Generated using version 3.0 of the official AMS LATEX template
Generation of Low-Frequency Spiciness Variability in the
Thermocline
Thomas Kilpatrick
∗
and Niklas Schneider
Department of Oceanography, and International Pacific Research Center,
University of Hawaii at Manoa, Honolulu, Hawaii
Emanuele Di Lorenzo
School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia
∗
Corresponding author address: Thomas Kilpatrick, Department of Oceanography, University of Hawaii
at Manoa, 1000 Pope Rd. Honolulu, HI 96822.
E-mail: [email protected]
1
ABSTRACT
The generation of variance by anomalous advection of a passive tracer in the thermocline is
investigated using the example of spiciness, density-compensated temperature and salinity
anomalies. A coupled Markov model in which wind stress curl forces the baroclinic pressure
that in turn controls anomalous geostrophic advection of spiciness predicts that white noise
atmospheric forcing results in a frequency (ω) spectrum of spiciness that decays proportional
to ω −4 . This “double integration” of atmospheric forcing results in spiciness variability that
is concentrated at low frequencies.
This mechanism is studied using an eddy-permitting regional model 1950–2007 hindcast of the Northeast Pacific. As predicted, large-scale spiciness variability is exceptionally
smooth with a frequency spectrum ∝ ω −4 for frequencies greater than 0.2 cpy, though the
slope of the spectrum is wavenumber-dependent. At high wavenumbers the eddies whiten
the spiciness spectrum, but for wavelengths greater than ∼500 km the high-frequency variability cancels and the -4 slope of anomalous geostrophic advection emerges. Large-scale
and long-term measurements are needed to observe the variance of spiciness, or any other
passive tracer subject to anomalous advection in the thermocline.
1
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, while 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 North- 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 variability has been observed in the California Current (Chelton 1981; 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) past observation points such as the Hawaii Ocean Timeseries (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
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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). Ocean dynamics low-pass filter this stochastic forcing with the
high-frequency cutoff determined by the negative feedback mechanism (Hasselmann 1976).
This filtering accounts for the ubiquitous frequency spectra of sea surface temperature, ocean
pressure and surface temperature climate indices such as the Pacific decadal oscillation, that
are white for low frequencies and sport a decrease of power proportional to the inverse of
frequency squared, 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 simple theory for spiciness spectra
that result from anomalous geostrophic advection. These dynamics are explored in multiple
realizations of a high-resolution, eddy-permitting model that enables a comparison of the
spiciness variability forced by the atmosphere, and that due to oceanic intrinsic variability.
The model and integrations are introduced in Section 3. Section 4 identifies the deterministic
spiciness signal, that is shown in Section 5 to result from wind forcing of the geostrophic
flow. Section 6 discusses the detection of the atmospherically forced spiciness signals in a
strong ocean eddy field. The dual contributions of anomalous advection and freshwater flux
3
variability to interior spiciness are compared in Section 7, and Section 8 provides a summary
and discussion.
2. Theory for anomalous geostrophic advection
Conservation of salinity can be written using potential density (σθ ) as the vertical coordinate,
∂S
∂S
+ uh · ∇h S + σ̇θ
= 0,
∂t
∂σθ
(1)
where sub-gridscale fluxes are neglected, ∇h is taken along constant-σθ isopycnal surfaces
and σ̇θ =
Dσθ
Dt
[Eq. (3.157) in Vallis (2006)]. Consistent with ventilated thermocline theory
(Luyten et al. 1983) σ̇θ can be neglected in the interior, resulting in an equation for salinity
on an isopycnal surface, or spiciness. Reynolds averaging Eq. (1) and adding linear damping
then yields
D ′
S = −u′h · ∇h S − Γ − αS ′ ,
Dt
(2)
where overbars represent a space–time monthly mean and primes represent deviations from
the mean. The influence of mean advection is included in
D
Dt
= ∂t + uh · ∇h . The eddy
forcing term is
′
Γ = ∇h · (u′h S ′ ) .
(3)
Lateral and vertical mixing processes are represented by αS ′ and assumed to damp interior
spiciness anomalies toward the climatological mean.
Compressibility of seawater impacts the thermal and haline expansion coefficients and
thus acts as a source term on the right side of Eq. (2), amplifying or attenuating spiciness
4
anomalies as pressure changes along an advection path (Tailleux et al. 2005). This effect,
important for a depth scale of 15 km and time scale of 1000 yr (Müller and Willebrand 1986),
is relevant 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.
The solution to Eq. (2) is found by integrating the anomalous advection and eddy forcing
terms along mean isopycnal streamlines,
′
S (ξ, t) =
−α
′
Ssurf
e
(ξ−ξ0 )
|uh |
+
Z
t
t−
ξ−ξ0
|uh |
dt̂ e−α(t−t̂) −u′h · ∇h S − Γ
ξ−|uh |(t−t̂),t̂
(4)
where ξ is an along-stream coordinate, ξ0 is the outcrop location, and the outcrop anomaly
′
′
0
). Ssurf
is generated at the surface and subducted into the thermocline;
Ssurf
= S ′ (ξ0 , t − ξ−ξ
|uh |
its decay time scale α−1 depends on the interior mixing processes.
For the case of no eddy forcing (Γ = 0), Eq. (2) simplifies and spiciness is only forced by
anomalous advection. In the thermocline, u′h should be geostrophically balanced, so one can
use the Montgomery potential M (Montgomery 1937) to approximate the streamfunction on
a σθ -surface (McDougall 1989),
f k̂ × u′h = −∇h M ′ ,
(5)
where the unit vector k̂ points in the vertical direction.
The circulation in the North Pacific subtropical gyre is mostly baroclinic, so M corresponds to the baroclinic streamfunction in the 2-layer model of Qiu (2002) and one can use
SSH to approximate M. The component of SSH affecting the baroclinic streamfunction is
governed by Ekman pumping,
∂η ′
g ′ He2 ∇ × τ ′
=−
,
∂t
ρ0 gf0 H12
(6)
where η is SSH, g ′ is the reduced gravity, H1 is the layer-1 depth and He is the equivalent
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depth [Eq. (17) in Qiu (2002)]. Rossby waves are neglected because the study area is near
the eastern boundary (Cummins and Lagerloef 2004).
Eq. (2) can be rewritten as a Markov equation to explicitly show ocean pressure forcing
spiciness. For the case of weak mean advection and no eddy forcing, a coupled Markov model
is formed with Eq. (6),
∂S ′
= −αS ′ (t) + βη ′(t),
∂t
∂η ′
= −λη ′ (t) + γC ′ (t),
∂t
(7)
(8)
where β and γ are scaling coefficients, C(t) is the wind stress curl, and λ represents negative
feedback processes on SSH.
Because of the time-scale separation between the ocean and atmosphere, the frequency
spectrum of ocean pressure is
Fηη (ω) =
FCC (0)
,
ω 2 + λ2
(9)
where FCC (0) represents the constant input spectrum of the wind stress curl over the frequency range relevant to the ocean (Hasselmann 1976). Eqs. (8)–(9) have been invoked before
to explain thermocline depth anomalies in the North Pacific (Frankignoul and Hasselmann
1977; Lagerloef 1995; Cummins and Lagerloef 2002, 2004).
The frequency spectrum of spiciness derived from Eqs. (7)–(8) is
FSS (ω) =
=
Fηη (ω)
ω 2 + α2
(10)
FCC (0)
.
ω 4 + (λ2 + α2 )ω 2 + λ2 α2
(11)
The “double integration” of atmospheric forcing results in FSS ∝ ω −4 at high frequencies, a
-4 slope on a log–log plot (Fig. 1). If α and λ have similar magnitude, the spiciness spectrum
6
transitions smoothly from a 0 slope for ω < min(α, λ) to a -4 slope for ω > max(α, λ). If α
and λ differ greatly, an intermediate -2 slope region exists for min(α, λ) < ω < max(α, λ).
3. Primitive equation model
To test whether the frequency spectra of spiciness show the predicted -4 slope requires
a very long time series of temperature and salinity. Lacking such observational data sets,
numerical simulations are performed with the Regional Ocean Modeling System (ROMS).
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◦ N 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. For the 0.25◦ -grid, the model was integrated continuously through a 53-year
spinup, then R20a, then R20b, with the wind forcing reset from 2004 to 1950 between realizations. Thus 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 55-year spinup 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
7
(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 year for flow out of the domain.
The wind stress is from the National Center for Environmental Prediction (NCEP)–
National Center for Atmospheric Research (NCAR) reanalysis for 1950–2007 (Kalnay et al.
1996). NCEP–NCAR surface heat fluxes are also used, with a relaxation to National Oceanic
and Atmospheric Administration SST (Smith and Reynolds 2004). The nudging time scale
is 1 month.
No correction is used for surface salinity, in contrast to GCMs such as OFES (Masumoto
et al. 2004). Without a correction, large salinity errors can accumulate in long GCM integrations due to errors in boundary conditions, mixing, or flow fields. These errors can
accumulate even in coupled ocean–atmosphere models because of the weak atmospheric
feedback on salinity. Some of these problems are avoided here by using a regional model,
thereby limiting the residence time of parcels in the domain.
Freshwater fluxes in this study contain a seasonal cycle but no interannual variability, so
interannual salinity variability is due only to changes in the flow field and mixing. Freshwater
fluxes were determined from a prior “climatological” run (not shown in table) that corrected
surface salinity; the corrections were stored and converted to a climatological freshwater flux
for use here. Note that since ROMS uses the Boussinesq approximation it conserves volume
rather than mass, and thus uses the “mixed boundary condition” described by Huang (1993).
8
a. 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 CalCoFI 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. However, the objective of this paper is not to reproduce observations
in the surface layer but rather to describe the generation of spiciness variability in the
thermocline by anomalous geostrophic advection.
b. Data processing
All ROMS output was saved as monthly means. A linear trend of about 0.05 psu was
removed, and then to isolate the nonseasonal variability the mean seasonal cycle was also
removed.
The R10 mean salinity distribution on the σθ –26 kg m−3 isopycnal surface shows the fresh
tongue of the California Current extending southward, co-located with a local minimum in
variance (Fig. 2). Strong gradients in mean salinity to the southwest are co-located with
the highest variance. White points indicate locations where the isopycnal outcropped for at
9
least one month.
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 deterministic 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 interpreted as deterministic variability and the remainder as intrinsic. In this section
the intrinsic variability’s importance is estimated, before being filtered out to focus on the
deterministic signal and its forcing mechanism. Note one cannot say a priori that either the
anomalous advection or eddy forcing term in Eq. (2) is exclusively deterministic or intrinsic.
To locate regions of deterministic variability, the σθ -26 kg m−3 isopycnal salinity was first
spatially averaged over 550 km×550 km squares to filter high-wavenumber variance associated with the eddy field, and then the correlation was measured between realizations R20a
and R20b (Fig. 3). The strongest correlations exceed 0.95 and are found near 45 ◦ N, 140 ◦ W,
but the focus of this study is the region south of 40◦ N, where correlations exceed 0.84 and M
isolines indicate mean flow in the equatorward direction. A mask is formed in this southern
region.
The isopycnal salinity anomalies averaged spatially over this mask for realizations R20a
and R20b are defined as S20a and S20b , respectively (Fig. 4). All isopycnal salinity signals in
10
this paper are summarized in Table 2. S20a and S20b are nearly identical, with a correlation
of 0.95, and very smooth. It is emphasized that no time-averaging or smoothing has been
applied—S20a and S20b contain the full monthly resolution for 1950–2004.
It is preferable to use R10 for analysis because of its finer resolution and longer integration time. The deterministic signal is found in R10 with a slightly adjusted mask shape
(Fig. 2), chosen by maximizing the correlation with S20a and S20b . The spatially averaged
isopycnal salinity over this mask is defined as S10 and looks very similar to S20a and S20b ,
with correlations of 0.93 and 0.91, respectively (Fig. 4). The S10 signal is the focus of this
study.
The mask was chosen using the criterion of deterministic spiciness variability. However,
the deterministic signal does not correspond to the highest variance on the isopycnal surface
(Fig. 2). The higher variance to the southwest is more intrinsic (Fig. 3). It is hypothesized
the intrinsic variability is due to the combination of strong spiciness fronts and weak mean
flow, conditions in which the eddy term dominates Eq. (2).
Correlations of S10 to the prior isopycnal salinity field at lags of 9, 18, and 27 months
show that only a small part of S10 is explained by the upstream variability (Fig. 5). It is
concluded that the influence of mean advection is weak and S10 is mostly generated at the
mask location, i.e.
D
Dt
≈ ∂t on the left side of Eq. (2).
S10 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.
11
5. Wind forcing
A smooth, deterministic 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
[Eqs. (7)–(8)].
a. Forcing by anomalous geostrophic advection
The anomalous geostrophic advection model is tested by fitting S10 and the SSH anomaly
at every grid point to Eq. (7),
∂S10
= −αS10 (t) + β(x, y)η(x, y, t),
∂t
(12)
where η is used as an index for the isopycnal streamfunction, as explained in Section 2. The
damping term α is estimated from the S10 frequency spectrum and fixed at 0.5 yr−1 . At
each grid point, the coefficient β(x, y) is determined from a least-squares fit of S10 (t) and
η(x, y, t) to a discretized Eq. (12). Then S10 is reconstructed by an Euler integration of Eq.
(12) from the S10 initial value. The correlation between S10 and the reconstruction (Fig. 7,
shade) shows SSH has skill along the coast and in a broad area in the southwest part of the
model domain.
The coefficient β(x, y) is positive along the California coast and negative in the southwest
part of the domain (Fig. 7, white contours), indicating that high coastal SSH anomalies and
low offshore anomalies lead to salty conditions. This phasing is consistent with anomalous
geostrophic advection in the Northeast Pacific, where reduced southward transport of fresh
water results in saltier conditions.
12
To test anomalous geostrophic advection further, two indices are created, based on where
the Eq. (12) reconstruction has skill (Fig. 7, thick white lines). An index for the strength of
the southward flow is created from the difference between the SSH anomalies averaged over
the coastal and offshore masks,
∆η = ηcoast − η10 .
(13)
The SSH indices are summarized in Table 2. Since the SSH masks are located outside the
salinity mask (Fig. 7), ∆η is an index for the pressure gradient across the salinity mask.
S10 lags ∆η (Fig. 4, middle), consistent with Eq. (7). S10 is also much smoother than
∆η, with nearly all variance at frequencies below 0.2 cpy. This smoothness is evident in
S10 ’s frequency spectrum (Fig. 8) which shows a -4 slope for frequencies greater than 0.2 cpy,
consistent with the anomalous advection model of Section 2.
Now ∆η can be substituted as the forcing term in Eq. (7),
∂S
= −αS(t) + β ∆η(t).
∂t
(14)
Eq. (14) is integrated with α = 0.5 yr−1 and β = 0.65 psu yr−1 m−1 to form a reconstruction
of S10 , defined as S∆η . The coefficient β was selected so that S∆η has the same phase and
variance as S10 . Though deviations occur during 1963–1965, 1971–1973, 1974–1976, and
2003–2004 (Fig. 4, bottom), possibly due to upstream perturbations that reach the interior
through mean advection but are not included in Eq. (7), S10 and S∆η have an outstanding
correspondence overall and a correlation of 0.89. The frequency spectrum of S∆η also shows
a -4 slope (Fig. 8). Thus the anomalous geostrophic advection model reproduces the phase
and frequency content of the spiciness signal.
The next step is to connect ∆η to the wind stress. This requires two Markov models of
13
the form of Eq. (8) since ∆η is comprised of two SSH indices. However, since forcing Eq.
(7) with η10 alone results in a correlation to S10 of 0.85, while using ηcoast alone lowers the
correlation to 0.76, one can say the offshore SSH variability is more important in forcing
S10 . Furthermore, η10 and ηcoast covary at low frequencies, as their 24-month running means
have a -0.65 correlation. For these reasons the next section focuses solely on the Ekman
pumping-forced offshore SSH.
b. Forcing by Ekman pumping
As described in the previous section, the forcing of SSH variability by Ekman pumping
is only considered in the offshore region (Fig. 7). The offshore SSH η10 is fit to Eq. (8),
∂η10
= −λη10 (t) − γC10 (t),
∂t
(15)
where C10 (t) is the spatially averaged offshore wind stress curl (Table 2). The damping
coefficient λ = 0.6 yr−1 is determined from the η10 frequency spectrum and the scaling
coefficient γ = −1.15×10−9 kg−1 m3 yr is selected so that the reconstructed SSH ηcurl , formed
by integrating Eq. (15), has the same phase and variance as η10 . The correlation between η10
and ηcurl is 0.72 (Fig. 9, top) and the signals have similar frequency spectra (Fig. 8). This
local Ekman pumping model captures the variability in η10 , consistent with the results of
Cummins and Lagerloef (2004) for a larger domain in the Northeast Pacific.
The reconstructed SSH, ηcurl , can be used to force Eq. (7). The resulting salinity reconstruction Scurl is essentially a double integration of the wind stress curl, and has a correlation
to S10 of 0.70 (Fig. 9, bottom) for α = 0.5 yr−1 and β = −1.0 psu yr−1 m−1 . Scurl captures
the freshening trend of 1950–1955, the salty period from 1963–1966, the freshening from
14
1975–1979, the salty period from 1983–1989, and the large salinification and subsequent
freshening from 1995–2005. But the deviations are wider than for S∆η , particularly for
1957–1962, 1972–1974, 1980–1982, and 1990-1995 (cf. Fig. 4). Nevertheless, the ability of
Scurl to capture half of S10 ’s variance illustrates how the ocean generates spiciness variability
in the thermocline through the double-integration of atmospheric forcing.
The frequency spectrum of C10 has nearly a 0 slope, while η10 and ηcurl are near -2, and
S10 is near -4 (Fig. 8). In this picture,
∇ × τ −→ η −→ S,
0
-2
(16)
-4
the wind stress curl ∇×τ forces ocean pressure, and pressure forces spiciness. Each successive
integration in this forced linear system changes the spectral slope by -2, such that spiciness
has virtually none of the high-frequency variance input by the atmosphere.
6. Wavenumber dependence
The anomalous advection model considered so far explains the phase and -4 frequency
spectrum of the spatially-averaged isopycnal salinity while ignoring the role of eddies [Γ = 0
in Eq. (2)]. But, the eddies cannot be ignored at smaller spatial scales. If the salinity
frequency spectrum is computed separately at each grid point in the mask (Fig. 2) and then
averaged, the resulting spectral slope is close to -2, rather than -4 (Fig. 10).
The frequency spectrum of isopycnal salinity at a single grid point integrates over all
wavenumbers, thereby capturing all the variance. A spatial average filters out the highwavenumber variability. Thus the deterministic, -4 slope signal is hidden in a high-wavenumber,
15
high variance eddy-driven signal.
To illustrate this further the σθ -26 kg m−3 isopycnal salinity field is Fourier transformed
into wavenumber–frequency space, and then the power is computed 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.
S10 is a low-wavenumber signal with a -4 slope.
Only after filtering out the high-
wavenumber variability associated with the eddy field, either by Fourier transform or spatial
average, is the -4 slope signal isolated. Verification of the -4 signal in observations would
thus require a long-term, large-spatial-scale record of salinity.
7. Surface vs. 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. The dual contributions of surface and interior processes are represented
on the right side of Eq. (4). Integration of the anomalous geostrophic advection term determines the low-frequency, low-wavenumber variability in the model and leaves a signature
-4 spectral slope. At the surface, variable heat fluxes cause outcrop lines to move and thus
′
introduce some variability in Ssurf
(Nonaka and Sasaki 2007; Bindoff and McDougall 1994),
but unlike previous SSS modeling studies (Spall 1993; Mignot and Frankignoul 2003) the
freshwater fluxes used here contain only seasonal variability. Since variable freshwater fluxes
′
are a major contributor to Ssurf
in the ocean, the model has limited value for comparing
16
surface and interior processes’ relative contributions to decadal spiciness variability.
One way to gauge how much variance is missed by excluding freshwater flux variability
is to compare the S10 signal to observations at HOT, which is located downstream of the
model domain. Although S10 is not correlated to the salinity record at HOT, the standard
deviation of S10 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). One must be cautious in comparing
an area-average from the model to observations at one location; however, the similar order
of magnitude suggests that anomalous geostrophic advection, rather than freshwater flux
variability, could be the dominant process affecting low-frequency spiciness variability in the
thermocline.
Prior studies have attempted to link the hydrographic changes observed at HOT to
changes in freshwater flux variability only (Lukas 2001; Lukas and Santiago-Mandujano
2008). And 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 to a future study to quantify the relative importance of
freshwater flux variability and Ekman pumping-forced anomalous advection.
Another limitation of the model used here is its vertical resolution, which is ∼30 m at
100 m depth. Recent modeling results and observations in the Southeast Pacific indicate that
O(10 m) vertical mixing can inject large salinity anomalies into the thermocline (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, including parts of the subtropical
North Pacific (Fig. 6). Diapycnal mixing that can alter subducted isopycnals has been
17
ignored here, but if injection occurs close to an isopycnal’s outcrop location then it would
′
be lumped with the surface processes (Ssurf
) in Eq. (4).
The dominance of anomalous geostrophic advection in the model is broadly consistent
with salinity observations in the Pacific. Kessler (1999) found that salinity variability south
of the equator at 165◦ E during 1984–1997 was consistent with changes in zonal advection.
Suga et al. (2000) was unable to link subsurface salinity variability at 137◦ E in the North
Pacific to upstream freshwater flux variability, 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 a low-frequency spiciness, or density-compensated salinity signal in
the thermocline of the Northeast Pacific is studied using an eddy-permitting regional model
hindcast of 1950–2007. 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.
The main feature of the spiciness signal in the model is its smoothness in time, which is
manifest in the frequency spectrum as a -4 slope in a log–log plot for frequencies greater than
0.2 cpy. The signal is so smooth because it is forced by anomalous geostrophic advection, or
18
changes in ocean pressure, rather than being directly forced by the atmosphere. A Markov
model forced by an index of the large-scale SSH gradient reproduces the phase of the spiciness
signal and its -4 spectral slope.
A simple theory for anomalous geostrophic advection is developed by coupling two
Markov models. The first is for wind stress curl forcing ocean pressure, and the second
is for pressure forcing spiciness. This “double integration” of atmospheric forcing results in
a spiciness spectrum with a -4 slope for high frequencies and a 0 slope for low frequencies,
separated by a smooth transition around the damping coefficients α and λ (Fig. 1).
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, with nearly all variance occurring 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).
The -4 slope signal of anomalous geostrophic advection is hidden in the high-wavenumber,
high-frequency eddy field. The isopycnal salinity frequency spectrum at one grid point, which
integrates variance over all wavenumbers, shows a slope close to -2 rather than -4 (Fig. 10).
Only after applying a spatial average or low-wavenumber band-pass 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 salinity signal. The implication is that a large spatial array of
19
measurements, such as Argo, is necessary to observe the -4 slope signal.
Spiciness is affected by processes acting at the surface and in the interior [Eq. (4)]. Surface
processes determine the spiciness at an isopycnal’s outcrop location and include anomalous
freshwater fluxes (Lukas 2001), heat fluxes (Nonaka and Sasaki 2007), and Ekman advection.
Since surface processes are directly forced by the atmosphere, their spectral signature is
expected to be a -2 slope. The dominant interior process is anomalous geostrophic advection,
which alters spiciness on subsurface isopycnals and leaves a signature -4 spectral slope.
The damping coefficients α = 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 α and λ correspond to have not been explored
here. Only in the simplified physics of Eqs. (7)–(8) are α and λ constant, as Rossby waves
cause λ to vary with distance from the eastern boundary (Frankignoul et al. 1997), while the
curving trajectory of the mean flow, outcrop patterns, and mean advection (Frankignoul and
Reynolds 1983) affect the spatial distribution of α. 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.
The authors thank Drs. Bo Qiu and Peter Müller for helpful discussions and comments on
the manuscript. This research was supported by the National Science Foundation through
20
grant OCE-0550233. Additional support was provided by the Japan Agency for Marine–
Earth Science and Technology (JAMSTEC), by NASA through grant NNX07AG53G, and
by NOAA through grant NA17RJ1230, which sponsor research at the International Pacific
Research Center. This is IPRC/SOEST contribution number XXXX/XXXX.
21
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29
List of Tables
1
Realizations of ROMS simulations.
31
2
Summary of isopycnal salinity (S), SSH (η), and wind stress curl (C) indices.
32
30
Table 1. Realizations of Northeast Pacific ROMS simulations. The boundary conditions
and forcing are the same for each realization but initial conditions differ.
Realiz.
R20a
R20b
R10
Zonal res.
0.25◦
0.25◦
0.125◦
Spatial res.
14–24 km
14–24 km
7–12 km
Grid pts. (Y×X×Z)
210×274×30
210×274×30
418×546×30
31
Integr. period
1950–2004
1950–2004
1950–2007
Table 2. Summary of isopycnal salinity (S), SSH (η), and wind stress curl (C) indices.
Index
S20a
S20b
S10
S∆η
Scurl
Realiz.
R20a
R20b
R10
R10
R10
Defined as
Area avg.
Area avg.
Area avg.
Reconstr.
Reconstr.
Reconstr. from
—
—
—
∆η
ηcurl
Mask
Fig. 3 thick line
Fig. 3 thick line
Fig. 2 thick line
—
—
η10
ηcoast
∆η
ηcurl
R10
R10
R10
R10
Area avg.
Area avg.
= ηcoast − η10
Reconstr.
—
—
—
C10
Fig. 7 offshore mask
Fig. 7 coastal mask
—
—
C10
R10
Area avg.
—
Fig. 7 offshore mask
32
List of Figures
1
Predicted spiciness and SSH spectra for anomalous geostrophic advection.
2
Mean salinity and nonseasonal standard deviation on the σθ –26 kg m−3 isopycnal. 35
3
Spiciness correlation between realizations R20a and R20b.
36
4
Isopycnal salinity and SSH indices.
37
5
Lag correlation map of S10 to prior isopycnal salinity field.
38
6
Section at 35◦ N showing vertical expression of S10 and mean meridional velocity. 39
7
Markov model for SSH forcing salinity.
40
8
Frequency spectra of isopycnal salinity, SSH, and wind stress curl indices.
41
9
Comparing SSH and salinity to Markov reconstructions for the offshore mask.
42
10
Salinity frequency spectrum computed two different ways.
43
11
Wavenumber–frequency spectrum of salinity.
44
33
34
10
10
power
10
4
2
10
FSS
10
0
10
4
2
FSS
0
-4
−2
-4
−2
10
10
Fηη
Fηη
−4
−4
10
10
-2
−6
α
10
10
−2
10
-2
−6
λ
−1
ω
10
λ
10
0
10
1
10
−2
10
α
−1
ω
10
0
10
1
Fig. 1. Predicted spiciness and SSH frequency spectra for anomalous geostrophic advection,
given by Eq. (9) and Eq. (11). Left plot is for the case α < λ and right plot is for α > λ.
The axes are dimensionless; only spectral slopes are considered. Note that ω is the angular
frequency.
34
0.105
60°N
0.09
50°N
0.075
33.45
0.06
33.55
40°N
33.7
5
33.85
33.9
3
34.
5
15 4.05
33.6
0.045
5
0.03
30°N
160°W
140°W
120°W
Fig. 2. 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. White
space in the northwest part of the domain represents grid points that outcropped for at least
one month.
35
60°N
1.0
0.95
50°N
0.84
.2
−0.16
−0
0.7
0.5
40°N
4
−0
.08
0
8
.04
−0
.12
6
.2 0.1
−0 −
0.0
−0
0.0
0.3
0
30°N
160°W
140°W
120°W
Fig. 3. σθ –26 kg m−3 isopycnal salinity correlation between realizations R20a and R20b
(shade; note nonlinear grayscale). The isopycnal salinity was first spatially averaged over
550 km×550 km squares, but not time averaged. The mask used to define S20a and S20b (black
line) follows the 0.84 contour. Mean M/g (m; white contours), where M is the Montgomery
potential, indicates equatorward flow through the southern half of the isopycnal. The dotted
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.
36
0.1
S10
S20a
S20b
psu
0.05
0
−0.05
1950
0.1
1960
1970
1980
1990
2000
S10
Δη
0.05
0
0
−0.05
1950
0.1
−0.075
1960
1970
1980
1990
2000
2010
S10
SΔη
0.05
psu
0.075
m
psu
2010
0.15
0
−0.05
1950
1960
1970
1980
year
1990
2000
2010
Fig. 4. 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 ∆η
(m); high values of ∆η 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 S∆η , which
have a correlation of 0.89.
37
60°N
lag 0 mo
50°N
1
40°N
30°N
160°W
140°W
60°N
120°W
0.8
lag 9 mo
0.6
50°N
40°N
30°N
0.4
160°W
140°W
60°N
120°W
lag 18 mo
0.2
50°N
40°N
0
30°N
160°W
140°W
60°N
120°W
lag 27 mo
−0.5
50°N
40°N
30°N
160°W
140°W
120°W
Fig. 5. Correlation of S10 to the prior σθ -26 kg m−3 isopycnal salinity at lags of 0, 9, 18, and
27 months (shade; 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.
38
33.
.7
33
33.9
5
0.7
3
33.
0.6
−100
Z (m)
0.5
0.3
−200
0
−0.3
−300
150°W
140°W
130°W
0
−0.
04
0.08
0.04
−0.0
0.04
0
Z (m)
2
0.04
−100
0
−0.02
−200
−0.04
−300
150°W
−0.08
140°W
130°W
Fig. 6. Vertical sections at 35◦ N (cf. dotted line in Fig. 3). Top: Salinity correlation to
S10 computed along constant z-surfaces (shade) and mean salinity (contours; psu). 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 (top) corresponds
to the strongest equatorward velocity (bottom), located in the core of the California Current,
but S10 has its strongest expression in the weaker and deeper flow to the west.
39
60°N
0.8
0.4
0.2
0.4
0.4
0.2
50°N
0.7
ηcoast
0
η10
0
-0.4
0.2
-0.2
0.4
30°N
160°W
0.3
0.4
-0.4
0.5
0.6
40°N
0.8
-0.2
0.6
140°W
0
120°W
Fig. 7. Skill of the Markov model for SSH forcing S10 [Eq. (12)], measured at each grid
point by the correlation between S10 and the reconstructed spiciness (shade). The SSH was
spatially smoothed over 350 km×350 km squares prior to testing the Markov model. Thin
white contours indicate the value of β (psu yr−1 m−1 ), determined from a least-squares fit of
the data to Eq. (12) with fixed α = 0.5 yr−1 . Note that β ≤ 0 and β > 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). The
thick black line outlines the S10 mask.
40
10
−2
S10
SΔη
10
-4
−6
power
10
−4
10
10
η10
ηcurl
−8
-2
−10
C10
10
−12
10
−2
−1
0
10
10
frequency (cyc yr-1)
10
1
Fig. 8. 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.
41
m
0.05
0
η10
ηcurl
−0.05
−0.1
1950
1960
1970
1980
1990
2000
psu
0.1
2010
S10
Scurl
0.05
0
−0.05
1950
1960
1970
1980
year
1990
2000
2010
Fig. 9. Top: η10 and ηcurl (m); the correlation is 0.72. Bottom: S10 and Scurl (psu); the
correlation is 0.70. See Table 2 for descriptions of the isopycnal salinity and SSH indices.
42
10
10
−2
−3
-2
power (psu2 yr)
10
10
10
10
10
10
−4
-4
−5
−6
−7
−8
S10
pt-by-pt
−9
10
−2
−1
0
10
10
frequency (cyc yr-1)
10
1
Fig. 10. Frequency spectrum of S10 , the spatially-averaged isopycnal salinity (black); compare to 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.
43
10
9
k
2π
power (psu2 yr m)
10
10
10
10
10
−1
= 1330 km
8
7
k
2π
−1
k
2π
−1
6
5
k
2π
= 570 km
= 270 km
−1
= 160 km
4
-4
3
10 −2
10
−1
0
10
10
frequency (cyc yr-1)
10
1
Fig. 11. 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.
44