Uncertainties in eddy covariance air-sea CO 2 flux measurements and 1 implications for gas transfer velocity parameterisations

. Air-sea carbon dioxide (CO 2 ) flux is often indirectly estimated by the bulk method 11 using the air-sea difference in CO 2 fugacity (  f CO 2 ) and a parameterisation of the gas transfer 12 velocity ( K ). Direct flux measurements by eddy covariance (EC) provide an independent 13 reference for bulk flux estimates and are often used to study processes that drive K . However, 14 inherent uncertainties in EC air-sea CO 2 flux measurements from ships have not been well 15 quantified and may confound analyses of K . This paper evaluates the uncertainties in EC CO 2 16 fluxes from four cruises. Fluxes were measured with two state-of-the-art closed-path CO 2 17 analysers on two ships. The mean bias in the EC CO 2 flux is low but the random error is 18 relatively large over short time scales. The uncertainty (1 standard deviation) in hourly 19 averaged EC air-sea CO 2 fluxes (cruise-mean) ranges from 1.4 to 3.2 mmol m -2 day -1 . This 20 corresponds to a relative uncertainty of ~20% during two Arctic cruises that observed large 21 CO 2 flux magnitude. The relative uncertainty was greater (~50%) when the CO 2 flux magnitude 22 was small during two Atlantic cruises. Random uncertainty in the EC CO 2 flux is mostly caused 23 by sampling error. Instrument noise is relatively unimportant. Random uncertainty in EC CO 2 24 fluxes can be reduced by averaging for longer. However, averaging for too long will result in 25 the inclusion of more natural variability. Auto-covariance analysis of CO 2 fluxes suggests that 26 the optimal timescale for averaging EC CO 2 et al. (2014), Butterworth and Miller (2016), Prytherch et al. (2017); 50 µatm, 581 Landwehr et al. (2018)). Analysis of the data presented here suggests that a |  f CO 2 | threshold 582 of at least 20 µatm is reasonable for hourly K 660 measurements, leading to  K 660 of ~ 10 cm h -1 583 (  𝐾 660 𝐾 660 ⁄ ~ 1/3) or less on average. At very large |  f CO 2 | of over 100 µatm,  K 660 is reduced 584 to only a few cm h -1 (  𝐾 660 𝐾 660 ⁄ ~ 1/5). At longer flux averaging time scales, it may be possible 585 to relax the minimal |  f CO 2 | threshold. 586


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Since the Industrial Revolution, atmospheric CO2 levels have risen steeply due to human 33 activities (Broecker and Peng, 1993). The ocean plays a key role in the global carbon cycle, 34 having taken up roughly one quarter of anthropogenic CO2 emissions over the last decade 35 (Friedlingstein et al., 2020). Accurate estimates of air-sea CO2 flux are vital to forecast climate 36 change and to quantify the effects of ocean CO2 uptake on the marine biosphere.

Gas analyser
Picarro G2311-f Picarro G2311-f Picarro G2311-f LI-7200 118 The CO2 flux and data logging systems installed on the JCR and Discovery were operated 119 autonomously. The EC systems were approximately 20 m above mean sea level on both ships 120 (at the top of the foremasts, Fig. 1) to minimise flow distortion and exposure to sea spray.

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Computational fluid dynamics (CFD) simulation indicates that the airflow distortion at the top 122 of the JCR foremast is small (~1% of the free stream wind speed when the ship is head to wind, 123 Moat and Yelland, 2015). The hull structure of RRS Discovery is nearly identical to that of 124 RRS James Cook. CFD simulation of the James Cook indicates that the airflow at the top 125 foremast is distorted by ~2% for bow-on flows (Moat et al., 2006). 126 The EC system on the JCR consists of a three-dimensional sonic anemometer (Metek Inc.,

Ship motion
Flux uncertainty from an earlier version of the motion correction procedure (less rigorous than the one used by ourselves) is estimated to be 10-20% (Edson et al. 1998

Airflow distortion
The

Inlet effects (high-frequency flux attenuation and CO2 sampling delay)
High-frequency flux signal attenuation (in the inlet tube, particle filter and dryer) is evaluated by the CO2 signal response to a puff of N2 gas. Flux attenuation is calculated from the 'inlet puff' response and applied as a correction (< 10%, see Sect. 2.2). The uncertainty in the attenuation correction is about 1% for unstable/neutral atmospheric conditions, which is generally the case over the ocean (e.g. 93% of the time for the Atlantic cruises, 80% of the time for the Arctic cruises). During stable conditions, the attenuation correction is larger (Landwehr et al., 2018) and the uncertainty is also greater (~20%).
The lag time adjustment prior to the flux calculation aligns the CO2 and wind signals. Two methods are used to estimate the optimal lag time: puff injection and maximum covariance. The two lag estimates are in good agreement (Sect. 2.2). Random adjustment of ± 0.2 s (1 σ of the puff test result) to the optimal lag time impacts the CO2 flux by < 1%.
< 2% for vast majority of the cruises ,

Spatial separation between the sonic anemometer and the gas inlet
The CO2 inlet is ~70 cm directly below the centre volume of the sonic anemometer. This distance is small relative to the size of the dominant flux-carrying eddies encountered by the EC measurement system height above sea level. The excellent agreement between the lag time determined by the puff system and by the optimal covariance method further confirms that the distance between the CO2 inlet and anemometer is sufficiently small.

Imperfect calibration of the sensors
The potential flux bias resulting from instrument calibration (gas analyser, anemometer and meteorological sensors required to calculate air density: air temperature, relative humidity and pressure) is up to 4% for the JCR setup. The largest instrument calibration uncertainty derives from the wind sensor accuracy (± 0.15 m s -1 at 4 m s -1 winds according to the Metek uSonic instrument specification). This bias is even lower (< 2%) for the Discovery setup because the Gill R3 sonic anemometer is more accurate.

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In addition to bias sources related to the instrument setup (Table 2) 2008), the total systematic error is less than 9% (= √7.5% 2 + 5% 2 ).  A. An empirical approach to estimate total random error involves shifting the w data relative ( 2 ) and white noise ( 2 ). The sources of variance are considered to be independent of each 301 other and the sonic anemometer is assumed to be relatively noise-free. According to 302 propagation of uncertainty theory (JCGM, 2008), the total random flux error can be defined as: where the constant a varies from √2 to 2, depending on the relationship between the covariance where 2 ( → 0) represents the extrapolation of auto-covariance to a zero shift, which is 340 considered equal to variance due to atmospheric processes ( 2 ). Figure 3 shows the normalised   Picarro G2311-f) and Atlantic cruises (AMT28, Picarro G2311-f; AMT29, LI-7200). Total CO2 388 variance ( 2 ) consists of white noise ( 2 ) and atmospheric processes ( 2 ). The latter can be further 389 broken down to the CO2 variance due to vertical flux ( 2 ) and due to other processes ( 2 ).

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CO2 variance (× 10 -3 ppm 2 ) JR18006 JR18007 AMT28 AMT29 found between all three estimates (Fig. C2, Appendix C) when √2 is used as the constant in The total uncertainty δ in the hourly average EC CO2 flux (estimated using Eq. 3) ranges 420 from 1.4 to 3.2 mmol m -2 day -1 in the mean for the four cruises (Table 4). Our EC flux system 421 setup was optimal and subsequent corrections have minimised any bias to < 9% (Sect. 2.3.2).

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Systematic error is on average much lower than random error ( The theoretical uncertainty estimates above can be compared with a portion of the AMT28 436 cruise data (15°−20° S, ~25° W; Fig. 4), when the ship encountered sea surface CO2 fugacity 437 close to equilibrium with the atmosphere (i.e. fCO2 ~0, Fig. A2, Appendix A). The data from   (Fig. 7a). All four cruises consistently demonstrate a non-linear reduction in the noise 500 contribution to the flux measurements when the averaging timescale increases (Fig. 8). The   The noise: signal also facilitates comparison of all four cruises (Fig. 8) and demonstrates the 510 consistent effect that increasing the averaging timescale has on noise: signal. Consistent with 511 Table 4, the Arctic cruises show much lower noise: signal because the flux magnitudes are 512 much larger. Typical detection limits in analytical science are often defined by a 1: 3 noise: 513 signal ratio. A 1: 3 noise: signal is achieved with a 1 h averaging timescale for the Arctic cruises.

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The Atlantic cruises encountered much lower air-sea CO2 fluxes and an averaging timescale of 515 at least 3 h is required to achieve the same 1: 3 noise: signal ratio.

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The flux measurement uncertainty at a 6-h averaging timescale for the AMT cruises is ~0.6 517 mmol m -2 day -1 . The analysis presented above permits an answer to the question posed at the The uncertainties in the EC CO2 air-sea flux measurement will influence the uncertainty that 533 translates to EC-based estimates of the gas transfer velocity, K. For illustration, K is computed 534 for Arctic cruise JR18007, which had a high flux signal: noise ratio of ~5 (Fig. 8). Any data 535 potentially influenced by ice and sea ice melt were excluded using a sea surface salinity filter 536 (data excluded when salinity < 32). Equation 1 is rearranged and used with concurrent 537 measurements of CO2 flux (F), fCO2, and sea surface temperature (SST) to obtain K adjusted 538 for the effect of temperature (K660).

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The determination coefficient (R 2 ) of the quadratic fit between wind speed (U10N) and EC-540 derived K660 (Fig. 9) demonstrates that wind speed explains 76% of the K660 variance during  The analysis above can be extended to assess how EC flux-derived uncertainty affects our 563 ability to parameterise K660 (e.g. as function of wind speed). To do so, a set of synthetic K660 564 data is generated (same U10N as the K660 measurements in Fig. 9). The synthetic K660 data are 565 initialised using a quadratic wind speed dependence that matches JR18007 (i.e. K660 = 566 0.22U10N 2 + 2.46). Random Gaussian noise is then added to the synthetic K660 data, with relative 567 noise level corresponding to the relative flux uncertainty values taken from JR18007 (mean of 568 20%, Table 4). The relative uncertainty in K660 due to EC flux uncertainty (K660/K660) shows 569 a wind speed dependence (Fig. S4a, Supplement), and the artificially-generated Gaussian noise 570 incorporates this wind speed dependence (Fig. S4b, Supplement). The R 2 of the quadratic fit to  (Table 4). Random flux uncertainty is primarily caused by variance in CO2 mixing ratio due to 601 atmospheric processes. The random error due to instrument noise for the Picarro G2311-f is 602 threefold smaller than for LI-7200 (Table 4 and Fig. D1, Appendix D). However, the 603 contribution of the instrument noise to the total random uncertainty is much smaller than the to quantify the optimal averaging timescale ( Fig. 7 and 8 Figure D1 shows a comparison between the performance of the Picarro 2311-f and the LI-7200 696 gas analysers. We estimated that the noise of the LI-7200 is on average 3 times higher than that 697 of the Picarro 2311-f (Table 3). Indeed, random error in the CO2 flux due to the white noise is 698 much higher for the LI-7200 than for the Picarro 2311-f, but the total flux uncertainty of the 699 EC system with the LI-7200 on AMT29 is only slightly higher than that of the EC system with 700 the Picarro 2311-f on AMT28 (Table 4). Again, this is because for both EC systems, sampling