﻿ 强度尺度分解方法在气候温度场检验中的应用 强度尺度分解方法在气候温度场检验中的应用
 大气科学  2016, Vol. 40 Issue (6): 1117-1126 PDF

1 中国科学院大气物理研究所国际气候与环境科学中心, 北京 100029
2 中国科学院大学, 北京 100049
3 南京信息工程大学气象灾害预报预警与评估协同创新中心, 南京 210044

Application of the Intensity-Scale Technique for Verification of Climatological Surface Temperature Simulation
LI Juan1,2, ZENG Xiaodong1,2,3, CHEN Hong1, CAI Qifa1
1 International Center for Climate and Environment Sciences, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
2 University of Chinese Academy of Sciences, Beijing 100049
3 Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disaster, Nanjing University of Information Science & Technology, Nanjing 210044
Abstract: The applicability of the intensity-scale approach for the verification of climate simulation is investigated in this paper.The monthly mean surface temperature simulated by a new generation of climate system model is taken as an example.While the traditional statistical verification cannot fully reflect the spatial information of the simulation error, the intensity-scale approach can quantitatively assess the spatial information of the simulation by calculating the mean square errors and skill scores of the spatial components with different wavelet scales and intensities.For example, in East Asia, the skill score of temperature threshold 230 K and spatial scale 1600 km is very low for simulations of both January of single year and multi-year average.This study shows that the intensity-scale approach is suitable for the verification of climatological temperature simulation, and can provide quantitative spatial information of the error.
Key words: The intensity-scale approach      Spatial verification      Surface temperature
1 引言

2 强度尺度分解方法原理 2.1 二进制误差分解

 ${I_X} = \left\{ {\begin{array}{*{20}{c}} 1&{X > u}\\ 0&{X \le u} \end{array}} \right.,{I_Y} = \left\{ {\begin{array}{*{20}{c}} 1&{Y > u}\\ 0&{X \le u} \end{array}} \right..$ (1)

 $Z = {I_Y} - {I_X}.$ (2)

 $Z = \sum\limits_{l = 1}^{L + {\rm{1}}} {{Z_l}} .$ (3)
2.2 二进制均方误差

 ${E_u} = \sum\limits_{l = 1}^{L + 1} {{E_{u,{\rm{ }}l}}} .$ (4)

 ${P_{u,{\rm{ }}l}} = (\frac{{{E_{u,{\rm{ }}l}}}}{{{E_u}}}) \times 100\% .$ (5)
2.3 强度尺度技巧评分

 ${E_{u,{\rm{rand}}}} \sim B \cdot s \cdot (1 - s) + s \cdot (1 - B \cdot s),$ (6)

 ${S_{u,l}} = 1 - \frac{{{E_{u,l}}}}{{{E_{u,{\rm{rand}}}}/(L + 1)}}.$ (7)

3 强度尺度分解方法在模拟评估中的应用 3.1 数据说明及区域选择

3.2 气候态及个例检验分析

 图 1 (a) CSM模式模拟的气候态地表温度；(b) CRUNECP观测的气候态地表温度；(c)模式模拟与观测的气候态地表温度之差。(d)、(e)、(f)同(a)、(b)、(c)，但为1982年1月平均的地表温度。单位：K Figure 1 (a) Climatological surface temperature simulated by CSM (Climate System Model developed by Institute of Atmospheric Physics, Chinese Academy of Sciences) during 1982-2010. (b) As in Fig. a, but for CRUNCEP (Climatic Research Unit and National Centers for Environmental Prediction) data. (c) The differences climatological surface temperature between CSM results and CRUNCEP data. (d, e, f) As in Figs. a, b, c, but for mean surface temperature of Jan 1982. Units: K
3.2.1 统计分析方法

 $r = \frac{{\sum\nolimits_{i = 1}^N {({M_i}} - \overline M )({O_i} - \overline O )}}{{\sqrt {\sum\nolimits_{i = 1}^N {{{({M_i} - \overline M )}^2}} } \sqrt {\sum\nolimits_{i = 1}^N {{{({O_i} - \overline O )}^2}} } }},$ (8)
 ${E_{{\rm{RMSE}}}} = \sqrt {\frac{{\sum\nolimits_{i = 1}^N {{{({M_i} - {O_i})}^2}} }}{N}} ,$ (9)

3.2.2 强度尺度分解方法

 图 2 粗阈值各空间尺度上的强度尺度技巧评分：(a)1982年；(b)气候态 Figure 2 Two-dimension plots of intensity-scale skill scores as a function of coarse threshold and spatial scale: (a) 1982; (b) climate state

 图 3 阈值230 K时的模拟与观测的二进制误差场 Figure 3 Binary field differences between the simulations and observations for the threshold of 230 K

 图 4 230 K阈值时二进制误差场经由二维离散Haar小波分解后获得的母小波成员 Figure 4 Mother wavelet scale components obtained from the binary error field, which is decomposed by a two-dimensional discrete Haar wavelet for the threshold of 230 K

 图 5 加密阈值各空间尺度上的强度尺度技巧评分 Figure 5 Two-dimension plot of the intensity-scale skill score as a function of fine threshold and spatial scale

 图 6 阈值225、228、229、230、231、235 K时模拟与观测的二进制误差场 Figure 6 Binary field differences between the simulations and observations for thresholds of 225, 228, 229, 230, 231, 235 K
3.3 强度尺度分解方法在多年模拟检验中的应用

 图 7 阈值230 K时不同空间尺度上的盒须图(1982~2010年) Figure 7 Box-whisker plot of the skill score versus error spatial scale during the period 1982-2010 for the threshold of 230 K
3.4 强度尺度分解方法在不同区域不同月份的检验应用

 图 8 1982年6月的月平均地表温度(单位：K)：(a) CSM模式模拟；(b) CRUNECP观测；(c)模拟与观测之差 Figure 8 Monthly mean surface temperature (units: K) of June 1982: (a) CSM results; (b) CRUNCEP data; (c) the differences between CSM results and CRUNCEP data

 图 9 加密阈值各空间尺度上的强度尺度技巧评分 Figure 9 Two-dimension plot of the intensity-scale skill score as a function of fine threshold and spatial scale
4 总结和讨论

(1)以1982年1月(亚洲东部)为例，应用三种方法分别对检验区域的地表月平均温度模拟场进行评估，可以得出：目测比较明显看出模拟场230 K范围线与观测场有较大的误差，经向方向的误差范围大约是在1300 km左右；统计分析方法仅能得出两个场具有较高的正相关，误差较大，无从反映误差场的空间信息；应用强度尺度分解方法后，可以发现230 K阈值在尺度5(大约1600 km)上模拟技巧非常低，定量地反映了误差场的空间信息，与目测结论基本一致。

(2)应用强度尺度分解方法对相同检验区域相同月份1982~2010年29年的模拟情况进行检验评估分析，发现在这29年中大部分年份都出现了与1982年相似的误差空间信息，即230 K阈值在尺度5(大约1600 km)上模拟技巧相对其他尺度明显低。这个误差在29年中大部分年份都出现了，说明模式对这个区域的模拟有待改进。

(3)改变检验区域和检验月份，通过强度尺度分解方法也定量得到了与目测比较相一致的误差空间信息。

 [] Briggs W M, Levine R A. 1997. Wavelets and field forecast verification[J]. Mon.Wea.Rev., 125(6) : 1329–1341 DOI:10.1175/1520-0493(1997)125<1329:WAFFV>2.0.CO; 2 [] Casati B, Ross G, Stephenson D B. 2004. A new intensity-scale verificaton approach for the verification of spatial precipitation on forecasts[J]. Meteor.Appl., 11(2) : 141–154 DOI:10.1017/S1350482704001239 [] Casati B. 2010. New developments of the intensity-scale technique within the spatial verification methods intercomparison project[J]. Wea.Forecasting, 25(1) : 113–143 DOI:10.1175/2009WAF2222257.1 [] Csima G, Ghelli A. 2008. On the use of the intensity-scale verification technique to assess operational precipitation forecasts[J]. Meteor.Appl., 15(1) : 145–154 DOI:10.1002/met.49 [] Dickinson R E, Oleson K W, Bonan C, et al. 2006. The community land model and its climate statistics as a component of the community climate system model[J]. J.Climate, 19(11) : 2302–2324 DOI:10.1175/JCLI3742.1 [] Jolliffe I T, Stephenson D B.2003. Forecast Verification:A Practitioner's Guide in Atmospheric Science[M]. New York: Wiley and Sons : 240pp . [] 孔荣, 王建捷, 梁丰, 等. 2010. 尺度分解技术在定量降水临近预报检验中的应用[J]. 应用气象学报, 21(5) : 535–544. Kong Rong, Wang Jianjie, Liang Feng, et al. 2010. Applying scale decomposition method to verification of quantitative precipitation nowcasts[J]. J.Appl.Meteor.Sci.(in Chinese), 21(5) : 535–544 DOI:10.11898/1001-7313.20100503 [] Kwiatkowski L, Halloran P R, Mumby P J, et al. 2014. What spatial scales are believable for climate model projections of sea surface temperature?[J]. Climate Dyn., 43(5-6) : 1483–1496 DOI:10.1007/s00382-013-1967-6 [] Liu Hailong, Zhang Xuehong, Li Wei, et al. 2004. An eddy-permitting oceanic general circulation model and its preliminary evaluation[J]. Adv.Atmos.Sci., 21(5) : 675–690 DOI:10.1007/BF02916365 [] Liu Hailong, Lin Pengfei, Yu Yongqiang, et al. 2012. The baseline evaluation of LASG/IAP climate system Ocean Model (LICOM) version 2[J]. Acta Meteor.Sinica, 26(3) : 318–329 DOI:10.1007/s13351-012-0305-y [] Mittermaier M P. 2006. Using an intensity-scale technique to assess the added benefit of high-resolution model precipitation forecasts[J]. Atmos.Sci.Lett., 7(2) : 36–42 DOI:10.1002/asl.127 [] Picart S S, Butenschön M, Shutler J D. 2012. Wavelet-based spatial comparison technique for analysing and evaluating two-dimensional geophysical model fields[J]. Geosci.Model Dev., 5(1) : 223–230 DOI:10.5194/gmd-5-223-2012 [] Su Tonghua, Xue Feng, Zhang He. 2014. Simulating the intraseasonal variation of the East Asian summer monsoon by IAP AGCM4.0[J]. Adv.Atmos.Sci., 31(3) : 570–580 DOI:10.1007/s00376-013-3029-8 [] 孙泓川, 周广庆, 曾庆存. 2012. IAP第四代大气环流模式的耦合气候系统模式模拟性能评估[J]. 大气科学, 36(2) : 215–233. Sun Hongchuan, Zhou Guangqing, Zeng Qingcun. 2012. Assessments of the climate system model (CAS-ESM-C) using IAP AGCM4 as its atmospheric component[J]. Chinese Journal of Atmospheric Sciences (in Chinese), 36(2) : 215–233 DOI:10.3878/j.issn.1006-9895.2011.11062 [] Wang Bin, Xie Xin, Li Lijuan. 2009. A review on aspects of climate simulation assessment[J]. Adv.Atmos.Sci., 26(4) : 736–747 DOI:10.1007/s00376-009-9038-y [] 徐同, 戴建华, 李佳, 等. 2012. 强度尺度方法在模式定量降水预报检验中的应用[J]. 气象与环境科学, 35(1) : 1–7. Xu Tong, Dai Jianhua, Li Jia, et al. 2012. Applying intensity-scale approach to verification of model quantitative precipitation forecast[J]. Meteor.Environ.Sci.(in Chinese), 35(1) : 1–7 DOI:10.3969/j.issn.1673-7148.2012.01.001 [] Yan Zhengbin, Lin Zhaohui, Zhang He. 2014. The relationship between the East Asian subtropical westerly jet and summer precipitation over East Asia as simulated by the IAP AGCM4.0[J]. Atmos.Oceanic Sci.Lett., 7(6) : 487–492 DOI:10.3878/AOSL20140048 [] 张贺, 林朝晖, 曾庆存. 2009. IAP AGCM-4动力框架的积分方案及模式检验[J]. 大气科学, 33(6) : 1267–1285. Zhang He, Lin Zhaohui, Zeng Qingcun. 2009. The computational scheme and the test for dynamical framework of IAP AGCM-4[J]. Chinese Journal of Atmospheric Sciences (in Chinese), 33(6) : 1267–1285 DOI:10.3878/j.issn.1006-9895.2009.06.13 [] Zhang He, Zhang Minghua, Zeng Qingcun. 2013. Sensitivity of simulated climate to two atmospheric models:Interpretation of differences between dry models and moist models[J]. Mon.Wea.Rev., 141(5) : 1558–1576 DOI:10.1175/MWR-D-11-00367.1