Introduction
Inland waters (streams, rivers, lakes, reservoirs, wetlands) receive carbon
from terrestrial landscapes, usually have a net heterotrophic metabolism, and
emit significant amounts of CO2 to the atmosphere (Kempe 1984; Cole et
al., 1994; Raymond et al., 2013). This terrestrial–aquatic–atmosphere link in
the global carbon cycle is controlled by complex biogeographical drivers that
generate strong spatial and temporal variations in the chemical composition
of freshwaters and the intensity of CO2 outgassing at the water–air
interface (e.g. Tamooh et al., 2013; Dinsmore et al., 2013; Abril et al.,
2014; Borges et al., 2014). Hence, large data sets are necessary in order to
describe the environmental factors controlling these CO2 emissions and
to quantify global CO2 fluxes from inland waters (Sobek et al., 2005;
Barros et al., 2011; Raymond et al., 2013). Dissolved inorganic carbon (DIC)
concentration and speciation in freshwaters greatly depend on the
lithological nature of watersheds (Meybeck 1987). For instance, rivers
draining watersheds rich in carbonate rocks have a high DIC concentration,
generally well above 1000 µmol L-1. Bicarbonate ions
contribute to most of the total alkalinity (TA) in these
waters, which have high conductivities and high pH. In these hard waters,
dissolved CO2 represents a minor fraction (5–15 %) of the DIC
compared to bicarbonates. In rivers draining organic-rich soils and
non-carbonate rocks, DIC concentrations are lower (typically a few
hundred µmol L-1) but dissolved organic carbon (DOC)
concentrations are higher, and commonly exceed the DIC concentrations.
Organic acid anions significantly contribute to TA of these soft
waters (Driscoll et al., 1989; Hemond 1990), which have low conductivities
and low pH. Dissolved CO2 represents a large, generally dominant,
fraction of DIC in these acidic, organic-rich waters.
Fluxes of CO2 between aquatic systems and the atmosphere can be computed
from the water–air gradient of the concentration of CO2 and the gas
transfer velocity (Liss and Slater, 1974) at local (e.g. Raymond et al.,
1997), regional (e.g. Teodoru et al., 2009), and global scales (e.g. Cole et
al., 1994; Raymond et al., 2013). The partial pressure of CO2
(pCO2) is relatively constant in the atmosphere compared to surface
freshwaters pCO2 that can vary by more than 4 orders of magnitude
spatially and temporally (Sobek et al., 2005; Abril et al., 2014).
Consequently, water pCO2 controls the intensity of the air–water flux,
together with the gas transfer velocity. At present, both measured and
calculated water pCO2 data are used to compute CO2 fluxes from
freshwater systems, although calculated pCO2 is overwhelmingly more
abundant than directly measured pCO2 (e.g. Cole et al., 1994; Raymond
et al., 2013). pCO2 can be calculated from the dissociation constants
of carbonic acid (which are a function of temperature) and any of the
following couples of measured variables: pH/TA, pH/DIC,
DIC/TA (Park, 1969). In a majority of cases, calculated
pCO2 is based on the measurements of pH/TA and water
temperature. These three parameters are routinely measured by many
environmental agencies, and constitute a very large database available for
the scientific community. Calculation of pCO2 from pH and
TA was initiated in world rivers in the 1970s (Kempe, 1984)
and relies on the dissociation constants of carbonic acid, and the solubility
of CO2, all of which are temperature-dependent (Harned and Scholes,
1941; Harned and Davis, 1943; Millero, 1979; Stumm and Morgan, 1996).
Measured pCO2 is based on water–air phase equilibration either on
discrete samples (headspace technique, e.g. Weiss, 1981) or continuously
(equilibrator technique, e.g. Frankignoulle et al., 2001) using various
systems and devices, followed by direct, generally infrared (IR), detection
of CO2 in the equilibrated gas. Commercial IR gas analysers are becoming
cheaper and more accurate, stable and compact, and provide a large range of
linear response well adapted to variability of pCO2 found in
freshwaters.
A limited number of studies have compared directly measured pCO2
to computed pCO2. Earlier examples provided a comparison between
pCO2 measured by headspace equilibration coupled to gas chromatography
(GC) and pCO2 calculated from pH and DIC (Kratz et al., 1997; Raymond
et al., 1997). Reports by these authors in Wisconsin lakes and the Hudson
River show that the pCO2 values were linearly correlated but showed a
variability of ±500 ppmv around the 1 : 1 line, over a range of measured
pCO2 from 300 to 4000 ppmv. Later, Frankignoulle and Borges (2001)
reported the first comparison of pCO2 calculated from pH and
TA and pCO2 measured by equilibration coupled to an IR
analyser in an estuary in Belgium. In this high TA
(2500–4800 µmol L-1) and high pH (> 7.4) system, they
found a good agreement between the two approaches, calculated pCO2 being
either overestimated or underestimated, but always by less than 7 %. In
2003, concomitant measurements of pH, TA and pCO2 were
performed in acidic, humic-rich (“black” type) waters of the Sinnamary
River in French Guiana (Abril et al., 2005, 2006). Calculation of pCO2
from pH (∼ 5) and TA (∼ 200 µmol L-1)
gave unrealistically high values compared to those measured directly with a
headspace technique (typically 30000 ppmv vs. 5000 ppmv). Direct
measurements of CO2 and CH4 outgassing fluxes with floating
chambers and the computation of the respective gas transfer velocities of
these two gases (Guérin et al., 2007) confirmed that pCO2 values
calculated from pH and TA were overestimated compared to direct
measurements in the Sinnamary River. More recently, Hunt et al. (2011) and
Wang et al. (2013) provided evidence that organic acid anions in DOC may
significantly contribute to TA in some rivers and generate an
overestimation of calculated pCO2. Butman and Raymond (2011) reported
higher calculated than measured pCO2 in some US streams and rivers,
but no information was available on the potential role of organic acids in
this overestimation. These authors concluded that the low number of samples
in their study reflected the need for more research on this topic.
Summary of the presented data set. Average, minimum, and maximum
values of temperature, DOC, pH (measured on the
NBS scale), total alkalinity (TA), and measured partial pressure
of CO2 (pCO2) in the different freshwater ecosystems.
Country
Watersheds
Temperature
DOC
pH
TA
Measured pCO2
N
(∘C)
(µmol L-1)
(NBS scale)
(µmol L-1)
(ppmv)
Av.
Min.
Max.
Av.
Min.
Max.
Av.
Min.
Max.
Av.
Min.
Max.
Av.
Min.
Max.
Brazil
Amazon
30.3
27.4
34.3
352
118
633
6.60
4.53
7.60
385
30
1092
4204
36
18400
155
Kenya
Athi-Galana-Sabaki
25.9
19.8
36.0
307
29
1133
7.69
6.49
8.57
2290
407
5042
2811
608
10 405
44
DRC
Congo
26.3
22.6
28.2
1002
149
3968
6.01
3.94
7.22
212
0
576
6093
1582
15 571
97
DRC/Rwanda
Lake Kivu
24.0
23.0
24.7
162
142
201
9.05
8.99
9.17
13 037
12 802
13 338
660
537
772
53
France
Leyre
12.5
7.9
19.2
588
142
3625
6.20
4.40
7.41
280
38
1082
4429
901
23 047
92
France
Loire
15.5
8.8
19.3
195
167
233
8.70
8.07
9.14
1768
1579
1886
284
65
717
18
Belgium
Meuse
18.1
13.3
25.9
229
102
404
7.89
6.95
8.59
2769
360
7141
2292
176
10 033
50
Madagascar
Rianila and Betsiboka
25.4
20.2
29.5
138
33
361
6.84
5.83
7.62
233
76
961
1701
508
3847
36
Kenya
Shimba Hills
25.1
21.9
31.8
214
36
548
7.37
6.22
8.93
1989
227
14 244
2751
546
9497
9
French Guiana
Sinnamary
27.1
24.1
28.7
419
213
596
5.50
5.08
6.30
143
66
290
7770
1358
15 622
49
Kenya
Tana
26.6
25.0
27.9
321
193
651
7.65
7.32
8.02
1619
1338
2009
2700
845
6014
51
Zambia/Mozambique
Zambezi
26.9
18.8
31.8
252
103
492
7.59
5.06
9.08
1245
52
3134
2695
151
14 004
107
Entire data set
24.6
7.9
36.0
408
29
3968
7.00
3.94
9.17
1731
0
14 244
3707
36
23 047
761
With the growing interest on pCO2 determination in freshwaters
globally, and given the apparent simplicity and low cost of pH and
TA measurements, the number of publications that report
calculated pCO2 in freshwaters has increased dramatically in the past
decade. Some of these publications report extremely high and potentially
biased pCO2 values in low-alkalinity and high-DOC systems. It has thus
become necessary to pay attention to this issue and investigate the
occurrence of such potential bias and its magnitude in the different types of
freshwaters. Here, we present a large data set of concomitant measurements of
temperature, pH, TA, pCO2, and DOC in freshwaters. This is
the first comprehensive data set to investigate the magnitude of the bias
between calculated and measured pCO2, as it covers the entire range of
variation of most parameters of the carbonate system in freshwaters. The
objective of this paper is to alert the scientific community to the
occurrence of a bias in pCO2 calculation from pH and TA in
acidic, poorly buffered and organic-rich freshwaters, to briefly discuss its
origin in terms of water chemistry, and to provide the range of pH,
TA, and DOC values where pCO2 calculation should be
abandoned and the range where it still gives relatively accurate results.
Material and methods
Sample collection
Our data set consists of 761 concomitant measurements of temperature, pH,
TA, water pCO2, and DOC in 12 contrasting tropical and
temperate systems in Europe, Amazonia, and Africa (Fig. 1; Table 1). These
samples were obtained in the Central Amazon River and floodplains system in
Brazil, the Athi-Galana-Sabaki River in Kenya, the Tana River (Kenya), small
rivers draining the Shimba Hills in southeastern Kenya, the Congo River and
tributaries in the Democratic Republic of the Congo (DRC), Lake Kivu in
Rwanda and DRC, the Leyre River and tributaries in France, the Loire River in
France, the Meuse River in Belgium, the Rianila and Betsiboka rivers in
Madagascar, the Sinnamary River downstream of the Petit Saut Reservoir in
French Guiana, and the Zambezi River in Zambia and Mozambique (Fig. 1).
Details on some of the sampling sites can be found in Abril et al. (2005,
2014), Borges et al. (2012, 2014), Marwick et al. (2014a, b), Polsenaere et
al. (2013), Tamooh et al. (2013), Teodoru et al. (2014). These watersheds
span a range of climates and are occupied by different types of land cover,
which include tropical rainforest (Amazon, Congo, Rianila), dry savannah
(Tana, Athi-Galana-Sabaki, Betsiboka, Zambezi), temperate pine forest growing
on podzols (Leyre), mixed temperate forest, grassland, and cropland (Meuse),
and cropland (Loire). Lithology is also extremely contrasted as it includes
for instance carbonate-rocks-dominated watershed as for the Meuse, sandstone-dominated silicates (Leyre), and precambrian crystalline magmatic and
metamorphic rocks with a small proportion of carbonate and evaporite rocks
for the Congo river.
Location of the sampling sites in Africa, Amazonia, and Europe.
Field and laboratory measurements
Although pH measurements might seem almost trivial, highly accurate and
precise pH data are in fact not easy to obtain, especially in low-ionic
strength waters, where electrode readings are generally less stable. Even
though pH measurements in the laboratory might be more accurate, it is
crucial to measure pH in situ or immediately after sampling, as pH
determination several hours or days after sampling will be affected by
CO2 degassing and/or microbial respiration (Frankignoulle and Borges,
2001). In this work, water temperature and pH were measured in the field with
different probes depending on the origin of the data set. However, all the pH
data were obtained with glass electrodes and rely on daily calibration with
two-point United States National Bureau of Standards (NBS) standards (4 and
7). Measurements were performed directly in the surface water, or in
collected water immediately after sampling.
Several techniques were used to measure water pCO2. Water–gas
equilibration was performed with a marbles-type equilibrator (Frankignoulle
et al., 2001) for the Amazon, Loire, Leyre, Sinnamary, and Congo rivers
(December 2013) as well for Lake Kivu, or with a Liqui-Cel MiniModule
membrane contactor equilibrator (see Teodoru et al., 2009, 2014) for the
Zambezi and some sites within the Congo basin (December 2012): water was
pumped either continuously from a ship, or on an ad hoc basis from the bank
of the rivers after waiting ∼ 15 min for complete equilibration; air
was continuously pumped from the equilibrator to the gas analyser (see e.g.
Abril et al., 2014 for a more detailed description of the system). A
syringe-headspace technique (Kratz et al., 1997; Teodoru et al., 2009) was
used in the field in all African rivers and in the Meuse River: 30 mL volume
of atmospheric air was equilibrated with 30 mL volume of river water by
vigorously shaking during 5–10 min in four replicate gas-tight syringes.
The four replicates 30 mL of equilibrated gas and a sample of atmospheric
air were injected in an IR gas analyser
(Li-Cor® models 820 or 840, or PP
systems® model EGM-4); the first gas
injection served as a purge for the air circuit and cell and the three other
injections were used as triplicate pCO2 determination (average
repeatability of ±1 %). The pCO2 in the river water was
deduced from that measured in the headspace accounting for the initial
pCO2 in the air used for equilibration, water temperature in the river
and in the water at equilibrium in the syringe, and based on Henry's law.
Comparison between syringe-headspace and marbles or membrane equilibrator was
made during two cruises on the Congo River and three cruises in the Zambezi
basin and gave very consistent results, deviation from the 1 : 1 line being
always less than 15 % (see Fig. 2). This highlights the consistency of
the present data set of direct pCO2 measurements although different
techniques were used. A serum bottle-headspace technique (Hope et al., 1995)
was also used on the Sinnamary River; surface water was sampled in 120 mL
serum bottles that were poisoned with HgCl2 and sealed excluding air
bubbles. Back in the laboratory, a 40 mL headspace was created with pure
N2 (Abril et al., 2005). The CO2 concentration of equilibrated gas
in the headspace was analysed by injecting small volumes (0.5 mL) of gas in
a gas chromatograph calibrated with certified gas mixtures.
Immediately after water–gas phase equilibration, CO2 was detected and
quantified in most samples with non-dispersive IR gas analysers
(Frankignoulle et al., 2001; Abril et al., 2014). The gas analysers were
calibrated before each field cruise, with air circulating through soda lime
or pure N2 for zero and with a certified gas standard for the span.
Depending on the cruises and expected pCO2 ranges, we used gas
standard concentration of 1000–2000 ppmv, or a set of calibration gases at
400, 800, 4000 and 8000 ppmv. Stability of the instrument was checked after
the cruise, and deviation of the signal was always less than 5 %. These
instruments offer a large range of linear response, depending on
manufacturer and model: 0–20 000 ppmv or 0–60 000 ppmv. The linearity
of an Li-COR® Li-820 gas analyser was verified
by connecting it to a closed circuit of gas equipped with a rubber septum to
allow injection of pure CO2 with a syringe. Linearity was checked by
injecting increasing volumes of CO2 in order to cover the whole range of
measurement and was excellent between zero and ∼ 20000 ppmv. In
addition to the IR analysers generally used in this work, in the Sinnamary
River, pCO2 was also measured with an
INNOVA® 1312 optical filter IR photoacoustic
gas analyser (range 0–25 000 ppmv) connected to an equilibrator and with a
Hewlett Packard® 5890 gas chromatograph equipped with a
thermal conductivity detector (TCD); both analysers were calibrated with a
gas mixture of 5000 ppmv of CO2. Both methods gave results consistent
at ±15 % in the 0–13 000 ppmv range (Abril et al., 2006).
Sinnamary data reported here are from headspace and GC determination.
TA was analysed by automated electro-titration on 50 mL filtered
samples with 0.1N HCl as titrant. Equivalence point was determined with a
Gran method from pH between 4 and 3 (Gran, 1952). Precision based on replicate
analyses was better than ±5 µmol L-1. TA
measurements should be done on filtered samples; otherwise some
overestimation would occur in turbid samples, which may contain significant
amounts of acid-neutralizing particles (e.g. calcium carbonate). In contrast
to TA measurements based on titration to an endpoint of 5.6 (e.g.
Wallin et al., 2014), the Gran titration method allows the determination of
TA values in samples with in situ pH down to ∼ 4.5, i.e. very
close to the dissociation constant of HCO3- / H2CO3. In
most acidic samples with low TA, reproducibility was improved by
slightly increasing the pH by up to 0.2 units by vigorously stirring during
∼ 15 min in order to degas as much CO2 as possible before
starting the titration. DOC was measured on samples filtered through
pre-combusted (490 ∘C) glass fibre filter with a porosity of
0.7 µm and stored acidified with ultrapure H3PO4 in
borosilicate vials capped with polytetrafluoroethylene stoppers. Analysis was
performed with a Shimadzu TOC5000 analyser based on high-temperature
catalytic oxidation, after removal of dissolved CO2 for samples from
Amazon, Loire, Leyre, and Sinnamary rivers. DOC concentrations were measured
with a customized wet oxidation TOC analyser (Thermo HiperTOC, or IO
Analytical Aurora 1030W) coupled to a Delta+XL or Delta V IRMS.
Comparison of results of different water–air equilibration
designs for direct pCO2 measurements; pCO2 measured with a
marbles equilibrator (Congo) and with a membrane equilibrator (Congo and
Zambezi) are plotted against pCO2 measured with a syringe headspace
technique. Detection was made with an IR gas analyser.
Plot of carbon variables vs. pH in the studied
freshwater systems. Top panels are shown with a linear scale and bottom
panels with a logarithmic scale; (a, b): measured pCO2; (c, d) total
alkalinity; (e, f) DOC. Zero TA values are
plotted as 0.001 in order to be visible on the log pCO2 scale. Rianila
and Betsiboka are plotted together although they belong to different
watersheds in Madagascar.
pCO2 calculation from pH and TA
We calculated pCO2 from TA, pH, and temperature
measurements using carbonic acid dissociation constants of Millero (1979)
(based on those of Harned and Scholes, 1941 and Harned and Davis, 1943) and
the CO2 solubility from Weiss (1974) as implemented in the CO2SYS
program. Hunt et al. (2011) reported discrepancy lower than 2 % for
pCO2 computed this way with those obtained with the PHREEQC program
(Parkhurst and Appelo, 1999). Differences in software or dissociation
constants cannot account for the large bias in calculated pCO2
compared to measured pCO2 we report in this paper.
Median and average values of DOC, pH
(measured on the NBS scale), total alkalinity (TA), and
calculated minus measured pCO2
in the data set.
N
% of
cal – meas pCO2
cal – meas pCO2
pH
TA
DOC
samples
(ppmv)
(% of meas pCO2)
(µmol L-1)
(µmol L-1)
Med.
Av.
Med.
Av.
Med.
Av.
Med.
Av.
Med.
Av.
All samples
761
100 %
+611
+10692
+23%
+194%
6.94
7.00
467
1731
315
408
Ranked by calculated – measured
pCO2 as % of measured pCO2
< -10 %
122
16 %
-540
-890
-34 %
-36 %
7.89
7.85
1269
1766
259
275
±10 %
174
23 %
+15
+50
+2%
+1%
7.67
7.78
1576
3735
228
273
> +10 %
465
61 %
+2430
+17710
+72%
+327%
6.52
6.49
308
972
360
497
> +50 %
280
37 %
+5490
+28660
+162%
+526%
6.18
6.14
192
460
375
567
> +100 %
199
26 %
+9080
+39120
+270%
+710%
5.89
5.96
166
364
389
602
Ranked by pH
pH > 7
368
48 %
+1
+82
+1%
+15%
7.82
7.92
1572
3284
231
255
pH < 7
393
52 %
+3280
+20630
+71%
+362%
6.30
6.13
232
277
413
558
pH 6–7
256
34 %
+1580
+2710
+40%
+96%
6.58
6.55
334
370
350
427
pH < 6
136
18 %
+18410
+54486
+308%
+864%
5.50
5.35
93
101
487
828
pH < 5
25
3 %
+115580
+209910
+1645%
+3180%
4.53
4.53
41
45
1427
1,843
Ranked by TA
TA > 2000 µmol L-1
110
14 %
+20
+340
+2%
+12%
8.58
8.47
7023
8326
163
202
TA 1000–2000 µmol L-1
157
21 %
-8
-163
-2 %
-9 %
7.81
7.83
1566
1534
271
295
TA 500–1000 µmol L-1
99
13 %
+1307
+1900
+28%
+72%
6.97
7.11
651
697
304
318
TA < 500 µmol L-1
395
52 %
+2070
+20090
+64%
+350%
6.30
6.24
222
232
400
538
TA < 100 µmol L-1
82
11 %
+6840
+60560
+230%
+1040%
5.50
5.35
59
56
603
988
Ranked by DOC
DOC < 200 µmol L-1
179
24 %
+40
+776
+5%
+62%
7.89
7.92
1579
4807
163
149
DOC 200–300 µmol L-1
167
22 %
+102
+2755
+5%
+69%
7.56
7.37
1132
1259
258
252
DOC 300–400 µmol L-1
165
22 %
+887
+4473
+25%
+101%
6.90
6.93
499
866
341
344
DOC > 400 µmol L-1
250
33 %
+3070
+27197
+59%
+434%
6.15
6.14
200
415
555
765
DOC > 800 µmol L-1
79
10 %
+4995
+62784
+92%
+886%
5.80
5.62
94
180
1099
1438
Discussion
Origin of overestimation of calculated pCO2
Our data set (Fig. 3; Table 1) probably covers the full range of conditions of
carbon speciation that can be encountered in continental surface waters. A
pCO2 overestimation negatively correlated with pH (p=0.001) and
TA (p=0.005) and positively correlated with DOC
(p < 0.001) (Fig. 5) is consistent with the observations of Cai et
al. (1998) in the freshwater end-members of some estuaries in Georgia, USA,
and of Hunt et al. (2011) in rivers in New England (USA) and New Brunswick
(Canada). These authors performed NaOH back-titration in order to measure
non-carbonate alkalinity (NCA). They found that NCA accounted for a large
fraction (in some cases the greater part) of TA; in addition, the
contribution of inorganic species other than carbonate was assumed negligible
and most of the NCA was attributed to organic acid anions. Hunt et al. (2011)
also showed that in the absence of direct titration of NCA, which is
labour-intensive and whose precision may be poor, this parameter could be
calculated as the difference between the measured TA and the
alkalinity calculated from measurements of pH and DIC and the dissociation
constants of carbonic acid. Using the latter approach, Wang et al. (2013)
obtained a positive correlation between NCA and DOC concentrations in the
Congo River, evidencing the predominant role of organic acids in DIC
speciation and pH in such acidic system. Because we did not directly measure
DIC in this study, we could not calculate NCA with the same procedure as
these studies. We attempted to calculate TA from our measured pH
and pCO2 with the CO2SYS program. However, TA values
calculated this way were inconsistent with other measured variables (with
sometimes negative values). Indeed, because pH and pCO2 are too
interdependent in the carbonate system, very small analytical errors on these
variables lead to large uncertainties in the calculated TA
(Cullison Gray et al., 2011). A second attempt to correct our TA
data from NCA consisted in calculating organic alkalinity using pH and DOC as
input parameters. We compared the model of Driscoll et al. (1989), which
assumes a single pK value for all organic acids, and the triprotic model of
Hruska et al. (2003), which assumes three apparent pK values for organic
acids. These two models applied to our pH and DOC gave very similar organic
alkalinity values, which could be subtracted from the measured
TA. In the most acidic samples (e.g. some sites from the Congo
basin), modelled organic alkalinities were larger than measured
TA and the difference was thus negative. Nevertheless, we then
recalculated pCO2 from the measured pH and the TA
corrected from organic alkalinity. Calculated pCO2 values corrected with that
method were, however, still very different from those measured in the field,
being sometimes higher and sometimes lower than the measured pCO2,
without any meaningful pattern (indeed, corrected pCO2 was negatively
correlated (p < 0.001) with measured pCO2). Consequently, we
were unable to derive any empirical relationship to correct for the bias in
pCO2 calculation from pH and TA. Nevertheless, the
negative correlation between pH and DOC and positive correlation between pH
and TA (Fig. 3) confirm a strong control of organic acids on pH
and DIC speciation across the entire data set.
As discussed by Hunt et al. (2011), a significant contribution of organic
acids to TA leads to an overestimation of calculated pCO2
with the CO2SYS program, or with any program that accounts only for the
inorganic species that contribute to TA. It is thus obvious that
the observed increase in pCO2 overestimation when pH decreases
(Figs. 4b and 5; Table 2) is due to an increasing contribution of organic
acid anions to TA. However, this effect is not the only driver of
the observed overestimation of pCO2, which is also due to a decrease
in the buffering capacity of the carbonate system at acidic pH. To
investigate the magnitude of this second effect, we calculated the factor
dpCO2 / dTA (in ppmv mol-1), which describes the
change in calculated pCO2 induced by a change in TA. This
factor, which is the opposite of a buffer factor as it reflects the
sensitivity of pCO2 calculation to the TA, increases
exponentially when pH decreases (Fig. 6a), i.e. it is proportional to the
H+ concentration. To go further in this theoretical analysis, we
computed the difference between the pCO2 calculated at a given
TA value and the one calculated at a slightly higher
TA value (TA+X µmol L-1). These
calculations reveal an extreme sensitivity of calculated pCO2 to
TA at acidic pH (Fig. 6b). For instance, increasing
TA by 5 µmol L-1 (a value close to the precision
of TA titrations) increases the calculated pCO2 by
31 ppmv at pH 7, by 307 ppmv at pH 6 and by 3070 at pH 5. Increasing
TA by 100 µmol L-1 (a typical value of NCA found
in freshwaters; Driscoll et al., 1994; Cai et al., 1998; Hunt et al., 2011),
increases the calculated pCO2 by 615 ppmv at pH 7, by 6156 ppmv at
pH 6 and by 61560 ppmv at pH 5. Note that this increase in calculated
pCO2 is independent of the chosen initial TA value. The
difference between calculated and measured pCO2 from our data set
shows that an NCA contribution around 100 µmol L-1 is
sufficient to explain the overestimation of calculated pCO2 of most
samples at pH< 6, whereas an NCA contribution higher than
500 µmol L-1 would be necessary for several samples at
circumneutral and slightly basic pH (Fig. 5b). Samples requiring this high
NCA contribution are from the Athi-Galana-Sabaki and Zambezi watersheds, and
correspond to TA values well above 1000 µmol L-1.
An NCA value of 500 µmol L-1 in these samples is thus
plausible.
We have no definitive explanation for lower calculated than measured
pCO2, which is observed mainly at neutral to slightly basic pH, for example
in the Zambezi River (Fig. 4). In most of these samples, owing to the
relatively high TA value, an overestimation of pH of less than
0.2 units is sufficient to account for the low calculated pCO2
compared to measured values. In general, it is not easy to judge the accuracy
of pH measurements, especially when data come from environmental
agencies. Thus, one factor of variability throughout the data set as well as
in literature data is the accuracy of pH measurements – despite the care
taken (e.g. calibrations with NBS buffers for each day of measurements), we
cannot rule out that drift or malfunction of pH electrodes contributes to the
observed variability, constituting an additional disadvantage compared to
direct pCO2 measurements with very stable gas analysers.
Impact on estimates of CO2 emissions from freshwaters
According to our analysis, overestimation of calculated pCO2 is
largest in acidic, poorly buffered and organic-rich waters. Consequently, the
overestimation of regional and global CO2 emissions computed from
calculated pCO2 depends on the relative contribution of these types of
waters worldwide. In their analysis, Raymond et al. (2013) have discarded all
calculated pCO2 values with a pH value of less than 5.4, as well as
all pCO2 values above 100 000 ppmv. These criteria would exclude
only 8 % of samples from our data set. Indeed, from our analysis, it
appears that overestimation of calculated pCO2 occurs at pH much
higher than 5.4 (Figs. 4, 5 and 6; Table 2). The two techniques were consistent at
±10 % on average in only 5 of the 12 studied systems, which
combine a circumneutral to basic pH with a TA concentration well
above 1000 µmol L-1 (Fig. 5). Although it would not be
sufficient for the cases of the Zambezi and Athi-Galana-Sabaki rivers, where
overestimation is still significant, a TA value above
1000 µmol L-1 appears as a more robust criterion than
a pH threshold to separate calculated pCO2 values affected by bias from
those consistent with measured pCO2 (Table 2). In fact, pCO2
calculation from pH and TA in freshwaters historically relies on
theoretical background and validation data in high-alkalinity waters (Neal et
al., 1998), including karstic waters (Kempe, 1975). At the global scale, high
TA typically occurs in rivers draining watersheds with a
significant proportion of carbonate rocks, typically > 30 % of their
surface area if the criterion of
TA > 1000 µmol L-1 is chosen and the
normalized weathering rates of Meybeck (1987) are applied. According to
Meybeck (1987), the average and discharge-weighted TA is around
900 µmol L-1 for world rivers and around
600 µmol L-1 for tropical rivers. Among the 25 largest rivers
in the world, 15 have a TA > 1000 µmol L-1
according to Cai et al. (2008). The two largest rivers in the world in terms
of discharge, the Amazon and the Congo, are also well below this limit of
1000 µmol L-1 and have large overestimation in calculated
pCO2 (on average 200 and 360 %, respectively). Very low
TA and pH and high DOC values have also been reported in boreal
streams and rivers (Humborg et al., 2010; Dinsmore et al., 2012; Wallin et
al., 2014).
In lakes, the highest pCO2 values in the literature come from tropical
black water lakes and were also calculated rather than directly measured
(Sobek et al., 2005). Calculated pCO2 was 65 250 ppmv in Lago Tupé
in the Brazilian Amazon, a Ria lake connected to the Rio Negro, where,
according to our own data set, pH is below 5 and TA is around
70 µmol L-1. It was 18 950 ppmv in Kambanain Lake in Papua
New Guinea, corresponding to a pH value of 6.1 and a TA value of
350 µmol L-1 (Vyverman, 1994). This suggests a widespread
overestimation of calculated pCO2 that significantly impacts the
estimation of global CO2 emissions from inland waters. However, a
precise analysis based on exact quantitative information on the relative
contribution of acidic and high- and low-alkalinity waters to the total
surface area of inland waters is necessary in order to evaluate the exact
magnitude of the overestimation.
Conclusions
From our analysis, it appears that the validity of calculating pCO2
from pH, TA and temperature is most robust in freshwaters with
circumneutral to basic pH and with TA exceeding
1000 µmol L-1. At lower TA and pH, however,
calculated pCO2 (and hence, CO2 degassing rates) are
overestimated by 50 to 300 % relative to direct, in situ pCO2
measurements. Since a large majority of freshwater systems globally have
characteristics outside the range of applicability of pCO2
calculation, it appears reasonable to assume that recent estimates of global
CO2 emission from lakes and rivers, which are based exclusively on
calculated pCO2 data, are too high. We propose that while
TA and pH measurements remain useful to describe the aquatic
chemistry, data on pCO2 should in the future rely on direct
measurements of pCO2. Even if some studies report relatively robust
calculation of pCO2 from pH and DIC measurements (Raymond et al.,
1997; Kratz et al., 1997; Aberg and Wallin, 2014), direct pCO2 values in the
field are stable, precise and straightforward and do not depend on the
quality of pH measurements, which are often uncertain. Further, high-quality
DIC measurements are very time-consuming, fairly complicated to set up and do
not allow continuous measurements to be carried out in a simple and
straightforward fashion. Although there are some practical limitations to
their use in the field, submerged IR sensors, which allow high temporal
resolution, are also promising (Johnson et al., 2010). Long-term
instrument stability and accuracy based on newly developed off-axis
integrated cavity output spectroscopy and cavity ring-down spectroscopy
technologies seem to improve in comparison to traditional IR instruments,
although the latter are more affordable, more compact and have lower power
requirements. Joint international efforts are necessary to define the most
appropriate protocols for the measurement of DIC
parameters in freshwaters.