10.1029/2022GL100574
Key Points:• A
 common method for isolating
the internal component of Atlantic
Multidecadal Variability is to remove
fluctuations associated with globalmean temperature• This method introduces spurious
Indo-Pacific connections in model
Large Ensembles and observations
due to internal variations in globalmean temperature• A revised method based on removing
fluctuations associated with theforced component of global-meantemperature mitigates this issue
Supporting Information:

Supporting Information may be found in
the online version of this article.
Correspondence to:
C. Deser,cdeser@ucar.edu
Citation:

Deser, C., & Phillips, A. S. (2023).
Spurious Indo-Pacific connections tointernal Atlantic Multidecadal Variability
introduced by the global temperature
residual method. Geophysical Research
Letters, 50, e2022GL100574. https://doi.
org/10.1029/2022GL100574
Received 24 JUL 2022
Accepted 14 JAN 2023
Author Contributions:Conceptualization: Clara Deser
Data curation: Adam S. Phillips
Formal analysis: Clara Deser
Investigation: Clara Deser
Methodology: Clara Deser
Software: Adam S. Phillips
Visualization: Adam S. Phillips
Writing – original draft: Clara Deser© 2023. The Authors.
This is an open access article under
the terms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

DESER AND PHILLIPS

Spurious Indo-Pacific Connections to Internal Atlantic
Multidecadal Variability Introduced by the Global
Temperature Residual Method
Clara Deser1

and Adam S. Phillips1

National Center for Atmospheric Research, Boulder, CO, USA

1

Abstract The relative contributions of external forcing and internal processes to the observed spatial andtemporal characteristics of “Atlantic Multidecadal Variability” (AMV) are still under debate. Here, the efficacyof the commonly-used “global temperature residual method” for isolating the internal component of AMV isinvestigated by means of model Large Ensembles where the truth is known a priori. In this method, local sea
surface temperature variability associated with global-mean temperature (G) is removed via linear regression,and the residuals regressed upon the North Atlantic residual timeseries. We show that this method introduces
spurious connections over the Indo-Pacific due to the fact that G in any single realization includes both external
and internal components: the latter dominated by influences from Pacific Decadal Variability independent of
AMV. This methodological shortcoming can be overcome by using the forced component of G in the residual
method applied to individual model realizations and to observations.
Plain Language Summary The phenomenon known as “Atlantic Multidecadal Variability”(AMV) has been widely studied and has important climate effects over Africa, Asia, Europe, and eastern North
America. Recently, there has been considerable debate regarding the relative contributions of natural processes
within the coupled ocean-atmosphere system versus human influences related to aerosol emissions on thespatial and temporal character of AMV. An accurate separation of these natural and anthropogenic contributions
has proven challenging due to limitations of the data record. Statistical techniques aimed at isolating the naturalcomponent of AMV often yield conflicting results. Here, we investigate one widely-used approach based on
removing variability associated with global-mean temperatures. We show that the conventional applicationof this method aliases another well-known phenomenon, “Interdecadal Pacific Variability,” onto the patternof natural AMV. However, with a simple modification to the method, the true pattern of natural AMV can berecovered.
1. Introduction
The climate phenomenon known as “Atlantic Multidecadal Variability” (AMV) is characterized by basin-scale
fluctuations in sea surface temperatures (SSTs) over the North Atlantic, accompanied by changes in atmosphericcirculation and associated hydrological impacts over Africa, Europe, and eastern North America [for example,
Zhang et al., 2019 (Z19) and references therein]. The spatial and temporal characteristics of AMV derive fromprocesses internal to the coupled ocean-atmosphere coupled system, and are also influenced by external radiative
forcing, primarily anthropogenic aerosols [for example, Qin et al., 2020 (Q20) and references therein]. However,quantifying the relative contributions of internal and external drivers of AMV remains an ongoing challenge, with
implications for prediction. Statistical approaches aimed at separating forced and internal components of observed
AMV are sensitive to methodological choices, leading to conflicting results (e.g., Frankignoul et al., 2017). In
particular, simple procedures such as subtracting global-mean temperature (Trenberth & Shea, 2006) or linear
detrending (Enfield et al., 2001; Murphy et al., 2017) alias the pattern of forced climate change onto the structure of internal AMV (iAMV) as shown by Deser and Phillips (2021; hereafter DP21) and Baek et al. (2022).
The modeling framework of “Single Model Initial-condition Large Ensembles” (LEs; Deser et al., 2020), which
provides a priori knowledge of forced and internal contributions in any individual simulation, has served as aneffective testbed for evaluating these and other methods (Baek et al., 2022; DP21; Frankignoul et al., 2017; Q20).
Another simple and widely-used empirical technique for isolating iAMV (and internal variability in general) is
the “global temperature residual method” (G-Res method), which employs linear regression analysis to remove
variability at each location that is linearly congruent with variability in global-mean SST (G; DP21; Q20; Yan
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10.1029/2022GL100574

et al., 2019; Z19). The resulting “residual” SST anomalies are then used to construct an iAMV index timeseries[typically, the North Atlantic (NA; 0°–60°N, 80°W–0°E) area-average], and an associated iAMV spatial patternobtained by regressing the residual SSTs onto the iAMV index. The rationale behind this approach is that variations in G are mainly a reflection of external radiative forcing, making it a convenient metric for tracking the
temporal evolution of forced climate change. The extent to which internal variations in G (henceforth, iG) affectthe efficacy of the G-Res method has not been elucidated, apart from Q20 who noted its impact on the inferred
iAMV timeseries in observations. The purpose of this study is to explicitly clarify the impact of iG on the spatial
pattern of simulated and observed iAMV, using LEs from multiple global coupled climate models as a methodological testbed.

2. Data and Methods
2.1. Model LEs and Observational Data
We analyze seven global coupled model LEs with ensemble sizes ranging from 30 to 100 and spanning the years
1950–2100 under historical and future radiative forcing (see Table S1 in Supporting Information S1 for modeland forcing details). We also make use of gridded observational products of SST, sea level pressure (PSL),
and terrestrial precipitation (PR) spanning 1950–2020 (Table S2 in Supporting Information S1). We computemonthly anomalies by subtracting the long-term (1950–2020 or 2030–2100) mean for each month separately,
form annual averages from the monthly anomalies, and apply a 10-year low-pass Butterworth filter. All data sets
are bi-linearly interpolated to the nominal 1° spatial resolution of Community Earth System Model version 2.
2.2. Methods
The true internal component (i) of low-pass filtered annual SST, PSL, and PR anomalies in each ensemble
member of a given model LE are defined as:iSST(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥) = SST(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥)–SST(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥𝑥𝑥)



iPSL(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥) = PSL(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥)–PSL(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥𝑥𝑥)

iPR(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥) = PR(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥)–PR(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥𝑥𝑥)

where x is grid box location, t is time, e is ensemble member, and em is the ensemble-mean.
The estimated internal component of low-pass filtered annual SST, PSL, and PR anomalies based on the G-Res
method are computed as:gresSST(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥) = SST(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥)–𝐺𝐺(𝑡𝑡𝑡𝑡𝑡) × GSSTreg(𝑥𝑥𝑥 𝑥𝑥)

gresPSL(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥) = PSL(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥)–𝐺𝐺(𝑡𝑡𝑡𝑡𝑡) × GPSLreg(𝑥𝑥𝑥 𝑥𝑥)

gresPR(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥) = PR(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥)–𝐺𝐺(𝑡𝑡𝑡𝑡𝑡) × GPRreg(𝑥𝑥𝑥 𝑥𝑥)

where G(t,e) is the global-mean (60°N-60°S) SST, GSSTreg(x,e) is the linear regression of SST(x,t,e) ontoG(t,e), GPSLreg(x,e) is the linear regression of PSL(x,t,e) onto G(t,e), and GPRreg(x,e) is the linear regression ofPR(x,t,e) onto G(t,e).
We next construct iAMV indices for each ensemble member of a given model LE by computing NA area-weighted
averages of iSST(x,t,e) and gresSST(x,t,e), hereafter referred to as iNA(t,e) and gresNA(t,e), respectively. To
compute the spatial patterns of iAMV in each ensemble member of a given model LE, we linearly regress iSST(x,t,e),
iPSL(x,t,e), and iPR(x,t,e) onto the standardized iNA(t,e); similarly, we regress gresSST(x,t,e), gresPSL(x,t,e),
and gresPR(x,t,e) onto the standardized gresNA(t,e). These sets of regression maps will be referred to as
iAMVtruthNA and iAMVgres, respectively. To enhance the robustness of the patterns, we then average the regression maps across the individual members of a given model LE, denoted [iAMVtruthNA] and [iAMVgres]. We also
compute the multi-model LE (MMLE) average of the seven [iAMVtruthNA] and [iAMVgres] regression maps.
By construction, gresSST(x,t,e), gresPSL(x,t,e), and gresPR(x,t,e) contain no global-mean component.
Thus, in order to provide an “apples-to-apples” comparison of the G-Res and Truth methods, we define
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Geophysical Research Letters10.1029/2022GL100574

Figure 1. Multi-model Large Ensemble internal Atlantic Multidecadal Variability (iAMV) regression maps for sea surface
temperature (SST) (color shading) and sea level pressure (PSL) (contours; negative values dashed) based on 1950–2020 using
the following methods: (a) [iAMVgres]; (b) [iAMVtruthNA-G]; (c) [iAMVfgres]; (d) [iAMVtruthNA]; (e) a–c; (f) b–d. See text
for explanation.

iSST*(x,t,e) = iSST(x,t,e) – iG(t,e), where iG(t,e) is the global-mean (60°N-60°S) of iSST(x,t,e) (and similarly for iPSL and iPR), as well as a new index iNA*(t,e) = iNA(t,e) – iG(t,e). We then construct regression
maps of iSST*(x,t,e), iPSL*(x,t,e), and iPR*(x,t,e) onto the standardized iNA*(t,e), denoted iAMVtruthNA-G (and[iAMVtruthNA-G] for the ensemble mean).
For a given model LE, G(t,e) can be decomposed into a forced component fG(t), estimated as G(t,em), and an internal component iG(t,e), estimated by subtracting G(t,em) from G(t,e). The term iG(t,e) can be further decomposed
into a part that is congruent with iNA(t,e) [denoted iGNA(t,e) and obtained by scaling iNA(t,e) by the regressionof iG(t,e) onto iNA(t,e)], and a part that is orthogonal to iNA(t,e) [denoted iG*(t,e) and obtained by subtractingiGNA(t,e) from iG(t,e)]. Unless stated otherwise, all pattern correlations (r) are based on area-weighted data overthe global domain (60°N-60°S). “Interdecadal Pacific Variability” (IPV; Power et al., 1999) is defined as theleading Empirical Orthogonal Function of low-pass filtered iSST over the domain (40°S-60°N, 110°E-70°W). A
glossary of acronyms is provided in Table S3 in Supporting Information S1.

3. Results
3.1. G-Res Method Versus Truth
Figure 1a shows the MMLE [iAMVgres] regression maps for SST and PSL over the period 1950–2020. The
large number of simulations across the seven model LEs (420 in total) used to construct these fields ensures
their robustness to sampling and model uncertainty (note that there is also good structural agreement amongst
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Geophysical Research Letters10.1029/2022GL100574

the individual model LE [iAMVgres] regression maps; Figure S1 in Supporting Information S1). The MMLE
[iAMVgres] patterns exhibit canonical signatures of AMV in the Atlantic sector, with horseshoe-shaped warming
north of the equator and weaker cooling to the south, accompanied by a dipole structure in PSL over the North
Atlantic that resembles the negative phase of the North Atlantic Oscillation (NAO; Figure 1a). They also showprominent expression in the Pacific reminiscent of the negative phase of IPV, with negative SST anomalies in thetropics and extending poleward along the eastern sides of the basin, accompanied by anticyclonic PSL anomalies
in midlatitudes and cyclonic anomalies farther poleward in both hemispheres.
The MMLE [iAMVgres] regression patterns are very similar to those based on MMLE [iAMVtruthNA-G] (r = 0.96
for SST and 0.98 for PSL), with some small (∼25%) differences in amplitude over the Pacific sector (Figure 1b).
This close resemblance attests to the high skill of the G-Res method in isolating the true structure of iAMV in the
MMLE; high skill (r generally >0.9) is also found for each model LE individually (compare Figures S1 and S2
in Supporting Information S1, and see Table S4a in Supporting Information S1).
The MMLE [iAMVtruthNA] regression patterns display striking differences from [iAMVtruthNA-G] outside of theAtlantic sector, with anomalies generally of opposite sign and weaker magnitude (Figure 1d). In particular, theformer shows positive and eastward-intensified SST anomalies in the tropical Pacific accompanied by nega tive
(positive) PSL anomalies in the Gulf of Alaska (Amundsen-Bellinghausen Seas), whereas the latter shows negative and westward-amplified tropical Pacific SST anomalies, accompanied by regional PSL features that are
opposite in sign and displaced equatorward and westward. Qualitatively similar contrasts between [iAMVtruthNA]and [iAMVtruthNA-G] are found for each model LE individually (Figure S2 in Supporting Information S1). We
emphasize that there is no a priori physical justification for using iAMVtruthNA-G to define iAMV; our purpose
here is to simply provide an “apples-to-apples” comparison with [iAMVgres], which implicitly removes variability associated with G(t,e).
The stark differences between the MMLE [iAMVtruthNA] and [iAMVtruthNA-G] regression patterns indicate thatiSST associations with iG(t,e) dominate over those with iNA(t,e) in regions outside the Atlantic (and vice versa
within the Atlantic). To explicitly highlight the influence of iG(t,e), we plot the difference between MMLE
[iAMVtruthNA] and MMLE [iAMVtruthNA-G] (Figure 1f). This difference map is dominated by a negative
IPV-like structure, evidenced by the high pattern correlations with the MMLE [IPV] (r = 0.94 for SST and 0.98
for PSL). That the difference map resembles IPV is not surprising, given the extensive literature documenting its
association with internal variations in observed and simulated G (e.g., Dai et al., 2015; Kosaka & Xie, 2013). The
salient point here is that the G-Res method implicitly removes variability associated with IPV (via iG), thereby
imparting a spurious negative IPV-like structure to iAMV. This distortion of iAMV by IPV in the G-Res method
is also found for each model LE individually (Figure S2 in Supporting Information S1).
As discussed in Section 2.2, iG(t,e) is the sum of iGNA(t,e) and iG*(t,e). Thus, the difference map in Figure 1f
reflects not only the association of iSST(x,t,e) with iG*(t,e), but also its association with iGNA(t,e). However,
because the standard deviation (σ) of iGNA is small (<10%) compared to that of iG* (both for the MMLE and foreach individual model LE), the difference map is dominated by variability associated with iG*(t,e).
Here, we propose a reformulation of the G-Res method such that only fluctuations associated with the forced
component of G(t,e) are removed, thereby circumventing the issues discussed above. This “forced-G” Residual
Method (hereafter, “fG-Res method”) is defined as follows:

fgresSST(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥) = SST(𝑥𝑥𝑥 𝑥𝑥𝑥 𝑥𝑥)–fG(𝑡𝑡) × fGreg(𝑥𝑥𝑥 𝑥𝑥)

where fGreg(x,e) is the linear regression of SST(x,t,e) onto fG(t) for a given model LE; similar equations wereobtained for PSL and PR. We then define fgresNA(t,e) as the NA area-average of fgresSST(x,t,e), and construct
iAMV maps for each ensemble member by regressing fgresSST(x,t,e) (and the analogous PSL and PR fields)
onto the standardized fgresNA(t,e) index. These regression maps are referred to as iAMVfgres.
The MMLE [iAMVfgres] and [iAMVtruthNA] regression patterns are nearly identical (r = 0.98 for SST and
0.97 for PSL), demonstrating the high skill of the fG-Res method (compare Figures 1c and 1d); similar skill isfound for each individual model LE (Table S4b; Figures S1 and S2 in Supporting Information S1). Differencing MMLE [iAMVfgres] from MMLE [iAMVgres] reveals the impact of iG on the pattern of iAMV estimatedwith the G-Res method. This difference map (Figure 1e) is nearly identical to that between [iAMVtruthNA] and[iAMVtruthNA-G], with r = 0.97 for SST and 0.99 for PSL; similar results are found for each model LE (Table S4c;
Figures S1 and S2 in Supporting Information S1).
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Figure 2. As in Figure 1 but for precipitation.

Results for PR are analogous to those for SST and PSL (Figure 2). In particular, the G-Res method (Figure 2a)
introduces a pronounced but spurious negative IPV structure (Figure 2e) that overwhelms the true linkage to a
weak positive IPV seen with the fG-Res approach (Figure 2c); it also introduces spurious drying over much of theUnited States (compare Figures 2a and 2c). Both G-Res and fG-Res show high skill (r = 0.97 and 0.96, respectively) in reproducing the MMLE iAMV PR regression patterns of their “Truth” counterparts (compare left andright columns of Figure 2); similar skill is found for each model LE individually (Figures S3 and S4; Table S4 in
Supporting Information S1).
All of the above conclusions hold for the future (2030–2100) patterns of iAMV (Figures S5 and S6; Table S4 in
Supporting Information S1). We also note that the iAMV SST patterns in the models' preindustrial control simulations are very similar to those in the historical (1950–2020) LEs based on the Truth method, confirming theefficacy of the Truth method for isolating internal variability (Figure S7 in Supporting Information S1).
3.2. Sampling Variability of Model iAMV Patterns
Here we address the issue of sampling variability of the iAMV SST regression maps estimated with the G-Res
and fG-Res methods in each model LE by computing pattern correlations between each ensemble member (e.g.,iAMVgres) and the ensemble-mean (e.g., [iAMVgres]). This metric quantifies how well the ensemble-meaniAMV SST pattern obtained with either G-Res or fG-Res can be isolated in any individual realization, given“noise” from unrelated patterns of internal variability. The distribution of pattern correlations will be particularly
relevant for contextualizing the observational results in Section 3c.
Figure 3 shows the distribution of SST pattern correlations (r) for each model LE based on: (a) G-Res; (b) fG-Res;and (c) the difference between G-Res and fG-Res. Most models show a large range of r for each method, often
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Figure 3. Distribution of internal Atlantic Multidecadal Variability (iAMV) sea surface temperature (SST) patterncorrelations between each ensemble member and the ensemble-mean (gray dots) for each model Large Ensemble (LE) basedon 1950–2020 using the following methods: (a) iAMVgres; (b) iAMVfgres; and (c) iAMVgres minus iAMVfgres. Boxes
outline the 25th-to-75th percentile range, and whiskers show the 5th-to-95th percentile range. Black dots indicate correlations
between observations and the model ensemble-means. Panel (d): (upper curves) observed iNA SST index (°C) based on
iAMVgres (red) and iAMVfgres (blue); (lower curves) their difference (black) and the inverted IPV index shifted by 1 year
(gray; Henley et al., 2015).

spanning values as low as 0.1 to as high as 0.9 across the individual members. For the majority of models, the5th-to-95th percentile range of r values (which takes into account the different ensemble sizes of the various
model LEs) is about 0.3–0.8, and the median value is about 0.6–0.8. These results indicate that the spatial patternof iAMV estimated in any single model simulation may be obscured by additional sources of internal variability that are independent of iAMV. For most models, the range of r is smaller and the median r is higher for the
Atlantic sector (80°W-30°E) compared to the Indo-Pacific (defined as the region outside the Atlantic; Figure S8
in Supporting Information S1).
3.3. Application of the G-Res and fG-Res Methods to Observations
We now apply the G-Res and fG-Res methods to the observations for the period 1950–2020 as follows:

gresSST_Obs(𝑥𝑥𝑥 𝑥𝑥) = SST_Obs(𝑥𝑥𝑥 𝑥𝑥) –G_Obs(𝑡𝑡) × GSSTreg_Obs(𝑥𝑥)where SST_Obs(x,t) is the observed low-pass filtered annual SST, G_Obs(t) is the global-mean (60°N-60°S) of
SST_Obs(x,t), and GSSTreg_Obs(x) is the linear regression of SST_Obs(x,t) onto G_Obs(t).

DESER AND PHILLIPS

fgresSST_Obs(𝑥𝑥𝑥 𝑥𝑥) = SST_Obs(𝑥𝑥𝑥 𝑥𝑥)–fG(𝑡𝑡) × fGSSTreg_Obs(𝑥𝑥)6 of 10

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Figure 4. Observed internal Atlantic Multidecadal Variability (iAMV) sea surface temperature (SST) (left) and terrestrial
precipitation (PR) (right) regression maps based on 1950–2020 using the following methods: (a and b) iAMVgres_Obs; (cand d) iAMVfgres_Obs; and (e and f) iAMVgres_Obs minus iAMVfgres_Obs. See text for explanation.

where fG(t) is the MMLE G(t,em) and fGSSTreg_Obs(x) is the linear regression of SST_Obs(x,t) onto fG(t).
We construct observed iAMV patterns by regressing gresSST_Obs(x,t) onto the normalized NA average of
gresSST_Obs(x,t), and regressing fgresSST_Obs(x,t) onto the normalized NA average of fgresSST_Obs(x,t);these regression patterns are denoted iAMVgres_Obs and iAMVfgres_Obs, respectively. Analogous procedures
are used for PSL and PR. Note that no model information is used to construct iAMVgres_Obs, and the only
model information used to construct iAMVfgres_Obs is MMLE G(t,em). For reference, the G_Obs(t) and fG(t)timeseries are shown in Figure S9 in Supporting Information S1.
The observed iNA SST timeseries obtained with the G-Res method has a visibly larger amplitude than thatobtained with the fG-Res method (standard deviation σ = 1.4°C vs. 0.9°C), and exhibits notable differences intiming including a more pronounced negative phase from the mid-1970s to the mid-1990s (compare red andblue curves in Figure 3d). The difference between the two iNA timeseries (black curve) closely resembles theobserved (inverted) IPV timeseries (gray curve), with a correlation coefficient of 0.83 at zero-lag and 0.88 whenthe IPV Index leads by 1 year (correlation distributions in the model LEs are shown in Figure S10 in Supporting
Information S1).
The iAMVgres_Obs SST pattern exhibits an interhemispheric dipole structure in the Atlantic sector and anegative IPV-like pattern in the Indo-Pacific accompanied by negative anomalies across the Southern Ocean(Figure 4a). Compared to iAMVgres_Obs, iAMVfgres_Obs shows a weaker and more amorphous structure in
the Pacific sector (Figure 4c). Their difference (iAMVgres_Obs minus iAMVfgres_Obs) displays a pronounced
negative IPV pattern (also for PSL, see Figure S11 in Supporting Information S1), as well as positive SST
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Geophysical Research Letters10.1029/2022GL100574

anomalies along the US east coast and Norwegian Sea (Figure 4c). Thus, the observational results are largely
analogous to the findings based on the seven model LEs, namely that inclusion of internal G variability via the
G-Res method imparts a spurious negative IPV-like connection to iAMV. The observational results bear an evenstronger resemblance to the model LE results when the analysis period is extended back to 1900 (Figure S12 in
Supporting Information S1).
As noted above, one should not expect a perfect match between the observational and model results, even if themodel has a “perfect” representation of iAMV, due to the presence of sampling variability (recall Figure 3).
Indeed, the iAMV SST pattern correlation between observations and the ensemble-mean of each LE falls within
the 5th-to-95th (and mostly within the 25th-to-75th) percentile range of the distribution for each model, regardless of the method used (black circles in Figures 3a–3c); the same holds for the Atlantic and Indo-Pacific domains(Figure S8 in Supporting Information S1). This indicates that the observed iAMV SST regression patterns(including the difference between the G-Res and fG-Res methods) are consistent with those drawn from the
population of individual members of each model LE.
The observed iAMV PR regression maps also show notable differences between the G-Res and fG-Res methods(Figures 4b and 4d). In particular, the inclusion of “observed” internal G in the definition of iAMV introduces
spurious drying over the western US, enhanced wetting over the Amazon and eastern Australia, and a tripolar
pattern over the African continent (wetting over the Sahel, drying over equatorial Africa and wetting over South
Africa), all consistent with a negative IPV and similar to the model LE results (Figure 4f).

4. Summary and Discussion
We have shown that the G-Res method, widely used for isolating internal modes of climate variability, distorts
the spatial pattern of iAMV (conventionally defined based on low-pass filtered NA SST) by introducing spurious signals over the Indo-Pacific basin in seven different model LEs and in observations. This distortion occurs
because the global-mean SST timeseries used in the method to define (and remove) the spatial pattern of
externally-forced climate variability contains internal variability in addition to a forced response. The internal
component of G(t) is predominantly associated with fluctuations in the leading mode of Indo-Pacific SST variability (IPV), consistent with previous literature. This deficiency of the G-Res method can be overcome by using
the forced component of G(t) in place of the total G(t). This modified version of the G-Res method (termed
fG-Res) skillfully reveals the true spatial pattern of iAMV in each of the seven model LEs, a pattern which isprimarily confined to the NA and adjacent Arctic Ocean. Some models also show a weak connection to thetropical Pacific and the far northern Pacific. Importantly, these Pacific connections are opposite in sign to thoseobtained with the conventional G-Res method.
All seven model LEs show high member-to-member variability in their simulated iAMV SST regression patterns
based on 1950–2020 (and 2030–2100; not shown), indicating that a single 70-year realization is not adequate toisolate iAMV from other sources of internal variability. Because the observational record captures only one ofmany possible trajectories of internal variability during 1950–2020 (superimposed upon an externally-forced
response), assessment of model fidelity must take into account sampling uncertainty. By this measure, all of
the models examined produce realistic iAMV SST patterns according to the fG-Res method. Further, they also
simulate realistic amplitudes of iNA SST variability based on the fG-Res method, evidenced by the fact that theobserved iNA σ lies within the 5th-to-95th percentile range of iNA σ values across the individual members ofeach model LE (not shown).
What is the minimum ensemble size needed to robustly estimate [iAMVfgres] and iAMVfgres_Obs? Using
random sampling procedures described in the Supporting Information S1, we find that approximately 20 members
are needed to reproduce the SST pattern of [iAMVfgres] in each model LE (Figure S13 in Supporting Information S1), and that six members are needed to compute fG(t) in the calculation of the SST iAMVfgres_Obs pattern(Figure S14 in Supporting Information S1; note that this pattern is still subject to the same level of sampling
variability as that shown in Figure 3b).
It is beyond the scope of this study to undertake a detailed investigation of the underlying physical causes of
iAMV in the model LEs. Here, we briefly examine the role of the Atlantic Meridional Overturning Circulation(AMOC) since it has been identified as a key mechanism for iAMV-related SST fluctuations in the NA (especially, the subpolar NA; SPNA) via changes in ocean heat transport that may be predictable out to decadal lead
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times (e.g., Kim et al., 2020; Yeager et al., 2020). Using the our “Truth” methodology, we have constructed
MMLE regression maps of SST and PSL upon the models' standardized iAMOC timeseries leading by 4 years(the lag of maximum correlation between iNA SST and iAMOC; not shown). These iAMOC regression patterns
show the expected SST warming over the NA (especially the SPNA) and adjacent Arctic Ocean, with a weak
positive PSL anomaly over the midlatitude NA (Figure S15b in Supporting Information S1); however, the magnitude of the AMOC-related warming is <50% of the warming associated with a 1σ departure of the iNA SST index(Figure S15a in Supporting Information S1). Differencing the NA and AMOC regression maps reveals a tripolar
SST pattern over the NA accompanied by a negative NAO-like PSL pattern (Figure S15c in Supporting Information S1), qualitatively consistent with the thermodynamic response of the upper-ocean mixed layer to atmosphericforcing (e.g., Clement et al., 2015; Deser et al., 2010). This difference map also shows a weak positive ENSO-likesignature in the Indo-Pacific (SST warming in the tropical eastern Pacific, weakened tropical Pacific PSL gradient, and negative PSL anomalies in the eastern North Pacific), which may reflect the well-known teleconnection
from the Pacific to the Atlantic (e.g., Deser et al., 2010; Meehl et al., 2021). In support of this causal inference,
we note that the “Truth method” regression map of net surface heat flux upon the iNA SST index exhibits positive(downward) values over the tropical North Atlantic, implying that the atmosphere is driving the iAMV SSTs inthis region and not vice versa (not shown). This direction of causality is consistent with IPV “Pacemaker” (butinconsistent with AMV “Pacemaker”) experiments reported in Meehl et al. (2021). Thus, caution is needed wheninterpreting the relevance of regional “Pacemaker” experiments. In summary, our results support the notion thatboth AMOC and thermodynamic air-sea interaction independent of AMOC contribute to the simulated patternof iAMV defined on the basis of iNA SST. Application of the fG-Res method to define iAMV in paleoclimate
simulations (Fang et al., 2021; Wang et al., 2017) is left to future work.

Data Availability Statement
All observational data sets used in this study are publicly available from: www.ncei.noaa.gov/products/extended-reconstructed-sst; www.dwd.de/EN/ourservices/gpcc/gpcc.html; and www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5. All model simulations used in this study are publicly available from: https://www.cesm.
ucar.edu/community-projects/mmlea; and https://esgf-node.llnl.gov/search/cmip6/. Analysis code is posted athttps://www.cesm.ucar.edu/projects/cvdp-le/code.
Acknowledgments
We thank the anonymous reviewers
for their constructive comments andsuggestions. The National Center for
Atmospheric Research is sponsored by
the National Science Foundation.

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