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The question of how climate model projections have tracked the actual evolution of global mean surface air temperature is important in establishing the credibility of their projections. Some studies and the IPCC Fifth Assessment Report suggest that the recent 15-year period (1998–2012) provides evidence that models are overestimating current temperature evolution. Such comparisons are not evidence against model trends because they represent only one realization where the decadal natural variability component of the model climate is generally not in phase with observations. We present a more appropriate test of models where only those models with natural variability (represented by El Niño/Southern Oscillation) largely in phase with observations are selected from multi-model ensembles for comparison with observations. These tests show that climate models have provided good estimates of 15-year trends, including for recent periods and for Pacific spatial trend patterns.

The differences between climate model forecasts and projections¹ have come to prominence over interpretation of model simulations of recent temperature trends. A key difference between a climate forecast and a climate projection is that the former attempts to account for the correct phase of natural internal climate variations whereas the latter does not and can not.

A weather forecast attempts to account for the growth of particular synoptic eddies and is said to have lost skill when model eddies no longer correspond one to one with those in the real world. Similarly, a climate forecast of seasonal or decadal climate attempts to account for the growth of disturbances on the timescale of those forecasts. This means that the model must be initialized to the current state of the coupled ocean–atmosphere system and the perturbations in the model ensemble must track the growth of El Niño/Southern Oscillation^{2, 3} (ENSO) and other subsurface disturbances⁴ driving decadal variation. Once the coupled climate model no longer keeps track of the current phase of modes such as ENSO, it has lost forecast skill for seasonal to decadal timescales. The model can still simulate the statistical properties of climate features from this point, but that then becomes a projection, not a forecast.

The Coupled Model Intercomparison Project 5 (CMIP5) series of coupled climate models have been run in climate projections mode⁵ and, to a limited extent, in decadal forecasting mode⁶. The models run as climate projections apply best estimates of the historical sequence of radiative forcing of climate for the past (until 2005), followed by specified future forcing scenarios. That means that until 2005 the models attempt to stay in sequence only with the year to year and decade to decade fluctuations in climate caused by the historical variation in radiative forcing (and not with internal variations).

Decadal variations in surface climate are due to a range of factors^{7, 8}. These factors include radiative forcing variations, but they are not the only, or even the most important, factors. Natural internal variations in the climate system also drive decadal variations^{9, 10, 11}. These can occur for example through variations in the rate at which the ocean circulation takes up the additional heat added to the atmosphere from greenhouse forcing^{12, 13}. Long-term variations in the preference of the coupled system for La Niña and El Niño states (the Pacific Decadal Oscillation¹⁴ (PDO)) change the rate of ocean heat uptake and are a key driver of decadal variability^{13, 15}.

In the CMIP5 models run using historical forcing there is no way to ensure that the model has the same sequence of ENSO events as the real world. This will occur only by chance and only for limited periods, because natural variability in the models is not constrained to occur in the same sequence as the real world. For any 15-year period the rate of warming in the real world may accelerate or decelerate depending on the phase of ENSO predominant over the period. That means that for a set of model projections well calibrated to the range of natural variability, there will be some 15-year periods where the observed rate of warming is in the low tail of the distribution of model trends for that 15-year period, and some 15-year periods where the observed rate of warming is in the high tail of the model distribution. These cases are illustrated by the 15-year observed trend and CMIP5 model trend distribution for 1998–2012 (Fig. 1a) and 1984–1998 (Fig. 1b). These two periods are no more meaningful in evaluating projections than any other 15-year periods, and we focus on the former here only to evaluate claims made about model projections in the most recent 15-year period^{7, 16}.

a,b, Histogram of trends for 1998–2012 (a) and 1984–1998 (b) for the CMIP5 multi-model ensemble. The thin vertical lines show the observed trend for these periods from HadCRUT4 (dashed red), GISS (blue) and Cowtan and Way (red).

The desired solution to this problem is to do a climate forecast, not a projection. For a climate forecast one would test models that were initialized in 1998 and run with ensemble perturbations designed to track the major decadal instability modes (ENSO, PDO) in the ocean. Decadal forecasting efforts so far show some improvements due to initialization, but are still in relative infancy²⁰.

Another approach to ensure that the models have the same ENSO phase as the real world is to impose observed sea surface temperatures²¹ (SSTs) or observed winds²² in the tropical Pacific region of the model. This approach can be applied to ocean-only models. For coupled models this method requires that the model SST or wind stress field be restored rapidly to the observed fields. The forced/restored projection forces the models to lock phase with observed ENSO, although this partly specifies a temperature outcome consistent with observations. When applied in coupled models the results are also unphysical in that part of the model surface field is effectively specified and part is free. Other approaches include post hoc removal of a regression estimate of the ENSO phase contribution from model ensemble mean temperature²³.

Here we develop and apply an alternative simple, but natural (unforced), method to analyse model projections in phase with the real world. The models are not given any information about the observed state in this approach. The method takes advantage of the fact that, by chance, some of the CMIP5 model runs will be at least partially in phase at any given time with internal variability in the real world. One of the major processes driving variability in the rate of ocean heat uptake is ENSO (ref. 13). The long-term cycle of ENSO in switching between El Niño-preferred periods (slower ocean heat uptake decades) and La Niña-preferred periods (faster ocean heat uptake decades) will by chance line up in some of the CMIP5 models. To select this subset of models for any 15-year period, we calculate the 15-year trend in Niño3.4 index²⁴ in observations and in CMIP5 models and select only those models with a Niño3.4 trend within a tolerance window of ± 0.01K y⁻¹ of the observed Niño3.4 trend. This approach ensures that we select only models with a phasing of ENSO regime and ocean heat uptake largely in line with observations. In this case we select the subset of models in phase with observations from a reduced set of 18 CMIP5 models where Niño3.4 data were available²⁵ and for the period since 1950 when Niño3.4 indices are more reliable in observations.

Figure 4 shows the running 15-year trends for observations in red (Goddard Institute for Space Studies¹⁸ (GISS) top row; Cowtan and Way¹⁷ bottom row) and for the subset of CMIP5 models that fell within the Niño3.4 trend tolerance window in blue in the left column. The right column shows model 15-year trends for the subset of models in grey that were furthest from the observed Niño3.4 slope (least in phase with observations), where the subset of models is constrained so that it contains the same number of models that fell within the best-fit tolerance window. The size of plotting symbol for model trends is proportional to the number of models that fell within the Niño3.4 tolerance window. The solid lines are loess-smoothed fits to the trend points. The loess smoothing is weighted by the number of models that contributed to each observation. The shaded areas surrounding each loess line represent approximate 95% confidence intervals.

a–d, The red dots on the thin red line correspond to the 15-year observed trends for each 15-year period in GISS (a,b) and Cowtan and Way (c,d). The red envelope shows a 2.5–97.5 percentile loess-smoothed fit to the observed 15-year trends. The blue dots (a,c) show the 15-year average trends from only those CMIP5 runs in each 15-year period where the model Niño3.4 trend is close to the observed Niño3.4 trend. The size of the blue dot is proportional to the number of models selected. If fewer than two models are selected in a period, they are not included in the plot. The blue envelope is a 2.5–97.5 percentile loess-smoothed fit to the model 15-year trends weighted by the number of models at each point. b and d contain the same observed trends in red for GISS and Cowtan and Way respectively. The grey dots show the average 15-year trends for only the models with the worst correspondence to the observed Niño3.4 trend. The grey envelope in b and d is defined as for the blue envelope in a and c. Results for HadCRUT4 (not shown) are broadly similar to those of Cowtan and Way.

Observational and model data.

Three observational data sets are used to represent annual GMST: GISS (ref. 18); HadCRUT4 (ref. 29); and Cowtan and Way¹⁷. GMST is also taken from 38 CMIP5 models with multiple runs per model generating a multi-model ensemble with 82 runs. The CMIP5 ensemble runs span 1880–2012 with historical forcing for the period 1880–2005 and Representative Concentration Pathway 8.5 (RCP8.5; ref. 30) forcing from 2006 to 2012. As the latter time period is so short, the choice of RCP scenario is not critical here. Results were repeated using RCP4.5 for the latter period and are very similar. A subset of 18 of the 38 CMIP5 models were available to us with SST data to compute Niño3.4 (ref. 24) indices. The subset of models are indicated in bold in the set below. The reduced set of 18 models provides a similar model ensemble trend distribution to the larger model set. Niño3.4 values for observations were downloaded from NOAA at http://www.esrl.noaa.gov/psd/data/climateindices/list/. Spatial SST trends were calculated from HadISST data³¹.

The set of CMIP5 models used are: ACCESS1-0, ACCESS1-3, bcc-csm1-1, bcc-csm1-1-m, BNU-ESM, CanESM2, CCSM4, CESM1-BGC, CESM1-CAM5, CMCC-CM, CMCC-CMS, CNRM-CM5, CSIRO-Mk3-6-0, EC-EARTH, FGOALS-s2, FIO-ESM, GFDL-CM3, GFDL-ESM2G, GFDL-ESM2M, GISS-E2-H, GISS-E2-H-CC, GISS-E2-R, GISS-E2-R-CC, HadGEM2-AO, HadGEM2-CC, HadGEM2-ES, INMCM4, IPSL-CM5A-LR, IPSL-CM5A-MR, IPSL-CM5B-LR, MIROC-ESM, MIROC-ESM-CHEM, MIROC5, MPI-ESM-LR, MPI-ESM-MR, MRI-CGCM3, NorESM1-M and NorESM1-ME.

Phase-selected climate projection.

The method of phase-selected climate projection is based on selecting a feature of the climate that one wishes to align to the real-world phase of the feature. As we are interested in tracking decadal fluctuations in GMST, we need to follow natural variations in ocean heat uptake on this timescale. These are driven by a range of processes in tropical and high-latitude oceans^{11, 32}, but ENSO is one of the important ones and is at least broadly simulated by the coupled models.

Climate models cannot simulate every ENSO phase transition, but that is not critical here. To approximate the phase of ocean heat uptake in a 15-year period one may need to capture only the general sense of whether the models are El Niño or La Niña dominated over the period. To this end we use Niño3.4 as an index of ENSO phase and calculate the trend in Niño3.4 over the period to indicate the general tendency of the system towards regimes dominated by either ENSO state (similar to PDO phases). Models with a similar Niño3.4 trend to observations are then selected to represent the subset of models from the projection ensemble that just happen to have a similar response of ENSO over the 15-year period. This approach selects models with a statistical similarity that is related to the desired feature (ocean heat uptake). The approach does not guarantee any kind of dynamical consistency between models for each 15-year period.

The choice to fit 15-year trends to Niño3.4 is not the only way to estimate the phase of ocean heat uptake rates. We also tested a method based on trends of low-pass Niño3.4 values to more directly mimic the PDO. Results were repeated where we detrended the Niño3.4 series in observations and models and compared the low-pass Niño3.4 slopes to select in-phase models. The results for the low-pass method are very similar to those for the direct method shown.

The probability density function (PDF) of observed and modelled 15-year GMST trends in Fig. 3 is based on 82 model runs over 1880–2012, but only 3 observational data sets, and thus contains different sample sizes. To control for sample size, the model PDFs were recalculated with 500 random samples of model 15-year trends with the same sample size as the number of observed trends. This yields very similar model distributions to those in Fig. 3, indicating that any differences between the model and observed PDF are mostly not due to sample size differences.

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