Understanding Differences in Event Attribution Results Arising from Modeling Strategy

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  • While there is high confidence that human activities have increased the likelihood and severity of hot extreme events over many parts of the world, there is notable spread in quantitative estimates of anthropogenic influence even on a single event. To better understand the uncertainty of attribution results, here we compare different event attribution methods using the 2015 July–August record-breaking heat event in northwestern China as a case study. To address the anthropogenic influence on the likelihood of the extreme event, we employ attribution runs with two modeling strategies—atmosphere-only and coupled simulations—with different conditioning. In atmosphere-only attribution runs, given the observed sea surface boundary conditions and external forcings in 2015, it is estimated that anthropogenic forcing has increased the likelihood of hot extremes such as that observed in 2015 in the target region, by approximately 27 and 12 times in MIROC5 and HadGEM3-A-N216, respectively. In Coupled Model Intercomparison Project Phase 5 (CMIP5) fully coupled attribution runs, given the external forcing at the 1961–2015 level and regardless of sea surface boundary conditions, there is a 21-fold increase in the likelihood of similar heat events due to anthropogenic forcing. The differences in quantitative attribution results can arise from modeling strategies, which are tightly linked to different conditioning in attribution. Specifically, different ocean boundary conditions, external forcings, and air-sea coupling processes contribute to different attribution results between the two modeling strategies. Within each modeling strategy, model uncertainty affects quantitative attribution conclusions. The comparison of different attribution methods provides a better understanding of the uncertainty of attribution results, which is useful in synthesizing and interpreting attribution results.
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  • Fig. 1.  Observed characteristics of the 2015 July–August heat event in northwestern China. (a) Time series of the July–August mean surface air temperature anomaly over northwestern China (west of 100°E and north of 35°N, indicated by blue lines). (b) July–August mean surface air temperature anomalies (°C) in 2015. (c) Number of heatwave days (daily maximum temperature ≥ 35 °C) in July–August of 2015. (d) The anomalous number of heatwave days in July–August of 2015. All anomalies are relative to the climatology in 1961–1990.

    Fig. 2.  2015 July–August surface air temperature anomalies (°C, shadings) and geopotential height anomalies at 500 hPa with zonal mean subtracted (m, contours) relative to the 1961–1990 climatology for (a) observations (CN05.1 and ERA-Interim); (b–c) ensemble mean of ALL-Hist members in 2015; (d–e) The 10 hottest members in the ALL-Hist ensemble over northwestern China. (b) and (d) are for MIROC5, and (c) and (e) are for HadGEM3-A-N216.

    Fig. 3.  2015 March-to-August mean surface (0–10 cm) soil moisture anomalies (unit: kg m-2) relative to the 2000–2014 mean for (a) GLDAS; (b–c) Ensemble mean of ALL-Hist members in 2015; (d–e) The 10 hottest members in the ALL-Hist ensemble over northwestern China. (b) and (d) are for MIROC5, and (c) and (e) are for HadGEM3-A-N216. Dots denote where at least 70% of ensemble members agree on the sign of difference.

    Fig. 4.  Model evaluation. (a–b) Time series of the July–August mean surface air temperature anomaly (°C) over northwestern China from 1961 to 2015 relative to 1961–1990. (c–d) Histograms and the corresponding kernel fit of the temperature time series. Black curves denote observations; red curves denote All-Hist simulations with shading indicating the ensemble range. (a) and (c) are for MIROC5, and (b) and (d) are for HadGEM3-A-N216.

    Fig. 5.  The histogram and kernel fit of the July–August mean surface air temperature anomaly (°C) averaged over northwestern China in 2015 in (a) MIROC5 and (b) HadGEM3-A-N216 in the Nat-Hist (blue) and All-Hist (red) experiments. The vertical dashed lines denote the observed 2015 SAT anomaly.

    Fig. 6.  (a) Time series of July–August mean surface air temperature anomaly (°C) over northwestern China in the observation (black) and CMIP5 ensemble mean (red; historical and RCP8.5 simulations) over 1961–2015 relative to 1961–1990. Shading denotes the CMIP5 ensemble range. (b) Histograms and the corresponding kernel fit of the temperature anomalies in 1961–2015 for the observation (black) and CMIP5 models (red; historical and RCP8.5 simulations). (c) Histograms and kernel fit of July–August mean surface air temperature anomalies (°C) in natural-forcing (historicalNat; 1961–2005; blue) and all-forcing (historical and RCP8.5; 1961–2015; red) simulations. The vertical dashed black line denotes the observed event in 2015.

    Fig. 7.  FAR/PR curves for surface air temperature anomalies for MIROC5 (red), HadGEM3-A-N216 (blue) and CMIP5 (black). The vertical black line denotes the observed event in 2015.

    Table 1.  Information of CMIP5 models used

    ModelHistorical & RCP8.5:
    Number of realizations
    HistoricalNat:
    Number of realizations
    bcc-csm11
    BNU-ESM11
    CanESM255
    CCSM433
    CNRM-CM533
    CSIRO-Mk3-6-011
    FGOALS-g211
    GFDL-CM311
    GFDL-ESM2M11
    GISS-E2-H11
    GISS-E2-R11
    HadGEM2-ES44
    IPSL-CM5A-LR33
    MIROC-ESM11
    MIROC-ESM-CHEM11
    MRI-CGCM311
    NorESM1-M11
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Understanding Differences in Event Attribution Results Arising from Modeling Strategy

    Corresponding author: Tianjun ZHOU, zhoutj@lasg.iap.ac.cn
  • 1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029
  • 2. University of Chinese Academy of Sciences, Beijing 100049
Funds: Supported by the National Key Research and Development Program of China (2018YFC1507701).

Abstract: While there is high confidence that human activities have increased the likelihood and severity of hot extreme events over many parts of the world, there is notable spread in quantitative estimates of anthropogenic influence even on a single event. To better understand the uncertainty of attribution results, here we compare different event attribution methods using the 2015 July–August record-breaking heat event in northwestern China as a case study. To address the anthropogenic influence on the likelihood of the extreme event, we employ attribution runs with two modeling strategies—atmosphere-only and coupled simulations—with different conditioning. In atmosphere-only attribution runs, given the observed sea surface boundary conditions and external forcings in 2015, it is estimated that anthropogenic forcing has increased the likelihood of hot extremes such as that observed in 2015 in the target region, by approximately 27 and 12 times in MIROC5 and HadGEM3-A-N216, respectively. In Coupled Model Intercomparison Project Phase 5 (CMIP5) fully coupled attribution runs, given the external forcing at the 1961–2015 level and regardless of sea surface boundary conditions, there is a 21-fold increase in the likelihood of similar heat events due to anthropogenic forcing. The differences in quantitative attribution results can arise from modeling strategies, which are tightly linked to different conditioning in attribution. Specifically, different ocean boundary conditions, external forcings, and air-sea coupling processes contribute to different attribution results between the two modeling strategies. Within each modeling strategy, model uncertainty affects quantitative attribution conclusions. The comparison of different attribution methods provides a better understanding of the uncertainty of attribution results, which is useful in synthesizing and interpreting attribution results.

    • The rapidly growing occurrences of high-temperature extremes worldwide in recent decades have caused vast socioeconomic impacts, raising issues in public health, agriculture, drought, etc. and challenging infrastructures such as energy demand (IPCC, 2012, 2014). In the context of anthropogenic global warming, it has been concluded that human influence, particularly greenhouse gas emissions, is very likely the main contributor to the observed increase in the likelihood and severity of hot extremes on most continents based on multiple lines of evidence from detection and attribution studies (e.g., Meehl and Tebaldi, 2004; Stott et al., 2004; Bindoff et al., 2013; Sun et al., 2014; Zhou et al., 2014; Stott et al., 2016; Ma et al., 2017; Kim et al., 2018).

      In addition to the long-term trend, there has also been growing interest in the recent decade, from both the climate research community and the public, in the human influence on specific extreme weather and climate events, commonly termed “event attribution” (National Academies of Sciences, Engineering, and Medicine, 2016). Event attribution addresses how anthropogenic forcing alters the likelihood or severity of particular extreme events (Allen, 2003; Stott et al., 2004; Sun et al., 2014; Otto, 2017). There are generally two basic approaches in event attribution studies that are aimed at differently framed questions. One is the risk-based approach, which, from a probabilistic perspective, assesses whether and to what extent anthropogenic climate change has altered the odds of events typical of the one in question. A quite different framing is the storyline approach, which answers the question that given the dynamic field (such as atmospheric circulations) leading to the event, how the known anthropogenic warming has affected the specific event and its impacts, from a magnitude perspective (Trenberth et al., 2015; Shepherd, 2016). The storyline approach is physically based in that it is conditioned on dynamical situations leading to the event, but it does not address potential changes in these dynamical situations.

      The risk-based event attribution is typically achieved by comparing climate model simulations of the factual world (as observed) with those of the counterfactual world that could have been without anthropogenic influence. Two modeling strategies are widely employed to generate these attribution simulations, both extensively used in event attribution studies (such as in the Bulletin of the American Meteorological Society special issues on Explaining Extreme Events; e.g., Herring et al., 2020). The first type is standalone atmosphere-only attribution simulations with prescribed observed ocean states, such as those participating in the C20C+ Detection and Attribution (D&A) Project (Stone et al., 2019). The other type is coupled attribution runs, comprising historical simulations driven by individual external forcings, mostly from the Coupled Model Intercomparison Project Phase 5 (CMIP5) and CMIP6 archives (e.g., the Detection and Attribution Model Intercomparison Project in CMIP6; Gillett et al., 2016).

      The atmosphere-only and coupled attribution frameworks have their own advantages. Atmosphere model-based event attribution is conditional on the observed ocean state, which is useful in describing conditional cases (e.g., if events are related to an El Niño). In addition, atmosphere-only models require lower computational cost than coupled simulations and thus generally have higher resolution, enabling a better representation of extreme events that are usually localized. In addition, larger ensemble sizes can be generated under the atmosphere-only framework, which improves the sampling of extreme events. Nevertheless, the atmosphere-only attribution framework does not account for air-sea interactions.

      To synthesize and provide a fuller picture of attribution results, it is necessary to compare different approaches and to understand the associated uncertainty. For this purpose, in this study, focusing on the risk-based perspective, we compare attribution results from different modeling strategies and models, taking the 2015 July–August heatwave in northwestern China as a case study.

      In 2015, northwestern China experienced the historically hottest summer, breaking the records of regionally averaged seasonal mean temperature, annual maxima of daily maximum and daily minimum temperatures. The long-lasting heatwave resulted in severe damage to agriculture and other sectors (CMA, 2016). Notably, heatwaves in northwestern China can result in devastating consequences through accelerating or exacerbating mountainous snow/ice melting and associated runoff, potentially leading to floods and mudslides (Ma et al., 2015). Event attribution studies have consistently demonstrated the human influence in increasing the likelihood of such heat events (Miao et al., 2016; Sun et al., 2016). Focusing on the summer highest daily maximum and minimum temperatures, using reconstructed model responses to anthropogenic and natural forcings in CMIP5 derived from an optimal fingerprinting method, it is estimated that human influence has increased the probability of the highest daily maximum and minimum temperatures by approximately 10-fold and 89-fold, respectively (Sun et al., 2016). Using July mean maximum daily temperature as the indicator, CMIP5 models suggest an approximately threefold increase in the likelihood of such an extreme event by anthropogenic climate change (Miao et al., 2016). Due to the use of different indicators, region definitions, and data processing, it is difficult to directly compare attribution results from different studies, which further challenges the synthesis of attribution conclusions.

      In this work, we aim to synthesize the attribution results from different modeling strategies and models and to explore the associated uncertainty for this particular extreme event as a case study. Considering the long persistence of the heatwave, and that current models are more robust in reproducing the statistics of monthly/seasonal means than daily extremes (Lewis and Karoly, 2013), we focus on July–August mean surface air temperature. Specifically, we focus on the anthropogenic influence on the likelihood of similar extreme events.

      The remainder of the paper is organized as follows. Section 2 introduces the observational and model data, as well as the methods. Section 3 presents the attribution results from different modeling strategies and models and discusses the associated uncertainty. Section 4 summarizes concluding remarks.

    2.   Data and methods
    • The gridded monthly mean near-surface air temperature and daily maximum temperature from the CN05.1 dataset are used, with a spatial resolution of 0.25° × 0.25° and covering 1961 to present. The dataset is compiled and quality-controlled by the National Meteorological Information Center of China based on station data (Xu et al., 2009; Wu and Gao, 2013). In addition, the monthly mean geopotential height at 500 hPa from the ERA Interim reanalysis is used to investigate the atmospheric circulation anomalies associated with the heat event (Dee et al., 2011).

      To explore soil moisture conditions associated with heatwaves, we use soil moisture data from the Global Land Data Assimilation System (GLDAS) generated by the Noah model (Rodell et al., 2004). Constrained by ground and satellite observations, this global and high-resolution offline terrestrial modeling system aims to provide optimal simulations of global land surface states and fluxes (Rodell et al., 2004). GLDAS soil moisture data have been widely used in climate studies. It shows reasonable consistency in soil moisture anomalies on a global scale with multi-satellite retrieved products (Liu et al., 2019) and in terrestrial water storage over northwestern China with the GRACE (Gravity Recovery and Climate Experiment) satellite product (Yang and Chen, 2015).

      Different versions of GLDAS products use different forcing data, with the GLDAS-2.0 (from 1948 to 2014) forced with the Princeton meteorological forcing data and the GLDAS-2.1 (from 2000 to present) forced with a combination of model and observations (https://ldas.gsfc.nasa.gov/gldas). To exclude the influence of systematic differences from forcing data, we only use the GLDAS-2.1 version for monthly surface (0−10 cm) soil moisture data covering 2000 to present with a resolution of 0.25° × 0.25°. Therefore, the soil moisture anomalies associated with the 2015 heatwave are derived with respect to the mean state in 2000–2014.

      For attribution analysis, to assess the methodological dependency of attribution results, two types of attribution runs—atmosphere-only and coupled simulations—are used. Atmosphere-only attribution runs are derived from the C20C+ D&A project (Stone et al., 2019), including MIROC5 (1.4° × 1.4°; Shiogama et al., 2013, 2014) and HadGEM3-A-N216 (0.56°×0.83°; Ciavarella et al., 2018). The attribution system comprises a pair of ensembles. One represents the factual world, which is driven by both natural and anthropogenic forcings, with observed sea surface temperatures (SSTs) and sea ice concentration (SIC) (hereafter termed All-Hist). The other ensemble represents the counterfactual world without human influence, which is driven by time-varying natural forcings with anthropogenic forcings fixed at pre-industrial levels (hereafter termed Nat-Hist). In Nat-Hist simulations, the prescribed SST and SIC fields are constructed from observations with the anthropogenic contribution (which is estimated from the CMIP5 ensemble) subtracted.

      For MIROC5, there are 10 members of historical simulations spanning 1961 to 2015 and 100 members from 2006 onward. For HadGEM3-A-N216, there are 15 members of historical simulations for 1961–2013 and 105 members for 2014–2015. For both models, the multi-member historical simulations (All-Hist) of 1961–2015 are used in model evaluation (for HadGEM3-A-N216, the 15 members extending to 2015 are used). The ensemble simulations of 2015 are used in attribution.

      Fully coupled simulations from the CMIP5 ensemble with 17 models are also used (Table 1; Taylor et al., 2012). The factual world is represented by historical simulations from 1961 to 2005, extended to 2015 using Representative Concentration Pathway (RCP) 8.5 scenario projections, which is the most representative of global CO2 emissions from 2005 to present (Peters et al., 2012). The counterfactual world without anthropogenic influence is represented by the historicalNat simulations, which are forced with time-varying natural forcings alone and cover 1961–2005.

      ModelHistorical & RCP8.5:
      Number of realizations
      HistoricalNat:
      Number of realizations
      bcc-csm11
      BNU-ESM11
      CanESM255
      CCSM433
      CNRM-CM533
      CSIRO-Mk3-6-011
      FGOALS-g211
      GFDL-CM311
      GFDL-ESM2M11
      GISS-E2-H11
      GISS-E2-R11
      HadGEM2-ES44
      IPSL-CM5A-LR33
      MIROC-ESM11
      MIROC-ESM-CHEM11
      MRI-CGCM311
      NorESM1-M11

      Table 1.  Information of CMIP5 models used

    • To evaluate the model-simulated statistics, specifically the distributions, of temperature indices, we use the Kolmogorov–Smirnov (K–S) goodness-of-fit test (Wilks, 2006). To quantify the anthropogenic influence on the likelihood of the observed extreme event, the probability ratio (PR; Allen, 2003; Stott et al., 2004) is computed:

      $$ {\rm PR} = {\rm PAll} / {\rm PNat}, $$ (1)

      where $ {\mathrm{P}}_{\mathrm{A}\mathrm{l}\mathrm{l}} $ and $ {\mathrm{P}}_{\mathrm{N}\mathrm{a}\mathrm{t}} $ denote the probability of occurrence of extreme events with a magnitude equal to or greater than the observed threshold in the factual and counterfactual worlds, respectively. Alternatively, the fraction of attributable risk (FAR =$ 1-{\mathrm{P}}_{\mathrm{N}\mathrm{a}\mathrm{t}}/{\mathrm{P}}_{\mathrm{A}\mathrm{l}\mathrm{l}} $; Stott et al., 2004) is also used when PR approaches infinity. The probability of occurrence is estimated using the kernel fit for July–August mean temperature. The uncertainty of PR is estimated by bootstrapping 1000 times by resampling all ensemble members with replacement. The 95% confidence intervals are shown.

    3.   Results
    • The summer of 2015 and July–August in particular, saw the historically heat in northwestern China (NWC; west of 100°E, north of 35°N; blue lines in Fig. 1). The regional average July–August mean temperature over NWC reached 1.7 °C above the 1961–1990 climatology, setting new records in observations since 1961 (Fig. 1a). Local temperatures even reached 2.4 °C warmer than climatology (Fig. 1b). Meanwhile, the number of heatwave days (daily maximum temperature ≥ 35 °C) reached 20 days over a large area of this region and even exceeded 50 days in the Turpan Basin (approximately 40°N, 90°E) during July–August of 2015 (Fig. 1c). Compared to the 1961–1990 baseline, a large area south of Tianshan (37°−43°N, 80°E−95°E) experienced 8 more heatwave days than normal and even exceeded 16 days over Tarim and Junggar Basin (Fig. 1d).

      Figure 1.  Observed characteristics of the 2015 July–August heat event in northwestern China. (a) Time series of the July–August mean surface air temperature anomaly over northwestern China (west of 100°E and north of 35°N, indicated by blue lines). (b) July–August mean surface air temperature anomalies (°C) in 2015. (c) Number of heatwave days (daily maximum temperature ≥ 35 °C) in July–August of 2015. (d) The anomalous number of heatwave days in July–August of 2015. All anomalies are relative to the climatology in 1961–1990.

      The persistent heat event was associated with a high-pressure anomaly at 500 hPa, which extended from northwestern China to East Siberia (Fig. 2a). The high-pressure anomaly, accompanied by enhanced sinking motion and clear-sky conditions, maintains surface warming via radiative heating and subsidence warming (Luo et al., 2020). In addition, anomalous drying soils persisting from spring to summer may also have contributed to this summer heatwave through local-to-regional land-air interactions (Fig. 3a). Soil moisture deficit is mainly seen in northern northwestern China through Mongolia to East Siberia, generally corresponding to the high-pressure anomaly in the upper air (Fig. 3a, Fig. 2a). It has been noted that summer heatwaves in northwestern China can be affected by anomalous soil preconditions in adjacent regions (Yang et al., 2019). The lack of soil moisture leads to reduced latent cooling, thereby amplifying or maintaining surface high temperatures (Fischer et al., 2007; Lian et al., 2020). This land-air interaction is particularly important in northwestern China—a typical dry area characterized by a water-limited evaporative regime—and has also been reported in previous studies (Wang et al., 2018).

      Figure 2.  2015 July–August surface air temperature anomalies (°C, shadings) and geopotential height anomalies at 500 hPa with zonal mean subtracted (m, contours) relative to the 1961–1990 climatology for (a) observations (CN05.1 and ERA-Interim); (b–c) ensemble mean of ALL-Hist members in 2015; (d–e) The 10 hottest members in the ALL-Hist ensemble over northwestern China. (b) and (d) are for MIROC5, and (c) and (e) are for HadGEM3-A-N216.

      Figure 3.  2015 March-to-August mean surface (0–10 cm) soil moisture anomalies (unit: kg m-2) relative to the 2000–2014 mean for (a) GLDAS; (b–c) Ensemble mean of ALL-Hist members in 2015; (d–e) The 10 hottest members in the ALL-Hist ensemble over northwestern China. (b) and (d) are for MIROC5, and (c) and (e) are for HadGEM3-A-N216. Dots denote where at least 70% of ensemble members agree on the sign of difference.

    • We first validate the simulated July–August mean surface air temperature over NWC against observations. Both MIROC5 and HadGEM3-A-N216 reproduce the temporal evolution of the regional average temperature over NWC compared to observations, with correlation coefficients of 0.73 and 0.68 (without detrending), respectively, both significant at the 0.01 level, indicating a reasonable representation of combined long-term trends and interannual-to-decadal variations (Figs. 4a, b). In addition, both models can well reproduce the statistical distribution and variability of the temperature anomalies (Figs. 4c, d). This is supported by the K-S test, which indicates that there is no significant difference between the temperature distributions in the observation and simulations at the 0.05 level (with p values of 0.60 and 0.09 for MIROC5 and HadGEM3-A-N216, respectively). This provides a solid basis for assessing the anthropogenic influence on the extreme event.

      Figure 4.  Model evaluation. (a–b) Time series of the July–August mean surface air temperature anomaly (°C) over northwestern China from 1961 to 2015 relative to 1961–1990. (c–d) Histograms and the corresponding kernel fit of the temperature time series. Black curves denote observations; red curves denote All-Hist simulations with shading indicating the ensemble range. (a) and (c) are for MIROC5, and (b) and (d) are for HadGEM3-A-N216.

      We first focus on the magnitude of the 2015 heat event. In both models with all forcings (All-Hist) for 2015, the ensemble mean, which represents the response to all external forcings and the prescribed observed boundary conditions, shows weaker temperature anomalies than the observation (Figs. 4a, b). This is associated with the weaker high-pressure anomaly in the troposphere (Figs. 2a–c) and weaker preconditioned soil drying (Figs. 3a–c) in the model ensemble means compared to observations. Moreover, we note that the observed temperature anomaly lies in the upper bound of the ensemble spread, indicating a substantial role of atmospheric internal variability in the magnitude of the observed heatwave (Figs. 4a, b). In particular, within the All-Hist ensemble, the 10 members showing the hottest anomaly over NWC can better reproduce the magnitude of the observed event, with an intensified high-pressure anomaly in the upper air (mainly seen in MIROC5) and strengthened soil drying (mainly seen in HadGEM3-A-N216), compared to the All-Hist ensemble mean (Figs. 2d–e, Figs. 3d–e). This suggests that both models can partly simulate the physical processes leading to heatwaves in northwestern China—either the high-pressure anomaly or the preconditioned soil moisture deficit.

      How does anthropogenic forcing influence the likelihood of such heat events? We then compare the temperature distributions of 2015 under all-forcing and natural-forcing simulations (Fig. 5; hereafter termed ALL and NAT distributions, respectively). With anthropogenic forcing included, the ALL distribution shifts toward a warmer state compared to the NAT distribution in both models, which is mainly related to the background mean warming. The overall shift of the distribution leads to increased odds of hot extremes lying in the upper tail. In the counterfactual world, the probability of hot extremes exceeding the 2015 observed threshold is 0.78% (95% CI: 0.004%−2.09%) and 0.62% (95% CI: 0.000005%−1.94%) in MIROC5 and HadGEM3-A-N216, respectively. Correspondingly, this occurrence probability increases to 21.38% (95% CI: 14.33%−28.18%) and 7.51% (95% CI: 3.55%−12.01%), respectively, in the factual world with anthropogenic influence. This translates to probability ratios of 27 (95% CI: 9-535) and 12 (95% CI: 4-9848), respectively. That is, conditional on the boundary conditions of 2015, anthropogenic influence has increased the probability of heat events similar to that observed in NWC by approximately 27 times in MIROC5 and 12 times in HadGEM3-A-N216.

      Figure 5.  The histogram and kernel fit of the July–August mean surface air temperature anomaly (°C) averaged over northwestern China in 2015 in (a) MIROC5 and (b) HadGEM3-A-N216 in the Nat-Hist (blue) and All-Hist (red) experiments. The vertical dashed lines denote the observed 2015 SAT anomaly.

      We conclude that while the magnitude of the observed heat event is partly contributed by atmospheric internal variability, anthropogenic forcing has increased the likelihood of similar events.

    • To confirm the robustness of the attribution results and to investigate the methodological dependency, we also employ the fully coupled attribution runs from the CMIP5 ensemble. The CMIP5 historical and RCP8.5 simulations reproduce well the long-term warming trend over NWC over 1961–2015, as in the observations (Fig. 6a). The simulated temperature variability covers the range of observed variability due to additional oceanic variability in the coupled model ensemble (Fig. 6a). In terms of the statistical distribution, the multimodels can reasonably reproduce the temperature distributions compared to that observed, as they cannot be distinguished by the K-S test at the 0.05 level (Fig. 6b).

      Figure 6.  (a) Time series of July–August mean surface air temperature anomaly (°C) over northwestern China in the observation (black) and CMIP5 ensemble mean (red; historical and RCP8.5 simulations) over 1961–2015 relative to 1961–1990. Shading denotes the CMIP5 ensemble range. (b) Histograms and the corresponding kernel fit of the temperature anomalies in 1961–2015 for the observation (black) and CMIP5 models (red; historical and RCP8.5 simulations). (c) Histograms and kernel fit of July–August mean surface air temperature anomalies (°C) in natural-forcing (historicalNat; 1961–2005; blue) and all-forcing (historical and RCP8.5; 1961–2015; red) simulations. The vertical dashed black line denotes the observed event in 2015.

      Comparing the factual and counterfactual worlds, there is a rightward shift, as well as a widening of the temperature distribution when anthropogenic influence is included (Fig. 6c). Both the shift and widening of the distribution led to a higher occurrence probability of hot extremes similar to that observed in 2015. The probability increases from 0.51% (95% CI: 0.21%–0.85%) under natural forcings to 11.04% (95% CI: 9.76%–12.41%) under all forcings. This gives a probability ratio of 21 (95% CI: 13–52). In other words, there is an approximately 21-fold increase in the risk of the 2015 heat event in NWC due to human activities.

    • The estimates of anthropogenic contribution to the likelihood of extreme events strongly depend on event thresholds. To investigate how anthropogenic influence varies with event thresholds (as in Kim et al., 2018), we estimate the probability ratio given hypothetical temperature thresholds ranging from -3 °C to 4 °C (relative to the 1961–1990 baseline), which is generally applicable to any extreme temperature events over this selected NWC region. Considering that the probability ratio can be infinity (when PNAT = 0), we also show the corresponding FAR value, which is bounded between 0 and 1 (Fig. 7). Both the atmosphere-only and coupled attribution runs consistently show that anthropogenic contributions to the likelihood of hot extremes generally increase with higher event thresholds. For hotter extremes, the human contribution is larger.

      Figure 7.  FAR/PR curves for surface air temperature anomalies for MIROC5 (red), HadGEM3-A-N216 (blue) and CMIP5 (black). The vertical black line denotes the observed event in 2015.

      We then focus on the differences in the FAR/PR curves among different modeling strategies and models. The FAR/PR curve is directly linked to the temperature distributions under all and natural forcings. There are two critical points on the FAR/PR curve. One is the lower boundary (i.e., FAR = 0 and PR = 1), which corresponds to the lower bound of the NAT distribution. The other is the upper boundary (i.e., FAR = 1 and PR approaches infinity), which corresponds to the upper bound of the NAT distribution. This means that events warmer than this threshold would not have occurred without anthropogenic influence. The two atmosphere-only models, MIROC5 and HadGEM3-A-N216, have consistent critical points bounded between approximately -1.5 °C and 2.3 °C (red and blue curves in Fig. 7). This suggests that they agree well on the range of temperature anomalies that could occur over the target region without anthropogenic forcing. This range is slightly larger in the CMIP5 multimodels (bounded between -2.0 °C and 2.4 °C; black curve in Fig. 7) due to additional oceanic variability.

      Another important feature of the FAR/PR curve is the growth rate (i.e., slope), which is closely related to the shift between the ALL and NAT distributions, as well as the shape of the distributions. A larger shift between ALL and NAT distributions, representing greater background warming due to anthropogenic forcing, favors a larger FAR and PR, assuming that the shape of the distribution remains unchanged.

      Comparing HadGEM3-A-N216 with MIROC5 (blue vs. red curve in Fig. 7), the FAR/PR curve for HadGEM3-A-N216 grows faster in the beginning but then grows more slowly when approaching saturation. The faster increase in the FAR/PR curve in the beginning is related to the larger mean warming magnitude between the ALL and NAT distributions in HadGEM3-A-N216 (1.22 °C) than in MIROC5 (1.05 °C) (Fig. 5). When the FAR/PR curve approaches saturation, corresponding to high event thresholds lying in the upper tail of NAT distributions, the slower growth rate of FAR/PR in HadGEM3-A-N216 is partly related to its positive skew and heavier upper tail than MIROC5 (Fig. 5).

      The FAR/PR curve of CMIP5 lies in between, with a similar growth rate to the two atmosphere-only models (black curve in Fig. 7). This is a result of two competing effects. On the one hand, the mean state warming between the ALL and NAT simulations is weaker in CMIP5 (0.45 °C) than in MIROC5 (1.05 °C) and HadGEM3-A-N216 (1.22 °C). The resulting smaller shift between ALL and NAT distributions tends to slow the growth of FAR/PR in CMIP5. On the other hand, with anthropogenic forcing included, the ALL distribution becomes wider than the NAT distribution in CMIP5 (Fig. 6c). The wider upper tail indicates larger occurrences of hot extremes in all forcing simulations and thus favors a fast growth of FAR/PR in CMIP5. The widening of distributions in ALL compared to NAT distributions implies an amplified variability under anthropogenic forcing in coupled models, which is not seen in atmosphere-only models. The above two effects offset each other, consequently resulting in a FAR/PR curve of CMIP5 similar to the atmosphere-only models.

    • The quantitative attribution results, i.e., the anthropogenic contribution to the likelihood of extreme events, differ among the three sets of simulations used, which can be clearly seen from the FAR/PR curves. Here, we discuss the possible sources of differences to synthesize and provide a better understanding of the attribution results.

    • The attribution runs from MIROC5 and HadGEM3-A-N216, both under the protocol of the C20C+ D&A Project, have identical experimental designs, including prescribed boundary conditions and external forcings. The differences in attribution results mainly arise from model uncertainty. On the one hand, the differences in FAR/PR stem from different shifts between ALL and NAT distributions, which represent the mean state warming magnitude due to anthropogenic forcing (1.05 °C in MIROC5 and 1.22 °C in HadGEM3-A-N216; Fig. 5). The anthropogenic warming is dominated by the forced responses to greenhouse gases and anthropogenic aerosols. It has been shown that the inter-model scatter of the anthropogenic warming rate over East Asia can be largely explained by the diverse temperature responses to anthropogenic aerosols, while the spread in greenhouse gas warming plays a minor role (Kim et al., 2018).

      In addition, the differences in FAR/PR are related to different shapes of temperature distributions. As discussed in Section 3.3, HadGEM3-A-N216 has a heavier upper tail than MIROC5, contributing to a smaller FAR/PR at very high event thresholds (Fig. 5, Fig. 7). This is related to simulated temperature variability, which is further linked to atmospheric internal variability in atmosphere-only models.

    • Event attribution based on atmosphere-only and coupled models differs in the conditioning of attribution. The former aims to address the anthropogenic influence on the likelihood of extreme events similar to that observed in 2015, given SST/SIC boundary conditions and external forcings of 2015. However, the latter aims to estimate the anthropogenic influence over the long period of 1961–2015 and is unconditional on ocean states.

      Thus, the differences in attribution results between the two modeling strategies first arise from ocean boundary conditions. This can lead to substantial differences if the extreme events considered are significantly affected by SST modes such as ENSO.

      Second, in terms of anthropogenic forcing, atmosphere-only attribution runs are driven by external forcing in a particular year (2015, in this case), while coupled attribution runs represent a mean forcing level over 1961–2015, which is generally weaker than that in the former. The weaker anthropogenic forcing in CMIP5 explains the weaker anthropogenic warming magnitude than that in the atmosphere-only models, which is reflected in the smaller shift between ALL and NAT distributions and favors a smaller FAR/PR.

      Third, with anthropogenic forcing included, the ALL distribution becomes wider than the NAT distribution in CMIP5, favoring a larger FAR/PR, which is absent in atmosphere-only runs. There are two possible causes for the widening of the temperature distribution in coupled runs. On the one hand, anthropogenic forcing may amplify oceanic variability. On the other hand, the air-sea interaction may be enhanced under anthropogenic forcing, which further amplifies temperature variability. These processes deserve further investigation.

      To recap, to synthesize attribution results from different methods and models, the attribution question should be specified. Different modeling strategies involve different aspects of conditioning, including ocean boundary conditions, external forcings, and air-sea coupling processes, all of which could contribute to differences in attribution results. Within each modeling strategy, model uncertainty also affects quantitative attribution conclusions.

    4.   Concluding remarks
    • While there is high confidence that human activities, in particular greenhouse gas emissions, have increased the likelihood and severity of hot extreme events over many parts of the world, there is notable spread in quantitative estimates of anthropogenic influence from different attribution studies even for a single event. The uncertainty of attribution results can arise from the different modeling strategies and models employed. To synthesize attribution results and to better understand the associated uncertainty, we performed attribution analyses using commonly used methods for a particular extreme event.

      The selected event is the 2015 July–August hot extreme in northwestern China. The regionally averaged July–August mean surface air temperature over northwestern China is used as the indicator, which broke the observational record since 1961 in 2015. To address the anthropogenic influence on the likelihood of the extreme event, we employed attribution runs with two modeling strategies with different conditioning in attribution. The first type is atmosphere-only attribution runs participating in the C20C+ D&A Project. Given the observed SST/SIC boundary conditions and external forcings in 2015, it is estimated that anthropogenic forcing has increased the likelihood of hot extremes such as that observed in 2015 in the target region, by approximately 27 and 12 times in MIROC5 and HadGEM3-A-N216, respectively. The second type is fully coupled attribution runs from the CMIP5 multimodel ensemble. Given the external forcings over the 1961–2015 level and regardless of SST/SIC conditions, there is a 21-fold increase in the occurrence probability of similar heat events due to anthropogenic forcing.

      The differences in attribution results can be further revealed by the FAR/PR curves given all possible hypothetical event thresholds. The sources of differences first arise from different conditioning in attribution. Depending on whether the attribution is conditional (i.e., whether the boundary conditions of that particular year are of interest), different modeling strategies—atmosphere-only or coupled simulations—should be employed. Between the two modeling strategies, boundary conditions, external forcings and air-sea coupling processes all contribute to the differences in attribution results. Within each modeling strategy, quantitative attribution conclusions are affected by model uncertainty, which involves the forced response to individual forcing components (e.g., greenhouse gases and anthropogenic aerosols), as well as the representation of variability. Moreover, as models have their own deficiency in representing physical processes related to extreme events, it is highly recommended to evaluate model performance in terms of physics and take them into account as potential sources of uncertainty in attribution results.

      It is worth noting that, in the atmosphere-only attribution framework, additional uncertainty may arise from methods used for removing human-caused warming in SST and sea ice in naturalized simulations. The two atmosphere-only models used in this study, both derived from the C20C+ D&A protocol, are naturalized using the same estimates of anthropogenic SST warming from the CMIP5 ensemble. Ideally, however, different estimates of anthropogenic SST warming patterns can be used, which have been shown to affect estimated probability ratios partly by modulating the locations of temperature distributions in naturalized simulations (Sparrow et al., 2018). Therefore, the potential uncertainty arising from naturalized SST patterns also deserves attention.

      Our comparison of the two attribution methods provides a better understanding of the uncertainty of attribution results, particularly that arising from modeling strategies and model uncertainty. We highlight the importance of clarifying the conditioning in attribution and associated model experimental design, as well as taking into account model uncertainty, in the interpretation and communication of attribution results. Moreover, more comprehensive comparisons incorporating other attribution approaches, such as the circulation-conditioned storyline approach (e.g., Stott et al., 2016; Ye and Qian, 2021), are encouraged to provide a more integrated assessment of uncertainty.

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