Background
Introduction
Observations demonstrate that dissolved CO2 concentrations in the
surface ocean have been increasing nearly everywhere, roughly following the
atmospheric CO2 increase but with large regional and temporal
variability (Takahashi et al., 2009; McKinley et al., 2011). In general,
tropical waters release CO2 into the atmosphere, whereas high-latitude
oceans take up CO2 from the atmosphere. Accurate knowledge of air–sea
fluxes of heat, gas and momentum is essential for assessing the ocean's role
in climate variability, understanding climate dynamics, and forcing
ocean/atmosphere models for predictions from days to centuries (Wanninkhof et
al., 2009).
The European Space Agency OceanFlux Greenhouse Gases (GHG) project
(http://www.oceanflux-ghg.org/) is an initiative to improve the
quantification of air–sea exchanges of greenhouse gases such as CO2.
The project has developed data sets suitable for computation of gas flux
climatology in which mean gridded values are computed from multiple
measurements over different years. The gas flux calculation requires accurate
values of gas transfer velocity, in addition to the concentrations of the
dissolved gas above and below the air–water interface (Liss and Merlivat,
1986). The project has relied heavily on the data sets successfully developed
and maintained by the Surface Ocean CO2 Atlas (SOCAT, Bakker et al.,
2014; Pfeil et al., 2013; Sabine et al., 2013). SOCAT has collated and
carefully quality controlled the largest collection of ocean
CO2 observations providing data in an agreed and controlled format for
scientific activities. Recognising that some groups may have difficulty
working with millions of measurements, the SOCAT gridded product (Sabine et
al., 2013) was then generated to provide a robust, regularly spaced
fCO2 product with minimal spatial and temporal interpolation.
This gridded data set is useful for evaluating models and for studying and
characterising fCO2 variations within regions in a format that
is easy to exploit. In this paper we present the OceanFlux-GHG methodology
for creating a climatology of fCO2 suitable for use in air–sea
gas flux studies.
Gas concentrations of CO2 in the upper ocean can be derived from SOCAT's
underway sea surface measurements of fugacity, fCO2
(pCO2 adjusted to account for the fact that the gas is not ideal
regarding molecular interactions between the gas and the air). The aquatic
CO2 concentration can be expressed as the product of fCO2
and solubility of CO2; the product of CO2 concentration difference
and gas transfer velocity, k, then gives us the air–sea gas flux.
Different authors of CO2 ocean–atmosphere gas flux products use either
a mean value of fCO2 (e.g. Schuster et al., 2009; Sabine et al.,
2013) or pCO2 (e.g. Takahashi et al., 2002, 2009;
Landschützer et al., 2013; Jones et al., 2012; Rödenbeck et al.,
2013) within a grid box for a particular measurement month and year. Many
studies have used the pCO2 climatology of Takahashi et
al. (2002, 2009) as a basis to estimate their own air–sea fluxes (e.g.
Kettle et al., 2005, 2009; Fangohr and Woolf, 2007; Land et al., 2013). The
data sets from Takahashi et al. (2002, 2009) and Sabine et al. (2013) are
calculated using in situ SST obtained at depth, SSTdepth. In situ
fCO2 is derived from fCO2 measured in the shipboard
equilibrator using the difference between the temperature of sea water in the
equilibrator and SSTdepth. Because fCO2 is highly
sensitive to temperature fluctuations, an instantaneous measurement of
fCO2 is only really valid for its concurrent in situ
SSTdepth measurement. Takahashi et al. (2009) note there is a bias
between the temperatures associated with the partial pressure measurements
(and their gridded and interpolated values) and the SSTdepth
product used in their calculation of solubility (and thus fluxes). That
inconsistency implies a bias between the upper ocean pCO2 values
with the true climatological mean values. They estimate a mean
+0.08 ∘C temperature difference, introducing a systematic
bias of about +1.3 µatm in the mean surface water
pCO2 over all monthly mean values obtained in their study. They
apply a correction to the global CO2 flux on that basis. Takahashi et
al. (2009) also acknowledge that by using SSTdepth in their
calculations, surface-layer effects could introduce systematic errors in the
sea–air pCO2 differences. Additional SST biases are also likely
introduced by different measurement systems that measure SST at sea (Donlon
et al., 2002), each with their own characteristic measurement biases.
All biases in SST, and hence in fCO2, contribute to uncertainties in the
true monthly means of fCO2. Also for the purposes of calculating
fluxes, each grid-cell value of fugacity must be paired with a SST value,
such that temperature products are used consistently and correctly
throughout the flux calculation. A true monthly mean value of fCO2
should therefore be estimated by calculating fCO2 for a monthly mean
value at a consistent SST appropriate to the gas flux calculation. As
explained in detail below, we use a representative, accurate and consistent
value of SST for each grid-cell value of fCO2.
The focus of this paper is to critically assess fCO2 calculations and the application of fCO2
for CO2 ocean gas flux climatology
development, with an emphasis on the need to properly address
inconsistencies in SST measurement methods. In other respects, we use simple
approaches to the calculation of a climatology (for example, simple
geospatial interpolation). We first review the importance of SST to the
calculation of fCO2 and the use of satellite SST data. We then review
the monthly composite SST data that we derived from SOCAT's regional
synthesis files and compare those to satellite observations of SST. In Sect.
2 we briefly describe the SOCAT data set and methods, followed by an
explanation of our approach to compute a climatological fCO2 from the
SOCAT in situ fCO2 data (Sect. 3). In Sect. 4 the spatial
interpolation using ordinary block kriging is detailed and in Sect. 5 the
resulting fCO2 climatology and a range of possible errors are discussed.
Our application of the recently released SOCAT “version 2” data set is the
subject of Sect. 6. The month January is used as an illustrative example of
the data treatment throughout this paper. In the conclusion (Sect. 7) SOCAT
version 1.5 and 2 and their uses are compared and a recommendation for
future versions of SOCAT is given.
In this paper, we explain the reasons for our conversion of fCO2
for in situ SST to fCO2 for monthly composite SST from
satellites and the methodology of our conversion in detail. The resulting
data sets are useful for air–sea gas flux studies and are given as a
supplement to this publication. We will not interpret the oceanographic
features that can or cannot be distinguished in our maps. We leave that to
continuing work within and beyond the OceanFlux-GHG project.
Complexities of in situ SST measurements and implications for fCO2
As already discussed, fCO2 is highly sensitive to temperature.
Similarly, accurate knowledge of SST and, to a lesser extent, salinity, is
essential when calculating air–sea gas fluxes. SST vertical profiles are
complex and variable. SST can also vary over relatively short time scales
within relatively small regions and variations in the temperature measured
can also arise from the method and instrumentation used for measuring it. All
of these issues can cause problems when using in situ data to construct a
fCO2 climatology. These issues are now discussed. We begin with
issues surrounding individual measurements of SST and then consider the
quality of composite values of in situ derived SST (i.e. averages over a
defined grid cell).
A schematic of the surface ocean, depicting the definition of the
mass boundary layer (MBL), thermal skin and temperatures at various depths
(Donlon et al., 2002). SSTdepth can be from centimetres to metres
below the surface, but is commonly around 5 m in the SOCAT data.
The structure of the upper ocean (∼ 10 m) vertical temperature profile
depends on the level of shear-driven ocean turbulence and the air–sea fluxes
of heat, moisture and momentum. Every SST observation depends on the
measurement technique and sensor that is used, the vertical position of the
measurement within the water column, the local history of all components of
the heat flux conditions and, the time of day the measurement was obtained
(Donlon et al., 2002). The subsurface SST, SSTdepth (Fig. 1), will
encompass any temperature within the water column where turbulent heat
transfer processes dominate (Donlon et al., 2007). Such a measurement may be
significantly influenced by local solar heating, the variations of which have
a time scale of hours, and typically temperature will vary with depth.
Diurnal warming and the formation of a “warm layer” may occur at the sea
surface when incoming shortwave radiation leads to stratification of the
surface water. In the absence of wind-induced mixing, temperature differences
of > 3 K can occur across the surface warm layer (Ward et al.,
2004), which in turn will enhance the outgassing flux of CO2 (Jeffrey et
al., 2007, 2008; Kettle et al., 2009). In order to address such issues, the
international Group on High Resolution Sea Surface Temperature (GHRSST)
states that SSTdepth should always be quoted at a specific depth in
the water column; for example, SST5m refers to the SST at a
depth of 5 m. However, SSTdepth data can be measured using a
variety of different temperature sensors mounted on buoys, profilers and
ships at any depth beneath the water skin and the depth of the measurement is
often not recorded. Different measurement systems that are used to measure
SST (e.g. hull mounted thermistors, inboard thermosalinograph systems) have
evolved over time using different techniques that are prone to different
error characteristics (e.g. for a good review see Kennedy, 2013; Kennedy et
al., 2011a, b), such as warming of water as it passes through the ships'
internal pipes before reaching an inboard thermosalinograph (e.g. Kent et
al., 1993; Emery et al., 2001; Reynolds et al., 2010; Kennedy, 2013), poor
calibration or biases due to the location and warming of hull mounted
temperature sensors (e.g. Emery et al., 1997, 2001), inadequate
knowledge of temperature sensor depth (e.g. Emery et al., 1997; Donlon et
al., 2007), poor knowledge of temperature sensor calibration performance and
local thermal stratification during a diurnal cycle (e.g. Kawai and Wada,
2007). This means that if not carefully controlled, SST biases of
> 1 K may easily be introduced into an in situ SST data set.
An additional set of issues surrounds the calculation of gridded values of
SST derived from in situ data. Here, in addition to potential biases in
individual measurements, we should consider whether the sampling by in situ
methods is sufficient. In respect to the SST measurements paired to CO2
measurements, there is an issue (Takahashi et al., 2009), which is likely to
result from a combination of undersampling, temperature gradients and
measurement bias.
All of these issues mean that directly using SST and fCO2
measurement pairs from a large data set (i.e. that resulting from a large
number of different instrument set-ups and methods) for a fCO2
climatology for studying air–sea gas fluxes is likely to introduce errors.
In summary, three steps must be achieved to estimate true monthly mean values
of fCO2 to (1) adjust for errors due to the vertical SST
gradient, (2) minimise the bias due to undersampling (related to grid-box
averaging of the measurement data), and (3) minimise errors due to the
different methods and instrumentation. Therefore, we propose that correcting
all of the fCO2 data back to a consistent surface SST data set is
clearly advantageous, and this is where satellite data can be useful.
The use of satellite sea surface temperature data
Satellite Earth observation thermal infrared radiometers have been in orbit
around the Earth since the 1990s and global SST products based on these
instruments are available. The radiometers are sensitive to thermal radiation
from the “radiometric skin” of the ocean and more recent products are
calibrated exclusively against other “skin SST” measurements (rather than
SST measurements at depth). In addition to individual measurements, composite
or gridded values of SST are calculated and these have a low sampling
uncertainty for monthly values. These satellite products have been shown to
have a higher accuracy and precision for studying SST than in situ methods
(e.g. O'Carroll et al., 2008) and such data are now available as a climate
data record (Merchant et al., 2008, 2012). We used satellite derived SST
values from the Along Track Scanning Radiometers, ATSRs, Reprocessing for
Climate project, ARC (Merchant et al., 2012). This climate data record is a
global, long-term, homogenous, highly stable SST data set based on
satellite-derived SST observations.
We have mentioned thermal gradients within the upper metres of the ocean, and
particularly warm layers, in the previous section, but it is also important
to note that the very surface of the ocean and the radiometric skin are
typically one to two tenths of a Kelvin cooler than the water millimetres
below, due to cooling at the sea surface and limited eddy transport within
the top millimetre of the ocean. Thus, a thermal skin is defined as shown
schematically in Fig. 1. The low eddy transport also affects gas transport
and a mass boundary layer, MBL (Fig. 1), is defined for air–sea gas
exchange. Though both the thermal skin and MBL are products of limited eddy
transport, MBL is thinner than the thermal skin due to the lower molecular
diffusivity of dissolved gases. The concentration difference across MBL is
the driving force behind the air–sea flux of CO2. A calculation of the
concentration difference requires attention to vertical thermal gradients
both in the top millimetre and in the several metres below. As discussed
previously, in situ sub-surface seawater fugacity is normally measured
several metres below the surface. The direct application of these
measurements for deriving air–sea fluxes (e.g. Takahashi et al., 2009)
implicitly assumes that the measured fugacity values at depth are the same as
those at the bottom of the MBL. The formation of warm layers will certainly
undermine this assumption and the thermal skin adds a significant additional
complication. Satellites directly provide a radiometric temperature virtually
equivalent to the temperature at the top of the thermal skin and MBL. At wind
speeds of approximately 6 m s-1 and above, the relationship between
SSTskin (at the top of the skin) and SSTsubskin (Fig. 1)
is well characterised for both day- and night-time conditions by a cool bias
(e.g. Donlon et al., 2002). Therefore a skin temperature value from Earth
observation with an appropriate correction for the cool skin bias can be used
to describe the temperature at the base of the thermal skin, thus avoiding
the effects of warm layers and other thermal gradients below the skin.
Temperatures within the thermal skin (for example, defined for the base of
the MBL) are not a standard product, but could also be estimated from
SSTskin. There are some remaining ambiguities regarding precisely
which satellite-based temperature product is optimal for generating a
climatology, but any temperature calculated from composite satellite derived
SSTs is preferable (to calculate composite values of CO2 parameters at
the base of the MBL) in comparison to an in situ SSTdepth product.
The practical differences between satellite and in situ temperature products
are described in the next section.
A comparison between SST data sets
In air–sea gas flux calculations, an estimate of the water side
fCO2, and hence the temperature, is required at the base of the
mass boundary layer. However, ARC SST data are measurements of the sea
surface skin, SSTskin, which is characteristically cooler than the
water just below it. Since gas transfer velocities are low in low wind
speeds, it is more important to have a reasonably accurate estimate of the
thermal skin effect in moderate and high wind speeds. Donlon et al. (1999)
reported a mean cool skin ΔT=0.14 (±0.1) K for wind speeds in
excess of 6 ms-1 and so we used this to derive
SSTsubskin (the SST at the base of the thermal boundary layer,
Fig. 1) from ARC SSTskin.
The ARC data set provides daily day-time and night-time averages of
SSTskin (K) from infrared imagery gridded to a 0.1∘
latitude–longitude resolution (Merchant et al., 2012). For each year from 01
August 1991 to 31 December 2010, we calculated the monthly mean
SSTskin distributions, averaged over a
1∘ × 1∘ grid without differentiating between day-
and night-time measurements
(http://www.oceanflux-ghg.org/Products/OceanFlux-data/Monthly-composite-datasets).
These SSTskin grid points were linearly interpolated to the ith
SOCAT measurement location (SSTskin,i). We defined
Tym (K) as the 1∘ × 1∘ grid box mean of
Tym,i = SSTskin,i + 0.14 K in the
measurement year “y” and measurement month “m”. The fCO2
values were then re-computed from in situ SST to satellite
Tym,i for our climatology (Sect. 3.2).
Histogram of temperature difference (K) between monthly gridded data
of subskin SST derived from ARC, Tym, and in situ SST from SOCAT
version 1.5 using global data from August 1991 to 31 December 2007. The bin
widths are 0.25 K, and the average and median dT are both -0.09 K.
Using 1∘ × 1∘ grid box means of the difference
between Tym,i and SOCAT's instantaneous in situ SST measurement
(generally obtained at 5 m nominal depth) converted to unit K and all data
from the years 1991 to 2007, a histogram of dT=Tym - SST (K) was
produced (Fig. 2). It shows that dT was distributed around a median and mean
of -0.09 K with a standard deviation of 0.55 K. Assuming the cool skin
effect has been corrected accurately, this difference implies that the
gridded in situ SST systematically overestimated Tym (our estimate of
SSTsubskin). The corresponding histogram of 1∘ × 1∘ grid box means of the difference between fCO2 converted to
a monthly composite and the original SOCAT's in situ fCO2 (dfCO2=fCO2(Tym)-fCO2) using data from all years (not
shown) revealed a similar distribution with a mean of -1.21 µatm and
standard deviation of 9.36 µatm. The temperature differences were
found to be positive as well as negative (Fig. 2). Positive dT can be a
consequence of diurnal warming when the top layer heats up by solar
radiation during the day. This heat is lost again during the night. Cooling
of the top layer (negative dT) is a less described phenomenon but can be
expected in colder environments. Alternatively, it is possible that negative
dT results because the in situ data are biased warm, perhaps because the
warming before reaching a ship-board thermosalinograph is systematically
underestimated. We found more negative dT during the winter months and at high
latitudes. The temperature profile in the sea depends on wind speed as wind
mixes the water column, i.e. for strong winds SST is expected to be more
constant in the vertical. Figure 3 illustrates the wind speed dependence of
dT for the North Atlantic. This region was chosen because it has the highest
SOCAT data density. For each dT we retrieved the monthly 1∘ × 1∘ grid box mean of 10 m wind speed, U10 (m s-1),
using the Oceanflux-GHG's composite of GlobWave merged altimeter wind speed
data (http://www.oceanflux-ghg.org/Products/OceanFlux-data/Monthly-composite-datasets).
The scatter plot of dT as a function of U10, averaged over in 1 ms-1
U10 bins, (Fig. 3) shows that dT decreased with increasing U10 becoming negative for wind speeds over about 10 ms-1. Similar trends
were seen in the other regions, but with dT turning negative for different
wind speeds: North Pacific 9 m s-1; Coastal 8 m s-1; Tropical
Atlantic and Southern Ocean 6 m s-1; Tropical Pacific, Indian Ocean
and Arctic 4 m s-1. The Tropical Atlantic was different in that dT became
less negative for wind speed over ∼ 8 m s-1, turning
positive over ∼ 10 m s-1. If only North Atlantic data
from the winter months December, January and February were included, nearly
all dT values were negative. The analyses of SST differences described above,
suggest strongly that the original in situ temperatures are biased and that
bias varies spatially and seasonally. Therefore, a correction of CO2
parameters for temperature is appropriate.
Scatter plot of temperature difference (K) between monthly gridded data of
subskin SST derived from ARC, Tym, and in situ SST from SOCAT version 1.5, using
data from all available years in the North Atlantic, binned in 1 ms-1 U10 bins.
The error bar indicates the standard error of the mean.
Corrections of fCO2 for SST
Having concluded that the temperature originally paired with a CO2
measurement is not suitable for a gridded air–sea flux calculation, we
require a guiding principle to calculate “revised values” that can be
paired with consistent and appropriate SST values throughout the flux
calculations. The principle that we apply is that for changes in temperature
within each grid cell, the fugacity changes can be calculated to a good
approximation by assuming the changes in the carbonate system are
isochemical. That principle is standard for corrections within a measurement
system (for example where the sample water is warmed between collection and
measurement in an equilibrator) and can also be applied with some confidence
to the changes effected by warm layer formation and destruction (Olsen et
al., 2004; Jeffery et al., 2007). Applying the principle more broadly is less
satisfactory, but given the value of calculating consistent and robust values
of temperature and carbonate parameters for air–sea flux calculations, it is
a reasonable action. Essentially, we assume that there will not be systematic
sample biases in alkalinity or total dissolved inorganic carbon within the
grid cell, but the original temperatures may be poorly measured, poorly
sampled or affected by vertical temperature gradients. Dissolved inorganic
carbon is partitioned between dissolved gas, bicarbonate ions and carbonate
ions and the fractions of each is temperature dependent. An isochemical
change in the system changes the concentration and fugacity of the dissolved
gas without altering the alkalinity or the total dissolved inorganic carbon.
In Sect. 3, we describe the recalculation of fugacities and partial pressures
by applying this principle.
An important subtlety is that we recalculate fugacity at SSTsubskin
rather than the theoretical temperature at the base of MBL. Some of the
reasons are simply pragmatic: e.g. calculating SSTsubskin is quite
standard and the correction to composite values of this temperature achieves
the primary objective, since the temperature difference with in situ
temperatures (Figs. 2 and 3) is generally larger than those within the
thermal skin. Another reason is theoretical: the response time of the
carbonate system is limited by the hydration reaction and it is unlikely
that substantial repartitioning (and changes in the concentration of the
dissolved gas) will occur between the base of the thermal skin and the base
of the MBL. Therefore a concentration calculated from the solubility and
fugacity at SSTsubskin should also be appropriate for the base of the
MBL.
An overview of all the different parameters used in our re-computation is
presented in Appendix A1. The SOCAT measurements and methods are described
in Sect. 2 and Appendix A2 and our re-computation in Sect. 3 and Appendix A3.
SOCAT version 1.5 CO2 fugacity (µatm) data shown
in the online Cruise Data Viewer at http://www.socat.info/ for the month January from 1992 to 2007.
Our re-computation for climatological fugacity in the year 2010
In our re-computation of fCO2 for SOCAT's in situ SST to monthly
composite fCO2 we only used “good” records (WOCE_flag = 2) with valid fCO2,is and SST. Our re-computation required multiple
steps (see Appendix A1 for definitions of variables):
estimate original pCO2 measurement at Teq;
convert pCO2(Teq) to pCO2(Tym,i);
calculate fCO2(Tym,i) from pCO2(Tym,i);
apply linear trend to extrapolate fCO2(Tym,i) and pCO2(Tym,i) to year 2010;
bin the data by month and in 1∘ × 1∘ grid boxes;
spatially interpolate the grid boxes.
The first three steps were necessary because mole fraction
xCO2,is, and partial pressures
pCO2,is and pCO2(Teq) are not
given in the SOCAT regional synthesis files (so Eqs. A2 and 4 could not be
used directly to calculate fCO2,ym,i). The first step of
estimating the original measurement of pCO2(Teq) is
described in Appendix A3. Note also that by first returning to the partial
pressure at the equilibrator temperature, any measurement bias in the in situ
temperature is removed thereafter. If Teq was not given we skipped
step 1 and used SST to convert pCO2(SST) to
pCO2,ym,i in step 2; those records will carry the effect
of any measurement bias in the in situ temperature into the recalculated
values. The next step was to convert partial pressure at equilibrator
temperature to partial pressure at Tym,i for each SOCAT
measurement. Because ARC ATSR data were available from 01 August 1991 we
converted SOCAT data from 01 August 1991 until 31 December 2007. As a
consequence 95249 (1.4 %) of valid fCO2 observations were
not used from the SOCAT v1.5 data set (from 119 cruises spread all over the
globe). We note that the ESA SST Climate Change Initiative (CCI) project is
now working on an extended SST climate data record from satellite extending
back to 1981, which is expected to be made available in 2015. We used Eq. (4)
to correct for the difference between monthly composite and equilibrator
temperature in ∘C resulting in
pCO2,ym,i=pCO2(Teq)exp0.0433(Tym,i-Teq)-4.35×10-5(Tym,i2-Teq2)
The subscript “ym” indicates a “single year monthly composite” and
“i” interpolated to SOCAT sample location (Sect. 1.4). As explained in Sect. 1.5, Eq. (4) was applied on the basis that an isochemical transformation
between SST and Tym is a reasonable assumption. In a third step,
monthly composite estimations of fCO2,ym,i (µatm) were calculated
from pCO2,ym,i by inverting Eq. (A2),
fCO2,ym,i=pCO2,ym,iexpB+21-pCO2(Teq)Peq,ym2δPeq,ymR⋅Tym,i
with B=B (CO2, Tym,i) (Eq. A3) and δ=δ (CO2, Tym,i) (Eq. A4) and temperatures in K. We estimated
Peq,ym from sea level pressure estimated at closest grid value from 6
hourly NCEP/NCAR as given in SOCAT's merged synthesis files
(ncep_slp in hPa). To account for the overpressure that is
normally maintained inside a ship 3 hPa was added (Peq,ym = ncep_slp + 3 hPa) (Takahashi et al., 2009)
and Peq,ym was converted to unit atm. Note that we recomputed SOCAT's fCO2 for
monthly composite SST and atmospheric pressure, but not for monthly
composite salinity. However, if in situ salinity was not provided by the
investigator, SOCAT used a monthly composite sea surface salinity from the
World Ocean Atlas 2005 (woa_sss) for their computation of
fCO2,is. The consequences of absent salinity values are assessed in
Sect. 5.7. For all years pCO2,ym,i and fCO2,ym,i were extrapolated
to the year 2010, producing pCO2,cl,i and fCO2,cl,i referenced to
2010, using the same mean rate of change (1.5 ± 0.3 µatm y-1) as Takahashi et al. (2009)
used for pCO2. The Takahashi et al. (2009) study extrapolated to the year 2000 only, so if the rate of change
has increased since then, our estimates for 2010 could be biased low.
Finally, the fCO2,cl,i and pCO2,cl,i data were grouped by month and
averaged over 1∘ × 1∘ squares. Not all
1∘ × 1∘ grid boxes were filled and we
horizontally interpolated between filled values to produce global
pCO2,cl and fCO2,cl distributions (Sect. 4).
Variogram for global fCO2,cl data in 2010 for the month
January, derived from fCO2,is shown in Fig. 4. The numbers next to
each data point are the number of data pairs.
Horizontal extrapolation using ordinary block kriging
Unlike Takahashi et al. (2009), our climatology includes data from El
Niño years and coastal locations. We added pCO2,cl
for those who prefer to use partial pressure; pCO2,cl
levels were slightly higher (less than 2 µatm) than
fCO2,cl. For the spatial interpolation of the gridded
data on a 1∘ × 1∘ mask map of the global oceans, we
used the variograms and kriging options within gstat, which is an open source
tool for multivariable geostatistical modelling, prediction and simulation
(gstat home page: http://www.gstat.org/). Gstat finds the best linear
unbiased prediction (the expected value) with its prediction error for a
variable at a location, given observations and a model for their spatial
variation (Pebesma, 1999, 2004). We used the “ordinary block kriging”
option. We quantified the prediction error as standard deviation, SD (square
root of the variance given by gstat). As would be expected, the prediction
errors were large in areas with data sparsity. First, we modelled the
variogram for fCO2,cl for each month using gstat's
interactive user interface (Pebesma, 1999, 2004). A variogram describes how
the data vary spatially and can be represented by a plot of semivariance
against distance. The variograms best fitted combinations of a nugget and a
spherical model, a Nug(0) + b Sph(c), and for each month variogram
parameters a, b and c were derived (e.g. Fig. 5). Figure 5 shows that
at small separation distances, the semivariance in fCO2
(computed as one-half of the difference in fCO2 squared) is
small, so that points that are close together have similar fCO2
values. After a certain level of separation (c), the variance in the
fCO2 values becomes rather random and the model variogram
flattens out to a value corresponding to the average semivariance (a+b).
The model variogram is used to compute the weights used in the kriging. The
variogram coefficients were different for each month because each monthly
data set had a different data distribution. The fitted variogram models were
applied in the kriging of both fCO2,cl and
pCO2,cl because the difference with
fCO2,cl was negligible compared to the spatial variation.
By using the variogram to compute the weights for the interpolation, the
expected estimation error is minimised in a least squares sense so that the
kriging produces the best linear unbiased estimate.
We applied ordinary kriging on mask map locations because it is the default
action when observations, variogram, and prediction locations are specified
(Pebesma, 1999). We performed local ordinary block kriging directly on a
1∘ × 1∘ mask map of the global oceans with minimum
(min) of 4, maximum (max) of 20, and radius of 60∘. Thus, after
selecting all data points at (euclidian) distances from the prediction
location less or equal to 60∘, the 20 closest were chosen when more
than 20 were found and a missing value was generated if less than 4 points
were found. It should be noted that the interpolation did not necessarily
stop at land barriers in areas with few or no data points. Also the
decorrelation length was most likely shorter than 60∘ kriging radius
for the majority of the grid cells (Jones et al., 2012). Jones et al. (2012)
do not show that changes in surface-ocean pCO2 are larger in
either the east–west direction or the north–south direction. We had to
choose between a small kriging radius and generating a few high-quality grid
cells but many empty grid cells, or a large kriging radius and generating few
empty grid cell values but many with high SDs. We chose the latter in order
to produce almost complete maps and with the option that a quality filter
could be applied later. The data were smoothed by averaging over square
shaped 5∘ × 5∘ sized blocks. Thus gstat produced the
fCO2,cl (and pCO2,cl) prediction and
variance values located at the grid cell centres of the (non-missing valued)
cells in the grid map mask. These results were compared with results from
different kriging options min, max, radius and block size (Sect. 5.3).
Our approach to the interpolation of these sparse data is simpler and more
straightforward than other previous methods. This choice was deliberate as
optimal interpolation of such sparse environmental data is itself a focus of
international research. For example, the spatial interpolation on a
4∘ × 5∘ grid of Takahashi et al. (2009) applies a
knowledge of ocean circulation. Available observations were first propagated
to neighbouring pixels with no observations by including the values in
neighbouring areas for ±4∘ latitude, ±5∘ longitude
and ±1 day from the center of a pixel. The values of the pixels that are
still without observations after this procedure are computed by a continuity
equation based on a 2-D diffusion–advection transport equation for surface
waters. All daily pixel values are used to calculate monthly mean values.
Takahashi et al. (2009) estimate that the global mean surface water
pCO2,cl obtained in their study may be biased by about
+1.3 µatm due to under sampling and their interpolation method.
Our use of a consistent and unbiased temperature for fCO2
calculations should reduce this bias. Further examples of more advanced
interpolation schemes include: Landschützer et al. (2013) who applied a
two-step neural network to interpolate SOCAT observations in space and time
and derive basin-wide monthly maps of pCO2 on a
1∘ × 1∘ grid. The neural networks fit the
observations with almost no bias. Rödenbeck et al. (2013) used a model of
surface-ocean biogeochemistry to temporally and spatially resolve (with
respective resolutions of 1 day and 4∘ × 5∘) global
surface-ocean pCO2 from the SOCAT's fCO2 database
and Park et al. (2010) construct monthly climatological maps of
pCO2 on a global 4∘ × 5∘ grid using
sub-annual δpCO2/δ SST trends and inter-annual SST
anomalies.
Monthly fCO2,cl values (µatm) in the global oceans
estimated for January 2010 on a 200–600 µatm scale; data were interpolated to
a 1∘ × 1∘ grid using ordinary block kriging with min = 4, max = 20, radius = 60∘ and block
size 5∘ × 5∘.
Results
Monthly global maps
The prediction distributions of fCO2,cl produced by the
ordinary block kriging are shown in Fig. 6 for January; Fig. 7 shows the
associated standard deviations and Fig. 8 the fCO2,cl
predictions with high prediction errors (SD > 25 µatm)
masked. Grid-box values, as shown in Fig. 8 for January, were averaged over 3
months (an empty grid box was generated if it did not contain at least one
valid value with SD < 25 µatm) resulting in four seasonal
distributions of fCO2,cl (Fig. 9). The 12-monthly global
distribution data have been made available in 12 NetCDF files in the
supplement related to this article. These files contain
fCO2,cl, pCO2,cl, their kriging
errors, and ARC's SSTskin for the year 2010, all on a
1∘ × 1∘ grid. The variable names are respectively
fCO2_2010_krig_pred, pCO2_2010_krig_pred,
fCO2_2010_krig_std, pCO2_2010_krig_std, and Tcl_2010
(Tym as defined in Sect. 1.4 for the year 2010). Also given is
vCO2_2010, the mole fraction of CO2 in dry air (ppm) in 2010 from the
Earth System Research Laboratory of the National Oceanic and Atmospheric
Administration, NOAA ESRL, (Dlugokencky et al., 2014) on the
1∘ × 1∘ grid. This variable is not used in our
re-computation, but is included because it is used in air–sea flux
calculations. The important differences with the Takahashi climatology are
summarised in Table 1.
Standard deviation in fCO2,cl (µatm) estimated
for January 2010 on a 0–50 µatm scale, associated with the
ordinary block kriging shown in Fig. 6.
Comparison between Takahashi climatology and climatology presented in this paper (both using trend of 1.5 µatm yr-1).
Takahashi et al. (2009)
This study
Data source
LDEO database (NDP-088) http://cdiac.ornl.gov/oceans/doc.html (Takahashi et al., 2009)
SOCAT versions 1.5 and 2 (synthesis data files) http://www.socat.info/ (Pfeil et al., 2013; Bakker et al., 2014)
Period covered
1970–2007
01 August 1991–31 December 2007/11(SOCAT v1.5/2)
Reference year
2000
2010
Resolution
4∘ × 5∘ and 1month
1∘ × 1∘ and 1 month
Data
Excludes El Niño periods in theequatorial Pacific and coastal data
Includes El Niño and coastal data
Spatial interpolation
Involves continuity equation based on a 2-D diffusion–advection transportequation for surface waters
Ordinary block kriging (without continuity equation)
Parameter
pCO2 (µatm)
fCO2 (and pCO2) (µatm)
Trend
+1.5 µatm yr-1
+1.5 µatm yr-1
fCO2 taken at
Instantaneous intake temperature SSTdepth
Monthly composite sub-skin SST from ARC
A comparison between the Takahashi climatology, normalised to the year 2010
by adding 15 µatm
(= 1.5 µatm yr-1 × 10 y), and OceanFlux
pCO2,cl is shown in Fig. 10. The general distribution is
similar with large differences mainly confined to poorly sampled regions such
as the Arctic and some coastal zones. For the well-sampled zone
14–50∘ N in the North Atlantic and North Pacific, the climatologies
are satisfactorily similar, with the discrepancies of the respective seasonal
pCO2,cl averages being less than
∼ 2.4 and ∼ 4.4 µatm (Table 2), but
there are some interesting if subtle differences. For instance, both products
exhibit a seasonal signal in the North Atlantic but the amplitude of that
seasonal signal is noticeably stronger in the new product (thus positive
difference in summer, negative difference in the winter).
Seasonal averages in µatm of OceanFlux pCO2,cl
and pCO2,cl from Takahashi (2009) normalised to 2010 by adding
15 µatm (= 1.5 µatm yr-1 × 10 yr) in the
North Atlantic and North Pacific in the zone 14–50∘ N.
Ocean basin
Method
Winter
Spring
Summer
Autumn
Atlantic (14–50∘ N)
OceanFlux
356.8
356.6
382.0
374.7
Takahashi
358.2
356.9
379.5
372.6
Difference
-1.4
-0.3
2.5
2.1
Pacific (14–50∘ N)
OceanFlux
348.8
351.8
379.3
365.6
Takahashi
353.2
354.8
375.6
369.1
Difference
-4.4
-3.0
3.7
-3.5
Differences with Takahashi and other climatologies arise for four key
reasons.
The selection of data. Our product relies on quality control within SOCAT
and should in this respect be comparable to other products derived from
SOCAT, but may differ significantly from Takahashi et al. (2009) for which
the selection of data is less transparent.
The handling of temperature. Our methods differ substantially from those
used previously. As explained earlier, we are convinced our handling is more
rational and consistent with the eventual calculation of fluxes. Though the
mean difference in temperature is fairly small, we have noted already that
some regional and seasonal differences are large.
The interpolation methods. We have deliberately used a very simple
interpolation method based on block kriging. As shown by Figs. 7 and A4, the
resulting standard deviations are large and the appearance in poorly sampled
regions and seasons is poor. These sparsely sampled regions are not the only
regions that show some very obvious differences with Takahashi, for example
the eastern-central equatorial Pacific. Other methods produce superficially
more pleasing results in the sparsely sampled regions, but they rely on
relationships with other variables (e.g. circulation or temperature) that may
or may not be robust.
The reference year and assumed secular trends. These are clearly
significant, but the sensitivity to secular trends in oceanic pCO2 will
need to be investigated in a later study.
As Fig. 6 but with SD > 25 µatm (Fig. 7)
blanked out.
Calculating all errors is difficult, but we considered the following errors.
The prediction errors were estimated by taking the square root of the
variances of the kriging. The different kriging approaches themselves were
evaluated by calculating the mean and standard deviations of the varying
fCO2,cl kriging results using the options shown in Table 3. The specific
timing and path of ship tracks can affect the results. Therefore we used a
bootstrapping approach to investigate if certain cruises dominated the
mapped results. Other errors that were analysed were the “temporal
extrapolation error”, the “inversion error” related to the different
starting points of the conversion, the consequences of the absent values in
our re-computation, and the propagations of the uncertainties in the SOCAT
measurements and Tym,i. These errors are discussed in the next sub
sections and the final subsection gives a summary overview.
Seasonal fCO2,cl values (µatm) in the global
oceans estimated for 2010 in DJF (December–February), MAM (March–May), JJA
(July–August) and SON (September–November) on a 200–600 µatm
scale; grid-box values as shown in Fig. 8 for January were averaged over the
3 months.
Spatial interpolation errors
The standard deviations (SDs) of the prediction produced by the kriging were
calculated by taking the square root of the variance values produced by gstat
(Pebesma 1999). These prediction errors were related to the available SOCAT
data density in each measurement month (e.g. Figs. 4 and 7) and also to
errors in the grid point values of fCO2,cl themselves as
they are propagated in the kriging operation. For each month we calculated
the global mean, min and max of the SD. Over the 12 months, the monthly SD
over all grid points was 20 ± 5 µatm on average (mean over
all monthly means ± SD of the mean). The average monthly
minimum/maximum SD values were 6.3 ± 2.6/50 ± 8.7 µatm
(mean over all monthly min max values ±SD of the mean). Areas with large
SD emerged where no SOCAT data were available, for example in the western
Southern Ocean and the Arctic. Spatial interpolation errors were lowest in
the North Atlantic and North Pacific where SOCAT data was densest. The month
April showed the highest errors, this could be a consequence of the variogram
range, c, being the smallest, implying that the covariance between the
locations dropped quickly with distance In other words, the spatial
autocorrelation length was short in April (24∘), indicating that
fCO2 was spatially less stable in April (Jones et al., 2012),
and the consequent error was recognised by the kriging method. Our variogram
model of combination of a nugget and a spherical model did not fit November
data satisfactorily as the semivariance was almost independent of distance,
meaning that spatial dependence was random, i.e. a near-zero spatial
autocorrelation length; thus the low standard deviations in November were
therefore probably not representative of the true error due to the kriging
method. The low spatial stability in April and November was likely explained
by SST or biological activity (or both) being less spatially stable in these
months (Jones et al., 2012). Standard deviations of the kriging are included
in our presented data files; a bias should not be introduced by the kriging
itself (Pebesma, 1999).
The different kriging options that were applied to the monthly data
sets of fCOcl for 2010; ordinary block kriging was applied with
min, max, radius, dx and dy as explained in Sect. 4.
Min
Max
Radius (∘)
dx (∘)
dy (∘)
4
20
60
5
5
4
20
40
5
5
4
20
100
5
5
4
20
60
1
1
4
20
60
10
10
4
10
60
5
5
4
40
60
5
5
2
20
60
5
5
10
20
60
5
5
A comparison of the different kriging approaches
The ordinary block kriging of the fCO2,cl data was repeated using a
range of sensible kriging parameters (Table 3). The standard deviation of
the mean over the different kriging results was less than 5 µatm in
most places, with higher values seen near the coasts, Arctic, and the
western Tropical Pacific and Southern Ocean. These standard deviations were
considerably smaller than those of the kriging itself (Figs. 7 and A4) but
could be significant in a few places especially, but not exclusively, in the
Arctic and coastal regions where the SOCAT data are particularly sparse.
Are some cruises more important than others?
The specific timing and track of a cruise may give an unrepresentative sample
of that region and season. Therefore, it is important to investigate whether
or not the final results are highly dependent on individual cruises. That
possibility was studied using the bootstrap method, a statistical technique
which permits the assessment of variability in an estimate using just the
available data (Wilmott et al., 1985). Bootstrapping creates synthetic sets
of data by random resampling from the original data with replacement. We
bootstrapped the SOCAT data 10 times by cruise to estimate the variability of
the mean monthly fCO2,cl distributions. Due to the size
of the data set we applied the bootstrapping in two stages, first by the
cruise's unique identifier (cruise ID) for each year and region, and then by
year and region. Each of the 10 resulting synthetic
fCO2,cl data sets were kriged as described in Sect. 4
(for each month in each synthetic data set the optimal variogram model was
fitted and applied). The mean monthly distributions showed that in regions of
fewer cruises (i.e. all regions except the North Atlantic and North Pacific)
significant variation in fCO2,cl could occur; the
resulting variations can have a SD of up to 50 µatm. We conclude
that the final results are highly sensitive to individual cruises in many
regions and additional caution in the results should be considered. High
variability in the eastern–central equatorial Pacific could be a consequence
of not excluding the El Niño years.
Seasonal differences between OceanFlux pCO2,cl and
pCO2,cl from Takahashi (2009) normalised to 2010 by adding
15 µatm (= 1.5 µatm yr-1 × 10 yr).
Temporal extrapolation error
The 1.5 µatm yr-1 rate of change in pCO2 has an
estimated precision of ±0.3 µatm yr-1 (Takahashi et al.,
2009) and the trend for fCO2,cl should follow the trend
for pCO2,cl (Eq. 6). The error in
fCO2,cl (before the kriging step 6 in Sect. 3) due to
uncertainty of the pCO2,cl trend was therefore estimated
for each sample station as
±(2010-year) × 0.3 µatm yr-1 and binned by month
and in 1∘ × 1∘ grid boxes ranged between
±(0.9–5.7) µatm. The error was lowest in the North Atlantic
Ocean and in the Pacific Ocean because more cruises were performed there in
recent times. The absolute monthly mean extrapolation error over all grid
points was estimated at 3.0 ± 0.1 µatm (average over all
monthly means ± standard deviation). This implies that if in reality the
rate of change since 1991 was 1.8 instead of 1.5 µatm yr-1,
our fCO2,cl would be underestimated by
∼ 3 µatm on average. Recent research has shown that an error
of this magnitude, or perhaps greater, is probable, since Takahashi et
al. (2014) present an updated oceanic pCO2 trend of
1.9 µatm yr-1 observed during the 20-year period 1993–2012,
a value supported by McKinley et al. (2011).
Inversion error
Our conversion of fCO2,is to
pCO2(Teq) could introduce an error if the data was not
based on xCO2 analysis (cruise flags not A or B), but on
fCO2 calculated from a spectrophotometer (very few cruises;
Bakker et al., 2014), or if the investigator only provided
fCO2,is or pCO2,is and did not use
Eq. (A1) to correct for the temperature difference. This error was assessed
by calculating the conversion from fCO2,is to
fCO2,ym,i (Eq. 6) using SST and Peq instead
of Tym and Peq, ym (expressed as
fCO2,ym,i=is). This conversion would ideally produce the original
SOCAT fCO2,is value. A difference betweenfCO2,is and fCO2,ym,i=is implied that our re-computation
differed from the one applied by SOCAT or the investigator and we called this
difference averaged over one grid box “inversion error”. Note that the
error was the same for the measurement year as for the year 2010. This
resultant calculated error was a small positive bias between 0 and
4 µatm; mostly near zero in the North Atlantic and several other
areas, but with some higher levels in the Southern Ocean. The monthly mean
inversion bias over all grid points was 1.0 ± 0.2 µatm
(average over all monthly means ± standard deviation).
Absent values in our full fCO2 re-computation
A problem related to the inversion error was introduced by absent data in our
full fCO2 re-computation (Sect. 3.3). By absent values we mean
instances where in situ fCO2 exist in the SOCAT data, but the
related instantaneous variables were not measured, or not reported. The
impact of these absent values did not always propagate into an inversion
error because we made an effort to handle these absent values following SOCAT
(Pfeil et al., 2014). For instance, if the in situ salinity or pressure data
were not submitted to SOCAT, SOCAT used values from the respectively the
World Ocean Atlas 2005 and NCEP for their conversion method. We note that
absent values of temperature and pressure at the equilibrator could introduce
systematic errors. Over all months and all years the percentages of these
absent values were salinity 14 %, Teq 17 %, P 37 %,
and Peq 41 %. The fCO2,ym,i
calculations were most sensitive to temperature. If Teq was not
provided, we used in situ SST. In that case, the inversion error would be
near zero but could lead to significant systematic
fCO2,ym,i errors. We therefore also reproduced our
fCO2,cl distribution maps using only data points with valid
Teq values (not shown). These maps appeared to reveal fewer high
fCO2,cl outliers. If only data with valid Teq
were selected the data quality was believed to be better, but the number of
data points was compromised. Standard deviations calculated with the reduced
data set were higher or lower than the standard values, depending on location
and month. The monthly mean difference fCO2,cl(all) –
fCO2,cl (valid Teq) ranged between
-3.3 µatm (November) and 3.7 µatm (January) and was
-0.4 µatm on average over all months. This result illustrates
again that both the data sparsity and occasional missing equilibrator
temperature data significantly affect the quality of our final
fCO2 climatology.
Measurement errors
Errors in the SOCAT measurements (fCO2,is, Teq,
Peq and SST) naturally propagated into
fCO2,cl uncertainty. The total of n independent errors
±Δx1, ±Δx2,…±Δxn is estimated by
(x1)2+(x2)2+…+(xn)2. The accuracies for
the SOCAT measurements that comply with the Standard Operating Procedures,
SOP, criteria (Dickson et al., 2007; Pierrot et al., 2009) are given by Pfeil
et al. (2013); these accuracies were the highest that could be expected as
not all SOCAT data are of this high standard. Data sets with flags of C and D
(59 % in version 1; Bakker et al., 2014) do not meet SOP criteria. (In
case of a flag of D the data may meet SOP criteria, but the metadata are
incomplete). Likewise, the uncertainty in Tym,i had to be taken
into account. Our NetCDF data give the SD values and counts (number of sea
surface temperature pixels) with the mean SSTskin values from ARC
on a 1∘ × 1∘ grid. The average standard error,
(SD/count), over all monthly grid boxes that had
fCO2 values (all years and months) was ±0.17 K. The
uncertainty in the SST difference with subskin SST is ±0.1 K (Donlon et
al., 1999). The total uncertainty in Tym, i was therefore
estimated to be ±0.2 K ((0.172+0.12)). We estimated the
propagation of these errors by applying the error for each parameter, x,
and recalculating fCO2,cl. (We calculated
fCO2,cl for the upper limit, x+Δx, and lower
limit, x–Δx, and calculated the mean of the half of the resulting
fCO2,cl difference, ΔfCO2,cl=mean{(fCO2,cl(x+Δx)-fCO2,cl(x-Δx))/2}. The results are
listed in Table 4. The total error caused by known uncertainties in the
parameters was estimated to be > 3.7 µatm
(0.752+0.0152+22+32).
Summary of errors
The standard deviations produced by the kriging method (Sect. 5.2) are a
function of both spatial variation of the data points and random errors in
the fCO2,cl values. The errors caused by the uncertainty
of the rate of pCO2 change (temporal extrapolation error) and
measurement errors are such random fCO2,cl errors but the
magnitude of their propagation in the kriging procedure is difficult to
calculate. Their monthly averages were estimated at ±3.0 µatm
(Sect. 5.5) and ±3.7 µatm (Sect. 5.8) respectively and their
total 4.8 µatm (3.02+3.72). Note that an error of
4.8 µatm is smaller than the average monthly minimum SD of the
prediction of 6.3 ± 2.6 µatm (Sect. 5.2). The above analysis
shows that the SD of the prediction (termed error) was dominated by the
spatial variation of the data, an issue that is closely linked to data
density (or sparsity). If we use the standard deviation of the kriging as an
estimate of the prediction error, the prediction error of
fCO2,cl in a single grid cell ranged between ∼ 6
and ∼ 50 µatm and was ∼ 20 µatm average.
As Fig. 8 but using SOCAT version 2 data.
We estimated a bias of ∼ 1 µatm, introduced by the inversion
step in the fCO2,is to fCO2,ym,i
conversion (Sect. 5.6). The mean fCO2,cl over all months
had a bias of -0.4 µatm due to absent SOCAT values (Salinity,
Teq, P and Peq) in the re-computation (Sect. 5.7), so
for the total bias of an annual average fCO2,cl we
estimate a value of ∼ 0.6 µatm. This is less than the
systematic bias in the global mean mean surface water pCO2 of
about 1.3 µatm as estimated by Takahashi et al. (2009) due to under
sampling and their interpolation. The total bias in
fCO2,cl was dominated by the propagation of the
uncertainty in the pCO2,cl trend of
±3 µatm. Notice that the errors could be larger or smaller for
individual months or regions. The difference between
fCO2,ym,i and fCO2,is averaged over
all years and grid boxes is relatively small (-1.21 µatm)
compared to the uncertainty and biases in thefCO2,cl
estimations, and the consequence of our fCO2 correction may not
be large for calculation of the global mean climatological value of
fCO2. However, the standard deviation of the mean difference,
±9.36 µatm, is not small and there are areas and periods where
the bias is significant, especially when the sample density is high. The
analysis of SST differences in Sect. 1.4 suggests that the original in situ
temperatures, and therefore in situ fCO2 values, are biased and
that bias strongly varies spatially and seasonally. For regional and seasonal
studies our conversion could therefore be much more relevant.
Error estimations of the parameters involved in the
fCO2,cl computation and their consequent errors ΔfCO2,cl (µatm).
Parameter x
Unit
Error
ΔfCO2,cl
ΔSST
∘C
±0.05*
±0.75
ΔTeq
∘C
±0.05*
±0.015
ΔPeq
hPa
±0.5*
∼ 0
ΔfCO2,is
µatm
±2*
±2
ΔTym,i
K or ∘C
±0.2
±3
* For SOP data (Pfeil et al., 2013).
In summary, it is clear that prediction errors are generally dominated by
the effects of sparse sampling for most regions and seasons. Note that value
of standard deviation in Fig. A4 varies from 5 to 57 µatm.
Some of the prediction errors exceed 25 µatm and it is doubtful if the
product is useful in those regions and seasons. Note that while other
methods do not have such large explicit errors, it is possible that their
true error is similar or greater, but that the error is obscured by a false
assumption. Our method has the advantage that the problem with sparse
sampling is explicit. The only reliable solution is better sampling and it
is worth noting that the inclusion of new data in SOCAT v2 yields definite
improvements (see next section). The most significant of the other sources
of random errors are apparent from Table 4. The propagation of errors within
the computation of fCO2,cl prior to temporal extrapolation and kriging,
is described in Sect. 5.8 and based on measurement errors estimated in
Table 4. Note that the errors in fCO2,is and Tym,i are the most
significant. The total random error in each calculation of fCO2,cl is
estimated at > ∼ 3.7 µatm in Sect. 5.8. That
error will contribute significantly to the prediction error in some of the
better sampled regions. The systematic bias in measurements is relatively
low and will result in only a small systematic global bias in fCO2,cl
(< ∼ 1 µatm). However, the assumed oceanic
pCO2 trend may be a greater source of systematic bias (perhaps 3 µatm), but that bias is difficult to put a firm value on without further
study.
Conclusions
We have combined SOCAT in situ data sets with a climate-quality SST data set
(ARC) to produce consistent sets of SST and CO2 parameters suitable for
climate change research of air–sea gas exchange. The fCO2 (and
pCO2) predictions and standard deviations are computed for the
year 2010 and interpolated to a global 1∘ × 1∘ grid,
and have been made available together with other climatological data
necessary to calculate global oceanic CO2 fluxes. Two climatology data
sets are presented as an online supplement to this paper, each consisting of
12 monthly NetCDF files: one using all SOCAT v1.5 data and one using
all data of the recent update SOCAT v2. We identified and calculated
various possible errors. The random errors due to the spatial interpolation,
closely related to data density, dominated, but all errors vary spatially.
The data quality/density in the North Atlantic and North Pacific proved to be
superior, and thus these regions have the lowest
prediction errors (∼ 6 µatm in the best sampled areas). The
products have been verified by checking that key and established features
such as the seasonal amplitude in the North Atlantic and North Pacific are
similar to those reported in other studies. Other regions show much larger
prediction errors (often exceeding 25 µatm), highlighting the issue
of insufficient sampling. Other interpolation methods may yield nominally
lower prediction errors, but that may only obscure the issue of sparse
sampling. If we use the standard deviation of the kriging to calculate the
prediction error, the prediction error of fCO2,cl in a
single grid cell ranged between ∼ 6 and ∼ 50 µatm and
was ∼ 20 µatm on average.
Our products are referenced to a particular year (2010), but can be
corrected to a reasonable estimate for another year by reapplying the
assumed trend in oceanic pCO2 (1.5 µatm yr-1). The necessity
of using multi-year in situ oceanic CO2 data to supply adequate data
for global calculations is invidious; it would be preferable to make genuine
single-year calculations. The bias uncertainty in fCO2,cl was
dominated by the assumed value of the oceanic pCO2 trend, which might
introduce a systematic global bias of about ±3 µatm into the
2010 products.
Our data set based on SOCAT version 2 is very similar to that derived from
SOCAT version 1.5. However, we recommend that users exploit the version that
is based on SOCAT version 2, as it is derived from a larger in situ data set
and higher quality data. SOCAT asks all data providers to include
Teq in their data submission. The absence of equilibrator
temperatures from some data sets submitted to SOCAT is unfortunate. It would
benefit climatological applications if the equilibrator temperature and
fCO2 at the equilibrator temperature was always included in
future versions of SOCAT, negating the need for the inversion step described
in this paper. Conversion between the temperature of sea water in the
equilibrator and a monthly composite temperature from a global, long-term,
homogenous, highly stable SST data set such as ARC (Eqs. 5 and 6) could also
be included as an additional parameter to provide another standard product in
parallel with the direct in situ products.