A significant difference, now of some 16 years' duration, has been shown to exist between the observed global surface temperature trend and that expected from the majority of climate simulations. For its own sake, and to enable better climate prediction for policy use, the reasons behind this mismatch need to be better understood. While an increasing number of possible causes have been proposed, the candidate causes have not yet converged.

With this background, this paper reinvestigates the relationship between
change in the level of CO

Using time-series analysis in the form of dynamic regression modelling with
autocorrelation correction, it is shown that first-difference CO

It is shown that the first-difference CO

These results may contribute to the prediction of future trends for global temperature and ENSO.

Interannual variability in the growth rate of atmospheric CO

Monthly data,

Understanding current global climate requires an understanding of trends both in Earth's atmospheric temperature and the El Niño–Southern Oscillation (ENSO), a characteristic large-scale distribution of warm water in the tropical Pacific Ocean and the dominant global mode of year-to-year climate variability (Holbrook et al., 2009). However, despite much effort, the average projection of current climate models has become statistically significantly different from the 21st century global surface temperature trend (Fyfe et al., 2013; Fyfe and Gillett, 2014) and has failed to reflect the statistically significant evidence that annual-mean global temperature has not risen in the 21st century (Fyfe et al., 2013; Kosaka and Shang-Ping, 2013).

The situation is illustrated visually in Fig. 1 which shows the increasing departure over recent years of the global surface temperature trend from that projected by a representative mid-range global climate model (GCM) for global surface temperature – the CMIP5, RCP4.5 scenario model (Taylor et al., 2012).

It is noted that recent studies have reconsidered the correct quantification of this model–observation difference: they report analysis suggesting that it is in effect less evident (Cowtan and Way, 2014; Karl et al., 2015).

The effect of these alternative quantifications on the model–observation difference is also shown in Fig. 1.

Figure 1 shows the departure over recent years of a standard time series of temperature (HadCRUT4) from that projected by a representative mid-range global climate model (GCM) for global surface temperature – the CMIP3, SRESA1B scenario model (Meehl et al., 2007). The figure also shows the alternative temperature series (Cowtan and Way, 2014; Karl et al., 2015).

Figure 1 shows that the alternative quantifications reduce the scale of the difference seen using HadCRUT4 but do not eliminate it.

It is noted that the level of atmospheric CO

Turning to ENSO, the extremes of its variability cause extreme weather events (such as floods and droughts) in many regions of the world. Modelling provides a wide range of predictions for future ENSO variability, some showing an increase, others a decrease, and some no change (Guilyardi et al., 2012; Bellenger et al., 2014).

A wide range of physical explanations has now been proposed for the global warming slowdown. These involve proposals either for changes in the way the radiative mechanism itself is working or for the increased influence of other physical mechanisms. Chen and Tung (2014) place these proposed explanations into two categories. The first involves a reduction in radiative forcing: by a decrease in stratospheric water vapour, an increase in background stratospheric volcanic aerosols, by 17 small volcano eruptions since 1999, increasing coal-burning in China, the indirect effect of time-varying anthropogenic aerosols, a low solar minimum, or a combination of these. The second category of candidate explanation involves planetary sinks for the excess heat. The major focus for the source of this sink has been physical and has involved ocean heat sequestration. However, evidence for the precise nature of the ocean sinks is not yet converging: according to Chen and Tung (2014) their study followed the original proposal of Meehl et al. (2011) that global deep-ocean heat sequestration is centred on the Pacific. However, their observational results were that such deep-ocean heat sequestration is mainly occurring in the Atlantic and the Southern oceans.

Alongside the foregoing possible physical causes, Hansen et al. (2013) have suggested that the mechanism for the pause in the global temperature increase since 1998 might be the planetary biota, in particular the terrestrial biosphere: that is (IPCC, 2007), the fabric of soils, vegetation and other biological components, the processes that connect them and the carbon, water and energy that they store.

It is widely considered that the interannual variability in the growth rate
of atmospheric CO

Again, IPCC (2007) states the following: “the atmospheric CO

In the IPCC Fourth Assessment Report, Denman et al. (2007) state (italics
denote present author emphasis): “Interannual and inter-decadal variability
in the growth rate of atmospheric CO

Denman et al. (2007) also note that many studies have confirmed that the
variability of CO

The activity of the land sink can also be estimated directly. The terrestrial
biosphere carbon sink is created by photosynthesis: a major way of measuring
global land photosynthesis is by means of satellite measurements of potential
photosynthesis from greenness estimates. The measure predominantly used is
the Normalized Difference Vegetation Index (NDVI) (Running et al., 2004;
Zhang et al., 2014). NDVI data are available from the start of satellite
observations in 1980 to the present. For this period the trend signature in
NDVI has been shown to correlate closely with that for atmospheric CO

Before considering further material, it is helpful now to consider a range of methodological issues and concepts. The first concept is to do with the notion of causality.

According to Hidalgo and Sekhon (2011) there are four prerequisites to enable an assertion of causality. The first is that the cause must be prior to the effect. The second prerequisite is “constant conjunction” between variables (Hume, 1751, cited in Hidalgo and Sekhon, 2011). This relates to the degree of fit between variables. The final requirements are those concerning manipulation and random placement into experimental and control categories. It is noted that each of the four prerequisites is necessary but not sufficient on its own for causality.

With regard to the last two criteria, the problem for global studies such as global climate studies is that manipulation and random placement into experimental and control categories cannot be carried out.

One method using correlational data, however, approaches more closely the
quality of information derived from random placement into experimental and
control categories. The concept is that of Granger causality (Granger, 1969).
According to Stern and Kaufmann (2014), a time-series variable “

Reference to the above four aspects of causality will be made to help structure the review of materials in the following sections.

What has been considered to influence the biota's creation of the pattern
observed in the trend in the growth rate of atmospheric CO

This lack of attention to the influence of the biosphere on climate variables
seems to have come about for two reasons, one concerning ENSO, the other,
temperature. For ENSO, the reason is that the statistical studies are
unambiguous that ENSO leads rate of change of CO

In the first published study on this question, Kuo et al. (1990) provided
evidence that the signature of interannual atmospheric CO

The relative fits of both the level of and change in the level of atmospheric
CO

Concerning signature, while clearly first-difference CO

Kuo et al. (1990) also provided evidence concerning another of the causality
prerequisites – priority. This was that the signature of first-difference
CO

Another perspective on the relative effects of rising atmospheric CO

In looking at leading and lagging climate series more generally, the first
finding of correlations between the rate of change (in the form of the
first-difference) of atmospheric CO

In light of the foregoing, this paper reanalyses by means of time-series
regression analysis which of first-difference CO

The foregoing also shows that a strong case can be made for further
investigating the planetary biota, influenced by atmospheric CO

A number of Granger causality studies have been carried out on climate time
series (see review in Attanasio et al., 2013). We found six papers which
assessed atmospheric CO

As well, all studies used annual rather than monthly data. For Granger causality analysis,
the data series used must display the statistical property of stationarity (see Sect. 3:
Data and methods). Such annual data for each of atmospheric CO

Rather than using a formal Granger causality analysis, a number of authors have instead used conventional multiple regression models in attempts to quantify the relative importance of natural and anthropogenic influencing factors on climate outcomes such as global surface temperature. These regression models use contemporaneous explanatory variables. For example, see Lean and Rind (2008, 2009); Foster and Rahmstorf (2011); Kopp and Lean (2011); Zhou and Tung (2013). This type of analysis effectively assumes a causal direction between the variables being modelled. It is incapable of providing a proper basis for testing for the presence or absence of causality. In some cases account has been taken of autocorrelation in the model's errors, but this does not overcome the fundamental weakness of standard multiple regression in this context. In contrast, Granger causality analysis that we adopt in this paper provides a formal testing of both the presence and direction of this causality (Granger 1969).

From such multiple regression studies, a common set of main influencing factors (also called
explanatory or predictor variables) has emerged. These are (Lockwood, 2008;
Folland et al., 2013; Zhou and Tung, 2013): El Niño–Southern Oscillation
(ENSO), or Southern Oscillation Index (SOI) alone; volcanic aerosol optical
depth; total solar irradiance; and the trend in anthropogenic greenhouse gas
(the predominant anthropogenic greenhouse gas being CO

With this background, this paper first presents an analysis concerning
whether the first-difference of atmospheric CO

Correlations are assessed at a range of timescales to seek the time extent
over which relationships are held, and thus whether they are a special case
or possibly longer term in nature. The timescales involved are, using
instrumental data, over two periods starting, respectively, from 1959 and 1877;
and, using paleoclimate data, over a period commencing from 1515. The
correlations are assessed by means of regression models explicitly
incorporating autocorrelation using dynamic modelling methods. Granger
causality between CO

We present results of time-series analyses of climate data. The data
assessed are global surface temperature, atmospheric carbon dioxide
(CO

The second batch of studies is for data able to be set at monthly resolution
not involving CO

The final batch of analyses utilises annual data. These studies use data starting variously in the 16th or 18th centuries.

Data from 1877 and more recently are from instrumental sources; earlier data are from paleoclimate sources. Data from the mid-range outputs of two climate models are also used.

For instrumental data sources for global surface temperature, we used the
Hadley Centre–Climate Research Unit combined land SAT and SST (HadCRUT)
version 4.2.0.0 (Morice et al., 2012), for atmospheric CO

With regard to the El Niño–Southern Oscillation, according to IPCC (2014) the term El Niño was initially used to describe a warm-water current that periodically flows along the coast of Ecuador and Peru, disrupting the local fishery. It has since become identified with a basin-wide warming of the tropical Pacific Ocean east of the dateline. This oceanic event is associated with a fluctuation of a global-scale tropical and subtropical surface atmospheric pressure pattern called the Southern Oscillation. This atmosphere–ocean phenomenon is coupled, with typical timescales of 2 to about 7 years, and known as the El Niño–Southern Oscillation (ENSO).

The El Niño (temperature) component of ENSO is measured by changes in the sea surface temperature of the central and eastern equatorial Pacific relative to the average temperature. The Southern Oscillation (atmospheric pressure) ENSO component is often measured by the surface pressure anomaly difference between Tahiti and Darwin.

For the present study we choose the SOI atmospheric pressure component rather than the temperature component of ENSO to stand for ENSO as a whole. This is because it is considered to be more valid to conduct an analysis in which temperature is an outcome (dependent variable) without also having temperature as an input (independent variable). The correlation between SOI and the other ENSO indices is high, so we believe this assumption is robust.

Palaeoclimate data sources are: atmospheric CO

Normalized Difference Vegetation Index (NDVI) monthly data from 1980 to 2006 are from the GIMMS (Global Inventory Modeling and Mapping Studies) data set (Tucker et al., 2005). NDVI data from 2006 to 2013 were provided by the Institute of Surveying, Remote Sensing and Land Information, University of Natural Resources and Life Sciences, Vienna. Data series projected from two representative mid-range global climate models (GCMs) for global surface temperature were used. Series were from the CMIP3, SRESA1B scenario model (Meehl et al., 2007) and the CMIP5, RCP4.5 scenario model (Taylor et al., 2012).

Statistical methods used are standard (Greene, 2012). Categories of methods used are normalisation; differentiation (approximated by differencing); and time-series analysis. Within time-series analysis, methods used are smoothing; leading or lagging of data series relative to one another to achieve best fit; assessing a prerequisite for using data series in time-series analysis, that of stationarity; including autocorrelation in models by use of dynamic regression models; and investigating causality by means of a multivariate time-series model, known as a vector autoregression (VAR) and its associated Granger causality test. These methods will now be described in turn.

To make it easier to assess the relationship between the key climate
variables visually, the data were normalised using statistical

Individual figure legends contain details on the series lengths.

In the time-series analyses, SOI and global atmospheric surface temperature
are the dependent variables. We tested the relationship between each of these
variables and (1) the change in atmospheric CO

Smoothing methods are used to the degree needed to produce similar amounts of
smoothing for each data series in any given comparison. Notably, to achieve
this outcome, series resulting from higher levels of differences require more
smoothing. Smoothing is carried out initially by means of a 13-month moving
average – this also minimises any remaining seasonal effects. If further
smoothing is required, then this is achieved by taking a second moving
average of the initial moving average (to produce a double moving average)
(Hyndman, 2010). Often, this is performed by means of a further 13-month
moving average to produce a

It is important to consider what effects this filtering of our data may have
on the ensuing statistical analysis. In these analyses, only the CO

Second, there is extensive evidence that while the effect of seasonal
adjustment (via smoothing) on the usual tests for unit roots in time-series
data is to reduce their power in small samples, this distortion is

Finally, seasonally adjusting the data by a range of alternative approaches did not qualitatively change the results discussed in the paper. The results of these assessments are given in the Supplement.

This means that our results relating to the existence of Granger causality should not be affected adversely by the smoothing of the data that has been undertaken.

Variables are led or lagged relative to one another to achieve best fit. These leads or lags were determined by means of time-lagged correlations (correlograms). The correlograms were calculated by shifting the series back and forth relative to each other, 1 month at a time.

With this background, the convention used in this paper for unambiguously
labelling data series and their treatment after smoothing or leading or
lagging is depicted in the following example. The atmospheric CO

Note that to assist readability in text involving repeated references,
atmospheric CO

The time-series methodology used in this paper involves the following procedures.

First, any two or more time series being assessed by time-series regression analysis must be what is termed stationary in the first instance, or be capable of transformed into a new stationary series (by differencing). A series is stationary if its properties (mean, variance, covariances) do not change with time (Greene, 2012). The (augmented) Dickey–Fuller test is applied to each variable. For this test, the null hypothesis is that the series has a unit root, and hence is non-stationary. The alternative hypothesis is that the series is integrated of order zero.

Second, the residuals from any time-series regression analysis then conducted must not be significantly different from white noise. This is done seeking correct model specification for the analysis.

After Greene (2012) it is noted that the results of standard ordinary least squares (OLS) regression analysis assume that the errors in the model are uncorrelated. Autocorrelation of the errors violates this assumption. This means that the OLS estimators are no longer the best linear unbiased estimators (BLUE). Notably and importantly this does not bias the OLS coefficient estimates. However statistical significance can be overestimated, and possibly greatly so, when the autocorrelations of the errors at low lags are positive.

Addressing autocorrelation can take either of two alternative forms:

Lag of first-difference CO

In the latter approach, the autocorrelation is taken to be a consequence of an inadequate specification of the temporal dynamics of the relationship being estimated. The method of dynamic modelling (Pankratz, 1991) addresses this by seeking to explain the current behaviour of the dependent variable in terms of both contemporaneous and past values of variables. In this paper the dynamic modelling approach is taken.

To assess the extent of autocorrelation in the residuals of the initial
non-dynamic OLS models run, the Breusch–Godfrey procedure is used. Dynamic
models are then used to take account of such autocorrelation. To assess the
extent to which the dynamic models achieve this, Kiviet's Lagrange multiplier

Hypotheses related to Granger causality (see Introduction) are tested by
estimating a multivariate time-series model, known as a vector autoregression
(VAR), for level of and first-difference CO

Stern and Kander (2011) observe that Granger causality is not identical to
causation in the classical philosophical sense, but it does demonstrate the
likelihood of such causation or the lack of such causation more forcefully
than does simple contemporaneous correlation. However, where a third
variable,

Correlograms of first-difference CO

Figure 2 shows that, while clearly first-difference CO

The first question assessed is that of priority: which of first-difference
atmospheric CO

To quantify the degree of difference in phasing between the variables,
time-lagged correlations (correlograms) were calculated by shifting the
series back and forth relative to each other, 1 month at a time. These
correlograms are given in Fig. 4 for global and regional data. For all four
relationships shown, first-difference CO

Correlograms of first-difference CO

It is possible for a lead to exist overall on average but for a lag to occur
for one or other specific subsets of the data. This question is explored in
Fig. 5 and Table 2. Here the full 1959–2012 period of monthly data – some
640 months – for each of the temperature categories is divided into three
approximately equal sub-periods, to provide 12 correlograms. It can be seen
that in all 12 cases, first-difference CO

Lag of first-difference CO

The second prerequisite for causality, close correspondence, is also
seen between first-difference CO

Both first-difference CO

Augmented Dickey–Fuller (ADF) tests for stationarity of
unit roots in both monthly and annual data 1969 to 2012 for level of
atmospheric CO

The order of integration, denoted

By means of the augmented Dickey–Fuller (ADF) test for unit roots, Table 3
provides the information concerning stationarity for the level of, and
first-difference of, CO

The results show that for both the monthly and annual series used, the
variables TEMP and FIRST-DIFFERENCE CO

In contrast, Beenstock et al. (2012), using annual data, report that their
series for the level of atmospheric CO

“In the presence of these different measurements exhibiting structural
changes, a unit-root test on the entire sample could easily not reject the
null hypothesis of

Pretis and Hendry (2013) give their results for CO

Pretis and Hendry (2013) also state the following:

“Unit-root tests are used to determine the level of integration of time
series. Rejection of the null hypothesis provides evidence against the
presence of a unit-root and suggests that the series is

… based on augmented Dickey–Fuller (ADF) tests (see Dickey and
Fuller, 1981), the first-difference of annual radiative forcing of CO

Hence for annual data Pretis and Hendry (2013) find first-difference CO

With this question of the order of integration of the time series considered,
we now turn to the next step of the time-series analysis. As Table 3, above,
and Pretis and Hendry (2013) show, the variable of the level of CO

OLS dynamic regression between first-difference
atmospheric CO

Pairwise correlations (correlation coefficients (

For TEMP and FIRST-DIFFERENCE CO

Autocorrelation is a consequence of an inadequate specification of the
temporal dynamics of the relationship being estimated. With this in mind, a
dynamic model (Greene, 2012) with two lagged values of the dependent variable
as additional independent variables has been estimated. Results are shown in
Table 4. The LMF test shows that there is now no statistically significant
unaccounted-for autocorrelation, thus supporting the use of this dynamic
model specification. Table 4 shows that a highly statistically significant
model has been established. First it shows that the temperature in a given
period is strongly influenced by the temperature of closely preceding periods
(see Sect. 5 for a possible mechanism for this). Further, it provides
evidence that there is also a clear, highly statistically significant role in
the model for first-difference CO

We now can turn to assessing if first-difference atmospheric CO

Recalling that both TEMP and FIRST-DIFFERENCE CO

the estimated model was dynamically stable (i.e. all of the inverted roots of the characteristic equation lie inside the unit circle);

the errors of the equations were serially independent.

We recognise that as temperature is stationary, while CO

Once again, the levels of both series are used. For each VAR model, the
maximum lag length (

With the above two assessments done, it is significant that with regard to
global surface temperature we are able to discount causality involving the
level of CO

Pairwise correlations (correlation coefficients (

Given the results of this exploration of correlations involving
first-difference atmospheric CO

Figure 6 shows that, alongside the close similarity between first-difference
CO

Recalling that (even uncorrected for any autocorrelation) correlational data
still hold information concerning regression coefficients, we initially use
OLS correlations without assessing autocorrelation to provide descriptive
statistics. Table 5 includes, without any phase-shifting to maximise fit, the
six pairwise correlations arising from all possible combinations of the four
variables other than with themselves. Here it can be seen that the two
highest correlation coefficients (in bold in the table) are firstly between
first-difference CO

OLS dynamic regression between second-difference
atmospheric CO

In Table 6, phase shifting has been carried out to maximise fit (shifts shown
in the titles of the variables in the table). This results in an even higher correlation
coefficient for second-difference CO

The link between all three variable realms – CO

Looking at the differences between the curves shown in Fig. 7, two of the major departures between the curves coincide with volcanic aerosols – from the El Chichon volcanic eruption in 1982 and the Pinatubo eruption in 1992 (Lean and Rind, 2009). With these volcanism-related factors taken into account, it is notable (when expressed in the form of the transformations in Fig. 7) that the signatures of all three curves are so essentially similar that it is almost as if all three curves are different versions of – or responses to – the same initial signal.

So, a case can be made that first- and second-difference CO

We now assess more formally the relationship between second-difference
CO

Table 7 shows the results of a dynamic model with the dependent variable used at each of the two lags as further independent variables; there is now no statistically significant autocorrelation which has not been accounted for.

As Table 7 shows, a highly statistically significant model has been
established. As for temperature, it shows that the SOI in a given period is
strongly influenced by the SOI of closely preceding periods. Again as for
temperature, it provides evidence that there is a clear role in the model for
second-difference CO

OLS dynamic regression between first-difference global surface temperature and reversed Southern Oscillation Index for monthly data for the period 1877–2012, with autocorrelation taken into account.

With this established, it is noted that while the length of series in the
foregoing analysis was limited by the start date of the atmospheric CO

Turning to regression analysis, as previously the Breusch–Godfrey procedure shows that for lags up to lag 12, the majority of autocorrelation is again restricted to the first two lags. Table 8 shows the results of a dynamic model with the dependent variable used at each of the two lags as further independent variables.

In comparison with Table 7, the extended time series modelled in Table 8
shows a remarkably similar

This section assesses whether second-difference CO

Results of stationarity tests for each series are given in Table 9. Each series is shown to be stationary. These results imply that we can approach the issue of possible Granger causality by using a conventional VAR model, in the levels of the data, with no need to use a “modified” Wald test (as used in the Toda and Yamamoto (1995) methodology).

Augmented Dickey–Fuller (ADF) test for stationarity for
monthly data 1959–2012 for second-difference CO

Simple OLS regressions of SOI against separate lagged values of
second-difference CO

A two-equation VAR model is needed for reverse-sign SOI and second-difference
CO

VAR Residual Serial Correlation LM Tests component of
Granger causality testing of relationship between second-difference CO

This suggests that the maximum lag length for the variables needs to be increased. The best results (in terms of lack of autocorrelation) were found when the maximum lag length is 3. (Beyond this value, the autocorrelation results deteriorated substantially, but the conclusions below, regarding Granger causality, were not altered.)

Table 11 shows that the preferred, 3-lag model, still suffers a little from autocorrelation. However, as we have a relatively large sample size, this will not impact adversely on the Wald test for Granger causality.

The relevant EViews output from the VAR model is entitled VAR Granger
causality/block exogeneity Wald tests and documents the following summary
results – Wald Statistic (

The forgoing Wald statistic shows that the null hypothesis is strongly
rejected – in other words, there is very strong evidence of Granger
causality from second-difference CO

So far, the time period considered in this study has been pushed back in the
instrumental data realm to 1877. If non-instrumental paleoclimate proxy
sources are used, CO

Visual inspection of the figure shows that there is a strong overall likeness
in signature between the two temperature series, and between them and
first-difference CO

Using the Normalized Difference Vegetation Index (NDVI) time series as a measure of the activity of the land biosphere, this section now investigates the land biosphere as a candidate mechanism for the issue, identified in the Introduction, of the increasing difference between the observed global surface temperature trend and that suggested by general circulation climate models.

VAR Residual Serial Correlation LM Tests component of
Granger causality testing of relationship between second-difference CO

The trend in the terrestrial CO

Globally aggregated GIMMS NDVI data from the Global Land Cover Facility site are available from 1980 to 2006. This data set is referred to here as NDVIG. Spatially disaggregated GIMMS NDVI data from the GLCF site is available from 1980 to the end of 2013. An analogous global aggregation of this spatially disaggregated GIMMS NDVI data – from 1985 to end 2013 – was obtained from the Institute of Surveying, Remote Sensing and Land Information, University of Natural Resources and Life Sciences, Vienna. This data set is labelled NDVIV.

Correlations (

Order of integration test results for NDVI series for monthly data from 1981–2012. The Schwartz information criterion (SIC) was used to select an optimal maximum lag length in the tests.

Pooling the two series enabled the longest time span of data aggregated at
global level. The two series were pooled as follows. Figure 10 shows the
appearance of the two series. Each series is

Pretis and Hendry (2013) observe that pooling data (i) from very different measurement systems and (ii) displaying different behaviour in the sub-samples can lead to errors in the estimation of the level of integration of the pooled series.

The first risk of error (from differences in measurement systems) is overcome here as both the NDVI series are from the same original disaggregated data set. The risk associated with the sub-samples displaying different behaviour and leading to errors in levels of integration is considered in the following section by assessing the order of each input series separately, and then the order of the pooled series.

Table 13 provides order of integration test results for the three NDVI
series. The analysis shows all series are stationary (

As discussed in the Introduction, Fig. 1 shows that since around the year 2000 there is an increasing difference between the temperature projected by a mid-level IPCC model and that observed. Any cause for this increasing difference must itself show an increase in activity over this period.

The purpose of this section is, therefore: (i) to derive an initial simple indicative quantification of the increasing difference between the temperature model and observation; and (ii) to assess whether global NDVI is increasing. If NDVI is increasing, this is support for NDVI being a candidate for the cause of the temperature model–observation difference. If there is a statistically significant relationship between the two increases, this is further support for NDVI being a candidate for the cause of the model–observation difference, and hence worthy of further detailed research. A full analysis of this question is beyond the scope of the present paper.

A simple quantification of the difference between the temperature projected
from a mid-level IPCC model and that observed can be derived by subtracting
the (

Figure 11, displaying monthly data, compares NDVI with the difference between the temperature projected from an IPCC mid-range scenario model (CMIP3, SRESA1B scenario run for the IPPC fourth assessment report; IPCC, 2007) and global surface temperature (red dotted curve). Both curves rise in more recent years.

The trends for the 36-month pooled data in Fig. 12 show considerable
commonality. OLS regression analysis of the relationship between the curves
in Fig. 12 shows that the best fit between the curves involves no lead or
lag. The correlation between the curves displays an adjusted

The results in this paper show that there are clear links at the highest
standard of non-experimental causality – that of Granger causality –
between first- and second-difference CO

Relationships between first- and second-difference CO

Given the timescales over which these effects are observed, the results
taken as a whole clearly suggest that the mechanism observed is long-term,
and not, for example, a creation of the period of the steepest increase in
anthropogenic CO

Taking autocorrelation fully into account in the time-series analyses
demonstrates the major role of immediate past instances of the dependent
variable (temperature, and SOI) in influencing its own present state. This
was found in all cases where time-series models could be prepared. This was
not to detract from the role of first- and second-difference CO

According to Mudelsee (2010) and Wilks (2011), such autocorrelation in the atmospheric sciences (also called persistence or “memory”) is characteristic of many types of climatic fluctuations.

In the specific case of the temperature and first-difference CO

The anthropogenic global warming (AGW) hypothesis has two main dimensions
(IPCC, 2007; Pierrehumbert, 2011): (i) that increasing CO

The results presented in this paper are supportive of the AGW hypothesis for
two reasons: firstly, increasing atmospheric CO

The difference between this evidence for the effect of CO

On the face of it, then, this model seems to leave little room for the linear radiative forcing aspect of the AGW hypothesis. However more research is needed in this area.

Reflection on Fig. 1 shows that the radiative mechanism would be supported if a second mechanism existed to cause the difference between the temperature projected for the radiative mechanism and the temperature observed. The observed temperature would then be seen to result from the addition of the effects of these two mechanisms.

As discussed in the Introduction, Hansen et al. (2013) have suggested that the mechanism for the pause in the global temperature increase since 1998 may be the planetary biota, in particular the terrestrial biosphere. As an initial indicative quantified characterisation of this possibility, Sect. 4.4 derived a simple measure of the increasing difference between the global surface temperature trend projected from a mid-range scenario climate model and the observed trend. This depiction of the difference displayed a rising trend. The time-series trend for the globally aggregated Normalized Difference Vegetation Index – which represents the changing levels of photosynthetic activity of the terrestrial biosphere – was also presented. This was shown also to display a rising trend.

If by further research, for example by Granger causality analysis, the global
vegetation can be shown to embody the second mechanism, this would be
evidence that the observed global temperature does result from the effects of
two mechanisms in operation together – the radiative, level-of-CO

Hence the biosphere mechanism would supplement, rather than replace, the radiative mechanism.

Further comprehensive time-series analysis of the NDVI data and relevant climate data, beyond the scope of the present paper, could throw light on these questions.

The authors would like to acknowledge with appreciation the support and advice of J. Gordon and C. Dawson, and the comments of the two anonymous referees of the paper which we consider to have improved it markedly. Edited by: R. MacKenzie