Technical note : CO 2 is not like CH 4 – limits of and corrections to the 3 headspace method to analyse pCO 2 in water

Headspace analysis of CO2 frequently has been used to quantify the concentration of CO2 in freshwater. According 18 to basic chemical theory, not considering chemical equilibration of the carbonate system in the sample vials will result in a 19 systematic error. In this paper we provide a method to quantify the potential error resulting from simple application of Henry ́s 20 law to headspace CO2 samples. By analysing the potential error for different types of water and experimental conditions we 21 conclude that the error incurred by headspace analysis of CO2 is less than 5% for samples with pH <7.5. However, the simple 22 headspace calculations can lead to high error (up to -800%) or even impossible negative values in highly undersaturated 23 samples equilibrated with ambient air, unless the shift in carbonate equilibrium is explicitly considered. The precision of the 24 method can be improved by lowering the headspace ratio and/or the equilibration temperature and use of a CO2 free gas for 25 headspace creation. We provide a direct method to correct CO2 headspace results using separately measured alkalinity. 26 https://doi.org/10.5194/bg-2020-307 Preprint. Discussion started: 2 September 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction 27
The analysis of dissolved CO2 in water is an important basis for the assessment of the role of surface waters in the global 28 carbon cycle (Raymond et al., 2013). Indirect methods like calculating CO2 from other alkalinity and pH (Lewis and Wallace,29 1998; Robbins et al., 2010) are affected by considerable random and systematic errors (Golub et al., 2017) caused e.g. by 30 dissolved organic carbon which may result in significant over estimation of the CO2 partial pressure (pCO2) (Abril et al., 31 2015). Thus, direct measurement of CO2 is highly recommended, particularly in softwaters. 32 Headspace analysis is a standard method to analyse the concentration of dissolved gasses in liquids (Kampbell et al., 1989). In 33 principle, a liquid sample is equilibrated with a gaseous headspace in a closed vessel under defined temperature. The partial 34 pressure of the gas in the headspace is analysed, in most cases either by gas chromatography or infra-red spectroscopy. The 35 concentration of the dissolved gas in solution is then calculated by applying Henry´s law after correction for the amount of gas 36 transferred from the solution to the headspace. 37 In freshwater research this is the widely applied standard method to analyse the concentration of the greenhouse gases such as 38 CH4 and N2O (UNESCO/IHA, 2010). The method is handy, does not depend on sophisticated equipment in the field, and 39 provides reliable results. Surprisingly, papers and protocols have been published which use this method also to analyse 40 dissolved CO2 concentrations in freshwaters (UNESCO/IHA, 2010;Cawley, 2018; Lambert and Fréchette, 2005). However 41 CO2 cannot be treated like CH4 because CO2 is in dynamic chemical equilibrium with other carbonate species in water while 42 CH4 is not (Stumm and Morgan, 1981;Sander, 1999). Depending on the CO2 concentration and pH, reactions of the carbonate 43 equilibrium will either produce or consume some CO2 in the sample vessel (Cole and Prairie systematic error when applying simple headspace analysis on CO2 on typical freshwaters is missing. The underlying 47 assumption is that "the effect is likely small" (Hope et al., 1995). In this paper we aim to quantify the error associated with the 48 simple application of Henry´s law on headspace CO2 data, present practical guidelines describing conditions under which the 49 simple headspace analysis of CO2 can give acceptable results, and offer a tool for exact CO2 calculation using a complete 50 headspace method that accounts for the carbonate equilibrium in the sample vessel, which can also be used for correcting 51 results obtained by simple headspace analysis of CO2 using additional information regarding the carbonate system (i.e. 52 alkalinity or DIC). Lastly, we tested the proposed correction procedure to a set of field measurements where pCO2 was 53 determined with independent methods (with and without headspace equilibration). 54 https://doi.org/10.5194/bg-2020-307 Preprint. Discussion started: 2 September 2020 c Author(s) 2020. CC BY 4.0 License.

Theoretical considerations 56
If a water sample is equilibrated with a headspace containing a given pCO2 (zero in case N2 or other CO2-free gas is used), 57 some CO2 is exchanged between water and headspace resulting in an altered dissolve inorganic carbon (DIC) concentration in 58 the water of the sample thereby altering the equilibrium of the carbonate system in the water. Depending on partial pressures 59 of CO2 in the water relative to the headspace gas prior to equilibration, some CO2 will either be produced from HCO3or 60 converted to HCO3 -. The exact amount will depend on temperature, pH, alkalinity, and the original pCO2 of the water sample. 61 If an N2 headspace was applied, the vessel will finally contain more CO2 than before equilibration and consequently simply 62 applying Henry´s law results in a too high pCO2 value. If an air headspace is applied, the error becomes negative in under-63 saturated samples. 64 To calculate this error we implemented an R-script that simulates the above mentioned physical and chemical equilibration for 65 a wide range of hypothetical pCO2, alkalinity, temperature, and headspace ratio (HR = Vgas / Vliquid) values. As output, we then 66 compared the corrected (for the chemical equilibrium shift) and non-corrected pCO2 values. 67

Field data 68
We routinely sampled water in 4 German reservoirs and 11 Canadian lakes exhibiting a wide range of total alkalinity (TA) 69 between 0.2 and 2.4 meq L -1 . Two techniques were used to measure water pCO2 in each sampling site: in situ NDIR technique 70 and headspace equilibration technique. First, for the in situ NDIR technique, the water is pumped through the lumen side of a 71 membrane contactor (mini module, Membrana, U.S.A.) (Cole and Prairie, 2009) and the gas side is connected to a NDIR 72 analyser (EGM4, PP-Systems, U.S.A. or LGR ultra-portable gas analyser) in a counter-flow recirculating loop. Readings were 73 taken when the CO2 [ppmv] values of the NDIR analyser became stable (usually less than a minute) at which point the gas 74 loop is in direct equilibrium with the sampled water. Final pCO2 of the water was calculated by multiplying the CO2 mixing 75 ratio by the ambient atmospheric pressure. Second, for the headspace technique, the water samples were taken in 60 mL 76 syringes. In the German reservoirs, about 40 mL of water sample were taken and eventually occurring bubbles were pushed 77 out by adjusting the sample volume to 30 mL. Samples were stored at 4° C and analysed within 1 day. In the laboratory, 30 78 mL of pure N2 gas was added to the syringes after the samples had reached laboratory temperature and the syringes were 79 shaken for one hour at laboratory temperature. After headspace equilibration water was discarded from the syringes and the 80 headspace was manually injected into a gas chromatograph equipped with a flame ionization detector (FID) and a methanizer 81 The difference between the two methods was divided by the pCO2 measured by the in situ NDIR analysis and expressed as % 92 error. In addition, temperature and pH of the water were measured in situ by a CTD probe (Sea and Sun, Germany) or a portable 93 pH meter (pH meter 913, Metrohm Ltd, Canada). In 12 samples from Canadian lakes, total alkalinity (TA) was analysed by 94 titration with 0.11N HCl. 95

Simulations from chemical equilibrium 97
Applying a CO2-free gas as headspace always resulted in a positive error (over-estimation of the real pCO2, Figure 1a). If air 98 is applied as headspace the error becomes negative in case of under saturated samples (Figure 1b). The error tends to be lower 99 if ambient air is used for headspace equilibration (Figure 1b) compared to equilibration with CO2-free gas (Figure 1a). This is 100 because less CO2 is exchanged between water and headspace during the equilibration procedure. The error will be quite low 101 in high CO2, low alkalinity samples which are typical for boreal regions. However, the error can be higher than 100% if the 102 samples are under saturated. The magnitude of the error is predictable from pH. Because of the carbonate equilibrium reactions, 103 high pH is necessarily accompanied by low pCO2 for a given alkalinity. Consequently, the error is large at high pH while it is 104 below 10 % at pH < 8 (headspace ratio 1:1). 105 Our field dataset is consistent with the theoretical predictions. The fit between both methods is rather good (Figure 2a air was applied as headspace (Figure 2b). 112

Error magnitude depends on the experimental procedure 113
The maximum error (errormax) depends on how much gas is exchanged between water and headspace. The more gas is 114 exchanged between water and headspace the higher the error is. Thus, the error increases with decreasing solubility coefficient 115 https://doi.org/10.5194/bg-2020-307 Preprint. Discussion started: 2 September 2020 c Author(s) 2020. CC BY 4.0 License. or HR. In high alkalinity samples, the error can be significantly reduced by using a larger headspace to water ratio (Figure 3). 116 By raising the headspace ratio from 1 to 5 at 20° the error can be reduced from about 50% to about 10%. 117 Since solubility of CO2 depends on temperature, the equilibration temperature also affects headspace equilibration. Due to 118 lower solubility at higher temperature, more gas evades into the headspace and thus, the error increases with increasing 119 temperature (Figure 3). At a HR of 1, the error increases from 97 % at 20° to 111 % at 25°C in a high (1 meq L -1 ) alkalinity 120 sample. Thus, the error can be significantly reduced by lowering the equilibration temperature. A possible way to take 121 advantage of this is to perform headspace equilibration at in situ temperature in the field, as have been done in several studies. 122 If in situ water temperature is lower than typical laboratory temperature, the error is thereby reduced. However, care must be 123 taken to make sure that the exact equilibration temperature is known. headspace equilibration and the chemical system can be assumed always to be in equilibrium. Thus, the reactions of the 130 carbonate system have to be fully considered in headspace analysis of CO2. 131

Correction of CO2 headspace data 132
If other information regarding the carbonate system of the sample is known (alkalinity or DIC), one can correct for the bias 133 induced by simple headspace calculations. The procedure involves estimating the exact pH of the equilibrium solution before 134 and after equilibration. Here, we develop the procedure when the alkalinity of the sample is known, in addition to the usual 135 parameters required for headspace calculations: water temperature of equilibration and in the field, pCO2 after equilibration, 136 pCO2 of the headspace gas before equilibration, and headspace ratio.

142
Where K1 and K2 are the temperature -dependent equilibrium constants for the dissociation reactions for bicarbonates and 143 carbonates, respectively (Millero, 1979). Kw is the dissociation constant of water into H + and OH - (Millero, 1979 is determined for the water temperature during field sample collection. We applied the above correction 155 procedure to the Canadian samples where pCO2 was measured in several samples using both headspace and in situ NDIR 156 methods together with measured alkalinity data. Figure 4 shows that the corrected values matched the in situ NDIR values 157 nearly perfectly (r 2 =0.997) whereas the simple headspace calculations resulted, as expected, in significant underestimation for 158 undersaturated samples equilibrated with ambient air. 159 We examined the sensitivity of the correction procedure to the precision of the alkalinity measurements and found that the 160 error associated with alkalinity determination does not severely impact the final pCO2 estimate when using N2 as a headspace 161 gas. For example, the error in the corrected pCO2 values is always below 20% even when the alkalinity is known only to within 162 50% error (Fig. 3c). However, more precise alkalinity values are required when using ambient air as a headspace gas in 163 undersaturated conditions (Fig. 3d). 164 The correction calculations have been implemented in an R script and, for a user-friendly interface, as an JMP add-in (or JSL 165 script) (https://github.com/icra/headspace). Roots of the polynomials (Eqs. 2 and 5) can be solved using either standard 166 analytical formulas (e.g. Zwillinger (2018)) or by iterative algorithms. Analytical solution are faster than iterative algorithms 167 but can suffer small instabilities (SD≈ 1 ppmv) in extreme situations (alkalinity >4000 µeq L-1 and pCO2 <100 ppmv) due to 168 limitations inherent to double precision numerical calculations. 169

Conclusions 170
The headspace method has been used in several studies about CO2 fluxes from surface waters. Our error analysis shows that 171 the usual headspace method can be used (error<5%) if the pH is below 7.5 or pCO2 is above 1000 µatm (TA<1700, air 172 headspace), a typical situation in most boreal systems. However, the standard headspace introduces large errors and cannot be 173 used reliably for under saturated samples, which are typical of eutrophic or low DOC systems. In all other cases, not accounting 174 for the chemical equilibrium shift leads to a systematic over estimation. The magnitude of the error can be reduced by 175 increasing the water/headspace ratio, lowering the equilibration temperature, and/or using air instead of N2 as headspace. The 176 https://doi.org/10.5194/bg-2020-307 Preprint. Discussion started: 2 September 2020 c Author(s) 2020. CC BY 4.0 License. magnitude of that error can be roughly estimated from Figure 1. If alkalinity is known, pCO2 obtained from headspace 177 equilibration can be corrected by the provided scripts. We therefore recommend to always measure alkalinity if the headspace 178 method is to be used for pCO2 determinations. The procedure can also be used to correct historical pCO2 data. Our field data 179 showed that the correction works well even in highly undersaturated conditions and is not very sensitive to the precise 180 determination of alkalinity if N2 is used as a headspace gas. The precision of the corrected pCO2 is similar to that obtained 181 from direct pCO2 measurement using a field NDIR analyser coupled to an on-line equilibrator (Cole and Prairie, 2009;Yoon 182 et al., 2016). 183

Data availability 186
All data can be found in the supplemental information file. 187