Geophysical Research Letters
Supporting Information for
Intra-seasonal variability linked to sampling alias in air – sea CO2 fluxes in the
Southern Ocean
Pedro M.S. Monteiro1,2, Luke Gregor1,2, Marina Lévy3, Stacy Maenner4, Christopher L.
Sabine4, Sebastiaan Swart1,2
1
Southern Ocean Carbon - Climate Observatory, CSIR, Rosebank 7700, Cape Town,
South Africa
2
Department of Oceanography, University of Cape Town, Rondebosch 7700, South
Africa
3
Sorbonne Université (UPMC, Paris 6)/CNRS/UPMC/IRD/MNHN, Laboratoire
d’Océanographie et du Climat (LOCEAN), Institut Pierre, Simon Laplace (IPSL), Paris
Cedex 05 75252, France
4
NOAA/PMEL, 7600 Sand Point Way NE, Seattle, WA USA 98115
Contents of this file
Text S1 to S5
Figures S1 to S5
Introduction
This supporting material provides additional methodological details such as the sampling
location, sampling sensors and strategy (S1), the methods for the sampling period
sensitivity analysis (S2), and the methods through which the adaptive sampling strategy
was derived (S3). It also provides the results of a comparative sensitivity analysis that
was carried out on a 0.5x0.5o model output, which showed increased alias uncertainties in
elevated Eddy Kinetic Energy (EKE) domains.
1
S1. Gliders, sensors and glider sampling strategy
Two gliders, a Liquid Robotics Carbon Wave Glider and an iRobot Seaglider were
deployed in the SAZ approximately 1300km SW of Cape Town and steered towards a
long-term position at 43oS, 8.5oE (Figure S1a-c). There, the wave-glider was placed in a
polygon sampling pattern approximately 16km in diameter with the buoyancy glider
profiling the water column approximately 5 times a day inside the polygon from 21
November 2013 to 8 February 2014 spanning the summer to late-summer parts of the
seasonal cycle (Figure S1a-c).
The pCO2 sensor on the wave glider is derived from the MAPCO2 technology developed
at NOAA – PMEL and widely used in the TOGA buoy-mooring arrays in the Pacific
Ocean (Sutton et al., 2014). The system works very much on the same principle as the
larger ship based equilibrator CO2 units (Pierrot et al., 2009) with two main differences:
firstly, the glider only carried one reference gas and a chemically produced zero CO2
reference gas which were used to calibrate the detector. The zero-span-calibration cycle
is repeated before every set of atmospheric and seawater measurements. This enables the
highest levels of accuracy to be achieved, which in some instances was as good as the
larger ship based instruments with uncertainties of < 1uatm but overall, in this study,
these were at least < 3uatm.
The data set consisted of directly observed sea water and atmospheric fCO2 and
calculated fluxes of CO2 (FCO2) using the Nightingale 2000 formulation using in situ
temperatures and salinities to derive the solubility and scatterometer winds to derive the
gas exchange rates with a Sc660 Schmidt number (see Figure 2a in main
text)(Nightingale et al., 2000).
Month
(a)
La tude
(b)
Longitude
8km
Month
La tude
(c)
Longitude
Figure S1a-c: (a) Sampling location the gliders (dashed box) overlaid on the regional austral summer
mean SeaWIFS chlorophyll-a. (b) Entire sampling domain of the Liquid Robotics Carbon Wave Glider
2
from deployment in the northwest quadrant to its long term pseudo-mooring polygon sampling pattern in
the central SAZ, located 1300km southwest of Cape Town, South Africa. Black dashed box represents the
zoom of (c) of the polygon sampling pattern of the Wave Glider, with the radius of the polygon indicated.
The centre of the polygon represents the mean location of the Seaglider profiling to 1000m depth. The
color shading in (b) and (c) represents the temporal evolution of the experiment.
Our analysis includes the whole data set, which incorporates the initial transit up until
17th November and the pseudo-mooring period (17 November 2013 to 8 February
2014)(Figures 2a and S1a-c). This raises the question of whether spatial mesoscale
variability in the initial transit could play a role in the observed sampling alias. We ran
the analysis on a sub-set which excludes the initial transit period and found almost
identical trends with only slightly reduced sensitivities because of the exclusion of part of
the high temporal variability associated with the spring to early summer period. On this
basis we used the whole data set for this analysis.
S2. Sampling period sensitivity analysis
The two sampling period sensitivity plots in Figure 2b,c (main text) were obtained
through simulated sampling of the mean of the time series (ΔfCO2 and FCO2). Each of
the time series (t) was sub-sampled for a continuous range of sampling periods (S) from 1
to 720 hours (30 days). In order to obtain many realizations of a mean, the starting time
(ti) was shifted iteratively by an hour for each sampling interval (Sk). This means that for
each sampling period k, there were Sk mean values. For example, sampling at a two-hour
interval would return two mean values, sampling every three days results in 72 possible
mean values and similarly sampling every 10 days would result in 240 possible mean
values. These mean values were then plotted as a scatter plot (Figure 2b,c: main text).
A two dimensional histogram of this figure was then calculated, showing the frequency
of a mean occurring in a bin with a size of 0.5 day and 0.002 mmol/m2/h-1. The likelihood
of sampling in each bin was then calculated with respect to sampling interval. This was
achieved by normalizing each sampling interval bin to the sum of itself, i.e. the sum of
each column in the histogram equals one. The number of bins divided each column of the
histogram with one or more observation. The likelihood of sampling the true mean at a
sampling interval of one hour is thus 1. These results are shown in Figures (2b, c) in the
main text.
S3. Sampling uncertainties and adaptive sampling periods across the different
variability regimes in the Southern Ocean
Here we combine the correlation (r2) ranges for seasonal cycle reproducibility depicted in
Figure (1) with the mean flux errors derived from our observations in Figure (2b.c) to
derive a spatial distribution of the sampling error from a fixed 10-day sampling period
(Figure 4) and the sampling periods required to produce an annual mean flux with an
error below the 10% threshold.
3
Firstly, in order to constrain a relationship between variability and sampling period error,
the true mean of the data was subtracted from the distribution of means (from Figure
2b,c), centering the data around 0. Then the 90th percentile of the absolute value of this
difference was taken, depicted (blue line) in Figure (S2a.) The 90th percentile plot shows
that beyond ~23 days the error does not increase as rapidly. An exponential curve was
fitted to the data (dashed line).
Figure S2a-c: The models (S2a,b) used to generate the sampling error plot (Figure 4-main
text) by combining the seasonal cycle correlations in Figure 1 with the mean flux error
plots in Figures 2c. It shows the line for the 90th % of the mean absolute error (Blue) and
a non-linear fitted function (Equation 1). The red point (10% error) and the green point
(10-day sampling error at SAZ site) together with assumptions 3 and 4 were used to
formulate Figure S2b. It links the mean absolute error to the seasonal cycle
reproducibility correlation. The third model (S2c) was used to generate the adaptive
sampling strategy plot (Figure S3). It is a non-linear model linking the extreme
constraints to the 10% error constraint.
The coefficients for this fit are shown below:
𝑓(𝑥) = −0.090 𝑒 −0.044𝑥 + 0.0893
Equation S1
The curve asymptotes to 0.0893 mmol.m-2.hr-1 (Equation S1) and we now assume that
this is the hypothetical maximum error that could occur, regardless of sampling interval.
We then related this curve to Figure 1, the correlation of seasonal cycle reproducibility,
through the following assumptions:
1) The chlorophyll seasonal cycle reproducibility (CSCR – % of Chl variance
explained by the seasonal cycle) is a reasonable proxy for the range of variability
modes for the CO2 air–sea flux.
4
2) The CO2 aliasing errors observed by the glider dataset at 43oS, 8.5oE can be
correlated to the CSCR for that particular location and then generalized through
the CSCR depicted in Figure 1 .
3) When the CSCR is 1.0 the error is 0 mmol.m-2.hr-1
4) When CSCR is 0.0 the error is 0.089 mmol.m-2.hr-1 – the potential maximum error
based on the asymptote of the exponential curve in Figure 3a.
5) The maximum sampling interval is 90 days (sampling ~4 times a year); this
correlates to a maximum error close to the asymptote (0.088 mmol.m-2.hr-1)
6) The causal connection between the variables used in Figures S2b,c remain
consistent throughout the Southern Ocean
These six assumptions allow us to define the black (described by assumptions 3 and 4),
red and greed dots in Figure (S2b). The red and green dots, described below, are
intercepts from the exponential curve in Figure S2a:
a) the sampling interval at the 10% uncertainty threshold used in the rest of this
study (red dot)
b) the error at the 10 day sampling period (green dot)
These error constraints from Figure S2a and assumptions 3 and 4 were then used to make
two non-linear fit plots, which relate the Southern Ocean-wide error at a 10-day sampling
period (Figure S2b) and the sampling period that is required to maintain the sampling
error at the 10% threshold (Figure S2c). Power law curves were fitted to these points for
Figures S2b-c – the coefficients for these curves are shown in the figure legends. Note
that the lowest CSCR score reported is 0.022, which equates to an error of 0.053
mmol.m-2.hr-1; similarly the highest CSCR is 0.86 ~ error of 0.003 mmol.m-2.hr-1.
These curves were used to create Southern Ocean-scale plots of mean sampling error at
the 10 day interval (Figure 4 in the main text) and the adaptive sampling strategy plot
(Figure S3), which illustrated the sampling strategy that may be required to meet the
required < 10% uncertainty threshold across the whole Southern Ocean (Lenton et al.,
2006; Monteiro et al., 2010). The correlation coefficient for the seasonal cycle
reproducibility in Figure 4 was normalised to the local mean chlorophyll between 1998
and 2007. This was done so that the contribution that the magnitude of the intra-seasonal
variability makes to the 10-day sampling alias error (Figure 4) was scaled to the
magnitude of the biogeochemical driver of CO2.
We express caution about the confidence limits of this generalization because it relies on
a single data set and the assumptions listed abobe. This is however the only data we have
for now and our objective is to illustrate conceptually how the important idea of sampling
period alias errors emerging from our observations may influence how we approach the
wider problem of optimizing sampling effort at the basin scale. We point to the wider
5
need of comparable data across contrasting intra-seasonal variability regimes in the
Southern Ocean in order to put more robust constraints on Figures 4 and S3.
Figure S3: A map showing a mean for the adaptive sampling interval (in days) required
to achieve the 10% error threshold in the Southern Ocean discussed in Lenton et al.
(2006). It was derived from combining the models in Figures 2a and2 c. It shows that
sampling periods of 1 – 3 days are necessary in areas of elevated sub-seasonal dynamics
and 5 – 10 days in areas characterized by mainly seasonal modes. Note that the scale of
this figure extends beyond the limits given in the scale bar.
S4: Wavelet Analysis of the ΔfCO2 and FCO2 data sets
A wavelet analysis was carried out to support the conceptual model (Figure 3 in main
text), which explains why synoptic scale intra-seasonal or event scale variability of FCO2
has a higher sampling-linked alias error than ΔfCO2.
For both ΔfCO2 and FCO2 data sets the seasonal trend and the sub-12h hour periods were
removed using Empirical Mode Decomposition (EMD), a powerful signal analysis
algorithm [Huang et al.,1998; Rilling et al., 2007]. The signal is broken into a number of
Intrinsic Mode Functions (IMF) each of which make a significant and proportional
contribution to the overall variability such that, if all the IMFs are summed, the original
signal is recovered.
The Continuous Wavelet Transform (CWT) analysis shows the strength of the energy
density or signal/noise ratio for the local signal of the time series in the frequency
(period) space. It shows that although ΔfCO2 has some limited variability in the 24 hour
6
range most of its energy lies in the 48 – 240 hour range whereas the frequency range for
FCO2 is 1 – 6 days (24 – 144 hours). This narrower and higher frequency modes for
FCO2 explains why it is more susceptible to sampling scale error than ΔfCO2 (see also
conceptual Figure 3 in the text)
Figure. S4a,b: Depicts the Wavelet Analyses of the ΔfCO2 and FCO2 data sets whose
frequencies higher than daily have been removed to highlight the 1 – 10 day period (24 –
240 hours). It shows that although ΔfCO2 has some limited variability in the 24 hour
range most of its energy lies in the 48 – 240 hour range whereas the frequency range for
FCO2 is 1 – 6 days (24 – 144 hours). The scale represents the comparative magnitude of
the energy density of the time domain of the signal in the frequency (period) domain.
References: Methods
Huang, N.E., Z. Shen, S.R. Long, M.L. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung and H.H.
Liu (1998) The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis, Proc. Roy. Soc. London A, 454, pp. 903–995.
Lenton, A., R.J. Matear, and B. Tilbrook. (2006), Design of an observational strategy for
quantifying the Southern Ocean uptake of CO2. Global Biogeochemical Cycles 20(4): DOI:
10.1029/2005GB002620
Monteiro, PMS, U. Schuster,, M. Hood, A. Lenton, N. Metzl,, A. Olsen,, K. Rogers,, C. Sabine,,
T. Takahashi,, B. Tilbrook, , J. Yoder, J, R. Wanninkhof,, A.J. Watson,, (2010) A global sea
surface carbon observing system: assessment of changing sea surface CO2 and air-sea CO2
fluxes. Hall, J., Harrison D.E. and Stammer, D., Eds., Proceedings of the "OceanObs’09:
Sustained Ocean Observations and Information for Society" Conference, Venice, Italy, 21-25
September 2009, ESA Publication WPP-306; doi:10.5270/OceanObs09.cwp.64
7
Nightingale, P. D., Malin, G., Law, C. S., Watson, A. J., Liss, P. S., Liddicoat, M. I., ... & UpstillGoddard, R. C., 2000, In situ evaluation of air-sea gas exchange parameterizations using novel
conservative and volatile tracers. Global Biogeochemical Cycles, 14(1), 373-387
Pierrot, D., Neill, C., Sullivan, K., Castle, R., Wanninkhof, R., Lüger, H., ... & Cosca, C. E.
(2009). Recommendations for autonomous underway pCO 2 measuring systems and datareduction routines. Deep Sea Research Part II: Topical Studies in Oceanography, 56(8), 512522. doi:10.1016/j.dsr2.2008.12.005
Flandrin, P., G. Rilling and P. Gonçalves (2004) Empirical Mode Decomposition as a Filter Bank.
IEEE Signal Processing Letters. 11(2): 112-114
Sutton, A.J. et al. (2014), A high-frequency atmospheric and seawater pCO2 data set from 14
open ocean sites using a moored autonomous system. Open access, Earth Sys. Sci. Data, 6,
353–366, doi: 10.5194/essd-6-353-2014
S5: Model based analysis of the sampling alias
The sampling alias and error sensitivity was also examined in a NEMO-PISCES 0.5o
peri-Antarctic model with a 5-day mean output (Figure S4). The model output was subsampled at 15-day intervals and the %error was calculated as the anomaly of the mean of
the 5-day BPA output and the mean of the 15-day sampling (BPA-15D)/BPA. Despite
the relative coarseness of the 5-day output this analysis shows that the model has strongly
contrasting areas of error sensitivity, which correspond to areas of stronger intra seasonal
dynamics (Figure S4). We predict that a comparable analysis on a higher spatial
resolution daily model output will produce sampling error sensitivities that are more
comparable to the data. This has significant implications for the types of models that are
used for observing system simulation experiments to optimize sampling strategies.
8
Figure S5 shows a plot of a comparable temporal aliasing of FCO2 from Bio-PeriAntarctic model (NEMO-PISCES05). It highlights a higher sampling frequency
sensitivity in regions of elevated EKE where the summer is characterized by stronger
intra-seasonal variability in the physics and biogeochemistry in the surface boundary
layer. The error shown is calculated by subsampling the model at 15 days (every 3rd time
step), creating three possible subsample means. The absolute values of the differences
between the subsampled mean values and the true mean is taken. The absolute of these
differences are averaged to arrive at a mean error for sub-sampled data. The mean error is
expressed as a percentage of the mean FCO2. This is shown in the equation where BPA is
the model data and 15di is the subsampled data:
% 𝑒𝑟𝑟𝑜𝑟 =
̅̅̅̅̅̅ − ̅̅̅̅̅
∑3𝑖|𝐵𝑃𝐴
15𝑑 𝑖 |
× 100
̅̅̅̅̅̅
𝐵𝑃𝐴 × 3
9