)

 ${F_{{\rm{cdfo}}}}({x_{{\rm{bc}}}}) = {F_{{\rm{cdfm2}}}}({x_{{\rm{m2}}}}),$ (7)

（5）非参数转换RQUANT。该方法与QUANT类似，所不同的是使用局部线性最小二乘回归对模式与观测的经验CDF进行拟合，拟合传递值之间的插值类型选择线性插值。

（6）非参数转换SSPLIN。该方法与QUANT类似，所不同的是使用三次光滑样条拟合观测与模式数据之间的分位数关系，其中样条曲线的光滑参数用广义交叉验证的方法确定。

 图 1 基于格点（39.75°N，116.25°E）的夏季日降水量建立的传递函数及订正结果：（a）观测结果及6种方法所建立的传递函数，横坐标为模式原始输出值，黑色圆圈对应的纵坐标为观测值，各曲线对应的纵坐标为订正值；（b）RQUANT方法（红色）和SSPLIN方法（紫色）的订正结果，横坐标为订正值，纵坐标为观测值 Figure 1 Transfer functions and simulated/bias corrected precipitation at grid point (39.75°N, 116.25°E) in JJA: (a) The observations and transfer functions of six methods; (b) the bias corrected precipitation by RQUANT (red) and SSPLIN (purple) methods. In Fig. a, the x-axis represents simulations, and y-axis represents observations for the black circles and bias corrected simulations for the curves. In Fig. b, the x-and y-axis represent simulation and observation, respectively

2.3 分析方法

 ${r_{{\rm{MAE}}}} = \frac{1}{n}\sum\limits_{i = 1}^n {\left| {{y_i} - \left. {{x_i}} \right|{\rm{ }}} \right.},$ (8)
 ${r_{{\rm{RMSE}}}} = \sqrt {\frac{1}{n}\sum\limits_{i = 1}^n {{{({y_i} - {x_i})}^2}} } {\rm{ }},$ (9)

 ${C_{\rm{V}}} = \frac{{\sqrt {\frac{1}{n}\sum\limits_{i = 1}^n {{{({X_i} - \bar X)}^2}} } }}{{\bar X}}{\rm{ }},$ (10)

3 结果 3.1 不同误差订正方法的比较

 图 2 验证时段中，中国区域平均的冬、夏季不同百分位数区段（0~100%）及总降水量（TOT）的模拟和不同订正方法结果与观测数据的MAE及RMSE：（a）冬季MAE；（b）冬季RMSE；（c）夏季MAE；（d）夏季RMSE。MAE和RMSE在夏季90%~100%区段的模式模拟值9.4和16.0，因超出现有纵坐标范围而未给出 Figure 2 The mean MAE and RMSE in the simulated and bias corrected precipitation by different methods compared to observations in DJF and JJA for different percentiles (0–100%) and the total (TOT): (a) MAE in DJF; (b) RMSE in DJF; (c) MAE in JJA; (d) RMSE in JJA. The MAE and RMSE of the model simulation for 90%–100% (9.4 and 16.0, respectively) are not shown due to the values exceeding y-axis range

3.2 RQUANT方法的订正结果 3.2.1 平均降水

 图 3 验证时段中，中国地区的平均降水量（单位：mm）：（a）冬季观测；（b）夏季观测；（c）冬季模拟；（d）夏季模拟；（e）冬季订正后结果；（f）夏季订正后结果 Figure 3 Mean precipitation over China during the validation period: (a) Observations in DJF; (b) observations in JJA; (c) simulation in DJF; (d) simulation in JJA; (e) simulation after bias correction in DJF; (f) simulation after bias correction in JJA

 图 4 验证时段中，中国地区平均降水量的相对偏差：（a）冬季模式模拟；（b）夏季模式模拟；（c）冬季订正结果；（d）夏季订正结果 Figure 4 Relative biases of mean precipitation over China during the validation period: (a) Simulation in DJF; (b) simulation in JJA; (c) bias correction in DJF; (d) bias correction in JJA

3.2.2 年际变率

 图 5 同图 3，但为降水的变异系数 Figure 5 As in Fig. 3, but for coefficient variations
3.2.3 极端事件

 图 6 验证时段中，中国地区的连续干旱日数（CDD，单位：d）和强降水指数（SDII，单位：mm d-1）分布：（a）观测的CDD；（b）观测的SDII；（c）模式模拟的CDD；（d）模式模拟的SDII；（e）订正后的CDD结果；（f）订正后的SDII结果 Figure 6 The maximum number of consecutive dry days (CDD, units: d) and simple daily intensity index (SDII, units: mm d-1) over China during the validation period: (a) CDD from observations, (b) SDII from observations, (c) CDD from simulation, (d) SDII from simulation, (e) CDD after the bias correction, (f) SDII after the bias correction

4 结论和讨论

（1）不同误差订正方法对于平均降水均有很好的订正效果，使得模式模拟与观测值之间的误差大大缩小。各方法对不同百分位区间的降水也都有较好的订正效果，但订正效果在高段降水较差，未来需要对这一区段单独进行订正。

（2）在各种方法中，RQUANT相对更好一些，除平均降水外，同时有效地改进了模式对年际变率和极端事件的模拟结果。

（3）在使用误差订正方法时，应注意观测资料的可靠性，在一些因为缺少台站观测或观测误差较大的地区，应用误差订正可能会取得不好的结果。