Enhanced multi-year predictability after El Niño and La Niña events

Liu, Yiling; Donat, Markus. G.; England, Matthew. H.; Alexander, Lisa. V.; Hirsch, Annette L.; Delgado-Torres, Carlos

doi:10.1038/s41467-023-42113-9

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Published: 11 October 2023

Enhanced multi-year predictability after El Niño and La Niña events

Nature Communications volume 14, Article number: 6387 (2023) Cite this article

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An Author Correction to this article was published on 27 November 2023

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Abstract

Several aspects of regional climate including near-surface temperature and precipitation are predictable on interannual to decadal time scales. Despite indications that some climate states may provide higher predictability than others, previous studies analysing decadal predictions typically sample a variety of initial conditions. Here we assess multi-year predictability conditional on the phase of the El Niño–Southern Oscillation (ENSO) at the time of prediction initialisation. We find that predictions starting with El Niño or La Niña conditions exhibit higher skill in predicting near-surface air temperature and precipitation multiple years in advance, compared to predictions initialised from neutral ENSO conditions. This holds true in idealised prediction experiments with the Community Climate System Model Version 4 and to a lesser extent also real-world predictions using the Community Earth System Model and a multi-model ensemble of hindcasts contributed to the Coupled Model Intercomparison Project Phase 6 Decadal Climate Prediction Project. This enhanced predictability following ENSO events is related to phase transitions as part of the ENSO cycle, and related global teleconnections. Our results indicate that certain initial states provide increased predictability, revealing windows of opportunity for more skillful multi-year predictions.

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Introduction

Interannual to decadal climate predictions aim to predict the climate state for the following year and up to 10 years into the future. These decadal predictions are affected by both external forcing and internal climate variability and are performed by initialising a climate model with observations or reanalyses and integrating them for 10 years after initialisation^1,2. A general warming trend, associated with increasing greenhouse gas forcing, provides some skill for temperature on decadal time scales almost everywhere³. Aligning the climate variability by initialising the predictions with the observed climate has been shown to add skill in some regions, including the North Atlantic, the Amundsen Sea, and some land regions including Europe, the Middle East and Africa^2,3,4. Even precipitation, which has lower decadal predictability than temperature, exhibits significant forecast skill on multi-year to decadal time scales over some regions, including parts of Europe, Asia, the Sahel, and North America^3,5,6.

Studies of decadal climate predictability usually quantify skill using predictions started from all initialised states. This approach determines the general level of predictability, but it neglects possible forecasting windows related to more predictable situations that could enable more skilful predictions under certain conditions, as in a Lorenz system⁷. For example, on weather time scales (e.g. hours to days), high-pressure weather systems are usually linked to more predictable weather (i.e. persistent fine conditions) compared to storms within low-pressure systems, that are generally more transient and variable⁸. For conditional predictability on seasonal time scales, forecasts initialised in June show modest skill in predicting sea surface temperature (SST) in the eastern tropical Pacific for up to 6–9 months compared with less skilful forecasts initialised before the boreal spring predictability barrier in April and May⁹. On decadal time scales, increased predictability has been found when initialising from strong Atlantic Meridional Overturning Circulation (AMOC) or Atlantic Ocean Heat Transport (OHT) than from weak AMOC or OHT conditions^10,11. A recent effort to reconstruct states of the tropical Pacific suggested it exhibits different predictability depending on the climate state at the time of initialisation¹².

As one of the globally dominant modes of interannual climate variability, El Niño-Southern Oscillation (ENSO) is related to ocean temperature and coupled atmospheric circulation anomalies in the tropical Pacific, affecting many remote parts of the globe via teleconnections^{13,14,15,16,17}. ENSO has also recently been shown to contribute to decadal predictability in the South Pacific¹⁸, and inter-annual rainfall predictions for monsoon regions were shown to be more skilful when ENSO is active¹⁹. ENSO has also been shown to possibly trigger transitions in the Interdecadal Pacific Oscillation, which could be a source of multi-annual predictability²⁰. However, no previous studies have systematically investigated multi-year to decadal predictions starting from different ENSO phases at a global scale. In this study, using perfect-model prediction experiments and retrospective predictions of the observed climate, we investigate multi-year climate predictability and its sensitivity to ENSO phase when the predictions are initialised²¹. We classify the predictions according to ENSO phase at the time when the predictions are initialised with El Niño, La Niña and neutral conditions, and compare the forecast accuracy between these three different phases.

Results

Higher multi-year predictability after El Niño and La Niña events

The perfect-model predictions show positive potential skill in most regions of the globe for multi-year to decadal predictions of near-surface temperature (Fig. 1); a previous study showed that added skill from initialisation is found primarily in the first two forecast years across the sample of all starting years²¹. Analysing the potential skill for the different groups according to ENSO conditions at the beginning of the predictions, we also find large areas of the globe where the mean squared skill score (MSSS; see Methods) is positive (Fig. 1 for predictions started in El Niño and La Niña conditions, and Supplementary Fig. S1 for predictions started in neutral conditions). In the first year after initialisation, the skill for predictions started in neutral conditions is still high, so that the differences between the different groups are small. For multi-year forecast times beyond the first year, however, substantially larger regions of the globe exhibit skill in predictions starting from El Niño or La Niña conditions, when compared to predictions starting from neutral years. This is particularly the case in the tropical Pacific and tropical Atlantic, as well as over parts of Africa, for the average of forecast years 2–3 (Fig. 1h, k). For the 4–6 year forecasting period, enhanced skill is found over the extratropical North Pacific and parts of the Southern Ocean (Fig. 1i, l).

**Fig. 1: Potential skill dependence on initial El Niño-Southern Oscillation (ENSO) state.**

Figure 2 shows about half of the global area exhibits significant skill in predicting annual averages of near-surface temperature at 3, 4, 5 and 6 years in advance when starting from El Niño and La Niña events. In contrast, <20% of the global area has significant skill when starting from neutral conditions. For multi-year averages, the skilful areas are even larger: for example, more than 80% of the area exhibits significant skill after El Niño conditions for the 2–3 year prediction period, versus ~50% for predictions initialised in neutral years. The areas of significant prediction skill are ~90% (after El Niño years) versus 60% (neutral years) for the 4–6 year forecast period. In addition, the curve of classical neutral conditions (i.e. defined as all years that are not classified as El Niño or La Niña) is always above the curve of persistent neutral conditions (defined as years when there are no excursions to La Niña or El Niño conditions (see Methods); grey line in Fig. 2). This indicates predictability is even lower when initialising predictions from persistent neutral conditions during November, December and January (NDJ) and when average SST anomalies over these 3 months are smaller. Based on the MSSS differences (the two right-most columns in Fig. 1), potential skill is higher after El Niño conditions than after neutral conditions in more than 30% (forecast years 2–3) and more than 20% (forecast years 4–6) of the globe (Supplementary Fig. S2). After La Niña conditions, about 10% of the globe shows positive MSSS differences, whereas area fractions where MSSS is higher after neutral conditions are very small.

Composite maps of predictions initialised with El Niño and La Niña conditions show distinct temperature anomaly patterns reflecting the ENSO phase and related teleconnections during the first forecast year (Fig. 3). These include warm anomalies in most tropical regions (extending to higher latitudes along the west coasts of North and South America) and cold anomalies in the extratropical North and South Pacific in the first year after El Niño events, and largely opposite sign anomalies after La Niña events. In contrast, local mean anomalies are small in predictions initialised from neutral conditions. The average temperature anomaly over forecast years 2 and 3 shows anomaly patterns of mostly opposite sign compared to the first forecast year, suggesting that the climate in these simulations exhibits a tendency to evolve to the opposite ENSO phase of the initial state in the second or third year after initialisation. The average over forecast years 4–6 again shows similar anomalies to the first year, particularly across the tropical Pacific, indicating that the climate system tends to evolve back towards the initial ENSO phase at some point during this period, affecting the 3-year average (over forecast years 4, 5, and 6) accordingly. These tendencies for the Pacific to evolve into the opposite phase of ENSO over a 2-3 year time scale are not a given of course; the enhanced predictability is merely indicative of likelihoods given the initial climate state in the forecast.

**Fig. 3: Agreement of local temperature anomalies.**

The global anomaly patterns from the initialised perfect-model predictions closely resemble the patterns derived from the reference run of the perfect-model predictions (compare Fig. 3 and Supplementary Fig. S3) for up to 3 years after El Niño and La Niña conditions (pattern correlations >0.7). In particular, pattern correlations between the predicted anomalies and the reference run anomalies are higher than the pattern correlations of the historical (uninitialized) simulations with the reference run (maps are shown in Supplementary Fig. S4; pattern correlations for both initialised and uninitialized predictions are shown above each map in Fig. 3). This is true for the 2–3 year forecast period after both El Niño and La Niña events, and for the 4–6 year forecast period after El Niño, indicating added skill from initialisation at the global scale. In contrast, pattern correlations are low, and anomalies comparably smaller for predictions initialised from neutral conditions. Further, when starting from neutral conditions, pattern correlations show no additional skill from initialisation beyond the first forecast year. Overall similar results are also found for precipitation anomaly patterns (Fig. S5), indicating enhanced precipitation predictability and added value from initialisation for multiple years after El Niño and La Niña events. Note that the different rows in Figs. 3, S3 and S4 average over a different number of years (i.e. 1, 2 and 3 years), and this averaging will lead to different spatial correlations across the different rows. The key information for this comparison is that the initialised predictions show a more similar pattern to the reference run than the uninitialized predictions.

ENSO cycle determines the conditional predictability

The added skill in the tropical Pacific may be explained by ENSO periodicity. For example, in the tropical Pacific region where SST variations related to ENSO are strongest, predictions starting from either El Niño or La Niña are more skilful than those starting from neutral conditions (Fig. 1h, i, k, l). This could be indicative of the potential skill in capturing ENSO variations subsequent to El Niño/La Niña events^22,23,24. The model exhibits an ENSO periodicity of 3–6 years, consistent with observations (Fig. S6). Therefore, it seems plausible that the enhanced predictability after ENSO peak phases (i.e. after either El Niño or La Niña events) could be related to the dominant periodicity of the ENSO cycle as seen in the tendency for evolution to the opposite ENSO phase after 2–3 years and back to initial phase after 4–6 years (Fig. 3). This hypothesis is confirmed by analysing the potential skill in predicting ENSO itself, measured e.g. by the Niño3.4 index (Fig. S7). Predictions started from El Niño and La Niña states are more skilful in predicting the Niño3.4 index compared to predictions started in neutral conditions, or skill calculated based on all annual initialisations for the forecast years 2–3 and forecast years 4–6 (although uncertainty ranges based on bootstrapping the relatively small samples are large). In forecast year 1 the potential skill of predictions started in neutral conditions (and in particular persistent neutral conditions) is very high. This is likely due to the relatively small temperature variations in such cases when no ENSO phase transition happens in the months following initialisation, and SST anomalies remain relatively small.

The predictable tropical Pacific conditions also appear to result in higher potential skill in other remote locations due to both inter-basin and tropical-extratropical teleconnections. For example, tropical Pacific SST anomalies related to ENSO cycles teleconnect to both high southern and northern latitudes, and the tropical Pacific is known to interact with both the tropical Indian and Atlantic Oceans via adjustments in the Walker circulation^{25,26,27,28,29}. In particular, the simulated anomaly in the tropical Pacific region co-exists with same-sign high-latitude anomalies over North America, the Arctic, and the Amundsen Sea regions for both temperature (Fig. 3) and precipitation (Fig. S5). Such correspondence of regional anomalies is found during e.g. 1, 2–3 and 4–6 years after El Niño, years 1 and 2–3 after La Niña in Fig. 3; and years 1 and 2–3 after El Niño and La Niña in Fig. S5).

From an oscillator point of view, peak phases of the ENSO oscillation (i.e. El Niño and La Niña events) are most likely followed by a transition towards the opposite phase, except in a few cases when these events (in particular La Niña) can endure for a second year³⁰. In contrast, after neutral start years, there is less predictive skill as the system could evolve towards either El Niño or La Niña, or indeed remain neutral. In order to compare transition probabilities based on different initial conditions in our perfect-model experiment, we investigate the average transition probabilities over all forecasting members of the El Niño, La Niña and neutral starting points respectively during different forecasting times; namely 1, 2–3 and 4–6 years (Table S2). This analysis confirms that El Niño start years are mostly followed by neutral or La Niña years in the first year after initialisation; while La Niña start years are more likely followed by neutral or El Niño years. The simulations have an increased probability to transition into the opposite phase during forecast year 2 or 3 after initialisation compared to transitioning into the initial phase. In particular, simulations started in El Niño conditions have a probability to transition into La Niña at some point during forecast year 2 or 3 of 32%, whereas only 19% transition back to El Niño, and simulations started in La Niña conditions have a probability of 37% to transition into El Niño during forecast year 2 or 3, but only 22% probability to transition back into La Niña. During forecast years 4, 5 or 6 there is a slightly increased probability for the simulations to transition back into the initial state (i.e. after El Niño to El Niño and after La Niña to La Niña) than into the opposite phase. In contrast, for the neutral start years, the probability of transition to El Niño is comparable to La Niña for the 2–3 year and 4–6 year forecast periods. Inconsistent variations (i.e. of opposite sign) across ensemble members following different neutral initial states tend to cancel one another out, so that average anomalies after neutral conditions are relatively small (Figs. 3 and S6).

The interannual phase variations of ENSO are driven by the recharge and discharge of heat along the tropical Pacific Ocean over a dominant 3-6 year time scale³¹. Capturing the ENSO phase in the initial state appears to be the primary agent for improved multi-year predictability, with the reliability of these predictions dependent on the representation of the dominant time scales of ENSO variability (e.g. the power spectral analysis of Fig. S6). In the context of this study, when initialising from either El Niño or La Niña phases, the non-equilibrium component between the zonal mean equatorial thermocline depth and wind stress of the recharge-discharge oscillator is included in the initialisation. Initialising from neutral states, however, does not guarantee the inclusion of the imbalance between the subsurface ocean temperature and atmospheric winds, as the SST, sea level pressure, sea surface height and surface wind anomalies are very weak. Indeed, we found the difference in prediction skill between ENSO peak phases and neutral states to be more pronounced for persistent neutral states (i.e. those not exceeding the El Niño or La Niña threshold in any single month during NDJ) than for the classical neutral states (i.e. those not identified as El Niño or La Niña). That is, without any (even brief) excursion to El Niño or La Niña states, as in the persistent neutral states, there may be less non-equilibrium information embedded in the initialisation. This finding suggests that, in addition to the simulated ENSO cycle, stronger initial SST anomalies in the tropical Pacific may lead to enhanced skill. This is plausible when a stronger non-equilibrium component of the recharge-discharge oscillator is related to a lower error growth rate and a better-defined attractor evolution, compared to situations with smaller SST anomalies and related non-equilibrium components.

Windows of opportunity in real-world predictions

Both the model and the observational data indicate a peak in the spectral intensity of Niño3.4 SST at around 3–6 years (Fig. S6). This indicates similar ENSO periodicity in the model and real-world, consistent also with previous evaluations that showed realistic ENSO characteristics of the model version used here^32,33, and suggests that we may also achieve enhanced skill following ENSO events in real-world predictions. In fact, the real-world hindcasts also show enhanced skill for predictions starting from El Niño and La Niña compared to neutral conditions for the forecast periods 2–3 and 4–6 years, in particular in the Pacific Ocean (Fig. 4 for predictions started in El Niño and La Niña conditions, and Supplementary Fig. S8 for predictions started in neutral conditions), while some negative MSSS differences are found in other regions outside the Pacific. Despite the generally lower skill compared to the perfect-model predictions, there is positive MSSS in the central Pacific in forecast years 2–3 after El Niño events, whereas skill in this region is negative after neutral initial conditions—pointing to a window of opportunity also in real-world predictions. As the enhanced multi-annual skill after El Niño and La Niña conditions is spatially more limited to the Pacific, also the global area fraction with positive skill differences is substantially smaller compared to the perfect-model predictions (Supplementary Fig S9).

**Fig. 4: Skill dependence on initial El Niño-Southern Oscillation (ENSO) status in decadal hindcasts of the real-world climate.**

These results based on the CESM model are largely consistent with the retrospective predictions provided within the Coupled Model Intercomparison Project phase 6 (CMIP6) Decadal Climate Prediction Project (DCPP)³⁴. The multi-model ensemble of decadal hindcasts (which does not include the CESM; see the list of DCPP models in Supplementary Table S4) also shows enhanced skill in particular in parts of the Pacific in predictions initialised in El Niño and La Niña conditions compared to predictions initialised in neutral conditions (Supplementary Fig. S10)³⁵. Similar to the real-world predictions with the CESM model, this enhanced skill is not transferred to other regions outside the Pacific (in particular for multi-annual timescale predictions), possibly due to inconsistent representation of relevant teleconnections in the different models^36,37,38. Still these results indicate windows of opportunity for multi-annual predictions related to the ENSO state for large parts of the Pacific Ocean (including SSTs in the NINO3.4 region, Supplementary Fig. S11), and improved models may in the future transfer the enhanced skill also to other regions.

Given the similar ENSO periodicity between the CESM model and observations and the generally low skill over the Pacific region in the real-world predictions, it is likely that this overall lower skill in the real-world hindcasts compared to the perfect-model is related to non-ideal initialisation of the hindcasts and related adjustments⁵, unresolved ocean dynamics, or inconsistent representation of long-term trends between model and observations in the Pacific^{5,21,39,40,41}. Therefore, real-world predictions may be improved with improved initialisation, in terms of both observational coverage and model-observation consistency, to reduce both the uncertainty of the observed initial state and the shock and drift of the simulations after initialisation.

ENSO transition probabilities calculated from observations also indicate an increased chance for the opposite phase to occur 2 or 3 years in particular after La Niña events (Table S3), consistent with the transitions in the model. No clear probability differences are found for the pooling of forecast years 4, 5, 6. However, there is an increased probability of La Niña events compared to El Niño 5, 6 or 7 years after La Niña events—pointing to possibly slightly longer ENSO cyclicity in observations compared to the model.

Discussion

We have demonstrated that multi-year predictions started from El Niño and La Niña conditions show significantly higher potential and actual skill than predictions started from neutral conditions, based on perfect-model prediction experiments with the Community Climate System Model Version 4 and real-world hindcasts with CESM and a CMIP6 multi-model ensemble. This enhanced skill seems to be related to the simulated ENSO cycles and related teleconnections after ENSO peak phases, while after neutral conditions a cancellation of different phase transitions reduces predictability. The simulated ENSO cycles imply some multi-year predictability of ENSO events, consistent with the finding that some ENSO events can be predicted as much as four years ahead in real-world hindcasts⁴². Our results also suggest that enhanced predictive skill related to ENSO is potentially achievable if remaining shortcomings related to the initialisation of the model predictions could be improved, as well as the representation of relevant dynamics in the model. Despite the generally lower skill in comparison to the perfect-model case, there are instances where skill over parts of the Pacific is positive after El Niño or La Niña conditions and negative after neutral conditions—hinting to windows of opportunity also in the real-world predictions. Even though the actual skill is low, this gives hope that if the general weakness of low skill in the Pacific can be improved in decadal prediction systems, the conditional predictability on ENSO may provide more skilful ‘windows of opportunity’.

Temporal variations in predictability that indicate ‘windows of forecast opportunity’ have previously been noted in sub-seasonal to seasonal predictions, where certain regimes and persistent anomalies can provide added information above the weather noise⁴³. For example, El Niño or La Niña events can provide forecasting windows on seasonal time scales⁴³. Furthermore, ENSO predictability can undergo pronounced multi-decadal variations and the multi-decadal variability in the strength of ENSO teleconnections affects the predictive skill of extratropical teleconnections^44,45. Our work indicates that such windows of opportunity also exist for multi-annual predictions, where predictions starting from El Niño and La Niña states exhibit larger predictable regions compared to those starting from neutral years for forecast times longer than one year. Our study suggests that conditionally enhanced prediction skill from specific climate states can yield improved predictions at certain points in time. This paves the way for climate services to provide more credible multi-year predictions at certain times with specific climate states.

Methods

We investigate multi-year predictability conditional on the ENSO phase at the time of initialisation in both perfect-model predictions and hindcasts of the real-world climate. To study the perfect-model predictability, we performed experiments with the Community Earth System Model (CESM) version 1.0.5, a fully coupled model comprising atmospheric, oceanic, land and sea ice models. We used a configuration of the model that corresponds to the Community Climate System Model Version 4 (CCSM4), i.e. with the atmospheric component Community Atmosphere Model (CAM4) (at a horizontal resolution of 1.25° × 0.9°, with 26 vertical layers)⁴⁶; the ocean component Parallel Ocean Program version 2 (at a 1 degree horizontal resolution and 60 vertical levels on a displaced-pole grid)⁴⁷; the land component Community Land Model version 4 (run in the atmospheric grid)⁴⁸; and the sea ice component Community Ice Code version 4 (run in the ocean grid)⁴⁹. This is the same model configuration used for the CCSM4 contributions to Coupled Model Intercomparison Project phase 5 (CMIP5) historical and Representative Concentration Pathway (RCP) scenarios from which we are using transient historical simulations as uninitialized reference. For simplicity, we therefore refer to our perfect-model predictability experiments as CCSM4.

The first set of simulations includes perfect-model predictions that were performed by initialising an ensemble of decadal simulations from annual restart files of a transient historical simulation²¹. The term ‘perfect-model predictions’ refers to experiments in which a model is used to predict the climate evolution of that same model as opposed to a real-world climate, meaning that the model is a physically perfect representation of the reference it is aiming to predict, meaning that predictability estimates are thus not affected by inconsistencies between model and real-world climate. These initialised perfect-model predictions include five ensemble members initialised from every January 1st of the 46 initialisation years from 1961 to 2006. The ensemble members were generated by adding small Gaussian perturbations (order of 10⁻⁵K) to the atmospheric temperatures, with all other variables being identical, to simulate the case of perfectly known initial conditions²¹. The potential skill is then evaluated by quantifying how well these decadal simulations predict the transient reference simulation from which they were initialised. We compare the potential skill of the perfect-model predictions against the second set of uninitialized, transient climate simulations that contributed to CMIP5. These simulations are performed with the same model as the reference simulation they are used to predict, so we refer to these as uninitialized perfect-model predictions. Same as the initialised perfect-model predictions and the transiently forced reference run, these simulations use historical forcing until 2005 and then follow the RCP4.5 scenario from 2006 to 2015. For these uninitialized perfect-model predictions, we also use five ensemble members (started from different states of a pre-industrial control simulation to sample a wider range of internal variability), available within CMIP5, matching the ensemble size of the initialised perfect-model predictions²¹. Note that the ENSO periodicity was overly biennial in older versions of the CCSM model, e.g. CCSM3, but these issues have been much improved in the CCSM4 version which shows a typical ENSO periodicity of 3-6 years, consistent with observations as seen in the power spectrum shown in Fig. S6^32,33,50. CCSM4, CESM1 and the newer version CESM2 were shown to simulate ENSO characteristics such as periodicity and transitions reasonably similar to observations³³.

For real-world predictions, we utilise the CESM decadal prediction large ensemble (CESM-DPLE), which has 40 ensemble members each initialised on November 1st from 1954 to 2015 that are integrated for 122 months⁵. Note the atmospheric component of CCSM4 that we use for the perfect-model experiment is the Community Atmosphere Model 4 (CAM4)⁴⁶. CESM-DPLE used in the real-world hindcast utilises the Community Atmosphere Model 5 (CAM5) as its atmospheric component⁵. As we do not directly compare perfect-model predictions and real-world hindcasts, our conclusions do not require identical model versions or configurations for these different experiments.

Classifying the starting years of the perfect model and the real-world predictions from 1961 to 2006 according to ENSO phase, the basic methodology of the analyses in this study is to analyse skill measures and composites for these different ENSO groups of predictions. Detrended 5-month running means of monthly SSTs from the Nino3.4 region are used to estimate the Nino3.4 index. The detrending is done by subtracting the 30-year moving climatology preceding the year under consideration. This Nino3.4 index is used to classify each of the starting years as either El Niño, La Niña or neutral. El Niño start years are when the Nino3.4 index exceeds the upper quartile threshold (computed over the 1960–2015 period) from November to January (NDJ). La Niña start years are when the Nino3.4 index is below the lowest quartile. All remaining years are classified as neutral (this is referred to as the ‘classical’ neutral year definition in this paper). However, in the conventional neutral year definition (i.e. all years that are not classified as El Niño or La Niña), neutral years are not always characterised by persistent neutral conditions over all the 3 months (NDJ), because the Nino3.4 Index can exceed the quartile thresholds for 1 or 2 months. Therefore, we also consider a second neutral year classification (referred to as persistent neutral), which only includes the years when all 3 months (i.e. November, December and January) exhibit neutral conditions (i.e. excluding those years with intermittent positive or negative conditions during NDJ). The classification of starting years for the perfect-model predictions and real-world predictions are shown in Table S1.

While this ENSO classification includes some information from after the initialisation of the predictions (i.e. January SST, the first forecast month of the perfect-model predictions), this is still useful for interannual or multi-year predictions that target forecast times several years after initialisation. January is included in the classification to consider the entire season when ENSO events typically peak. For classifying ENSO in the real-world hindcasts, which are initialised on November 1st each year (i.e. 2 months earlier than the perfect model), we use the same months (November, December and January, i.e. the first three forecast months of the hindcasts). This classification therefore matches the perfect-model decadal prediction and the ENSO peak period, keeping the definitions consistent between the perfect-model and the real-world predictions.

To examine decadal prediction accuracy, we use the mean squared skill score (MSSS) as the primary deterministic verification metric and follow the framework for evaluating decadal predictions^{14,51,52,53,54}. MSSS can be decomposed as a function of the hindcasts, climatological forecast and observations when the climatological forecast is used as the reference, namely:

$${{{{{\rm{MSSS}}}}}}\left(H,\bar{O,}\,O\right)={r}_{{HO}}^{2}-{\left[{r}_{{HO}}-\frac{{S}_{H}}{{S}_{O}}\right]}^{2}-{\left[\frac{\bar{H}-\bar{O}}{{S}_{O}}\right]}^{2}$$

(1)

where ${r}_{{HO}}$ represents the sample correlation between the hindcasts (H) and the observations (O), ${{S}_{H}}^{2}$ is the sample variance of the ensemble mean hindcasts, S_O² denotes the sample variance of the observations, $\bar{O}={\sum }_{j=1}^{n}{O}_{j}$ is the climatological forecast (of which ${O}_{j}$ represents the observations, or perfect-model reference respectively, over j = 1,...,n starting times), and $\bar{H}$ is the mean hindcast.

The evaluation process is implemented in the Miklip evaluation system⁵⁵. The temperature and precipitation data are remapped to a 10° × 10° grid prior to calculating the skill measures to reduce small‐scale noise effects⁵¹. To account for model drift (which is a pertinent issue in the initialised real-world predictions), anomalies are calculated from lead-time dependent climatologies. We use 1000 bootstrap realisations (with replacement) to test the significance level of MSSS and skill differences between the different ENSO initialisations and estimate the p values of the local grid points. Each bootstrap realisation differs in a combination of starting years, and 5-year blocks are maintained to preserve temporal autocorrelation related to low‐frequency variability in resampling⁵¹. We further assess field significance and control for the false discovery rate (FDR), thereby minimising potential overinterpretation related to multiple significance testing⁵⁶. For a local grid point to pass the adjusted significance test with controlled P_FDR, its p value (p(i) as shown in Eq. 2) has to be smaller than the P_FDR calculated from the following equation:

$${P}_{{FDR}}=\max [p(i):p(i)*(i/N)*{\alpha }_{{FDR}}](i=1,\ldots,N)$$

(2)

where N is the total number of grid points and i is the rank of sorted p values. Significance is assessed at ${\alpha }_{{FDR}}$ = 0.2 in this case. For fields with moderate to high auto-correlation ${\alpha }_{{FDR}}$ = 0.2 corresponds to the significance level of ${\alpha }_{{global}}$ = 0.1⁵⁶.

To estimate the uncertainty of global area fractions with significant skill (e.g. Fig. 2), we also use the 1000 bootstrap realisations described above to estimate the significance of skill values. To obtain a range of p values for each grid cell (based on which then areas with skill can be calculated), we subsample 1000 times 100 of these realisations (with replacement).

To avoid some systematic differences in temperature caused by the uneven distribution of La Niña or El Niño years over the investigation period (note our historical reference run used to initialise the perfect-model predictions exhibits the majority of El Niño events in the later, warmer, part of the investigation period), we remove the forced signal in the temperature and precipitation fields before compositing them. These composite maps (e.g. Fig. 3) therefore demonstrate common features of internal variability. To do this, we use the ensemble mean of six CCSM4 historical simulations from CMIP5 together with our own historical simulation (i.e. seven members in total) to determine the forced response at each grid point for each year. We also apply an 11-year running average to the ensemble to remove responses to other short-term forcing, such as volcanoes⁵⁷. We then deduct the smoothed ensemble mean from the reference run and the decadal predictions to obtain the detrended data. Subsequently, El Niño, La Niña and neutral group anomaly composite maps are calculated by subtracting the composite of all years from each group. For both the temperature and precipitation composite maps, we normalise the anomalies by dividing them by the standard deviation of the temperature and precipitation time series with annual or multi-annual (i.e. for forecast years 2–3 and 4–6) averages on each grid point in order to ensure anomalies in the composite maps are comparable across regions (e.g. tropics where temperature variability is usually small versus high latitudes where variability is larger).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

The perfect-model prediction output data used in this study are available in NCI Australia data collections⁵⁸. The CESM-DPLE data used in this study are available for downloading through https://www.cesm.ucar.edu/community-projects/dple. The temperature observation data used in this study are accessible at https://www.metoffice.gov.uk/hadobs/hadcrut4/; https://www.metoffice.gov.uk/hadobs/hadisst/; https://data.giss.nasa.gov/gistemp/; https://psl.noaa.gov/data/gridded/data.mlost.html.

Code availability

The tool that calculates the Mean Squared Skill Score (MSSS) is available through Github at https://github.com/illing2005/murcss.

Change history

27 November 2023
A Correction to this paper has been published: https://doi.org/10.1038/s41467-023-43407-8

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Acknowledgements

This study was supported by the Australian Commonwealth through an Australian Government Research Training Program Scholarship (Y.L.), the Australian Research Council grants CE110001028 (A.L.H., L.V.A., M.H.E., M.G.D., Y.L.), CE170100023 (A.L.H., L.V.A., M.H.E., M.G.D., Y.L.), DE150100456 (M.G.D) and DP150101331 (M.H.E), the Australia-Germany Joint Research Co-operation (German Academic Exchange Service, DAAD) Grant ID 57219579 (M.G.D). M.G.D. is grateful for support by the Spanish Ministry of Economy, Industry and Competitivity Ramon y Cajal grant RYC-2017-22964, the Horizon Europe ASPECT project (Grant 101081460) and the AXA Research Fund (M.G.D).

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Authors and Affiliations

Climate Change Research Centre and ARC Centre of Excellence for Climate Extremes, UNSW, Sydney, NSW, 2052, Australia
Yiling Liu, Lisa. V. Alexander & Annette L. Hirsch
National Computational Infrastructure (NCI), The Australian National University, Canberra, ACT, 2601, Australia
Yiling Liu
Barcelona Supercomputing Center (BSC), Barcelona, Spain
Markus. G. Donat & Carlos Delgado-Torres
Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
Markus. G. Donat
Centre for Marine Science and Innovation and Australian Centre for Excellence in Antarctic Science, UNSW, Sydney, NSW, 2052, Australia
Matthew. H. England

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Yiling Liu
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Markus. G. Donat
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Lisa. V. Alexander
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Annette L. Hirsch
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Carlos Delgado-Torres
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Y.L. and M.G.D. conceived the study. Y.L. led the data processing and paper writing. C.D.T. performed the analysis of the CMIP6-DCPP hindcasts. Y.L., M.G.D., M.H.E., L.V.A. and A.L.H. discussed the results and implications and collaborated on writing the paper at all stages.

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Correspondence to Yiling Liu.

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Liu, Y., Donat, M.G., England, M.H. et al. Enhanced multi-year predictability after El Niño and La Niña events. Nat Commun 14, 6387 (2023). https://doi.org/10.1038/s41467-023-42113-9

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Received: 31 January 2021
Accepted: 27 September 2023
Published: 11 October 2023
DOI: https://doi.org/10.1038/s41467-023-42113-9

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