Introduction

Northwestern China (NWC), situated in the Eurasian inland, is a typical arid and semi-arid region1,2. The climatological summer precipitation in NWC is less than 3 mm per day3 except over high mountain areas such as the Tianshan Mountains4. Like the East Asian monsoon region, more than half of the annual rainfall was in summer (June–August)5,6. The local ecological environment is sensitive to precipitation changes; even subtle changes can cause substantial environmental and socioeconomic impacts7,8. Summer precipitation in this region exhibits pronounced decadal variations5,8,9,10,11 and a significant long-term increase8,12. Understanding the physical mechanisms and accurately predicting the decadal variations are of considerable scientific value and instrumental in making the medium to long-term climate adaptation plan.

Decadal prediction largely depends on coupled global climate models (CGCMs)13,14,15,16. Decadal prediction skill for SST has significantly improved in many ocean basins, owing to advances in initialization techniques17. However, CGCMs almost have no skills for decadal precipitation variations over land, including NWC18,19,20. Decadal prediction of precipitation is affected by both internal variability of the climate system and external forcing21,22,23. Climate models have an excessively strong dependence on responses to anthropogenic forcing, but they are incapable of capturing the internal variabilities responsible for decadal variations, limiting models’ performance for decadal predictions18,24,25,26,27,28. Thus, decadal prediction of internal variability of the NWC summer precipitation remains a vital target for further investigation.

Given the limitations of the dynamical models, we need to consider an alternative method for the decadal prediction. The hybrid dynamical conceptual model has proven to be a valuable approach for increasing the decadal prediction skills in precipitation29,30,31,32,33,34. Given that decadal climate internal variability is primarily regulated by SST variability35,36,37,38,39,40,41, a hybrid dynamical conceptual model for decadal precipitation is established based on the statistical relationship between observed SST and precipitation, combined with the SST predicted by the dynamical model. The key to this method is to understand the physical mechanism of how the SST modulates precipitation variation.

Recent studies have investigated the linkages between the decadal changes of summer precipitation over NWC and SSTA across various ocean basins. For instance, around 1987, the Atlantic Multidecadal Oscillation drove the decadal shift of summer precipitation over NWC via the Silk Road Pattern teleconnection10. Since the early 1990s, the warming SSTA in the Indo-Pacific Warm Pool has potentially weakened the thermal contrast between land and sea, favoring northeasterly water vapor transport from high latitudes over East Asia and resulting in a decadal increase in summer precipitation over NWC9. Around 1998, the eastern tropical Pacific and western North Pacific SSTAs contributed to the decadal shift of summer precipitation over NWC by altering the position of the Asian jet stream and inducing zonal teleconnections in the mid-troposphere, respectively11. However, which ocean plays a dominant role for the decadal variation of NWC summer precipitation has yet to be well elucidated. In addition, as summer precipitation over NWC exhibits a significant long-term trend8,12, this trend may also influence the decadal physical processes linking SST and precipitation identified in previous studies.

Whereas external forcing contributes to the trend42,43,44,45, decadal variations are dominated by internal variability through SSTA35,36,37,38,39,40,41. In our case, separating the external forcing and internal variability signals is necessary to identify the sources of decadal variability, understand the physical mechanisms and improve decadal prediction skills for internal variability.

This study aims to address the following two questions: (1) What is the critical SST forcing governing the decadal internal variability of summer precipitation over NWC, and what are the underlying physical mechanisms? (2) How predictable is the decadal summer precipitation over NWC?

Results

Sources and physical basis for the internal variability of decadal NWCP

To facilitate the study, we define the domain-averaged summer precipitation over NWC (NWCP) index, which is a meaningful measure of summer precipitation over NWC (see Methods). The decadal NWCP index displays a significant linear trend (0.026 mm day−1 decade−1) during 1961–2021, along with pronounced decadal fluctuations (Fig. 1). To better identify the sources of decadal fluctuations and facilitate prediction, by utilizing multi-model ensemble mean of Coupled Model Intercomparison Project phase 6 (CMIP6) models with good performance (Supplementary Fig. 1; see Methods) and observed data, the external forcing signal (NWCP-F) and internal variability signal (NWCP-I) are derived from NWCP index (Fig. 1; see Methods). The NWCP-F exhibits a quasi-linear trend and explains about 16% of the total variance of the NWCP index. The NWCP-I primarily features decadal oscillations. The temporal correlation coefficient (TCC) between NWCP-I and NWCP index is 0.91, explaining 84% of the total variance. This means that the internal variability signal plays a dominant role in the decadal variation of the NWCP index. Note that NWCP-I has contributed greatly to the increasing trend in the NWCP index during the past 20 years (Fig. 1).

Fig. 1: Decadal variation of Northwest China summer precipitation and its internal variability and external forcing signals.
Fig. 1: Decadal variation of Northwest China summer precipitation and its internal variability and external forcing signals.
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The internal variability component (blue line) and the external forcing component (red line) of the decadal NWCP index (black line, mm day−1). The orange shading indicates the 95% confidence interval of the external forcing component. The 4-year running mean is applied for all data to obtain the decadal component.

To detect the causes of the decadal variation of NWCP-I, we first explore the circulation anomalies associated with the decadal NWCP-I index. Figure 2a, b indicate that the decadal variation of NWCP-I is associated with a quasi-barotropic Rossby wave train over the Eurasian continent. This wave train originated from the British Isles. It splits into two branches, propagating downstream along the polar front jet and subtropical jet, eventually merging near the Mongolian Plateau to the north of NWC. A wet NWC corresponds to an anomalous Mongolian Low, with positive precipitation anomalies occurring along its southern flank. Although the anomalous Mongolia low is not significant at 500 hPa, its induced cyclonic shear winds over NWC exhibit statistical significance at this level (Fig. 2b). The near-surface winds, represented by the averaged winds between 850 and 700 hPa, also show a significant cyclonic trough over the Tian Shan mountains (Fig. 2c). Strong low-level cyclonic shear vorticity induces upward moisture transport, forming the precipitation bend (Fig. 2c). It has been demonstrated that terrestrial recycled moisture are the dominant moisture sources for NWCP4,46,47,48.

Fig. 2: Circulation and sea surface temperature anomalies associated with the internal variability of the decadal NWCP index.
Fig. 2: Circulation and sea surface temperature anomalies associated with the internal variability of the decadal NWCP index.
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The regression coefficient map of a decadal summer (JJA) 200-hPa geopotential height (shading; gpm) and wave activity flux (vectors; m2 s−2), b 500-hPa geopotential height (shading; gpm) and 500-hPa wind (vectors; m s−1), and c precipitation (shading; mm day−1) and averaged wind between 850 and 700 hPa (vectors; m s−1) with respect to the standardized NWCP-I index during 1961–2002 (the training period, see Methods). The red curves outline the boundary of NWC. d The correlation coefficient map of SSTA (°C) with respect to the decadal NWCP-I index during 1961–2002. The rectangles indicate the critical regions for defining the SST indices. Dotted areas indicate that the regression/correlation coefficients are significant at the 90% confidence level based on the Monte Carlo test. The black arrows represent the regression coefficients of wind components (either zonal or meridional) that are significant at the 90% confidence level based on the Monte Carlo test. The 4-year running mean is applied for all data to obtain the decadal component.

Figure 2d illustrates that the decadal NWCP-I significantly correlates with the Indian Ocean (IO) SSTA, the Pacific Decadal Oscillation (PDO)-like SSTA, and the dipolar SSTA over the North Atlantic (NA). Thus, three SST indices are constructed: the North Atlantic Dipole (NAD) index, the IO index, and the PDO index (see Methods). The NAD and PDO indices exhibit prominent decadal oscillations. In contrast, the IO index is characterized as a quasi-linear trend (Supplementary Fig. 2). The NWCP-I significantly correlates with all three indices (Monte Carlo test at a 99% confidence level, see Methods). The TCC is 0.77, 0.73, and 0.64 for the NAD index, the PDO index, and the IO index, respectively (Supplementary Table 1). Noted that both IO and PDO indices are highly correlated with the NAD index (Supplementary Table 1). After excluding the influence of NAD (see Methods), the IO index and PDO index are no longer significantly correlated with NWCP-I at 95% confidence level (Supplementary Table 2). However, after removing the impacts of IO or PDO, the TCC between NAD index and NWCP-I remains significant (95% confidence level, Supplementary Table 2). It suggests that the correlation between the IO (or PDO) index and NWCP-I may link to the NAD index, and NAD may be the dominating factor in regulating NWCP-I. This may also hint that global decadal SSTA could be driven by the NA SSTA49,50.

How does NAD SSTA regulate the decadal variation of NWCP-I? The 200-hPa geopotential height associated with the NAD index (Fig. 3a) resembles the Eurasian Rossby wave train revealed in Fig. 2a. It means NAD may excite or enhance the downstream Rossby wave train that affects the decadal change of NWCP-I. The SSTA at mid-to-high latitude could adjust seasonal mean geopotential height tendencies by affecting transient eddies51,52,53,54,55. The NAD with warming in the south and cooling in the north could enhance the meridional SST gradient at the mid-to-high latitude, providing favorable conditions for the increase of the background atmospheric baroclinicity, thus the available potential energy (APE)56,57,58. Furthermore, the APE of the mean flow can convert into the APE of transient eddies through baroclinic energy conversion, then turn into the kinetic energy (KE) of transient eddies, inducing more active transient eddy activity59,60,61 (Supplementary Fig. 3a, b; see Methods). The barotropic energy conversion between the mean flow and transient eddies is negligibly small (Supplementary Fig. 3c). Figure 3b shows that the NAD is linked with the intensification of the transient eddy activity, thus the strengthened transient eddy vorticity forcing over the NA. The increased transient eddy vorticity forcing could induce a positive geopotential height tendency in the upper troposphere (200 hPa) from the NA to the British Isles (Fig. 3c, see Methods). This disturbance and wave activity flux62 propagates downstream, forming the Rossby wave train over the Eurasian continent, intensifying the anomalous Mongolian cyclone (Fig. 3a), thereby modulating the decadal variation of NWCP-I.

Fig. 3: Observed and model-simulated decadal anomalies associated with NAD.
Fig. 3: Observed and model-simulated decadal anomalies associated with NAD.
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a Observed anomalous summer 200-hPa geopotential height (shading; gpm) and wave activity flux (vectors; m2 s−2), b 200-hPa transient eddy activity (variance of 2.5–6-day bandpass-filtered geopotential height) (shading; dagpm2), and c 200-hPa geopotential height tendency induced by transient eddy (gpm day−1) that are regressed onto the NAD index during 1961–2002 (the training period). d Model simulated responses of 200-hPa transient eddy activity (dagpm2), e 200-hPa geopotential height (shading; gpm) and wave activity flux (vectors; m2 s−2) anomalies to the NAD SSTA forcing. Contours in (b) denote the climatological summer 200-hPa transient eddy activity during 1961–2002 in observation (contours; from 16 dagpm2 to 26 dagpm2 with an interval of 2 dagpm2). Dotted areas in (a–c) indicate where the regression coefficients are significant at the 90% confidence level based on the Monte Carlo test. The red curves in (a) and (e) outline the boundary of NWC. The 4-year running mean is applied to obtain the decadal component for all data.

To verify the physical mechanisms by which NAD SSTA impacts the NWCP-I, we conduct a set of numerical experiments using the ECHAM5 model with NAD SSTA as the forcing (see Methods). The numerical experiment simulations closely replicate the observed anomalous 200-hPa transient eddy activity and geopotential height (Fig. 3d, e). With the NAD SSTA forcing, the transient eddy activity over the mid-to-high latitude North Atlantic is active (Fig. 3d), resulting in an enhanced high anomaly around the British Isles and a Rossby wave train propagating along the subtropical jet stream over Eurasia, thereby enhancing the cyclonic anomaly to the north of the NWC (Fig. 3e). In general, the numerical experiment suggests that the decadal variation of NWCP-I is likely a result of the NAD SSTA.

Decadal prediction of NWCP index using a hybrid dynamic conceptual model

The link between the NWCP-I and NAD suggests that the decadal variability of NWCP-I might be rooted in the NAD. Thus, the decadal NWCP-I can be predicted by the NAD index. To make a parallel comparison to dynamical models, we employ a 10-year forward-rolling reforecast (see Methods) to NWCP-I. By using the observed NAD index as a predictor, the TCC and mean square skill score (MSSS) skill for the “perfect” prediction of NWCP-I can reach 0.73 and 0.10, respectively, during independent prediction period (2003–2021) (Supplementary Fig. 4). Note that more significant discrepancies can be seen between “predicted” and observed values in recent 20 years when external forcing has increasing contributions (Fig. 1). Hence, we added the NWCP-F derived from the multi-model ensemble mean and the “predicted” NWCP-I to improve the decadal prediction skill for NWCP index. Figure 4a suggests that superposing of NWCP-F and “predicted” NWCP-I indices raised the prediction skill for NWCP during 2003–2021, with TCC and MSSS of 0.82 and 0.36, respectively. The perfect predictions’ TCC skill for NWCP index at lead times of 1–4, 2–5, 3–6, 4–7, 5–8, 6–9, and 7–10 years (Fig. 4b; see Methods) are all significant at the 95% confidence level, with the MSSS skill all above 0.25 (Fig. 4c). It means that the decadal NWCP index can be predicted up to 7–10 years in advance if the NAD index can be perfectly predicted.

Fig. 4: Decadal hindcast skills of NWCP index.
Fig. 4: Decadal hindcast skills of NWCP index.
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a “Perfect” 10-year rolling prediction of NWCP index (obtained by adding the NWCP-F to the “perfect” predicted NWCP-I) using observed NAD index as a predictor (see Methods). Different lead times are indicated by different shades. The light orange (blue) shaded area represents the training period of 1961–2002 (independent prediction period of 2003–2021). b TCC skills derived from “perfect” prediction (red), hybrid dynamical conceptual prediction (blue), persistent prediction (black), and model direct rainfall prediction (green) for NWCP index as functions of lead time for the time series of 1992–2017 (i.e., the 4-year running mean from the period of 1991–2019; see Methods). The light green shading indicates the inter-model spread. Stars indicate that the TCC is significant at the 95% confidence level based on the Monte Carlo test. c as in (b), but for the MSSS.

Can the NAD index be skillfully predicted by dynamic models? The CMIP6 decadal hindcasts’ ensemble mean shows that the NAD index can be predicted at all lead times with significant TCCs exceeding 0.76 and MSSSs surpassing 0.52 (Supplementary Fig. 5). Thus, the hybrid dynamic conceptual model for NWCP-I can be established by using dynamic model predicted NAD index as the input predictor (see Methods). After superposing NWCP-F, Fig. 4b shows that 29-year hindcast (1991–2019) of the NWCP index achieves a significant TCC of 0.61 at the 7–10-years lead time. The MSSS values made by this hybrid prediction exceed 0.03 for all lead times (Fig. 4c). Note that the ensemble means of CMIP6 models direct decadal hindcasts for NWCP index has no skills, with TCC ranging from −0.56 to 0.02 and MSSS from −0.37 to −0.18 (Fig. 4b, c). The inter-model spread of the prediction skills is large. The persistent prediction skills are also poor (Fig. 4b, c). It suggests that the hybrid dynamic conceptual model is markedly higher than the corresponding dynamical models’ direct predictions and persistence forecasts for the NWCP index (Fig. 4b, c), opens a potential pathway for the decadal prediction of summer precipitation over NWC. The hybrid dynamic conceptual model’s prediction provides an estimate of practical predictability, indicating that 37% of the decadal variance of the NWCP is predictable 7–10 years in advance.

Discussion

This study explores the decadal predictability and prediction of NWCP. We find that the decadal variability of NWCP is dominated by the signal of internal variability, which accounts for 84% of the total variance, far beyond the contribution from external forcing (16%). By separating the external forcing component (NWCP-F) and internal variability of the decadal variability (NWCP-I), we show that North Atlantic dipole (NAD) SSTA is the primary driver and reveal the related physical mechanism using the observed data and numerical experiments. The warmer subtropical and colder subpolar NAD SSTA could induce more active transient eddy activity over the mid-to-high latitude NA, which in turn generates the local summer-mean geopotential height tendency through eddy vorticity forcing, ultimately linking to the Rossby wave train over the Eurasian continent. This Rossby wave train can strengthen the anomalous Mongolian cyclone, thereby increasing the NWCP through the cyclonic vorticity-generated upward moisture transport. Although the definition of the NAD and the examination of its underlying physical mechanisms are established during the training period, the stable sliding correlations between NAD and NWCP-I during the post-training period (Supplementary Fig. 6) demonstrate these physical mechanisms remain valid in recent decades.

Utilizing a conceptual model linking NAD and NWCP-I and the dynamical models’ predicted NAD index, the hybrid dynamic conceptual model was established to predict NWCP-I. After adding the NWCP-F, NWCP can be skillfully predicted 7–10 years in advance, with a significant TCC of 0.61 and MSSS of 0.03. These skills are significantly higher than persistent prediction and direct dynamical prediction. It suggests that about 37% of the decadal variance of the NWCP can be predicted 7–10 years in advance, providing a promising way for the decadal predictions of rainfall over dry regions of central Eurasia.

Our findings for the physical linkage between NWCP and NAD SSTA offer a crucial clue for dynamic models’ validation and improvement. Models’ capability in simulating NA SSTA, the relationship between NWCP and NAD SSTA and the circulation anomalies associated with NAD SSTA could determine the decadal prediction skills of NWCP. For instance, the models’ limited NWCP decadal prediction skill may stem from the significant negative TCC (−0.72) between NAD SSTA and NWCP, as well as their inability to accurately simulate either the British Isles high anomalies or the Eurasian 200-hPa wave train associated with NAD SSTA (Figure not shown). In addition, we find that the PDO, and IO indices are all significantly correlated with the NWCP-I index, but their high correlation coefficients may relate to their linkage with the NAD index. Whether they have independent physical linkage or how they link to each other still calls for further investigation. Moreover, the relationship between NAD and NWCP-I index may possibly change in the future, so exploration and implementation of predictability sources are imperative.

Methods

Data and the decadal variation component

Observed monthly precipitation over China is obtained from the CN05.1 dataset63 with a resolution of 1° × 1°. Global monthly precipitation data are derived from the NOAA global monthly precipitation reconstruction (PREC) dataset64, which has a resolution of 2.5° × 2.5°. Monthly SST is acquired from the NOAA Extended Reconstructed SST version 5 (ERSST v5)65 with a 2° × 2° resolution. Monthly or daily geopotential height, wind fields, temperature, and vertical velocity are obtained from the fifth generation of the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis (ERA5)66 at a resolution of 2.5° × 2.5°. All these observational datasets cover the period from 1961 to 2021.

To extract the external forcing signal, monthly precipitation data from historical simulations (1961–2014) and SSP2-4.5 projections (2015–2021) of 14 CMIP6 models (63 members) are used (Supplementary Table 3). These models are selected because of their high spatial resolution (100–250 km), taking the effects of NWC’s complex topography on precipitation into account. To estimate the dynamical prediction skills, monthly precipitation and SST data from the decadal hindcast experiments (dcppA-hindcast) of 4 CMIP6 models (20 members) are utilized, which include 59 sets of 10-year retrospective predictions initialized each year from 1960 to 2018 (Supplementary Table 4). The dynamic prediction skills are all based on the ensemble mean of all members with equal weights.

The 4-year running mean is applied to extract the decadal variation component, which is widely used to identify the decadal variability20,67,68. The yearly mark in the 4-year running mean time series represents the second year of the 4-year mean period.

NWCP index

Following Xing and Wang3, the region in Northwest China with climatological summer precipitation less than 3 mm day−1 is defined as the study area (Supplementary Fig. 7). Due to the data missing in the western part of the Tibetan Plateau (west of 92°E, the gray marked area in Supplementary Fig. 7) in the CN05.1 dataset caused by the scarcity of available stations63, this portion of the Tibetan Plateau is excluded. The leading empirical orthogonal function (EOF) of decadal anomalies of the summer percentage of precipitation over NWC, displays a uniform pattern throughout the entire region (Supplementary Fig. 8a), which accounts for 39.5% of the total variance. Thus, we define the domain-averaged summer precipitation over NWC as the NWCP index. The index significantly correlates with the first principal component with the TCC of 0.83 on the decadal time scale (Supplementary Fig. 8b). It is a meaningful measure of the variability of summer precipitation over NWC.

Separating the signals of external forcing and internal variability

Precipitation data from multi-model ensemble members of CMIP6 historical simulations (1961–2014) and SSP2-4.5 projections (2015–2021) (Supplementary Table 3) and observed precipitation data are used to separate the signals from external forcing and internal variability21,22. Nine models (44 members) which exhibited high simulation skill (pattern correlation coefficient (PCC) > 0.7 and root mean square error (RMSE) < 1.2) in simulating the mean state of NWCP are selected to extract the external forcing signal (Supplementary Fig. 1).

Observed precipitation anomaly, denoted as \(P\), can be considered to consist of the externally forced component (\({P}_{F}\), generated by external forcings such as greenhouse gases, aerosols, solar cycles, and other external forcing) and an internal variability component (\({P}_{I}\)):

$$P\left(n\right)={P}_{F}\left(n\right)+{P}_{I}\left(n\right)$$
(1)

where \(n\) represents the year.

In the CMIP6 historical and SSP2-4.5 experiments, all model ensemble members are driven by identical external forcing but with different initial conditions, resulting in the same externally forced signals but different internal variability signals across members69. Thus, the signal related to external forcing can be retained by averaging a large number of ensemble members to offset the uncorrelated internal variability signals21,22. Therefore, \({P}_{F}\left(n\right)\) can be estimated as:

$${P}_{F}\left(n\right)={b}_{F}{P}_{m}\left(n\right)$$
(2)

where \({P}_{m}\left(n\right)\) is the multi-model ensemble mean of precipitation anomaly, \({b}_{F}\) (used to correct the systematic bias of the models) is the regression slope in \(P(n)={b}_{F}{P}_{m}(n)+\varepsilon\), in which \(\varepsilon\) represents the residual.

Furthermore, the internal variability component \({P}_{I}\) can be obtained as:

$${P}_{I}\left(n\right)=P\left(n\right)-{b}_{F}{P}_{m}\left(n\right)$$
(3)

This definition ensures that \({P}_{I}\left(n\right)\) and \({P}_{F}\left(n\right)\) are uncorrelated, as the portion of \(P\left(n\right)\) correlated with \({P}_{m}\left(n\right)\) has been removed through the above equation.

Monte Carlo test

We employ the Monte Carlo approach to test the significance of the correlation coefficient between two decadal time series with 4-year running mean70,71. The process consists of three main steps: First, two independent random time series are generated and subjected to a 4-year running mean. Second, the correlation coefficient between the two 4-year running mean time series is calculated. Third, the first and second steps are repeated 5000 times, and the absolute values of the resulting 5000 correlation coefficients are sorted in ascending order to identify the correlation coefficient at the 95% (90%) percentile, which serves as the critical correlation coefficient at the 95% (90%) confidence level. This procedure is repeated 50 times, and the average of the critical correlation coefficients is taken as the result.

SST index

The SST index is defined as:

$${In}{dex}\left(t\right)={\left[{SSTA}\left(t,{lat},{lon}\right)\times {sign}\left({TCC}\left({lat},{lon}\right)\right)\right]}^{* },{where}\,p < 0.1$$
(4)

where \({TCC}\) represents the temporal correlation coefficient between the decadal NWCP-I and summer SSTA during the training period (1961–2002), the \({sign}\) function equals to 1 (−1) when TCC is positive (negative), square brackets denote the areal mean within the key region, and the asterisk indicates standardization of the time series. Both NWCP-I and SSTA are subjected to a 4-year running mean, and only regions with p < 0.1 (dotted areas in Fig. 2d) are calculated. The ranges of key regions and the number of grid points used to calculate the NAD, PDO, and IO indices are provided in Supplementary Table 5.

Partial correlation coefficient

The partial correlation coefficient can be used to measure the linear correlation between two variables, holding constant of other variables:

$${r}_{a,b\left(c\right)}=\frac{{r}_{a,b}-{r}_{a,c}{r}_{b,c}}{\sqrt{1-{r}_{a,\,c}^{2}}\sqrt{1-{r}_{b,\,c}^{2}}}$$
(5)

Here, \({r}_{a,{b}\left(c\right)}\) represents the partial correlation coefficient between \(a\) and \(b\) when excluding the effect of \(c\). \({r}_{a,b}\), \({r}_{a,c}\), and \({r}_{b,c}\) denote the Pearson correlation coefficients between \(a\) and \(b\), \(a\) and \(c\), and \(b\) and \(c\), respectively.

Energy conversion between mean flow and transient eddies

According to the quasi-geostrophic model proposed by Cai et al.59, the barotropic energy conversion from mean flow KE to transient eddy KE (BTEC), the baroclinic energy conversion from mean flow APE to transient eddy APE (BCEC1), and the baroclinic energy conversion from transient eddy APE to transient eddy KE (BCEC2) can be calculated as follows:

$${BTEC}=\frac{{P}_{0}}{g}\left\{\frac{1}{2}\left(\overline{{v}^{{\prime} 2}}-\overline{{u}^{{\prime} 2}}\right)\left(\frac{\partial \overline{u}}{\partial x}-\frac{\partial \overline{v}}{\partial y}\right)+\left(-\overline{{u}^{{\prime} }{v}^{{\prime} }}\right)\left(\frac{\partial \overline{v}}{\partial x}+\frac{\partial \overline{u}}{\partial y}\right)\right\}$$
(6)
$${BCEC}1=-{C}_{1}{\left(\frac{{P}_{0}}{p}\right)}^{\frac{R}{{C}_{p}}}{\left(-\frac{d\theta }{{dp}}\right)}^{-1}\left(\overline{{u}^{{\prime} }{T}^{{\prime} }}\frac{\partial \overline{T}}{\partial x}+\overline{{v}^{{\prime} }{T}^{{\prime} }}\frac{\partial \overline{T}}{\partial y}\right)$$
(7)
$${BCEC}2=-{C}_{1}\left(\overline{{\omega }^{{\prime} }{T}^{{\prime} }}\right)$$
(8)

In the equation, \({C}_{1}={\left(\frac{{P}_{0}}{p}\right)}^{\frac{{C}_{v}}{{C}_{p}}}\left(\frac{R}{g}\right)\), \({P}_{0}\) is 1000 hPa, \({C}_{v}\) and \({C}_{p}\) are the specific heat capacities of dry air at constant volume and constant pressure, respectively, \(g\) is the gravitational acceleration, \(R\) is the gas constant for dry air, \(\theta\) is the potential temperature, \(u\) and \(v\) are the zonal and meridional wind components, and \(\omega\) and \(T\) represent the vertical velocity and temperature. The overbar and prime denote the summer mean and synoptic-scale (2.5–6-day bandpass filtered) transient perturbations, respectively.

Geopotential height tendency induced by transient eddy

The variance of 2.5–6-day bandpass filtered daily 200-hPa geopotential height in summer is used to reflect the activity of summer transient eddies72.

Transient eddies can induce low-frequency atmospheric circulation anomalies through eddy vorticity and heat fluxes51,52, and the impact of vorticity fluxes is usually much more substantial than that of heat flux in the upper troposphere52,53. Therefore, considering only the effect of eddy vorticity flux, transient eddies’ impact on the seasonal mean circulation can be described by the geopotential height tendency induced by transient eddies:

$${\left(\frac{\partial Z}{\partial t}\right)}_{{eddy}}=\frac{f}{g}{\nabla }^{-2}\left(-\nabla \cdot \left(\overline{\vec{{V}^{\prime}}{\rm{\xi }}^{\prime} }\right)\right)$$
(9)

In the equation, \(Z\) represents the summer mean geopotential height, \(g\) is the gravitational acceleration, \(f\) denotes the Coriolis parameter, and \({\nabla }^{-2}\) indicates the inverse Laplacian. \(\vec{V^{\prime} }\) and \(\xi^{\prime}\) represent the synoptic-scale (2.5–6-day bandpass filtered) wind and relative vorticity, respectively. The overbar signifies the summer mean.

ECHAM5 numerical experiments

The fifth generation Max Planck Institute model in Hamburg (ECHAM5)73 is employed to investigate the atmospheric circulation response to the forcing of NAD SSTA. The model has 31 vertical levels and a horizontal resolution of T42. We perform two simulations: a control experiment and a sensitivity experiment. The control experiment is driven by the climatological monthly SST, while the sensitivity experiment is driven by the climatological monthly SST superimposed with the summer NAD SSTA (Supplementary Fig. 9). Both simulations are integrated for 20 years, and the composite differences of the last 15 summers are considered as the model response.

Hybrid dynamic conceptual forecast model

A hybrid dynamic conceptual forecast model was developed to predict the NWCP. The hybrid model mainly includes the following steps: First, a conceptual prediction model based on linear regression is established by linking the NWCP-I with SST index. Then, the SST index predicted by the multi-dynamic model ensemble mean (decadal hindcast experiments) are used to predict the NWCP-I. Finally, the predicted NWCP-I is superposed with the NWCP-F extracted from the multi-model ensemble mean (historical/SSP2-4.5 experiments) to obtain the forecasted NWCP.

To avoid the artificial bias caused by the period overlapping in predictor selection and verification, the entire study period (1961–2021) is divided into the training period (1961–2002) and the independent prediction period (2003–2021). The analyses, including the regression maps related to the physical mechanism, and the selection of predictors, are all based on data during the training period.

TCC and MSSS skills for decadal prediction

Temporal correlation coefficient (TCC) and mean square skill score (MSSS) are used to evaluate the skill of decadal prediction. TCC is the correlation coefficient between the observed and forecast time series, which is used to measure the similarity between them. MSSS reflects the percentage reduction in the mean square error (MSE) of the model forecast, compared to the MSE of the “climatological forecast”:

$${MSSS}=1-\frac{{MSE}}{{MS}{E}_{c}}$$
(10)

where \({MS}{E}_{c}={n}^{-1}{\sum }_{i=1}^{n}{\left({x}_{i}-\overline{x}\right)}^{2}\), \({MSE}={n}^{-1}{\sum }_{i=1}^{n}{\left({f}_{i}-{x}_{i}\right)}^{2}\), \({x}_{i}\) and \({f}_{i}\) denote the time series of the observations and prediction, respectively. A positive (negative) MSSS indicates that the model forecast is better (worse) than the climatological forecast.

Rolling retrospective forecast

The 10-year forward-rolling prediction approach was employed to conduct the “perfect” and hybrid dynamical conceptual predictions, enabling parallel comparisons with the predictions from dynamical models30,33. The conceptual prediction models are established using 25 years data prior to the initial date of the dynamical prediction, and the forecasts are made for the subsequent 10 years. For example, for the prediction initialized in the end of 1985 (corresponding to the dcppA-hindcast s1985 experiment of the dynamical model), the conceptual model is established using data from 1961 to 1985 and predictions are made for the ensuing 10 years (1986–1995); for the prediction initialized in the end of 1986 (corresponding to the s1986 experiment), the conceptual model is constructed based on data from 1962 to 1986 to make the ensuing 10 years (1987–1996), and so on. A key advantage of rolling prediction is its ability to continuously update regression coefficients and constants (Supplementary Table 6), thereby partially capturing evolving relationships within the fitting period. For instance, in the final equations (Supplementary Table 6), the increasing magnitude of the constant term compensates for the amplitude discrepancy between NAD and NWCP-I, particularly during the later years (Supplementary Fig. 2). This result in a higher perfect-prediction skill (TCC = 0.73, Supplementary Fig. 4) than the direct correlation between NAD and NWCP-I (TCC = 0.67) during 2003–2021.

As the available period for dynamical model is from 1962–2017 after applying 4-year running mean. In total, 32 segments of 10-year forward-rolling conceptual predictions were conducted from 1986 to 2017. Then, seven time series are obtained by averaging lead times of 1–4, 2–5, 3–6, 4–7, 5–8, 6–9, 7–10 years, respectively. The time series start from 1986 to 2017 for lead times 1–4 years, 1987–2017 for lead time 2–5 years, and so on to 1992–2017 for 7–10 years can be obtained. To make a fair comparison of the skills among the seven lead times, the common period, i.e., 1992–2017, is used. The “perfect” prediction (hybrid dynamical conceptual prediction) is achieved by using the predictor from the observation (dynamical model).