Volume 45, Issue 4 p. 2014-2021
Research Letter
Open Access

Decadal Monsoon-ENSO Relationships Reexamined

Kyung-Sook Yun

Kyung-Sook Yun

Center for Climate Physics, Institute for Basic Science, Busan, South Korea

Pusan National University, Busan, South Korea

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Axel Timmermann

Corresponding Author

Axel Timmermann

Center for Climate Physics, Institute for Basic Science, Busan, South Korea

Pusan National University, Busan, South Korea

Correspondence to: A. Timmermann,

[email protected]

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First published: 09 February 2018
Citations: 60


The strength of the El Niño-Southern Oscillation (ENSO)-Indian summer monsoon rainfall (ISMR) relationship shows considerable decadal fluctuations, which have been previously linked to low-frequency climatic processes such as shifts in ENSO's center of action or the Atlantic Multidecadal Oscillation. However, random variability can also cause similar variations in the relationship between climate phenomena. Here we propose a statistical test to determine whether the observed time-evolving correlations between ENSO and ISMR are different from those expected from a simple stochastic null hypothesis model. The analysis focuses on the time evolution of moving correlations, their expected variance, and probabilities for rapid transitions. The results indicate that the time evolution of the observed running correlation between these climate modes is indistinguishable from a system in which the ISMR signal can be expressed as a stochastically perturbed ENSO signal. This challenges previous deterministic interpretations. Our results are further corroborated by the analysis of climate model simulations.

Key Points

  • We develop a statistical test to determine whether time-evolving ISMR/ENSO correlations are different from a stochastic null hypothesis
  • The time evolution of the running correlation between ISMR and ENSO is indistinguishable from a white noise perturbation process
  • Our study challenges previous deterministic interpretations on ISMR/ENSO relationship

1 Introduction

The El Niño-Southern Oscillation (ENSO) is a major driver of global climate variability (Trenberth et al., 1998) with impacts on ecosystems and human activities. ENSO is also interacting with other modes of climate variability, such as the Indian summer monsoon rainfall (ISMR). Figure 1 shows the well-documented inverse relationship between ISMR and ENSO during boreal summer (e.g., Kumar et al., 1999; Torrence & Webster, 1999; Krishnamurthy & Goswami, 2000). Evidently, the relationship is modulated on decadal timescales, as seen by the running correlation in a 21 year window (see Figure 1b). Recent studies link these changes in the ENSO/ISMR relationship to the influences of the Atlantic Multidecadal Oscillation (Lu et al., 2006; Kucharski et al., 2009; Chen et al., 2010), greenhouse or aerosol impacts (Azad & Rajeevan, 2016; Kumar et al., 1999; Wang et al., 2015), and to zonal shifts in ENSO's center from eastern Pacific to central Pacific (Fan et al., 2017; Kumar et al., 2006). An alternative explanation for the decadal modulation of ENSO/ISMR correlation is the presence of stochastic fluctuations in a statistically undersampled system (Cash et al., 2017; DelSole & Shukla, 2012; Gershunov et al., 2001; van Oldenborgh & Burgers, 2005). Despite considerable efforts from previous studies, there is still an ongoing debate as to whether the decadal monsoon-ENSO relationship is caused by random perturbations or is a result of low-frequency deterministic processes. To shed more light on the issue of determinism versus stochasticity and nonstationarity versus stationarity, we develop a new statistical test. Using observational data sets and ensembles of climate model simulations, we examine if time variations in the ENSO/ISMR correlation are inconsistent with a stochastic perturbation process.

Details are in the caption following the image
(a) Correlation coefficient between boreal summer Niño3 sea surface temperature anomaly (SSTA) index and precipitation anomalies (shading over land) and between Indian summer monsoon rainfall (ISMR) index averaged over the red box domain [5°N–25°N, 70°E–90°E] and SSTAs (shading over ocean) during 1901–2012. Here SST and precipitation data are obtained from extended reconstruction of global sea surface temperature and Climatic Research Unit, respectively. (b) Twenty-one-year window moving correlation coefficient between El Niño-Southern Oscillation (i.e., boreal summer Niño3 or Niño4) and Indian summer monsoon rainfall (ISMR; i.e., ISMR or all ISMR). The black dot-and-dash line indicates the 95% confidence level tested by t-statistics using 19 numbers of degrees of freedom.

2 Data and Methods

2.1 Observation, CMIP5, and CESM-LM Experiments

To characterize boreal summer tropical Pacific sea surface temperature (SST) we used seasonal (June-July-August) mean SST from two data sets: the Met Office Hadley Centre Sea Ice and SST (HadISST) since 1870 (Rayner et al., 2003) and the extended reconstruction of global SST (ERSST) version 4 since 1854 (Huang et al., 2014). Both Niño 3 [5°S–5°N, 150°W–90°W] and Niño 4 [5°S–5°N, 160°E–150°W] SST anomaly (SSTA) indices are used in our analysis. ISMR variability was computed from the Climatic Research Unit Time Series (TS) version 3.21 precipitation data during 1901–2012 (Harris et al., 2014), area-averaged over India region [5°N–25°N, 70°E–90°E]. This area is chosen for its high negative correlation with boreal summer Niño 3 SSTA index (Figure 1a). To show the robustness of our analyses, the all ISMR data from the Indian rain gauge network (Parthasarathy et al., 1994) were also used. Because of the availability of the observational record, we focus on the period from 1901–2012. The correlation coefficient (CC) between the two Indian rainfall indices during this period is 0.57.

We also used the 40 Coupled Model Intercomparison Project Phase 5 (CMIP5) member multimodel ensemble of historical Coupled General Circulation Model (CGCM) simulations covering the industrial period from 1900–2005 and the Representative Concentration Pathway (RCP) 8.5 simulations from 2006 to 2099 to study the greenhouse warming response (Taylor et al., 2012). More details on the CMIP5 data can be found in Yun et al., (2016). All model data were interpolated to a common grid of 2.5° × 2.5°, consistent with previous studies on monsoon-ENSO relationship (e.g., Chen et al., 2010; Wu & Jiao, 2017). To further highlight the fact that the monsoon-ENSO relationship in a suite of CGCM simulations is consistent with a stochastic perturbation process, we used a 10-member ensemble of externally forced Last Millennium (LM) simulations from 850 to 2005 conducted with the Community Earth System Model (CESM) (Otto-Bliesner et al., 2016). The CESM-LM simulations include solar, volcanic, land use, greenhouse gas, and orbital forcings.

2.2 Stochastic Process With White Noise

Standard deviations (SDs) of moving CCs are computed for a variety of window lengths. The abruptness of shifts in CC is then quantified by the maximum of 10 year moving linear regression coefficients (Xtrend) of moving CCs for a suite of window lengths. Before calculating moving correlations, all raw data were individually detrended within each window. The reference moving correlation window length is 21 years consistent with previous studies (e.g., Chen et al., 2010; Fan et al., 2017).

We test the following null-hypothesis (H0):

The time evolution of moving correlations between ENSO and ISMR is consistent with the assumption of a stationary stochastic perturbation process
where zt corresponds to Gaussian-distributed white noise and a is a scaling factor representing the noise amplitude. We hypothesize that the SD of moving correlations between ENSO and ISMR is indistinguishable at a 95% level from that of ENSO and ISMR*.

H0 is tested by first calculating the moving correlation between two ENSO indices (observed and simulated boreal summer Niño 3 or Niño 4 SSTA) and the ISMR TS for a number of window lengths and then by calculating the SD of the resulting TS. The results are then compared against the same calculations applied to 1,000 random realizations of ISMR* through equation 1 using the observed and simulated ENSO indices and Gaussian distributed white noise.

The noise amplitude a (relative to the amplitude of ENSO) is chosen such that the long-term mean CC between ISMR*, generated by the stochastic model 1 and ENSO, matches the value between ISMR and ENSO over the entire time period from the original data (1901–2012 for the observations, 1900–2005 in historical simulations of CMIP5, and 850–2005 in CESM LM). For these observational and model data sets we calculated the moving correlations between Niño indices and ISMR indices and their SDs in 21 year moving windows (Table 1). The CC between ISMR* and ENSO shows a steady decline as the noise amplitude a increases (see Figure S1 in the supporting information). For further comparisons of ISMR and ENSO relationships in future RCP8.5 greenhouse warming simulations, we used the noise amplitude estimated from the respective historical simulations.

Table 1. Basic Statistics on El Niño-Southern Oscillation (ENSO) and ENSO-Indian Summer Monsoon Rainfall (ISMR) Correlation in Observations and Six CMIP5 Models and Four Ensemble Simulations of CESM Last Millennium (LM) Experiment
Dataset Standard deviation of 21 year moving correlation coef. Correlation coef. (ISMR, ENSO)
Niño3 Niño4 Niño3 Niño4
Observation (1901–2012) ERSST 0.18 0.20 −0.47 −0.24
HadISST 0.16 0.17 −0.42 −0.30
CMIP5 historical simulation (1900–2005)/RCP8.5 simulation (2006–2099) CESM1-CAM5.1-FV2 0.16/0.22 0.22/0.21 −0.47/−0.09 −0.40/−0.09
FIO-ESM 0.09/0.17 0.17/0.11 −0.53/−0.46 −0.26/−0.36
IPSL-CM5A-LR 0.14/0.07 0.12/0.05 −0.75/−0.75 −0.74/−0.78
IPSL-CM5A-MR 0.16/0.15 0.14/0.13 −0.62/−0.59 −0.65/−0.64
NorESM1-M 0.12/0.12 0.09/0.22 −0.66/−0.47 −0.49/−0.35
NorESM1-ME 0.16/0.11 0.19/0.18 −0.48/−0.54 −0.27/−0.45
CESM lm (850–2005) E002 0.24 0.25 −0.15 −0.04
E003 0.23 0.21 −0.12 −0.04
E006 0.21 0.19 −0.13 −0.05
E009 0.24 0.21 −0.13 −0.04

3 Results

3.1 Strength of Decadal Variability

We first reexamine the robustness of decadal changes in the ENSO-ISMR relationship during the period from 1901–2012 using different combinations of observational data sets (Figure 1b). The 21 year moving correlation between the ENSO indices chosen here and ISMR shows considerable decadal variability, as reported in many previous studies (e.g., Kumar et al., 1999) and a weakening tendency over the past decades. The decadal change shows notable differences not only in CCs between Niño3 and Niño4 but also in those between ERSST and HadISST. Note that the differences are mostly seen in the first half of the century, which illustrates the observational uncertainties in SST during the first half of the century.

Given these uncertainties, we have decided to further study the observed relationships between ISMR and Niño3/Niño4 in both ERSST and HadISST data sets. Figure 2 examines the statistical significance of the observed variability in moving CC between ENSO and ISMR indices relative to the stochastic linear perturbation process (i.e., equation 1). As expected, the observed SD of moving CCs between ENSO and ISMR decreases for increasing window lengths. Our results document that the observed statistics are indistinguishable at a 95% confidence level from that of our simple stochastic stationary linear null hypothesis model (H0). Therefore, we conclude that to explain the observed shifts in ENSO/ISMR relationships, no external low-frequency climate processes involving other modes of variability (e.g., Chen et al., 2010; Krishnan & Sugi, 2003) need to be invoked. Our results support the conclusions from an earlier study by Gershunov et al. (2001).

Details are in the caption following the image
Standard deviation of moving correlation coefficients between observed El Niño-Southern Oscillation (ENSO) and Indian summer monsoon rainfall as a function of window length (shown by black thick line): (a) for Niño3 from extended reconstruction of global sea surface temperature (ERSST), (b) for Niño4 from ERSST, (c) for Niño3 from Hadley Centre Sea Ice and Sea Surface Temperature (HadISST), and (d) for Niño4 from HadISST. The red solid line and yellow shading indicate the mean for 1,000 random realizations of standard deviations calculated from moving correlation coefficients between ENSO and the stochastic white noise perturbation model for Indian summer monsoon rainfall (ISMR)* (equation 1) and the corresponding 95% confidence interval. The variability of observed ENSO/ISMR relationships is indistinguishable from that of the stochastic null hypothesis model.

3.2 Strength of Abrupt Decadal Change

Previous studies have reported several fast climatic shifts such as the shift in moving ENSO/ISMR CC in the late 1970s and 1990s (e.g., Fan et al., 2017; Wang et al., 2015). Here we investigate if the simple H0 stochastic null hypothesis can also explain these rapid linear trends in the relationship between ENSO and ISMR, or if other external drivers need to be invoked. We calculated the probability distribution of linear trends in the ENSO-ISMR moving CC relationship in comparison with those obtained from 1,000 realizations of equation 1. The results are shown in Figure 3 for ERSST and Figure S2 for HadISST for three window lengths (11, 21, and 31 years). The observed trend statistics denoted by the vertical dashed line do not exceed the 95% confidence level of our stationary white noise H0. The result is further corroborated for both Niño 3 and Niño 4 for a wider set of window lengths, as shown in the right panels of Figure 3. A similar conclusion is also drawn when using the HadISST data instead (Figure S2).

Details are in the caption following the image
(left) Frequency histogram for 1,000 random realizations of maximum 10 year trend coefficients of 11-, 21-, and 31-year moving correlation coefficients between (a) Niño3 and (c) Niño4 and white noise time series for 112 years of extended reconstruction of global sea surface temperature data. The vertical dashed line in each color indicates the observed maximum 10 year trend coefficients of 11-, 21-, and 31-year moving correlation coefficients between El Niño-Southern Oscillation (ENSO) and Indian summer monsoon rainfall. (right) Maximum 10 year trend coefficients of moving correlation coefficients with (b) Niño3 and (d) Niño4 as a function of window length. The black line indicates the maximum 10 year trend coefficients of the observed moving correlation coefficient, while the red solid line and yellow shading denote the mean for 1,000 realizations of those between ENSO and white noise time series and its 95% confidence interval.

3.3 Sampling Variability Using Various Model Experiments

To summarize, the observed strengths of the decadal variability in both Niño 3-ISMR and Niño 4-ISMR relationships cannot be distinguished from a simple random null hypothesis test in which the Indian summer monsoon is mimicked as a summer ENSO signal and some fixed-amplitude white noise. Because the sample size from the observations is relatively limited, Cash et al. (2017) analyzed the sampling variability using large ensemble model simulations drawn from nearly similar background states during 32 year simulation segments. To further test these results in a CGCM framework we use the 10-member CESM LM experiments, the CMIP5 RCP8.5 scenario simulations from 2006 to 2099, and the CMIP5 historical experiments covering the periods from 1900 to 2005. We will, in particular, address the question whether potential effects of greenhouse warming on the ENSO/ISMR relationship can be detected against the proposed null hypothesis H0.

The ENSO-ISMR relationship and its strength in decadal variability, based on ensemble mean June-July-August Niño3 and ISMR TS during the historical run of 1900–2005 and RCP8.5 run of 2006–2099, differ greatly among different CMIP5 models both for present and future climates (see Figures S3 to S5). We thus selected six models that can realistically capture the observed ISMR-ENSO relationship in the historical run of 1900–2005 (i.e., greater negative CC of Niño 3-ISMR than the observed −0.47). The selected models are CESM1-CAM5.1-FV2, FIO-ESM, IPSL-CM5A-LR, IPSL-CM5A-MR, NorESM1-M, and NorESM1-ME (Figure S3), which are used to test the ISMR-ENSO relationship against the H0 hypothesis. The long-term simulation of the CESM LM experiment reveals a weak time-averaged ENSO-ISMR relationship during the entire period of 850–2005 and as a result very strong decadal variability in the moving CC (see Figure S6). Therefore, the 21 year window moving CCs between Niño3 and ISMR shows a remarkable spread ranging from −0.84 to 0.64, thereby leading to larger strength of decadal variability than the observed ones: 0.18 for ERSST, 0.16 for HadISST, and 0.21 to 0.28 throughout 10 ensembles of the CESM LM. This large-amplitude modulation of decadal relationships in the CESM LM experiment is consistent with the action of random fluctuations in the Monsoon systems. For simplicity, we display only four ensemble simulations that have a relatively small SD of moving CCs among 10 members, that is, E002, E003, E006, and E009.

A summary for the variability in ENSO/ISMR relationships in 21 year running windows (Figure 4a) and corresponding abrupt decadal changes (Figure 4b) for the number of CGCM experiments is presented in Figures 4a and 4b. For the majority of model simulations the stochastic null hypothesis cannot be rejected at the 95% confidence level of a white noise process. However, there are a few exceptions. One CMIP5 simulation (i.e., CESM-CAM5-FV2) out of 6 models and 2 members (i.e., E005 and E007) for Niño3 and 1 member (i.e., E006) for Niño4 out of 10 ensembles of the CESM LM are distinguishable from the white noise variability (Figure 4a). All results for the abrupt decadal change are also indistinguishable from the white noise process (Figure 4b). Examples on statistics from the model results are displayed in Figures S7 to S11.

Details are in the caption following the image
Overview for (a) standard deviations and (b) maximum 10 year trend coefficients of 21 year moving correlation coefficients between El Niño-Southern Oscillation (ENSO) and Indian summer monsoon rainfall indies obtained from the observations (2 × 112 years), the historical simulations of six Coupled Model Intercomparison Project Phase 5 (CMIP5) models (6 × 106 years), and four ensemble simulations of Community Earth System Model Last Millennium experiment (4 × 1,156 years) (denoted by black circle for Niño3 and green triangle symbols for Niño4, respectively). The red circle (blue triangle) and error bar denote the mean for 1,000 random realizations of those between ENSO and white noise time series and its 95% confidence intervals for Niño3 (Niño4), respectively. The star/square symbols and dashed error bar in CMIP5 models indicate the results from the Representative Concentration Pathway 8.5 simulations (94 years).

4 Discussion

The temporal evolution of the observed ENSO-monsoon relationship during the past century is fully consistent with a linear stationary stochastic perturbation process (equation 1), which approximates the ISMR signal as a randomized boreal summer ENSO signal. This is quite different from the approach taken by Gershunov et al. (2001), which uses two random surrogate TSs that are correlated at the same level as the observed ENSO and ISMR indices. Their approach ignores other ENSO characteristics (e.g., amplitude, autocorrelation, and phase). In general, our more physically motivated null hypothesis is based on the notion that ISMR variability can be explained as a noisy ENSO TS, even though our test gives similar results to those discussed by Gershunov et al. (2001) (Figure S12). Given the fact that the decadal change in ENSO teleconnections is largely attributable to ENSO variance itself (Chowdary et al., 2012), our test could be more broadly applied in further analyses of decadal variabilities between different climate indices, especially for climate modes involving unique physical properties. We further analyzed various model outputs to reexamine the sampling variability and therefore concluded that the mechanisms presented earlier such as zonal shifts in ENSO's center (e.g., Fan et al., 2017) and global warming effects (e.g., Azad & Rajeevan, 2016) are not necessary to explain the observed decadal modulation of ENSO/monsoon relationships.

Although recent studies (e.g., Stuecker et al., 2015; Wu & Jiao, 2017) recognized the critical role of internal stochastic process in time-evolving variability of large-scale climate dynamics, many studies have not thoroughly tested the results of moving correlations against simple stochastic processes. We suggest that a statistical test on the white noise null hypothesis should be required prior to investigating the role of a changing climate mean state or low-frequency process. This study challenges the long-held assumption that variability of moving correlations between climate variables necessarily implies some kind of nonstationarity. We clearly demonstrated that for the ENSO/ISMR relationship, statistically indistinguishable results can be generated by a linear stationary stochastic perturbation process that does not require any low-frequency modulation of the ENSO/ISMR relationship caused by other climate modes, such as Atlantic Multidecadal Oscillation, shifts in ENSO, or greenhouse warming. This study could provide a significant contribution to an ongoing discussion in climate research.


This study was supported by the Institute for Basic Science (project code IBS-R028-D1). K. S. Yun was supported by NRF 2015R1C1A1A01054992. This is ICCP publication 3. We acknowledge the data providers for the ERSST (https://doi.org/10.7289/v5kd1vvf), HadISST (http://catalogue.ceda.ac.uk/uuid/facafa2ae494597166217a9121a62d3c), CRU (https://doi.org/10.5285/d0e1585d-3417-485f-87ae-4fcecf10a992, and AISMR (http://www.tropmet.res.in/static_page.php?page_id=53) data and the WCRP working group on coupled modeling for CMIP5 models (http://pcmdi9.llnl.gov/) and CESM LM ensemble project (http://www.cesm.ucar.edu/projects/community-projects/LME/).