Introduction

An inter-decadal transition of the pattern of annual precipitation was observed over eastern China during the second half of the twentieth century. This transition occurred around the late 1970s and caused a long-term drying trend in North China and a wetting trend in South China, commonly referred to as the “south flood–north drought” (SFND) pattern1,2,3,4,5,6. In association with this inter-decadal transition, the summer surface air temperature (SAT) also shows a cooling trend over the Yangtze River basin under the current background of global warming5,7,8. Severe drought/flood disasters resulting from these anomalous precipitation patterns have major effects on water resources, agriculture, ecosystems and human society in eastern China9,10,11,12. A number of factors have been identified that can affect the inter-decadal transition in the SFND pattern13,14,15,16, but their relative contribution to the inter-decadal climate transition has received little attention. Understanding the causes of the inter-decadal climate transition around the late 1970s is of great importance in climate predictions on a decadal scale.

Both observational data and modeling studies suggest that the anomalous precipitation and temperature patterns in eastern China are linked to internal climate variability—that is, the Pacific decadal oscillation (PDO) and the Atlantic multi-decadal oscillation13,14,17,18. The SFND pattern occurs in the PDO warm phase19. A combination of the warm phase of the PDO and the cold phase of the Atlantic multi-decadal oscillation further enhances the SFND pattern14. The abrupt increase in spring snow depth on the Tibetan Plateau after the late 1970s contributed to wetting of the Yangtze River basin15,20,21. This increase in snow depth led to a decrease in the land–sea thermal contrast and weakened the Asian summer monsoon, which favored drying in North China and wetting in South China.

Many studies have argued that external forcing also affects the SFND pattern. A rapid increase in greenhouse gas concentrations could induce a westward shift of the western North Pacific subtropical high, causing more precipitation over the Yangtze River basin22. Anthropogenic aerosols suppress convection precipitation in North China and enhance precipitation in South China16,23,24. The cooling effect of anthropogenic aerosols also reduces the land–sea thermal contrast, weakening the East Asian summer monsoon and altering the distribution of rain belts in eastern China22,25,26,27,28.

How much of this inter-decadal transition of precipitation over eastern China is attributable to internal variability and how much is due to external forcing remains unclear26,29. Most numerical simulation studies have focused on the attribution of the inter-decadal variance in the pan-Pacific, the North Atlantic or the Northern Hemisphere30,31,32,33. The attribution of the phase transition in inter-decadal variations of the Earth’s climate is hindered by the inability of coupled models to capture the observed temporal evolution of climate and the model biases in the multi-decadal variability of precipitation and temperature in East Asia34,35.

Some studies have assumed that the externally forced responses are linear and independent of internal climate variability. Linear trends and generalized linear regression-based optimal fingerprint method have been widely applied to climate detection and attribution studies36,37,38. However, the linear trends may lead to biases in the phase estimation of the internal variability39,40, which is crucial in decadal climate attribution. Moreover, the optimal fingerprint method is not well applicable at the regional scale and may miss forcing factors41,42. Other studies have used ensemble empirical mode decomposition (EEMD) or quadratic trends42 to identify the nonlinear climate response to external forcing. However, the linear and nonlinear trends are unable to represent the external forcing without a clear trend, e.g., volcanic eruptions.

Because the internal variation in individual realizations of coupled models varies independently43, averaging over a large number of members can greatly remove the internal variability and retain the response to changes in external forcing42,44,45,46,47. The difference between the observed climate and the multi-model ensemble (MME) mean can therefore be treated as a less biased presentation of internal climate variability, especially for phase estimations40,48.

To identify the response of the East Asian climate to external forcing and internal climate variability, we carried out two numerical simulations with the Weather Research and Forecasting (WRF) model during the time period 1958–2002 (see “Methods”). The first WRF simulation was driven by the ERA40 reanalysis dataset representing the joint impacts of internal variability and external forcing (the HIST simulation). The second WRF simulation was driven by the difference between the ERA40 data and the MME of 51 members from the Coupled Model Intercomparison Project Phase 5 (CMIP5) representing the impact of internal climate variability (the IV simulation). The externally forced response was represented by the historical (HIST) run minus the internal variability (IV) run, referred to here as the external forcing effect (EF). These WRF simulations can isolate the response of the regional climate to the global internal climate variability and external forcing.

Results and discussion

Observed and simulated precipitation and SAT variations in eastern China

The observed annual precipitation over eastern China (22°–43°N, 110°–122°E) shows a dipole pattern, characterized by a drying trend in the north and a wetting trend in the south (Fig. 1a). The coarse-resolution reanalysis data ERA40 (Fig. 2b), the CMIP5 MME (Fig. 2c) and a HIST experiment with 2.5° grid spacing (Supplementary Fig. 2) were unable to reproduce the observed change in precipitation. However, the HIST experiment with 0.5° grid spacing, driven by the ERA40 reanalysis dataset, was able to successfully capture the observed dipole pattern of the precipitation (Figs. 1b and 2d), and the corresponding temporal variation (Fig. 1e, f). The ERA5 dataset, which has a finer resolution than the ERA40 dataset, can also reproduce the observed inter-decadal transition of the annual precipitation (Supplementary Fig. 3). The different performance between coarse and finer resolution simulations is likely related to their ability to resolve complex terrain. Compared with the smooth terrain in coarse resolution model, the small-scale terrain with higher elevation in finer resolution model can easily trigger convection process when large-scale circulation brings more water vapor to South China. Consequently, the finer resolution model can better capture the dipole pattern of precipitation in eastern China (Supplementary information; Supplementary Figs. 4–6). This indicates that reanalysis-driven dynamic downscaling with a higher spatial resolution is conducive to the simulation of the inter-decadal transition of the annual precipitation in eastern China. We were therefore able to quantify the relative contributions of the internal variability and external forcing to the inter-decadal climate transition in eastern China during the second half of the twentieth century based on the HIST and IV simulations.

Fig. 1: Linear trends in the annual mean precipitation.
figure 1

Linear trends (mm day−1 decade−1) in a observational data (CN05.1 and APHRO), b the WRF historical (HIST) run, c the response to external forcing (EF), and d the WRF internal variability (IV) run during the time period 1959–2001. The hatched areas and asterisks denote a significance level of 0.05. The two boxes in a indicating the location of North China (35–43°N, 110–122°E) and South China (24°–32°N, 110°–122°E). The two gray lines on the map show the location of the Yellow River in North China and the Yangtze River in central China. The time series of regional mean precipitation anomalies (shaded areas; mm day−1) and the linear trends (lines; mm day−1 yr−1) over e North China and f South China. The correlation coefficients between HIST and observation are shown in the upper right corner of each panel.

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Fig. 2: Spatial patterns of the first leading empirical orthogonal functions and time series of the principal components in the annual mean precipitation during the time period 1959–2001 in eastern China.
figure 2

a Observational data (CN05.1 and APHRO), b ERA40 reanalysis data, c the MME of 17 CMIP5 models, d the WRF historical (HIST) run, e the WRF internal variability (IV) run, and f the response to external forcing (EF). The black thick solid lines are 9-year running mean of the principal components.

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The leading empirical orthogonal function (EOF) modes of both the HIST and IV experiments showed dipole patterns (Figs. 2d, e), which are similar to the spatial pattern of linear trends of annual precipitation (Fig. 1b, d). The WRF simulations with internal climate variability (HIST and IV) reasonably captured the temporal variation of the observed precipitation—in particular, the inter-decadal transition from a negative phase to a positive phase in the late 1970s. This indicates that the internal climate variability dominated the inter-decadal transition of the anomalous precipitation pattern over eastern China during the second half of the twentieth century. Previous studies suggested that the PDO is one of the important modes of internal variability affecting the decadal variation of precipitation in eastern China14,18. The warm phase of the PDO tends to generate a cyclonic anomaly at 850-hPa over the Pacific Ocean with northwesterly wind anomalies over northern China. Consequently, the rain belt retreats to southern China and leads to a SFND pattern14. In contrast, external forcing tends to cause a drying trend over the eastern China (Fig. 1c, f). Such a drying trend can be further attributed to the increasing anthropogenic aerosol over the second half of the twentieth century (Supplementary Fig. 10). The heavy aerosols over East Asian region can result in suppression of precipitation via the decrease in droplet radius49,50,51. Aerosol particles act as cloud condensation nucleus to form cloud droplets. The aerosol particles compete for available water vapor. Consequently, the droplets become too small to fall as rain52,53.

The observed annual mean SAT generally showed a clear warming trend over eastern China, especially in North China (Fig. 3a). The WRF simulations show high consistency with the observed SAT changes, having significant (p < 0.05) correlation coefficients over North China (0.86) and South China (0.64) (Fig. 3e, f). This warming pattern was also seen in the first EOF mode derived from both the observed SAT54 and the HIST simulation (figure not shown), with the second and third EOF modes displaying a south–north dipole and tri-pole patterns, respectively. In addition to the overall warming in eastern China, the HIST experiment also showed a slight cooling trend over the Yangtze River basin, which became clearer in the IV experiment (Fig. 3). This indicates that the cooling trend over the Yangtze River basin primarily results from the internal climate variability. Note that the decrease in the SAT was particularly significant in summer in both the HIST experiment and the observations (Supplementary Fig. 8)5,7,8.

Fig. 3: Linear trends in the annual mean temperature at 2 m.
figure 3

Linear trends (°C decade–1) in a Observational data (CRU and UDEL), b the WRF historical (HIST) run, c the response to external forcing (EF), and d the WRF internal variability (IV) run during the time period 1959–2001. The hatched areas and asterisks denote a significance level of 0.05. The two gray lines on the map show the location of the Yellow River in North China and the Yangtze River in central China. The time series of regional mean temperature anomalies (shaded areas; °C) and the linear trends (lines; °C yr–1) over e North China (35°–43°N, 110°–122°E) and f South China (24°–32°N, 110°–122°E). The correlation coefficients between HIST and observation are shown in the upper right corner of each panel.

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In addition to cooling over the Yangtze River basin, the IV experiment also showed a cooling trend in northeast China and a warming trend in North China (Fig. 3d). The external forcing produced a significant (p < 0.05) warming pattern over eastern China during the second half of the twentieth century (Fig. 3c). Comparisons among the HIST, IV and EF experiments suggested that the warming of North China resulted from both external forcing and internal variability. However, the internal variability canceled out the warming trend induced by external forcing over the Yangtze River basin and amplified the warming trend over North China. The decrease in the annual mean SAT induced by IV mainly occurs in summer (Supplementary Fig. 8) when the Yangtze River basin experiences excessive rainfall in response to the internal climate variability (Supplementary Fig. 7). The cooling (warming) trend generally corresponds to a wetting (drying) trend. An increase in precipitation is usually associated with more cloud cover, which reduces the downward solar radiation and cools the land surface. A wetter (dryer) land surface tends to partition more energy into latent (sensible) heat, leading to cooling (warming) of the land surface. Synergistic changes in the SAT and precipitation over the Yangtze River basin have also been reported in previous observational and modeling studies5,55,56,57.

Relative contributions of internal and external forcing to the dipole climate pattern

Considering that both internal variability and external forcing contribute to the inter-decadal climate transition over eastern China, we carried out a relative weight analysis (RWA)58 based on the HIST and IV experiments to quantify their relative contributions to the annual mean precipitation and SAT. RWA is an effective approach to quantify the relative contribution among predictors of collinearity58,59,60. Here, the RWA was applied to intrinsic mode functions (IMFs) from EEMD, which allows us to quantify the relative contribution of internal variability and external forcing to temperature or precipitation variations at different time scales.

The results showed that internal variability can explain the majority (about 85–90%) of the interannual variation in annual precipitation over eastern China (Fig. 4a). External forcing becomes more important in determining the variation of precipitation and SAT on longer timescales—for example, external forcing accounts for about 10% (35–55%) of the interannual variability (inter-decadal transition) of the annual precipitation. Notably, external forcing and internal variability make comparable contributions to the decadal variability and inter-decadal transition of precipitation in North China (Fig. 4a).

Fig. 4: Relative weight analysis of the annual mean precipitation and temperature.
figure 4

Relative weight analysis was applied to quantify the contributions of internal variability (IV) and external forcing (EF) to various timescales of the annual mean precipitation/temperature at 2 m over the grids in North China (NC: 35–43°N, 110–122°E; gold), South China (SC: 24–32°N, 110–122°E; green) and eastern China (EC: 22–43°N, 110–122°E; gray), respectively. Different combinations of intrinsic mode functions (IMFs) from EEMD represent the interannual variability (IMF1 + 2), decadal variability (IMF3 + 4) and nonlinear trend (IMF5), respectively. The nonlinear trend corresponds to the inter-decadal transition of a the annual precipitation pattern or b the warming trend. Bootstrap sampling with replacement was performed 1000 times on the spatial fields of the combinations of IMFs to estimate the uncertainty range of the relative weights of IV and EF. Box-plot elements: center line, median; dots, mean; box limits, upper (75th) and lower (25th) percentiles; whiskers, 1.5 times the interquartile range.

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The intensified drought in North China during the last few decades is related to the weakened East Asian monsoon resulting from both the phase transition of the PDO61 and the direct effect of increased aerosols (precipitation efficiency decreases as the number and radius of cloud droplets increase)62. The indirect effect of anthropogenic aerosols can also suppress precipitation in North China via a reduction in droplet size49. By contrast, the internal climate variability is more important in explaining the variations in precipitation over South China, with the proportion of variance explained ranging from about 65 to 90% on different timescales.

Similarly, the internal variability also dominates the interannual and decadal variation of the SAT over eastern China—for example, the internal variability accounts for about 90% of the interannual to decadal variability of the SAT in both North China and South China (Fig. 4b). By contrast, external forcing dominates the nonlinear warming trend, with an explained variance of about 70–75% over eastern China. In addition to the nonlinear warming trend, the long-term linear trend of the SAT is also dominated by external forcing (Supplementary Table 1). Compared with precipitation, SAT shows stronger response to external forcing, which is likely related to the strong long-range persistence of SAT47.

In summary, the annual precipitation over eastern China showed an inter-decadal transition during the second half of the twentieth century, with a decrease in precipitation in North China and an increase in South China. In association with the changes in precipitation, the SAT also showed an inter-decadal variability over eastern China. Our results suggest that internal climate variability accounted for about 65% (55%) of the inter-decadal transition in anomalous precipitation in South (North) China during the second half of the twentieth century. The internal climate variability clearly dominates the inter-decadal transition in precipitation over South China. However, both the internal climate variability and external forcing have important roles in determining drying tendency in North China. In terms of the changes in the annual mean SAT, external forcing accounts for 70% of the warming trend over North China. By contrast, the internal variability dominates the cooling trend of the summer SAT over the Yangtze River basin.

Unlike previous studies that have focused on the attribution of changes in the mean climate or variance induced by various external forcing factors, we examined the relative contribution of internal variability and time-varying external forcing to the phase transition of the inter-decadal climate variation in eastern China. We proposed a dynamical downscaling approach to separate the response of the regional climate to internal climate variability from external forcing. This study provides a novel framework for the attribution of decadal climate change that could also be applied to other regions, such as North America and northeastern Australia.

The results presented in this paper should be interpreted with caution. Firstly, we used an ensemble mean of 51 members of CMIP5 models to separate external forcing response from internal climate variability. Ensemble mean over such an ensemble size may still contain a small portion of internal climate variation, which may slightly affect the quantitative estimation of the relative contribution of internal variability and external forcing to regional climate transition over eastern China. Secondly, our WRF simulations used a simplified aerosol treatment. Although the direct and indirect effects of water- and ice-friendly aerosols were considered, the simplified treatment may still cause an inaccurate estimation of the aerosol effect to a certain degree. Lastly, we assumed the internal climate variation and external forcing are independent of each other. However, recent studies suggested that the internal climate variation (e.g. Pacific Decadal Oscillation/Inter-decadal Pacific Oscillation, Atlantic Multidecadal Oscillation) may be partly affected by external forcing (e.g., GHG and aerosols), particularly since the early 1990s31,32. It remains a challenge to quantify the contribution of external forcing, through modulating PDO/IPO and AMO, to the inter-decadal climate transition in East Asia. These issues still warrant for further study.

Methods

Data

Gauged precipitation and temperature

The observational monthly precipitation data were from the National Climate Center China CN05.1 dataset63 and the Asian Precipitation–Highly-Resolved Observational Data Integration Towards the Evaluation of Water Resources (APHRODITE‐MA) project of Japan64. The CN05.1 dataset was constructed from >2400 observational stations across China and interpolated to a resolution of (0.25° × 0.25°) using the anomaly approach65. The dataset covers the time period 1961–2014 and is widely used in studies of the impact of climate change66,67 and model evaluations68,69. The monthly SAT data were from the gridded Climatic Research Unit Time-Series Version 4.03 (CRU TS4.03) dataset and the University of Delaware Precipitation and Air Temperature (UDEL v501) dataset.

Reanalysis and CMIP5 data

The European Centre for Medium-Range Weather Forecasts Reanalysis-40 (ERA40) dataset and the CMIP5 MME were used to generate the large-scale driving fields for the WRF model. We used historical simulations derived from 17 CMIP5 models, each with three ensemble runs. The ensemble mean was calculated using 51 historical runs (17 models × 3 ensemble runs; Table 1). The historical experiments of the CMIP5 models were forced by time-varying observed natural and anthropogenic forcing, including atmospheric greenhouse gases, solar forcing, natural and anthropogenic aerosols, and land use70. Detailed model information can be obtained from http://cmip-pcmdi.llnl.gov/cmip5. In addition, ERA5 data was also used to examine the impact of model spatial resolution on the simulation of precipitation over eastern China.

Table 1 CMIP5 models used in this study.
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Model experimental design and construction of WRF lateral boundary conditions

The ensemble mean over a large number of models can remove sufficient amounts of the internal climate variability because the internal variations among individual global climate model simulations are unrelated. The MME of the CMIP5 historical simulations therefore mainly contains the response to changes in historical external forcing42,44,45,46,47. The MME mean can better identify the forced climate response and has been used to assess various statistical methods of extracting the external forcing signal (e.g., linear trends, quadratic trends and EEMD nonlinear trends)42. By contrast, the reanalysis or observational data contain both internal and external forcing signals. The internal climate variability can be obtained by subtracting the MME from the observation/reanalysis data39.

The ERA reanalysis data can be divided into a climatological mean plus an anomaly:

$${{{\mathrm{ERA}}}} = \overline {{{{\mathrm{ERA}}}}} |_{1959 - 2001} + {{{\mathrm{ERA}}}}^\prime$$
(1)
$${{{\mathrm{ERA}}}}^\prime = {{{\mathrm{ERA}}}}^\prime |_{{\rm{FC}}} + {{{\mathrm{ERA}}}}^\prime |_{{\rm{IV}}}$$
(2)

where \({{{\mathrm{ERA}}}}^\prime |_{\rm{FC}}\) and \({{{\mathrm{ERA}}}}^\prime |_{\rm{IV}}\) are the externally forced response and the internal climate variability of the reanalysis data, respectively.

The anomalous MME is:

$${{{\mathrm{MME}}}}^\prime = {{{\mathrm{MME}}}} - \overline {{{{\mathrm{MME}}}}}$$
(3)

where \(\overline {{{{\mathrm{MME}}}}}\) is the climatological mean of MME. Because the ensemble mean over a number of CMIP5 models largely cancels out the internal variabilities, the \({{{\mathrm{MME}}}}^\prime\) is assumed to contain mainly the effect of external forcing (e.g., solar radiation, volcanic activity, greenhouse gas-induced warming trends and anthropogenic aerosols). If it is assumed that the MME can reasonably represent the temporal response of the climate to external forcing, then

$${{{\mathrm{MME}}}}^\prime = {{{\mathrm{ERA}}}}^\prime |_{{\rm{FC}}}$$
(4)

To examine the difference between the MME and the observations in representing external forcing, we calculated the nonlinear trends of the regional mean SAT derived from the MME and various observational datasets. The results indicate that the root-mean-square difference between the MME and the observations is comparable with, or even smaller than, that between various observations (Supplementary Fig. 1). This suggests that the MME approach can reasonably isolate the climate response to external forcing.

We use the ERA reanalysis data as the lateral boundary conditions (LBCs) of the historical (HIST) experiment:

$$\begin{array}{l}{{{\mathrm{LBC}}}}|_{{\rm{HIST}}} = {\rm{ERA}}\\ \qquad\quad\quad\; = \overline {{{{\mathrm{ERA}}}}} |_{1959 - 2001} + {{{\mathrm{ERA}}}}^\prime \\ \qquad\quad\quad\; = \overline {{{{\mathrm{ERA}}}}} |_{1959 - 2001} + {{{\mathrm{ERA}}}}^\prime |_{{\rm{FC}}} + {{{\mathrm{ERA}}}}^\prime |_{{\rm{IV}}}\end{array}$$
(5)

Using Eqs. (1–4), we constructed the LBCs for the internal variability (IV) experiment:

$$\begin{array}{l}{{{\mathrm{LBC}}}}|_{{\rm{IV}}} = \overline {{{{\mathrm{ERA}}}}} |_{1959 - 2001} + {{{\mathrm{ERA}}}}^\prime |_{{\rm{IV}}}\\ \qquad\quad\;\; = \overline {{{{\mathrm{ERA}}}}} |_{1959 - 2001} + {{{\mathrm{ERA}}}}^\prime - {{{\mathrm{ERA}}}}^\prime |_{{\rm{FC}}}\\ \qquad\quad\;\;= \overline {{{{\mathrm{ERA}}}}} |_{1959 - 2001} + {{{\mathrm{ERA}}}}^\prime - {{{\mathrm{MME}}}}^\prime \\ \qquad\quad\;\;= {{{\mathrm{ERA}}}} - {{{\mathrm{MME}}}}^\prime \end{array}$$
(6)

Note that, similar to Eq. (5), the LBCs in Eq. (6) have a reanalysis-based mean climate, which removes the mean bias in the MME and generates more reliable dynamical downscaling simulations for the historical climate.

We carried out two sets of WRF simulations (HIST and IV) driven by the large-scale forcing variables, including SST, surface pressure, sea level pressure, air temperature, zonal wind, meridional wind, relative humidity, and geopotential height, constructed in Eqs. (5) and (6), respectively (Table 2). In the HIST experiment, the WRF simulations considered the observed transient variation of natural and anthropogenic external forcing factors (e.g., solar radiation, volcanic aerosols, ozone, greenhouse gases, anthropogenic aerosols, and changes in land use and land cover; see Supplementary Information). In the IV experiment, the natural and external forcings were fixed at their climatological mean to remove the temporal variation of external forcing. The HIST experiment considered the time-varying external forcing and internal climate variability in both the WRF inner domain and its LBCs. By contrast, the IV experiment considered the internal variability only and held the external forcing factors at their climatological means in the WRF model and the external forcings were removed from its LBCs. Both the LBCs of the HIST and IV experiment inherit the internal climate variability from the ERA40 reanalysis.

Table 2 WRF model attribution experiments.
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The effect of external forcing can be represented by the difference between the HIST and IV experiments (HIST − IV), which isolates the climate response to external forcing under realistic internal climate variability. The HIST − IV and CMIP5 MME show comparable temporal variation in eastern China, which gives us more confidence to use the HIST − IV representing external forcing effect (Supplementary Fig. 11).

Relative weight analysis

We used Johnson’s relative weight analysis (RWA)58 to quantify the relative importance of internal variability (IV) and external forcing (EF). RWA addresses the problem of collinearity among predictors in the attribution based on multivariate linear regression59,60. It first creates a new set of uncorrelated predictors Z(zk) by orthogonally transforming the original set of predictors X(xj). Two regression analyses are then conducted using the orthogonal predictors: one generates the standardized regression coefficient β by regressing the dependent variable Y on Z. Another generates the standardized regression coefficient λ by regressing the original predictor X on Z. The relative contribution of the original variable X to the dependent variable Y is then obtained through combining β with λ:

$$\varepsilon _j = \mathop {\sum}\limits_{k = 1}^p {\lambda _{jk}^2\beta _k^2}$$
(7)

where εj is the relative importance of predictor j, which is IV or EF in this study. \(\beta _k^2\) and \(\lambda _{jk}^2\) are the squares of the standardized regression coefficients linking orthogonal predictor k with the dependent variable and original predictor j, respectively. The actual relative contributions of IV and EF are quantified as \(\frac{{\varepsilon _{{\rm{IV}}}}}{{\varepsilon _{{\rm{IV}}} + \varepsilon _{{\rm{EF}}}}}\) and \(\frac{{\varepsilon _{{\rm{EF}}}}}{{\varepsilon _{{\rm{IV}}} + \varepsilon _{{\rm{EF}}}}}\), respectively. The RWA method was successfully applied to the quantification of the relative contributions of different external drivers and internal variability to regional changes in temperature71, the relative contribution rate of meteorological and land use factors to a reduction in surface runoff72 and the biophysical and socioeconomic drivers of changes in forest and agricultural land73.

RWA was performed on different combinations of the intrinsic mode functions (IMFs) of the ensemble empirical mode decomposition in the annual mean precipitation and surface air temperature. Different combinations of IMFs represent the information in various timescales of climate variations74,75,76. We obtained four IMFs and the residual based on the ensemble empirical mode decomposition of the 43-year time series from 1959 to 2001. The first and second IMFs are of high-frequency oscillation signals on timescale <10 years, representing internal variability. The third and fourth IMFs are decadal oscillation signals with timescales >10 years. The residual component is a nonlinear trend that describe the inter-decadal transition in the second half of the twentieth century (Supplementary Figs. 12 and 13). Bootstrap sampling with replacement was performed 1000 times on the spatial fields of different combinations of IMFs to estimate the uncertainty range of the RWA analysis of the IV and EF effects.