# Assessing CMIP Models' Ability to Detect Observed Surface Warming Signals Related to Climate Change

Suresh Gopika, Matthieu Lengaigne, Iyyappan Suresh, Takeshi Izumo, Sadhvi

Kwatra, Suresh Neetu, Jérôme Vialard

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Suresh Gopika, Matthieu Lengaigne, Iyyappan Suresh, Takeshi Izumo, Sadhvi Kwatra, et al. Assessing CMIP Models' Ability to Detect Observed Surface Warming Signals Related to Climate Change. Journal of Climate, 2024, 37, pp.6011-6027. 10.1175/JCLI-D-24-0102.1. insu-04821264

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Assessing CMIP Models' Ability to Detect Observed Surface Warming Signals Related to Climate Change

SURESH GOPIKA<sup>a,b</sup>, MATTHIEU LENGAIGNE<sup>c</sup>, IYYAPPAN SURESH<sup>a,d</sup>, TAKESHI IZUMO<sup>e</sup>, SADHVI KWATRA<sup>b</sup>
S. NEETU,<sup>a</sup> AND JÉRÔME VIALARD<sup>f</sup>

<sup>a</sup> CSIR-National Institute of Oceanography, Goa, India

<sup>b</sup> School of Earth, Ocean and Atmospheric Sciences, Goa University, Goa, India

<sup>c</sup> MARBEC, University of Montpellier, CNRS, IFREMER, IRD, Sète, France

<sup>d</sup> Digital University Kerala, Trivandrum, Kerala, India

<sup>e</sup> UMR 241 EIO, Université de Polynésie Française, Tahiti, France

<sup>f</sup> LOCEAN/IPSL, Sorbonne Universités (UPMC, Univ Paris 06) -CNRS-IRD-MNHN, Paris, France

(Manuscript received 13 February 2024, in final form 1 August 2024, accepted 8 August 2024)

**ABSTRACT:** Assessing if CMIP models can detect observed climate change signals is crucial for evaluating their realism and strengthening confidence in future projections. These signals can only be compared once distinguishable from the background climate “noise.” Built for impact studies but not detection purpose, the time of emergence (ToE) estimates when this occurs using a fixed signal-to-noise ratio. To more accurately assess models’ ability to reproduce observed climate change signals, we introduce the time of detection (ToD), which employs a statistical significance test of the nonlinear trend, accounting for the time series length. ToD and ToE are computed for sea surface temperature (SST) and relative SST (RSST) across four observational and 69 CMIP5/6 historical and shared socioeconomic pathways 5–8.5 (SSP5–8.5) scenario datasets. ToD precedes ToE and is less sensitive to the chosen threshold. While already detectable in most of the tropics, SST warming in the equatorial Pacific is detectable in ~90% of models but only one out of four observational datasets, due to a stronger modeled warming. Because RSST signals are weaker than SST signals, they do not emerge anywhere but are detectable in two regions. The enhanced warming in the western Indian Ocean, detected in ~45% of models, is not robust in observations when excluding pre-1960 dubious data. Conversely, the subdued southeast Pacific warming detected in observations and ~80% of models is robust and consistent with a poleward extension of the Southern Hemisphere Hadley cell. The ToD’s ability to detect subtle signals allows for assessing the realism of the CMIP warming pattern in this region.

**SIGNIFICANCE STATEMENT:** Recent studies emphasize the importance of the climate change warming pattern and its apparent discrepancy between climate models and observations in the equatorial Pacific. We argue that our newly proposed time of detection (ToD) is better suited than the well-known time of emergence (ToE) for investigating where modeled and observed warming patterns can be confidently compared. In agreement with previous studies, our analysis indicates model–observations disagreement over the equatorial Pacific. Using ToD instead of ToE allows for detecting a robust subdued warming (i.e., weaker than the tropical average) in the southeast Pacific and therefore confirms the realism of the CMIP warming pattern in this region.

**KEYWORDS:** Tropics; Sea surface temperature; Climate change; Climate variability; Coupled models; Model comparison

# 1. Introduction

The world's oceans have experienced a pronounced warming since the advent of the industrial era, attributed to anthropogenic forcing, with greenhouse gas emissions playing a key role (IPCC 2021). This article focuses on tropical oceans, which host some of the world's most susceptible ecosystems

and exert a strong influence on vulnerable societies (Cai et al. 2013; IPCC 2014). The observed average warming of tropical oceans (~0.7° relative to the 1891–1950 period in 2022; Fig. 1a) aligns with the warming range (0.6°–1.1°) in historical simulations from phases 5 and 6 of CMIP (CMIP5+6) databases (Fig. 1a). Future projections indicate that this warming will intensify in the coming decades, with the highest emission scenario leading to a 3°–5°C increase by the end of the twenty-first century (Fig. 1a).

The observed and modeled tropical sea surface temperature (SST) warming is nonuniform (see Figs. 1b,c; Xie et al. 2010). This tropical warming pattern has very important implications, as it influences tropical rainfall and circulation (Xie et al. 2010), global teleconnection patterns, and modes of natural climate variability (Cai et al. 2013, 2020) and modulates global climate sensitivity (Andrews et al. 2015). CMIP models project that the warming pattern will intensify in the future

<sup>a</sup> Denotes content that is immediately available upon publication as open access.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-24-0102.s1.

Corresponding author: Suresh Gopika, gopikasurvay@gmail.com
<figure><img src="image_2.png" /><figcaption>FIG. 1. Tropical SST warming in observations and CMIP5/6 models. (a) Time evolution of average 30°S-30°N warming (°C; relative to the 1891-1950 climatology) for the MOM (green line, with fourth-order polynomial fit in red) and the CMIP5+6 historical simulations and RCP8.5/SSP5-8.5 scenarios MMM (black dashed line, with a gray shading for the 10th-90th percentile). Maps of the SST warming signal (b) for the MOM in 2022 and for the CMIP5+6 MMM in (c) 2022 and (d) 2100. The warming signal (°C) is estimated from a regression of SST at each point to the normalized tropical average warming index of the model or observed dataset (see section 3 for details).</figcaption></figure>

(cf. Figs. 1c,d). This pattern is characterized by subdued warming in the southeast Pacific (SEP; Figs. 1b-d; Jebri et al. 2020; Power et al. 2021) and the southern subtropics. On the other hand, CMIP models project enhanced warming in the central and eastern equatorial Pacific (e.g., Xie et al. 2010), often referred to as an “El Niño-like pattern.” The equatorial Indian Ocean exhibits a pattern reminiscent of a positive Indian Ocean dipole, featuring enhanced warming in the equatorial western Indian Ocean (WIO; Figs. 1c,d) and reduced warming in the east (Zheng et al. 2013; Gopika et al. 2020; Sharma et al. 2023). While model projections align with observations in terms of tropical average warming (Fig. 1a) and subdued SEP warming (Figs. 1b,c), there are significant disparities in the equatorial Pacific, where models indicate enhanced warming, and observations muted warming or cooling. These discrepancies in eastern equatorial Pacific (EEP) SST trends lead to the question of whether the Walker circulation has strengthened or weakened over

the past century (Xie et al. 2010; Cai et al. 2020; Power et al. 2021).

The overall tropical warming can confidently be attributed to anthropogenic forcing (Bindoff et al. 2013; Fig. 1a). However, the substantial tropical climate internal variability contributes significantly to regional SST trends over the historical period (Chung et al. 2019; Gopika et al. 2020; Wu et al. 2021). The observed subdued EEP warming may, for instance, be related to a negative trend in the interdecadal Pacific oscillation (IPO), concealing a more subtle anthropogenic warming trend (e.g., Power et al. 2021). This questions whether the inconsistent trends in Figs. 1b and 1c simply indicate aliasing by internal climate variability or also point to an erroneous tropical Pacific warming pattern in CMIP models. In other words, models can only be reliably compared to observations in regions where long-term anthropogenic trends (hereafter “signal”) are distinguishable from the background climate variability (hereafter “noise”).
Time of emergence (ToE) estimates when climate change signals emerge from the background natural variability. ToE is usually defined as the time when the anthropogenic signal (S) to natural climate noise (N) S/N ratio permanently exceeds a given threshold (e.g., Giorgi and Bi 2009). ToE was initially developed to estimate when local climate departs from its historical range, hence leading to impacts, especially in vulnerable ecosystems with limited adaptive capacity (Beaumont et al. 2011; Deutsch et al. 2008). ToE was first applied to terrestrial areas (e.g., Giorgi and Bi 2009; Diffenbaugh and Scherer 2011) and later to oceanic variables such as SST (e.g., Ying et al. 2022; hereafter Y22), sea level (e.g., Lyu et al. 2014; Walker et al. 2022), or marine ecosystem drivers (Rodgers et al. 2015; Keller et al. 2014; Schlunegger et al. 2020). For instance, Y22 applied ToE to tropical SST in CMIP models and observations, underlining emerging signals around 1990, except in the EEP where no discernible signal has emerged in data in half of the models and observational records. This delayed EEP ToE is related to the strong natural climate variability associated with El Niño–Southern Oscillation (ENSO) (Zhong et al. 2023).

Regions with detectable observed climate change signals allow assessing the realism of modeled climate change signals over the historical period. For instance, Y22 identified emerging EEP warming in models but not in observations, which questions the consistency of CMIP projections and historical data in this region. The original purpose of ToE is focused on impacts rather than detection, typically using a relatively large signal-to-noise ratio (of one or more) to identify significant deviations from the present-day climate. However, this approach with large thresholds may miss more subtle yet detectable signals. Assessing how models are able to detect even subtle climate change signals observed in nature is crucial for evaluating model realism and strengthening our confidence in their future projections. Detecting a trend amid a noisy time series requires a statistical significance test. As detailed in section 3, this test involves a signal-to-noise ratio threshold, as in the ToE method. But contrary to ToE, this threshold is modulated by the length of the available time series, to account for the fact that a signal is more easily detectable with a larger sample. Here, we introduce the “time of detection” (ToD) methodology. Building upon the ToE principles, ToD incorporates a rigorous statistical significance test for trends. While ToE uses a fixed threshold to highlight strong changes relevant to impact studies, accounting for actual degrees of freedom makes ToD more sensitive to subtle signals, rendering it more appropriate for detection. ToD is not designed as a replacement for ToE, which remains the best tool for impact studies. Instead, ToD is designed to facilitate comparisons between climate models and observations, particularly for detecting weak, late-emerging signals. In previous literature (e.g., Y22), the words “detection” and “emergence” were often used interchangeably to refer to ToE. In the present paper, detection will specifically refer to the date identified through the ToD methodology (i.e., a statistically significant trend), and emergence will refer to the date identified through the ToE methodology (i.e., a signal that exceeds a given signal-to-noise ratio).

The methodology underpinning the ToD framework was originally introduced by Gopika et al. (2020, hereafter G20) though not explicitly labeled as ToD. Their study assessed changes in SST and relative SST [RSST; SST minus its tropical mean, a clear indicator for changes in the SST pattern and a proxy for atmospheric stability in the tropics, e.g., Vecchi and Soden (2007a,b) and Izumo et al. (2020)] in the Indian Ocean. Their primary conclusion was that changes in the SST pattern, as represented by RSST changes, become detectable much later than changes in SST. This is because RSST signals are much smaller than those in SST when subtracting tropical average warming, while they both share the same “climate noise” amplitude makes. However, G20 did not explicitly discuss the conceptual difference between the ToD and ToE, nor compare these two metrics. In the present paper, our objectives are to 1) establish a ToD precise definition, 2) compare ToD and ToE for CMIP and observed SST, and 3) employ ToD to identify regions where CMIP models can already be evaluated against observations.

This paper is structured as follows. In section 2, we describe the CMIP simulations, observational datasets, and data processing methods used in this study. In section 3, we remind the ToE computation method and then present our methodology for estimating the ToD. In section 4, we compare ToE and ToD for observed and CMIP5+6 tropical SST. In section 5, we focus on the ToD of RSST, in order to identify regions where the observed and modeled warming patterns can be compared. This, in particular, allows identifying two regions for which RSST signals (i.e., warming pattern signals) are detectable in observations using ToD but not ToE (the southeastern Pacific and western Indian Ocean), thereby allowing us to compare models with observations there. We summarize our findings and discuss their implications in section 6.

## 2. Data and processing

### a. CMIP and observed datasets

We employ SST data from 34 CMIP5 (Riahi et al. 2011) and 35 CMIP6 (Eyring et al. 2016) models (Table S1 in the online supplemental material). We used the first available ensemble member of each model, to ensure equal model weights. Although we specifically focus on SST in the current study, our model selection was guided by the availability of key climate variables (e.g., precipitation, wind). The CMIP5 historical simulations cover 1850–2005, while CMIP6 simulations cover 1850–2014. When combined with future projections, CMIP5/6 simulations cover 1891–2100. We use projections based on an unmitigated emission scenario with a radiative forcing of 8.5 W m⁻² by the end of the twenty-first century: representative concentration pathway 8.5 (RCP8.5) for CMIP5 and shared socioeconomic pathways 5–8.5 (SSP5–8.5) for CMIP6.

We consider the latest versions of four widely used long-term SST observational products over 1891–2022: the Centennial in situ Observation-Based Estimates of SST, version 2 (COBE SST2; Folland and Parker 1995); Hadley Centre Sea Ice and SST dataset, version 1.1 (HadISST v1.1; Rayner et al. 2003); Extended Reconstructed SST, version 5 (ERSST.v5;
Huang et al. 2017); and Kaplan extended SST version 2 (Kaplan-SST v2; Kaplan et al. 1998). Refer to the data avail- ability statement at the end of this article for links to these datasets.

b. Data processing

We focus on the 30°S–30°N band. All datasets are interpo- lated onto a 2° × 2° standardized grid. All the analyses in this paper are based on annual-mean SST anomalies, computed relative to the 1891–1950 reference period, selected because it precedes the post-1950 accelerated warming (Fig. 1a). To em- phasize changes in the SST pattern, which influences atmo- spheric stability (Xie et al. 2010; Izumo et al. 2020), we employ RSST, defined by subtracting the 30°S–30°N average SST for each year and at grid point.

The results of CMIP5 and CMIP6 are similar (not shown): we combined the 34 CMIP5 and 35 CMIP6 models into a sin- gle dataset, referred to as CMIP5+6. We use the multimodel median (MMM) value to summarize results from this CMIP5+6 dataset (Table S1). We used the median, which is less sensitive to outliers than the mean, but using the mean yields similar results (not shown). Similarly, we present the multiobserv- ational median (MOM) derived from the four observational datasets (an extended version of the median, defined as the aver- age of the second and third highest values).

3. Methodology for estimating ToE and ToD

In this section, we will describe the methods for estimating ToE and ToD. We encourage the readers to consult Hawkins and Sutton (2012) (hereafter HS) for ToE. The ToD method- ology below is refined from that of G20. We aim for our method to be applicable to both observations and models; hence, we do not compute the climate signal based on a sce- nario minus a preindustrial control simulation (or their en- semble average), as some studies have done. Along the lines in HS, we define a tropical warming index, which allows us to estimate that signal.

a. Tropical warming index

Linear fits are inadequate to estimate anthropogenic trends that are nonlinear (curved shape of the curves in Fig. 1a). HS thus introduced a nonlinear “index of global warming.” We adopt a similar approach. Instead of a global warming index, we create a “tropical SST warming index” for each model by averaging 30°S–30°N SST [results are robust when employing a global warming index (not shown)]. We obtain a smooth in- dex W(t) from a fourth-order polynomial fit over 1921–2100 (1921–2022 for observations).

In some CMIP models, the early decades of the tropical- averaged SST time series exhibit pronounced low-frequency drifts (Fig. S1). We use “zero padding” to address this issue (i.e., we set the tropical average SST to zero over the 1861–1920 period prior to applying the fourth-order polynomial fit. This process ensures that there is a near-zero trend in the early deca- des of the time series (Fig. S1).

b. ToE estimation methodology

Our method for calculating ToE is close to that of HS. At each grid point, we estimated the signal S(t) by performing a regression of the local SST or RSST, denoted as Y(t) (Fig. 2a, black line for an example based on the equatorial Pacific SST in one CMIP model), onto the tropical warming index W(t):

$$
Y(t) = \alpha W(t) + \beta + \varepsilon(t). \tag{1}
$$

The regression described above is performed over 1921–2100 (models) or 1921–2022 (observations). We will justify estimat- ing the climate change signal only based on post-1920 data in section 5c: data coverage is questionable before World War I (e.g., Deser et al. 2010) and leads to unstable ToD and ToE estimates. The intercept β is nearly zero due to zero-padding in the early decades. The ε(t) is the residual of the regression, representing natural climate variability. The signal (Fig. 2a dashed line) is defined as

$$
S(t) = \alpha W(t) + \beta. \tag{2}
$$

The noise N is defined as the standard deviation of ε(t). Fol- lowing HS, the ToE is defined as the “first” year when the signal-to-noise ratio, S(t)/N (dashed black line in Fig. 2a), crosses a specified threshold. The ToE approach is illustrated in Figs. 2a and 2c with a threshold of 1.6 (see section 3c for a justification of this choice) for the MRI-ESM2-0 model, which exhibits ToD values (section 3c) close to the CMIP5+6 median. The ToE map for this model indicates that tropical SST warming signals have either already emerged (before 2022) or will emerge within the next decade (Fig. 2c).

c. ToD estimation methodology

Unlike ToE, where the regression [Eq. (2)] is performed over the entire time series, the signal calculation for the ToD estimation is computed for a varying time window from 1921 to T. The variable T varies from 1922 to the endpoint year T_e (2100 for models and 2022 for observations). Specifically, we perform the regression for each time interval [1921, T], with T varying from 1922 to T_e:

$$
Y_T(t) = \alpha_T W_T(t) + \beta_T + \epsilon_T(t). \quad (3)
$$

Signals at time T are defined as

$$
S(T) = \alpha_T W_T(T) + \beta_T. \tag{4}
$$

ToD is defined as the “last” year when the regression coeffi- cient becomes statistically significant at a chosen significance level threshold (e.g., 95%) and remains significant until the endpoint year T_e. That is, we define a detectable signal at date T when the time series has a regression coefficient to the trop- ical warming index that is statistically significant over the [1921, T] period and remains significant for later endpoints.

To test the significance of the regression coefficient, we em- ploy a one-tailed t test. We estimate the “effective” number of degrees of freedom of the time series according to Bayley and Hammersley (1946) as n/∑1/2 ρ2 ≤ (jτ), where n is the size
<figure><img src="image_3.png" /><figcaption>FIG. 2. Illustration of the ToE and ToD computation methodology for SST in the MRI-ESM2-0 model. This model was chosen as an example because its ToD and ToE were close to the CMIP5+6 median values. (a) Time series of EEP [see box in (c) and (d)] SST relative to the 1891–1950 climatology (°C; black line) along with the anthropogenic warming signal computed following HS (dashed black line, see section 3 for details). The light gray shading indicates signals which are less than 1.6 times the noise *N* in absolute value. The vertical gray line marks the ToE for an *S/N* threshold of 1.6. (b) Average EEP SST anomaly and estimated warming signal as in (a) as well as the signal computed over a time-varying window [1921, *T*] (blue curve, see below and section 3c for details), and the associated statistical significance (red, see below and section 3c for details). The vertical red line indicates the ToD when statistical significance irreversibly exceeds some threshold, here set at 95%. Unlike HS, where the signal is derived through a regression to the warming index over the entire period, we compute the signal at a time *T* through a regression over the [1921, *T*] period (with *T* varied from 1922 to 2100). The red line indicates the statistical significance of the hypothesis that the regression slope is not zero. (c) ToE and (d) ToD maps for SST in this specific model.</figcaption></figure>

of the time series (i.e., *n* = *T* – 1921 + 1). The denominator is an estimate of the decorrelation time scale, derived from the lagged autocorrelations *ρ*(*j*τ) of the time series. For SST or RSST, the autocorrelation time scale is usually a bit more than 1 year, and results are not sensitive to using Bayley and Hammersley (1946) or simply one degree of freedom (DOF) per year minus 1 (not shown). Note that we compared our signal estimation method with the Theil–Sen robust estimator and our significance computation with a bootstrap method that does not require Gaussian input data (Yue and Pilon 2004; G20). Both comparisons yielded very similar results to our approach (Fig. S2 and G20), underlining the robustness of our methodology.

Figures 2b and 2d illustrate the ToD methodology using the same model as in Fig. 2a. In this case, the significance of the regression coefficient αT (red curve) crosses the 95% significance level shortly before 2020 for the eastern Pacific. The ToD indicates detectable tropical SST warming everywhere in the tropics (Fig. 2d).

There are a few differences between the ToD computation here and in G20: G20 used a linear trend instead of the non-linear tropical warming index, the 1891–2020 instead of the

1921–2022 period (we will demonstrate in section 5 that ToD and signal estimates are more robust over that data-richer period in observations), and they did not use the effective number of degrees of freedom above. We will discuss the differences between G20 and our results in the discussion.

For a normal distribution, statistical significance levels of 99%, 95%, 90%, and 85%, respectively, correspond to signal-to-noise ratios of 2.4, 1.6, 1.3, and 1 (based on the *t* distribution). The Fig. 2 example was provided for the comparable 1.6 *S/N* for ToE and 95% significance thresholds for ToD, indicating that ToD occurs earlier than ToE for comparable threshold values. This ToD/ToE comparison will be done more systematically in the following section.

4. Comparing time of detection and emergence for tropical SST

In this section, we compute the tropical SST ToD and ToE for CMIP5+6 models and four observational products. Our objectives include comparing ToD and ToE, examining their sensitivity to the chosen threshold, and comparing CMIP to observations. We will also investigate
<figure><img src="image_4.png" /><figcaption>FIG. 3. SST ToD vs ToE in CMIP5+6 and observations. SST ToD (95% threshold) vs ToE (1.6 S/N threshold) scatterplot (plotted as a density distribution for all grid points and datasets) for (a) CMIP5+6 models and (b) the four observational SST datasets. The 95% and 1.6 thresholds are comparable (see the end of section 3c for details). Percentage of the tropical ocean surface (for all grid points and datasets) where a signal is detectable (dashed lines: red for 99%, orange for 95%, green for 90%, and blue for 85% significance thresholds) or has emerged (solid lines: red for 2.4, orange for 1.6, green for 1.3, and blue for 1 S/N thresholds) in (c) CMIP5+6 models and (d) the four observational SST datasets.</figcaption></figure>

whether the inconsistent EEP trends in models and observations are detectable.

### a. Tropical SST ToD and ToE in CMIP and observations

Figures 3a and 3b display scatterplots of ToD versus ToE for CMIP and observed SST (across all models/datasets tropical grid points). ToD and ToE are, respectively, computed using comparable thresholds of 95% significance and 1.6 S/N ratio (see end of section 3c). The ToD and ToE are correlated ($r$ = 0.73 and 0.58 in CMIP and observations, respectively), indicating that regions where a signal is detected early also

tend to emerge from the background natural variability early. SST signals are generally detectable before they emerge from the background noise in both CMIP (67% of grid points across models) and observations (62%). The peak density concentration occurs primarily from 1960 to 2010 for ToD and from 1970 to 2022 for ToE. ToD is thus detected earlier than ToE at equivalent thresholds, with a median ToE minus ToD of 5 (6) years in models (observations). Consequently, the SST signal is already detectable (ToD ≤ 2022) almost everywhere in the tropics (97% of models and 93% of observational datasets grid points), while there are still regions where the SST signal has not emerged (9% in models, 22% in observations).
<figure><img src="image_5.png" /><figcaption>FIG. 4. Maps of SST ToD and ToE and their controls CMIP5+6 median SST (a) ToD (95% significance threshold), (b) ToE (1.6 S/N threshold), (c) noise, and (d) 2100 signal. Four observational datasets median (e) ToD (95% significance threshold), and (f) ToE (1.6 S/N threshold). The EEP box, as defined in Y22, is outlined by blue frames in (a), (b), (d), and (e). Black dots indicate regions where 75% or more of models/observations are already detectable or have emerged (i.e., ToD/ToE before 2022).</figcaption></figure>

Prior research has demonstrated that the ToE strongly depends on the chosen S/N threshold (e.g., Lyu et al. 2014). Let us explore the ToD sensitivity to the significance threshold. Figures 3c and 3d provide a comparison of the percentage of tropical areas with detectable/emerging signals using the comparable thresholds discussed at the end of section 3c: 1% and 85%, 1.3% and 90%, 1.6% and 95%, and 2.4% and 99%. This analysis reveals that ToE is more sensitive to the threshold choice than ToD for both models (Fig. 3c) and observations (Fig. 3d). For ToE, there is indeed a range of ~30 years for the two extreme signal-to-noise ratio thresholds, while ToD varies by only ~15 years. The tropical area where a signal is detected is systematically larger than that where it has emerged for comparable thresholds. Even the most stringent detection threshold (99%) results in an earlier detection than the 1.6 S/N threshold.

Figures 4a and 4b, respectively, display the median ToD and ToE maps for CMIP5+6 models, with black dots indicating regions where more than 75% of models have a ToD/ToE before 2022. The ToD and ToE spatial patterns are quite

similar. Warming is detected almost everywhere, except in the equatorial and southeast Pacific. It has emerged from the background climate variability in most regions, except in the equatorial and southeastern tropical Pacific.

Figures 4c and 4d, respectively, display the median noise and 2100 signal for CMIP models. The ToD and ToE patterns are very similar to that of the noise, with centered pattern correlations (i.e., mean removed) of 0.77 for ToD and 0.87 for ToE. In contrast, the pattern correlation with the signal is generally weak, with values of 0.03 for ToD and -0.11 for ToE. This indicates that the background climate variability has a more significant influence in shaping the SST ToD and ToE patterns than the amplitude of the signal. For instance, the large climate noise associated with ENSO in the eastern Pacific results in late ToE and ToD. The later ToD and ToE poleward of 20° latitude are also associated with increased noise, attributable to factors like oceanic eddies, midlatitude stochastic atmospheric forcing, and ENSO teleconnections (e.g., Alexander et al. 2002). The equatorial Indian Ocean tends to exhibit earlier detection and emergence due to its
lower noise levels (e.g., Guemas et al. 2013). These results are robust when analyzing CMIP5 and CMIP6 data separately (Fig. S4). The CMIP6 warming signal is larger than that of CMIP5 due to the higher climate sensitivity in CMIP6 (Figs. S4e,f; Fredriksen et al. 2023). However, the internal climate variability noise also tends to be slightly larger in CMIP6 compared to CMIP5 (Figs. S4g,h). These differences tend to compensate for each other, resulting in similar ToD and ToE in CMIP5 and CMIP6 although with slightly later emergence and detection times in CMIP6 (Fig. S4).

Figures 4e and 4f, respectively, provide the median ToD and ToE patterns for observations. The observed pattern resembles the one from CMIP although with approximately 1 to 2 decades earlier detection/emergence in regions such as the equatorial Indian Ocean, equatorial and South Atlantic, and west Pacific. In contrast, the equatorial Pacific warming is not detectable in the MOM (Fig. 4e), unlike in most CMIP models (Fig. 4a).

## b. Eastern equatorial Pacific focus

Numerous studies have underlined the EEP warming trend and the slowing down of trade winds in climate models (e.g., Xie et al. 2010; Power et al. 2021). Observations, on the other hand, point to a weak EEP warming trend or even a cooling, in response to increased trade winds. This discrepancy motivated Y22 to compute the EEP SST ToE. Below, we consider the same box as Y22: averaging SST within this box smooths small-scale noise and may result in an earlier detection/emergence than the Fig. 4 maps, based on pointwise data.

Figure 5a presents the median EEP warming signal in CMIP5+6 models, along with its 10th–90th percentile range. The median filters internal climate variability out, emphasizing the EEP warming signal, slightly above 1°C over the past century (Fig. 5a). Internal variability is very consistent across the four observational datasets. Figure 5b provides histograms of the 2022 EEP warming signal (continuous) and noise (dashed) for CMIP5+6 models. Vertical lines indicate the corresponding signal (continuous) and noise (dashed) for the four observational datasets. The level of observed ENSO climate noise is within the CMIP distribution. Three out of four observational datasets (Kaplan, HadISST, and COBE SST2) indicate modest warming of less than 0.5°C, which lies outside the simulated range (0.5°–1.7°C). ERSST displays a larger 0.75°C warming signal that is more consistent with the modeled range.

Y22 employed a smaller set of 23 models (69 here) and a less stringent S/N ToE threshold of 1 (1.6 here). Despite these differences, our results are consistent with Y22: approximately half of the models but no observational dataset indicate an emergent EEP warming (Fig. 5d). This led Y22 to argue for a model–observation discrepancy. Let us now discuss whether using ToD instead of ToE leads to a different interpretation. EEP warming signals are already detectable (Fig. 5c) in 91% of models (between 1980 and 2022), whereas only one out of four observational products detect the signal. The notable ERSST warming signal results in an early detection around 1992, at the early end of the modeled range. This

detection in ERSST is robust with a stricter 99% significance threshold (not shown). But overall, using ToD does not change the conclusions of Y22 and still points to overestimated warming signals in models, leading to more detection (or emergence) by 2022 than in observations.

## c. Section summary

In this section, we have compared the SST ToD (designed for comparing signals in models and observations) and ToE (more appropriate for impact studies). The SST ToD typically precedes ToE by 0–15 years for both CMIP and observations. This underscores the importance of accounting for the size of the sample when trying to detect a climate change signal. Tropical SST warming is already detectable almost everywhere in models and observations. One exception is the EEP, where the warming is detectable in over 90% of the models but only in one out of four observational datasets (with weaker warming signal amplitudes in observations than in models).

# 5. Time of detection of relative SST signals

RSST highlights the SST pattern and is a proxy for atmospheric stability (Xie et al. 2010). In this section, we compute the RSST ToD for CMIP5+6 and observations. We first compare ToD and ToE in CMIP models and observations. While ToE does not allow picking any emerging RSST signal in observations, ToD points to a detectable RSST warming in the western Indian Ocean and cooling in the southeastern Pacific. We therefore compare the model and observed signals in those two regions in more detail. We end by discussing observational uncertainties, related to the limited pre-1920 coverage.

## a. RSST ToD and ToE in CMIP5+6 and observations

Figure 6 is similar to Figs. 3a and 3b but for RSST. The relationship between RSST ToD and ToE (Fig. 6a) is weaker than that of SST (Fig. 3a) ($r = 0.5$ against 0.73 in CMIP; $r = 0.4$ against 0.58 in observations). These insignificant correlations indicate that the early detection of an RSST signal does not consistently correspond to an early emergence, unlike the case for SST. The temporal lag between ToE and ToD is also considerably larger for RSST (~35 years) than for SST (~5 years). RSST signals are almost always detectable before they emerge from the background noise in both CMIP (98%) and observations (93%). Consequently, the modeled (observed) RSST signal is already detectable on 16% (40%) of tropical oceans but has only emerged over 1% (14%). RSST becomes detectable in over 76% of the tropical oceans by the end of the twenty-first century in models, against 34% for ToE. These large differences between ToE and ToD arise from accounting for the number of degrees of freedom in the ToD computation. This makes the detection of signals more sensitive as the length of the time series, and therefore, the number of degrees of freedom "n" increases, effectively reducing the noise level by a factor of $1/\sqrt{n}$. ToD will thus indicate a much earlier date than ToE for signals which tend to emerge late, such as RSST (G20).
<figure><img src="image_6.png" /><figcaption>FIG. 5. Eastern Pacific SST warming. (a) Time series of average EEP (box in Fig. 4) yearly SST anomalies (°C; relative to the 1891–1950 climatology) for the four observational datasets (red for HadISST, blue for ERSST, yellow for Kaplan, and purple for COBE), along with average EEP CMIP5+6 median SST signal (black) and 10th–90th percentile (light gray shading). (b) Histogram of CMIP5+6 average EEP SST noise (dashed black) and signal (black) in 2022. Vertical lines mark the corresponding values for observational products (continuous for signal and dashed for noise). (c) Histogram of CMIP5+6 average EEP SST ToD (95% threshold) in 5-yr bins, with the solid gray line indicating the percentage of models for which the EEP warming is already detectable. Vertical lines indicate ToD for the four observational products. (d) As in (c), but for ToE (1.6 S/N threshold).</figcaption></figure>

Figure 7a displays the median map of the CMIP5+6 ToD, with black dots indicating grid points where more than 75% of models have ToD/ToE before 2022. While SST signals are already detectable in nearly all tropical areas (97%), RSST signals are only currently detectable in a few regions (16%), specifically the southeastern Pacific and western Indian Ocean. On average, RSST signals become detectable 60–70 years later than SST signals (also a result of G20). As detailed in G20, this is because RSST signals are considerably weaker (Fig. 7d) than SST signals (Fig. 4d), as the mean tropical warming signal is removed when calculating RSST, but the noise (interannual SST variability) is the same for SST and RSST. This smaller signal but similar noise for RSST leads to a later detection (and emergence) than for SST. The late RSST emergence and detection imply a longer time series, more degrees of freedom, and therefore a larger difference between ToD and ToE for RSST. By the end of the twenty-first century, RSST signals become detectable in most regions (76%) (Fig. 7a).

The RSST ToD spatial pattern is very different from that of SST (−0.09 pattern correlation). Contrary to SST, the ToD RSST pattern is largely controlled by that of the signal

amplitude (−0.73 pattern correlation), rather than that of the noise (0.05 pattern correlation). This leads to earlier detection in regions of large RSST signals such as the southeastern Pacific, western Indian Ocean, and equatorial Atlantic. The central equatorial Pacific is an exception: the signal is large, but the ENSO-related noise delays detection.

Figure 7b displays the median ToD map based on observations. Consistent with CMIP results (Fig. 7a), observed signals are detected in two main regions: the southeastern Pacific and the equatorial Indian Ocean (but shifted east relative to CMIP). We investigate these two regions in the following subsection.

### b. Regional focus

Figure 8a presents the CMIP5+6 median southeastern Pacific RSST evolution and its 10th–90th percentiles. The CMIP RSST signal started decreasing after 1980, reaching −0.2°C in 2022. All observational datasets align with the timing and amplitude of this CMIP relative cooling. Figure 8b provides an RSST ToD histogram for this region. The SEP relative cooling is detected before 2022 in ~80% of the models, with ToD ranging from 1970 to 2022. Observed ToD values (ranging from 1990 to 2015) fall within the CMIP distribution.
<figure><img src="image_7.png" /><figcaption>FIG. 6. RSST ToD vs ToE in CMIP5+6 and observations. RSST ToD (95% threshold) vs ToE (1.6 S/N threshold) scatterplot (plotted as a density distribution for all grid points and datasets) for (a) CMIP5+6 models and (b) the four observational SST datasets. The 95% and 1.6 thresholds are comparable (see the end of section 3c for details).</figcaption></figure>

This agreement can be attributed to the consistent signal and noise levels in models and observations (Fig. 8c).

Figure 8d displays the model and observed WIO RSST evolution. The observed relative warming is about 4 times larger than that of the CMIP MMM (Fig. 8d) and above the modeled

range (Fig. 8f). This leads to a consistently earlier ToD in observations (in the 70s) than in models (mostly after the 90s, with only 45% of detectable signals today; Fig. 8e).

Overall, this subsection points to detectable warming pattern signals that are consistent in observations and models in

<figure><img src="image_8.png" /><figcaption>FIG. 7. Maps of RSST ToD and their controls. Median RSST ToD (95% threshold) for (a) CMIP5+6 and (b) the four observational datasets. Black dots indicate regions where 75% or more models/observations are already detectable or have emerged by 2022. The blue frames in (a) and (b) indicate the WIO and SEP boxes for observations and CMIP RSST ToD. CMIP5+6 median RSST (c) noise and (d) 2100 signal.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>FIG. 8. SEP and WIO average RSST ToD. (a) Time series of annual mean average SEP (see Fig. 7) RSST anomalies (°C; relative to the 1891–1950 climatology) for the four observational products (red for HadISST, blue for ERSST, yellow for Kaplan, and purple for COBE), along with average SEP CMIP5+6 median RSST signal (black) and 10th–90th percentile (light gray shading). (b) Histogram of CMIP5+6 average SEP RSST ToD (95% threshold) in 5-yr bins, with the solid gray line indicating the percentage of models for which the SEP relative warming is detectable. Vertical lines indicate ToD for the four observational products. (c) Histogram of the CMIP5+6 average SEP RSST noise (dashed black) and 2022 signal (continuous black). The corresponding observational product values are marked by vertical lines (continuous for signal and dashed for noise). (d)–(f) As in (a)–(c), but for WIO RSST.</figcaption></figure>

the southeastern tropical Pacific (relative cooling) and in the western Indian Ocean (relative warming).

### c. *Observational uncertainties*

The observed ToD is highly sensitive to the observational dataset: the equatorial Pacific SST ToD, for instance, varies between 1992 and no detection (section 4b). This uncertainty likely stems from the limited observational coverage before

the satellite era, which started in 1979. Figure 9 illustrates the observed ToD sensitivity to the trend estimation starting date, varied from 1890 to 1980, for the EEP SST (Fig. 9a) and SEP (Fig. 9b) and WIO (Fig. 9c) RSST.

Throughout the paper, we have estimated ToD (and ToE) for post-1921 (vertical line in Fig. 9) data. This choice is partly guided by the data gaps during the World War I period (e.g., G20; Deser et al. 2010; Izumo et al. 2014). Figure 9 confirms a
<figure><img src="image_10.png" /><figcaption>FIG. 9. Observational ToD uncertainties: ToD (95% significance) sensitivity to the starting date of the estimation period (varied from 1890 to 1980, with the end of the period set to 2022) for four observational products (red for HadISST, blue for ERSST, yellow for Kaplan, and purple for COBE) for (a) EEP SST, (b) SEP RSST, and (c) WIO RSST. The vertical gray line indicates 1920, the starting date that is considered for estimating ToD and ToE throughout the paper.</figcaption></figure>

substantial ToD sensitivity to starting dates before 1921 in the SEP for Kaplan (Fig. 9b) and in the WIO for Kaplan and COBE SST2 (Fig. 9c) with ERSST before the 1930s. Considering data prior to 1921 also leads to a dubious pre-1940 warming detection in the South tropical Atlantic in all observational products (Fig. S3). This justifies our consistent use of the 1921 start date throughout the paper.

The EEP SST warming ToD for the ERSST dataset (the only dataset for which a warming is detected) is robust (i.e.,

insensitive to choosing any starting date). The SEP relative cooling ToD is robust for post-1920 starting dates, with clear detection in the four products for start dates until 1970 (Fig. 9b). In contrast, the ToD for the WIO relative warming is very sensitive to the starting date (Fig. 9c). This sensitivity is related to two periods of fast warming in the WIO during 1900–20 and shortly after 1960 (Fig. 8d). Those fast and early signals are very unlikely attributable to anthropogenic forcing (they occur before the strong anthropogenic forcing period) and are probably rather attributable to large data gaps in the Indian Ocean during both World Wars (Deser et al. 2010; G20), which may be responsible for those “jumps” in all observational time series (Fig. 8d). Restricting the period to post-1960 higher quality data only yields detection in a single observational dataset (Fig. 9c) and weaker signals that are more consistent with those in models (not shown). The observed WIO relative warming detection is therefore questionable (e.g., G20).

### d. Section summary

In this section, we have demonstrated that departures from the mean tropical warming are already detectable in observations and CMIP models in two regions: the western Indian Ocean (where observed detectability is questionable due to large pre-1960 data gaps) and the southeastern Pacific (where the observed detectability is very robust and modeled and observed signals agree well). The larger signal-to-noise ratio thresholds used in the ToE method did not allow identifying an emerging RSST signals in those regions. This, therefore, supports the view that, by allowing the detection of subtle signals, ToD is more appropriate than ToE for comparing models with observations.

## 6. Summary and discussion

### a. Summary

Evaluating the ability of models to detect even subtle climate change signals observed in nature is essential for assessing their realism and increasing our confidence in their future projections. This goal is contingent upon determining if these signals can be distinguished from the background natural variability. To that end, we introduce ToD, measuring when the fit of a local time series to a nonlinear tropical average warming index becomes and stays statistically significant. Unlike ToE which relies on a signal-to-noise ratio, ToD adjusts this ratio based on the effective number of degrees of freedom in the times series, enabling the detection of subtle signals in long time series. ToD is meant to detect subtle signals that do not emerge using the standard ToE definition.

We have computed ToD and ToE for SST and RSST (a proxy for the warming pattern and for changes in atmospheric stability and circulation) in four observational datasets and 69 CMIP5/6 historical and future simulations under the RCP8.5/SSP5-8.5 scenarios. Our analysis excludes pre-1921 data due to the scarcity of observations during this period. ToD is less sensitive to the chosen significance level than ToE is to the selected signal-to-noise threshold. ToD and ToE patterns are
relatively similar and determined by the noise level for SST and by the signal amplitude for RSST. However, for comparable thresholds, detection precedes emergence, with a lead of ~5 years for SST and ~35 years for RSST.

The tropical SST warming signal is detectable everywhere before 2022 in models and observations, except in the equatorial Pacific. There, warming is detectable in 91% of models, but only in one (ERSST) of the four observed datasets due to weaker observed warming signals than in models (Fig. 10a). This detection of an equatorial Pacific warming in ERSST is robust to the trend estimation period.

RSST signals are considerably smaller than SST signals (due to the tropical average warming signal subtraction) but with the same noise level (associated with SST internal variability). Consequently, RSST detection lags that of SST by ~60-70 years. And while SST signals have not emerged, two regions exhibit detectable RSST signals in observations and models. An RSST cooling is already detectable in the southeastern tropical Pacific in all observational datasets and ~80% of the CMIP5+6 models. This observed detection is robust, with consistent signal amplitudes with models (Fig. 10c). An RSST warming trend has been detectable in the western Indian Ocean since the second half of the twentieth century in observations but only after the eighties in ~45% of the models. This observed RSST warming detection is sensitive to the trend estimation period, with detection in one dataset only when excluding dubious pre-1960 data (Fig. 10b). Overall, the EEP SST and WIO RSST signals are only detectable in one out of four observational datasets. In contrast, the southeastern Pacific relative cooling detection is robust in observations, and the observed signals' amplitude agrees with the modeled ones. The SEP is therefore an appropriate region to serve as a testbed to evaluate the ability of climate models to replicate regional warming trends. In the next subsection, we discuss the implications of these results for the realism of circulation changes projected by CMIP models.

By applying a rigorous statistical significance test, which reduces the critical signal-to-noise ratio as the length of the considered time series increases, the ToD framework allows the detection of subtle signals that have not yet emerged. This is for instance the case for the observed southeastern tropical Pacific relative cooling, allowing it to confirm consistent signals in models in this region. ToD is therefore more appropriate than ToE for comparing models with observations, while ToE (which focuses on larger signals) is more adapted for impact studies.

## b. Discussion

The ToD methodology was originally applied to the Indian Ocean warming by G20. The present study refines the ToD methodology in (i) adopting a nonlinear instead of a linear trend estimate, (ii) estimating trends since 1921 rather than since 1891, and (iii) incorporating an improved estimate of the effective number of degrees of freedom (Bayley and Hammersley 1946). The use of a linear trend tends to underestimate signal and overestimate noise, delaying detection. Section 5c also demonstrates that excluding the data-poor

1891-1920 period makes the ToD estimates more robust. We thus estimate that our refined method is more robust than that in G20. Moreover, G20 used a different significance threshold (90% instead of 95%), focused on regional warming differences (Arabian Sea minus the Bay of Bengal, or western minus eastern IO) instead of RSST, and different averaging boxes. It is thus difficult to compare the results between the two studies. Both studies, however, point to a broad observed relative warming in the western IO, which is sensitive to the trend estimation period (Fig. 10b).

We find a robust southeastern tropical Pacific relative cooling in observations and models since the eighties (Fig. 10c). This early detection matches the early emergence of decreasing sea level signals in the south tropical Pacific (Lyu et al. 2014). The SEP relative cooling is attributed to the poleward expansion of the Southern Hemisphere Hadley cell since 1979 (Belmadani et al. 2014; Jebri et al. 2020), a response attributed to ozone depletion and rising concentration of greenhouse gases (e.g., Grise et al. 2019). This expansion intensifies the southeastern Pacific trade winds, coastal upwelling, and evaporative cooling, thereby tempering the warming trend in this area (Power et al. 2021). Our results furthermore indicate a similar timing between this cooling trend and the reported Hadley cell shift. Overall, these results provide strong evidence for a detectable poleward expansion of the Hadley cell in response to anthropogenic forcing.

We identified a WIO relative warming in all observational datasets, but its detection is sensitive to the trend estimation period, with weaker signals and detection in only one out of four datasets when excluding pre-1960 dubious data. This may explain the mismatch with the weaker relative warming that is only detectable in 45% of models (Fig. 10b). This enhanced warming is potentially important, as it has been linked to the Indian monsoon rainfall observed decreasing trend (Roxy et al. 2015). This relative warming has either been linked to the WIO thermocline deepening in response to a slowdown of the Indian Ocean branch of the Walker cell (Dong et al. 2014; Vecchi and Soden 2007b), enhanced downwelling longwave radiation (Xie et al. 2010; Zhang and Li 2014), or an increase in the frequency of positive IOD (Rao et al. 2012) or El Niño events (Roxy et al. 2014). Li et al. (2016) have questioned the realism of this modeled WIO relative warming, connecting it to present-day biases within CMIP models. The limited detection in models, the sensitivity of the observational results, and the potential impacts of model biases all question the reality of this relative WIO warming. While plausible, more research is required to confirm its reality.

Recent studies have underlined the inconsistency between the EEP observed cooling and CMIP warming trends over recent decades. While some interpret the observed cooling trend as internal variability associated with the interdecadal Pacific oscillation (Chung et al. 2019; Watanabe et al. 2020), others question the accuracy of CMIP projections (Kociuba and Power 2015; Seager et al. 2022). This mismatch might stem from the model underestimating processes that impede EEP warming. An example is the ocean thermostat (Clement et al. 1996), by which upwelling of cold deep water counters
Summary of Regional signals detection in observation and models

<figure><img src="image_11.png" /><figcaption>FIG. 10. Summary of regional SST and RSST signals detection in models and observations for selected boxes. Average 2022 SST signal (whiskers; °C relative to 1891–1950) and percentage of detection before 2022 (pie charts, percentage-based 95% threshold ToD) for (a) EEP SST, (b) WIO RSST, and (c) SEP RSST. The sign of the SST/RSST signal is indicated by shading (red for warming and blue for cooling) and the overall agreement between model and observation by a tick mark (agree) or question mark (partial agreement).</figcaption></figure>

surface anthropogenic warming. Alternatively, this discrep-
ancy could result from an overestimation of processes that
amplify the warming, such as the evaporative damping reduc-
tion over the cold EEP or cloud feedback (Power et al. 2021).
Differing from most previous studies that focused on recent
decades, our analysis spans the entire 1921–2022 period. We
identified a weaker EEP warming trend in the four observa-
tional products than in models, detectable in only one of them
for which the warming lies in the lower range of CMIP models
(Fig. 5b). This aligns with previous studies pointing to an
overestimated eastern Pacific warming in models.

To develop this point, Fig. 11 displays the average 2022 and
2100 warming and ToD maps for the 10 models with, re-
spectively, the weakest and strongest 2022 EEP warming.
In the “weakest” group, the tropical Pacific warming pattern

displays weaker warming in the EEP region, resembling obser-
vations (Fig. 1b). Conversely, models in the “strongest” group
(Fig. 11b) display an enhanced EEP warming. Both groups con-
verge toward an enhanced EEP warming (relative warming)
by the end of the twenty-first century, albeit with a larger
amplitude in the strongest group. This result can be inter-
preted as an initially stronger oceanic thermostat in the
weakest group that later becomes less efficient as the warm-
ing signal makes its way to the equatorial thermocline
(Heede and Fedorov 2021, 2023) so that all models simulate
enhanced equatorial warming by the end of the twenty-first
century. Additionally, models in the weakest group show a
ToD near 2020 in the EEP region (2021 median vs 2000 for
the strongest group), aligning with an observed warming
trend on the brink of detection.
<figure><img src="image_12.png" /><figcaption>FIG. 11. Tropical SST warming pattern diversity in CMIP5/6. Average SST warming pattern in (a) 2022, (c) 2100, and (e) corresponding ToD for the 10 models with the weakest 2022 EEP warming. (b), (d), (f) As in (a), (c), and (e), but for the 10 models with the largest 2022 EEP warming. The 10 models with the strongest and weakest 2022 EEP warming are listed in Table S1.</figcaption></figure>

A CMIP5+6 subset is thus quite consistent with observed SST trends, with subdued EEP warming, potentially linked to the ocean thermostat mechanism (Heede and Fedorov 2021, 2023). But what about the longer-term Walker cell weakening and “El Niño-like” warming pattern common to most CMIP models? Our results indicate that the EEP relative SST warming will not be detectable before several decades, due to the strong ENSO “climate noise.” Turning our attention to the Indian Ocean branch of the Walker cell might offer insights. The borderline detection of an observed WIO warming in our results may point to a zonal circulation that has already weakened in that basin. As changes in the Walker Cell exert significant impacts on the global climate, further research is needed to unravel their mechanisms in models and observations.

**Acknowledgments.** This work is an integral part of the Ph.D. thesis of G. S. registered at the School of Earth, Ocean and Atmospheric Sciences of Goa University, and the CSIR-National Institute of Oceanography (CSIR-NIO), G. S. acknowledges the Council of Scientific and Industrial Research (CSIR), New Delhi, for funding her Ph.D. We thank the director of CSIR-NIO and the vice chancellor of Goa University for their support. I. S. acknowledges funding from CSIR, New Delhi, under the climate change project. The authors acknowledge the funding from Institut de Recherche pour le Développement (IRD). The authors also acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and the climate modeling groups (listed in Table S1) for producing and making their model outputs available. This is NIO contribution 7284.

**Data availability statement.** The sea surface temperature observational datasets were obtained from multiple sources, including COBE-SST2 (available at https://psl.noaa.gov/data/gridded/data.cobe2.html and https://ds.data.jma.go.jp/goos/data/pub/JMA-product/cobe2_sst_glb_M/), the HADISST

(available at https://www.metoffice.gov.uk/hadobs/hadisst/data/download.html), the ERSSTv5 (available at https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html), and the Kaplan-SST (available at https://psl.noaa.gov/data/gridded/data.kaplan_sst.html). The CMIP simulations used in this study can be downloaded from CMIP5 search interface (https://data.ceda.ac.uk/badc/cmip5/ or https://esgf-node.llnl.gov/search/cmip5/) and CMIP6 search interface (https://data.ceda.ac.uk/badc/cmip6/ or https://esgf-node.llnl.gov/projects/cmip6/). The code used to produce all the figures can be obtained upon request to the corresponding author.

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