Northern Hemisphere climate indices

We started by analysing climate indices that have been derived from the dominant spatial patterns of variability in Northern Hemisphere sea surface temperature data, specifically the Pacific Decadal Oscillation (PDO), the Atlantic Multi-decadal Oscillation (AMO), and the Atlantic Tripole. The latter represents the lagged response of ocean surface temperatures to the dominant mode of North Atlantic pressure variability, the North Atlantic Oscillation (NAO), which we also analyse for completeness (noting that atmospheric pressure variability has far less memory – i.e. much lower autocorrelation – than sea surface temperatures).

We find consistent trends in the character of fluctuations in the chosen climate indices (Fig. 1). Standardising the interval of comparison to the ERA-40 reanalysis16 interval 1957–2002 (Fig. 1), relative to longer original datasets (Figs S1–S5), has little qualitative effect on the results (compare Figs 1 and S5), with the exception that variance in the PDO index increases more markedly over 1957–2002 than over 1948–2016 (as an interval of high initial variance is removed). The signs of the autocorrelation and variance trends are generally robust to choice of filtering bandwidth and sliding window size used in the analysis, although their magnitude varies (Figs 1 and S5–6). Over 1957–2002 (Figs 1 and S6 and Table 1), the PDO index shows a strong increase in autocorrelation (median Kendall τ = 0.84) and variance (τ = 0.68), as examined previously7. The AMO index shows increases in both autocorrelation (τ = 0.47) and variance (τ = 0.53). The Atlantic tripole index also shows increases in both autocorrelation (τ = 0.36) and variance (τ = 0.61), whereas the NAO index shows no overall trend in autocorrelation (τ = 0.04) and a strong decline in variance (τ = −0.68).

Figure 1 Autocorrelation and variance trends in climate indices. For the ERA-40 interval (09/1957-08/2002). Distribution of Kendall τ trends in AR(1) and standard deviation for all combinations of sliding window and bandwidth size in observational climate indices (blue-green) and null models (red; from 1000 time-series with same frequency spectrum) (see Methods sections Sensitivity analysis, Significance testing). The percentages represent the fraction of results from the observational indices that are significantly different to the null models (p = 0.1 two tailed). Full size image

Table 1 Autocorrelation and variance trends in observational climate indices (1957–2002). Full size table

To establish whether these trends in autocorrelation and variance are significant we test against a null model of 1000 time-series of surrogate data with the same frequency spectrum (see Methods). Over 1957–2002 (Fig. 1), the increase in autocorrelation in the observed PDO index is the most significant, with 100% of the trends from different filtering bandwidth-sliding window combinations significantly different to those from the null model. 91% of the increasing variance trends in the PDO index are significant. For the increases in autocorrelation and variance in the AMO index, 46% and 56% respectively of the trends are significant. For the increases in autocorrelation and variance in the Atlantic Tripole index 30% and 67% respectively of the trends are significant. For the decline in variance in the NAO index 87% of the trends are significant.

Interestingly, when shortening the interval in which autocorrelation and variance trends are calculated to 22.5 years (half the 1957–2002 series) and varying the timing of that 22.5 year interval, the sign of calculated autocorrelation and variance trends can vary (Figs 2, S7 and S8). The PDO autocorrelation trend is strongly positive initially, weakens then strengthens again, whereas the PDO variance trend starts weakly positive, switches to weakly negative then recovers to strongly positive. The AMO autocorrelation trend is generally positive but weak and fluctuates in strength with a ~15 year period. The AMO variance trends switches from strongly negative to strongly positive then back to strongly negative, in antiphase with the index itself – indicating that an interval of negative AMO is associated with increasing short-term variability of North Atlantic SST fluctuations. The Atlantic Tripole autocorrelation trend switches between positive and negative on a ~15 year period (somewhat similar to AMO autocorrelation trends). The Atlantic Tripole variance trend is more predominantly positive but follows a similar pattern. The NAO autocorrelation trend switches from negative to positive roughly in phase with the overall negative to positive shift in the index itself, whereas the variance trend is initially strongly negative, switches to positive then returns to strongly negative.

Figure 2 Decadal variability in autocorrelation and variance trends in climate indices. For 22.5 year intervals (within 1957–2002) analysed with filtering bandwidth and sliding window length of half the interval (11 years 3 months). Also plotted is the mean value of the climate index over the same 22.5 year intervals. (top left) AMO, (top right) Atlantic Tripole, (bottom left) NAO, (bottom right) PDO. Full size image

Whilst some of the (multi)decadal variability in autocorrelation and variance trends could occur by chance in a red-noise system (due to finite sampling), the results (Figs 2, S7 and S8) also suggest that the low-frequency internal modes of climate variability themselves may cause changes in the autocorrelation and variance of shorter-term fluctuations. This seems mechanistically plausible if, for example, a shift within a mode of variability is accompanied by systematic regional changes in wind strength and/or ocean mixed layer depth, which affect the decay rate of sea surface temperature fluctuations17. Despite the decadal variability in autocorrelation and variance trends there are still overall positive trends over the full 1957–2002 interval, especially in the PDO index (which also shows increasing autocorrelation and variance over longer intervals)7, leaving open the possibility of a forced component to such longer term trends.

Model historical simulations

To examine further whether any anthropogenic forced component is apparent in observed autocorrelation and variance trends, we analysed fluctuations in the AMO and PDO indices simulated by nine climate models from the CMIP5 database over the same historical interval 1957–2002 (see Methods). The results (Fig. 3 and Table 2) show generally weak and mixed autocorrelation and variance trends in the modelled AMO and PDO indices, as may be expected by chance (without a strong forced component). None of the models reproduce the strength of positive trend in autocorrelation in the observed AMO index (median τ = 0.47), although one model (GISS-E2-H) produces a comparable positive trend in variance (τ = 0.58) to the observations (τ = 0.53). None of the models reproduce the strength of positive trends in autocorrelation (τ = 0.84) and variance (τ = 0.68) seen in the observed PDO index, and only one model (HadGEM2-ES) produces robustly positive trends in both autocorrelation (τ = 0.48) and variance (τ = 0.54) in its modelled PDO index.

Figure 3 Modelled historical trends in autocorrelation and variance in the PDO and AMO indices. Results for nine models in the CMIP5 database under historical forcing (followed by RCP8.5) for the ERA-40 interval (09/1957-08/2002). Distribution of Kendall τ trends in AR(1) (red) and standard deviation (purple) for all combinations of sliding window and bandwidth size (see Methods section Sensitivity). The percentages represent the fraction of results from the modelled indices that are significantly different to null models (p = 0.1 two tailed). Full size image

Table 2 Autocorrelation and variance trends in model simulations of the AMO and PDO climate indices (1957–2002). Full size table

Thus, there is no consistent signal of an anthropogenic forced trend in either autocorrelation or variance in either the AMO or PDO as simulated across these model runs. This could be because the models fail to respond to forcing correctly. The models are known to be of varying quality in their ability to capture internal (multi)decadal variability and in no case would the timing of low-frequency variability be expected to match the real system because these are not data-assimilated model runs. Hence given the small number of model realisations, the results are consistent with the interpretation that historical trends in autocorrelation and variance in the climate indices are influenced by (multi)decadal internal variability of the climate system. The fact that there are significant long-term positive trends in autocorrelation and variance in the observations (Fig. 1), most strongly for the PDO index, but also in the AMO and Atlantic Tripole indices, leaves open the possibility that there is a forced component to these trends which the models are failing to capture.

Spatial trends in persistence and variance

Having established that there have been some long-term trends in autocorrelation and variance of key Northern Hemisphere climate indices as well as (multi)decadal modulation of those trends, we considered the spatial pattern of trends in autocorrelation and variance. For this we analysed the HadCRUT418 and GISTEMP19 surface temperature datasets and the atmospheric reanalysis dataset ERA-4016 again over the common interval 1957–2002. Whilst the two temperature datasets come as anomalies relative to a baseline period, which can bias estimates of variance outside of the reference period15, the reanalysis dataset comes in absolute values allowing us to remove a running mean and thus avoid biasing the variance estimates15.

The analysis of spatial temperature data over 1957–2002 shows somewhat different global spatial patterns of trends for either autocorrelation or variance across different datasets, but also large regions of agreement (Fig. 4). Focusing on the HadCRUT4 regions (where there is good raw data coverage), the different datasets agree that autocorrelation increased across large parts of the North Pacific, the North Atlantic, North America, and the Mediterranean, and in the Arabian Sea. They agree that variance increased in broadly the same regions, with the increase in variance being more widespread (than increasing autocorrelation) across the North Atlantic and Europe. (The spatial pattern of change in inter-monthly temperature variance is also broadly similar to the previously published pattern of change in inter-annual temperature variability)13.

Figure 4 Consistency in autocorrelation and variance trends between temperature datasets. Monthly temperature datasets HadCRUT4, GISTEMP and ERA-40 in the interval 1957–2002, processed with filtering bandwidth 10 years and sliding window length 25 years. (a) AR(1). (b) Standard deviation. Red (3) indicates all 3 datasets agree on a positive trend, dark blue (−3) indicates all 3 datasets agree on a negative trend, green (2) indicates 2 datasets give a positive trend, 1 gives a negative trend, cyan (−2) indicates 2 datasets give a negative trend, 1 gives a positive trend. Maps were created using NCAR Command Language (Version 6.2.1) [Software]. (2014). Boulder, Colorado: UCAR/NCAR/CISL/TDD. http://dx.doi.org/10.5065/D6WD3XH5. Full size image

Within individual temperature datasets, there are thus typically consistent increases in both autocorrelation and variance across large parts of the North Pacific, North America, in a SW-NE band across the North Atlantic, and through the Mediterranean (Fig. S9). In other regions, e.g. much of Siberian Russia, there are consistent decreases in autocorrelation and variance. Within each dataset there are also cross-over regions with inconsistent trends in autocorrelation and variance. Trends in autocorrelation and variance are thus not related globally in a systematic way.

Examining the strength of the autocorrelation and variance trends in each dataset (Fig. 5), the strongest increasing trends in variance and autocorrelation (i.e. ‘slowing down’) are typically around 30–40°N in the North Pacific, in a SW-NE band across the North Atlantic, in a SW-NE band across North America, and in the central Mediterranean. The North Pacific and North Atlantic spatial signals are broadly consistent with the increasing autocorrelation and variance trends seen in the PDO, AMO and Atlantic Tripole indices. Tests for significance of the spatial trends (see Methods) suggest they are significant at the 90% confidence level in many places, including the increasing autocorrelation and variance across SW-NE North America and in the Mediterranean.

Figure 5 Trends in autocorrelation and variance in different temperature datasets 1957–2002. Monthly temperature datasets processed with filtering bandwidth 10 years and sliding window length 25 years: (a,b) HadCRUT4; (c,d) GISTEMP; (e,f) ERA-40. Trends in: (a,c,e) AR(1) and (b,d,f) standard deviation, measured as Kendall τ values. Significance at the 90% confidence interval relative to a null model (see Methods) is indicated with cross-hatching. Maps were created using NCAR Command Language (Version 6.2.1) [Software]. (2014). Boulder, Colorado: UCAR/NCAR/CISL/TDD. http://dx.doi.org/10.5065/D6WD3XH5. Full size image

We also analysed HadCRUT4, GISTEMP19 and the ERA-Interim20 reanalysis over its interval 1979–2015. The spatial results (Fig. S10) show an overall shift toward more negative trends in autocorrelation and variance compared to the earlier overlapping interval (1957–2002), although some regions, e.g. in the NE Pacific, show strong increases in both autocorrelation and variance. Such (multi)decadal variability in autocorrelation and variance trends, particularly in the North Atlantic sector, is consistent with the behaviour seen in aggregate climate indices (Figs 2 and S8). The persistence of positive autocorrelation and variance trends in the North Pacific region is also consistent with results for the PDO index (Fig. S1) and previous work7.