Advanced Search
Article Contents

Attributing Analysis on the Model Bias in Surface Temperature in the Climate System Model FGOALS-s2 through a Process-Based Decomposition Method

Fund Project:

doi: 10.1007/s00376-014-4061-z

  • This study uses the coupled atmosphere-surface climate feedback-response analysis method (CFRAM) to analyze the surface temperature biases in the Flexible Global Ocean-Atmosphere-Land System model, spectral version 2 (FGOALS-s2) in January and July. The process-based decomposition of the surface temperature biases, defined as the difference between the model and ERA-Interim during 1979-2005, enables us to attribute the model surface temperature biases to individual radiative processes including ozone, water vapor, cloud, and surface albedo; and non-radiative processes including surface sensible and latent heat fluxes, and dynamic processes at the surface and in the atmosphere. The results show that significant model surface temperature biases are almost globally present, are generally larger over land than over oceans, and are relatively larger in summer than in winter. Relative to the model biases in non-radiative processes, which tend to dominate the surface temperature biases in most parts of the world, biases in radiative processes are much smaller, except in the sub-polar Antarctic region where the cold biases from the much overestimated surface albedo are compensated for by the warm biases from non-radiative processes. The larger biases in non-radiative processes mainly lie in surface heat fluxes and in surface dynamics, which are twice as large in the Southern Hemisphere as in the Northern Hemisphere and always tend to compensate for each other. In particular, the upward/downward heat fluxes are systematically underestimated/overestimated in most parts of the world, and are mainly compensated for by surface dynamic processes including the increased heat storage in deep oceans across the globe.
  • 加载中
  • Bao Q., G. X. Wu, Y. M. Liu, J. Yang, Z. Z. Wang, and T. J. Zhou, 2010: An introduction to the coupled model FGOALS1.1-s and its performance in East Asia. Adv. Atmos. Sci.,27, 1131-1142, doi: 10.1007/s00376-010-9177-1.
    Bao Q., Coauthors, 2013: The flexible global ocean-atmosphere-land system model, spectral version 2: FGOALS-s2. Adv. Atmos. Sci., 30, 561-576, doi: 10.1007/s00376-012-2113-9.
    Cai M., J. H. Lu, 2009: A new framework for isolating individual feedback processes in coupled general circulation climate models. Part II: Method demonstrations and comparisons. Climate Dyn., 32, 887- 900.
    Cai M., K. K. Tung, 2012: Robustness of dynamical feedbacks from radiative forcing: 2% solar versus 2\times CO2 experiments in an idealized GCM. J. Atmos. Sci., 69, 2256- 2271.
    Cess, R. D., Coauthors, 1990: Intercomparison and interpretation of climate feedback processes in 19 atmospheric general circulation models. J. Geophys. Res., 95, 16 601- 16 615.
    Chapman W. L., J. E. Walsh, 2007: Simulations of Arctic temperature and pressure by global coupled models . J.Climate, 20, 609- 632.
    Collins, W. D., Coauthors, 2006: The community climate system model version 3 (CCSM3). J.Climate, 19, 2122- 2143.
    Dee, D. P., Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553- 597.
    Deng Y., T. W. Park, and M. Cai, 2013: Radiative and dynamical forcing of the surface and atmospheric temperature anomalies associated with the northern annular mode. J.Climate, 26, 5124- 5138.
    Dessler A. E., Z. Zhang, and P. Yang, 2008: Water-vapor climate feedback inferred from climate fluctuations, 2003-2008. Geophys. Res. Lett. , 35,L20704, doi:10.1029/2008GL 035333.
    Fu Q., K. N. Liou, 1992: On the correlated k-distribution method for radiative transfer in nonhomogeneous atmospheres. J. Atmos. Sci., 49, 2139- 2156.
    Fu Q., K. N. Liou, 1993: Parameterization of the radiative properties of cirrus clouds. J. Atmos. Sci., 50, 2008- 2025.
    Held I. M., B. J. Soden, 2000: Water vapor feedback and global warming. Annu. Rev. Energy Environ., 25, 441- 475.
    Huang W. Y., B. Wang, L. J. Li, and Y. Q. Yu, 2014: Improvements in LICOM2. Part II: Arctic Circulation. J. Atmos. Ocea. Tech., 31, 233- 245.
    Kharin V. V., F. W. Zwiers, X. B. Zhang, and G. C. Hegerl, 2007: Changes in temperature and precipitation extremes in the IPCC ensemble of global coupled model simulations. J.Climate, 20, 1419- 1444.
    Kimoto M., 2005: Simulated change of the East Asian circulation under global warming scenario. Geophys. Res. Lett.,32, doi: 10.1029/2005GL023383.
    Li G. Q., S. P. Harrison, P. J. Bartlein, K. Izumi, and I. C. Prentice, 2013a: Precipitation scaling with temperature in warm and cold climates: An analysis of CMIP5 simulations. Geophys. Res. Lett.,40, 4018-4024, doi: 10.1002/grl.50730.
    Li, L. J., Coauthors, 2013b: The flexible global ocean-atmosphere-land system model,grid-point Version 2: FGOALS-g2. Adv. Atmos. Sci., 30, 543-560, doi: 10.1007/ s00376-012-2140-6.
    Lin P. F., Y. Q. Yu, and H. L. Liu, 2013a: Long-term stability and oceanic mean state simulated by the coupled model FGOALS-s2. Adv. Atmos. Sci.,30, 175-192, doi: 10.1007/ s00376-012-2042-7.
    Lin P. F., Y. Q. Yu, and H. L. Liu, 2013b: Oceanic climatology in the coupled model FGOALS-g2: Improvements and biases. Adv. Atmos. Sci.,30, 819-840, doi: 10.1007/s00376-012-2137-1.
    Liu H. L., P. F. Lin, Y. Q. Yu, and X. H. Zhang, 2012: The baseline evaluation of LASG/IAP climate system ocean model (LICOM) version 2. Acta Meteorologica Sinica, 26, 318- 329.
    Lu J. H., M. Cai, 2009: A new framework for isolating individual feedback processes in coupled general circulation climate models. Part I: Formulation. Climate Dyn., 32, 873- 885.
    Lu J. H., M. Cai, 2010: Quantifying contributions to polar warming amplification in an idealized coupled general circulation model. Climate Dyn., 34, 669- 687.
    Oleson K.W., Coauthors, 2004: Technical description of the Community Land Model (CLM), NCAR Tech. Note TN-461+STR, 174 pp.
    Park T. W., Y. Deng, M. Cai, J. H. Jeong, and R. Zhou, 2013: A dissection of the surface temperature biases in the Community Earth System Model. Climate Dyn., doi: 10.1007/s00382-013-2029-9.
    Rand all, D. A., Coauthors, 2007: Climate Models and Their Evaluation. Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press,Cambridge, United Kingdom and New York, NY, USA, 996 pp.
    Solomon, S., Coauthors, 2007: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press,Cambridge, United Kingdom and New York, NY, USA, 996 pp.
    Sun H. C., G. Q. Zhou, and Q. C. Zeng, 2012: Assessments of the climate system model (CAS-ESM-C) using IAP AGCM4 as its atmospheric component. Chinese J. Atmos. Sci., 36, 215- 233. (in Chinese)
    Taylor P. C., M. Cai, A. Hu, J. Meehl, W. Washington, and G. J. Zhang, 2013: A decomposition of feedback contributions to polar warming amplification. J.Climate, 26, 7023- 7043.
    Wetherald R. T., S. Manabe, 1988: Cloud feedback processes in a general circulation model. J. Atmos. Sci., 45, 1397- 1416.
    Wu G. X., H. Liu, Y. C. Zhao, and W. P. Li, 1996: A nine-layer atmospheric general circulation model and its performance. Adv. Atmos. Sci., 13, 1- 18.
    Xu, S. M., Coauthors, 2013: Simulation of sea ice in FGOALS-g2: Climatology and late 20th century changes. Adv. Atmos. Sci., 30, 658-673, doi: 10.1007/s00376-013-2158-4.
    Zhang L. X., T. J. Zhou, 2014: An assessment of improvements in global monsoon precipitation simulation in FGOALS-s2. Adv. Atmos. Sci.,31, 165-178, doi: 10.1007/ s00376-013-2164-6.
    Zhou T. J., R. C. Yu, 2006: Twentieth-century surface air temperature over China and the globe simulated by coupled climate models. J.Climate, 19, 5843- 5858.
    Zhou, T. J., Coauthors, 2005: The climate system model FGOALS-s using LASG/IAP spectral AGCM SAMIL as its atmospheric component. Acta Meteorologica Sinica, 63, 702- 715.
  • [1] XIA Kun, WANG Bin, LI Lijuan, SHEN Si, HUANG Wenyu, XU Shiming, DONG Li, LIU Li, 2014: Evaluation of Snow Depth and Snow Cover Fraction Simulated by Two Versions of the Flexible Global Ocean-Atmosphere-Land System Model, ADVANCES IN ATMOSPHERIC SCIENCES, 31, 407-420.  doi: 10.1007/s00376-013-3026-y
    [2] REN Rongcai, YANG Yang, 2012: Changes in Winter Stratospheric Circulation in CMIP5 Scenarios Simulated by the Climate System Model FGOALS-s2, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1374-1389.  doi: 10.1007/s00376-012-1184-y
    [3] MA Shuangmei, ZHOU Tianjun, 2015: Precipitation Changes in Wet and Dry Seasons over the 20th Century Simulated by Two Versions of the FGOALS Model, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 839-854.  doi: 10.1007/s00376-014-4136-x
    [4] Yang YANG, Rongcai REN, 2017: On the Contrasting Decadal Changes of Diurnal Surface Temperature Range between the Tibetan Plateau and Southeastern China during the 1980s-2000s, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 181-198.  doi: 10.1007/s00376-016-6077-z
    [5] Ya WANG, Gang HUANG, Baoxiang PAN, Pengfei LIN, Niklas BOERS, Weichen TAO, Yutong CHEN, BO LIU, Haijie LI, 2024: Correcting Climate Model Sea Surface Temperature Simulations with Generative Adversarial Networks: Climatology, Interannual Variability, and Extremes, ADVANCES IN ATMOSPHERIC SCIENCES.  doi: 10.1007/s00376-024-3288-6
    [6] Xiaolei CHEN, Yimin LIU, Guoxiong WU, 2017: Understanding the Surface Temperature Cold Bias in CMIP5 AGCMs over the Tibetan Plateau, ADVANCES IN ATMOSPHERIC SCIENCES, 34, 1447-1460.  doi: 10.1007s00376-017-6326-9
    [7] Shang-Min LONG, Kai-Ming HU, Gen LI, Gang HUANG, Xia QU, 2021: Surface Temperature Changes Projected by FGOALS Models under Low Warming Scenarios in CMIP5 and CMIP6, ADVANCES IN ATMOSPHERIC SCIENCES, 38, 203-220.  doi: 10.1007/s00376-020-0177-5
    [8] REN Guoyu, DING Yihui, ZHAO Zongci, ZHENG Jingyun, WU Tongwen, TANG Guoli, XU Ying, 2012: Recent Progress in Studies of Climate Change in China, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 958-977.  doi: 10.1007/s00376-012-1200-2
    [9] Jeong-Hyeong LEE, Byungsoo KIM, Keon-Tae SOHN, Won-Tae KOWN, Seung-Ki MIN, 2005: Climate Change Signal Analysis for Northeast Asian Surface Temperature, ADVANCES IN ATMOSPHERIC SCIENCES, 22, 159-171.  doi: 10.1007/BF02918506
    [10] Kai Chi WONG, Senfeng LIU, Andrew G. TURNER, Reinhard K. SCHIEMANN, 2018: Different Asian Monsoon Rainfall Responses to Idealized Orography Sensitivity Experiments in the HadGEM3-GA6 and FGOALS-FAMIL Global Climate Models, ADVANCES IN ATMOSPHERIC SCIENCES, 35, 1049-1062.  doi: 10.1007/s00376-018-7269-5
    [11] Banglin ZHANG, Vijay TALLAPRAGADA, Fuzhong WENG, Jason SIPPEL, Zaizhong MA, 2016: Estimation and Correction of Model Bias in the NASA/GMAO GEOS5 Data Assimilation System: Sequential Implementation, ADVANCES IN ATMOSPHERIC SCIENCES, 33, 659-672.  doi: 10.1007/ s00376-015-5155-y
    [12] Pengfei LIN, Zhipeng YU, Hailong LIU, Yongqiang YU, Yiwen LI, Jirong JIANG, Wei XUE, Kangjun CHEN, Qian YANG, Bowen ZHAO, Jilin WEI, Mengrong DING, Zhikuo SUN, Yaqi WANG, Yao MENG, Weipeng ZHENG, Jinfeng MA, 2020: LICOM Model Datasets for the CMIP6 Ocean Model Intercomparison Project, ADVANCES IN ATMOSPHERIC SCIENCES, 37, 239-249.  doi: 10.1007/s00376-019-9208-5
    [13] Ruth GEEN, Marianne PIETSCHNIG, Shubhi AGRAWAL, Dipanjan DEY, F. Hugo LAMBERT, Geoffrey K. VALLIS, 2023: The Relationship between Model Biases in East Asian Summer Monsoon Rainfall and Land Evaporation, ADVANCES IN ATMOSPHERIC SCIENCES, 40, 2029-2042.  doi: 10.1007/s00376-023-2297-1
    [14] ZHU Jiawen, ZENG Xiaodong, 2015: Comprehensive Study on the Influence of Evapotranspiration and Albedo on Surface Temperature Related to Changes in the Leaf Area Index, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 935-942.  doi: 10.1007/s00376-014-4045-z
    [15] Jiang Hao, Wang Keli, 2001: Analysis of the Surface Temperature on the Tibetan Plateau from Satellite, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 1215-1223.  doi: 10.1007/s00376-001-0035-z
    [16] Laura DE LA TORRE, Luis GIMENO, Juan Antonio A\~NEL, Raquel NIETO, 2007: The Role of the Solar Cycle in the Relationship Between the North Atlantic Oscillation and Northern Hemisphere Surface Temperatures, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 191-198.  doi: 10.1007/s00376-007-0191-x
    [17] LIU Peng, QIAN Yongfu, HUANG Anning, 2009: Impacts of Land Surface and Sea Surface Temperatures on the Onset Date of the South China Sea Summer Monsoon, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 493-502.  doi: 10.1007/s00376-009-0493-2
    [18] ZHOU Tianjun, SONG Fengfei, and CHEN Xiaolong, 2013: Historical Evolution of Global and Regional Surface Air Temperature Simulated by FGOALS-s2 and FGOALS-g2: How Reliable Are the Model Results?, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 638-657.  doi: 10.1007/s00376-013-2205-1
    [19] Bo FU, Jingyi LI, Thomas GASSER, Philippe CIAIS, Shilong PIAO, Shu TAO, Guofeng SHEN, Yuqin LAI, Luchao HAN, Bengang LI, 2022: Climate Warming Mitigation from Nationally Determined Contributions, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 1217-1228.  doi: 10.1007/s00376-022-1396-8
    [20] Lijing CHENG, John ABRAHAM, Kevin E. TRENBERTH, John FASULLO, Tim BOYER, Michael E. MANN, Jiang ZHU, Fan WANG, Ricardo LOCARNINI, Yuanlong LI, Bin ZHANG, Zhetao TAN, Fujiang YU, Liying WAN, Xingrong CHEN, Xiangzhou SONG, Yulong LIU, Franco RESEGHETTI, Simona SIMONCELLI, Viktor GOURETSKI, Gengxin CHEN, Alexey MISHONOV, Jim REAGAN, 2022: Another Record: Ocean Warming Continues through 2021 despite La Niña Conditions, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 373-385.  doi: 10.1007/s00376-022-1461-3

Get Citation+

Export:  

Share Article

Manuscript History

Manuscript received: 01 April 2014
Manuscript revised: 16 July 2014
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Attributing Analysis on the Model Bias in Surface Temperature in the Climate System Model FGOALS-s2 through a Process-Based Decomposition Method

    Corresponding author: REN Rongcai; 
  • 1. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics,Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;
  • 2. University of Chinese Academy of Sciences, Beijing 100049;
  • 3. Department of Earth, Ocean, and Atmospheric Science, Florida State University, Tallahassee, Florida 32306, USA
Fund Project:  This study was jointly supported by projects XDA11010402 GYHY201406001 and the National Basic Key Project (973) 2010CB428603 and 2010CB950400. The authors thank Dr. Sergio A. SEJAS from Florida State University for his comments on the manuscript.

Abstract: This study uses the coupled atmosphere-surface climate feedback-response analysis method (CFRAM) to analyze the surface temperature biases in the Flexible Global Ocean-Atmosphere-Land System model, spectral version 2 (FGOALS-s2) in January and July. The process-based decomposition of the surface temperature biases, defined as the difference between the model and ERA-Interim during 1979-2005, enables us to attribute the model surface temperature biases to individual radiative processes including ozone, water vapor, cloud, and surface albedo; and non-radiative processes including surface sensible and latent heat fluxes, and dynamic processes at the surface and in the atmosphere. The results show that significant model surface temperature biases are almost globally present, are generally larger over land than over oceans, and are relatively larger in summer than in winter. Relative to the model biases in non-radiative processes, which tend to dominate the surface temperature biases in most parts of the world, biases in radiative processes are much smaller, except in the sub-polar Antarctic region where the cold biases from the much overestimated surface albedo are compensated for by the warm biases from non-radiative processes. The larger biases in non-radiative processes mainly lie in surface heat fluxes and in surface dynamics, which are twice as large in the Southern Hemisphere as in the Northern Hemisphere and always tend to compensate for each other. In particular, the upward/downward heat fluxes are systematically underestimated/overestimated in most parts of the world, and are mainly compensated for by surface dynamic processes including the increased heat storage in deep oceans across the globe.

1. Introduction
  • As an elementary variable that is used to characterize climate state, temperature and its spatiotemporal evolutions are key parts of climate change, and they have a big influence on changes in other climate variables in the climate system. For example, precipitation increases/decreases in warmer/colder climates (Li et al., 2013a); and the frequency of climate (warm) extremes varies following changes in the summertime mean temperature (Kharin et al., 2007). Therefore, reproducibility of the spatial and temporal changes of surface and atmospheric temperature in climate models is always regarded as an important indicator of a model's performance. In particular, surface temperature (T s) has been regarded as a useful metric for gauging the credibility of model perfor- mance. Adequate reproducibility of the historical and current states of the climate is also the basis for reliable future climate projections by models (Kimoto, 2005). It is known that temperature biases in climate models can be attributed to model biases in physical processes such as external forcing, surface albedo, cloud, ozone, water vapor, and atmospheric and surface dynamic feedback processes (Randall et al., 2007; Solomon et al., 2007).

    Previous assessments of FGOALS-s2 (the Flexible Global Ocean-Atmosphere-Land System model, spectral version 2) indicate that the warm biases along the eastern coast of the Pacific and Atlantic oceans could be related to the overestimated (∼50 W m-2 more) shortwave radiation due to the underestimation of low-level clouds in these regions (Lin et al., 2013a). The cold atmospheric biases over the western Pacific in FGOALS-s2 (Lin et al., 2013a; Zhang and Zhou, 2014), in the grid version of FGOALS (FGOALS-g2) (Lin et al., 2013b), and in the climate system component of the Chinese Academy of Sciences Earth System Model (CAS-ESM-C) (Sun et al., 2012), coincide with the model underestimation of net heat flux in this region. It is argued that the improvement of the double ITCZ bias in the early version of FGOALS (FGOALS1.1-s) benefited from the implemented special low-cloud parameterization scheme (Bao et al., 2010). It has also been indicated that the overestimated sea ice cover in the northern polar region in the grid version of FGOALS (FGOALS-g2) (Li et al., 2013b; Xu et al., 2013), as well as in the other 14 IPCC Fourth Assessment Report (AR4) GCMs (Chapman and Walsh, 2007) contribute to the cooling change in this region, which in turn leads to even more sea ice and a stronger Atlantic Meridional Overturning Circulation (AMOC) (Zhou et al., 2005). (Huang et al., 2014) pointed out that the sea ice accumulated near the North Pole in FGOALS-g2 is related to the "artificial island" used by its ocean component. Therefore, understanding the model biases in representing the related physical processes is always important to eventually improve the model's reproducibility of surface temperature. However, significant biases of temperature, as well as other variables, are still globally present for most climate models due to our lack of knowledge of the physical processes responsible for the temperature biases in particular models.

    Recently, a coupled surface-atmosphere climate feed- back-response analysis method (CFRAM) was developed by (Lu and Cai, 2009) and (Cai and Lu, 2009). The process-based CFRAM was originally developed for diagnosing climate sensitivity and feedback processes (Lu and Cai, 2010; Cai and Tung, 2012). Based on the local energy balance, CFRAM can quantitatively attribute the temperature difference between two climate states to individual physical processes, including radiative processes such as external forcing, surface albedo, cloud, ozone, and water vapor; and non-radiative processes including surface sensible and latent heat fluxes and other dynamic processes in the atmosphere and at the surface. (Taylor et al., 2013) applied CFRAM to global warming and indicated that the surface albedo feedback and the net cloud feedback are the largest two contributors to the annual mean polar warming amplification. (Deng et al., 2013) applied CFRAM to Northern Annular Mode (NAM)-related temperature anomalies and demonstrated that cloud and ozone feedbacks are important for NAM anomalies in the tropical upper troposphere. (Park et al., 2013) applied CFRAM to examine the annual mean T s biases in the Community Earth System Model Version 1 (CESM1) and indicated that the model biases due to radiative processes account for a larger part of the T s biases than the model biases due to non-radiative processes.

    The purpose of this study is to apply CFRAM to the model surface temperature biases in FGOALS-s2, and examine the relative contributions from the model biases in representing various physical processes to the total model biases of T s in boreal winter (January) and boreal summer (July). Through decomposition of the model temperature biases into process-contributed components, the results can provide valuable information for effective model improvement of this model system, and can also be referenced for improvements to other models.

    The remainder of the paper is organized as follows. Section 2 describes the data used, the climate system model FGOALS-s2, and the CFRAM method. Section 3 demonstrates the T s biases in FGOALS-s2 and presents a validation of the CFRAM results. In section 4, we present the decomposition results and analyze the partial contributions of individual processes to the total temperature biases. A summary and concluding remarks are provided in section 5.

2. Model, data and method
  • FGOALS-s2 is a global coupled climate model developed by the State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG), Institute of Atmospheric Physics (IAP), Chinese Academy of Sciences (CAS), which consists of four components of atmosphere, ocean, land, and sea ice and a flux coupler. The atmospheric component is version 2 of the Spectral Atmospheric Model of IAP/LASG (SAMIL2) (Wu et al., 1996), with a horizontal resolution of R42, approximately 2.81° (lon) × 1.66° (lat), and 26 levels in the vertical direction. The oceanic component is version 2 of the LASG/IAP Climate Ocean Model (LICOM2) with a horizontal resolution of normally 1°× 1°, but increased to 1° (lon) ×0.5° (lat) in the tropics, and 30 vertical levels (Liu et al., 2012). The land component is version 3 of the Community Land Model (CLM3) (Oleson et al., 2004) and the sea ice component is version 5 of the Community Sea Ice Model (CSIM5) (Collins et al., 2006). The four components are coupled by a flux coupler (Collins et al., 2006). For more detailed descriptions of the model and information on a basic assessment of its general performance, see (Bao et al., 2013).

  • In this paper, the ensemble mean of the three members of the historical runs (1850-2005) of FGOALS-s2 for CMIP5 (Coupled Model Intercomparison Project Phase 5) is used to derive the model climatology in boreal winter (January) and boreal summer (July). The observation dataset used is the European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis Interim (ERA-Interim) dataset (Dee et al., 2011). ERA-Interim is a global atmospheric reanalysis dataset covering the period from 1979 to the present. It has a horizontal resolution of 1.5°× 1.5° with 37 pressure levels ranging from 1000 hPa to 1 hPa. The model temperature biases are then defined as the differences of temperature climatology between FGOALS-s2 and ERA-Interim in the period from 1979 to 2005. The ERA-Interim dataset provides all the variables required by the CFRAM calculation, which includes shortwave radiation at the top of the atmosphere (TOA), surface albedo, cloud amount, cloud liquid/ice water content, specific humidity, ozone mixing ratio, sensible and latent heat fluxes, air temperature, and surface temperature (T s, skin temperature over land and sea surface temperature over ocean).

  • Based on the energy balance equation, CFRAM considers the entire atmospheric column and the surface as a coupled surface-atmosphere system. CFRAM is different from traditional TOA-based feedback diagnostic methods, such as the Partial Radiative Perturbation (PRP) method (Wetherald and Manabe, 1988) and the Cloud Radiative Forcing (CRF) analysis method (Cess et al., 1990), in which only the radiative feedback processes can be explicitly considered while the non-radiative feedback processes are all hidden in changes of the lapse rate, because it directly measures the addible contributions of individual feedback processes to the total temperature changes and explicitly distinguishes the radiative and non-radiative feedback processes (Cai and Lu, 2009; Lu and Cai, 2009).

    For a surface-atmosphere column at a given horizontal grid point, CFRAM describes the difference () of the total energy balance between two climate states as

    \begin{equation} \Delta S-\Delta R+\Delta Q_{\rm NRad}=0 . (1)\end{equation}

    Note that here we consider the difference between the model climatology and the climatology from ERA-Interim. ∆ R and ∆ S are respectively the difference in divergence of the longwave radiation flux and the convergence of shortwave radiation flux between FGOALS-s2 and ERA-Interim. ∆ Q NRad represents the difference between FGOALS-s2 and ERA-Interim in convergence of the total energy flux mainly due to the surface sensible heat flux (∆ Q SH), surface latent heat flux (∆ Q LH), dynamic processes (∆ Q dyn_sfc) involving net energy convergence at the surface (i.e., land and oceanic surface energy transport and energy storage), and dynamic processes in the atmosphere at all scales (∆ Q dyn_atm) including turbulence, convection, and large-scale atmospheric motions:

    \begin{equation} \Delta Q_{\rm NRad}=\Delta Q_{\rm SH}+\Delta Q_{\rm LH}+\Delta Q_{\rm dyn_sfc}+\Delta Q_{\rm dyn_atm} . (2)\end{equation}

    According to the linear approximation in CFRAM, the nonlinear interactions among various radiative feedback processes are assumed negligible. Thus, ∆ S and ∆ R can be linearly decomposed into the sum of partial energy perturbations due to individual radiative processes such as incoming solar energy flux at TOA (o), ozone (O3), water vapor (w), cloud (c), surface albedo (α), and that due to the temperature differences (∆ T) between FGOALS-s2 and ERA-Interim:

    \begin{eqnarray} \label{eq2} \Delta S&\approx&\Delta F_o+\Delta S_{{\rm O}_3}+\Delta S_w+\Delta S_c+\Delta S_\alpha ,\\ \label{eq3} \Delta R&\approx&\Delta R_{{\rm O}_3}+\Delta R_w+\Delta R_c+\left(\dfrac{\partial R}{\partial T}\right)\Delta T , (4)\end{eqnarray}

    where (∂ R/∂ T) is the Planck feedback matrix whose jth column corresponds to the vertical profile of the radiative energy perturbation due to 1-K warming at the jth layer from the ERA-Interim state to the FGOALS-s2 state; (∂ R/∂ T)∆ T represents the difference in divergence of the longwave radiation energy flux due to the temperature difference ∆ T. By substituting Eqs. (2-4) into Eq. (1), rearranging the terms and multiplying both sides of the resultant equation by (∂ R/∂ T)-1, we obtain

    \begin{eqnarray} \label{eq4} \Delta T&\approx&\left(\dfrac{\partial R}{\partial T}\right)^{-1}[\Delta F_o\!+\!\Delta (S\!-\!R)_{{\rm O}_3}+\Delta (S\!-\!R)_w\!+\!\Delta (S\!-\!R)_c+\nonumber\\ &&\Delta S_\alpha+\Delta Q_{\rm SH}+\Delta Q_{\rm LH}+\Delta Q_{\rm dyn_sfc}+\Delta Q_{\rm dyn_atm}]. (5)\end{eqnarray}

    It follows that the local T s difference at each grid point between FGOALS-s2 and ERA-Interim (∆ T) can be directly attributed to the model biases in representing the radiative processes including [left to right in Eq. (5)] incident solar radiation at the TOA, ozone, water vapor, cloud, and surface albedo; and non-radiative processes including surface sensible heat flux, surface latent heat flux, surface dynamics, and atmospheric dynamics. Among the radiative processes, the difference in solar forcing and surface albedo only contribute to the shortwave radiative energy perturbation, while ozone, cloud, and water vapor can contribute to both the shortwave and the longwave radiative energy perturbation.

    To calculate the radiative energy perturbation terms in Eq. (5), the Fu-Liou radiative transfer model (Fu and Liou, 1992, 1993) is adopted in CFRAM. Specifically, the radiative forcing ∆ Fo is given by

    \begin{equation} \Delta F_o=[F(o_{\rm M},{\rm O}_{3{\rm E}},w_{\rm E},c_{\rm E},\alpha_{\rm E})-F(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm E}, c_{\rm E},\alpha_{\rm E})] , (6)\end{equation}

    where the subscripts "M" and "E" indicate that the variable is for the model or for the ERA-Interim. Similarly, the radiative energy perturbation terms ∆ (S-R) O3,∆ (S-R)w,∆ (S-R)c, and ∆ Sα are given by

    \begin{eqnarray} \Delta(S-R)_{{\rm O}_3}&=&[\Delta(S-R)(o_{\rm E},{\rm O}_{3{\rm M}},w_{\rm E},c_{\rm E},\alpha_{\rm E})-\qquad\nonumber\\ &&\Delta(S-R)(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm E},c_{\rm E},\alpha_{\rm E})] ,\\ \Delta(S-R)_w &=&[\Delta(S-R)(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm M},c_{\rm E},\alpha_{\rm E})-\nonumber\\ &&\Delta(S-R)(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm E},c_{\rm E},\alpha_{\rm E})] ,\\ \Delta(S-R)_c&=&[\Delta(S-R)(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm E},c_{\rm M},\alpha_{\rm E})-\nonumber\\ &&\Delta(S-R)(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm E},c_{\rm E},\alpha_{\rm E})] ,\\ \Delta S_\alpha&=&[S(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm E},c_{\rm E},\alpha_{\rm M})-\nonumber\\ &&S(o_{\rm E},{\rm O}_{3{\rm E}},w_{\rm E},c_{\rm E},\alpha_{\rm E})] . \end{eqnarray}

    Figure 1.  Winter (January) surface temperature climatology (units: °C, left) from (a) ERA-Interim and (b) FGOALS-s2; (c) the model biases in terms of the difference between (b) and (a); and (d) the sum of all the partial surface temperature biases obtained from CFRAM decomposition. Dotted areas in (c) mark the 99% confidence level according to the t-test. Panels (e-h) are the same as (a-d) except for summer (July).

    For the non-radiative processes, the energy perturbation by surface sensible heat and latent heat fluxes can be directly obtained from the difference between the model and ERA-Interim. However, because layer-by-layer data fields of energy fluxes related to dynamic processes are generally unavailable in both model and reanalysis datasets, ∆ Q dyn_sfc and ∆ Q dyn_atm have to be inferred from Eqs. (1) and (2) as the residual of energy fluxes between radiative processes and the surface sensible and latent heat processes,

    \begin{equation} \label{eq5} \Delta Q_{\rm dyn_sfc}+\Delta Q_{\rm dyn_atm}=-(\Delta S-\Delta R)-\Delta Q_{\rm SH}-\Delta Q_{\rm LH} . (11)\end{equation}

    Since by definition ∆ Q dyn_sfc has zero values in the atmospheric layers, while ∆ Q dyn_atm has zero values at the surface layer in CFRAM, we can further distinguish ∆ Q dyn_sfc and ∆ Q dyn_atm from each other within the residual.

    Before examining the partial contributions from each of the individual physical processes listed in Eq. (5), it should be pointed out that the differences in incident solar radiation at TOA between FGOALS-s2 and ERA-Interim are not model biases. This difference exists because the solar constant applied to define the solar radiation in FGOALS-s2 is 1365-1366 W m-2, which is recommended by CMIP5, while that applied in ERA-Interim is 1370 W m-2, which is estimated from multiple sources of data but has been shown to, on average, overestimate global solar radiation by about 2 W m-2 (Dee et al., 2011). The difference in the annual mean T s between HadCRU4 (Hadley Climate Research Unit version 4) and ERA-Interim reported in (Park et al., 2013) confirms the possible effect of the overestimated solar coefficient.

3. T s biases in FGOALS-s2 and validation of the CFRAM decomposition results
  • Figure 2.  (a) Solar insolation at TOA (units: W m-2, left) in January from ERA-Interim (contours) and the difference between that defined in FGOALS-s2 and that in ERA-Interim (shading); (b) the partial surface temperature differences (units: K) in CFRAM due to solar external forcing perturbation; and (c) the total model biases in surface temperature with the partial surface temperature differences due to solar perturbation excluded. Panels (d-f) are the same as (a-c) except for July.

    Figure 1 shows the climatological mean T s in January (Figs. 1a and b) and in July (Figs. 1e and f) derived from ERA-Interim and FGOALS-s2, respectively, and their differences (Figs. 1c and g). It is seen that the general patterns of T s in winter and summer are reproduced well by FGOALS-s2, including the features of the western Pacific and Indian Ocean warm pool and the eastern Pacific cold tongue, and the warmer/colder land/ocean in the summer hemisphere and the colder/warmer land/ocean in the winter hemisphere. However, significant temperature biases are present. Specifically, the cold biases in the warm pool region and the warm biases in the cold tongue region in January (Fig. 1c) and July (Fig. 1g) indicate that the warm pool and the cold tongue are both underestimated by the model, and thus the zonal temperature gradient in the tropical Pacific is also underestimated throughout the year. The underestimation of the warm pool and the cold tongue by FGOALS-s2 was also reported in (Bao et al., 2013). Besides, cold biases prevail in both the Arctic and the Antarctic region, and they are both relatively stronger in their respective winter season. Warm biases exist in most of the land regions in both the winter and summer hemispheres, and the warm biases are especially strong in the summer hemisphere (up to 10 K in southern Europe in July), suggesting that the cold land in winter is generally less cold, and the warm land in summer is much warmer in the model than in ERA-Interim. Over the extratropical oceans, stronger warm biases and weaker cold biases exist in the summer hemisphere, while stronger cold biases and weaker warm biases tend to prevail in the winter hemisphere. Overall, the meridional temperature gradient tends to be slightly weaker, and the zonal land-sea thermal contrast in the tropical latitudes tends to be relatively stronger in the model, especially in the summer hemisphere.

    To validate the decomposition results by CFRAM, we also show the sum of the partial T s differences calculated in CFRAM in Figs. 1d and h. It is clear that the distributions as well as the magnitudes of the total temperature biases obtained in CFRAM are almost identical to the actual temperature differences shown in Figs. 1c and g. This confirms that the linearization of the radiative transfer model adopted by CFRAM is quantitatively reliable and could be used to examine the processes responsible for local biases.

    Figure 2 displays the global distributions of the solar radiation at TOA in ERA-Interim in January and in July (contours in Figs. 2a and d) and the solar radiation differences between FGOALS-s2 and ERA-Interim (shading in Figs. 2a and d). Due to the relatively lower solar constant in FGOALS-s2, there is a global shortage of shortwave solar radiation in the model relative to ERA-Interim, and the maximum shortage is up to -8 W m-2 from the tropics to the summer hemisphere. Correspondingly, the CFRAM decomposition indicates that cold partial temperature biases due to the difference in solar forcing prevail globally, and the maximum bias is over -2 K from the tropics to the summer hemisphere (Figs. 2b and e). Since the partial temperature biases by individual processes in CFRAM are linearly addible, we can remove the partial temperature bias solely due to the solar difference from the total temperature bias, to effectively distinguish the contributions from the model biases in their representation of other physical processes including surface and atmospheric dynamics, ozone, water vapor and so on. Figures 2c and f show the remaining total temperature biases by all other processes. It is seen that without the contribution from the solar difference, the temperature biases due to model biases in their representation of other processes turn out to be dominated by warm biases except over the Arctic and Antarctic in both January and July. Nevertheless, since the partial biases by the solar forcing difference are uniformly negative and zonally homogeneous, the spatial features of the temperature biases in Figs. 2c and f are still largely similar to those in Figs. 1c and g, and in Figs. 1d and h. Next, we identify the partial temperature biases term-by-term, and try to quantify their relative contributions to the remaining total temperature biases. We refer to these remaining total temperature biases as the total model biases in T s for ease of reference.

4. Contributions from individual radiative and non-radiative processes to the total T s biases
  • In this section, we analyze the quantitative contributions to the total T s biases from model biases in the individual physical processes listed in Eq. (5). Note that the climate feedback processes are largely similar between the Northern and the Southern Hemispheres. We then analyze term-by-term the contributions of each of the radiative and non-radiative processes to the model biases, and provide the contribution results for regional T s biases for January. For conciseness, we only do latter for July.

  • 4.1.1 Ozone

    Relative to its highly effective shortwave radiation effect, ozone's longwave radiation effect is trivial. Therefore, ozone in the atmosphere mainly acts to absorb shortwave radiation and results in less shortwave radiation reaching the surface. The ozone distribution in ERA-Interim is based on multiple observation sources and a prognostic ozone model (Dee et al., 2011), while that in the FGOALS-s2 historical run is from the AC&C/SPARC (Atmospheric Chemistry and Climate/ Stratospheric Processes and their Role in Climate) ozone database provided by CMIP5. Due to the different distributions of ozone in the atmosphere (though not statistically significant), radiation energy received by the surface is modulated. Figure 3 shows the global distribution of the atmospheric column accumulated ozone content in January from ERA-Interim (contours) and the differences (shading) between the model and ERA-Interim. It can be seen that ozone is mainly concentrated in the Northern Hemisphere in January with a center of about 400 Dobson Units (DU; 1 DU =2.69× 1016 mol cm-2) over East Asia (contours in Fig. 3a). FGOALS-s2 underestimates this ozone center by more than 50 DU and generally overestimates the ozone in other regions (shading in Fig. 3a). However, because of less solar radiation received in the Northern Hemisphere in January, the radiation energy perturbation at the surface due to the model biases in ozone turns out to be mainly in the tropics and the Southern Hemisphere (up to -0.8 W m-2), though the ozone biases in these regions are relatively smaller (within 30 DU) (contours in Fig. 3b). Corresponding to the negative energy perturbation due to the positive ozone biases in the tropics and the Southern Hemisphere, the negative partial temperature biases [∆ T O3] are about -0.1 to -0.3 K.

    4.1.2 Water vapor

    Based on the radiative nature of water vapor, changes of water vapor in the atmosphere will lead to energy perturbations at the surface involving both shortwave and longwave radiation, as indicated by the term ∆ (S-R)w in Eq. (5). As one of the important greenhouse gases, water vapor in the atmosphere acts to warm the surface by causing increased emission of longwave radiation downward to the surface. On the other hand, water vapor also has a cooling effect on the surface by blocking part of the shortwave radiation. However, the longwave effect of water vapor always dominates its shortwave effect (Held and Soden, 2000; Dessler et al., 2008). The tropospheric column water vapor content (surface to 250 hPa) from ERA-Interim (contours) and the model bias (shading) in January are shown in Fig. 4a. Obviously, water vapor content centers in the tropics and decreases poleward (contours in Fig. 4a). Generally, there are overestimations of tropospheric water vapor in the midlatitudes of the two hemispheres, especially over the northern continents, and underestimations of water vapor in the lower latitudes, especially over tropical land (shading in Fig. 4a). The energy perturbation resulting from the model bias in water vapor closely follows its distribution, exhibiting negative/positive energy perturbation in regions with negative/positive biases of water vapor content (contours vs. shading in Fig. 4b). In turn, the negative/positive energy perturbations generally correspond to cold/warm temperature biases at the surface. The coincidence of cold/warm temperature biases with the negative/positive biases in water vapor content confirms that the longwave effect of water vapor usually dominates its shortwave effect. The range of energy perturbation at the surface by the model bias in water vapor is -30 W m-2 to 15 W m-2, and the partial temperature biases' range is -6 K to 4 K. Comparing Fig. 4 and Fig. 1c shows that the negative water vapor biases may largely contribute to the local cold biases in the equatorial warm pool region (Fig. 1c), while the positive water vapor biases in the cold tongue region may largely contribute to the local warm biases there (Fig. 1c).

    Figure 3.  (a) Column accumulated ozone content (units: DU) from ERA-Interim (contours) and the difference between FGOALS-s2 and ERA-Interim (shading) in January; (b) the same as (a) except the contours are the partial energy perturbation (units: W m-2) in CFRAM due to model biases in ozone; and (c) the same as (b) except the shading represents the partial surface temperature bias (units: K). Dotted areas in (a) mark the 99% confidence level according to the t-test.

    Figure 4.  (a) Tropospheric water vapor content from the surface to 250 hPa (units: kg m-2) from ERA-Interim (contours) and the difference between FGOALS-s2 and ERA-Interim (shading) in January; (b) the same as (a) except the contours are the partial energy perturbation (units: W m-2) in CFRAM due to the model biases in water vapor; and (c) the same as (b) except the shading represents the partial surface temperature biases (units: K). Dotted areas in (a) mark the 99% confidence level according to the t-test.

    Figure 5.  (a) Column mean cloud amount from ERA-Interim (contours) and the difference between FGOALS-s2 and ERA-Interim (shading) in January; (b) the shortwave and (c) the longwave radiation energy perturbation (units: W m-2, contours) in CFRAM due to the model bias in cloud amount (shading); (d) the total radiation energy perturbation (contours) and the partial surface temperature biases (units: K, shadings) due to cloud biases. Panels (e-f) are the same as (d) except for (e) shortwave and (f) longwave radiation. Dotted areas in (a) mark the 99% confidence level according to the t-test.

    4.1.3 Cloud

    Similar to water vapor, the radiation effects of cloud [∆(S-R)c] also involve energy perturbation of both shortwave and longwave radiation. It blocks downward shortwave radiation from reaching the surface, and reflects upward longwave radiation back to the surface. Therefore, the shortwave and longwave effects of cloud are opposite. Namely, positive/negative cloud cover biases in the model yield negative/positive shortwave energy perturbations (Fig. 5b), but positive/negative longwave energy perturbations (Fig. 5c). However, because of the trivial biases of cloud amount (within 0.1, Fig. 5a), the magnitudes of the shortwave energy perturbation (contours in Figs. 5b and e), as well as the longwave radiative energy perturbation (contours in Figs. 5c and f), are both very small (within 0.8 W m-2). As a result, the corresponding partial temperature biases (shading in Figs.5e and f) due to model bias in the cloud amount are within 0.2 K. The total radiation effect is even weaker due to the cancellation between the shortwave and longwave effect (Fig. 5d). In general, the model biases in cloud are trivial and their effects are very small and negligible compared to the effects of biases in other processes.

    4.1.4 Surface albedo

    Surface albedo defines the reflectivity of the surface to the downward shortwave radiation. Figure 6a shows the average surface albedo in January from ERA-Interim (contours) and the model biases (shading). It is seen that in January, higher albedo mainly appears over the northern continents (0.2-0.6) and in the southern sub-polar region (up to 0.8). The lack of higher albedo in the northern polar region is due to the lack of shortwave radiation there in boreal winter. Generally, the model overestimates the albedo in higher albedo regions, such as the southern sub-polar region and most continental regions, especially in the northern high latitudes. Also the biases in the northern Pacific and Atlantic seem to increase systematically with latitude. The largest biases (above 0.3) are found in the sub-polar regions of both the Northern and Southern Hemisphere. The albedo over the southern Atlantic, Pacific and Indian oceans is, however, slightly underestimated.

    Corresponding to the model biases in surface albedo, the radiative energy perturbation ∆ Sα (Fig. 6b) is generally negative/positive in regions of overestimated/underestimated albedo. The energy perturbation over most land ranges from -50 to 50 W m-2, which corresponds to the partial temperature biases due to albedo ranging from -30 to 30 K (Fig. 6c). The noticeably overestimated albedo along the rim of the Antarctic continent corresponds to a maximum, in terms of magnitude, energy perturbation of up to -200 W m-2 and a partial temperature bias of up to -60 K.

    In summary for radiative processes, water vapor bias mainly contributes to the T s biases over ocean, while albedo bias mainly contributes to the T s biases over land, particularly along the rim of the Antarctic continent. The contributions from ozone and cloud bias are much smaller, relatively.

  • 4.2.1 Energy perturbation

    Figure 7 shows the energy perturbations (downward positive) due to the bias in surface sensible heat flux (Fig. 7a), surface latent heat flux (Fig. 7b), and surface dynamics (Fig. 7c). It can be seen that significant positive biases in both the surface sensible heat flux and the surface latent heat flux are up to tens of W m-2 across the globe, except in the coastal regions of the Northern Hemisphere, the northeast Atlantic, and parts of the Southern Hemispheric continents, implying that the upward/downward heat fluxes between the surface and the atmosphere are systematically underestimated/overestimated in the model. On the other hand, the energy perturbations due to bias in surface dynamic processes (Fig. 7c) are globally negative, except along the rim of the Antarctic continent, in the northeast Atlantic, and along the coastal regions of the North Pacific, and tend to compensate for those in Figs. 7a and b. Since dynamic processes at the surface may include horizontal heat diffusion in soil and heat transport by run-off over land, horizontal and vertical energy transport by ocean streams, and heat storage mainly in oceans, the globally negative energy perturbations in Fig. 7c may indicate that the model is retaining more energy in the deep ocean, or showing a higher oceanic energy storage.

    4.2.2. T s biases

    As already mentioned in section 2, though the energy perturbations at the surface due to the bias in atmospheric dynamics are zero by definition in CFRAM, atmospheric dynamic processes can still yield T s bias due to their effect on the atmospheric temperature. Figures 8a-d respectively show the T s biases related to the surface sensible heat fluxes, surface latent heat fluxes, surface dynamic processes, and atmospheric dynamic processes. In agreement with the systematic underestimated/overestimated upward/downward heat fluxes in the model (Figs. 7a and b), the partial T s biases have similar patterns to the energy perturbations and are generally positive across the globe. Specifically, the warm biases due to sensible heat flux are generally over 10 K in the Northern Hemisphere and in the southern midlatitude oceans (Fig. 8a); the warm biases due to latent heat flux are globally over 10 K and even over 30 K in some regions in the tropics (Fig. 8b). Associated with the generally negative energy perturbations of surface dynamics, T s biases due to surface dynamics are mostly negative across the globe, except along the rim of the Antarctic continent, over the northeast Atlantic, and along the coastal lines of the North Pacific (Fig. 8c). It should be noted that the up to 30 K warm biases in the southern sub-polar region (Fig. 8c), plus the warm biases due to surface heat fluxes in this region (Figs. 8a and b), act to compensate for the cold biases due to the overestimated albedo (shown in Fig. 6). This may imply that the cooling effect of the overestimated albedo is largely balanced by the warming effect of the locally reduced ocean upwelling and the decreased/increased upward/downward heat fluxes.

    Figure 6.  (a) Surface albedo from ERA-Interim (contours) and the difference between FGOALS-s2 and ERA-Interim (shading) in January; (b) partial energy perturbation (units: W m-2); and (c) partial surface temperature biases (units: K) due to the model bias in surface albedo. Dotted areas in (a) mark the 99% confidence level according to the t-test.

    It is also noticeable that over the North Atlantic, the stronger partial T s biases due to latent heat flux, which exhibit a positive-to-negative pattern from the west to the east Atlantic (Fig. 8b), are generally compensated for by the partial T s biases due to surface dynamics, which exhibit an opposite negative-to-positive pattern from the west to the east Atlantic (Fig. 8c). This may correspond to an anomalously stronger North Atlantic Current in the model, which is the northern branch of the North Atlantic gyre in the North Atlantic (Lin et al., 2013a). Compared with the T s biases due to these non-radiative processes, the T s biases due to atmospheric dynamics (Fig. 8d) are much smaller (-4 K to 6 K). They tend to be mostly positive and partially cancel the cold biases from the surface dynamics in the mid and high latitudes.

    Figure 7.  The energy difference (units: W m-2) of non-radiative processes: (a) surface sensible heat flux; (b) surface latent heat flux between FGOALS-s2 and ERA-Interim in January; and (c) energy perturbation in CFRAM due to model biases in surface dynamic processes. Dotted areas in (a) and (b) mark the 99% confidence level according to the t-test.

    Figure 8.  Partial surface temperature biases (units: K) due to non-radiative processes: (a) surface sensible heat flux; (b) surface latent heat flux; (c) dynamic processes at the surface; and (d) dynamic processes in the atmosphere in January.

  • Based on the results shown above, Fig. 9 displays the total contributions from all radiative processes (Fig. 9a) and from all non-radiative processes (Fig. 9b). It can be seen that the contributions from the two kinds of processes always tend to cancel each other, except in the southern midlatitudes, the northwest Pacific region, and the northern polar region. The most evident cancellations can be found over most continental areas, in the tropical Atlantic and the Antarctic regions, manifesting the synchronized and compensatory interactions between the radiative and non-radiative processes within the coupled surface-atmosphere system. Comparing Figs. 9a and b and Fig. 2c indicates that, generally, the non-radiative processes are relatively more dominant than the radiative processes for the total T s biases across the globe, except in the Antarctic region, particularly along the rim of the Antarctic continent where the radiative and non-radiative processes largely counteract and compensate for each other.

    Figure 9.  Partial surface temperature biases (units: K) due to the model bias in (a) radiative processes and (b) non-radiative processes in January.

    Figure 10.  (a) Area-weighted mean total surface temperature biases (bar) in each of the nine regions in January (blue) and July (red); (b-j) PAP coefficients of the partial temperature bias by ozone, water vapor, cloud, surface albedo, surface sensible and latent heat flux, surface dynamic processes, atmospheric dynamic processes, the sum of radiative processes, and the sum of non-radiative processes over (b) Eurasia, (c) North America, (d) North Pacific, (e) North Atlantic, (f) South Africa, (g) South America, (h) South Pacific, (i) South Atlantic, and (j) Indian Ocean.

  • To further quantify the relative contributions to the model Ts biases from the individual processes, next we choose nine key regions including four land regions and five ocean regions, as denoted by the blue boxes in Fig. 2c. The four land regions are Eurasia (EuA), North America (NAm), South America (SAm), and South Africa (SAf), and the five ocean regions are the North Pacific (NPa), North Atlantic (NAt), South Pacific (SPa), South Atlantic (SAt), and Indian Ocean (IO). Following (Deng et al., 2013), we calculate the Pattern Amplitude Projection (PAP) values for each process to measure the contributions from individual processes to the total T s biases in different regions. The PAP is defined as

    \begin{equation} {\rm PAP}_i\!=A^{-1}\!\!\int_A{a^2\Delta T\cos\varphi d\lambda d\varphi}\cdot\dfrac{\displaystyle A^{-1}\!\!\int_A{a^2\Delta T_i\Delta T\cos\varphi d\lambda d\varphi}} {\displaystyle A^{-1}\!\!\int_A{a^2(\Delta T)^2\cos\varphi d\lambda d\varphi}} , \end{equation}

    where φ and Λ are the latitude and longitude, respectively; a is the mean radius of the Earth; and A is the area of the region under consideration. ∆ T is a matrix whose elements are the total temperature bias at each grid point, and ∆ Ti is the ith matrix whose elements are the partial temperature bias at each grid point due to the ith physical process [from the 2nd to 9th term in Eq. (5)]. Obviously, PAPi measures the relative contributions from the ith process and the sum of the eight PAP coefficients for a given region equals the area-averaged T s bias by definition.

    Before showing the PAP for each region, we first show in Fig. 10a the area-weighted mean total T s biases in each of the nine regions in January (blue) and July (red). It is evident that the biases are consistently positive in all regions and, on average, the model biases over land are relatively much larger than over the oceans, particularly in boreal summer and for the northern continents. The biases over the South Pacific, South Atlantic, and Indian oceans are larger on average in January than in July. Specifically, from Figs.10b and c, it can be seen that for the much stronger warm T s biases over the northern continents in July, the partial biases due to model bias in surface dynamics and in surface latent heat flux are dominant but are canceled by other processes, while the relatively weaker warm temperature biases in January are co-contributed by multiple processes and only canceled by surface dynamics. In general, the radiative and non-radiative processes compensate each other in July, with the latter dominating the total T s bias; while in January, they co-contribute to the much weaker T s bias. For the positive T s biases over the Northern Hemispheric oceans, the North Pacific (Fig. 10d), and the North Atlantic (Fig. 10e) in both January and July, contributions from all radiative processes are relatively much smaller than those from the non-radiative processes. However, because all the radiative processes tend to co-contribute, while the non-radiative processes tend to counteract, the overall contributions from the radiative processes and non-radiative processes are comparable and co-contribute to the positive T s bias in these regions.

    Compared with the Northern Hemisphere, the amplitudes of the contributions from individual non-radiative processes in the Southern Hemisphere and the Indian Ocean are much larger, especially in January, and are about twice those in the Northern Hemisphere (Figs. 10f-j). The total T s biases, however, are still comparable between the two hemispheres due to the counteractions among the non-radiative processes, particularly between the surface heat fluxes and surface dynamics. Also consistent among the southern continents and oceans and the Indian Ocean, are the much smaller contributions from radiative processes. The T s biases in July are relatively much weaker, particularly over the southern oceans and over the Indian Ocean (Figs. 10h-j), because of the even smaller contributions from both radiative and non-radiative processes in July.

5.Concluding remarks
  • This study adopts CFRAM to analyze the model biases in T s climatology in FGOALS-s2, with the model biases defined with respect to the ERA-Interim data record from 1979 to 2005. Through linear decomposition by CFRAM, local model biases in T s are quantitatively attributed to the model biases in representing individual physical processes, including radiative processes such as solar forcing, ozone, water vapor, cloud and albedo; and non-radiative processes such as surface sensible heat flux, surface latent heat flux, and dynamic processes at the surface and in the atmosphere. After removing the partial T s biases attributed in CFRAM to the difference in solar forcing between the model and ERA-Interim, the partial contributions from individual radiative and non-radiative processes are analyzed term-by-term. The results show that generally the model T s biases over land are relatively larger than those over the oceans, and the model T s biases in summer are relatively larger than those in winter.

    The decomposition analysis indicates that in FGOALS-s2, biases in non-radiative processes are always much larger than biases in radiative processes, and tend to dominate the T s biases. The model biases in radiative processes over land are relatively larger than over the oceans, and may act to partially compensate for the T s biases by non-radiative processes. Furthermore, among the four non-radiative processes, the contributions from the model bias in atmospheric dynamics are relatively much smaller; and contributions from the surface heat fluxes always tend to counteract those from the surface dynamics in most parts of the globe. Thus, the generally underestimated/overestimated upward/downward heat fluxes across the globe tend to be compensated for by the increased heat storage in the deep oceans.

    In general, CFRAM decomposition analysis has not only revealed to us the possible physical processes responsible for the local model T s biases, which conventional model assessments can also tell qualitatively, but has also provided us with quantitative contribution information, from each of the physical processes to the model biases within the energy balanced surface-atmosphere system. More importantly, since changes in these physical processes in CFRAM from one equilibrium climate state to another are required to be intimately synchronized or compensative, the quantitative contribution information provided by CFRAM is thus valuable for further dynamic diagnosis of the identified processes and related mechanisms responsible, and for us to understand the eventual source for the model biases and to improve the model. We leave this to future work due to the limited scope of the current study.

Reference

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint