The annual cycle is the largest variability for many climate variables outside the tropics. Whether human activities have affected the annual cycle at the regional scale is unclear. In this study, long-term changes in the amplitude of surface air temperature annual cycle in the observations are compared with those simulated by the climate models participating in phase 5 of the Coupled Model Intercomparison Project (CMIP5). Different spatial domains ranging from hemispheric to subcontinental scales in mid- to high-latitude land areas for the period 1950–2005 are considered. Both the optimal fingerprinting and a nonoptimal detection and attribution technique are used. The results show that the space–time pattern of model-simulated responses to the combined effect of anthropogenic and natural forcings is consistent with the observed changes. In particular, models capture not only the decrease in the temperature seasonality in the northern high latitudes and East Asia, but also the increase in the Mediterranean region. A human influence on the weakening in the temperature seasonality in the Northern Hemisphere is detected, particularly in the high latitudes (50°–70°N) where the influence of the anthropogenic forcing can be separated from that of the natural forcing.
Climate change refers to a change in the state of the climate that can be identified by changes in the mean and/or the variability of its properties (Stocker et al. 2013). The annual cycle is the dominant variability at the monthly and daily time scales for many climate variables in the regions away from the tropics. The annual cycle of surface air temperature is responsible for potentially more than 90% of temperature variance at the monthly and daily time scale in mid- to high-latitude land areas (e.g., Thomson 1995; Qian et al. 2011a). While changes in the annual mean temperatures have been extensively studied (e.g., Bindoff et al. 2013; Hartmann et al. 2013), much less attention has been paid to changes in the annual cycle. Indeed, changes in the amplitude and phase of the annual cycle of temperature have been observed (e.g., Thomson 1995; Mann and Park 1996; Wallace and Osborn 2002; Stine et al. 2009; Qian et al. 2011a,b; Stine and Huybers 2012). Changes in the amplitude of the annual cycle can affect the estimation of climate trends and variability (Qian et al. 2011a): for example, the classification of El Niño/La Niña years (Qian et al. 2011c). Changes in the amplitude of the annual cycle may also potentially affect performance of annual temperature reconstructions because high-frequency climate information obtained from some proxies is more indicative of “summer” conditions (Jones et al. 2003). In addition, the annual cycle has a strong influence on the biological system. It is therefore important to understand the causes of the observed changes in the amplitude of the annual cycle.
Human influence has been detected in the mean value and the extremes of temperatures at the global and regional scales (Bindoff et al. 2013). It is still unclear if human activities have had a detectable influence on the annual cycle of surface air temperature, despite some limited comparisons between observations and model simulations. Mann and Park (1996) showed consistent decreasing trends in the amplitudes of the annual cycle of the Northern Hemisphere mean temperature between the observations and those simulated by two climate models under CO2 forcing. Wallace and Osborn (2002) found that the weakening in the annual cycle of the Northern Hemisphere mean temperature during the twentieth century simulated by the HadCM2 forced with the combined effect of greenhouse gases and sulfate aerosols agrees well with that in the observations. Using an index representing the magnitude of the annual cycle averaged over global land areas for the period 1950–99, Braganza et al. (2004) found detectable responses to the combined effect of greenhouse gas and sulfate aerosol in the simulations by four out of the five climate models, and the responses are consistent with the observations. Using the same global index, Drost and Karoly (2012) found further that the trend in the magnitude of the annual cycle during the period 1900–2005 cannot be explained by natural forcings alone. Averaging at the global and the hemispheric scales may enhance signal-to-noise ratio if the long-term changes are of the same sign over the space. However, observed large-scale trends in the amplitude of the annual cycle may have different signs in different regions, as will be illustrated later in this study, averaging across regions of opposite signs of long-term change cancels the changes, thereby reducing the signal-to-noise ratio and masking important regional differences. It is therefore important to conduct regional detection and attribution analysis.
Here, we compare observed and model-simulated changes in the amplitude of the surface air temperature annual cycle in mid- to high-latitude land areas during 1950–2005 at the hemispheric and regional scales. We use simulations by multiple climate models participating in the World Climate Research Programme’s phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012). CMIP5 includes the latest generation of climate models, with an ability to simulate surface temperature that has improved in many aspects relative to the previous generation of models (CMIP3; Flato et al. 2013). We consider the effects of individual external forcings as well as the combined effect of multiple external forcings. The forcings under consideration include natural external forcing and anthropogenic forcing (greenhouse gas and anthropogenic aerosol concentrations and land-use change).
2. Data and methods
The latest version (184.108.40.206) of the gridded monthly land-based temperature anomalies from the Climatic Research Unit (CRU) of the University of East Anglia (CRUTEM4; Jones et al. 2012a,b) is used for the analyses presented in the main text. The data are on a 5° × 5° latitude–longitude grid. Finer-resolution grid temperature datasets exist [e.g., GISS at 2° × 2° and CRU time series, version 3.22 (CRU TS3.22), at 0.5° × 0.5°], but they do not offer much advantage over the CRUTEM4, since these datasets are based on similar station data and rely on data interpolation to fill in data void regions (Hansen et al. 2010; Harris et al. 2014). For the purpose of this study, we only consider extratropical areas south of 23.5°S or north of 23.5°N where annual cycles are distinct. For the Southern Hemisphere, areas south of 60°S are also excluded from the analysis because of limited data availability (Jones et al. 2012a,b). CRUTEM4 data are monthly anomalies relative to the base period 1961–90 (Jones et al. 2012a,b). To obtain monthly temperature at the grid point 67.5°N, 152.5°W that is illustrated in Fig. 1, we added the climatology of temperatures for the base period 1961–90 (Jones et al. 1999) to the monthly anomaly series for the location.
2) Climate model simulations
Monthly mean near-surface air temperature (tas) from the CMIP5 archive are used. We use historical simulations to estimate model-simulated temperature responses under different external forcings and preindustrial control simulations (piControl) to estimate natural internal climate variability. We consider climate model–simulated responses to historical forcings from six different experiments: namely, natural and anthropogenic forcings combined (ALL), natural (NAT), anthropogenic (ANT), greenhouse gas (GHG), anthropogenic aerosol (AA), and land-use (LU) forcing only. Most of these CMIP5 simulations end in 2005. Therefore, the detection and attribution analyses are conducted for the period 1950–2005. Simulations from an ensemble of 18 models have been used in the analysis. To reduce noise in the signal, we only consider simulations with multiple runs by the same model. Table 1 lists the number of simulations used from each model for different forcing experiments. Individual forcings runs are not available from every model, as the models in the CMIP5 archive are an “ensemble of opportunity.” Therefore, datasets for some of the experiments may not come from the same set of models as others; for example, ANT simulations come from only 40% of the models that provided ALL simulations.
b. Data preprocessing
To take into account missing values in CRUTEM4 data and different horizontal resolutions of CMIP5 models, the following steps were applied to CMIP5-forced simulations:
Monthly anomalies were calculated for each grid point and simulations by removing the relevant mean values over the base period 1961–90, as done in CRUTEM4. This corrects to some degree systematic bias in model-simulated climatology. Since there are elevation differences among stations, anomalies at each station are first calculated before 5° × 5° gridbox anomalies are computed for CRUTEM4 (Jones et al. 2012a,b). To be consistent with CRUTEM4, we also calculated anomalies at each model grid first.
The anomalies were then regridded to the common CRUTEM4 grid (5° × 5°).
The regridded anomalies were masked to mimic data availability of the CRUTEM4.
A forced response represented by relevant multimodel ensemble mean (MME) was obtained by first computing individual model ensemble mean and then averaging across available models. This gives equal weights for different models and avoids models with larger numbers of ensemble members dominating the statistics of the MME.
The detection and attribution analyses were conducted on the time evolution or space–time evolution of the annual cycle amplitudes. While time evolution of the average over the whole spatial domain under consideration may provide better signal-to-noise ratio, analysis with finer spatial details improves confidence in the results of the analysis. For this purpose, we computed area-weighted averages of monthly temperature anomalies over large land regions (Fig. 2a) and conducted the analyses for individual regions separately or for multiple regions combined. The analyses involved one or more space dimensions, including (i) the northern middle-to-high latitudes (23.5°–90°N) as one region (NH); (ii) the northern midlatitudes (23.5°–50°N) and the northern high latitudes (50°–70°N) as two regions; and (iii) dividing the mid- and high-latitude regions over North America (170°–25°W), western Eurasia (25°W–60°E) and eastern Eurasia (60°E–180°) to form six areas: Canada (50°–70°N, 170°–25°W), northern Europe (NorEurope; 50°–70°N, 25°W–60°E), northern Asia (NorAsia; 50°–70°N, 60°E–180°), the United States of America (USA; 23.5°–50°N, 170°–25°W), the Mediterranean region (23.5°–50°N, 25°W–60°E), and East Asia (EastAsia; 23.5°–50°N, 60°E–180°,). The names of these six areas do not necessarily align well with geopolitical boundaries and are used for easier referencing.
PiControl simulations (Table 1) were divided into multiple nonoverlapping 56-yr segments, with the last segments discarded if shorter than 56 yr. The number of 56-yr segments is listed in Table 1 for each model. There are a total of 234 pieces of 56-yr segments. Each segment was treated as a 1950–2005 time series and processed in the same way as the forced simulations using the steps described above, except without step 4.
c. Methods for the estimation of the annual cycle amplitude
A temporally local and adaptive filter named the ensemble empirical mode decomposition (EEMD; Wu and Huang 2009; Huang and Wu 2008) has been used to isolate the 1-yr period annual cycle (Wu et al. 2008) and, subsequently, to estimate its amplitude (Qian et al. 2011a). The capability of the EEMD filter in isolating the annual cycle, which has strong amplitude–frequency modulation, from a climate variable has been validated through analyzing synthetic data, monthly sea surface temperature data, and daily temperature records (Wu et al. 2008; Qian et al. 2011b,c). Figures 1a and 1b show a schematic diagram of an application of the EEMD filter to the monthly mean temperature (monthly temperature anomalies from CRUTEM4 plus climatology) for the 5° × 5° grid box centered at 67.5°N, 152.5°W to isolate this time-varying annual cycle at the location and the resulting amplitude, respectively. The amplitude is shown as annual mean and anomaly relative to 1961–90. Qian et al. (2011c) provide a detailed description of procedure on how to obtain this annual cycle and its amplitude. This method is computation intensive. As we need to process a large number of model simulations, we also consider a simplified scheme. Since we are interested in changes in the amplitude rather than the actual value of the amplitude, we consider the following simplified scheme:
where Amplitude is the amplitude anomaly at a grid or a region, and Tsummer and Twinter are the summer and winter mean temperature anomalies, respectively. Summer is defined as June–August (JJA) in NH and as December–February (DJF) in SH, while winter is defined as DJF in NH and JJA in SH. Therefore, Eq. (1) can be rewritten as
Here, TJJA and TDJF are temperature anomalies in the current JJA and the following DJF for both NH and SH. In total, the monthly anomaly data for the period 1950–2005 resulted in amplitude anomalies for 55 yr (1950/51–2004/05). The use of seasonal mean temperatures in the simplified method produces a smaller magnitude of the annual cycle amplitude when compared with that computed from EEMD-based scheme (not shown). However, there is little difference in the decadal variability (after 11-yr running mean) in the relevant anomaly time series (Fig. 1b). More importantly, trends in the two time series are almost identical (Fig. 1b). To reduce the computational need when processing the model data, we use the simplified method to compute the amplitude anomaly for the subsequent analysis and simply refer to the amplitude anomaly as “amplitude.”
d. Trend analysis
To illustrate long-term changes, we estimate linear trend in the amplitudes from the observation data for individual grid boxes separately (Fig. 2). The amplitude of the year is calculated using the mean temperature anomalies from the available months within each season if there is at least one monthly value both in JJA and in DJF. Otherwise, the seasonal mean temperature anomalies for both seasons and the amplitude for that year are treated as missing. A trend is not estimated for a grid box if there are more than ⅓ missing values in the 55-yr amplitude time series. A more strict requirement for data availability reduces the number of grid boxes for trend estimation, especially in East Asia, but this does not change the spatial pattern of the trend and does not affect the detection and attribution results.
We also estimate the linear trends in the area-averaged amplitude using an ordinary least squares method. To consider possible autocorrelation in the time series of regional averages, the statistical significance of the trends is tested with the Mann–Kendall test and with a prewhitening approach that removes the first-order autocorrelation (von Storch and Navarra 1995). The first-order autocorrelation is calculated through an iterative process proposed by Zhang et al. (2000) and refined by Wang and Swail (2001). Note that, while it is useful to provide a visual presentation of the long-term trends, our main conclusion on the detection of changes against internal variability is based on the more formal detection and attribution analysis outlined below.
e. Methods for detection and attribution
To quantify possible influence of external forcings on amplitude, we conduct detection and attribution analyses on nonoverlapping 5-yr mean values over large regions described in section 2b. A 55-yr amplitude anomaly series provides 11 5-yr mean values (1950/51–1954/55, 1955/56–1959/60, …, 2000/01–2004/05). We compare observations with model-simulated responses to ALL, ANT, and NAT to identify observational evidence of climate responses to anthropogenic forcing and natural external forcing. We use two different methods (described below) to test robustness of the results: one is a correlation-based nonoptimal method (Santer et al. 1995; Wan et al. 2015), and the other is the optimal fingerprinting approach (Allen and Stott 2003) with a regularized covariance estimate (Ribes et al. 2009, 2013).
1) Correlation-based method
We use an easy-to-understand approach to provide a qualitative measure of the similarity between the space–time evolution of the amplitude in the observations and in the model-simulated responses to external forcings. In doing so, we compute correlation coefficients between observations and signals for ALL, ANT, or NAT separately. We use a one-sided test to determine statistical significance of the correlation. To this end, we also compute correlation coefficients between observations and each of the 234 chunks of piControl simulations. If the correlation coefficient between the observation and a signal is above the 90th percentile of the correlation coefficients between observations and the piControl chunks, we consider that correlation to be statistically significant at the 10% level over internal variability and that the forced response is detected in the observation.
2) Regularized optimal fingerprinting
We use a total least squares–based optimal fingerprinting approach (Allen and Stott 2003) to quantify the consistency between model-simulated responses and observations. The statistical model is based on the generalized linear regression and takes noise in the response patterns into consideration:
where y is the space–time observation vector; xi is the ith model-simulated response pattern from finite ensemble members and is, therefore, contained with sampling noise ξi; m is the number of signals; β is a vector of regression coefficients or scaling factors to be estimated; and ε is the noise in the observations.
Estimating the scaling factors β and their uncertainty requires the estimation of the covariance matrix for ε. Two independent estimates of the matrices and are required for optimization and for uncertainty analysis (Hegerl et al. 1996; Allen and Stott 2003). We divide the 234 piControl segments into two halves to calculate and , respectively. We use the Scilab code of Ribes et al. (2013) to conduct the detection and attribution analyses. This includes 1) the use of a more robust regularized estimator for , 2) taking into account noise in all variables proposed by Allen and Stott (2003) when estimating the uncertainties in β, and 3) a Monte Carlo–based residual consistency test. Temporal centering, achieved by removing the mean over the full period, had been applied to all the variables prior to input into Eq. (4).
a. Observed changes
Figure 1a shows clearly that the annual cycle is the dominant variability, explaining 93% of the total variance of monthly mean temperature for a high-latitude grid box centered at 67.5°N, 152.5°W. For regionally averaged temperature series at mid- to high-latitude land areas, the annual cycle is also the dominant variability. For example, the annual cycle of the China-averaged daily temperature series contributes 96% of the total variance (Qian et al. 2011a). The annual cycle has been separated from the trend (Fig. 1a) and is therefore independent of the warming trend. The linear trend in the amplitude for the period 1950–2004 is −0.31°C decade−1 (Fig. 1b). The overall decrease during this 55-yr period is about one-tenth of the mean absolute amplitude (16.95°C) estimated from half of the difference between summer and winter mean temperature for the period 1950–2005 and is quite large.
Globally, amplitudes in many of the land regions are decreasing (Fig. 2b), indicating a weakening of the seasonality. This is especially the case in the NH high latitudes, where trends at some grid boxes are below −0.4°C decade−1. In most parts of this region, especially in Canada and central Eurasia, winter warms much faster than summer (Figs. 2c,d). However, there are also regional differences, particularly in the Mediterranean region, where summer warms faster than winter, resulting in slightly increasing amplitudes. In the SH, changes in the amplitudes are very small and with opposing signs in different regions. The spatial pattern of amplitude trends presented here is consistent with that estimated from the yearly sinusoidal component using the Fourier transform (Stine et al. 2009). However, our estimates are based on data from more grid boxes, as newly incorporated in CRUTEM4.
The NH area-averaged amplitude (Fig. 3a) has a decreasing trend of −0.059°C decade−1, which is statistically significant at the 1% level. In contrast, the trend in the SH area-averaged amplitude (Fig. 3b) is negligible. This difference in the amplitude trends in the two hemispheric mid- to high-latitude land areas where annual mean temperatures have significantly increased (Figs. 3c,d) suggests that changes in the amplitude are not necessarily related to changes in the annual mean temperature. At the annual time scale, the correlation between the NH average annual mean temperature and the amplitude is not significant (Fig. 4a). The correlation between the amplitude and summer temperature is weaker (Fig. 4b), whereas the correlation between the amplitude and winter temperature is significant at the 1% level (Fig. 4c), with a correlation coefficient of −0.85. For the smaller NH regions analyzed here, the results (Table 2) are similar, with the exception for the Mediterranean region, where the correlation between amplitude and summer temperature is also significant at the 1% level. The effective number of degrees of freedom used in the determination of statistical significance of these correlations was estimated based on the first-order autoregressive process (Bretherton et al. 1999).
The model-simulated spatial patterns of the changes in the amplitude, JJA mean temperature, and DJF mean temperature (Figs. 2e–g) are similar to those in the observations (Figs. 2b–d). In the following section, we present results from our detection and attribution analyses to identify possible human influence.
b. Correlation-based detection and attribution analyses
1) Average over NH
The correlation coefficients between the observations and the model-simulated responses to ALL, ANT, and NAT are 0.73, 0.60, and 0.21, respectively. The one-sided Monte Carlo test conducted with piControl simulations indicates that the correlation between the observations and the model-simulated response to ALL or ANT forcing is significant, while that between the observation and simulated response to NAT forcing is not (Fig. 5a). These results suggest that the model-simulated response to ALL or ANT forcing is detectable, whereas that to NAT forcing is not detectable.
The trend in the model-simulated NH averaged amplitude is consistent with that of observations only if anthropogenic forcing is involved (Fig. 5b). The model-simulated response to ALL forcing shows a decreasing trend as in the observations, although the magnitude of the trend is weaker. The magnitude of trend under GHG forcing is much closer to, although still smaller than, that of the observations. Responses to NAT or AA forcing do not show discernible long-term trend. Note that there is a decadal transition from a decreasing trend to an increasing trend around the mid-1980s in the AA response, possibly reflecting the effect of the so-called “from dimming to brightening” phenomenon (Wild et al. 2005), which refers to the transition from a decreasing trend to an increasing trend in solar radiation reaching the land surface. Qian et al. (2011a) suggested, based on observational evidence in China, that changes in the surface solar radiation play a role in the changes in the amplitude of the temperature annual cycle. The evidence from model simulations presented here seems to supports this connection. LU forcing results in a small increase trend in the amplitude (Fig. 5b). Overall, the similarity in the long-term variation and changes between observations and model-simulated responses suggests that anthropogenic influence on the annual cycle amplitude is detectable and that the increase in GHG is the main contributor.
2) Space–time evolution in two subregions
Correlation analysis based on space–time evolution of the magnitude with two spatial dimensions (50°–70°N and 23.5°–50°N) over the NH indicates that the model-simulated response to ALL or ANT forcing in the NH is detectable in the observations, whereas that to NAT forcing is not (Fig. 6a). The result for the subregion 50°–70°N is similar. However, response to ALL or ANT forcing is not detectable in the subregion 23.5°–50°N.
Trends in the regionally averaged amplitude series for the subregion 50°–70°N (Fig. 6b) are similar to those of NH average discussed in the previous subsection. The observed decreasing trend of −0.108°C decade−1 is statistically significant at the 5% level. It appears that the detectable change in the ANT response mainly comes from GHG forcing, to which the model-simulated response is close to observations. In contrast, none of the forced signals is consistent with the observed small decreasing trend in the regional average amplitude for the subregion 23.5°–50°N (Fig. 6c).
3) Space–time evolution in six subregions
Correlation analysis based on space–time evolution of the magnitude with six spatial dimensions over the NH confirms the results of the above analyses that the response to ALL or ANT forcing is detectable in the observations, whereas that to NAT forcing is not (Fig. 7a). Results for each of the six individual regions vary. The response to ALL is detected at the 5% level in Canada and East Asia and at the 10% level in northern Europe and the Mediterranean region. The NAT signal alone cannot be detected in any of the six regions except for East Asia at the 10% level, and the ANT signal can only be detected in East Asia. These indicate correlation-based detection results deteriorate at a smaller spatial scale.
The time series in Figs. 7b–g show decreasing trends in observed amplitudes in all regions, except for the Mediterranean region. Model-simulated responses to NAT forcing show little trends in every region. In Canada, northern Europe, and northern Asia (Figs. 7b–d), the observed trends are at the rate of −0.106°, −0.104°, and −0.119°C decade−1, respectively. Model-simulated responses to the ALL forcing correctly reproduce the sign of the trends but underestimate the magnitude. Trends in the GHG responses are of similar magnitudes to that of the observations. Responses to AA exhibit a small increasing trend in Canada and northern Europe but a small decreasing trend in northern Asia. Responses to LU show little trend in Canada but small increasing trends in northern Europe and northern Asia. In these three regions, GHG forcing seems to be important for explaining the observed weakening in the seasonality, even though the ANT signal is not detected (Fig. 7a). In the USA, trends are weak in both the observations and model simulations (Fig. 7e). In the Mediterranean region (Fig. 7f), ALL and GHG simulations correctly reproduced positive trends as in the observation, but the magnitude of the trends is smaller than observed. The effect of AA is noticeable in this area, resulting in a weakening in the seasonality and, thus, an effect opposite to that of GHG. The effect of LU tends to weaken seasonality but is much smaller than that of AA. In East Asia (Fig. 7g), the observed trend of −0.117°C decade−1 is significant at the 1% level. It is reproduced in the ALL-forcing simulation, but the magnitude is much smaller than the observations. The effects of GHG and AA forcing both tend to weaken the seasonality, but the magnitude is very small. Trends in LU-forcing simulations are also very weak.
c. Optimal fingerprinting analyses
Figure 8 displays scaling factors and their 90% uncertainty range for the one-signal analyses. In all cases, the residual consistency tests do not indicate evidence of inconsistency between the regression residual and model-simulated variability.
Figure 8a shows the results for NH when the detection analyses are conducted with one, two, and six spatial dimensions. The scaling factors for the ALL-forcing signal are all significantly greater than 0 (10% two-sided test). Their best estimates are larger than 1, but their 90% confidence intervals still include 1. These indicate that the combined effect of anthropogenic and natural forcings is robustly detected in the observations, and the model-simulated response is consistent with the observed changes. The analyses conducted with ANT-forcing signal show similar results. When the ALL-forcing signal is estimated from the six models that produced the ANT-forcing simulations (ALL6), the detection results are also very similar to those when the ALL-forcing signal is estimated from all available ALL-forcing simulations.
Figure 8b shows the scaling factors for the high (50°–70°N) and middle (23.5°–50°N) northern latitude land areas when the analyses are conducted with one spatial dimension (regional mean) or three spatial dimensions that combine Canada, northern Europe, and northern Asia (High3) or USA, Mediterranean region, and East Asia (Mid3), respectively. For the 50°–70°N, both the one-dimensional and the three-dimensional analyses show a clear detection for the model-simulated responses to ALL and ANT forcings and these model-simulated responses are consistent with the observed changes. For 23.5°–50°N, ALL and ANT signals are not detected in one-dimensional analyses, but in the three-dimensional analyses, ALL is detected and the 5% lower bound for ANT scaling factor is just slightly under zero. These results suggest that averaging the amplitudes with the opposing signs of trend in the different regions of 23.5°–50°N does have an effect of reducing the signal-to-noise ratio.
Figure 8c displays the scaling factors and their 90% uncertainty range for individual area-averaged amplitude over the six regions separately. It is shown that in Canada, northern Europe, northern Asia, and the Mediterranean region, model-simulated response to ALL forcing is detected in the observations and is consistent with the observed changes. In USA, response to ALL forcing is not detected. In East Asia, response to ALL forcing is detected, although models may have underestimated the observed change. In Canada, the model-simulated response to ANT forcing is detected and is consistent with the observed changes. In East Asia, the model-simulated response to ANT forcing is detected, but the models may underestimate the observed change.
In an attempt to separate model-simulated responses to ANT and NAT forcings in the observations, we used two predictors in the regression involving both ANT and NAT signals. The NAT signal is estimated from the same six models that produced ANT-forcing (NAT6) simulations. It proved to be difficult to separate the signals, especially at the regional scale. Many of the scaling factors are either unbounded, or it is difficult to estimate the confidence interval. Figure 9 displays the scaling factors and their 90% marginal confidence interval if the confidence is successfully estimated. It appears that the response to ANT forcing may be separated from that to NAT forcing in a one-dimensional analysis for high latitude (50°–70°N) and for East Asia.
In simplistic terms, one may consider the amplitude of the annual cycle as the difference between the mean temperatures during the winter and summer seasons. Because the signals that exist in mean temperatures for both seasons are of the same sign, the difference between them would have a much-reduced magnitude. Therefore, the signal strength is much weaker in the amplitude of the annual cycle than in the seasonal mean temperatures. Additionally, the natural variability in the amplitude of the annual cycle would be larger than that in either seasonal mean temperature, because variance becomes larger when two random numbers are subtracted. Given the reduced signal strength and the increased natural variability, the signal-to-noise ratio in the annual cycle amplitude is expected to be much smaller than that in the seasonal mean temperature. This makes it much more challenging to detect external influence in the annual cycle amplitude than that in seasonal mean temperatures. Our results seem to confirm this. For example, ANT is not robustly detected in every region. To put this discussion in perspective, we also conducted detection and attribution analyses on seasonal mean temperatures for different spatial domains and spatial dimensions considered in this study. The results are summarized in Fig. 10. Model-simulated responses to ALL forcing are detected in the observations in almost all cases and are consistent with the observed changes in most cases for both the JJA and DJF mean temperatures (Fig. 10a). Additionally, ANT can be separated from NAT in the observations in the joint two-signal detection in most cases as well, and its magnitude is also consistent with observations for both the JJA and DJF mean temperatures (Figs. 10b,c). The robust detection of model-simulated responses to ALL and ANT forcings in observed winter and summer temperatures and the separation of response to ANT forcing from NAT forcing in the observations provide robust evidence that anthropogenic forcing has influenced both winter and summer temperature in the region. This provides strong collaborative evidence to support the detection results for the annual cycle amplitude reported in this study.
We have compared changes in the amplitude of the surface air temperature annual cycle in the observations and in the CMIP5 simulations at hemispheric-to-subcontinental scales for the period 1950–2005. Our analyses included the Northern Hemisphere mid- to high-latitude land areas, the high-latitude and the midlatitude regions, and six subcontinental areas. For most of the regions we analyzed, the CMIP5 multimodel ensemble mean performs reasonably well in simulating the observed changes. It captures the weakening of the seasonality in the northern high-latitude region and East Asia, as well as the strengthening of the seasonality in the Mediterranean region. The overall space–time pattern of the model-simulated response to external forcings is consistent with the observed changes. Anthropogenic influence can be detected in the space–time evolution of the northern mid- to high-latitude land areas, in the average over 50°–70°N, and in East Asia by using both the nonoptimal detection and optimal fingerprinting methods. In the 50°–70°N average and in East Asia, ANT forcing can further be separated from NAT forcing in the joint two-signal detection.
We thank Francis W. Zwiers, Brigitte Mueller, and three anonymous reviewers for their constructive comments. We acknowledge the Program for Climate Model Diagnosis and Intercomparison and the World Climate Research Programme’s Working Group on Coupled Modelling for their roles in making the WCRP CMIP multimodel datasets available. This study is jointly sponsored by the National Basic Research Program of China (Grant 2011CB952003) and the Jiangsu Collaborative Innovation Center for Climate Change.