1 Measuring oxygen concentrations improves the detection capabilities of an ocean circulation observation array Catherine E. Brennan 1 , Richard J. Matear 2 , and Klaus Keller 1* 1 Department of Geosciences, Penn State, University Park, PA 2 CSIRO Marine and Atmospheric Research, Hobart, Tasmania, Australia *corresponding author e-mail: [email protected]Running Title: BRENNAN ET AL.: OXYGEN OBSERVATIONS IMPROVE MOC DETECTION
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Measuring oxygen concentrations improves the detection capabilities of
an ocean circulation observation array
Catherine E. Brennan1, Richard J. Matear2, and Klaus Keller1*
1Department of Geosciences, Penn State, University Park, PA
2CSIRO Marine and Atmospheric Research, Hobart, Tasmania, Australia
and sea surface temperature [Matear and Hirst, 2003]. POM is remineralized below the
euphotic zone as a function of depth and Redfield stochiometry [Redfield, et al., 1963].
The control experiment is driven by a fixed atmospheric equivalent CO2
concentration of 330 μatm, while the forced experiment applies the IS92a radiative
forcing scenario, increasing the atmospheric equivalent CO2 concentration through year
2083 when a tripling of pre-industrial equivalent CO2 is achieved [Matear and Hirst,
2003]. Beyond 2083, atmospheric equivalent CO2 levels are held constant at 990 μatm.
The analyzed time series span the (model) years 1880 to 2100.
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Meridional and zonal maps of AOU (Figure 1) show the approximate location of the
boundary between NADW and AABW along the 90 μmol kg-1 contour line in model year
2006 (solid line). This water mass boundary shoals over the next century, displacing the
90 μmol kg-1 contour line upwards by model year 2100 (dashed line). The size of the
shoaling at 26 oN in the model ranges from approximately 90 to 500 m, increasing from
the eastern to the western edge of the basin. The prediction of the simple model was that
(i) a reduction of the MOC intensity leads to a shoaling of the interface between NADW
and AABW and (ii) that this shoaling would result in a cooling, freshening, and an
increase in AOU close to the interface. The trends simulated by the CSIRO model over
the next century are consistent with this prediction (Figure 2).
The strength of the MOC is represented by the maximum of the meridional stream
function at 26 °N in the North Atlantic basin (Figure 3). The deepwater AOU signal is
defined as the zonal mean AOU value between 2000 and 4500 meters in the western
basin (45 °W – 70 °W) at 26°N. We correct for potential artifacts due to model drift by
estimating linear signal trends in the control run and subtracting these trends from the
control and the forced runs. 26 °N was selected because is the approximate location of
the recently deployed NERC/RAPID mooring array [Marotzke, et al., 2002].
3. Methods
We approximate natural variability by the variability found in the control simulation.
The forced signal is the slope of the forced simulation time series, estimated by a least
squares linear fit. We expand on the trend detection method pioneered by Santer et al.
[1995] and refined by Baehr et al. [2007]. Specifically, we estimate trends of varying
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chunk length for the control and forced signals. The probability density function (pdf) of
the unforced trends is derived using a bootstrap method with random starting points.
This distribution then defines the 95% confidence limits for the unforced trends. A
forced signal trend of equal chunk length is estimated, with the year 2006 as the starting
point – the first year of the hypothetical observation system. A detection of a statistically
significant trend (p < 0.05) occurs when the forced signal is outside the 95% confidence
limits of the control (Figure 4).
Uncertainty in the analyzed signals affects the detection time. We estimate the effects
of observation errors and scenario uncertainty by superimposing representations of those
errors. Estimating realistic observation errors for the MOC and AOU signals is an area of
active research [e.g., Ganachaud, 2003; Keller et al, 2002; Min and Keller, 2005, Baehr et
al, 2007c]. For this proof-of-concept study, we choose illustrative values derived from
the published literature. For the MOC signal, we adopt the results from previous
modeling studies which suggest MOC errors around 1 Sv (standard deviation) [Baehr, et
al, 2004; Baehr et al, 2007c]. For the AOU signal, we derive an arguably conservative
estimate based on a simple error analysis. The error of an average AOU concentration
depends on (i) uncertainties introduced by oxygen measurement errors and eddy induced
variability, (ii) uncertainties due to the calculation of the derived AOU tracer, and (iii) the
effects of aggregating several independent observations to an average AOU
concentration. A quite conservative upper bound for the combined effects of oxygen
measurement errors and eddy-induced variability is 5 μmol kg-1 [Gouretski and Jancke,
2001]. Combining this with an upper estimate of 3 μmol kg-1 for the error introduced by
calculating the oxygen solubility [Weiss, 1970]) results in an error for single AOU
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observations of roughly 6 μmol kg-1. (assuming uncorrelated errors). One independent
check for this upper bound estimate of 6 μmol kg-1 for a single AOU observation is the
standard deviation of the trends in AOU observations at close-by (“crossover”) locations
between the GEOSECS and WOCE observations in North Pacific intermediate waters,
which has been estimated as roughly 4 μmol kg-1 [Keller et al, 2002]. The last step in
estimating the error for an average AOU concentration is to account for the effects of the
averaging process. This is important because the standard deviation of an average of N
statistically independent observations of a quantity decreases with 1/ N . Comparing
the typical station spacing of past hydrographic transects [Cunningham and Alderson;
2007] with the decorrelation length scale in the subtropical North Atlantic [Roemmich,
1983] suggest that N very likely exceeds ten. Hence we adopt a conservative error
estimate of 2 μmol kg-1 for the average AOU signal. Note that adopting smaller estimate
of this observation error would strengthen our forthcoming conclusions. We represent the
potential MOC and AOU observation errors by superimposing random draws from a
normal distribution with zero mean and a given standard deviation.
We additionally account for scenario uncertainty by creating multiple (103) time
series with the same trend and autoregressive properties as the original model MOC and
AOU signals. By drawing an ‘observation’ from a randomly-selected series, we
essentially superimpose the effects of varying initial conditions on the model MOC and
AOU signals (which otherwise would represent only one set of initial conditions). In
order to create the multiple time series, a smoothed fit (derived by a locally weighted
regression [Cleveland and Devlin, 1988]) is removed from the original MOC and AOU
signals. We fit autoregressive (AR) models to the MOC and AOU residuals such that the
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selected AR model coefficients result in a minimized Akaike Information Criterion (AIC)
using a maximum likelihood method [Gilgen, 2006, pp. 266-269]. Using the selected AR
models, we generate multiple series with the same AR properties (or “red noise”) as the
original signal. The smoothed fit is subsequently recombined with the series to produce a
set of time series with the same trend and autoregressive properties as the original MOC
and AOU model signals. We approximate the effects of scenario uncertainty by
randomly sampling these time series. The detection method is applied to the analyzed
period with varying levels of uncertainty for MOC observations alone, AOU observations
alone, and the combined MOC-AOU signal (described below). The detection frequency
of the resulting detection time provides a reliability level: a 95% reliable estimate
corresponds to the detection frequency of 0.95.
We analyze a statistically optimal fingerprint constructed from the MOC and AOU
signals, in addition to analyzing the separate MOC and AOU signals. The fingerprint is
optimized by choosing a time-independent weighting to maximize the signal-to-noise
ratio. Specifically, we approximate the MOC and AOU signals from the analyzed period
(2006 – 2070) as linear trends with random noise (the standard deviation of this noise is
estimated from the residuals of the linear fit). We derive an approximately optimal
fingerprint by varying the weighting (w and 1-w, w ∈[0,1]) on the approximated MOC
and AOU signals and plotting the signal-to-noise ratio of the resulting fingerprints
(Figure 5). The signal-to-noise ratio is calculated by dividing the magnitude of the
difference in the fingerprint over the analyzed period (model years 2006 to 2070) in the
forced experiment (i.e. the signal) by the standard deviation of the fingerprint over the
entire model run in the control experiment (i.e. the noise).
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4. Results and Discussion
In the control run, the MOC has a mean of 12.7 Sv (1 Sv = 106 m3 s-1) with a standard
deviation of 0.5 Sv (and a range of ~3.3 Sv) (Figure 3). The mean and the variability of
the MOC are within the range of other models [Gregory, et al., 2005; Schmittner, et al.,
2005]. The AOU signal shows less variability on interannual timescales than the MOC
signal. We hypothesize that the relatively low variability of the AOU signal on
interannual timescales results from the averaging over a relatively large region and the
analysis of a deepwater signal (where the interannual variability can be lower compared
to more shallow signals). There is no statistically significant correlation between MOC
and AOU signals in the control run (p > 0.05, accounting for serial correlation [Ebisuzaki,
1997]).
In the forced experiment (Figure 3), the MOC strength is relatively steady until 1980,
but then weakens to approximately 8 Sv by 2070. The average AOU concentration (26
°N, 2000 – 4500 m, 45 °W – 70 °W) has a mean value of 80 μmol kg-1 with a standard
deviation of 0.6 μmol kg-1 in the control run. In the forced run, the AOU signal begins to
considerably increase in the 1980s, roughly coinciding with the MOC weakening, and
rises by approximately 10 μmol kg-1 by 2070.
The relative changes in the forced AOU and MOC signals (Figure 3) are
approximately similar between the 1980’s and the 2030’s. Beyond the 2030’s, the
relative AOU changes exceed the relative MOC changes. The AOU and MOC signals in
the forced experiment show a statistically significant negative correlation (p < 0.05,
accounting for serial correlation [Ebisuzaki, 1997]). One possible explanation for the fact
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that the AOU and MOC signals are statistically significantly anticorrelated in the forced
run but not in the control run is that the anticorrelation observed in the forced run is
largely driven by the anthropogenic forcing, which is missing from the control run.
Detection time is a random variable as it depends on random realizations of
observation errors and scenario uncertainty. If one neglects observation errors and
scenario uncertainty, detection occurs by 2025 for the MOC signal alone (Figure 5, panel
a). With observation errors of 1 Sv on the MOC signal, detection time is a probabilistic
variable, and reliable detection occurs later: at 95% reliability, detection occurs in 2054.
Considering both observation error (1 Sv) and scenario uncertainty results in a 95%
reliable detection time in 2060. The detection frequency of the AOU signal alone (Figure
5, panel b) has the same pattern of increasing detection times with increasing uncertainty,
and is shifted to earlier detection times. If one neglects observation errors as well as
scenario uncertainty, the AOU signal is detectable by 2012. When observation errors of
2 μmol kg-1 are considered, 95% reliable detection occurs by 2045. Additionally
superimposing the effects of scenario uncertainty to the effects of 2 μmol kg-1
observation errors results in a 95% reliable detection time of 2050.
The analysis so far analyzes the MOC and the AOU signals separately. Combining
these two signals in a fingerprint can improve the signal-to-noise ratio and the detection
capabilities [Hasselmann, 1993]. The signal-to-noise ratio of this fingerprint as a
function of the weight (w) for the OUT signal is shown in Figure 6. A fingerprint with a
weighting of w = 0.5 is close to the maximum value and has a higher expected signal-to-
noise ratio than either the AOU or the MOC signal (Figure 6). This optimal fingerprint
(w = 0.5) enables an earlier detection than either signal alone (Figure 7). Whereas the
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95% reliable detection time using MOC observations alone is approximately five
decades, the deepwater AOU signal is detectable more than a decade earlier (Figure 7).
The optimal fingerprint achieves a 95% reliable detection time in three decades – roughly
two decades earlier than an observation system based on the MOC signal alone.
5. Caveats
Our simple analysis relies on several approximations. First, we analyze a single
model and are silent on the question of how robust the optimal fingerprint might be
across the range of structural uncertainty. Second, we neglect information contained in
tracers such as chlorofluorocarbons [Schlosser, et al., 1991; Smethie and Fine, 2001] or
129I [Edmonds, et al., 2001], which might well provide useful additional observations.
Third, potential changes in export production (different from those projected by the
model) will affect the ability to link changes in AOU to changes in MOC and hamper
detection. Fourth, our analysis focuses on the question of MOC change detection and is
silent on the arguably more relevant (but also much more complex) task of projecting the
future MOC intensity [Marotzke, 2000; Keller and McInerney, 2007]. Fifth, we use a
very simple approach to derive a statistical fingerprint. In addition, the link between
trends in hydrographic tracer concentrations and MOC changes is clearly more complex
than just a shoaling of the AABW/NADW boundary [cf. Matear and Hirst, 2003; Baehr et
al, 2007]. Last, but not least, the analyzed model likely underestimates the internal
variability of the signals as it does not resolve eddies [Hirst, et al., 2000].
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6. Conclusions
Given the aforementioned caveats, we draw two main conclusions. First, adding AOU
observations to an MOC observation system can improve the signal-to-noise ratio and
result in earlier detection of anthropogenic MOC trends. The effect of including AOU
can be sizeable: the reliable detection times in our model study improve by almost two
decades. AOU may hence be a valuable hydrographic tracer for increasing understanding
of changes in the MOC. Second, the consideration of uncertainties introduced by
observation errors and scenario uncertainty results in later detection times. Conclusions
of previous studies neglecting these arguably important uncertainties may hence need to
be revisited.
The current debate about the future fate of the MOC can be informed by an effective
monitoring system. We show that additionally observing AOU, a water mass tracer that
is mechanistically tied to circulation changes, can improve the detection capabilities of an
MOC observation system.
Acknowledgements
We thank Joshua Dorin, Dong-Ha Min, David McInerney, Ray Najjar, and Johanna
Baehr for helpful discussions. The comments of Raghu Murtugudde and two anonymous
reviewers considerably improved the presentation of the paper. We gratefully
acknowledge support from the National Science Foundation (SES #0345925) and the
Penn State Institute for the Environment. Opinions, findings and conclusions expressed
in this work are those of the authors, and do not necessarily reflect the views of funding
entities.
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Figure Captions
Figure 1. Meridional (panel a) and zonal (panel b) sections of AOU along 30 oW and 26 oN
(respectively) from model year 2006 in the CSIRO climate model [Matear and Hirst, 2003].
AOU is defined as the oxygen solubility at the in-situ temperature and salinity minus the
observed oxygen concentration. The contour lines of 90 μmol/kg AOU illustrate the
boundary between Antarctic Bottom Water (AABW) and North Atlantic Deep Water
(NADW). The dashed contour lines show the location of the boundary after approximately a
century of continued anthropogenic forcing (i.e., the model year 2100). See text for details.
Figure 2: Zonal sections of the projected changes over the twenty-first century (i.e., model
years 2100-2000) in temperature (panel a), salinity (panel b), and AOU (panel c) along 26 oN
in the CSIRO climate model [Matear and Hirst, 2003].
Figure 3. Annual maximum overturning (Sv, 1 Sv = 106 m3 s-1) at 26 °N (solid line) and
deepwater apparent oxygen utilization (AOU) (μmol kg-1) at 26 °N (averaged over 2000 to
4500 meters and 45 °W to 70 °W) (dashed line). Shown are the unforced (control) (a) and
the forced (b) experiments of the CSIRO climate model [Matear and Hirst, 2003]. We
perform the detection analysis from 2006 through 2070.
Figure 4. Illustration of the detection method. A statistically significant detection of forced
changes occurs when the forced signal (solid line) leaves the 95% confidence limits of the
unforced system (dashed lines). This illustration uses the MOC signal shown in Figure 3,
analyzes annual observations starting in 2006, and neglects the effects of observation errors
and uncertainty in the initial conditions (cf. Figure 6).
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Figure 5. Effect of observation errors and scenario uncertainty on the detection of forced
MOC (panel a) and AOU (panel b) changes. Observation errors are approximated by
superimposing random perturbations drawn from an identical and independently distributed
Gaussian distribution with zero mean and varying standard deviation on the model signal.
Scenario uncertainty, representing uncertain initial conditions, is simulated by randomly
drawing from an estimated time series model (see methods text for details). Shown are
results for the MOC (AOU) with zero Sv (zero μmol kg-1) standard deviation without
scenario uncertainty (dotted line), 1 Sv (2 μmol kg-1) standard deviation without scenario
uncertainty (dashed line), and 1 Sv (2 μmol kg-1) standard deviation with scenario
uncertainty (solid line).
Figure 6. Signal-to-noise ratio (S N-1) of the fingerprint resulting from varying the
weighting on the AOU (w) (plotted on the x-axis) and the MOC (1- w) (where the weights
sum to 1) for the cases of 1 Sv and 2 µmol kg-1 observation errors with scenario uncertainty.
The signal is the magnitude of the difference between the combined signal observed in 2006
and in 2070. The noise is the standard deviation of the resulting combined signal. The
maximum of the expected signal-to-noise ratio occurs with a w of approximately 0.5.
Figure 7. Frequency of the detection times (across 104 states of the world) with observation
errors (1 Sv and 2 μmol kg-1) and scenario uncertainty for the MOC signal alone (dashed
line), the deepwater AOU signal alone (solid line), and the optimal fingerprint (solid line
with open circles). A reliable detection occurs when 95% of the realizations detect a change.