Disentangling physical and dynamical drivers of the 2016/17 record-breaking warm winter in China

Understanding the physical and dynamical origin of regional climate extremes remains a major challenge in our effort to anticipate the occurrences and mitigate the adverse impacts of these extremes. China was hit by a record-breaking hot winter in 2016/17 with remarkable surface warming over the northern and southeastern regions. Here we made a quantitative attribution of this 2016/17 winter’s surface temperature anomalies utilizing an updated version of the coupled atmosphere-surface climate feedback response analysis method (CFRAM), that recently incorporates the effect of aerosols and more species of trace gases (CFRAM-A). The CFRAM-A analysis reveals that the overall warming pattern may be largely attributed to the effects of anomalous water vapor, atmospheric dynamics, and aerosols, followed by anomalies of surface albedo, clouds, solar irradiance, ozone, and carbon dioxide. The effect of methane turns out to be negligible. Anomalies in surface dynamics provides an overall cooling effect, compensating the warming associated with other processes to some extent. Among the three major positive contributors, effects of water vapor and atmospheric dynamics prevail over both northern and southeastern China while the impact of anthropogenic aerosols appears much more pronounced over southeastern China, likely due to the implementation of highly effective emission reduction policies in China since 2013. The CFRAM-A thus provides an efficient, model-free approach for quantitatively understanding sources of regional temperature extremes and for assessing the impacts of environmental policies regulating anthropogenic emissions of aerosols and atmospheric trace gases.


Introduction
According to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR6), global surface temperature during the most recent decade (2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020) was approximately 1 • C higher than 1850-1900, and extreme warm events became more frequent and more intense across most continents. Attribution of the climate warming or specific extreme events, a process of quantifying and evaluating the relative contributions from multiple causal factors, provides an important scientific basis for policymakers and stakeholders to formulate mitigation and adaptation strategies (Lashof and Ahuja 1990, Stott et al 2010, Hegerl and Zwiers 2011, Zhai et al 2018. In spite of remarkable progresses made so far in attribution studies, there is still a long way before we can obtain attribution results with low uncertainties (Rodhe 1990, Liebmann et al 2010, Najafi et al 2015, Qian and Zhang 2019. While insufficiency and imperfection of observational data is one of the factors to blame, limitations of existing attribution methods also contribute significantly to uncertainties in results obtained. To date, attribution studies rely primarily on sensitivity experiments conducted with climate models, which often lead to large uncertainties in quantitative results due to considerable model biases (Gu et al 2006, Hegerl and Zwiers 2011, Turnock et al 2015, Zhai et al 2018, Gong et al 2021.
The coupled atmosphere-surface climate feedback response analysis method (CFRAM) has proven to be an efficient off-line diagnostic tool that can directly decompose local temperature differences between two climate states into partial temperature changes associated with individual radiative and dynamical processes ). This method has been successfully applied to quantify the relative contributions of multiple processes to temperature anomalies associated with global warming (Chen et al 2017a, 2017b, El Niño-Southern Oscillation , Hu et al 2016, and the Northern Annular Mode (Deng et al 2013), etc. Nevertheless, a fly in the ointment is that the effect of aerosols, which is a key factor for temperature changes through aerosol-cloud-radiation interaction (Giorgi et al 2002, Li et al 2007, Jiang et al 2015, has not been included in the previous CFRAM analysis. Scientists basically reached an agreement on the qualitative effects of aerosols, but quantifying the contribution of aerosols to temperature change remains technically challenging for the attribution community (Ruckstuhl et al 2010, Turnock et al 2015.
As a region experienced rapid population growth, urbanization, and industrial development in the past century, China has become the major sources of anthropogenic aerosols around the world (Liao et al 2014, Li et al 2015. In order to achieve the reduction of particulate matter concentrations by 10%-25% in the year 2017 with respect to the 2013, the Action Plan on the Prevention and Control of Air Pollution was launched in 2013 with strengthened reduction of anthropogenic emissions across China (Zheng et al 2018, Filonchyk et al 2019, Fang et al 2020. Such human interventions would introduce both uncertainties and complexities to quantitative attribution studies. Owing to the limited observations and complex climate conditions, attribution studies of climate changes and extreme events remain inadequate in China (Zhai et al 2018). The nation-wide extreme warm winter will facilitate glacier retreat, snow melt, and degradation of permafrost over the Tibetan Plateau (Yao et al 2019, Zhang et al 2019a, Duan et al 2022, favor the serve haze events in eastern China (Cai et al 2017, Yin et al 2017, affect winter wheat production (Tian et al 2012, and disturb the ecosystems (Yu et al 2010, Zhang et al 2019c. The long-term increase of warm winters over China are favored by the global warming (Sun et al 2021), while the interannual variability of winter temperature is regulated by the atmospheric internal variabilities (e.g. the Siberian High, Arctic Oscillation, the East Asian winter monsoon) and external forcings (e.g. El Niño-Southern Oscillation, Arctic sea ice, North Atlantic sea surface temperature, Indian Ocean sea surface temperature; You et al 2013, Jiang et al 2014, Zuo et al 2015, 2022, Ma et al 2018, Xiao et al 2018, Xie et al 2019. The attribution research of extreme warm winter in China are relatively scarce. Jian et al (2020) and Pan et al (2021) investigated the roles of sea surface temperature anomalies and the East Asian winter monsoon in two regional extreme warm winters over China. However, the relative contributions of multi factors have not been comprehensively quantified. Recently, a record-breaking hot winter hit China in 2016/17, with the national averaged surface temperature nearly 2 • C higher than the 2005-2019 climatology (figure 1(a)). Until now, causal factors responsible for this extreme warm winter remain unknown. Based on the Modern-Era Retrospective Analysis for Research and Application, version 2 (MERRA-2) with long-term coupled meteorological and aerosol analysis, and an updated version of the CFRAM that innovatively includes the aerosol effect (CFRAM-A hereafter), this study provides a comprehensive and quantitative attribution of individual physical and dynamical processes for the surface temperature anomalies over China in the 2016/17 winter.

Data and methods
The CFRAM-A developed in this study is based on the total energy balance in an atmosphere-surface column consisting multi atmospheric layers and one surface layer ). Taking the difference (∆) of the total energy balance equation between two climate states (climate 'B' minus 'A'), and linearizing the radiative energy perturbations by neglecting the interactions among different radiative species, we may express ∆S (S denotes the convergence of shortwave radiation flux) and (R denotes the divergence of longwave radiation flux) as the sum of partial radiative energy flux convergence/divergence due to individual processes. Multiplying both sides by the inverse of the Planck feedback matrix ( ∂R ∂T ) −1 , which quantifies the change of the vertical profile of longwave radiative flux divergence due to 1 K warming (with respect to the climate state 'A' temperature) at an atmospheric or surface layer, and rearranging the terms (details referred to Chen et al 2017a), we obtain: where ∆T are the temperature differences between the two climate states in each layer. The convergence of total non-radiative energy due to changes in atmospheric dynamics ∆Q (atmos_dyn) and surface dynamics ∆Q (surf_dyn) is estimated as a residual from the radiative energy perturbations. The vertical profile of the temperature difference at a given location between two climate states could be decomposed into the vertical profile of partial temperature differences due to (from left to right in equation (1) changes in solar irradiance, CO 2 , CH 4 , cloud, surface albedo, water vapor, ozone, black carbon, organic carbon, sulfate, sea salt, dust, atmospheric dynamics (i.e. energy transport by convective and largescale atmospheric motions), and surface dynamics (including mainly energy gain in the column due to surface latent and sensible heat fluxes, runoff, soil heat diffusion, and snow/ice melting/freezing). Note that methane (CH 4 ) is the second most abundant anthropogenic greenhouse gas after carbon dioxide (CO 2 ). It has greenhouse effect, i.e. trapping the longwave radiation in the atmosphere, which is the same as CO 2 . The linearization of radiative perturbations by omitting the higher order terms of the interactions among different species (e.g. water vapor, clouds, aerosols) has been extensively validated and is now commonly adopted in many climate attribution methods (e.g. partial radiative perturbation method) in numerous studies (e.g. Wetherald and Manabe 1988, Bony et al 2006, Held and Soden 2006, Taylor et al 2011. Note that the partial temperature changes associated with aerosols are results from the direct radiative effects (i.e. cool the surface by reducing surface incoming sunlight). On the other hand, the energy perturbations due to the changes in clouds indeed include the indirect effects of aerosols. The rapid radiative transfer method (RRTM) for general circulation model (RRTMG) is an accelerated version of RRTM with minimal loss of accuracy (Iacono et al 2008), which has been evaluated and widely employed in many state-of-the-art climate models and weather models. The RRTMG version 5 is incorporated into the CFRAM-A to obtain the individual radiative energy perturbations in equation (1)  The input variables required for the off-line RRTMG radiative transfer calculations include solar irradiance at the top of the atmosphere (TOA), ozone mixing ratio, trace gases mixing ratio (CO 2 and CH 4 ), air/surface temperatures, specific humidity, geopotential height, cloud amount, cloud liquid/ice water content, black carbon/ organic carbon/sulfate aerosol/sea salt/dust mixing ratio, surface albedo, surface latent/sensible heat flux. All of these fields are obtained from the MERRA-2 reanalysis product (Gelaro et al 2017) except for the trace gases mixing ratio, whose values came from the Copernicus Atmosphere Monitoring Service (CAMS) global inversionoptimized greenhouse gas concentrations (https:// ads.atmosphere.copernicus.eu/cdsapp#!/dataset/cam s-global-greenhouse-gas-inversion). MERRA-2 is the latest and first long-term global atmospheric reanalysis to assimilate aerosols observations and represent aerosol-climate interactions from the National Aeronautics and Space Administration (NASA), which well captures the temporospatial variations of aerosols over China compared to the ground measurements (Song et al 2018. It has a 0.5 • × 0.625 • horizontal resolution with 42 pressure levels ranging from 1000 to 0.1 hPa, covering the period of 1980 to present. Note that the aerosols induced clouds changes are not separated in MERRA-2 as well as other reanalysis datasets, which cannot serve as an independent input in the CFRAM-A calculation to derive a contribution term of aerosol indirect effects. CAMS global inversion-optimized greenhouse gas concentrations have a 1.9 • × 3.75 • horizontal resolution with 39 model levels from surface to TOA, covering the period 1979-2020, for CO 2 concentration. It has a 2 • × 3 • horizontal resolution with 34 model levels from surface to TOA, covering the period 1990-2019, for CH 4 concentration. We consider the averaged winter (DJF) state of 2004/05-2018/19 as the base state (climate state 'A' as discussed previously), and 2016/17 DJF averaged state as the contrast to the base state (climate state 'B' as discussed previously). The number of assimilated observations in MERRA-2 doubled after 2002 to approximately 2 million per 6 h cycle, most of which are contributed by the A-train satellites (Gelaro 2017). Abundant observations assimilated in MERRA-2 could significantly improve the reanalysis quality and further reduce the uncertainties of model dependent fields such as clouds and aerosols, which are sensitive and crucial to assess the spatial patterns and magnitudes in attribution analysis. Therefore, we have chosen to use more accurate datasets covering a shorter period (2004/05-2018/19) rather than less accurate datasets covering a longer period, regarding similar results are obtained using 1995/96-2018/19 as the base state (figure not shown). In summary, the climatology of the most recent 15 years was selected as base state due to the availability of the high-quality reanalysis, a new era of historical climate simulations after 2005 in the phase 6 of the Coupled Model Intercomparison Project (CMIP6; Eyring et al 2016), and a rather 'clean' aerosol background without major volcanic eruptions.

Validation of the MERRA-2 quality and the CFRAM-A calculations
China has experienced an accelerated warming during the most recent decade, particularly in boreal winter (Li et al 2015, Qian and Zhang 2019, Xu et al 2020 (figure 1(a)). The most eye-catching warming occurred in the winter of 2016/17, with the surface temperature anomalies reaching the highest among recent years and seasons ( figure 1(a)). Except for southwestern China, significant warm anomalies, defined as values exceeding the 0.5 standard deviation of the 2005-2019 winter mean temperature are observed almost throughout the country from the in-situ observations ( figure 1(b)). Due to the different construction time of in-situ stations across the country, 2,133 stations were selected after quality control for the recent 15 years (2005-2019), while only 1,204 stations were selected for the 1970-2019 period in figure 1(a). Note that the similar results are obtained by using different sizes of stations for the two periods (figure not shown). MERRA-2 well captures the spatial pattern of surface warmings in the 2016/17 winter, including the prominent warming centers over northern and southeastern China and the mild warm anomalies over southwestern China ( figure 1(c)). The high degree of consistency between MERRA-2 and the observational data provide confidence to utilize this dataset as a proxy of observation for the subsequent analysis. A small patch of insignificant cold anomalies over northeastern China shown in MERRA-2 appears inconsistent with in-situ observations (figures 1(b) and (c)), and it is excluded from the subsequent attribution analysis.
To validate the CFRAM-A calculations, the surface temperature differences between the winters of 2016/17 and 2005-2019 base state derived from MERRA-2 and from summing the CFRAM-A derived partial temperature differences are presented in figures 2(a) and (b), respectively. The CFRAM-A calculation recovers the same spatial pattern as seen in the MERRA-2 (figures 2(a) and (b)). The area averaged surface temperature differences over China in MERRA-2 (1.61 K) and the CFRAM-A calculations (1.55 K) are quite close (figures 2(a) and (b)). Following Park et al (2012) and Chen et al (2017), the offline calculated radiative energy perturbations at the top of atmosphere (TOA) and the surface are validated through comparing with those in the MERRA-2 (figure not shown). The linearization errors are small at the surface, while positive biases are shown over western and central China at the TOA due to the linear solution tends to be very sensitive to the forcing in the stratosphere ). We focus on the surface temperature changes instead of the stratosphere temperature changes in this study. Therefore, the usage of time-mean fields in the offline radiative transfer calculations and the linearization of radiative energy perturbations in the CFRAM-A are reasonable.

The spatial structure of the process-based surface temperature attributions
With the CFRAM-A calculations validated, the derived partial surface temperature differences are used to quantify the relative contributions of individual physical and dynamical processes to the surface warming in the 2016/17 winter (figures 2(c)-(l)). Overall, the external forcings of solar irradiance and trace gases (ozone, CO 2 , and CH 4 ) provide uniform warmings over China, which all induce less than 0.1 K area-averaged warmings (figures 2(c)-(f)). The processes associated with atmospheric dynamics, aerosols, and water vapor contribute most to the warming in 2016/17 winter, generating the area-averaged partial temperature differences of 0.98 K, 0.67 K, and 0.38 K, respectively (figures 2(l), (j), and (h)). More specifically, the water vapor anomaly, dominated by the longwave (i.e. 'greenhouse') effect, provides a remarkable warming across China expect the Tibetan Plateau (figure 2(h)), and this is clearly linked to the above-normal perceptible water in the 2016/17 winter (figure S1(c)). The surface temperature difference due to the changes in aerosol is primarily found over southeastern China ( figure 2(h)). The effect of atmospheric dynamics is observed over most parts of China (figure 2(l)), which is likely linked to the weakening of large-scale cold air advection. This is supported by the positive phase of AO in the 2016/17 winter. This AO phase is associated with a weaker Siberian high and hence fewer episodes of cold surges affecting China (He et al 2017, Miao and. The weakening of the Siberian High also characterizes a weaker East Asian winter monsoon, which could lead to anomalous southerlies over China that were responsible for transporting more water vapor into land from adjacent ocean basins (Wu and Wang 2002). Although cloud changes provide an overall weak positive contribution to the warming (figure 2(i), 0.04 K), the effect is location sensitive with an obvious warming effect in southern China and cooling effect in central China. The cloud effects are dominated by its reflection of shortwave radiation and are directly related to changes in total cloud cover ( figure S1(b)). The surface dynamics is mainly associated with negative feedbacks between the surface heat fluxes and temperature providing a strong cooling effect (−0.62 K) that is mostly seen over the warming center in southeastern China ( figure 2(k)).
Surface albedo has an overall weak negative contribution to the warming (−0.04 K) with a significant local cooling effect in northeastern China and warming effect in the southwestern Tibetan Plateau that are directly linked to the local snow cover changes (figure S1(a). This result hints that the temperature bias in MERRA-2 over part of northeastern China is potentially caused by unrealistic representation of snow cover in MERRA-2. In summary, atmospheric dynamics and water vapor act as the main positive contributors to warming in northern China, compensated by the cooling effects of surface dynamics and clouds to some extent. In southeastern China, the warming is primarily attributed to the changes in atmospheric dynamics, aerosols, water vapor, and clouds, and is largely compensated by the cooling effect of surface dynamics. Unlike the other major contributors, which provide considerable effects in both northern and southern China, the aerosol effect is primarily concentrated over southern China.
The question is: Why the aerosol effect is crucial in southern China? To address this, we further decompose the total aerosol effect into partial effects associated with five aerosol types (figure 3). The effects of anthropogenic aerosols (black carbon, organic carbon, and sulfate) contribute 90% of the area-averaged warming associated with the total aerosol change, particularly over southeastern China (figures 3(b)-(d)). The change in dust provides a uniform warming over China, and the effect of sea salt is almost negligible (figures 2(e) and (f)). Typically, all five types of aerosols reduce the surface temperature through scattering or absorption of incoming shortwave solar radiation (in general the direct effect) (Menon et al 2008, Najafi et al 2015. The aerosol-related net warming effect found by CFRAM-A is therefore linked to the reduction of aerosols in the 2016/17 winter in comparison to the 2005-2019 climatology, particularly over southeastern China (figure S1(d)). The dominant role of anthropogenic aerosols demonstrates that the reduction of aerosols likely comes from government regulations. Specifically, southeastern China has experienced the fastest urbanization and industrialization development in the last few decades, and it is also the area with the most effective pollution reduction since the emission reduction policies were enforced in 2013 , Zheng 2018, Wei et al 2021. Following Park et al (2012) and Deng et al (2013), a spatial 'pattern-amplitude projection' (PAP) coefficient is calculated to further quantify the overall contributions of individual processes to the spatial distribution of surface temperature anomalies over China in the 2016/17 winter. The PAP coefficient is defined as:

Assessment of the overall contributions of individual processes to the surface temperature anomalies
where PAP i and ∆T i are the spatial PAP coefficient and partial surface temperature differences linked to the ith process, respectively. ∆T is the total surface temperature difference, and ⟨ ⟩ denotes the calculation of area average. The sum of all PAP i equals to the  area average of the total surface temperature differences shown in figure 2(b). As expected, the three major positive contributors to the warming pattern are atmospheric dynamics, water vapor, and aerosols (figure 4). Although the change of surface albedo has an area-averaged net cooling effect (figure 2(g)), it provides a considerable positive contribution to the spatial pattern of warming. Changes of solar irradiance, ozone, CO 2 , and clouds provide relatively smaller positive contributions to the spatial pattern while change of CH 4 shows a negligible impact. The only negative contributor is surface dynamics, which tends to cool the surface as the surface warms through transfer of sensible and latent heat to the atmosphere, providing negative feedback to surface temperature change.

Conclusion and discussion
The attribution of variations in surface temperature has attracted substantial interest and also generate lots of controversies within and beyond the climate community, especially with focuses now shifting from global to regional scales (Stott et al 2010, Najafi et al 2015, Zhai et al 2018. In this study, an updated CFRAM incorporating aerosol effects, namely the CFRAM-A, is developed and used to quantify the contributions from multiple radiative and dynamical processes responsible for the extreme warming over China in the 2016/17 winter.
The warming is observed throughout the country in this winter with remarkable warm anomalies over northern and southeastern China and relatively weak warm anomalies over southwestern China. The changes in atmospheric dynamics, water vapor, and aerosols contribute most to the magnitude and spatial structure of the warming. The effects of water vapor and atmospheric dynamics are detected over both northern and southeastern China, while the aerosol effect is primarily concentrated over southeastern China. The external forcings of solar irradiance, ozone, and CO 2 provide a moderate uniform warming throughout the country, while the effect of CH 4 is negligible. The effects of surface albedo and clouds are highly region-dependent. The surface albedo effect is important over high-latitudes or high-elevation regions, where significant snow cover changes are observed under global warming. The clouds effect is linked mainly to the regional total cloud cover changes, and to some degree includes indirect aerosol effects that cannot be isolated at this stage. The surface dynamics associated with negative feedbacks between the surface heat fluxes and surface temperature produces an overall cooling effect, compensating the warming in 2016/17 winter.
The CFRAM-A analysis reveals a considerable effect of warming associated with aerosols over southeastern China and this effect may ultimately be attributed to the effectiveness of emission reduction policies implemented in China since 2013 , 2019b, Zheng 2018, Zheng et al 2020, Wei et al 2021, given the dominant role of anthropogenic aerosols in the total aerosol effect. This finding suggests that mitigating pollution and reducing anthropogenic aerosols would accelerate regional warming, which likely occurred for Europe and North America after their emission reduction policies were issued in the last century (Ruckstuhl et al 2010, Turnock et al 2015. It should be noted that this study only provides a preliminary quantitative attribution analysis of one extreme temperature case, and more comprehensive results will be obtained in the near future with additional cases and updated reanalysis datasets. One particular goal for the future work is to further constrain the effects of aerosols and clouds using ground-based and remote sensing observations.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https:// disc.gsfc.nasa.gov/datasets?project=MERRA-2.