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  • View in gallery

    Linear rates of sea surface height change measured by satellite altimeters shown with annually averaged coastal sea level anomalies from selected North Pacific tide gauges. Note that the sign of the altimeter rates is consistent with rates measured by tide gauges during the altimeter period (gray shading). The satellite-derived values are courtesy of the University of Colorado Sea Level Research Group.

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    (a) Standard deviation of NCEP–NCAR reanalysis zonal wind stress during the period 1948–2010. (b) Difference in rates of zonal wind stress change between the 1992–2010 and 1948–91 periods. The white box in both panels represents the area over which zonal wind stress is averaged for the regression of San Diego sea level onto equatorial zonal wind stress.

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    (a) Vector combinations of zonal and meridional regression coefficients for regressions of annual average wind stress onto τeq (arrows) and the magnitude of the vectors (colors). (b) As in (a), but with increased detail near the tide gauges of interest. The regression coefficients are unitless and the color bar in (b) applies to both panels.

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    Detrended San Diego sea level (minus reconstructed global mean sea level) and the result of a multiple linear regression onto τeq, τls, and τxy. The least squares fitted coefficients are listed in Table 2.

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    Detrended tide gauge sea levels (minus reconstructed global mean sea level) along the Pacific North American coast (black lines) with the sum of the best fit of equatorial wind stress to San Diego (asd × τeq) and the sum of the best fit of the residual to local longshore wind stress (b × τls) and local WSC (c × τxy). The least squares fitted coefficients (b and c) at each location are listed in Table 2.

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    (right) Location of tide stations for (left),(middle) panels. (left) The fraction of variance accounted for by the equatorial (yellow), longshore (blue), WSCl (gray), and combined (red) components in the multiple regression. (middle) Linear rates of change during the altimeter period for the measured sea levels (black bar) and estimates of each contribution to the rate from the individual wind-forced components. Bars in this figure represent values for the orthogonalization when covariance between τls and τxy is removed from τxy. The black circles represent the case when the covariance is removed from τls.

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    (a) Annually averaged sea level (July–June) for San Diego (black) and Fremantle (red). (b) The 20-yr sea level change rates from San Diego (black) and Fremantle (red).

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    San Diego sea level (black) minus GMSL and least squares regressions of the SOI onto the sea level (red). Regressions are shown for annual averages centered on winter (July–June), winter averages (October–March), and summer averages (April–September).

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    Coefficients for regressions of zonal wind stress onto the SOI for (a) winter averages (October–March) and (b) summer averages (April–September). The wind stress time series and SOI were detrended over their common period before performing the regression. The regression is performed using the negative of the SOI, such that a positive coefficient represents stronger easterly winds during La Niña conditions.

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    San Francisco winter sea level minus GMSL (black) and winter averages of SOI (red) scaled as the best fit to San Diego sea level as in Fig. 8.

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    (a) San Francisco winter sea level (hSF) minus winter averages of the SOI scaled as the best fit to San Diego sea level (asd × SOI, thin black). A low-pass filter passing variability longer than 10 yr is applied to highlight decadal variability (thick black). (b) Low-pass filtered SLP records for San Francisco from various sources: HadSLP2 (black solid), HadSLP2 uninterpolated (black dashed), Miller and Douglas (2007) (red), and the Global Historical Climate Network version 2 (GHCNv2, blue).

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    Annual average time series of the SOI (black), PDO (red solid), and NPI (red dashed) smoothed with a convolution low-pass filter passing variability longer than about 15 yr.

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Wind-Driven Coastal Sea Level Variability in the Northeast Pacific

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  • 1 Department of Oceanography, University of Hawai‘i at Mānoa, Honolulu, Hawaii
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Abstract

The rate of coastal sea level change in the northeast Pacific (NEP) has decreased in recent decades. The relative contributions to the decreased rate from remote equatorial wind stress, local longshore wind stress, and local windstress curl are examined. Regressions of sea level onto wind stress time series and comparisons between NEP and Fremantle sea levels suggest that the decreased rate in the NEP is primarily due to oceanic adjustment to strengthened trade winds along the equatorial and coastal waveguides. When taking care to account for correlations between the various wind stress time series, the roles of longshore wind stress and local windstress curl are found to be of minor importance in comparison to equatorial forcing. The predictability of decadal sea level change rates along the NEP coastline is therefore largely determined by tropical variability. In addition, the importance of accounting for regional, wind-driven sea level variations when attempting to calculate accelerations in the long-term rate of sea level rise is demonstrated.

Corresponding author address: Philip R. Thompson, Department of Oceanography, University of Hawai‘i at Mānoa, 1000 Pope Rd., MSB 317, Honolulu, HI 96822. E-mail: philiprt@hawaii.edu

Abstract

The rate of coastal sea level change in the northeast Pacific (NEP) has decreased in recent decades. The relative contributions to the decreased rate from remote equatorial wind stress, local longshore wind stress, and local windstress curl are examined. Regressions of sea level onto wind stress time series and comparisons between NEP and Fremantle sea levels suggest that the decreased rate in the NEP is primarily due to oceanic adjustment to strengthened trade winds along the equatorial and coastal waveguides. When taking care to account for correlations between the various wind stress time series, the roles of longshore wind stress and local windstress curl are found to be of minor importance in comparison to equatorial forcing. The predictability of decadal sea level change rates along the NEP coastline is therefore largely determined by tropical variability. In addition, the importance of accounting for regional, wind-driven sea level variations when attempting to calculate accelerations in the long-term rate of sea level rise is demonstrated.

Corresponding author address: Philip R. Thompson, Department of Oceanography, University of Hawai‘i at Mānoa, 1000 Pope Rd., MSB 317, Honolulu, HI 96822. E-mail: philiprt@hawaii.edu

1. Introduction

Two decades of sea surface height (SSH) measurements by satellite altimeters reveal substantial spatial variability in the long-term rate of sea level change. Regional differences in the rate of change have been linked to differential heat fluxes at the ocean surface and redistributions of ocean volume by persistent changes in wind stress (Cazenave and Nerem 2004; Willis et al. 2004). Rates in the North Pacific are of particular interest due to a stark difference in the rate of change across the basin (Fig. 1). The global mean rate during the altimeter period (1993–present) is about 3 mm yr−1 (e.g., Nerem et al. 2010). Rates in the northeast Pacific (NEP), however, are near zero or negative (Bromirski et al. 2011), whereas rates in the western tropical Pacific (WTP) are up to 3 times larger than the global rate (Merrifield 2011).

Fig. 1.
Fig. 1.

Linear rates of sea surface height change measured by satellite altimeters shown with annually averaged coastal sea level anomalies from selected North Pacific tide gauges. Note that the sign of the altimeter rates is consistent with rates measured by tide gauges during the altimeter period (gray shading). The satellite-derived values are courtesy of the University of Colorado Sea Level Research Group.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

Sea level change rates from Pacific tide gauges agree with the satellite-derived rates of change (Merrifield 2011; Bromirski et al. 2011). Figure 1 shows annual averages of sea level from long tide gauge records on either side of the North Pacific basin, and the period of overlap with the altimeter record is highlighted in gray. It is apparent from the time series in Fig. 1 that the map of North Pacific SSH change rates would look quite different given a different temporal window. Long-term rates from tide gauges in the WTP were near zero over the four decades prior to the advent of satellite altimetry (Church et al. 2004; Merrifield 2011), and rates along the NEP coast were slightly greater than the global rate during much of the twentieth century (Church et al. 2004).

It is important to understand the mechanisms driving the spatial variability in rates of change, because regional rates can be large compared to the global rate and may persist for decades. The regional rates are thus independently relevant for local coastal planning, but from a global climate perspective they also mask the more subtle changes in the underlying global rate of change. Houston and Dean (2011), for example, concluded that sea level rise has decelerated along U.S. coastlines since 1930. This conclusion is valid in the particular period analyzed, but the authors did not explicitly account for regional decadal variability. Therefore, the results are sensitive to the time period chosen and not representative of global mean sea level (Rahmstorf and Vermeer 2011). Long-term future sea level change should not be inferred from such analyses, as correctly interpreting changes in the rate of regional sea level change in a global context requires accounting for wind-driven redistributions of ocean volume. The elevated rate of sea level change in the WTP during recent decades has been linked by multiple studies to intensified trade winds over the period of enhanced rise (e.g., Carton 2005; Köhl et al. 2007; Timmermann et al. 2010; Feng et al. 2011; Merrifield 2011; Merrifield and Maltrud 2011; Becker et al. 2012; Meyssignac et al. 2012), but the decreased rate along the NEP coast has received less attention.

The dynamics governing coastal sea level variability along the NEP coast are summarized in two seminal papers by Enfield and Allen (1980) and Chelton and Davis (1982). They found variability in monthly sea level anomalies from tide gauges to be dominated by coastally trapped waves of tropical origin south of San Francisco with large-scale, longshore winds becoming increasingly important to the north. Another possible driver of NEP sea level variability is wind-stress curl (WSC), which is known to be a primary driver of open-ocean SSH variability (Lagerloef 1995; Fu and Qiu 2002). The relationship between WSC and coastal sea level is less clear, however, as there is evidence both for (Bromirski et al. 2011) and against (Chelton and Davis 1982) the role of WSC as a leading-order driver of coastal sea level variability in the NEP region.

The results of Enfield and Allen (1980) and Chelton and Davis (1982) are echoed in a variety of studies, albeit primarily in the context of interannual and shorter sea level variations associated with El Niño–Southern Oscillation (ENSO). Tropical wind anomalies associated with strong ENSO events are known to produce equatorial Kelvin waves evident in equatorial sea level (Wyrtki 1975) that propagate along the equatorial and coastal waveguides as far north as the Gulf of Alaska (Clarke 1992; Ramp et al. 1997; Meyers et al. 1998; Strub and James 2002). Even moderate ENSO events can produce tropical anomalies that propagate to subpolar latitudes, although the amplitude is smaller and harder to detect (Lyman and Johnson 2008). Local longshore winds become increasingly important with increasing latitude, and a portion of this wind forcing is due to the relationship of the strength and position of the Aleutian low to the phase of ENSO (Emery and Hamilton 1985). The interplay between these two mechanisms of sea level variability has been analyzed for the 1997–98 El Niño event using both altimetry (Strub and James 2002) and a model (Hermann et al. 2009). In both cases, results indicate the dominance of remotely forced propagating anomalies between the equator and southern California, the dominance of local longshore winds north of the Pacific Northwest, and a mixed regime between. These results are consistent with the aforementioned studies of tide gauge sea levels.

There has been less emphasis on the role of these mechanisms in sea level variations with periods longer than interannual, but there is evidence that these mechanisms are applicable at longer time scales. Bromirski et al. (2011) reproduced decadal variations in NEP sea level across the 1970s climate transition using a numerical model forced by reanalysis winds and related recent changes in the rate of NEP sea level change to changes in the wind field over the North Pacific. It is unclear in this case, however, what physical mechanisms communicate the wind forcing to the coast. Clarke and Lebedev (1999) found that decadal and longer changes in eastern Pacific thermocline height at least as far north as Southern California are primarily driven remotely by variations in the strength of the equatorial trades. The response along the eastern boundary is expected to be proportional to the zonal wind stress and to be mirrored by a response in the west of similar magnitude and opposite sign (Li and Clarke 1994). As noted above, an increase in the strength of the trade winds in recent decades is well documented, as is the resultant effect on recent WTP sea level change rates. The impact of weakened trades has also been shown to be related to decadal sea level variations along the eastern boundary of the Indian Ocean at Fremantle (Feng et al. 2011), demonstrating the potential impact of tropical winds on sea level in remote locations. It is then logical to hypothesize that the deceleration of sea level rise in the NEP may also be at least partially due to the increase in trades.

The primary purpose of this paper is to use statistical methods to assess the relative roles of WSC and mechanisms detailed by Enfield and Allen (1980), Chelton and Davis (1982), and Clarke and Lebedev (1999) in the decline of NEP sea level change rates in recent decades. Based on our results, we propose a simple dynamical relationship between the observed increase in sea level change rates in the WTP since the early 1990s and the concurrent reduction in rates along the NEP coast. We also attempt to place the recent NEP rates of change in a broader context by comparing the longest NEP sea level records to climate indices and discussing the dynamical compatibility of the indices with coastal sea level variability. Finally, we assess the effect of removing variability associated with these mechanisms on estimates of sea level rise acceleration along the NEP coast and compare our calculations with those of Houston and Dean (2011).

2. Data

Monthly mean tide gauge sea levels are obtained from the Permanent Service for Mean Sea Level (PSMSL; http://www.psmsl.org). The majority of the analysis is focused on five tide gauge records situated in the northeast Pacific along the West Coast of North America: San Diego (1906–2010), San Francisco (1854–2010), Crescent City (1933–2010), Neah Bay (1934–2010), and Seattle (1899–2010). Sea levels from three gauges in the western tropical Pacific—Guam (1946–2010), Kwajalein (1948–2010), and Pago Pago (1946–2010)—and one gauge in the eastern Indian Ocean—Fremantle (1897–2010)—are also analyzed or shown for context. The inverted barometer (IB) effect on sea level is removed from the tide gauge data using the Hadley Center mean sea level pressure dataset (HadSLP2r; www.metoffice.gov.uk/hadobs/hadslp2/) (Allan and Ansell 2006).

A mean annual cycle is removed from each IB-corrected time series, and annual and seasonal averages are formed from the anomalies. Annual averages are calculated over July to June intervals when at least eight months are available in the PSMSL dataset. The year assigned to each annual value refers to January of the interval. We choose to calculate the annual averages over the July–June period because the interval is centered on winter. A majority of North Pacific wind forcing occurs in winter, and the intensity of this forcing is substantially modulated from year to year by interannual processes. One such process is ENSO, which is itself phase locked to the annual cycle and peaks in winter. Annual sea level averages centered on winter are therefore a more appropriate descriptor of interannual variability. Seasonal averages are calculated for winter (October–March) and summer (April–September) when at least four monthly averages are available.

Secular trends in sea level are assumed in this analysis to be due to processes not associated with the volume redistribution signals of interest. A portion of the secular trend at each location is due to global mean sea level (GMSL) change resulting from thermal expansion of the global ocean and mass exchange between ocean and land. GMSL change exhibits both a long-term trend and substantial decadal variability (e.g., Church et al. 2004). Our analysis is focused on redistributions of ocean volume about the global mean, and simply removing a linear trend to account for GMSL change would confound global and regional decadal variability. For this reason, we choose to account for GMSL change by subtracting a reconstruction of GMSL (Church and White 2011) from the individual sea level series analyzed. This choice limits our analysis to the 1880–2010 period over which the reconstruction is available. In section 3c, we show a time series of San Francisco sea level minus GMSL extending back to 1850. This was achieved by extrapolating the GMSL reconstruction back to 1850 via a quadratic fit to the 1880–2010 time series. The extrapolated portion of the time series was not used for any data analysis, but this technique was useful for showing the full length of the San Francisco sea level record without discontinuity.

Residual secular trends after removing the GMSL reconstruction are assumed to be due to ongoing glacial isostatic adjustment (GIA) and other vertical land motions. Trends due to GIA may be considered linear over the length of the tide gauge records and are removed via a linear least squares fit. Various time intervals are considered here, and in each case the trend is removed over a period common to all time series in that section of the analysis. We recognize that very low-frequency redistribution signals may be removed with the residual trend, but we are primarily interested in the reduction of sea level change rates along the NEP coast in recent decades and variability of similar temporal scale during other periods. Removing the residual trend does not impact our ability to draw conclusions about sea level variations of this scale.

Wind stress fields (1948–2010) were obtained from the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) Reanalysis 1 (NCEP1) project (Kalnay et al. 1996). Annual averages were computed as described above for the sea level time series, and linear trends were fit and removed to be consistent with the treatment of sea level data. The NCEP1 surface wind stress fields have been shown to produce spurious tropical Pacific SSH trends in an ocean model and to be inferior to the Wave and Anemometer-based Sea Surface Wind (WASWind) product in accounting for SSH variability measured by altimeters (McGregor et al. 2012). We attempted our analyses with both the NCEP1 and WASWind products, but found the longshore component of wind stress in the vicinity of the NEP tide gauges calculated from WASWind to have little skill in accounting for sea level variability compared to NCEP1. The spurious trends produced by NCEP1 in an ocean model are not of primary concern because we detrend the time series and focus on decadal variations. Furthermore, NCEP1 winds reasonably reproduced the pattern of SSH trends from altimetry in the tropical Pacific despite shortcomings in long-term trend magnitudes (McGregor et al. 2012). For these reasons, as well as the greater skill of longshore winds in the immediate vicinity of NEP tide gauges, we choose NCEP1 wind stress fields for our analysis.

As a proxy for wind stress variability over the tropical Pacific prior to the availability of reanalysis wind fields, we employ the Southern Oscillation index (SOI), which is defined to be the difference in sea level pressure between Tahiti and Darwin, Australia. Monthly values of the SOI (1876–present) were obtained from the Australian Bureau of Meteorology, National Climate Centre (http://www.bom.gov.au/climate/current/soihtm1.shtml). Decadal variability in the extratropical North Pacific is summarized by the Pacific decadal oscillation (PDO) index defined to be the leading principal component of North Pacific sea surface temperature poleward of 20°N (Zhang et al. 1997; Mantua et al. 1997). Monthly values of the PDO index (1900–present) were obtained from the Joint Institute for the Study of the Atmosphere and Ocean at the University of Washington (http://jisao.washington.edu/pdo/PDO.latest). In calculations involving both sea level and an index, the index is smoothed and detrended identically to the sea level.

3. Analysis

a. Wind stress regressions (1948–2010)

NEP coastal sea level variability with periods longer than about a month is most widely attributed to locally forced anomalies resulting from local longshore wind stress variability and remotely forced anomalies resulting from variability in equatorial wind stress (Enfield and Allen 1980; Chelton and Davis 1982; Strub and James 2002; Hermann et al. 2009). A third possibility is local WSC (Bromirski et al. 2011). The purpose of this analysis is to statistically identify the relative contributions of remotely forced anomalies originating in the tropics and local wind anomalies in the form of longshore wind stress and WSC to the recent reduction in the rate of NEP sea level change. The primary method is multiple linear regression with some adjustment to the basis functions due to correlations between them. Dynamically assessing the relative roles of various types of wind stress forcing could be achieved using numerical simulations, but this method will be reserved as the basis of future work. Here we focus on the five NEP gauges identified in section 2 over the 1948–2010 period for which both the NCEP1 reanalysis wind stress fields and GMSL reconstruction are available.

Equatorial wind stress (τeq) is defined to be the average zonal wind stress over the region spanning 6°S–6°N and 150°–280°E as shown by the white box in Fig. 2. The results presented here are not particularly sensitive to the latitudinal range selected. The amount of wind stress variability in this region is small relative to more poleward regions as shown by the small standard deviations in Fig. 2a. However, the magnitude of the rate of change in wind stress over this region has increased substantially in recent decades, particularly west of about 200°E (Fig. 2b). This variability in the rate of wind stress change may be related to the recent changes in rates of NEP sea level change. Local longshore wind stress (τls) is computed at each of the five tide gauge locations by interpolating the NCEP1 vector wind stresses to the tide gauge locations and projecting onto an approximate shoreline angle within a 2° radius of each location. WSC (τxy) is calculated via a line integral around approximately 4° × 4° boxes, such that the τxy grid lies on the vertices of the wind stress grid. Time series of τxy in the vicinity of each tide gauge used in the regression analysis are formed as the average of τxy time series within 600 km of each gauge. Annual averages are calculated from the monthly time series, GMSL is subtracted from the sea level records, and linear trends are removed from both sea level and wind stress time series over the 1948–2010 period as described in section 2.

Fig. 2.
Fig. 2.

(a) Standard deviation of NCEP–NCAR reanalysis zonal wind stress during the period 1948–2010. (b) Difference in rates of zonal wind stress change between the 1992–2010 and 1948–91 periods. The white box in both panels represents the area over which zonal wind stress is averaged for the regression of San Diego sea level onto equatorial zonal wind stress.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

The principal difficulty in statistically separating the relative contributions of remote and local wind forcing is the correlation between these time series. Correlations between τeq, τls, and τxy at each gauge location are given in Table 1, and correlations exceeding the 95% significance level are noted. The significance is based on a Monte Carlo distribution (104 iterations) of correlations created by calculating the Fourier transform of the each time series, randomizing the phase while preserving the amplitude of variability at each Fourier frequency, and performing the inverse transform to generate random realizations of the wind stress time series. The significant correlations between the wind stress time series imply that regressions of sea level onto these time series would produce ambiguous results.

Table 1.

Correlation coefficients between τeq, τls, and τxy at San Diego (SD), San Francisco (SF), Crescent City (CC), Seattle (SE), and Neah Bay (NB).

Table 1.

The correlation between longshore and equatorial winds at the four northernmost gauges is due to the relationship of extratropical atmospheric circulation, particularly the strength and position of the Aleutian low, to tropical variability (e.g., Bjerknes 1966; Emery and Hamilton 1985; Zhang et al. 1997). This relationship is illustrated in Fig. 3, which shows regressions of zonal and meridional wind stress over the Pacific onto τeq. The signature of the Aleutian low is apparent in the regression map over the North Pacific (Fig. 3a), such that weaker than normal equatorial trades (i.e., El Niño conditions) correspond to a deepened Aleutian low and increased longshore wind stress along the NEP coastline. The connection to the tropics also produces changes in the local WSC field near NEP tide gauges. The detailed view of the west coast of the United States (Fig. 3b) illustrates why the longshore winds at San Diego do not correlate with τeq. The coastline between San Diego and San Francisco is oriented in such a way that winds associated with the cyclonic structure of the Aleutian low impact San Francisco but not San Diego.

Fig. 3.
Fig. 3.

(a) Vector combinations of zonal and meridional regression coefficients for regressions of annual average wind stress onto τeq (arrows) and the magnitude of the vectors (colors). (b) As in (a), but with increased detail near the tide gauges of interest. The regression coefficients are unitless and the color bar in (b) applies to both panels.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

The independence of τeq and τls at San Diego allows for statistical separation in a regression, but the significant correlation between τeq and τxy is a concern. To achieve a completely independent basis for the regression at San Diego, τeq was regressed onto τxy at San Diego, and the portion of τeq variance covarying with τxy was removed. This resulted in only a minor adjustment to τeq, and the coefficient for τeq in the following regression at San Diego differs by less than one percent before and after the correction. We proceed with the adjusted τeq, because it provides a statistically independent basis for the regression. It is important to note that in the following regressions, we ignore time lags due to propagation, because the time scales associated with the propagation speeds and distances involved are on the order of a month, which is of little consequence in the annual averages employed.

San Diego sea level (ηsd) was regressed onto the wind stress and WSC time series in the form
e1
The result of the least squares multiple regression is shown in Fig. 4, and the regression coefficients for each component are given in the first column of Table 2. The wind stress and WSC time series scaled by their respective regression coefficients (Fig. 4) show that τls and τxy account for only a small fraction of sea level variance at San Diego compared to τeq. Given the independence of the time series input to the regression, the significant fraction of variance accounted for by τeq, and the location of San Diego relative to the wind field associated with the Aleutian low (Fig. 3b), we can assert that the product asd × τeq represents the sea level variability at San Diego resulting from equatorially forced anomalies. In addition, the magnitude of the regression coefficient for τeq at San Diego (asd = 4.79 m Pa−1) is dynamically reasonable as it is of the same order as one would expect from scaling the upper ocean balance between the gradient in sea surface height and wind stress at the equator (see appendix B in Clarke and Lebedev 1999).
Fig. 4.
Fig. 4.

Detrended San Diego sea level (minus reconstructed global mean sea level) and the result of a multiple linear regression onto τeq, τls, and τxy. The least squares fitted coefficients are listed in Table 2.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

Table 2.

Regression coefficients for τeq, τls, and τxy as defined in Eq. (2) and described in the text.

Table 2.

Large-amplitude sea level anomalies at San Diego resulting from equatorial forcing continue to propagate poleward and affect gauges to the north. The propensity of equatorially forced anomalies to reach subpolar latitudes is dependent on the amplitude and wavelength of the wave (Ramp et al. 1997), which are in turn dependent on the strength and duration of equatorial wind stress anomalies (Kessler et al. 1995). The greatest obstacle is the Gulf of California (GOC), which prevents the passage of small amplitude or short wavelength anomalies and alters the character and propagation speed of the large-amplitude, long-wavelength anomalies (Ramp et al. 1997; Strub and James 2002; Lyman and Johnson 2008). It can be difficult to clearly isolate all propagating anomalies north of the GOC as they are often obscured by the effects of local winds and seasonal currents (Ramp et al. 1997; Strub and James 2002), but the largest-amplitude pulses are coherent north of the GOC with little longshore difference in amplitude as observed in both altimetry (Strub and James 2002; Lyman and Johnson 2008) and high-resolution models (Ramp et al. 1997; Hermann et al. 2009).

It is the aggregate effect of the large-amplitude, large-scale wave pulses that dominates the equatorially forced component in our analysis of annual averages. One possible source of decay in this signal along the coast is radiation of coastally trapped energy away from the coast as Rossby waves. A majority of this radiation occurs at low latitudes south of San Diego, however, and is unlikely to cause significant decay in the coastally trapped signals over the relatively short distance between San Diego and Neah Bay compared to the total distance traveled by such anomalies. For these reasons we can assume the response of sea level at San Diego to remote equatorial forcing to be roughly constant at gauges to the north. This assumption allows us to circumvent the correlation between τeq and τls at gauges north of San Diego by performing a regression of the form
e2
where we assume a = asd at all gauges. We can then solve for b and c in a least squares sense at gauges other than San Diego by regressing onto residuals from the estimated response to equatorial forcing at San Diego:
e3

A simple test of the assumption that a = asd for all locations is to do a regression onto all three wind stress time series at San Francisco while taking advantage of the fact that only τeq and τls are significantly correlated (Table 1). This is similar to the situation at San Diego for which only τeq and τxy are correlated. An independent basis for a regression at San Francisco can therefore be achieved by subtracting the portion of variance that covaries with τls from τeq. The result of this calculation is a regression coefficient at San Francisco for the equatorial forcing (asd = 4.64 m Pa−1) that is very close to the value obtained for the same coefficient at San Diego. This test is not possible at the three northernmost gauges as all three inputs to the regression are significantly correlated, but the result at San Francisco supports the use of Eq. (3).

Fitted values of b and c in Eq. (3) must be interpreted carefully because of the correlation between τls and τxy at the three most northern gauges. To aid in the interpretation of these coefficients, we orthogonalize τls and τxy in two ways prior to regressions of sea level. First, covariance between τls and τxy is removed from τxy allowing for a maximum fraction of sea level variance to be accounted for by τls. We then removed the covariance from τls and repeated the regression, allowing τxy to account for a maximum fraction of variance. The coefficients for the latter case are referred to as b* and c*. Solving for the coefficients using these two sets of orthogonalized time series provides upper and lower bounds on the expected error in the coefficients due to the covariance between τls and τxy. The regression coefficients estimated in this way are given in the second and third rows of Table 2.

Figure 5 shows the time series of sea level corrected for GMSL at each gauge with the best estimate of the sea level variability from the sum over all three wind-forced contributions, which is independent of how τls and τxy are orthogonalized. The dominant temporal features of sea level variability along the west coast of North America are captured by the regression, including interannual variations associated with ENSO and the recent decrease in the sea level change rate relative to GMSL. We note the amplitude of the largest El Niño events is not fully accounted for in some locations (e.g., the 1982–83 El Niño at San Francisco). This indicates that there are other significant factors contributing to sea level anomalies during the large ENSO events. Possibilities include anomalous river flow for gauges near river mouths, a phenomenon known to affect sea level at San Francisco (Wang et al. 1997; Ryan and Noble 2007), and coastally trapped waves generated by tropical storms (Merrifield 1992).

Fig. 5.
Fig. 5.

Detrended tide gauge sea levels (minus reconstructed global mean sea level) along the Pacific North American coast (black lines) with the sum of the best fit of equatorial wind stress to San Diego (asd × τeq) and the sum of the best fit of the residual to local longshore wind stress (b × τls) and local WSC (c × τxy). The least squares fitted coefficients (b and c) at each location are listed in Table 2.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

The skill of the regression analysis is summarized in Fig. 6. The left bar plot shows the fraction of variance accounted for by the combined contributions of τeq, τls, and τxy, as well as the fraction accounted for by the individual components. The fraction of variance accounted for is calculated as one minus the ratio of residual variance to total variance. The colored bars for τls and τxy represent values for the orthogonalization resulting in coefficients b and c, whereas the black dots over each bar represent values for the orthogonalization resulting in coefficients b* and c*. The total variance fraction accounted for by the regressions is similar between all gauges with a maximum of 66% at Crescent City and a minimum of 53% at Neah Bay. It is interesting to note, however, that the relative importance of each individual component differs between the southern and northern gauges. At San Diego and San Francisco, the fraction of variance accounted for by local wind anomalies, τls and τxy, is small and variability of tropical origin dominates. Poleward of San Francisco, longshore wind becomes the dominant driver of sea level variability, which is consistent with the literature. If we allow for τxy to account for a maximum fraction of variance given the covariance between τls and τxy, then WSC contributes substantially at only the two northernmost gauges, which are in close proximity.

Fig. 6.
Fig. 6.

(right) Location of tide stations for (left),(middle) panels. (left) The fraction of variance accounted for by the equatorial (yellow), longshore (blue), WSCl (gray), and combined (red) components in the multiple regression. (middle) Linear rates of change during the altimeter period for the measured sea levels (black bar) and estimates of each contribution to the rate from the individual wind-forced components. Bars in this figure represent values for the orthogonalization when covariance between τls and τxy is removed from τxy. The black circles represent the case when the covariance is removed from τls.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

The right bar plot shows the rate of change in sea level over the 1992–2010 period, which is shaded in Fig. 5. Also shown are the rates of change (in mm yr−1) from each regression component scaled by the regression coefficient. The sum of the rates due to each of the components reproduces the actual rate of sea level change within 15% at all gauges with the exception of Neah Bay, where the reduction in rate is overestimated by the regression. This may reflect decay in the tropical anomalies propagating along the coast or some process not included in the regression. The recent rate at nearby Seattle, however, is consistent with the regression, which suggests the mismatch at Neah Bay may be due to a local process not included in the statistical model. The reason for the mismatch between rates in sea level and the best-fit regression at Neah Bay will be addressed in future work involving numerical simulations. The salient aspect of the calculations involving recent rates of change is that the combined contributions to the recent rate from τls and τxy is never greater than about 60% of the rate in the τeq component. This is in contrast to the fraction of variance explained by each component, where local wind anomalies dominate at more poleward locations. This suggests that although local longshore winds are an important driver of coastal sea level variability, the recent suppression of sea level rise along the NEP coastline is of primarily tropical origin resulting from adjustment along the waveguide to anomalous equatorial wind stress.

b. East–west connection

Amplification of Pacific trade winds in recent decades has led to a thickening of the upper ocean layer and increase in dynamic height in the WTP (e.g., Timmermann et al. 2010). If volume in the upper layer is conserved, then the thickening in the WTP must be balanced by a thinning of the upper layer elsewhere, and this adjustment necessarily occurs, at least initially, along the equatorial and coastal waveguides (Clarke and Lebedev 1996, 1997). We propose that this mechanism dynamically links long-term rates of coastal sea level change in the western and eastern Pacific and contributes to the zonal gradient in rates of change observed by altimeters (Fig. 1). If this is a viable explanation for the recent suppression of sea level rise along the NEP coast, however, it is unlikely that this mechanism is only active in recent decades. Therefore, we should be able to observe an out of phase relationship in sea level change rates across the Pacific basin during earlier periods.

We have shown that the San Diego tide gauge record is dominated by variability of tropical origin, as equatorial wind stress accounts for approximately 50% of the variance in annual sea level anomalies about the global mean (Fig. 6). The San Diego record is long and spans almost the entire twentieth century, which affords calculations of long-term sea level change rates in multiple independent periods. Records in the WTP are much shorter, however, constraining the period over which rates across the Pacific may be compared. An alternative to the WTP records is the Fremantle tide gauge on the eastern boundary of the Indian Ocean (Fig. 1). The Fremantle tide gauge record also spans the twentieth century and is located on a coastal waveguide along which anomalies originating in the tropical Pacific propagate (Pariwono et al. 1986; Feng et al. 2004). Fremantle sea level is also known to be related to wind forcing over the Pacific (Feng et al. 2010) and dominant Pacific climate modes such as the SOI and PDO (Feng et al. 2011).

Annual sea level time series from the San Diego and Fremantle tide gauges are compared in Fig. 7a. These series are not corrected for GMSL, and the rates of change over the twentieth century are similar to the global mean twentieth-century rate of about 2 mm yr−1. The twentieth-century trends from these two locations are likely representative of GMSL, because neither location is strongly influenced by land motion associated with GIA (Lambeck 2002). The correlation between the time series after subtracting GMSL from each is −0.56 (significant at the 99% level). This indicates an out-of-phase relationship between the two locations, but substantial interannual variability obscures the decadal and longer rates of change.

Fig. 7.
Fig. 7.

(a) Annually averaged sea level (July–June) for San Diego (black) and Fremantle (red). (b) The 20-yr sea level change rates from San Diego (black) and Fremantle (red).

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

To emphasize rates similar in temporal scale to those measured by satellite altimetry, 20-yr sea level change rates were calculated from the annual San Diego and Fremantle series (Fig. 7b). The 20-yr rates were calculated by smoothing first differences of the annual averages in Fig. 7a with a convolution low-pass filter passing half the amplitude at 20 years. We tested this method against the more straightforward method of calculating linear trend coefficients in running 20-yr windows and found smoothed first differences to be a more robust estimate of the 20-yr rates. The test consisted of adding noise to a simple analytic function with known rates of change and assessing the ability of each method to recover the known rates from the noise.

The resultant rate series from San Diego and Fremantle are surprisingly coherent during the twentieth century despite being located in different hemispheres and ocean basins. The correlation between the two rate series is −0.64, which is significant at the 99% level assuming 15 degrees of freedom. The only plausible explanation for the coherence is common tropical Pacific forcing communicated to each location along the equatorial and coastal waveguides. The relationship between long-term rates at San Diego and Fremantle coupled with results from the wind stress regressions leads to the conclusion that the recent suppression of coastal sea level rise along the NEP coast is the result of a thinning upper ocean layer in compensation for thickening in the WTP by anomalous equatorial winds. The thinning of the upper layer is communicated to the NEP coastline from the tropics via adjustment along the waveguide.

c. Sea level pressure analyses (1875–2010)

The coherence between rates of change at San Diego and Fremantle suggest that the mechanism responsible for the recent decrease in NEP sea level change rate is active during most of the twentieth century. It is then logical to assess the viability of this mechanism in accounting for the large-amplitude multidecadal sea level fluctuation in the San Francisco tide gauge record discussed by Miller and Douglas (2007). The multidecadal variation consists of rapid rise greater than 5 mm yr−1 from 1860 to 1880 and sea level fall of 3–4 mm yr−1 from 1880 to 1900. This large-amplitude fluctuation is followed by a slow increase in rate over the next 20 yr to a long-term rate of about 2 mm yr−1, which is maintained for much of the remaining century.

Wind stress time series are not available to assess the nature of the late nineteenth- and early twentieth-century variability, but we do have long records of sea level pressure (SLP) in the Pacific, which can serve as a proxy for wind forcing. To investigate the nature of the multidecadal fluctuation prior to the availability of wind stress reanalysis fields, we employ a method qualitatively similar to that of section 3a, but replacing wind stress with proxies derived from long time series of SLP. Instead of equatorial wind stress, we use the Southern Oscillation index. The SOI is not a direct measure of wind stress, but it is correlated with variability in equatorial winds. We scale the SOI to have units of wind stress (N m−2) by regressing τeq onto the SOI during the period over which they overlap and multiplying the SOI by the coefficient. We scale the SOI in this way such that the regression coefficients of sea level onto the SOI may be directly compared to the regressions of sea level onto τeq in section 3a. As shown in section 3a, sea level variability at San Diego is dominated by anomalies of tropical origin propagating along the waveguide, and local winds account for very little variance in San Diego sea level. Thus, we regress San Diego sea level onto the SOI and use the SOI multiplied by the regression coefficient as a proxy for equatorially forced variability along the NEP coast.

The result of regressing annual averages of the SOI onto annual averages of San Diego sea level is shown in the topmost pair of curves in Fig. 8. The agreement between the two time series is quite good, as the SOI accounts for more than 50% of the variance in annual sea level anomalies. A possible complication with this calculation is that the SOI is a Southern Hemisphere measurement, as Darwin and Tahiti are located at roughly 12.5° and 17.5°S, respectively. The locations of the SLP records suggest that the relationship of the SOI to equatorial wind stress is likely to be seasonally dependent. The seasonal dependence of the relationship between the SOI and equatorial wind stress is illustrated in Fig. 9, which shows coefficients for regressions of zonal wind stress onto the SOI during winter (October–March; Fig. 9a) and summer (April–September; Fig. 9b). Although the relationship between the SOI and zonal equatorial wind stress is positive during the summer season, the relationship is stronger and more concentrated about the equator in winter. The SOI is therefore a better proxy for equatorial wind forcing during boreal winter.

Fig. 8.
Fig. 8.

San Diego sea level (black) minus GMSL and least squares regressions of the SOI onto the sea level (red). Regressions are shown for annual averages centered on winter (July–June), winter averages (October–March), and summer averages (April–September).

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

Fig. 9.
Fig. 9.

Coefficients for regressions of zonal wind stress onto the SOI for (a) winter averages (October–March) and (b) summer averages (April–September). The wind stress time series and SOI were detrended over their common period before performing the regression. The regression is performed using the negative of the SOI, such that a positive coefficient represents stronger easterly winds during La Niña conditions.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

The seasonal nature of the SOI–wind stress relationship suggests that the SOI should be a better predictor of San Diego sea level in winter than in summer. This is indeed the case as shown in the bottom two pairs of curves in Fig. 8, which show regressions of seasonal averages of San Diego sea level onto seasonal averages of the SOI. Clearly, the relationship between annual averages of the SOI and San Diego sea level is primarily due to covariance during boreal winter; the summer months are not significantly related. During winter, the SOI accounts for 70% of the variance in San Diego sea level, whereas the SOI accounts for less than 15% of the variance in summer. The regression coefficient for SOI in winter is 5.14 m Pa−1, which is similar to the coefficient of 4.79 m Pa−1 achieved when regressing San Diego sea level directly onto wind stress in section 3a. It is interesting to note that not only does the SOI account for the reduction in the rate of change of winter sea level at San Diego in recent decades, but the reduction in rate itself is much less apparent in summer. We also note that there is doubt concerning the accuracy of the SOI prior to about 1930 (Trenberth 1997). This does not appear to be of concern in this analysis, however, as the relationship between sea level and the SOI is equally good in the early part of the record compared to later periods. Correlations between the SOI and the 25 years of San Diego sea level prior to 1930 are −0.72, −0.77, and −0.37 for annual, winter, and summer averages, respectively. After 1930, the correlations are −0.75, −0.86, and −0.36. Because of the strong relationship of the SOI to San Diego sea level during winter and the weak relationship during summer, we conclude that using the SOI as a proxy for equatorially forced NEP sea level anomalies is only appropriate during winter months, and all analyses concerning the SOI discussed in this section will be restricted to winter averages.

To assess if the multidecadal variation in the late nineteenth- and early twentieth-century San Francisco sea level is also due to remotely forced anomalies from the tropics, we compare the longer record of San Francisco winter sea level to winter averages of the SOI scaled by the regression coefficient from San Diego (Fig. 10). We use the coefficient from the San Diego gauge, because as shown in the wind stress regressions (section 3a), longshore winds at San Francisco are correlated with equatorial winds. Thus, regressing San Francisco sea level onto the SOI would produce ambiguous results. We note that there is also correlation between the equatorial winds and WSC at San Diego, which could indicate an initial ambiguity in the regression at San Diego, used to calculate the SOI coefficient. This is not found to be problematic, however, because the magnitude of the WSC variability near San Diego is not sufficient to account for the magnitude of the sea level variations based on the expected SSH response to Ekman pumping.

Fig. 10.
Fig. 10.

San Francisco winter sea level minus GMSL (black) and winter averages of SOI (red) scaled as the best fit to San Diego sea level as in Fig. 8.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

The SOI scaled by the regression coefficient at San Diego (asd × SOI) accounts for less variance at San Francisco (R2 = 0.52) than at San Diego (R2 = 0.70). This is due in part to the inability of the SOI to account for low-frequency variability in San Francisco sea level prior to about 1920 (Fig. 10). The decreased skill of the SOI during this period is further illustrated in Fig. 11a by the large differences between San Francisco sea level and the scaled SOI in the late nineteenth century. Residual variability not accounted for by the SOI is shown and then low-pass filtered to emphasize the long-term variability in the residuals. The convolution filter applied to the residuals passes variability with a time scale longer than about 10 years. By subtracting variability correlated with the SOI, low-frequency variability is suppressed during most of the record, but prior to 1900 there is substantial long-term variability not accounted for by equatorial forcing represented by the SOI. Recent low-frequency sea level variations at San Francisco since the 1980s are captured well by asd × SOI, but the SOI does not exhibit the negative rates in the late eighteenth and early nineteenth centuries identified by Miller and Douglas (2007).

Fig. 11.
Fig. 11.

(a) San Francisco winter sea level (hSF) minus winter averages of the SOI scaled as the best fit to San Diego sea level (asd × SOI, thin black). A low-pass filter passing variability longer than 10 yr is applied to highlight decadal variability (thick black). (b) Low-pass filtered SLP records for San Francisco from various sources: HadSLP2 (black solid), HadSLP2 uninterpolated (black dashed), Miller and Douglas (2007) (red), and the Global Historical Climate Network version 2 (GHCNv2, blue).

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

The length of the SOI prevents comparison with the first half of the multidecadal fluctuation prior to 1875, but if the SOI is unable to account for the second half of the fluctuation, it is unlikely to account for the first half. Miller and Douglas (2007) related this multidecadal variability to local SLP near San Francisco and the first empirical orthogonal function (EOF) of SLP over the North Pacific. They note that the amplitude of the sea level variability is too large to be accounted for by the inverted barometer effect, and thus is likely related to gyre-scale wind forcing. This variability is possibly related to the northern annular mode, as Miller and Douglas (2007) show a similar sea level fluctuation and SLP pattern in the North Atlantic during this period.

The specifics of the mechanism relating the gyre-scale wind forcing and the response at the coast are difficult to ascertain for a couple of reasons. First, the distribution of sea level and SLP records long enough to observe the late nineteenth century is sparse. Thus, we are relegated to extrapolating large-scale behavior from a limited number of point measurements. Second, multidecadal variability in time series of SLP differs substantially between various holdings of station SLP and gridded products. To illustrate these differences, four different time series of SLP at San Francisco are shown in Fig. 11b. Two time series from gridded products obtained from the Hadley Center (HadSLP2), one optimally interpolated and the other uninterpolated, are largely devoid of multidecadal variability akin to that observed in San Francisco sea level. On the other hand, two station records, one obtained from the Climate Research Unit (CRU) at East Anglia by Miller and Douglas (2007) and the other obtained from the Global Historical Climatology Network version 2 (GHCNv2) housed at the National Climatic Data Center (NCDC) exhibit multidecadal variations but differ substantially in phase and periodicity.

The SLP record that agrees best with the San Francisco sea level record is the one used by Miller and Douglas (2007) (red line in Fig. 11b). The low-passed time series of sea level (thick black line in Fig. 11a) and this particular SLP time series show similar low-frequency characteristics during the period prior to the 1920s shaded in Fig. 11. Miller and Douglas (2007) note that this particular record is the one that agrees best with the sea level and conclude that it is the correct one given the correspondence with sea level. Because of the inconsistencies between SLP time series between holdings, however, we do not attempt to investigate the details of the mechanism responsible for the multidecadal change in San Francisco sea level in the late nineteenth and early twentieth century. Instead, we simply agree with Miller and Douglas (2007) that the multidecadal fluctuation in the early portion of the San Francisco sea level record is unlikely to be due to tropical forcing as represented by the SOI, which contrasts with the recent reduction in the rate of NEP sea level change.

4. Discussion

a. Sea level change acceleration

Houston and Dean (2011) question whether global sea level rise has accelerated over the last century on the basis of linear least squares fits of individual tide gauge records to quadratic polynomials. They analyzed two sets of tide gauges: United States gauges and the set of gauges used by Douglas (1992). The authors calculated accelerations over the full record of each tide gauge and also over an 80-yr period from 1930 to 2010 where possible. From the quadratic fits, they determine that sea level has possibly decelerated during the last century and point out the contradiction this presents with the global temperature increase over the same period.

As pointed out by Rahmstorf and Vermeer (2011), however, the conclusions reached by Houston and Dean (2011) are suspect for a few of reasons. The reason most relevant to this study is that any given tide gauge primarily represents regional variability, and drawing conclusions about global sea level from tide gauge records requires accounting for local variations. This is most often done statistically via various sorts of weighted averages (Douglas 1997; Jevrejeva et al. 2006; Merrifield et al. 2009) or EOF reconstructions (Chambers et al. 2002; Church et al. 2004; Ray and Douglas 2011; Hamlington et al. 2011; Church and White 2011). A different approach would be to explicitly account for the regional variability via the dynamic relationship between wind stress and sea level. The primary purpose of this paper is not to isolate global mean sea level in NEP tide gauge records, but we can comment on the effect of explicitly accounting for regional variability in calculations similar to those of Houston and Dean (2011).

Accelerations were calculated by Houston and Dean (2011) via a least squares fit to a quadratic polynomial of the form
e4
where r is the average rate over the period in mm yr−1, and a is the acceleration in mm yr−2. We adopt the same method to illustrate the effect of accounting for regional variability in such calculations. Accelerations calculated by Houston and Dean (2011) for the gauges analyzed in this study are shown in the first row of Table 3. The authors find negative accelerations for all sea level records presented here over periods that vary from gauge to gauge. The values from Houston and Dean (2011) shown in Table 3 correspond to either the 1930–2010 period or the full length of the record, whichever is shorter. In all cases, the Houston and Dean (2011) period is longer than the 1948–2010 period analyzed in this study, which is dictated by the availability of reanalysis wind stress fields. The period since 1948 does exceed the minimum length of 60 years recommended by Douglas (1992) for analysis of global variability in tide gauge sea levels. We note, however, that the 60-yr criterion may be insufficient for separating regional and global variability when large-amplitude, multidecadal fluctuations in sea level (Miller and Douglas 2007; Chambers et al. 2012) are considered.
Table 3.

Acceleration coefficients (mm yr−2) during the period 1948–2010 from a linear least squares fit to a quadratic for annually averaged northeast Pacific sea level anomalies (ηtg) and anomalies minus estimated regional wind-driven variability (ηtgηws). Also shown are acceleration coefficients during the 1930–2010 period or entire record, whichever is shorter, from Houston and Dean (2011).

Table 3.

The second and third rows of Table 3 show acceleration values calculated over the period of wind stress availability prior to and after subtracting variability associated with wind-driven volume redistribution estimated via the methods in section 3a. Accelerations for all gauges prior to correcting for regional variability are negative and of similar magnitude as the values found by Houston and Dean (2011). After correcting for the wind-driven regional variability, however, recalculating the accelerations gives positive values for all gauges except San Francisco, which results in an acceleration near zero. The acceleration values after correcting for wind-forced variability at gauges excluding San Francisco are consistent with calculations of global mean sea level acceleration since 1950 (e.g., Fig. 1 in Rahmstorf and Vermeer 2011). The reason for a smaller acceleration at San Francisco relative to the other gauges is likely due to the inability of the regression to account for the large sea level variation associated with the 1982–83 El Niño event near the middle of the time series. Thus, attempting to correct for wind-driven regional variability, at least in the few gauges of interest here, appears to reverse the conclusion of Houston and Dean (2011). Accelerations calculated after correcting for regional variability are mostly positive and consistent with accelerations in GMSL over the same period as estimated by both EOF reconstructions and the semiempirical relationship of GMSL to global mean temperature.

b. What about the PDO?

The Pacific decadal oscillation is a mode of North Pacific extratropical sea surface temperature (SST) variability that manifests in a variety of indicators, including fisheries (Mantua et al. 1997), atmospheric circulation (Trenberth and Hurrell 1994; Deser and Blackmon 1995), observed open ocean dynamic heights (Lagerloef 1995; Cummins et al. 2005), and SSH from altimetry and models (e.g., Di Lorenzo et al. 2008; Zhang and Church 2012; Hamlington et al. 2012). Recent sea level change rates along the NEP coast are often associated with the PDO due to the similarity between the spatial pattern of North Pacific SSH rates measured by altimetry (Fig. 1) and the loading pattern of the PDO in SST (e.g., Mantua et al. 1997; Zhang et al. 1997). In addition to the spatial similarity, the recent decrease in the rate of NEP sea level change is coincident with a negative trend in the PDO index.

Despite these qualitative relationships, it is difficult to dynamically link open ocean variability associated with the PDO to the recent reduced rate of NEP sea level change. Studies of satellite altimetry data have shown significant skill in accounting for SSH variability in the interior of the North Pacific via the baroclinic response of the ocean to WSC (Lagerloef 1995; Cummins and Lagerloef 2002; Fu and Qiu 2002). However, dynamical constraints prevent WSC forcing over the interior from being communicated eastward to the coast. In addition, Rossby waves originating at the eastern boundary have little skill in accounting for interannual SSH variability outside of a few hundred kilometers offshore because they are overwhelmed by wind-driven Rossby waves in the interior (Fu and Qiu 2002). Thus, it is possible for sea level variability along the NEP coastline to be decoupled from variability in the basin interior due to differing mechanisms of variability. The characteristic “horseshoe” pattern in NEP SST and SSH associated with the PDO primarily reflects the baroclinic response to WSC forcing by the Aleutian low over the extratropics. In contrast, analyses presented here show that recent NEP coastal sea level trends are a response to remote tropical forcing.

Our analysis of NEP coastal sea level in the first half of the twentieth century focuses on the SOI instead of the PDO, because the SOI is a direct proxy for tropical wind strength. The PDO is generally considered to be a superposition of coupled tropical processes (i.e., ENSO) and the dynamical response of the ocean to extratropical wind forcing (e.g., Newman et al. 2003; Schneider and Cornuelle 2005). As a result of the connection between tropical variability and the PDO, the PDO index and the SOI show similar multidecadal phase transitions during the second half of the twentieth century (Fig. 12). Thus, based on the indices alone, it is not possible to determine the dynamical component of North Pacific decadal variability that drives sea level change in tide gauge records that only span the second half of the twentieth century (Merrifield et al. 2012). Earlier in the century, however, the two indices differ, as the PDO exhibits a multidecadal shift from positive to negative phase around 1945 that is not evident in the SOI time series. This contrasts with the climate shift in the late 1970s, when both indices show a change in phase.

Fig. 12.
Fig. 12.

Annual average time series of the SOI (black), PDO (red solid), and NPI (red dashed) smoothed with a convolution low-pass filter passing variability longer than about 15 yr.

Citation: Journal of Climate 27, 12; 10.1175/JCLI-D-13-00225.1

It is possible that the difference between the two indices in the early twentieth century is due to a degradation in the data used to create the indices, but evidence from other sources suggest this is not the case. The North Pacific index (NPI; Trenberth and Hurrell 1994) is a measure of the strength of the Aleutian low (deemed reliable after 1924) that also shows the midcentury phase transition evident in the PDO index. Reconstructions of the PDO from tree rings show this transition as well (e.g., Biondi et al. 2001). Furthermore, the long-term stability of the relationship between the SOI and sea level (Fig. 8) suggest that early twentieth-century variability in the SOI is also robust. Therefore, the multidecadal phase change in extratropical variability captured by the PDO index does not appear to be closely tied to the tropics in the same way as the more recent transition during the 1970s. The PDO index shows a significant positive correlation with the North Atlantic Oscillation in decades prior to the midcentury PDO transition, but the two show a small negative correlation in decades after (Zhao and Moore 2009). This indicates that Arctic modes of variability (e.g., the Arctic Oscillation) may play a more prominent role in the midcentury PDO phase change not captured by the SOI.

Coastal sea level records in the NEP are long enough to resolve the time period during which the SOI and PDO differ. As shown in Fig. 8, San Diego sea level is significantly related to the SOI, particularly in winter, and does not appear to show the 1940s transition evident in the PDO time series. Table 4 gives correlation coefficients between the three longest NEP sea level records—San Diego, San Francisco, and Seattle—and the SOI and PDO indices for annual, winter, and summer averages after 1900. Correlations are also given between sea level and PDO*, which is defined as PDO variability not accounted for in a linear regression of the PDO onto the SOI. The correlation between sea level and PDO* is essentially a partial correlation accounting for the covariance between SOI and PDO, where PDO* represents PDO variability with a nonzero lag relationship to tropical wind strength. We perform the calculation in this way, because the hypothesized relationship between tropical winds and NEP coastal sea level represents a direct proportionality consistent with the dynamics of anomalies propagating along the waveguides (Li and Clarke 1994; Clarke and Lebedev 1996, 1997). The idea is to assess whether PDO variability related to the extratropical atmospheric forcing or the coupled nonlinear relationship to tropical variability (PDO*) adds additional skill in accounting for NEP coastal sea level.

Table 4.

Correlation coefficients between sea level and climate indices by season after 1900. PDO* is PDO variability not accounted for by the SOI in a regression.

Table 4.

It is apparent in Table 4 that all three sea level records are more closely related to the SOI than the PDO in the annual and winter averages. In addition, lower correlations with PDO*- show that a substantial fraction of the correlation between NEP sea level and the PDO is due to the covariance of the PDO with the SOI. This likely reflects the relationship between tropical variability and the Aleutian low via the Hadley circulation (Alexander et al. 2002). The fraction of PDO variability that is not linearly related to tropical winds (PDO*), including the midcentury phase shift, is not a skilled predictor of NEP coastal sea level. The lack of PDO-like multidecadal variability in NEP sea level is consistent with the results of Chambers et al. (2012), who identified 60-yr periodicities in sea level records from a variety of coastal regions around the global ocean. The authors noted the existence of similar periodicities in climate indices, including the PDO, but oscillations of this time scale were found to be absent in sea level records from the NEP.

This has important implications for the predictability of NEP sea level change. Bromirski et al. (2011) postulate that an imminent change in PDO phase will result in a resumption of NEP coastal sea level rise. This may prove to be the case insofar as the PDO and tropical winds (SOI) continue to vary together as in recent decades. However, as evidenced by the difference between the SOI and PDO prior to 1950, the PDO is not a reliable proxy for tropical winds. It is the predictability of tropical wind stress forcing that governs the predictability of NEP coastal sea level, but the PDO is additionally influenced by extratropical and nonlinear dynamics that are not relevant for NEP coastal sea level. Therefore, in order to predict future changes in NEP coastal sea level, it is necessary to understand and monitor decadal and longer variability in tropical winds independently of the PDO index.

5. Concluding remarks

The strengthening of equatorial trade wind forcing in recent decades has led to a thickening of the upper ocean layer in the western Pacific, which is manifested in the increased rates of sea level rise observed in the region (e.g., Timmermann et al. 2010; Merrifield 2011). If volume in the upper layer is assumed to be conserved, then the thickening of the upper layer in the western Pacific must be compensated by thinning elsewhere. This adjustment occurs along the equatorial and coastal waveguides and is found via statistical methods to be the leading cause of the recent reduction in the rate of NEP sea level change.

The evidence presented for this mechanism is twofold. First, regressions of NEP sea level onto equatorial wind stress, local longshore wind stress, and local WSC show that although local wind anomalies account for a substantial fraction of sea level variance at the more poleward tide gauge locations, it is equatorial wind stress that accounts for a majority of the recent rate of change. Second, decadal rates of sea level change at San Diego and Fremantle are highly correlated and of opposite phase during the twentieth century. The only plausible explanation for this coherence is common tropical Pacific forcing communicated to each location along the equatorial and coastal waveguides. Future work will include analysis of numerical models to further investigate the viability of this mechanism. We note that the large-amplitude multidecadal fluctuation in San Francisco sea level around the turn of the twentieth century (Miller and Douglas 2007) does not appear to be due to the same equatorially forced mechanism involved in recent NEP rates of sea level change.

Accounting for regional wind-forced redistributions in tide gauge sea levels is a necessary step when drawing conclusions about the relationship between sea level and global climate. Calculations of acceleration in the rate of sea level change at the locations analyzed here give substantially different results when an attempt is made to account for regional variability. Volume redistribution in the North Pacific due to tropical forcing gives the impression that sea level is decelerating along the NEP coastline (Houston and Dean 2011). Accounting for regional variability changes the sign of the acceleration to positive with values consistent with the acceleration in GMSL over the same period.

Acknowledgments

Valuable discussions with Eric Firing in addition to assistance from Laury Miller and Bruce Douglas are greatly appreciated. Funding for this work was provided by the Office of Climate Observations, NOAA (NA09OAR4320075).

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