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

The relative contributions of external forcing and internal processes to the observed spatial and temporal characteristics of “Atlantic Multidecadal Variability” (AMV) are still

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 pattern obtained 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) affect the 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.

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 model and 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 compute monthly 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.

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: 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: 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) onto G(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 of PR(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 iAMVtruth NA and iAMVgres, respectively.To enhance the robustness of the patterns, we then average the regres-  Power et al., 1999) is defined as the leading 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.

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  1a).They also show prominent expression in the Pacific reminiscent of the negative phase of IPV, with negative SST anomalies in the tropics 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 [iAMVtruth NA-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 [iAMVtruth NA ] regression patterns display striking differences from [iAMVtruth NA-G ] outside of the Atlantic sector, with anomalies generally of opposite sign and weaker magnitude (Figure 1d).In particular, the former 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 [iAMVtruth NA ] and [iAMVtruth NA-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 iAMVtruth NA-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 [iAMVtruth NA ] and [iAMVtruth NA-G ] regression patterns indicate that iSST 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 [iAMVtruth NA ] and MMLE [iAMVtruth NA-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 iG NA (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 iG NA (t,e).However, because the standard deviation (σ) of iG NA is small (<10%) compared to that of iG* (both for the MMLE and for each 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: where fGreg(x,e) is the linear regression of SST(x,t,e) onto fG(t) for a given model LE; similar equations were obtained 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 [iAMVtruth NA ] 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 is found 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 estimated with the G-Res method.This difference map (Figure 1e) is nearly identical to that between [iAMVtruth NA ] and [iAMVtruth NA-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).
DESER AND PHILLIPS 10.1029/2022GL100574 5 of 10 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 the United 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 and right 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 the efficacy of the Truth method for isolating internal variability (Figure S7 in Supporting Information S1).

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-mean iAMV 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.spanning values as low as 0.1 to as high as 0.9 across the individual members.For the majority of models, the 5th-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 pattern of 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).

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( ) = SST_Obs( ) -G_Obs() × GSSTreg_Obs() 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).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 that obtained with the fG-Res method (standard deviation σ = 1.4°C vs. 0.9°C), and exhibits notable differences in timing including a more pronounced negative phase from the mid-1970s to the mid-1990s (compare red and blue curves in Figure 3d).The difference between the two iNA timeseries (black curve) closely resembles the observed (inverted) IPV timeseries (gray curve), with a correlation coefficient of 0.83 at zero-lag and 0.88 when the 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 a negative 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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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 the forced component of global-mean temperature mitigates this issue Supporting Information: Supporting Information may be found in the online version of this article.

Figure 3
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

Figure 2 .
Figure 2. As in Figure 1 but for precipitation.

Figure 3 .
Figure 3. Distribution of internal Atlantic Multidecadal Variability (iAMV) sea surface temperature (SST) pattern correlations between each ensemble member and the ensemble-mean (gray dots) for each model Large Ensemble (LE) based on 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).
sion maps across the individual members of a given model LE, denoted [iAMVtruth NA ] and [iAMVgres].We also compute the multi-model LE (MMLE) average of the seven [iAMVtruth NA ] and [iAMVgres] regression maps.
3 of 10 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 iAMVtruth NA-G (and [iAMVtruth NA-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 iG NA (t,e) and obtained by scaling iNA(t,e) by the regression of iG(t,e) onto iNA(t,e)], and a part that is orthogonal to iNA(t,e) [denoted iG*(t,e) and obtained by subtracting iG NA (t,e) from iG(t,e)].Unless stated otherwise, all pattern correlations (r) are based on area-weighted data over the global domain (60°N-60°S)."Interdecadal Pacific Variability" (IPV;