The changing physical and ecological meanings of North Pacific Ocean climate indices

Significance

The PDO and NPGO indices are important tools for summarizing and understanding climate variability. As with other climate indices, the PDO and NPGO are assumed to have stable relationships with the climate variables they synthesize. We found that a late-1980s North Pacific climate shift resulted in changing correlations between large-scale climate patterns and the PDO and NPGO, and widespread weakening in relationships between the PDO/NPGO and regional physical and ecological processes. These findings suggest that understanding based on observed correlations with PDO/NPGO variability may have limited utility when applied to different time periods. Time dependence in correlations with these static climate indices may accelerate in the future, as climate change is expected to further shuffle relationships among climate variables.

Abstract

Climate change is likely to change the relationships between commonly used climate indices and underlying patterns of climate variability, but this complexity is rarely considered in studies using climate indices. Here, we show that the physical and ecological conditions mapping onto the Pacific Decadal Oscillation (PDO) index and North Pacific Gyre Oscillation (NPGO) index have changed over multidecadal timescales. These changes apparently began around a 1988/1989 North Pacific climate shift that was marked by abrupt northeast Pacific warming, declining temporal variance in the Aleutian Low (a leading atmospheric driver of the PDO), and increasing correlation between the PDO and NPGO patterns. Sea level pressure and surface temperature patterns associated with each climate index changed after 1988/1989, indicating that identical index values reflect different states of basin-scale climate over time. The PDO and NPGO also show time-dependent skill as indices of regional northeast Pacific ecosystem variability. Since the late 1980s, both indices have become less relevant to physical–ecological variability in regional ecosystems from the Bering Sea to the southern California Current. Users of these climate indices should be aware of nonstationary relationships with underlying climate variability within the historical record, and the potential for further nonstationarity with ongoing climate change.

Climate indices reduce complex patterns of internal climate variability into single variables (1). The most commonly used indices, such as the North Atlantic Oscillation and Multivariate El Niño–Southern Oscillation indices, represent coupled atmosphere–ocean processes that are important drivers of climate variability (2). By summarizing multiple correlated climate variables, these indices often explain a higher proportion of ecological variance than do individual local climate variables (3). However, the future climate will likely be characterized by novel patterns of covariance among physical variables (4), and this may be particularly true for the internal modes of atmosphere–ocean variability that are commonly tracked by climate indices (2). These changes imply that the sets of correlated variables mapping onto climate indices are likely to change over time, so that the physical and ecological implications of an index value may be nonstationary (time dependent). Climate indices have been foundational to our understanding of the role that climate variability plays in physical, ecological, and social systems; nonstationary relationships between indices and underlying conditions raise the possibility that this understanding may fail when deployed for out-of-sample prediction (1, 5). This potential for time dependence in the physical and ecological meanings of climate indices is an underappreciated potential consequence of climate change (5, 6).

Here, we show how physical and ecological variables mapping onto two leading Pacific Ocean climate indices, the Pacific Decadal Oscillation (PDO) and North Pacific Gyre Oscillation (NPGO), have changed over multidecadal time scales. These indices are calculated as the first and second statistical modes (empirical orthogonal function [EOF] axes and corresponding principal component [PC] scores) for North Pacific Ocean sea surface temperature anomaly (SSTa) and sea surface height anomaly fields, respectively (7, 8). The PDO and NPGO patterns are leading modes in global SST variability (9) and play an important role in modulating Pacific (10) and global (11) temperature anomalies. Both indices are defined with EOF/PC analysis for a fixed period of the observational record [1900 to 1993 for the PDO (7), 1950 to 2004 for the NPGO (8)], and subsequent values of the index (the PC score) are calculated by “projecting” the initial EOF results onto subsequent observations (i.e., the observations are multiplied by the EOF loadings to generate a new index value). This commonly employed approach assumes a stationary relationship between evolving patterns of ocean climate variability and the patterns identified by the original statistical definitions. However, there are reasons to expect nonstationary relationships between the PDO and NPGO indices and underlying physical and ecological conditions. Both indices track statistical patterns that result from multiple physical processes. For instance, the PDO is driven primarily by the Aleutian Low, teleconnections from the tropics, and midlatitude ocean dynamics, with a range of individual driving processes within these larger categories (12). Because the individual generative processes operate on different timescales, a one-to-one correspondence between the index value and conditions mapping onto the index is not expected over time (12). Several lines of evidence, including increasing association between the NPGO and the first, rather than second, mode of North Pacific climate (13, 14), and changing associations between the PDO/NPGO and ecological variability (14–19), suggest that this assumption of stationarity may be increasingly invalid. However, no comprehensive investigation of nonstationary relationships with the PDO and NPGO has been conducted. We focus on changing relationships between the PDO/NPGO indices and regional physical and ecological conditions after a 1988/1989 climate shift in the North Pacific (13, 20). Examples of changing associations with the PDO/NPGO have been noted following this shift (14, 15, 17, 18), which appeared to involve a transition to novel patterns of extratropical atmospheric variability associated with the increased incidence of Central Pacific El Niño events (16, 21).

Results and Discussion

We begin our analysis by examining post-1988/1989 changes in basin-scale atmosphere–ocean processes reflected in the PDO and NPGO indices (7, 8, 12). This 1988/1989 shift involves simultaneous climate change in the ocean (a ∼0.3 °C step increase in mean winter SST; Fig. 1A) and atmosphere [a ∼33% decline in low-frequency temporal variability of the Aleutian Low (14); Fig. 1B]. A trend of strengthening negative correlation between the PDO and NPGO indices also commences shortly after 1988/1989 (Fig. 1C). This decay in independence contrasts with the orthogonal identity of the PDO and NPGO patterns under the EOF/PC methods used in their definition, and suggests that distinguishing the causative role of the two patterns as agents of regional physical–ecological change is increasingly problematic (22).

Fig. 1.

Changes in North Pacific atmosphere and ocean climate after 1988/1989. (A) Increasing winter SST anomalies. (B) Decreasing temporal variance (SD over 11-y rolling windows) in winter Aleutian Low SLPa values. (C) Increasing correlation between PDO and NPGO indices (correlation over 11-y or 132-mo rolling windows). The vertical dashed lines indicate 1988/1989; trend lines are best stepwise linear (A) or nonparametric (B and C) regressions.

These changes in the nature of basin-scale climate variability motivate us to examine changes in atmospheric patterns related to PDO and NPGO variability after 1988/1989. While several atmospheric processes are involved in producing the PDO and NPGO patterns (12), variability in sea level pressure (SLP) fields produces wind stress that drives heat fluxes, wind mixing, and Ekman transport, which are primary drivers of PDO/NPGO variability (7, 8, 12). Therefore, a common approach for identifying atmospheric patterns that act as proximate drivers involves regressing SLP fields onto the index in question (7, 8, 12). This approach identifies changes in the atmospheric drivers of both patterns after 1988/1989; the center of SLP variability associated with the PDO shifts southeastward and intensifies (Fig. 2 A–C), while SLP–NPGO regression coefficients decrease ∼70% (Fig. 2 D–F). Changing relationships between SLP fields and the PDO/NPGO indices imply changes in relationships with dependent wind stress fields that may change the ocean environmental variables that map onto the indices (14). This possibility is supported by self-organizing map (SOM) analysis that identifies leading patterns of winter SSTa fields associated with the indices over time (details in Methods). This analysis invokes six leading SSTa patterns, or nodes (Fig. 3). These nodes have a time-dependent distribution (Fig. 4). Nodes 1 and 2 reflect the spatial oscillation between coastal and central North Pacific temperature anomalies associated with the PDO pattern, while node 6 reflects the north–south dipole pattern of the NPGO. These three nodes invoking the canonical PDO/NPGO patterns occur predominantly prior to 1988/1989, and three other nodes (3–5) occur exclusively after 1988/1989 (Fig. 4). These results suggest that positive PDO values are increasingly associated with a larger area of positive temperature anomalies, shifted offshore in the northern North Pacific into a more NPGO-like pattern (node 4), while negative PDO values are increasingly associated with diminished negative coastal anomalies, and a much larger area of positive anomalies in the central and western basin (node 5). Similar temporal changes are seen for the expression of the NPGO, especially the increasing association of positive (negative) index values with node 3 (node 4). An important result of this analysis is the very recent incidence of node 4, with four of the eight occurrences observed after 2014 (Fig. 4), suggesting further changes to spatial patterns associated with the strong PDO/NPGO values observed since the onset of persistent heatwave conditions in the North Pacific (10, 23). This SOM analysis is conducted with SSTa data that have not been detrended and so is able to capture the changing association between the PDO/NPGO indices and SSTa fields as the North Pacific warms (24).

Fig. 2.

Differences in atmospheric forcing of the PDO and NPGO indices before and after 1988/1989. Coefficients (Pa) for regression of SLP (November to January) onto PDO (February to April) index (A) 1950 to 1988, (B) 1989 to 2012, and (C) Difference in era coefficients (1989 to 2012) − (1950 to 1988). (D–F) The same regressions for the NPGO index.

Fig. 3.

Dominant spatial patterns in winter (November to March) North Pacific SST anomalies, 1951 to 2018. Six leading patterns (nodes) from self-organizing map (SOM) analysis. (A and B) Nodes 1 and 2 are PDO-like patterns occurring primarily before 1988/1989, (C–E) nodes 3–5 occur only after 1988/1989, and (F) node 6 is a NPGO-like pattern occurring almost exclusively before 1988/1989.

Fig. 4.

Changing incidence of spatial patterns associated with the PDO and NPGO indices. Years of occurrence for the six nodes from SOM analysis (Fig. 3) plotted against corresponding winter (November to March) PDO–NPGO values.

These results show that basin-scale atmosphere and surface ocean variability associated with the PDO and NPGO changed after 1988/1989; we next ask whether similar nonstationary relationships are seen for regional-scale processes. While progress has been made in establishing mechanistic understanding of statistical relationships between climate indices and regional physical–ecological variability (25), such mechanistic understanding is contingent on regional details and thus impractical to invoke for multiple systems. This consideration is particularly relevant to the mechanistic understanding of linkages between nonstationary basin-scale processes and nonstationary PDO/NPGO effects in regional ecosystems, which have to date been investigated only in the Gulf of Alaska (14, 17, 26). We therefore take a statistical modeling approach to answer the question of whether PDO/NPGO effects have changed at a regional scale. We use hierarchical Bayesian linear regression models to test the hypothesis that the ability to predict large-scale patterns (the PDO and NPGO) based on observed values of regional physical and biological variables changed between the two eras, as indicated by slopes of the relationships that changed either in direction or magnitude (see Methods for details). This analysis uses a set of long-term environmental and biological time series from the Bering Sea, Gulf of Alaska, and northern, central, and southern California Current ecosystems (Fig. 5A and details in SI Appendix, Tables S1–S3). Time series were aggregated into groups representing environmental variables, salmon population data, and nonsalmon biological data, and separate hierarchical models were fit to data from each group. We allowed the slope of the relationship between each raw variable and the response (PDO, NPGO) to differ between the two eras (before and after 1988/1989). Changes in relationships were examined with the ratio of the two slopes (slope after 1988/1989:slope before 1988/1989; details in Methods). In this framework, a ratio near 1 indicates a relationship with the PDO or NPGO that is nearly constant between eras. A negative ratio indicates that the sign of the relationship has changed (for example, a positive correlation becomes negative). The magnitude of the ratio can be used to indicate whether the strength of the relationship has weakened (values between −1 and 1) or become stronger (values less than −1 or >1).

Fig. 5.

Changes in physical and ecological conditions mapping onto the PDO and NPGO indices. (A) Location of physical (environmental) and biological time series used in analysis. Numbers in parentheses indicate the number of individual time series in each group, spread over season, space, or species. (B–D) Bayesian linear regression results for changes in relationships between regional variables and the PDO and NPGO indices after 1988/1989: posterior distributions of the ratios of slope in era 2 (after 1988/1989) to slope in era 1 (before 1988/1989). Values between −1 and 1 indicate a slope that has become weaker or smaller in magnitude after 1989, values <0 indicate a switch in the sign of the relationship between eras, and values less than −1 or >1 indicate a stronger association (greater slope) in era 2. Separate models were fit to environmental variables (B), productivity for three salmon species (C), and other biology time series (D). The dots indicate posterior medians, light (heavy) horizontal lines indicate 90% (50%) range of distributions, and vertical line indicates ratio of 1, or no change in slope between eras.

These model results show evidence of widespread time-dependent physical and ecological meanings of the two indices (Fig. 5 B–D). Regional physical (environmental) variables mapping onto the PDO in the Bering Sea and Gulf of Alaska show declining associations after 1988/1989, while weaker evidence for changing PDO expression was observed in the California Current (Fig. 5B). Physical variables mapping onto the NPGO show consistent indications of weakening relationships since 1988/1989. Most estimated ratios for salmon population data show weaker relationships with the PDO/NPGO after 1988/1989, with some evidence of changing signs of relationships in the northern California Current (Fig. 5C). Relationships with other biological variables were also shifted toward zero (indicating weakening relationships), with the degree of change between eras varying by region (Fig. 5D). Thirty-seven of the 38 individual tests for changing relationships returned a median posterior less than 1, suggesting that weakening PDO/NPGO relationships were nearly ubiquitous after 1988/1989 (SI Appendix, Table S4).

The Gulf of Alaska results are consistent with a previously advanced hypothesis positing that declining variance in the Aleutian Low after 1988/1989 weakened atmosphere and ocean circulation that had previously driven correlated variability in regional environmental processes. Absent a strong signal of shared variability among regional climate variables that had previously responded in unison to Aleutian Low variability, the shared statistical response to PDO variability was also lost, apparently resulting in PDO–environment and PDO–biology relationships that weakened (shifted toward zero) (14, 17, 26). Similar mechanistic investigations are needed to better understand nonstationary expression of PDO/NPGO variability in other regions. We note that the strength of correlation between the indices (Fig. 1C) has reached a level that will make independent interpretation of PDO or NPGO effects in this context difficult (22). Until better mechanistic understanding is available, our results indicate the need to take care when making the assumption that the PDO and NPGO show stationary relationships with physical and biological variability around the northeast Pacific over multidecadal timescales. These findings underscore the importance of distinguishing phenomena that are correlated with climate indices from those that are predicted by climate indices; the former relationships are prone to nonstationarity, the latter less so (12). The importance of improved mechanistic understanding of correlative relationships with climate indices has long been recognized. However, given the short observational record, the complexity of multivariate physical and ecological variability, and the inability to satisfactorily model these complex interactions, mechanistic understanding of ecological correlations with climate indices remains poor. As a result, the PDO and NPGO indices are commonly employed as covariates in correlative studies that fit statistical models to estimate the effects of climate variability for fisheries management (25, 27, 28), hydrology (29–31), agriculture (32–34), and economic planning (35, 36). Statistical approaches commonly used in these correlative studies may produce era-dependent errors in inference when confronted with nonstationary relationships of the kind we document here (14, 26, 37, 38). Unfortunately, the vulnerability of correlative studies to violations of the assumption that underlying processes are stationary in time is rarely evaluated (6). In addition, observed PDO/NPGO relationships are often used to project relationships into the future (32–35), but nonstationarity in the physical and ecological variables mapping onto the PDO/NPGO would dramatically reduce out-of-sample predictive skill for these uses (1, 5, 6). This problem of the loss of predictive skill when relationships among physical covariates change has long been recognized in paleoecology (39) and global change ecology (40). In this context, we note that anthropogenic climate change is beginning to emerge from the envelope of natural variability in many ecosystems globally and involves rates of change that differ across different climate variables (41–43), implying a growing potential for changing relationships to climate indices with fixed statistical definitions. Recent extreme temperature anomalies over much of the northeast Pacific that have been attributed to anthropogenic radiative forcing (44, 45) have also been associated with novel patterns in SLP fields, leading to unusual Ekman transport, wind mixing, and heat fluxes (23). These same mechanisms are primary drivers of the PDO and NPGO patterns (7, 8, 12), so these previously unobserved combinations of atmospheric forcing and ocean responses suggest the potential for further nonstationarity in relationships between the PDO/NPGO indices and underlying conditions, beyond the post-1988/1989 changes documented here.

Materials and Methods

Basin-Scale Atmosphere and Ocean Patterns.

Trends in winter SST (Fig. 1A) were calculated from ERSSTv5 (46) data for the area 30° to 66°N, 150°E to 110°W. We removed the monthly mean for the period 1951 to 1981 from each cell, and then calculated area-wide average winter (November to March) anomalies for each year. Temporal variation in the Aleutian Low (Fig. 1B) was calculated as the SD over 11-y rolling windows for November to March SLPa values (monthly mean removed) from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis (47) averaged over cells with centers at 45° to 55°N, 152.5° to 167.5°W. Regression of SLP data onto the PDO/NPGO indices (Fig. 2) used SLP data from the NCEP/NCAR reanalysis for the area 20° to 67.5°N, 132.5°E to 110°W. For each cell, SLP values were averaged over the period November to January and then regressed on February to April PDO/NPGO index values, matching the time lag of the Aleutian Low–PDO relationship (12)

SOM Modeling.

SOMs are a type of neural network being increasingly employed for meteorological and oceanographic applications (48). Here, they are used to describe the shift that occurred in 1988/1989 in the characteristics of the winter mean patterns in North Pacific surface temperatures, and to determine how these patterns relate to the PDO and NPGO. The first data layer consists of gridded mean surface temperatures during winters (November to March) 1951 to 2018 (winter year corresponding to January) over the area 20° to 65°N, 120°E to 115°W. We used SST from the NCEP/NCAR Reanalysis, which itself is based on the product of Reynolds and Smith (49). These temperatures have not been detrended. We posit that the use of “raw” data without detrending is appropriate in our examination of potential shifts in physical conditions that are relevant to the ecosystem. The second and third data layers consisted of winter mean (November to March) values of the PDO and NPGO. The surface temperature data layer was weighted a factor of 1,000 times greater than the PDO and NPGO data layers, which made the sorting of the years completely dependent on the surface temperature distributions. We constructed SOMs with a variety of configurations, and subjectively settled on a 3 × 2 matrix (6 patterns). Each pattern is not independent in that the learning procedure leads to an ordered mapping of the input data, such that neighboring patterns (or nodes) are similar to one another and ones located far apart are more dissimilar. We carried out multiple SOM runs with different seed values. These replicates yielded similar if not identical groupings of years.

Modeling Time-Varying Relationships.

To model changing associations between climate indices (November to March PDO, NPGO) and individual predictor variables (environmental or biological), we used a hierarchical regression model that allowed for comparisons across regions, response variables, and predictors. Because we are working with anomalies, the average of these winter PDO/NPGO time series across years is approximately zero. For all models evaluating time-dependent relationships with biological time series, winter PDO/NPGO values were smoothed with 2-y running means (values from the year before and year of interest) in order to account for lagged effects. For the predictor variables, we utilized data from five different regions in the northeast Pacific Ocean (EBS, eastern Bering Sea; GOA, Gulf of Alaska; NCC, northern California Current; CCC, central California Current; SCC, southern California Current). From each region, we collated data on environmental variables and biological variables that have been linked to climate indices, or used as ecosystem indicators themselves. To allow for comparisons within and across regions, each of the environmental and biological variables was standardized. Tables describing the variables and mapping them to regions are provided in SI Appendix, Tables S1–S3.

After standardization, predictor variables from each region were included in a hierarchical linear model that allowed for relationships to change after 1988/1989. The general form of the model used is ${\widehat{y}}_{t,i}=x_{t,i}{b}_i\cdot \left(z_{t,i}\cdot r_i\right)$, where $x_{t,i}$ denotes the value of the independent variable at time t for time series i, $b_i$ is the estimated coefficient for time series i, $z_{t,i}$ is an indicator designating whether the data point corresponds to the first or second era (0 if 1988 and before, 1 if 1989 and after), and $r_i$ is the estimated ratio of the slopes in era 2 to era 1. For all models, we assumed the residuals were Gaussian, $y_{t,i}\sim N\left({\widehat{y}}_{t,i},{\sigma }_{resid}\right)$, and did not include an intercept because the response variables (PDO/NPGO anomalies) are centered on 0. Within the same region and response variable (PDO or NPGO), we allowed the slope for each predictor variable to vary hierarchically so that $b_i\sim N\left({\mu }_b,{\sigma }_b\right)$, where each variable is indexed by i, and ${\mu }_b$ and ${\sigma }_b$ are hyperparameters describing the population of estimated slopes across variables. The ratio $r_i$ allowed the percent change in slope to be different by variable (i) but was also estimated hierarchically, $r_i\sim N\left({\mu }_r,{\sigma }_r\right)$. Values of r_i greater than −1 and less than 1 indicate a slope that has become weaker or smaller in magnitude after 1989, $r_i<0$ indicates a switch in the direction of association with the predictor variable, and r_i less than −1 or $r_i>1$ indicates a stronger association (greater slope) in era 2.

We conducted estimation separately by region (EBS, GOA, NCC, CCC, SCC), response variable (PDO, NPGO), and variable type (environmental, biological). Estimation was performed in a Bayesian framework using R (50) and Stan (51). For each model, we ran three parallel Markov chain Monte Carlo chains for 6,000 iterations, discarding the first 3,000 samples. The R-hat statistic was used to assess convergence, with a threshold of 1.05 or below (52). Posterior summaries (medians, quantiles) were then generated to allow comparison across variables and regions.

Time-varying models for salmon stock-recruitment dynamics were structured in a similar fashion to those for other biological time series (described above), save for the addition of parameters representing density-dependent compensation and accounting for lag-1 autocorrelation in the residual error structure. Models for salmon data were based around a linearized version of the Ricker model (53), $ln\left(R_{i,t}/S_{i,t}\right)={\alpha }_i-{\beta }_i{S}_{i,t}+{\delta }_{i,t}{x}_{t,i}+{\epsilon }_{i,t}$, where $R_{i,t}$ is the recruitment of stock $i$ from the spawning abundance $S_{i,t}$ in brood year $t$, ${\alpha }_i$ is the density-independent Ricker productivity parameter for stock $i$, ${\beta }_i$ describes the strength of density-dependent compensation or the rate at which population productivity declines with increasing stock size, and ${\delta }_{i,t}$ describes the effect of a covariate ($x_{t,i}$) in year $t$ on stock $i$. Similar to the model structure described above, we quantified whether the relationship between salmon population productivity and climate indices (i.e., PDO and NPGO) had changed before and after 1988/1989 with a multiplicative effect of era ($r_j$):

$$\begin{array}{cc}{\delta }_{i,t}=b_i& t\le 1988,\\ {\delta }_{i,t}=b_i{r}_j& t\ge 1989.\end{array}$$

Era effects were estimated separately for each region $j$, such that the appropriate region-specific parameter $r_j$ was correctly indexed to each stock $i$.

Process errors in stock–recruitment relationships, ${\epsilon }_{i,t}$, were assumed to be autocorrelated such that ${\epsilon }_{i,t}={\varphi }_i{\epsilon }_{i,t-1}+{\mathit{ϵ}}_{i,t}$, where ${\varphi }_i$ is the lag-1 correlation coefficient and ${\mathit{ϵ}}_{i,t}$ are the uncorrelated errors which are normally distributed ${\mathit{ϵ}}_{i,t}\sim N\left(0,{\sigma }_{\mathit{ϵ}}^2\right)$. Separate models for each of the indices (PDO and NPGO) were fit to data from each salmon species separately. Within species-specific models, Ricker ${\alpha }_i$ parameters were structured hierarchically such that ${\alpha }_i\sim N\left({\mu }_{\alpha },{\sigma }_{\alpha }^2\right)$, where ${\mu }_{\alpha }$ and ${\sigma }_{\alpha }^2$ are hyperparameters describing the mean and variance in stock-specific parameters. Prior probability distributions for model parameters were mildly informative: ${\mu }_{\alpha }\sim N\left(0,5^2\right)$, ${\sigma }_{\alpha }^2\sim N\left(0,5^2\right)\left[0,\right]$, ${\beta }_i\sim N\left(0,{0.001}^2\right)$, ${\sigma }_{\mathit{ϵ}}^2\sim N\left(0,1^2\right)$, $b_i\sim N\left(0,1^2\right)$, $r_j\sim N\left(1,1^2\right)$, and ${\widehat{\varphi }}_i\sim N\left(0,2^2\right)$, where the model correlation coefficient was smoothly transformed onto the scale $-1$ as ${\varphi }_i=\left(2e^{{\widehat{\varphi }}_i}/1+e^{{\widehat{\varphi }}_i}\right)-1$.

Data Availability.

Data and code for reproducing all results are publicly available on the changing-pdo-npgo repository (https://github.com/mikelitzow/changing-pdo-npgo; DOI: 10.5281/zenodo.3635046). Data for reproducing Fig. 5 are also available in Datasets S1–S4.