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We analyse observed near-surface air temperature anomalies over land from the circumpolar region north of 65° N using gridded temperature observations from the CRUTEM4 (Climatic Research Unit gridded land temperature data, version 4) data set. Although spatial coverage over the Arctic remains limited by the availability of long-term station data, coverage is considerably improved compared with a previous version of the data set⁹. This data set consists of gridded (5° × 5°) monthly mean surface temperature anomalies that are expressed relative to the 1961–1990 climatology. To focus on long-term changes we calculate non-overlapping five-year seasonal and annual means for five-year periods beginning with 1913–1917 and ending with 2008–2012. Five-year means are calculated only when more than 50% of potentially available data are present over each period, and are otherwise flagged as missing. Grid cells for which 70% of five-year means can be calculated are included in the analysis.

We compare observed Arctic temperature anomalies with output from nine CMIP5 (Fifth Phase of the Coupled Model Intercomparison Project) climate models that provide climate simulations to 2012 with historical greenhouse-gas changes (GHG), historical natural forcing (NAT), and historical variations in all forcing agents combined (ALL), including greenhouse gases, aerosol, ozone, land cover and natural forcings. Note that overall, CMIP5 models have improved simulations of Arctic sea-ice changes compared with earlier generation models¹⁰. A total of 35 forced simulations were available for each forcing combination from the nine models combined (bcc-csm1-1, CanESM2, CNRM-CM5, CSIRO-Mk3-6-0, GISS-E2-H, GISS-E2-R, HadGEM2-ES, IPSL-CM5A-LR and NorESM1-M) as detailed in Supplementary Table 1. Most CMIP5 historical ALL simulations end in 2005, and thus we use either extended ALL simulations provided by some modelling centres or simulations extended from 2005 to 2012 with the corresponding RCP4.5 (Representative Concentration Pathway emissions scenario with approximate total radiative forcing in year 2100 relative to 1750 of 4.5 W m⁻²) simulations. In addition, we use 24,800 years of pre-industrial control simulation from 42 CMIP5 models (Supplementary Table 2) to assess internal climate variability.

Model output is processed to replicate the availability of the observations as closely as possible. CMIP5 near-surface air temperatures over land are re-gridded to the spatial resolution of CRUTEM4 (5° × 5°), and each simulation is masked by the observational coverage to ensure consistent spatial and temporal coverage with observations. We remove the seasonal cycle by subtracting the 1961–1990 climatology for individual months to produce monthly anomalies, and calculate non-overlapping five-year means as for the observations, using the same criteria for data availability.

Observations and historical simulations with ALL forcing agents show warming throughout the Arctic land regions (Fig. 1), with greater warming in Siberia, Alaska and Canada. The multi-model GHG forcing response, which does not include the cooling effect of anthropogenic aerosol emissions, shows a stronger warming trend than observed. The multi-model response to the other anthropogenic forcings consisting of aerosols, ozone and land use change (OANT), which is estimated by subtracting the responses to GHG and NAT forcings from ALL, exhibits a consistent cooling effect for all regions. Previous modelling results have demonstrated that the cooling effect of aerosols on Arctic climate is much larger than the small warming due to ozone changes, with land use change having a negligible effect¹¹; hence, OANT is dominated by aerosol changes. Note that NorESM1-M includes time-varying ozone in its single GHG simulation in contrast to all other models that include only the well-mixed greenhouse gases in their GHG simulations.

a–d, CRUTEM4 observations (a), and CMIP5 multi-model ensemble averages based on 9 models and 35 ensemble members for each type of forcing: ALL (b), GHG (c) and OANT (d). Land areas with no data are shaded dark grey and ocean areas are shaded the lighter grey indicated by ‘O’ on the colour scale. Trends are calculated from 5-yr means. ALL corresponds to simulations with all major anthropogenic and natural forcings, GHG corresponds to simulations forced by greenhouse-gas changes, and OANT corresponds to simulations forced by anthropogenic forcings other than greenhouse gases.

We used a total least-squares optimal fingerprinting approach^{14, 24} for detection and attribution, which uses a generalized linear regression model to represent observed changes as a linear combination of GHG-, OANT- and NAT-induced changes. The regression model represents observations as

where T_obs is a vector of observed temperature anomalies, T_ALL, T_NAT and T_GHG are estimates of the responses to ALL, NAT and GHG forcing respectively, the β terms are corresponding scaling factors and ε is residual variability that is generated internally in the climate system. Scaling factors for T_GHG, T_OANTandT_NAT are obtained by decomposing T_ALL as T_ALL = T_GHG + T_NAT + T_OANT and substituting as follows:

Fitting the regression model requires estimates of the covariance structure of internal climate variability, which are constructed using unforced control simulations. The regression model is fitted without resorting to an empirical orthogonal function truncation to reduce the dimension of the detection space because sufficient control simulations are available to estimate full-rank covariance matrices. A residual consistency test is used to compare model-simulated internal variability with observations.

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