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Interdecadal annual-mean temperature changes 1850-2014

Separating physically distinct influences on Pacific sea-surface temperature variability

A key challenge in climate science is to distinguish temperature changes in response to external forcing (e.g., global warming in response to anthropogenic greenhouse gasses) from temperature changes due to atmosphere-ocean internal variability. Extended integrations of forced and unforced climate models are often used for this purpose. In Wills et al. (2018), we demonstrated a novel method called low-frequency component analysis (LFCA), which separates modes of internal variability from global warming based on differences in time scales and spatial patterns, without relying on climate models.

We used LFCA to distinguish the influences of global warming, the Pacific Decadal Oscillation (PDO), and the El Niño-Southern Oscillation (ENSO) on the observed variability of Pacific sea-surface temperatures (SSTs). We found that the key features of PDO and ENSO are consistent with their being separate processes, with ENSO confined to the tropics and an uncorrelated PDO mostly confined to the midlatitude North Pacific. Additionally, we found two patterns of multidecadal SST variability that could either be modes of internal variability or responses to external forcing. In this blog post, we discuss LFCA (and the broader class of statistical analyses on which it is based) as a way to approach questions in climate science, we discuss the implications of our findings for our understanding of the PDO, and we discuss some potential explanations and implications of the yet to be explained modes of Pacific multidecadal variability.

Low Frequency Component Analysis (LFCA)

* Note: See list of acronyms used at the bottom of this post.

The goal of LFCA is to identify patterns of variability within spatiotemporal datasets that have the maximum possible ratio of slowly varying “signal” to higher-frequency “noise”. We define variability to be slowly varying or low-frequency if it makes it through a 10-year lowpass filter. The resulting low-frequency patterns (LFPs) are sorted by the ratio of low-frequency to high-frequency variance in their time series, which we call low-frequency components (LFCs) (Wills et al. 2018). In order to constrain the analysis to variability that has been sufficiently sampled within the dataset, it is applied only to the leading empirical orthogonal functions (EOFs), which are spatial patterns, obtained through principal component analysis, that explain the most variance in the dataset. The number of EOFs included is a key parameter in this analysis. However, there is no uniquely best way to determine the correct number of EOFs to use, so the best practice is to try various choices and focus on results that are robust across a range of parameters. In contrast to principal component analysis, which finds patterns (EOFs) that explain the most variance within a dataset, LFCA finds patterns (LFPs) that are the most distinctive of decadal timescales in that they maximize the ratio of interdecadal to intradecadal variance (as in the analysis of Schneider and Held (2001), which just uses a different way of defining low-frequency variance).

In general, this type of statistical analysis can be set up to maximize any type of signal of interest with respect to the noise within spatiotemporal datasets. This broader class of statistical analyses has been called optimal filtering or signal-to-noise maximizing EOF analysis. Their origins lie in linear discriminant analysis, a pattern recognition method that finds the optimal set of properties to best distinguish groups of data. For example, Schneider and Held (2001) used optimal filtering to maximize the ratio of interdecadal to intradecadal variance (defined with box filters) to isolate the signal of anthropogenic global warming in surface temperatures (see animations of the results here); Ting et al. (2009) used optimal filtering to identify the pattern of temperature change that is most robust across an ensemble of climate models. The advantage of these methods is that they are guaranteed to find the spatial anomaly pattern that maximizes the signal of interest.

We apply LFCA to observed Pacific SST anomalies (Smith et al. 2008). As a first example, we include only the first 3 EOFs. These EOFs are all mixtures of global warming, ENSO, and PDO (see Fig. S1 in the Supporting Information of Wills et al. 2018). LFCA transforms them to identify separate modes of variability for each process (Fig. 1), distinguishing them by their differences in spatial pattern and timescale. However, this result is unique to the case where 3 EOFs are included. Only when ~20 or more EOFs are included does LFCA converge on robust results for the leading LFCs. We show here the case where 30 EOFs are included (Fig. 2). The spatial pattern and time series of global warming (LFC 1) remains approximately the same for this case as in the original 3 EOF case. The PDO-like mode (LFC 2 in Fig. 1, LFC 4 in Fig. 2) has a higher ratio of interdecadal to intradecadal variance and retains less of its amplitude in the tropical Pacific. The 30 EOF analysis introduces two new patterns of multidecadal variability (LFCs 2 and 3 in Fig. 2), that we will return to at the end of this post. In the next section we discuss the implications of the PDO-like LFC 4 (“LFC-PDO”) for our understanding of the PDO.

Figure 1: First 3 LFPs and LFCs of Pacific SST anomalies (over the latitudes 45°S–70°N) when 3 EOFs are included. They represent (a) global warming, (b) Pacific Decadal Oscillation (PDO), and (c) El Niño–Southern Oscillation (ENSO). From Wills et al. (2018).


Figure 2: First 4 LFPs and LFCs of Pacific SST anomalies (over the latitudes 45°S–70°N) when 30 EOFs are included. Solid black lines show the LFCs filtered with a 6 year running average. Vertical dashed lines indicate years with major PDO transitions. Triangles on the x-axis of LFC 2 indicate anomalies of greater than 2𝜎 in the ENSO* index (LFC 3 in Figure 1) for three consecutive months. They represent (a) global warming, (b) La-Niña-like multidecadal variability that modulates the strength of ENSO, (c) multidecadal variability of the central equatorial Pacific, and (d) the interdecadal component of the PDO (which we refer to as the LFC-PDO). From Wills et al. (2018).

Implications for the PDO

Compared to the traditional definition of the PDO as the leading EOF of North Pacific SST anomalies (over latitudes 20°N-70°N, Mantua et al. 1997), the LFC-PDO has less amplitude in the tropical Pacific and the Kuroshio-Oyashio Extension (extending east from Japan at a latitude of 40°N), but just as much amplitude along the coast of North America (see side-by-side comparison in Fig. 3). The LFC-PDO’s interdecadal-to-intradecadal signal-to-noise ratio is double that of the traditional PDO index (0.79 vs. 0.37). It remains highly coherent with the PDO at decadal and longer timescales, where it accounts for 65% of the variance in the traditional PDO index (see Fig. S6 in the Supporting Information of Wills et al. 2018).

Figure 3: Side-by-side comparison of the traditional PDO and the LFC-PDO. (a) SST anomaly pattern associated with the traditional PDO definition (Mantua et al. 1997). (b) SST anomaly patterns associated with the LFC-PDO (from the analysis shown in Fig. 2). (c) Time series of the traditional PDO and the LFC-PDO. The LFC-PDO is rescaled by its 64% correlation with the traditional PDO. The difference between the PDO and the rescaled LFC-PDO is shown in the bottom panel of (c) and the SST regression onto this difference is shown in (d). From the Supporting Information of Wills et al. (2018).

One advantage of identifying an index of the PDO with a higher interdecadal-to-intradecadal signal-to-noise ratio is that we can isolate the physical mechanisms relevant at interdecadal timescales from those relevant at shorter timescales. For example, we have reexamined the relationship between PDO and ENSO based on the LFC-PDO index and found that it has a correlation of less than 0.2 with ENSO at all lead and lag times. In contrast, the traditional PDO index has a correlation of 0.5 with ENSO. We have found that the interdecadal component of the PDO is confined to the midlatitudes and is mostly independent of ENSO, in contrast to previous studies that suggest ENSO is a primary driver of the PDO (e.g., Newman et al. 2003).

In a forthcoming paper (Wills et al. 2019a), we show that the interdecadal component of the PDO is similarly confined to the North Pacific in state-of-the-art (CMIP5) coupled climate models. PDO variability (in models) results from the response of the near-surface ocean gyre circulation to stochastic changes in the atmospheric circulation over the North Pacific. Together, this model-based and observational evidence leads us to the conclusion that the interdecadal component of the PDO is separate from ENSO; it is a signature of the North Pacific subpolar gyre responding to variability in the atmospheric circulation over the North Pacific (see Wills et al. 2019a for further details).

Unexplained Pacific Multidecadal Variability

While LFCs 1 and 4 (from Fig. 2) have straightforward physical interpretations and clear analogues in climate models, LFCs 2 and 3 are more mysterious. LFP 2 shows warming in the midlatitude North Pacific and cooling in the eastern equatorial Pacific. It is marked by a prolonged positive phase from 1920 to 1970 followed by a prolonged negative phase from 1970 to 2015. This matches with observed variations in the Atlantic Multidecadal Oscillation (AMO) (Wills et al., 2019b), leaving open the possibility that this Pacific multidecadal variability is driven by the AMO. However, another possibility is that the Pacific LFC 2 and the AMO are both part of a global response to variations in climate forcing over the 20th century, such as from anthropogenic aerosol or stratospheric ozone changes. Whatever the physical mechanisms, this mode of variability and/or change is interesting for its possible modulation of the amplitude of ENSO. Large amplitude El Niño events (marked on the x-axis of Fig. 2) did not occur between 1920 and 1970, when LFC 2 was in its positive phase.

LFP 3 shows warming in the central equatorial Pacific and eastern subtropical Pacific (in both hemispheres), a pattern similar to that associated with the Pacific Meridional Mode (Chiang and Vimont, 2004). However, we are not aware of an explanation for the long timescale of the variability seen here, and it is possible that external forcing (aerosols and stratospheric ozone) plays a role here as well. An interesting feature of this variability is that it has a trend over the entire satellite era (since 1979), as does LFC 2. Together LFCs 2 and 3 show pronounced cooling of the eastern and central equatorial Pacific since 1979, a pattern that is not well simulated in the current generation of climate models, and which is thought to bias observational estimates of climate sensitivity low because of its influence on low cloud cover (Zhou et al., 2016). A key challenge in constraining the climate response to greenhouse gas forcing (especially the east-west SST gradient in the tropical Pacific and the Walker Circulation) is to determine whether these multidecadal changes are externally forced or are caused by internal variability of the atmosphere-ocean system.

Broader Implications

LFCA provides a valuable tool to study climate variability and change. It identifies the characteristic patterns of low-frequency variability and removes higher frequency noise. It does this without explicitly filtering the data, allowing better inferences about the mechanisms and causes of low-frequency climate variability. Because anthropogenic climate change manifests itself primarily on long timescales and with global spatial correlations, LFCA has the potential to isolate the climate response to anthropogenic forcing without using climate models (Schneider and Held 2001, Wills et al. 2018), and to identify the climate response in models without the use of large ensembles (Wills et al. 2017). However, there remain some patterns of SST variability for which it is not yet possible to tell whether they result from external forcing or internal variability, because we lack a full mechanistic understanding.

While we have applied LFCA here to SST anomalies on interdecadal timescales, it is potentially useful for any dataset where it is desirable to remove large-amplitude spatially coherent “noise” (here, the noise was ENSO). In the case where different physical mechanisms of variability operate on different timescales (as is the case for anthropogenic warming, PDO, and ENSO), LFCA has the potential to isolate physically distinct modes of variability.


List of Acronyms

LFCA – Low Frequency Component Analysis

LFC – Low-Frequency Component

LFP – Low-Frequency Pattern

EOF – Empirical Orthogonal Function

PDO – Pacific Decadal Oscillation

ENSO – El Niño-Southern Oscillation

CMIP5 – Coupled Model Intercomparison Project, phase 5



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