In December 2015, 195 countries agreed in Paris to “hold the increase in
global mean surface temperature (GMST) well below 2.0
Global mean surface temperature (GMST) is undoubtedly one of the key indicators of climate change. Tollefson (2015) denotes the GMST indicator as “the global thermostat”. Over the years many articles have been published in relation to GMST series and the patterns therein. These patterns combine an anthropogenic signal – induced by growing concentration of greenhouses and processes such as aerosol cooling – as well as natural variability. Natural variability can be regarded as a correlated noise process consisting of (i) internal random unforced (chaotic) variability and (ii) external radiatively forced changes. Here, internal variability is steered by short-term processes such as weather in the high latitudes or El Niño and La Niña, as well as by decadal processes such as the Interdecadal Pacific Oscillation (e.g. Trenberth, 2015; Fyfe et al., 2016; Xie, 2016; Meehl et al., 2016), and will result in correlated noise in GMSTs (Mudelsee, 2014; Roberts et al., 2015). Externally forced variability is mainly due to volcanic eruptions and variations in solar irradiance. It influences global temperatures on annual to centennial scales (IPCC, 2013 – chap. 10; Forster et al., 2013; Mann et al., 2016). A recent realization of internal variability led to a fierce debate in the popular media: GMSTs were showing a claimed “slowdown”, “pause” or “hiatus” from the year 1998 onwards (e.g. Lewandowski et al., 2015; Hedemann et al., 2017; Medhaug et al., 2017 – their Fig. 1).
GMST has been a crucial indicator in climate negotiations for a long time and
it has even become more so at the following 21st Conference of Parties
(COP21) in Paris, December 2015. The final accord, approved by 195 countries,
agreed on GMST targets which aim to avoid increases of 1.5 and
2.0
So far, little attention has been paid to this topic. IPCC (2013), in its
attempt to clarify the meaning of GMST measurements, applied linear trends to
three different GMST datasets. They reported a trend progression
Hawkins et al. found that the period 1720–1800 would be the most suitable in
physical terms, despite incomplete information about radiative
forcings and very few direct observations during this time. Additionally,
they concluded that the 1850–1900 period would be a reasonable surrogate for
pre-industrial GMSTs, being only 0.05
In this article, we build on the work of Hawkins et al. but we do not base our GMST progression estimates on linear regression models with non-stationary regressors. The drawback of this approach is simply the linearity assumed, while the climate system is (highly) non-linear with a number of feedback processes. The same holds for the approach proposed by Otto et al. (2015) and Haustein et al. (2017), who apply temperature responses to (i) human-induced forcings and (ii) natural drivers as explanatory variables in a multiple regression model where the dependent variable is given by one of the observational GMST datasets.
Therefore, we follow two other trend estimation approaches: (i) statistical trend models and (ii) global temperature trends derived from global climate models (GCMs). Furthermore, we avoid methods or presentations based on subjectively selected time windows (such as Moving Averages). The drawback of time windows is that averages over 21-year periods or similar do not give estimates for the beginning and ending of the sample period chosen (thus, we would have no trend estimates for the period 2007–2016).
A final topic we address is that of warming definitions. Should the Paris targets be interpreted as warming due to both anthropogenic and natural forcings, or as warming due to anthropogenic warming only? The terms “global warming” or “total warming” are interpreted in most literature as the sum of anthropogenic warming plus long-term (decadal to centennial) natural warming, consistent with the IPCC definition of climate change (IPCC Annex II, 2014). However, some researchers interpret “global warming” as anthropogenic warming only, consistent with the definition proposed by UNFCCC in their article 1 (Otto et al., 2015; Haustein et al., 2017; Millar et al., 2017). In both definitions, short-term natural variability – such as seen in “the hiatus period” – is smoothed from warming trends.
Our approach is that of an uncertainty and sensitivity analysis as promoted
by Saltelli et al. (2004), Saisana et al. (2005) and Visser et al. (2015). We
ask the following four major questions:
How robust are estimates for GMST progression to specific choices of trend
modelling, use of GCMs and specific choices of GMST datasets? How do these choices influence uncertainties in GMST progression in
relation to uncertainties due to forced and unforced natural variability? Does the choice for a specific pre-industrial baseline or period play a role? Does it matter if we interpret the Paris targets as total warming or
as anthropogenic warming only?
Summary of observational datasets used in this study. Descriptions of interpolation schemes are only short indications. Details are given in the references.
Since there is no “true” or “best” trend approach (Visser et al., 2015), we explore four trend methods and apply these to five leading GMST products (similar to Hawkins et al.). This leads to a 4-by-5 matrix of GMST trend progressions since 1880. As a parallel path, we compare these trend progressions to those deduced from GCMs. We analyse an ensemble of 42 GCM experiments from the Coupled Model Intercomparison Project phase 5 (CMIP5). GCMs are for a large part physics-based, in contrast to trend methods. However, there are also drawbacks, the main one being that GCMs are only approximations to the real climate system and have considerable biases. Although GCMs are tuned to meet the main characteristics of the present climate (Voosen, 2016), GMSTs derived from GCMs still exhibit a wide range of trend progression estimates, as we will show.
In the discussion section, we address the role of various assumptions as for pre-industrial baselines, and differences in trend progression if Paris targets are interpreted as “total warming” vs. “anthropogenic warming”.
Our analysis is confined to historical data only (up to and including 2016). Examples for GMST projections have been given by IPCC (2013 – chap. 12), Forster et al. (2013), Mann (2014) and Schurer et al. (2017). A short-term prediction model is given by Suckling et al. (2016). An example of an uncertainty and sensitivity analysis of GMST projections has been given by Visser et al. (2000).
Various research groups have published global GMST datasets. IPCC (2013 – Sect. 2.4.3) used three datasets, namely the HadCRUT4 series (Morice et al., 2012; Hope, 2016), the NOAA dataset (Vose et al., 2012) and the NASA/GISS dataset (Hansen et al., 2010). In the analysis here, we instead use a recent update of the NOAA data (Karl et al., 2015). Karl et al. applied a number of corrections which mainly deal with sea surface temperatures, such as the change from buckets to engine intake thermometers. In addition, we added two series, i.e. the version of the HadCRUT4 data in which the missing data have been filled in as published by Cowtan and Way (2014) and the GMST series by Rohde et al. (2013). Note that these datasets are not independent. They start from roughly the same station data over land, and more importantly are based on only two SST analyses: HadSST3 and ERSSTv4.
Cowtan and Way re-analysed the HadCRUT4 series by applying a statistical interpolation technique (kriging) and satellite data for regions where data are sparse. Their series shows higher GMST values in recent decades than the non-interpolated HadCRUT4 series due to the more-than-average warming of the poles. The land part of the GMST data of Rohde et al. (2013; Berkeley Earth group of researchers) systematically addressed major concerns of global warming sceptics, mainly dealing with potential bias from data selection, data adjustment, poor station quality and the urban heat island effect. The ocean part (about 70 %) is taken from HadSST3. A summary of observational data products is given in Table 1.
Graph taken from Callendar (1938). The fourth curve represents his
GMST series, based on temperature data of 147 stations. To highlight smooth
changes over time he used moving averages with a window of 10 years. It is
interesting to note that he also addressed the specific effect of
Since two out of five GMST products start in the year 1880, we use the period 1880–2016 as our period of analysis. We return to this point in the discussion section. All data were downloaded from the institution websites with 2016 as the final year.
Next to these instrumental-data-based GMSTs we analyse three sets of GCM
simulations all taken from CMIP5 (Taylor et al., 2012; IPCC, 2013 –
chap. 9–12). GMST is defined here as the global average of near-surface
temperature (temperature at surface, “tas”), in contrast to the
observational datasets that use SST over sea for practical reasons (also
denoted as “blended temperature series”; Cowtan et al., 2015). The first
set consists of GCM simulations where the input of greenhouse gases from 2005
onwards is taken from three representative concentration pathways (RCPs):
4.5, 6.0 and 8.5
Construction of 1000 surrogate trend series by MC simulation, based
on cubic splines. The AR(1) parameter estimated on the residuals of the
spline model in
The second set that we have analysed, consists of 37 GCM runs for natural variability, denoted as “historicalNat”. These runs comprise forced and unforced natural variability but no GHG forcing (1860–2005). See Forster et al. (2013) for details. Finally, we analysed 41 pre-industrial control (PiControl) runs with lengths varying between 200 and 1000 years. These runs simulate natural internal variability only. All CMIP5 runs were downloaded from the KNMI Climate Explorer website with one member per model (Trouet and Van Oldenborgh, 2013).
The tracking of signals or trends in GMST series has a long history. Callender (1938) studied in detail zonal and global temperatures, along with estimates for warming due to greenhouse gases (Fig. 1). To smooth changes he used moving averages with a window of 10 years. A wide range of methods have been applied since then to isolate long-term signals or “trends” in GMSTs. We have summarized trend techniques in Appendix A (Table A1).
As stated in the Introduction we choose statistical trend methods that allow for the quantification of trend progression where no window is needed and where uncertainty estimates are available for any incremental trend value. Furthermore, no specific period for pre-industrial has to be chosen (such as the mean of the 1851–1900 period or similar). “Pre-industrial” is reflected in the choice of the start of the sample period only.
Based on these considerations we have selected four trend approaches for our
sensitivity analysis: ordinary least squares (OLS) linear trends, integrated
random walk (IRW) trends and two approaches with splines. The first trend –
a linear fit by OLS – was chosen by IPCC (2013) as their main method.
Uncertainties simply follow from the linear model:
The second trend approach that fulfils our uncertainty requirements, are
sub-models from the class of structural time series models (STMs), in
combination with the Kalman filter (Harvey, 1989). From this group of models
we choose the IRW trend model. The IRW trend model
extends the linear regression trend line by a
Results for the IRW trend model as applied to the HadCRUT4 series.
Period: 1880–2016. Panel
The Kalman filter is the ideal filter here since it yields the so-called
minimum mean squared estimator (MMSE) for the trend component in the model.
The Kalman filter has been applied in many fields of research and is gaining
popularity in climate research recently (e.g. Hay et al., 2015). As with OLS
methods, residuals – or innovations in terms of the Kalman filter – should
be white noise. We will use the
A third and fourth approach applies a combination of a trend model and the statistical structure of natural internal variability as derived from PiControl runs. It can be seen as a hybrid approach. To do so we have chosen the cubic spline trend model, a trend approach also applied in the AR5 (IPCC, 2013 – Box 2.2, Fig. 1). For a theoretical background we refer to Hastie et al. (2001) and Chandler and Scott (2011 – Sect. 4.1.3).
Smoothing splines are not statistical in nature and, thus, do not generate
uncertainty estimates for GMST increments
To steer the flexibility of the cubic spline model we studied the correlation
structure of internal variability. This correlation structure can be
described by an AutoRegressive Moving Average (ARMA) model as proposed by
Hunt (2011) and Roberts et al. (2015). They estimated ARMA models to a range
of PiControl runs. Similarly, we analysed 41 PiControl runs with lengths
varying between 200 and 1000 years. We found that variability can reasonably
be characterized by AR(1) processes where the AR(1) parameter
We note that in some cases MA(1) or ARMA(1,1) models performed somewhat better as checked by comparing AIC values. Thus, the AR(1) model is a compromise to ease the analysis. Next to that AR(1) models are widely applied in climate research (e.g. Mudelsee, 2014).
All four trend methods are designed to smooth GMSTs for annual to decadal
natural variability (forced and unforced). However, if Paris targets should
be interpreted as anthropogenic warming only, we should estimate the role of
decadal to centennial forcings from volcanic and solar activity as well. To
estimate the role of volcanic eruptions we have extended the OLS linear trend
model and the IRW trend model by adding the aerosol optical depth (AOD) index
as regressor (Visser and Molenaar, 1995; Visser et al., 2015 – Fig. 4). The
extended IRW model reads as
We note that if the variance of noise process
Trend increments
Based on the 1880–2016 GMST sample period we have evaluated trend
progression values
As for the IRW trend estimates – formulated in Eq. (2) – we find reasonable
flexible patterns which closely resemble the spline trend shown in IPCC
(2013 – chap. 2: Box 2.2, Fig. 1b). An example for the HadCRUT4 dataset is
shown in Fig. 3. Data, trend and uncertainties are shown in the upper panel.
The trend increments [
Two smoothing spline estimates for the HadCRUT4 GMST series, with
uncertainties generated by MC simulation. All confidence limits are based on
1000 surrogate GMST series following the approach set out in Mudelsee
(2014 – Sect. 3.3.3).
As for smoothing splines, we have estimated trends in GMST series such that
the residual series exhibits an AR(1) process with a
It is interesting to note that none of the four trend methods show a sign of
a “hiatus”, “slowdown” or “pause”. That is not surprising for the
linear trend and the spline estimate with
Table 2 shows that differences between trend model and dataset combinations
can be considerable. The lowest
To quantify the role of trend methods in more detail we have averaged trend
estimates over the five GMST datasets and added it to Table 2 (bottom row).
It shows that the range of trend progressions is small:
[0.97, 1.01]
Histogram based on 42 GCM
Trend progression derived from GCMs have been analysed in a range of studies, e.g. IPCC (2013 – chap. 10), Forster et al. (2013), Marotzke and Forster (2015), Mann et al. (2016) and Meehl et al. (2016). Here, we derive trend progression since pre-industrial by taking an ensemble of 42 GCM all-forcing simulations 1861–2016. We note that underlying models have quite different characteristics, such as climate sensitivities, various models for greenhouse gas cycling models, cloud parametrization and aerosol forcing. However, we did not perform a sensitivity analysis for these factors.
GMST progression 1880–2016 with and without correction for volcanic activity (see Fig. 6). Values in bold are column averages.
Short-term forced and unforced natural variability in individual GCM
simulations is smoothed by estimating splines to each individual simulation
(both for
The GCM simulations analysed here differ from data products as for their
definition of temperatures (“tas only” vs. blended temperatures). Cowtan
et al. (2015) and Richardson et al. (2016 – Fig. 1) showed that tas
temperatures differ from blended temperatures by 0.10
The AOD index series as introduced by Sato et al. (1993). Period is 1850–2016.
We make three comments concerning the robustness of the results given in
Sect.
A second comment concerns a source of uncertainty dealing with the choice for
year or period that can be regarded as “pre-industrial”. As for the
analyses in Sect.
The choice for 1880 is consistent with that made by IPCC (2013) as for
historic trend progression (without claiming this to be “since
pre-industrial”). In Sect.
Would our results and conclusions from Table 2 or Figs. 3 and 4 be different if the sample period were enlarged, starting in 1400, 1720 or 1850? Strictly speaking, we cannot answer this question since we cannot extend our analyses to these starting years due to data availability. As for the instrumental dataset, we could perform some analyses from 1850 onwards but GMST estimates become inaccurate for these early decades. However, estimates based on GCM simulations are given by Hawkins et al. (2017) and Schurer et al. (2017).
Hawkins et al. show that the GMST difference between the two periods
1720–1800 and 1850–1900 is small, around 0.05
A third comment deals with differences in warming definitions as mentioned in
the Introduction. If the Paris targets are to be interpreted as anthropogenic
warming only, we should estimate these contributions as well. Clearly, the
incremental estimates
To estimate the role of long-term solar activity we did not choose for the time-series approach above since any explanatory variable in a regression model with some long-term trend will correlate and “explain” the long-term trend in the dependent variable (the cyclic pattern in solar radiance is not reflected in GMTs as shown by a number of studies, e.g. Schurer et al., 2017 – Fig. S3). Therefore, we prefer to use GCM estimates to quantify the role of solar activity.
IPCC (2013) estimates the role of solar variability to be small and on the
edge of significance. Incremental solar forcing for the period 1750–2011
accounts for 2 [0, 4] % of GHG forcing (Figure SPM.5 and Box 10.2).
Schurer et al. (2017 – Fig. S3) estimate the incremental contribution of
solar forcing on GMSTs to be 0.07 [0.02, 0.12]
Natural variability based on 37 GCM simulations. Shown are mean values along with 2 standard errors. Period is 1861–2005.
Next to these estimates we analysed an ensemble of 37 GCM simulations with
natural forcing only (“historicalNat”; IPCC, 2013 – Figs. 10.1 and 10.7;
Forster et al., 2013 – Fig. 2). The mean curve with 2 standard errors (SEs)
is shown in Fig. 7, along with major volcanic eruptions (eruptions with
a volcanic explosivity index of 5 and 6). Mean trend progression for these 37
runs accounts for 0.078
From these inferences we conclude that the difference between total warming
and anthropogenic warming lies around 0.10
Schurer et al. (2017) end their article with the recommendation that a consensus be reached as to what is meant by pre-industrial temperatures. In this way, the chance would be reduced of conclusions that appear contradictory being reached by different studies. Furthermore, it would allow for a more clearly defined framework for policymakers and stakeholders. We fully agree with this recommendation. However, our uncertainty and sensitivity analysis has shown that the choice of a proper pre-industrial baseline is not the only parameter that could lead to contradictory results. Decisions around data products and GCM simulations, various time series techniques, or assumptions on warming definitions should be taken into account as well.
Here, we make the following policy proposal which aims to be a reasonable
compromise. First, we propose to base GMST warming estimates on data products
rather than GCM simulations. Our argumentation is that
Second, since warming estimates vary as a function of the GMST data products chosen (Table 2), we propose to estimate trends on the annual averages of all five data products.
Third, we found that the choice for specific trend methods plays a minor role, with largest differences between stiff and more flexible trend models. Therefore, we propose to apply a flexible and a stiff trend method and average the warming estimates found.
Fourth, two studies on the role of pre-industrial baselines have been
published recently. Schurer et al. (2017) find a GHG-induced warming in the
range [0.02, 0.20]
Finally, we propose to interpret global warming in the context of “Paris”
as the sum of natural and anthropogenic warming, consistent with the IPCC
definition of climate change. One argument for this choice is that ecological
systems and human society will respond to total warming and induced shifts in
climate extremes
From these choices it follows that trend progression
We have addressed the issue of signal progression of GMST in relation to the
GMST targets agreed upon in Paris in December 2015. Although these targets
are clearly defined – avoiding increments of 1.5 and
2.0
IRW trends have been estimated by the TrendSpotter software. This software package is freely available from the first author. Splines have been estimated by the statistical package S-Plus, version 8.2. The scripts, which are highly similar to R, are available from the first author.
All five GMST datasets are open access and have been
downloaded from the authors websites. All CMIP5 runs named in
Sect.
In our study we have selected trend models which not only estimate a trend over time but also yield uncertainties for trend increments. However, this requirement appears to limit our model choices considerably. First, many methods are not statistical in nature, such as moving averages (Hansen et al., 2010; Smith et al., 2015; Fyfe et al., 2016), binomial filters (Morice et al., 2012), wavelets with scale dependencies (Lin and Franzke, 2015), EEMD decomposition (Wei et al., 2015; Yao et al., 2015) or linear trends based on stair-step averages with variable lengths (De Saedeleer, 2016). A historic example is given in Fig. 1, based on the work of Callender (1938).
Next to that, a number of methods do not generate estimates at the beginning and ending of the GMST series due to the dependence on “windows”. Examples are moving averages, OLS linear trends with moving windows (Risbey et al., 2015; Marotzke and Forster, 2015) and the staircase approach by De Saedeleer (2016).
Trend models applied to GMST datasets can be categorized methodological into
three groups:
Empirical models. These are trend models which are in principle data-based and may be steered by qualitative
physical insights, such as the choice of a fixed window in combination with
moving averages (Easterling and Wehner 2009; Hansen et al., 2010; Cowtan and
Way, 2014; Roberts et al., 2015). Other trend models are OLS linear trends
with varying sample periods (IPCC, 2013 – Box 2.2, Fig. 1a; Karl et al.,
2015; Rajaratnam et al., 2015), linear trends with change points (Cahill
et al., 2015), binomial filters (Morice et al., 2012), splines (IPCC, 2013 –
Box 2.2, Fig. b), EEMD decomposition (Wei et al., 2015; Yao et al., 2015),
structural time series models (Visser and Molenaar, 1995; Mills, 2006, 2010)
and long-memory trend models (Lennartz and Bunde, 2009; Rea et al., 2011). Semi-empirical methods with stationary regressors. These methods are also data-based but physics may enter trend
estimates by adding stationary climate indices in the context of regression
models. An example is given by Forster and Rahmstorf (2011), who apply
a linear regression model with three regressors (MEI, AOD and TSI). Other
references are Visser and Molenaar (1995), Yao et al. (2015) and Trenberth
(2015). Semi-empirical methods with non-stationary regressors. These models differ from semi-empirical models in that
non-stationary regressors are used as well, such as global
Summary of three groups of modelling approaches to global mean
temperatures: (i) empirical, (ii) semi-empirical with stationary regressors,
and (iii) semi-empirical with non-stationary regressors. In the fourth column
the presence of uncertainties for rates of change is given
([
A detailed description of methods is given in Table A1. For background information please see Chandler and Scott (2011), Mudelsee (2014) and Visser et al. (2015).
From the range of available trend methods we selected trend methods from the group of empirical models and semi-empirical models, with our main selection criterion being that models contain full uncertainty information for trend estimates and trend increments. Based on this criterion we selected Models (4), (8), (16), (19) and (21). As for Model (8) we explained the construction of uncertainties in Fig. 2.
Furthermore, we decided not to use models from the semi-empirical approaches with non-stationary regressors. First, there is a danger of finding associations rather than causal relations since any two series with a long-term trend correlate high, whatever their origin (Nuzzo, 2014). Second, relations in the climate system are (highly) non-linear and we prefer to rely on GCM simulations rather than forcing indicators for GHGs, aerosols or solar activity which serve as regressors in a multiple regression model. Thus, we prefer the models named in Table A1 under the heading “Semi-empirical approaches, stationary regressors” over “Semi-empirical approaches, non-stationary regressors”.
The authors declare that they have no conflict of interest.
We thank Geert Jan van Oldenborgh (KNMI, Climate Explorer) for thorough comments on an early version of this text. Furthermore, we thank Peter Thorne (Maynooth University), an anonymous reviewer and Lenny Smith (The London School of Economics and Political Science) for important comments on the manuscript. Edited by: Stefan Bronnimann Reviewed by: Peter Thorne and one anonymous referee