To isolate and analyze the low-frequency variability of the coupled ocean-atmosphere-land-vegetation system, we utilize single piControl realisations from 11 ESMs participating in the Coupled Model Intercomparison Project Phase 6 (CMIP6) . The selected ESMs are: ACCESS-ESM1-5 , CanESM5 , CMCC-ESM2 , CESM2 , EC-Earth3-Veg , GFDL-ESM4 , IPSL-CM6A-LR , MIROC-ES2L , MPI-ESM1-2-LR , NorESM2-LM , and UKESM1-0-LL . These models were chosen as they simulate interactive LAI in the piControl and historical runs (i.e., allowing the terrestrial biosphere to dynamically respond to simulated internal climate variability) and since they have output for LAI, NPP and GPP. Other CMIP6 ESMs with static vegetation, where LAI is fixed apart from a seasonal cycle, were excluded as they cannot capture the response to low-frequency climate variability.

Nonetheless, the representation of vegetation dynamics differs between the 11 models chosen. In eight models (CanESM5, CMCC-ESM2, CESM2, EC-Earth3-Veg, GFDL-ESM4, IPSL-CM6A-LR, MPI-ESM1-2-LR, UKESM1-0-LL) the fully interactive vegetation module is switched on, allowing for potential two-way feedbacks between changes in LAI and climate. Specifically, climate and its variability impact LAI by governing the availability of water, light, and thermal energy required for photosynthesis and phenology, while LAI in turn can modify the climate via changes in albedo, evapotranspiration, and aerodynamic roughness. However, only two models (GFDL-ESM4 and UKESM1-0-LL) explicitly model changes in the fractional coverage of Plant Functional Types (PFTs) in piControl, while the PFT distribution is fixed at 1850 levels for the remaining models.

For robust analysis of low-frequency variability, the first 500 years of available monthly data from each model's piControl run were used. This duration was chosen since it represents the minimum common length available across the selected ESMs. The terrestrial variables analyzed include:

Leaf Area Index (LAI): A key structural variable representing the total one-sided leaf area per unit ground area. LAI is controlled by relatively slow, model-dependent processes such as phenology, allocation (partitioning of assimilated carbon into different vegetation carbon pools), and growth, making it a suitable indicator for long-term vegetation memory.

Our analysis focuses on the impact of three major oceanic modes, namely ENSO, the PDO and AMV, on changes in vegetation variability. To analyse changes related to ENSO, we use the Niño3.4 SST index which is calculated as the area-weighted average of detrended seasonal SST anomalies over the central equatorial Pacific (5°S–5°N, 190–240°E) for each CMIP6 model and the observational data (Sect. ). We also examine the influence of the PDO as a mediator from ENSO variability to vegetation changes. The PDO index is calculated as the first principal component (PC1) of the detrended, seasonal SST anomalies over the North Pacific (20–70°N) . Additionally, we test the impact of the AMV on LAI where the AMV index is calculated as the area-weighted average of detrended seasonal SST anomalies over the North Atlantic (0–60°N, 80°W–0°). We note that we do not include a separate analysis of the Interdecadal Pacific Oscillation (IPO) since it has been shown that the IPO is not a distinct mode of Pacific SST variability but rather a blend of decadal-modulations of ENSO, the PDO, AMV and externally forced warming .

We use linear regression to quantify the spatial pattern and strength of the influence of these two oceanic modes on terrestrial variables (LAI, GPP, NPP). We calculate the regression coefficient r using the multi-dimensional dot product, which efficiently calculates the covariance across the time dimension: 1r(x)=1n-1v(t,x)⋅Inorm(t) where n is the length of the time series, v(t,x) is the terrestrial variable and Inorm(t) the oceanic index normalised by its standard deviation. The resulting regression coefficient map r(x) then represents the spatial pattern of change in the terrestrial variable v associated with a one-standard-deviation change in the oceanic index Inorm. Note that we use the notation of regression of variable Y on variable X (i.e., LAI regressed on Niño3.4 index) throughout the text.

To visualize the time evolution of the vegetation response associated with the oceanic mode, we compute an associated time series (TV) for the vegetation variable. This time series is obtained by projecting the gridded vegetation anomalies onto the calculated regression map r(x): 2TV(t)=vw(t,x)⋅r(x) where vw is the vegetation anomaly v weighted by the cosine of the latitude. Finally, the TV time series is normalized by its standard deviation to allow for comparisons across different terrestrial variables and models, and subscript V will be replaced by LAI, GPP, or NPP depending on the terrestrial variable used. This resulting time series represents the component of global vegetation variability linearly co-varying with the oceanic index across the full timeseries, similar to other standard pattern-extraction techniques like Maximum Covariance Analysis. Importantly, because the regression map r(x) is strictly constant in time, this methodology does not impose any explicit constraints or a priori assumptions on the temporal evolution or frequency profile of TV(t). The frequency content is inherited entirely from the underlying, time-dependent vegetation anomalies vw(t,x). Consequently, frequency-domain features, like spectral reddening or a multi-decadal gain greater than 1, reflect the dynamical response of the terrestrial system rather than artefacts of the index construction.

To validate the relationship between oceanic variability and vegetation dynamics found in the piControl simulations, we analyze historical CMIP6 simulations and satellite-based observations over the common historical period of 1982–2014. This period is chosen for consistency with the availability of both satellite vegetation data and the CMIP6 historical runs . However, it should be noted that this time period is significantly shorter than the 500 years of simulations used for the piControl-based analysis, which hinders an analysis of variability longer than 30 years. Additionally, it should be noted that this comparison focuses on the spatial consistency of the internal ENSO-vegetation coupling, acknowledging that the historical record also incorporates transient anthropogenic greenhouse gas and land use signals that are absent in the control simulations.

We use historical CMIP6 data for SST (to calculate Niño3.4), LAI, GPP and NPP from the same 11 ESMs remapped to 2.5°×2.5°. To compare these simulated relationships to observed ones, we used the Niño3.4 SST index from the HadISST1.1 product and monthly data for LAI, GPP and NPP from the Global Land Surface Satellite (GLASS) mission . The GLASS dataset, which is a product of the AVHRR multi-sensor data, was selected as it provides data for all three vegetation variables and temporal alignment with the CMIP6 historical period. The GLASS LAI product has been shown to provide high-quality and high-precision global long-term data, which has been validated against in situ measurements and intercompared with other satellite products . As described in Sect. , a regression analysis between the seasonal Niño3.4 and the seasonal vegetation indices was performed using the detrended historical CMIP6 simulations in comparison to the detrended observational data.

In order to study the causal pathway from variability in ENSO to LAI, we employ a mediation analysis framework, following the methodology established by and later used by and to study climate variability. In line with this literature, we use “causal” to describe a statistical relationship in which the direction of influence is established by a systematic causal inference methodology. Here, the Niño3.4 index is defined as the predictor or independent variable (X), and LAI regressed on Niño3.4 (TLAI) is the dependent or outcome variable (Y) (Fig. ). Mediation analysis then allows us to test the influence of the PDO (variable Z= PDO index), which is closely linked to the low-frequency modulations of ENSO, as a mediator of the relationship between ENSO and LAI. Specifically, we investigate whether simulated low-frequency coherence between LAI and the PDO are solely due to the coherence between ENSO and the PDO, which is then transmitted by the PDO to LAI, or if a direct causal relationship exists between ENSO and LAI at low frequencies even after accounting for the PDO's influence.

The relationships are examined using the following set of linear regression equations, omitting intercepts and residuals for clarity. The total effect of the predictor X on the outcome Y is given by the regression coefficient τ: 3Y=τX. This total effect τ comprises both the direct effect τZ from ENSO to LAI (X→Z), excluding the influence of the PDO, and the indirect (mediated) pathway via the PDO (X→Z→Y) (Fig. ).

The direct effect of the predictor X on the outcome Y, while excluding the effect of the mediator Z, is represented by the coefficient τZ. The influence of the mediator Z on the outcome Y, when excluding the effect of the predictor X, is given by the coefficient β. Thus, Y can be predicted by: 4Y=τZX+βZ. Additionally, the influence of the predictor X on the mediator Z is calculated by the coefficient α: 5Z=αX.

The portion of the total effect that is mediated (indirect effect) can then be calculated as the product of the path coefficients α and β. This indirect effect is also equivalent (up to differences in regression residuals) to the difference between the total and direct effects: αβ=τ-τZ.

According to the criteria for mediation from , the coefficients τ, α, and β must be significantly different from zero. Furthermore, τ and τZ must have the same sign, as the mediation is inconsistent otherwise.

The role of the mediator Z can be categorized based on the magnitude and significance of the direct effect τZ:

Perfect mediator: Z fully accounts for the relationship X→Y if τZ is not significantly different from zero.

Since we are interested in decadal to multi-decadal influence of ENSO on LAI, a 10-year low-pass filter is applied to all three variables (i.e., Niño3.4 index, PDO index and LAI regressed on Niño3.4) prior to the mediation analysis. Note that these filtered indices capture decadal modulations of these variables rather than representing independent climate modes. We then perform the regressions outlined in Eqs. ()–() for each model individually. This yields the direct effect (τZ), the indirect effect via the PDO (αβ), and the total effect (τ) for each model. The multi-model mean is then calculated as the mean across these model-specific coefficients.

We also perform analysis in the frequency domain to quantify the frequency-dependent relationships. We firstly calculate the power spectral density of the Niño3.4 index and vegetation variable regressed on Niño3.4 using Welch's method to analyse spectral reddening . The presence of enhanced power at longer periods in the spectrum of the LAI time series associated with the ENSO-driven component (i.e., TV from Eq. ) would provide key evidence for LAI translating the low-frequency ENSO signal into a multi-decadal vegetation response.

In order to quantify this reddening and determine spectral properties like coherence, gain, and phase between Niño3.4 and vegetation variables, we use the multi-taper method (MTM; ; ; ). MTM is a robust technique for the time-frequency analysis of signals that employs a set of orthogonal tapers, known as Discrete Prolate Spheroidal Sequences (DPSS) or Slepian functions. These multiple orthogonal tapers (DPSS) provide several statistically independent spectral estimates from the same data segment, significantly reducing the variance compared to single-taper methods. Without the use of tapers, the spectral analysis of finite time series is susceptible to spectral leakage, where power from one frequency band artificially spreads into others.

To examine the spatial distribution of ENSO-LAI effect and identify drivers of the global signal, we perform the spectral analysis at the gridcell level. We compute the MTM coherence squared and gain between the Niño3.4 index and standardized local LAI for every land grid cell across all 11 models. From these, we derive the MEM for interannual (2–4 years) and decadal and longer (> 10 years) period bands. Based on these gridcell maps, we define hotspot regions and compute regional vegetation time series by restricting the projection in Eq. () to these specific domains. This regional decomposition allows us to isolate whether the spectral reddening and gain observed at the global scale are uniform features or are disproportionately driven by specific ecosystems.

We validate the simulated ENSO impacts on vegetation in the CMIP6 ESMs by comparing model output with observations over the historical period (1980–2014). For this, we compare the regression patterns of seasonal anomalies in terrestrial variables (LAI, GPP, NPP) onto the Niño3.4 index, derived from the 11 ESMs with interactive LAI, with those calculated from satellite-based vegetation observations and the HadISST-based Niño3.4 index (Fig. ).

The CMIP6 MEM and observations exhibit a similar pattern over tropical and subtropical regions. The MEM successfully captures the main features of the ENSO teleconnections, such as positive vegetation anomalies over Argentina and eastern Africa, and negative vegetation anomalies over Brazil, Australia, India, and Southeast Asia. Notably, both the observations and the MEM demonstrate high internal consistency across the three vegetation variables showing nearly identical spatial response patterns to ENSO forcing.

However, discrepancies emerge regarding the intensity of these impacts. The CMIP6 MEM generally exhibits a stronger coupling than the satellite record, manifesting as higher-amplitude regression coefficients across all three variables. Furthermore, spatial differences between the satellite data and CMIP6 MEM are evident over central Africa and in the extent of the negative vegetation anomaly over eastern Brazil. Despite these localized differences in magnitude and reach, the overall consistency in the teleconnection patterns indicates that the models effectively capture the fundamental relationship between ENSO and vegetation dynamics, particularly across the tropics and subtropics.

We utilize 500 years of piControl simulations to examine the long-term variability and causal relationship between ENSO and vegetation structure (LAI). The MEM regression of the seasonal LAI anomaly onto the Niño3.4 index in the piControl runs (Fig. a) reveals a coherent spatial pattern highly consistent with the known ENSO teleconnections and the historical simulation results in Fig. b. The models agree on the strong teleconnection patterns over a range of different biome types, including the northern and northeastern Amazon, Argentina, India, Australia and the eastern United States. The notable exception is Central Africa (Fig. S1), where considerable inter-model spread likely reflects long-standing CMIP biases in central African climate .

To test whether vegetation acts as an amplifier of ENSO variability, particularly at low frequencies, we compare the power spectrum of the Niño3.4 index with the spectrum of TLAI (Eq. ), which is an index of the covariance of LAI anomalies with Niño3.4 (Fig. e). The TLAI spectrum shows a distinct spectral reddening compared to the Niño3.4 spectrum, characterized by greater power at periods longer than around 5 years and reduced power at interannual timescales.

We quantify the frequency dependence of the total influence (ENSO → LAI) using multi-taper spectral analysis. Strong coherence squared of up to 0.8 is observed at periods of 2–8 years (Fig. b). Crucially, the coherence remains statistically significant, with values around 0.4, even at periods past 30 years and up to centennial timescales, confirming a robust relationship across the entire spectrum. A distinct phase lag of around 45° (corresponding to 4–6 months) is observed on interannual to 20-year time scales (Fig. c), indicating that LAI changes follow ENSO changes. We can evaluate the reddening at these long timescales using the gain. The gain shows a strong increase (reddening) towards longer periods, consistent with the power spectrum (Fig. d–e). At multi-decadal to centennial timescales, the MEM gain is around 1.20–1.25. This signifies that the ENSO-driven vegetation variability is amplified by approximately 20 %–25 % at long timescales compared to the driving ENSO variability at those timescales. This is especially true in a relative sense when compared to the gain of 0.35–0.75 at 2–4 year timescales, which indicates a 25 %–65 % amplitude reduction of the vegetation variability at these timescales.

To identify the geographical drivers of this global signature, we first conducted a gridcell-resolved analysis (Fig. S2), which confirms that the strongest coherence and reddening are concentrated in tropical hotspots like Amazonia and Southeast Asia. By resolving the signal at each pixel, we verify that the global TLAI pattern reflects real local dynamics rather than an artifact of spatial cancellation between out-of-phase regional anomalies. These findings are supported by targeted regional spectral analysis of the major tropical rainforest regions (Amazon, Congo and Southeast Asia), which dominate global vegetation productivity and are strongly influenced by ENSO (Fig. S3). While the gains from this regional analysis are not directly comparable to the gain in the global TLAI index in a quantitative sense, the qualitative behavior in the Amazon and Southeast Asia shows pronounced spectral reddening and significant decadal coherence, mirroring the global amplification pattern. In contrast, the Congo region shows no coherence on long timescales, which might be related to low model agreement in this region (Fig. 3a).

However, a key question is whether this low-frequency LAI amplification arises directly from ENSO forcing or if it is instead mediated by the PDO, which is known to be closely related to the low-frequency modulation of ENSO (Fig. S4; ; ; ). A partial spectral analysis was performed to remove the linear influence of the PDO index on the ENSO → LAI relationship (Fig. f–h). When excluding the PDO, the partial coherence remains significant, with values of 0.25 at long periods. The partial gain still shows spectral reddening with a MEM gain of around 1 at long periods compared to a MEM gain of 0.35–0.75 at interannual timescales (2–4 years). These results indicate that the majority of the decadal variability in LAI is directly related to ENSO across interannual to centennial timescales and that there is a direct causal relationship between ENSO and decadal LAI variability. Mediation by the PDO accounts for only a small portion of the effect of ENSO on the LAI variability.

This is supported by a mediation analysis using 10-year low-pass filtered data, which yields a MEM total effect (τ) of ENSO on LAI of 1.01 and a direct effect (τZ) of ENSO on LAI excluding the influence of the PDO of 0.88, leaving an indirect effect (αβ) via the PDO of only 0.13. Similarly, we can use gain values for this mediation analysis between ENSO (E), LAI regressed on Niño3.4 index (L) and the PDO (P). The total gain (GEL) is 1.06 for periods larger than 10 years, the direct gain (GEL|P) is 0.95 and the indirect gain (GEP⋅GPL|E) is 0.11. The slight numerical discrepancy between the time-domain total effect (1.01) and the frequency-domain total gain (1.06) is expected since it arises from the different order of operations in spectral versus multi-model averaging. Nevertheless, these calculations consistently show that the PDO is only a weak partial mediator (accounting for around 12 % of the signal), and a significant portion (around 88 %) of the observed low-frequency amplification in LAI is due to a direct causal relationship between low-frequency ENSO variability and LAI.

Beyond Pacific climate modes, we evaluate the role of the AMV. Although the AMV shows significant coherence with LAI at multi-decadal periods, it does not produce spectral reddening (Fig. S5). A partial spectral analysis conditioning the ENSO → LAI relationship on the AMV index further showed that the multi-decadal gain and coherence remain unchanged (not shown). These results confirm that the AMV is not the driver of the observed low-frequency amplification and does not confound the ENSO-vegetation pathway, reinforcing that the spectral reddening is a property of the ENSO-LAI system.

To identify the physical mechanism of land-surface memory that leads to spectral reddening from ENSO to LAI, we used partial spectral analysis to sequentially exclude the influence of different climate controls. Vegetation productivity is primarily limited by light availability (energy-limited) or water stress (water-limited) rather than thermal energy, especially in the tropics . Additionally, temperature can be the dominant control over vegetation growth in mid- and high-latitude biomes . Consequently, we focus on four key variables, namely surface downwelling shortwave radiation (RSDS), near-surface soil moisture (MRSOS), deep-layer soil moisture (total soil moisture content MRSO minus MRSOS) and near-surface air temperature (TAS). MRSOS primarily controls soil evaporation and infiltration of precipitation, while MRSO - MRSOS serves as the deep vegetation water source. RSDS reflects fluctuations in surface light availability, acting as the primary energy-related driver for photosynthesis and vegetation growth. If the spectral relationship between ENSO and LAI remains unchanged after excluding one of the specific variables, it suggests that this variable is not a primary mediator of or memory reservoir for the ENSO signal.

Removing the linear influence of surface downwelling shortwave radiation in the ENSO → LAI pathway causes the partial coherence to drop below the 90 % significance threshold at all timescales (Fig. a). Similarly, when conditioning the transfer function on near-surface soil moisture, the coherence falls below the critical limit (Fig. d). This is also in line with the coherence breakdown of excluding the influence of net precipitation (precipitation P minus evapotranspiration E) – which determines the input into the soil (Fig. S6). In contrast, excluding near-surface air temperature still gives statistically significant partial coherence across annual to multi-decadal timescales and a persistent spectral reddening. Thus, both radiation and shallow soil moisture could be more critical mediators in the propagation of the ENSO signal to vegetation on a global scale than temperature, although inter-model spread persists. However, the behaviour of the partial gain reveals a key distinction in their roles. When radiation is excluded, the partial gain still exhibits a clear reddening characteristic, with the gain increasing toward lower frequencies and reaching 1.0 at multi-decadal scales (Fig. c). Contrarily, excluding near-surface soil moisture significantly flattens this spectral response (Fig. f).

These results suggest that while surface downwelling shortwave radiation is a critical driver of vegetation productivity, it cannot provide the memory required for low-frequency amplification in vegetation. Instead, near-surface soil moisture acts as a primary memory source for LAI by integrating precipitation anomalies over time, effectively filtering high-frequency ENSO variations into the sustained, low-frequency anomalies observed in LAI. Interestingly, while the gain from ENSO to near-surface soil moisture is around 1.0 at long periods (not shown), the gain of the total ENSO → LAI pathway reaches approximately 1.20–1.25 (Fig. d). This multi-step enhancement suggests that the near-surface soil moisture provides an underlying source of memory, which is subsequently amplified by internal vegetation dynamics at low frequencies.

Unlike the near-surface variables, removing the influence of deep-layer soil moisture does not break the ENSO-LAI link. The partial coherence remains significant at approximately 0.3 at long periods (Fig. g). Furthermore, the partial gain (Fig. i) maintains a strong reddening signature, reaching a value of 1.2 at multi-decadal timescales, which is nearly identical to the total impact of ENSO on LAI seen previously (Fig. ). This shows that while the deep layer may hold water for longer periods, the reddening of the ENSO signal is predominantly governed by the interplay between near-surface soil water content and vegetation processes.

Finally, we examine how the vegetation memory signal manifests in two ecosystem carbon fluxes variables, GPP and NPP. The regression pattern of GPP and NPP onto the Niño3.4 index (Fig. a, e) is very similar to LAI (Fig. a), however showing more model agreement (Figs. S7, S8). The coherence spectrum of GPP and NPP with ENSO is strongest at interannual time scales, but still significant at multi-decadal timescales (Fig. b, f). GPP preserves the low-frequency amplification signal, with a spectral gain of around of around 1.20–1.25 at multi-decadal periods and 0.4–0.6 at interannual timescales (Fig. d), comparable to the amplification found in LAI. However, while NPP shows spectral reddening, the signal amplification at decadal and longer periods is effectively lost (gain just below 1.0) (Fig. h). This means that while the low-frequency ENSO signal is transmitted to NPP, its relative amplitude is not amplified.

The loss of signal amplification in NPP compared to the gain found in GPP is driven by the internal coupling between gross uptake and autotrophic respiration (RA), where NPP=GPP-RA. Coherence analysis between the ENSO-regressed components of GPP and RA reveals that these fluxes are strongly synchronized at longer timescales (Fig. S9). While the squared coherence is low at sub-annual frequencies, it increases sharply for periods exceeding 2 years, reaching values between 0.8 and 0.9 at decadal and multi-decadal scales. This high coherence indicates that at low frequencies, RA tracks GPP almost perfectly. Consequently, the amplified low-frequency variability induced by soil moisture and vegetation memory in GPP is largely offset by a nearly identical response in RA. This internal buffering effectively cancels out the memory-driven amplification, resulting in an NPP gain that remains just below 1.0 despite the strong persistence signal present in the gross carbon exchange. Further studies could investigate whether this reflects a structural model behavior or a real-world biological process. Nonetheless, the result is important as it identifies a potential filtering mechanism that prevents gross productivity memory from translating into net decadal carbon sequestration.