1. Introduction
The dynamics of low-frequency temperature anomalies depend on whether a density signature exists (Iselin 1939; Liu and Shin 1999; Schneider 1999). Temperature anomalies with a density signature are governed by planetary wave dynamics, whereas those that are density compensated by salinity anomalies behave as a passive tracer in the upper ocean. Density-compensated salinity and temperature variability is known as spiciness (Veronis 1972; Munk 1981) with hot and salty water having high spiciness.
Advection of spiciness anomalies in the thermocline couples the mid- and low-latitude oceans and may play an important role in climate variations (Gu and Philander 1997; Williams et al. 2007). The northeast and southeast subtropical Pacific are favorable regions for generating surface spiciness variability due to a strong lateral spiciness gradient (Yeager and Large 2004, 2007; Johnson 2006; Nonaka and Sasaki 2007) and prominent interannual and decadal anomalies have been observed in the California Current (Chelton et al. 1982; Roemmich and McGowan 1995; Schwing and Mendelssohn 1997; Bograd and Lynn 2003; Schneider et al. 2005; Di Lorenzo et al. 2008). These midlatitude spiciness anomalies are subducted and propagate in the thermocline (Sasaki et al. 2010; Ren and Riser 2010) past observation points such as the Hawaii Ocean Time series (HOT) that show prominent water mass changes (Lukas 2001; Lukas and Santiago-Mandujano 2008). Part of these anomalies may resurface in the upwelling regions of the equatorial Pacific (Fukumori et al. 2004) and alter air–sea interaction and the tropical climate (Schneider 2004). A feedback loop results if the midlatitude imprint of this atmospheric response affects the generation region, producing low-frequency climate variations (Gu and Philander 1997; Schneider 2000). Aspects of these processes have been described in other ocean basins such as the South Pacific (Yeager and Large 2004, 2007; Luo et al. 2005; Nonaka and Sasaki 2007) and North Atlantic (Laurian et al. 2006, 2009).
Even in the absence of a feedback loop, decadal climate variability results from these processes when driven by stochastic atmospheric forcing that has variance at all time scales (James and James 1989). The ocean low pass filters this stochastic forcing (Hasselmann 1976), accounting for the ubiquitous frequency spectra of sea surface temperature, ocean pressure, and surface temperature climate indices such as the Pacific decadal oscillation, which are white for low frequencies and proportional to ω−2 for high frequencies, a −2 slope of the spectra in a log–log plot (Frankignoul and Hasselmann 1977; Frankignoul et al. 1997; Davis 1976; Mantua et al. 1997; Schneider and Cornuelle 2005).
Here, it is shown that stochastically forced anomalous advection in the thermocline leads to spiciness variability with frequency spectra cutoff at decadal time scales and a frequency slope of −4, an even sharper concentration of the variance at low frequencies. To this end, section 2 reviews spiciness dynamics and develops a coupled Markov model for anomalous geostrophic advection. These dynamics are explored in multiple realizations of a high-resolution primitive equation model that enables a comparison of the spiciness variability forced by the atmosphere and that due to oceanic nonlinear internal mechanisms. The model and integrations are introduced in section 3. Section 4 identifies the wind-forced spiciness signal, which is shown in section 5 to result from the Ekman pumping-forced geostrophic flow. Section 6 discusses the detection of atmospherically forced spiciness signals in a strong ocean eddy field. The dual contributions of anomalous advection and surface freshwater flux variability to interior spiciness are compared in section 7, and section 8 provides a summary and discussion.
2. Theory for anomalous geostrophic advection
This section reviews spiciness dynamics and develops a coupled Markov model to explain the spiciness frequency spectra resulting from stochastically forced anomalous geostrophic advection.
Compressibility of seawater impacts the thermal and haline expansion coefficients and thus acts as a source term on the rhs of Eq. (2), amplifying or attenuating spiciness anomalies as pressure changes along an advection path (Tailleux et al. 2005). The linear eigenmode analysis of Müller and Willebrand (1986) indicates that this effect has a characteristic depth scale of 15 km and time scale of 1000 yr and, therefore, may be important for the adjustment of the deep thermohaline circulation but can be neglected for the depth scale of the upper thermocline (∼300 m) of interest in this study.
Equations (12) and (13) represent the simplest possible model that can explain the FSS ∝ ω−4 dependence of spiciness variability generated by stochastically forced anomalous geostrophic advection. This model only applies to long-wavelength variability generated in the thermocline: that is, away from the surface where u′h includes higher-frequency Ekman currents. The orientation of ∇
3. Primitive equation model
To test whether the frequency spectra of long-wavelength spiciness show the predicted −4 slope requires very long time series of temperature and salinity. Lacking such observational datasets, numerical simulations are performed with the Regional Ocean Modeling System (ROMS).
a. ROMS configuration
ROMS is a free-surface primitive equation model described in detail in Marchesiello et al. (2003) and Shchepetkin and McWilliams (2005). The model realizations R20a, R20b, and R10 are summarized in Table 1. Two grids were used with the same domain and vertical resolution consisting of 30 levels, but different horizontal resolution. The domain extends zonally from 180° to 112°W and meridionally from 25° to 61°N. Zonal resolution is 0.25° for realizations R20a and R20b and 0.125° for R10. The spatial resolution increases toward the north to better resolve the deformation radius.
Boundary conditions and forcing are the same for all three realizations, but initial conditions differ. The 0.25° grid realizations R20a and R20b, each 55 years, were performed in succession after a 53-yr spinup. The wind forcing was reset from 2004 to 1950 between realizations, so the initial condition for R20a is the final state of the spinup and the initial condition for R20b is the final state of R20a, corresponding to December 2004. Likewise, the initial condition for R10 is the final state of a spinup run on the 0.125° grid.
Open boundary conditions (Marchesiello et al. 2001) are used at the western and southern lateral boundaries, where the model is nudged toward monthly mean climatological values (Levitus et al. 1994). A radiation boundary condition is used, with a nudging time scale of 1 day for flow into the model domain and a time scale of 1 yr for flow out of the domain.
The wind stress is from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis for 1950–2007 (Kalnay et al. 1996). The K-profile parameterization (KPP) vertical mixing scheme (Large et al. 1994) is used in the surface boundary layer; however, the use of 1-month-averaged wind stress results in model mixed layers that are unrealistically shallow (de Boyer Montégut et al. 2004).
NCEP–NCAR surface heat fluxes are also used, with a relaxation to the time-dependent monthly mean SST from the National Oceanic and Atmospheric Administration (Smith and Reynolds 2004). The nudging time scale is 1 month.
In contrast to GCMs such as the OGCM for the Earth Simulator (Masumoto et al. 2004), surface salinity is only forced by a prescribed surface freshwater flux. The freshwater flux contains a seasonal cycle but no interannual variability, so interannual salinity variability is due only to changes in the flow field and mixing. The freshwater flux was determined from a prior “climatological” run (not shown in table) that relaxed surface salinity to observed values; the corrections were stored and converted to a climatological freshwater flux for use here. Note that the use of a regional model limits the salinity errors that can grow large in long GCM integrations due to errors in boundary conditions, mixing, or flow fields.
All ROMS output was saved as monthly means. To isolate the nonseasonal variability, a linear trend of about 9 × 10−4 psu yr−1 and the mean seasonal cycle were removed.
b. Model validation
Realizations R20a and R20b give realistic results and have been used successfully in previous studies of the northeast Pacific: Di Lorenzo et al. (2008) showed that the model surface salinity near California compared well with observations from California Cooperative Oceanic Fisheries Investigations and Scripps Pier and tracked the North Pacific Gyre Oscillation (NPGO) index of SSH variability; Di Lorenzo et al. (2009) showed that model salinity at line P in the Gulf of Alaska also matched observations and tracked the NPGO; Chhak et al. (2009) showed that the first and second EOF patterns and principal components of model SSH matched the altimeter record for 1993–2004; and Combes and Di Lorenzo (2007) compared model SSH at individual grid points to tide gauges in the Gulf of Alaska and found that the model skill was comparable to satellite observations.
The R10 mean salinity distribution on the σθ = 26 kg m−3 isopycnal surface shows the fresh tongue of the California Current extending southward, collocated with a local minimum in variance (Fig. 2). Strong gradients in mean salinity to the southwest are collocated with the highest variance. The white area in the northwest part of the domain indicates where the isopycnal outcropped for at least one month. The salinity variance and mean distributions on the same isopycnal for R20a and R20b (not shown) look similar to Fig. 2.
Henceforth only nonseasonal variability is considered in isopycnal salinity, SSH, and wind stress curl, so the prime notation is dropped: S, η, and C represent anomalies. Note that S, η, and C are spatially averaged where indicated but the full monthly time resolution is retained for all analyses.
4. Identifying the wind-forced signal
The model solutions diverge because of their different initial conditions and the chaotic nature of the ocean circulation. Thus, the shared spiciness variance between R20a and R20b is attributed to the (identical) wind forcing and the remainder to oceanic nonlinear internal variability. In this section, the spiciness changes due to oceanic internal variability are filtered out to focus on the wind-forced signal. Large-scale wind-forced variability corresponds to the anomalous advection term on the rhs of Eq. (5) and oceanic internal variability to the eddy term, as previous analyses of the same ROMS experiments used here (Di Lorenzo et al. 2008; Chhak et al. 2009) have shown that large-scale winds dominate the low-frequency variability in the northeast Pacific and that chaotic large-scale, eddy-forced accelerations of the California Current System, hypothesized by Schneider et al. (2005), are not important for decadal variability.
The spiciness field on the σθ = 26 kg m−3 isopycnal (Fig. 2) includes high-variance, short-wavelength, eddy-forced anomalies (see section 6), so a 550 km × 550 km spatial average is applied to help isolate the large-scale wind-forced signal. High point-to-point correlations between the R20a and R20b spatially averaged isopycnal salinity fields indicate that wind-forced variability dominates in a “tongue” extending southeastward from the outcrop region (Fig. 3), whereas lower correlations to the southwest are evidence of oceanic internal variability. The northern part of the tongue is shallow and close to the outcrop, whereas the southern part is deep and removed from the surface mixed layer. It is shown below that the correlation of the spiciness signal in the southern half of the tongue among realizations is larger than the correlation to the upstream condition (outcrop) in individual realizations, indicating that the signal is generated locally. Thus, the southern half of the tongue is the optimal location for testing the anomalous advection dynamics of section 2.
A spiciness mask is formed along the 0.84 contour in the southern half of the tongue (Fig. 3, thick black line). The isopycnal salinity anomalies averaged spatially over the mask for realizations R20a and R20b are defined as S20a and S20b, respectively (Fig. 4, top). All isopycnal salinity signals in this paper are summarized in Table 2. The S20a and S20b indices are nearly identical, with a correlation of 0.95, and very smooth. A very similar signal is found in R10 with a slightly adjusted mask shape (Fig. 2), chosen by maximizing the correlation with S20a and S20b. The isopycnal salinity spatially averaged over this mask is defined as S10 and has correlations to S20a and S20b of 0.93 and 0.91, respectively (Fig. 4, top). The S10 signal is the focus of this study.
As mentioned above, the spiciness mask is selected as a region where the local wind-forced generation is stronger than the influence of subducting outcrop anomalies. The correlation between realizations exceeds 0.84 in the mask (Fig. 3), higher than the S10 correlations to the prior outcrop signal at lags of 9, 18, and 27 months (Fig. 5), indicating that S10 is generated locally and justifies the neglect of mean advection in the section 2 Markov model [Eqs. (12) and (13)].
The S10 signal is concentrated in the thermocline, with a weak expression at the surface. At 35°N, the maximum salinity correlations to S10 occur at 150–220-m depth, near the mean depth of the σθ = 26 kg m−3 isopycnal (Fig. 6, top). The maximum expression of S10 is thus deeper and farther west than the strongest equatorward flow (Fig. 6, bottom), indicating that S10 is associated more with the ventilated thermocline than the California Current.
5. Wind forcing
A smooth, wind-forced, long-wavelength spiciness signal exists in the model thermocline. In this section, it is shown that the signal is generated by local, wind-forced anomalous geostrophic advection.
a. Forcing by anomalous geostrophic advection
The coefficient ϵ(x, y) is positive along the coast and negative offshore (Fig. 7, white contours), suggesting that high pressure along the coast and low pressure offshore lead to salty anomalies. This phasing is consistent with anomalous geostrophic advection in the northeast Pacific, as in Eq. (11), where reduced southward transport of freshwater results in salty anomalies.
The S10 signal lags Δη (Fig. 4, middle), consistent with Eq. (19), and S10 is also much smoother than Δη with nearly all variance at frequencies below 0.2 cpy. This smoothness is evident in the frequency spectrum of S10 (Fig. 8), which shows a −4 slope for frequencies greater than 0.2 cpy, consistent with the anomalous advection model of section 2.
The next step is to connect Δη to the wind stress. In principle, this requires two Markov models of the form of Eq. (8) since Δη is comprised of two pressure indices. However, η10 and ηcoast covary at low frequencies, as their 24-month running means have a −0.65 correlation. Since integrating Eq. (19) with η10 as the sole forcing results in a correlation to S10 of 0.85, while using ηcoast alone lowers the correlation to 0.76, one can say the offshore pressure variability is more important in forcing S10. For these reasons the next section focuses solely on the Ekman pumping–forced offshore pressure, equivalent to setting Δη = −η10 in Eq. (20).
b. Forcing by Ekman pumping
6. Short-wavelength spiciness variability
The anomalous advection model of section 2 explains the phase and −4 slope frequency spectrum of the long-wavelength spiciness variability. However, for shorter wavelengths, mesoscale eddies become important and Γfor cannot be neglected in Eq. (5). This is evident when computing the frequency spectrum of isopycnal salinity separately at each grid point in the S10 mask and then averaging the spectra together. The resulting frequency spectrum integrates over all wavenumbers and is closer to a −2 slope than −4 (Fig. 10), whereas the spatial average used to form S10 filters out the high-wavenumber variance, resulting in a −4 slope. The long-wavelength, wind-forced, −4 slope signal is hidden in a short-wavelength, high-variance, eddy-driven signal.
A transition from the long-wavelength to the small-wavelength spiciness regime is seen by Fourier transforming the σθ = 26 kg m−3 isopycnal salinity field into wavenumber–frequency space and computing the power for varying horizontal wavenumber |k|. At the lowest resolved |k|, corresponding to a wavelength of 1330 km, a −4 slope is clearly seen in the frequency spectrum (Fig. 11). At higher wavenumbers, both diminishing power and a flatter spectral slope are observed. An analogous effect of eddies on the frequency spectra of SST is discussed in Frankignoul (1981) and Hall and Manabe (1997).
The −4 slope spiciness signal is isolated after filtering out the high-wavenumber variability associated with the eddy field, consistent with the section 2 anomalous advection model, which applies to long-wavelength variability only. Verification of the −4 signal in observations thus requires a long-term, large-spatial-scale record of temperature and salinity.
7. Surface versus interior processes
Spiciness variability in the thermocline is affected by surface processes that form anomalies at isopycnal outcrops and subsequent forcing in the interior that alters spiciness along advective pathways. Outcrop anomalies influence interior spiciness via the mean advection term on the lhs of Eq. (2), which has been neglected here because S10 is dominated by interior anomalous advection forcing (Fig. 5). Outcrop anomalies in the model are forced by realistic surface heat fluxes (Nonaka and Sasaki 2007; Bindoff and McDougall 1994), anomalous Ekman advection (Mignot and Frankignoul 2003), and small-scale eddy variability. However, surface freshwater fluxes contain only seasonal variability. The combination of too-shallow mixed layers (see section 3) and limited vertical resolution precludes faithful representation of the O(10 m) diapycnal mixing that can inject spiciness anomalies into the base of the mixed layer (Yeager and Large 2004; Luo et al. 2005; Johnson 2006; Yeager and Large 2007) in regions of unstable vertical salinity gradients and weak density stratification (Fig. 6).
A gauge of the missing surface processes’ importance is a comparison of the model spiciness variance to observations at HOT, which is located downstream of the model domain. Although the signals are not correlated, the S10 standard deviation is 0.03 psu, compared to 0.04 psu on the same isopycnal (σθ = 26 kg m−3) at HOT (Fig. 1 in Lukas and Santiago-Mandujano 2008); since the HOT signal is measured at one location, spatially averaging would likely reduce the variance somewhat, as shown in section 6. The similar order of magnitude of S10 and the HOT signal suggests that interior anomalous geostrophic advection, rather than surface processes, could be the dominant forcing of low-frequency spiciness variability at HOT.
Prior studies have attempted to link the HOT observations to surface freshwater fluxes only (Lukas 2001; Lukas and Santiago-Mandujano 2008). Although Lukas and Santiago-Mandujano (2008) did mention that wind stress curl variations are capable of affecting salinity by altering circulation patterns, a subsequent adjoint sensitivity analysis (Stammer et al. 2008) did not include wind stress curl as a possible forcing mechanism. Thus, it is left for future study to quantify the relative importance of freshwater flux variability and Ekman pumping–forced anomalous advection, though observations elsewhere in the Pacific support the anomalous advection hypothesis: Kessler (1999) found that subsurface salinity anomalies at 165°E during 1984–97 were consistent with changes in zonal advection and the wrong sign to be explained by subducting surface anomalies, whereas Suga et al. (2000) was unable to link subsurface salinity anomalies at 137°E to upstream freshwater fluxes and stated that “in situ processes such as anomalous advection or mixing can be just as important as changes of the thermohaline forcing at the outcrop regions, in forcing anomalies in the temperature and salinity along isopycnal and level surfaces.”
8. Summary and discussion
The generation of low-frequency variability of a passive tracer is investigated using the example of density-compensated temperature and salinity anomalies, or spiciness. In contrast to prior studies that linked subsurface spiciness variability directly to surface thermohaline forcing (Lukas 2001; Lukas and Santiago-Mandujano 2008; Nonaka and Sasaki 2007; Laurian et al. 2009), this study focuses on the generation of spiciness variability in the thermocline by anomalous geostrophic currents acting against mean spiciness gradients, or anomalous geostrophic advection. A coupled Markov model [Eqs. (12) and (13)] is developed in which stochastic wind stress curl forces the large-scale first baroclinic mode pressure, which in turn forces the anomalous geostrophic advection of spiciness. The Markov model predicts that this “double integration” of atmospheric forcing results in a frequency spectrum of large-scale spiciness that has a 0 slope for low frequencies and a −4 slope for high frequencies, separated by a smooth transition around the damping coefficients μ and λ (Fig. 1). An eddy-permitting regional model hindcast of the northeast Pacific (1950–2007) confirms that time series of large-scale spiciness variability are exceptionally smooth, with frequency spectra ∝ ω−4 for frequencies greater than 0.2 cpy.
The double integration that is fundamental to anomalous advection acts as an efficient low-pass filter and thus has consequences for decadal climate. Low-frequency variability in spiciness and other dynamically passive tracers can be efficiently generated in the thermocline by off-equatorial, stochastic Ekman pumping; nearly all variance in this study occurs at frequencies below 0.2 cpy. Spiciness variability can advect to the tropics and affect equatorial climate (Schneider 2004); this one-way forcing mechanism provides a null hypothesis for explaining equatorial climate anomalies. Anomalous advection also provides a null hypothesis for attributing decadal variability in biogeochemical tracers like oxygen (Ito and Deutsch 2010).
At shorter spatial scales (wavelengths less than ∼500 km), the spiciness frequency spectrum is whitened by mesoscale eddies. The spiciness frequency spectrum at one grid point, which integrates variance over all wavenumbers, shows a slope closer to −2 than −4 (Fig. 10). Only after applying a spatial average or low-wavenumber bandpass filter does the −4 slope signal emerge. The eddies can be averaged over, indicating they are not spatially coherent at the larger scale of the spiciness signal. The implication is that a large spatial array of measurements, such as Argo, is necessary to observe the variance of spiciness or any other passive tracer subject to anomalous advection in the thermocline.
This study has focused on the generation of spiciness variance in the thermocline, but anomalous geostrophic advection also influences surface spiciness (Mignot and Frankignoul 2003). However, other processes directly forced by the atmosphere are important at the surface, such as anomalous freshwater fluxes (Lukas 2001), heat fluxes (Nonaka and Sasaki 2007), and Ekman advection. The “fast” atmospheric forcings leave a signature −2 slope in the frequency spectrum of spiciness at the surface, where isopycnals outcrop; it is only in the thermocline where anomalous geostrophic advection becomes dominant, leaving its signature −4 slope. The frequency spectrum of interior spiciness therefore discerns whether variability is of surface or interior origin.
The damping coefficients μ = 0.5 yr−1 and λ = 0.6 yr−1 (radian frequency) were estimated from the frequency spectra of S10 and η10, respectively, and correspond to decadal time scales. The negative feedback processes that μ and λ correspond to have not been explored here. Only in the simplified physics of section 2 are μ and λ constant, because Rossby waves cause λ to vary with distance from the eastern boundary (Frankignoul et al. 1997), whereas the curving trajectory of the mean flow, outcrop patterns, and mean advection (Frankignoul and Reynolds 1983) affect the spatial distribution of μ. Dottori and Clarke (2009) showed the importance of Rossby waves for low-frequency variability off California but did not consider their effect on temperature and salinity spectra. It is thus left for future study to consider how the interplay between Rossby waves and anomalous advection causes spiciness spectra to vary in space.
Acknowledgments
This study benefited from discussions with Drs. Bo Qiu, Peter Müller, and Glenn Carter. The authors gratefully acknowledge the comments of two anonymous reviewers that helped improve an earlier version of the manuscript. This research was supported by the National Science Foundation through Grant OCE-0550233. The International Pacific Research Center is sponsored by the Japan Agency for Marine–Earth Science and Technology (JAMSTEC), by NASA through Grant NNX07AG53G, and by NOAA through Grant NA17RJ1230.
REFERENCES
Bindoff, N. L., and T. J. McDougall, 1994: Diagnosing climate change and ocean ventilation using hydrographic data. J. Phys. Oceanogr., 24 , 1137–1152.
Bograd, S. J., and R. J. Lynn, 2003: Long-term variability in the Southern California Current System. Deep-Sea Res. II, 50 , 2355–2370.
Chelton, D. B., P. A. Bernal, and J. A. McGowan, 1982: Large-scale interannual physical and biological interaction in the California Current. J. Mar. Res., 40 , 1095–1125.
Chhak, K. C., E. Di Lorenzo, P. Cummins, and N. Schneider, 2009: Forcing of low-frequency ocean variability in the northeast Pacific. J. Climate, 22 , 1255–1276.
Combes, V., and E. Di Lorenzo, 2007: Intrinsic and forced interannual variability of the Gulf of Alaska mesoscale circulation. Prog. Oceanogr., 75 , 266–286.
Cummins, P. F., and G. S. E. Lagerloef, 2002: Low-frequency pycnocline depth variability at Ocean Weather Station P in the northeast Pacific. J. Phys. Oceanogr., 32 , 3207–3215.
Cummins, P. F., and G. S. E. Lagerloef, 2004: Wind-driven interannual variability over the northeast Pacific Ocean. Deep-Sea Res. I, 51 , 2105–2121.
Davis, R. E., 1976: Predictability of sea surface temperature and sea level pressure anomalies over the North Pacific Ocean. J. Phys. Oceanogr., 6 , 249–266.
de Boyer Montégut, C., G. Madec, A. S. Fischer, A. Lazar, and D. Iudicone, 2004: Mixed layer depth over the global ocean: An examination of profile data and a profile-based climatology. J. Geophys. Res., 109 , C12003. doi:10.1029/2004JC002378.
Di Lorenzo, E., and Coauthors, 2008: North Pacific Gyre Oscillation links ocean climate and ecosystem change. Geophys. Res. Lett., 35 , L08607. doi:10.1029/2007GL032838.
Di Lorenzo, E., and Coauthors, 2009: Nutrient and salinity decadal variations in the central and eastern North Pacific. Geophys. Res. Lett., 36 , L14601. doi:10.1029/2009GL038261.
Dottori, M., and A. J. Clarke, 2009: Rossby waves and the interannual and interdecadal variability of temperature and salinity off California. J. Phys. Oceanogr., 39 , 2543–2561.
Frankignoul, C., 1981: Low-frequency temperature fluctuations off Bermuda. J. Geophys. Res., 86 , (C7). 6522–6528.
Frankignoul, C., and K. Hasselmann, 1977: Stochastic climate models, Part II. Application to sea-surface temperature anomalies and thermocline variability. Tellus, 29 , 289–305.
Frankignoul, C., and R. W. Reynolds, 1983: Testing a dynamical model for mid-latitude sea surface temperature anomalies. J. Phys. Oceanogr., 13 , 1131–1145.
Frankignoul, C., P. Müller, and E. Zorita, 1997: A simple model of the decadal response of the ocean to stochastic wind forcing. J. Phys. Oceanogr., 27 , 1533–1546.
Fukumori, I., T. Lee, B. Cheng, and D. Menemenlis, 2004: The origin, pathway, and destination of Niño-3 water estimated by a simulated passive tracer and its adjoint. J. Phys. Oceanogr., 34 , 582–604.
Gu, D., and S. G. H. Philander, 1997: Interdecadal climate fluctuations that depend on exchanges between the tropics and extratropics. Science, 275 , 805–807.
Hall, A., and S. Manabe, 1997: Can local linear stochastic theory explain sea surface temperature and salinity variability? Climate Dyn., 13 , 167–180.
Hasselmann, K., 1976: Stochastic climate models. Part 1, Theory. Tellus, 28 , 473–485.
Iselin, C. O. D., 1939: The influence of vertical and lateral turbulence on the characteristics of the waters at mid-depths. Trans. Amer. Geophys. Union, 20 , 414–417.
Ito, T., and C. Deutsch, 2010: A conceptual model for the temporal spectrum of oceanic oxygen variability. Geophys. Res. Lett., L03601. doi:10.1029/2009GL041595.
James, I. N., and P. M. James, 1989: Ultra-low-frequency variability in a simple atmospheric circulation model. Nature, 342 , 53–55.
Johnson, G. C., 2006: Generation and initial evolution of a mode water θ–S anomaly. J. Phys. Oceanogr., 36 , 739–751.
Kalnay, E., and Coauthors, 1996: The NCEP–NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437–471.
Kessler, W. S., 1999: Interannual variability of the subsurface high salinity tongue south of the equator at 165°E. J. Phys. Oceanogr., 29 , 2038–2049.
Lagerloef, G. S. E., 1995: Interdecadal variations in the Alaska gyre. J. Phys. Oceanogr., 25 , 2242–2258.
Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys., 32 , 363–403.
Laurian, A., A. Lazar, G. Reverdin, K. Rodgers, and P. Terray, 2006: Poleward propagation of spiciness anomalies in the North Atlantic Ocean. Geophys. Res. Lett., 33 , L13603. doi:10.1029/2006GL026155.
Laurian, A., A. Lazar, and G. Reverdin, 2009: Generation mechanism of spiciness anomalies: An OGCM analysis in the North Atlantic subtropical gyre. J. Phys. Oceanogr., 39 , 1003–1018.
Ledwell, J. R., A. J. Watson, and C. S. Law, 1993: Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature, 364 , 701–703.
Levitus, S., R. Burgett, and T. P. Boyer, 1994: Salinity. Vol. 3, World Ocean Atlas 1994, NOAA Atlas NESDIS 3, 99 pp.
Liu, Z., and S-I. Shin, 1999: On thermocline ventilation of active and passive tracers. Geophys. Res. Lett., 26 , 357–360.
Lukas, R., 2001: Freshening of the upper thermocline in the North Pacific subtropical gyre associated with decadal changes in rainfall. Geophys. Res. Lett., 28 , 3485–3488.
Lukas, R., and F. Santiago-Mandujano, 2008: Interannual to interdecadal salinity variations observed near Hawaii: Local and remote forcing by surface freshwater fluxes. Oceanography, 21 , 46–55.
Luo, Y., L. M. Rothstein, R-H. Zhang, and A. J. Busalacchi, 2005: On the connection between South Pacific subtropical spiciness anomalies and decadal equatorial variability in an ocean general circulation model. J. Geophys. Res., 110 , C10002. doi:10.1029/2004JC002655.
Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis, 1997: A Pacific interdecadal climate oscillation with impacts on salmon production. Bull. Amer. Meteor. Soc., 78 , 1069–1079.
Marchesiello, P., J. C. McWilliams, and A. Shchepetkin, 2001: Open boundary conditions for long-term integration of regional oceanic models. Ocean Modell., 3 , 1–20.
Marchesiello, P., J. C. McWilliams, and A. Shchepetkin, 2003: Equilibrium structure and dynamics of the California Current System. J. Phys. Oceanogr., 33 , 753–783.
Masumoto, Y., and Coauthors, 2004: A fifty-year eddy-resolving simulation of the World Ocean—Preliminary outcomes of OFES (OGCM for the Earth Simulator). J. Earth Simulator, 1 , 35–56.
Mignot, J., and C. Frankignoul, 2003: On the interannual variability of surface salinity in the Atlantic. Climate Dyn., 20 , 555–565.
Müller, P., and J. Willebrand, 1986: Compressibility effects in the thermohaline circulation: A manifestation of the temperature–salinity mode. Deep-Sea Res., 33 , 559–571.
Munk, W., 1981: Internal waves and small-scale processes. Evolution of Physical Oceanography, B. A. Warren and C. Wunsch, Eds., The MIT Press, 264–291.
Nonaka, M., and H. Sasaki, 2007: Formation mechanism for isopycnal temperature–salinity anomalies propagating from the eastern South Pacific to the equatorial region. J. Climate, 20 , 1305–1315.
Qiu, B., 2003: Kuroshio Extension variability and forcing of the Pacific decadal oscillations: Responses and potential feedback. J. Phys. Oceanogr., 33 , 2465–2482.
Ren, L., and S. C. Riser, 2010: Observations of decadal time scale salinity changes in the subtropical thermocline of the North Pacific Ocean. Deep-Sea Res. II, 57 , 1161–1170.
Roemmich, D., and J. McGowan, 1995: Climatic warming and the decline of zooplankton in the California Current. Science, 267 , 1324–1326.
Sasaki, Y. N., N. Schneider, N. Maximenko, and K. Lebedev, 2010: Observational evidence for propagation of decadal spiciness anomalies in the North Pacific. Geophys. Res. Lett., 37 , L07708. doi:10.1029/2010GL042716.
Schneider, N., 1999: Pacific thermocline bridge revisited. Geophys. Res. Lett., 26 , 1329–1332.
Schneider, N., 2000: A decadal spiciness mode in the tropics. Geophys. Res. Lett., 27 , 257–260.
Schneider, N., 2004: The response of tropical climate to the equatorial emergence of spiciness anomalies. J. Climate, 17 , 1083–1095.
Schneider, N., and B. D. Cornuelle, 2005: The forcing of the Pacific decadal oscillation. J. Climate, 18 , 4355–4373.
Schneider, N., E. Di Lorenzo, and P. P. Niiler, 2005: Salinity variations in the southern California Current. J. Phys. Oceanogr., 35 , 1421–1436.
Schwing, F. B., and R. Mendelssohn, 1997: Increased coastal upwelling in the California Current System. J. Geophys. Res., 102 , (C2). 3421–3438.
Shchepetkin, A., and J. C. McWilliams, 2005: The Regional Oceanic Modeling System (ROMS): A split-explicit, free-surface, topography-following-coordinate ocean model. Ocean Modell., 9 , 347–404.
Smith, T. M., and R. W. Reynolds, 2004: Improved extended reconstruction of SST (1854–1997). J. Climate, 17 , 2466–2477.
Spall, M. A., 1993: Variability of sea surface salinity in stochastically forced systems. Climate Dyn., 8 , 151–160.
Stammer, D., S. Park, A. Kohl, R. Lukas, and F. Santiago-Mandujano, 2008: Causes for large-scale hydrographic changes at the Hawaii Ocean time series station. J. Phys. Oceanogr., 38 , 1931–1948.
Suga, T., A. Kato, and K. Hanawa, 2000: North Pacific Tropical Water: Its climatology and temporal changes associated with the climate regime shift in the 1970s. Prog. Oceanogr., 47 , 223–256.
Tailleux, R., A. Lazar, and C. J. C. Reason, 2005: Physics and dynamics of density-compensated temperature and salinity anomalies. Part I: Theory. J. Phys. Oceanogr., 35 , 849–864.
Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics. Cambridge University Press, 745 pp.
Veronis, G., 1972: On properties of seawater defined by temperature, salinity, and pressure. J. Mar. Res., 30 , 227–255.
Williams, P. D., E. Guilyardi, R. Sutton, J. Gregory, and G. Madec, 2007: A new feedback on climate change from the hydrological cycle. Geophys. Res. Lett., 34 , L08706. doi:10.1029/2007GL029275.
Yeager, S. G., and W. G. Large, 2004: Late-winter generation of spiciness on subducted isopycnals. J. Phys. Oceanogr., 34 , 1528–1547.
Yeager, S. G., and W. G. Large, 2007: Observational evidence of winter spice injection. J. Phys. Oceanogr., 37 , 2895–2919.
Frequency spectra predicted by the anomalous geostrophic advection model [Eqs. (14) and (16)] for a single k corresponding to long-wavelength spiciness S and first baroclinic mode pressure η: (left) for the case μ < λ and (right) for μ > λ. The axes are dimensionless; only spectral slopes are considered. Note that ω is the angular frequency.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Salinity (psu) standard deviation (shade) and mean (thin contours) on the σθ = 26 kg m−3 isopycnal surface. The thick contour outlines the mask for the S10 signal. The white space in the northwest part of the domain indicates grid points that outcropped for at least one month.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
The σθ = 26 kg m−3 isopycnal salinity correlation between realizations R20a and R20b (shading; note nonlinear grayscale). The isopycnal salinity was first spatially averaged over 550 km × 550 km squares but not time averaged. The mask indicated by the thick black line, following the 0.84 contour, is used to define S20a and S20b. The dashed line at 35°N is the location of the vertical sections in Fig. 6. White space in the northwest part of the domain represents grid points that outcropped for at least one month. White contours show mean M/g (m), for the Montgomery potential, 
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Isopycnal salinity and SSH anomaly indices. Anomalies have been spatially averaged, but no time averaging has been applied. See Table 2 for descriptions of the indices. (top) Isopycnal salinity indices S10, S20a, and S20b (psu). The correlation between S20a and S20b is 0.95; between S10 and S20a is 0.93; and between S10 and S20b is 0.91. (middle) S10 and Δη (m); high values of Δη indicate weaker equatorward geostrophic transport. Note that the salinity scale is on the left and the SSH scale is on the right. (bottom) S10 and SΔη, which have a correlation of 0.89.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Correlation of S10 to the prior σθ = 26 kg m−3 isopycnal salinity at lags of 0, 9, 18, and 27 months (shading; note nonlinear grayscale). The isopycnal salinity was spatially averaged over 550 km × 550 km squares prior to computing the correlation. White contours show mean M/g (CI = 0.04 m) for realization R10, where M is the Montgomery potential.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Vertical sections at 35°N (cf. dashed line in Fig. 3): (top) salinity correlation to S10 computed along constant z surfaces (shade) and mean salinity (contours; psu) and (bottom) mean meridional velocity (m s−1). Note the nonlinear grayscales. In both plots, the dashed line is the mean depth of the σθ = 26 kg m−3 isopycnal. The salinity minimum corresponds to the strongest equatorward velocity located in the core of the California Current, but S10 has its strongest expression in the weaker and deeper flow to the west.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Skill of the Markov model for SSH forcing S10 [Eq. (17)], measured at each grid point by the correlation between S10 and the reconstructed spiciness (shade). The SSH was spatially averaged over 350 km × 350 km squares prior to testing the Markov model. Thin white contours indicate the value of ϵ (psu yr−1 m−1), determined from a least squares fit of the data to Eq. (17) with fixed μ = 0.5 yr−1. Note that ϵ ≤ 0 and ϵ > 0 are indicated by dashed and solid contours, respectively. The thick white line outlines the SSH mask used to create η10, the thick white line with black trace outlines the mask for ηcoast (Table 2), and the thick black line outlines the S10 mask.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Frequency spectra of isopycnal salinity, SSH, and wind stress curl indices. See Table 2 for a description of the indices. The y axis has no units; only spectral slopes are compared. The thin black lines show −4 and −2 slopes for reference.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Time series of (top) η10 and ηcurl (m), correlation is 0.72, and (bottom) S10 and Scurl (psu), correlation is 0.70. See Table 2 for descriptions of the isopycnal salinity and SSH indices.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Frequency spectrum of S10, the spatially averaged isopycnal salinity (black); compare to the isopycnal salinity spectrum computed separately at each point in mask and subsequently averaged over all points in mask (gray; psu2 yr). The thin black lines show −4 and −2 slopes for reference.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Wavenumber–frequency spectrum of salinity (psu2 yr m) on the σθ = 26 kg m−3 isopycnal for varying bands of horizontal wavenumber |k|. The thin black line shows a −4 slope for reference.
Citation: Journal of Physical Oceanography 41, 2; 10.1175/2010JPO4443.1
Realizations of northeast Pacific ROMS simulations. The boundary conditions and forcing are the same for each realization, but initial conditions differ.
Summary of isopycnal salinity (S), SSH (η), and wind stress curl (C) indices.