We explore the variability within the transient ensembles using surface temperatures globally, and then illustrate the magnitude of the irreducible uncertainty and consequences for regional near-term temperatures and precipitation with a case study over Europe.
Transient climate reponse
It has recently been suggested (Liang et al. 2013) that the initial conditions may be a significant source of uncertainty in estimating the global temperature change at the time of \(\hbox {CO}_2\) doubling, or transient climate response (TCR). The primary reason for the uncertainty identified by Liang et al. (2013) was that the spin-up or drift in the GCM considered would produce different estimates of TCR for well-spaced initial conditions. However, it is also possible that the TCR could vary depending on the initial condition in a well spun-up GCM, such as FAMOUS.
We estimate TCR in each FAMOUS simulation using the global mean surface temperature in years 61–80, minus the mean of the entire pre-industrial control simulation. The four FAMOUS ensembles show that the spread (which we take to be one standard deviation throughout) in estimates of TCR is between 0.06 and 0.08 K, with a minimum to maximum range of 2.25–2.64 K (Fig. 2). The standard deviation of 20-year means in global temperature in the FAMOUS control simulation is also 0.08 K, suggesting that the ensembles are effectively sampling the same internal variability but around the point of \(\hbox {CO}_2\) doubling and that the transient response itself does not add additional uncertainty.
In the CMIP5 ensemble, the estimated TCR ranges from 1.1 to 2.5 K (Forster et al. 2013). FAMOUS is clearly a high sensitivity GCM, but the relatively small initial condition uncertainty suggests that the spread in CMIP5 GCM estimates is dominated by model diversity. In addition, these results suggest that uncertainty in TCR estimates using control simulation variability may provide a good first estimate if only small ensembles are available. Such an approach would, however, substantially reduce the likelihood of identifying non-linear, model-dependent feedbacks which could affect the TCR in different models. Ensemble sizes should in any case be sufficiently large to make a good estimate of the mean.
In all four FAMOUS ensembles, the warming is greater for later initial states, which are characterised by their starting \(\hbox {CO}_2\) concentration in Fig. 3. This effect is commonly observed in CMIP3 and CMIP5 AOGCMs (Gregory and Forster 2008; Gregory et al. in press). The main reason is likely to be the decrease in efficiency of heat loss from the upper ocean to deeper layers as the latter become warmer, and is related to the cold-start effect (e.g. Keen and Murphy 1997) and the long-term commitment to surface warming after forcing is stabilised (as discussed by Gregory et al. in press). It does not imply a dependence of ocean heat uptake processes on the state of the climate. However, non-linear behaviours may also enhance the warming under successive doublings, for instance due to decrease in the global climate feedback parameter (Gregory et al. in press) and various regional phenomena (Good et al. 2015). Because the warming per unit increase in \(\hbox {CO}_2\) in forcing tends to increase, its value inferred from historical observations might underestimate the future response (Gregory and Forster 2008).
Global temperature trends
When considering shorter timescales, there is considerable variability in global mean temperatures. Figure 4 (top row) shows distributions of all possible overlapping trends for 10, 15 and 20 year periods in all the ensembles combined, with decadal trends ranging from –0.5 to over +1 K/decade. For example, ~8 % of decades show a cooling trend and ~1 % of 15-year trends show a cooling, even though the climate is warming in the long-term. However, the regional patterns and causes of each cooling period can be very different (Sutton et al. 2015). The longest period with a global cooling trend is 24 years in FAMOUS. All trends are calculated using standard linear regression against time.
The variability in these short-term trends inferred from the long control simulation (solid black curves) matches that of the large transient ensembles fairly well, indicating that lengthy control simulations are of considerable value in determining the range of possible future climate changes in this model (also see Deser et al. 2014). However, the magnitude of the variability decreases slightly over time in the transient simulations (see Sect. 3.4) suggesting there is a limit to the assumption of stationary variance.
Interestingly, it is also possible to consider what happens after a cooling period. The bottom row of Fig. 4 shows the distributions of global mean temperature trends immediately following periods of the same length that had a cooling trend. The mean of these distributions are shifted towards more positive values by between 15 and 25 %, indicating that cooling periods are more likely to be followed by higher rates of warming (or ‘surges’), with relevance to the recent observed slowdown in global temperatures. In addition, this shift is not simply due to the removal of the cooling periods from the distributions, except for 10-year trends where about half of the shift in the mean is due to this effect.
Local temperature trends
We next consider local temperature trends in the initial decades of the experiments, as an idealised analogue of the coming decades. Figure 5 illustrates the fraction of simulations which exhibit a cooling trend at each grid point over the first N years, for different values of N. In the MACRO case, one third or more of the simulations show a cooling trend over the first 20 years in many regions, especially in the extra-tropics. In the MICRO case, the fraction of simulations is increased over the North Atlantic, Europe and some of the Southern Ocean and north western Pacific. For longer trend lengths, the fractions of simulations exhibiting a cooling trend decreases and the two ensembles converge, although even over 30 years substantial areas still have significant fractions which show cooling.
The two MINI MICRO ensembles demonstrate that the probability of a cooling trend in any specific region is highly dependent on the particular ocean initial condition chosen. All three MICRO ensembles exhibit areas where more than 50 % of the simulations have a cooling trend over the first 20, and sometimes 30, years but the spatial patterns of ensemble behaviour are strikingly different. By 50 years in, the long term trend is positive almost everywhere and the few regions where a few simulations are negative are similar across the ensembles (also see Branstator and Teng 2010).
These differences between ensemble types highlight how a single ocean initial condition (as in each MICRO case) is not effectively sampling the uncertainty in future trends. For example, over Europe there is a high chance of a cooling trend in MICRO and MINI MICRO 2 due to a decline in the Atlantic Ocean heat transport (see Sect. 3.6), but in MINI MICRO 1, there is a near zero chance. Thus a single MICRO ensemble is not representative of the full uncertainty in the absence of knowledge of the initial ocean conditions. On the other hand it is representative of the irreducible uncertainty conditioned on a particular set of ocean/atmosphere initial conditions, in this model. This regional case study is explored further in Sect. 3.5 where we also highlight that the different MICRO ensembles have different predictability properties.
However, the ensembles are more consistent in the fraction of the globe which exhibits a cooling. Looking across all the simulations, a median of \(21\,\%\) (with a 5–95 % range of 12–43 %) of the globe shows a cooling over the first 20 years, and \(10\,\%\) (with a 5–95 % range of 4–19 %) over the first 30 years. No simulation exhibits a warming everywhere. But, the simulations differ in where the warming and cooling regions are. This type of quantification may be of use to help communicate the odds of ‘unexpected’ trends.
Ensemble spread and variability
We next consider how the ensemble spread changes over time, and the implications for predictability characteristics in the future.
The ensemble spread of the MICRO ensemble is initially smaller than the MACRO case, as expected, but they converge after a few years for global temperatures, and after around 20 years for European average temperatures (Fig. 6a, b) (also see Sect. 3.6 later).
There is therefore a potential initial reduction in ensemble spread and increase in predictive skill of the future within the model through conditioning on a particular initial ocean state. Whether some of this potential can be realised for real world predictions depends on the quality of the simulated climate and is an area of active ongoing research (Smith et al. 2007; Meehl et al. 2014).
Interestingly, the MINI MICRO 1 ensemble produces a very different growth of spread than MICRO and MINI MICRO 2 for Europe, even though they are all only sampling the irreducible initial condition uncertainty. These differences highlight possible state dependence of regional predictability - predictability from certain states may be greater than from others (Griffies and Bryan 1997). Both MINI MICRO ensembles are similar to MICRO for the global average (not shown).
In addition, the ensemble spread decreases as the climate warms, at least for the first 100 years. For the global mean, this reduction is around \(10\,\%\), and for Europe it is around \(20\,\%\), although there is significant variability in both the annual and the running mean of the spread. It is also seen that there is a flattening in the ensemble spread after around 100 years. This change in ensemble spread suggests a corresponding decrease in the magnitude of simulated interannual variability [also see Stouffer and Wetherald (2007) and Holmes et al. (2015)].
The ensemble spread decline is particularly evident in the North Atlantic, Nordic Seas and Scandinavia (Fig. 6c), suggesting that it is due to the sea-ice edge retreating in a warmer climate (also see Screen 2014). This would also explain why the reduction in ensemble spread does not continue indefinitely as the sea-ice retreats further into the Arctic.
Regional trends: a European case study
We now examine possible future temperature trends over Europe in these ensembles. The timeseries of winter (DJF) temperatures are shown in Fig. 7 for the four ensembles. Note that MACRO undergoes a rather smooth warming in the ensemble mean, but the different MICRO ensembles show consistent deviations from a smooth trend in the first couple of decades. The equivalent temperatures for JJA are shown in Fig. S1.
We also consider examples of 20 and 50 year projections of winter (DJF) in Figs. 8 and 9. The equivalent figures for summer (JJA) are shown in Figs. S2 and S3. Other seasons, regions and trend lengths can be viewed at an interactive website,Footnote 1 which includes results for both surface air temperature and precipitation.
The mean spatial trend for the MICRO and MACRO ensembles differ substantially when considering 20 year trends (Fig. 8). The MACRO ensemble shows a warming trend over the whole region. However, in the MICRO ensemble, there is a general cooling over Europe and much of the North Atlantic as a consequence of the particular ocean initial condition chosen. When considering each grid point independently there is the possibility of a trend smaller than –0.8 to larger than +0.8 K per decade for most land areas.
The histograms of trends for the European average temperature illustrate that the MACRO ensemble has a significantly wider spread than MICRO (at 99 % confidence using an f-test), and a mean which is positive, whereas the MICRO ensemble tends to produce a cooling, as seen in the maps.
However, the MINI MICRO ensembles clearly highlight how ocean initial conditions affect the subsequent distribution. Remarkably, the MINI MICRO 1 ensemble warms far more on average, and has no members which show a cooling. It also exhibits a distribution which hardly overlaps with the other MICRO ensembles.
When considering 50 year trends (Fig. 9), the differences between the ensembles have reduced, and all show a warming on average, and in all ensemble members (except one) for the European mean. However, considering grid points independently, it is still possible to have a cooling over Central and Eastern Europe. Again, the MACRO ensemble has a larger spread than the MICRO ensembles. The results for summer (JJA) give similar conclusions (Figs. S2, S3), but the variability is smaller, resulting in narrower distributions.
Regional trends: the role of the ocean state
The temperature timeseries for Europe in DJF (Fig. 7) show some interesting features. The particular ocean state chosen as the initial condition in each ensemble is clearly changing the distribution of the subsequent projections.
An important consequence of the initial ocean state, in this GCM, is the subsequent development of the Atlantic meridional overturning circulation (AMOC). Figure 10 shows the annual mean maximum of the AMOC streamfunction for the long FAMOUS control simulation. The filled circles represent the initial conditions used—green for the MICRO ensemble, orange and grey for MINI MICRO 1 and 2 respectively, and blue for the other MACRO states. We note again that a single realisation from each of the MICRO ensembles is also included in MACRO.
At first glance, there is nothing unusual about the chosen MICRO initial condition as the AMOC is relatively neutral. However, Fig. 11 shows that the vast majority of ensemble members follow a similar subsequent trajectory with an increase for a few years, followed by a rapid decline. There is a clear potentially predictable signal in the AMOC and the time structure matches the behaviour of temperatures over Europe.
Figure 12 shows the regression pattern between the AMOC and surface temperatures in the control simulation, highlighting the potential impact of the ocean on European temperatures in FAMOUS. In the control simulation, European temperatures change by around 0.17 K/Sv in response to the AMOC (also see Smith and Gregory 2009). This is in qualitative agreement with the variations seen in MICRO.
Figure 11 also shows the AMOC evolution for each MACRO state, reset to start from the same nominal year. Here the spread in projections is far wider initially, highlighting that a range of ocean states has been chosen. The ensemble spread of the MICRO experiments saturate to a similar level to MACRO after around 20–30 years (not shown), slightly longer than previous studies (Collins et al. 2006; Msadek et al. 2010).
The MINI MICRO 1 ensemble members undergo a rapid warming initially over Europe, consistent with the low state of the AMOC in the initial condition although the AMOC control timeseries does not reflect this (Figs. 10 and 11). It is not clear why MINI MICRO 1 has a high ensemble spread over Europe in the first few years (Fig. 6). In MINI MICRO 2, a similar situation to MICRO is seen, with an initial warming and subsequent cooling, also consistent with the AMOC initial state and evolution (Fig. 11).
The different behaviour of the ensembles over Europe are clearly related to the particular ocean initial condition in a complex fashion, highlighting the need to sample a wide range of ocean states to ensure a representative future ensemble.
Signal-to-noise in future trends
The issues of signal-to-noise in future temperature trends in this ensemble are summarised in Fig. 13. The mean signal (solid) and ensemble spread (dashed) are compared for two seasons (DJF & JJA) and two spatial averages (global & Europe).
The signal of the trend is larger than the ensemble spread for 20 year trends in global average temperature (top row)—i.e. where the dashed and solid lines cross, termed ‘emergence’. For Europe (middle row), this signal emergence time is later, at around 20–35 year trend length depending on the ensemble.
The ensemble spread declines as the period lengthens and the MACRO ensemble (blue) shows larger spreads than the MICRO ensemble (green) for all trend lengths in both seasons and both spatial averages. But, for trend lengths larger than around 40 years the differences are negligible. For shorter trends, the ocean initial conditions play a key role in determining the spread in future trends.
For precipitation, Fig. 13 (bottom row) demonstrates that the emergence times are generally later, except for DJF in MICRO, which is at a similar time to temperature. For European JJA rainfall, the signal remains smaller than the variability, even when considering trends of 90 years length.
Interestingly, the spreads in MICRO and MACRO do not completely converge, even for multi-decadal trend lengths, especially in DJF European temperature and precipitation. This suggests some memory of the initial conditions for an extended period.