Analysis of the PKT correction for direct CO 2 flux measurements over the ocean

Eddy covariance measurements of air–sea CO2 fluxes can be affected by cross-sensitivities of the CO2 measurement to water vapour, resulting in order-of-magnitude biases. Well established causes for these biases are (i) crosssensitivity of the broadband non-dispersive infrared sensors due to band-broadening and spectral overlap (commercial sensors typically correct for this) and (ii) the effect of air density fluctuations (removed by determining the dry air CO2 mixing ratio). Another bias related to water vapour fluctuations has recently been observed with open-path sensors, attributed to sea salt build-up and water films on sensor optics. Two very different approaches have been used to deal with these water vapour-related biases. Miller et al. (2010) employed a membrane drier to physically eliminate 97 % of the water vapour fluctuations in the sample air before it entered a closed-path gas analyser. Prytherch et al. (2010a) employed the empirical (Peter K. Taylor, PKT) post-processing correction to correct open-path sensor data. In this paper, we test these methods side by side using data from the Surface Ocean Aerosol Production (SOAP) experiment in the Southern Ocean. The air–sea CO2 flux was directly measured with four closed-path analysers, two of which were positioned down-stream of a membrane dryer. The CO2 fluxes from the two dried gas analysers matched each other and were in general agreement with common parameterisations. The flux estimates from the un-dried sensors agreed with the dried sensors only during periods with low latent heat flux (≤ 7 Wm−2). When latent heat flux was higher, CO2 flux estimates from the un-dried sensors exhibited large scatter and an order-of magnitude bias. Applying the PKT correction to the flux data from the un-dried analysers did not remove the bias when compared to the data from the dried gas analyser. The results of this study demonstrate the validity of measuring CO2 fluxes using a pre-dried air stream and show that the PKT correction is not valid for the correction of CO2 fluxes.


Introduction
Direct measurements of air-sea CO 2 flux contribute to the understanding of the earth climate system and can be used to study the fundamental physics of air-sea gas exchange. When direct flux measurements are combined with the measurement of the partial pressure gradient of CO 2 across the air-water interface, pCO 2 , the gas transfer velocity k can be derived as follows (e.g. Wanninkhof, 1992): where S is the solubility of CO 2 in sea water and F c is the vertical CO 2 flux. The ability to parameterise k is essential for modelling global air-sea CO 2 fluxes based on pCO 2 climatologies (Takahashi et al., 2002), as well as for increasing our understanding of the global oceanic uptake of CO 2 (Ward et al., 2004). In the eddy covariance (EC) method, the turbulent flux is directly calculated from the covariance of the fluctuations in the vertical wind speed (w ) and fluctuations in the CO 2 mixing ratio in dry air (x c ): where n d is the dry air density (here indicates a time average over a time interval t I and the primes denote deviations from the mean). The w and x c parameters need to be sampled fast enough to resolve the smallest flux-carrying eddies (typically 10 Hz), and the averaging interval needs to be long enough to include large-scale motions that contribute to the vertical flux, but short enough to ensure stationarity of the relevant parameters during the interval (typically t I are between 15 and 60 min) (Kaimal et al., 1972). The EC method thus allows the study of gas transfer with much higher time resolution than both dual tracer experiments (e.g Nightingale et al., 2000;Ho et al., 2006) and measurements of the 14 C concentration in sea water (e.g Wanninkhof, 1992;Sweeney et al., 2007).
Commonly used broadband infrared gas analysers (IR-GAs), such as LI-COR LI7500 and LI7200, measure the CO 2 concentration n c (number of molecules per volume), from which the mixing ratio needs to be calculated. Therefore, simultaneous measurements of temperature T , pressure P , and water vapour concentration n v are necessary to calculate the dry air density n d = (P /RT − n v ) and the CO 2 mixing ratio x c = n c n −1 d (Webb et al., 1980). Equation (2) can be written as the sum of the flux measured by the IRGA and a bias flux, caused by the fluctuations of the dry air density: For CO 2 , the bias terms due to the water vapour, temperature and pressure fluctuations in the sample volume (F q , F T and F P , respectively) can easily exceed the vertical flux by an order of magnitude because the fluctuations x c are small compared to the background x c (Webb et al., 1980). Equations (3) and (2) are fully equivalent. EC is considered a standard method over land, but the application over the open ocean has proved to be more challenging. In the case of ship-based studies, the wind speed measurement needs to be carefully corrected for platform motion (e.g Edson et al., 1998;Miller et al., 2008). Over land, the pressure term in Eq. (3) can be ignored, but at sea the platform motion-induced pressure fluctuations can introduce a further bias flux as they may correlate with residuals of ship motion signal in the motion-corrected wind speed (Miller et al., 2010). CO 2 fluxes over the ocean are typically much smaller than over land, and with currently available sensor technology (e.g. LI-COR 7500/7200 have a resolution of 0.11 ppm at 10 Hz sample rate), a relatively high airsea gradient pCO 2 ≥ 40 µatm is required to keep the uncertainty in the flux signal due to sensor resolution below 10 % (Rowe et al., 2011).
For EC, the trace gas measurement has to be carried out on the same air sample as the wind speed measurement. This can be done directly using an open-path (OP) IRGA, which is located close to the sonic anemometer (Kondo and Osamu, 2007;Yelland et al., 2009;Prytherch et al., 2010b). Alternatively, air can be pumped to a distant closed-path (CP) IRGA, at a sufficiently high flow rate (e.g. McGillis et al., 2001). This allows deliberate pre-conditioning of the air sample, such as removal of the temperature and water vapour fluctuations and the application of in-line particle filters to avoid the deposition of salt or dust particles on the sensor lenses. McGillis et al. (2001) were the first to carry out EC measurements of the air-sea CO 2 flux, which were in general agreement with common bulk flux formulae. Miller et al. (2010) developed a CP system where 97 % of the water vapour flux signal is removed by passing the air flow through a membrane dryer. This significantly lowered the magnitude of the air density correction term in Eq. (3).
Attenuation of the fluctuations within the sample tube of CP systems can lead to an underestimation of the turbulent transport carried by the small high-frequency eddies (Leuning and King, 1992). To minimise this effect the flow must be kept fully turbulent (with a Reynolds number Re 2100). This requires flow rates (O(100) slpm). Therefore, CP systems have higher power and maintenance requirements than OP systems.
In the oceanic environment, the lenses of OP IRGAs are prone to the build-up of salt particles, and flushing with fresh water is necessary to avoid degradation of the signal. The LI7500 has also been deployed with a shroud and a very high airflow (570 slpm) (Edson et al., 2011). This deployment mode is a hybrid of the OP and CP mode as the contamination with sea spray is reduced with minimal loss of high-frequency fluctuations. Even when the air density correction Eq. (3) has been applied carefully, reported CO 2 flux values based on OP and shrouded OP EC systems over the open ocean are typically an order of magnitude higher than expected based on generally accepted bulk flux parameterisations (Kondo and Osamu, 2007;Prytherch et al., 2010a;Lauvset et al., 2011;Edson et al., 2011).
The exact reason for the additional bias is still unclear. Kohsiek (2000) suggested that the build-up of water films on the sensor lenses could lead to a biased CO 2 measurement x cm with dependency on the relative humidity (RH). This will cause a bias in the CO 2 flux measurement F cm , which scales with the latent heat flux, because the fluctuations of the water vapour concentration in the sample volume will lead to artificial fluctuations in x cm . Removing this artificial cross-correlation is difficult because there is a natural correlation between the fluctuations of the two scalars x c and x v , which are both transported by the same turbulent eddies. Attempting to remove the artificial dependency x cm (RH) with regressions or polynomial fits can thus lead also to the removal of the turbulence-driven variations of x c and, therefore, of the CO 2 flux signal itself. Prytherch et al. (2010a) Atmos. Chem. Phys., 14, 3361-3372, 2014 www.atmos-chem-phys.net/14/3361/2014/ suggested that the accumulation of salt particles on the lens of the LI7500 OP IRGA could modulate the magnitude of the bias. Edson et al. (2011) reported that the accumulation of salt particles on their shrouded and regularly cleaned IRGAs was unlikely and suggested that a more suitable explanation was provided by the contamination of the optics with small particles from the ship's engines combined with organic deposits from sea spray. Prytherch et al. (2010a) went further and presented a correction method (called the Peter K. Taylor -PKT -method), which has since been used in several publications to correct OP CO 2 fluxes (e.g. Prytherch et al., 2010b;Lauvset et al., 2011;Edson et al., 2011;Huang et al., 2012;Ikawa et al., 2013). Huang et al. (2012) reported that the PKT correction did bring some of their CO 2 flux measurements closer to the bulk flux estimate, but found that for small water vapour fluxes the PKT method overcorrected the CO 2 flux and, in some cases, even resulted is a reversal of the flux direction. Ikawa et al. (2013) reported that the PKT correction resulted in increased scatter when applied to coastal tower-based CO 2 flux measurements, and decided not to apply the correction. A selection of the publications mentioned above are also listed in Table 1 together with a brief description of the deployed IRGAs and findings relevant to this contribution.
Here we present direct CO 2 flux measurements performed during the Surface Ocean Aerosol Production (SOAP) experiment in the Southern Ocean, where we deployed the SUNY Albany Air/Sea Flux system (Miller et al., 2010), consisting of dried and un-dried CP IRGAs. In order to rule out that the failure of an individual IRGA would suggest differences between the dried and un-dried deployment, the number of IRGAs was doubled using sensors from National University of Ireland Galway.
We show that even EC measurements using CP IRGAs can be affected by a large humidity bias when the sampled air is neither dried nor filtered. We applied the PKT method (which does not include any OP-specific assumptions) to the un-dried CP data as a test of its ability to remove the observed humidity flux-related bias in broadband non-dispersive infrared (NDIR) sensors. We further analyse and discuss this correction method (Prytherch et al., 2010a) in detail.

Experiment and methods
The SOAP field campaign was conducted from February to March 2012 on the R/V Tangaroa. The EC system described here consisted of two Csat3 sonic anemometers attached to the bow mast (12.6 m a.s.l.), which provide high-frequency measurements of the three components of the wind vector (u, v and w) and the speed of sound temperature (T s ), as well as four IRGAs of type LI7200 (×2) and LI7500 (×2), which were located inside the container laboratory on the bow deck and connected to the sample volume on the mast with a stainless steel tube (ID = 1 cm; L = 20 m). The inlet tube was heated to avoid condensation on the walls, which would lead to an underestimation of the EC latent heat flux. Although the tubing had a built-in self-regulated heating resistor (Parker SL-522-B0849A), the temperature in the tubing was not measured continuously. However the LI-COR temperature sensors recorded temperatures ranging from 23 to 36 • C at an outside air temperature ranging from 8 to 16 • C. A pump (Gast model 1423) delivered a continuous air stream from the mast at 100 slpm (Re ≈ 7500), where Re is computed as Re = Q·2R ν·π R 2 , using a flow rate Q ms −1 , the inner radius of the tubing R [m] and the kinematic viscosity of air ν ≈ 7.1 × 10 −6 m 2 s −1 . Figure 1 shows a schematic of the flux system.
A part of the main flow (17 slpm; ID = 6 mm; L = 2 m; Re ≈ 2100) was directed to the two LI7200s CP IRGAs (wetA, wetB) connected in sequence. Up to this point the air was not filtered. The air stream was subsequently divided and passed to two LI7500s, which were connected in parallel. The 7500 OP units were converted to CP, and each one was positioned downstream of a Nafion membrane dryer (PD-200T) to remove fast water vapour fluctuations as shown by Miller et al. (2010). They are described as dryA and dryB in the following text.
Zero air was injected periodically (every 6 h) into the sample inlet to measure the delay of the signal in the IRGAs. Pressure and temperature in each IRGA sample volume were also measured with external sensors (Mensor CPT6100 and a thermocouple, respectively). An inertial motion unit (IMU -Systron Donner MotionPak II) provided high-frequency acceleration and rate data, and a GPS compass and the ship's gyrocompass were used to completely describe the ship's motion. These data allowed the wind speed measurements from the Csat3 to be corrected for platform motion following Miller et al. (2008). All measurements were performed at 10 Hz.

Data analysis and flux calculations
The fluxes of momentum u * and the sonic sensible heat H sonic were calculated from the Csat3 data after motion correction (Miller et al., 2008) and rotation of the wind vector into the mean flow (McMillen, 1988). The latent heat flux Hl was calculated from the covariance of the vertical wind speed w with the water vapour mixing ratio x v from wetA and wetB after correction for the time delay. H sonic was corrected with the latent heat flux to derive the sensible heat flux H s , following Burns et al. (2012). The measured CO 2 density was converted to a mixing ratio (as described in Sect. 1), and ship motion contaminations of the signal due to flexing of the sensor or inertial forces on the filter wheel were removed using a linear regression with the acceleration and rate signal (as in Miller et al., 2010).
All flux calculations were performed over 25 min intervals. These intervals were divided into five 5 min subintervals and were excluded if any of the mean wind direction Table 1. Publications addressing the bias in NDIR CO 2 measurements that is related to relative humidity.

Publication
Configuration Notes Kohsiek (2000)  within the sub-intervals exceeded 100 • to the bow to minimise flow distortion effects. Flux intervals were also excluded when spikes were present in the wind speed or IRGA measurements. The remaining intervals were checked for signs of non-stationarity in the CO 2 co-spectra of the dryA and dryB, and the same criteria as in Bell et al. (2013) were applied. It has to be noted here that the co-spectra of CO 2 and H 2 O are similar. Therefore a cross-contamination of the CO 2 signal with H 2 O cannot be clearly identified by spectral analysis. A total of 327 from the 1039 available intervals passed the quality control for dryA as well as for dryB and were used for the analysis presented here. For wetA and wetB, only 273 and 269 intervals, respectively, passed because these analysers had been removed from the setup for about 1 day. Flux measurements from wetA and wetB passed both for 267 intervals, because spikes had compromised the data from the two sensors during different intervals.
The PKT correction, as presented by Prytherch et al. (2010a), was applied to the mixing ratios measured by the two analysers wetA and wetB. This method includes an iteration in which the correct flux value is approximated. The termination criterion for the iteration was chosen according to Prytherch et al. (2010a), to be |F Prytherch et al. (2010a) also suggested a rejection of the PKT results if the iteration did not converge within 10 steps or if F (j ) c exceeded ±400 mol m −2 yr −1 (which was considered unrealistically high). Thus the application of the PKT correction to the measurements from the un-dried IRGA led to a further reduction of the data set. measurements of the dried IRGAs. These results are presented in Sects. 3.1 and 3.2, respectively. The flux measurements are affected by air-flow distortion, which results in a bias that depends mostly on the relative wind direction (Popinet et al., 2004;O'Sullivan et al., 2013). For this submission, the flux measurements were not corrected for air flow distortion because we concentrate on the comparison of different IRGA signals that were all correlated with the same wind speed measurement. Air flow distortion does therefore not affect our conclusions. Figure 2 shows an overview of the conditions encountered during the SOAP experiment from 16 February to 5 March 2012 (DOY 47-65). The wind speed range was between 0 and 15 m s −1 (25 min average) and peaked at 20 m s −1 on DOY 61. Unfortunately, the uninterruptible power supply of the EC system was flooded during this storm event, leading to a 12 h gap in the record. The ship was steered into the wind as much as possible, except during survey periods or deployments of instruments. The air temperature was mostly colder than the water temperature (measured by the ship's thermosalinograph) except for a period between DOY 51 and 55, when a warm air mass led to negative turbulent heat fluxes. The air-water pCO 2 difference ranged between −40 and −120 µatm. These large pCO 2 values were easily within the 40 µatm criterion for EC flux measurements with the LI-COR IRGAs (Rowe et al., 2011).

Primary CO 2 flux results
The CO 2 flux measurements from the four CP IRGAs (without PKT correction) are plotted in Fig. 3 (top and middle). The CO 2 flux estimates from the dry gas analysers were in general agreement with each other and Sweeney et al. (2007), which is an updated version of the widely used parameterisation by Wanninkhof (1992), while the flux measurements from the un-dried gas analysers exhibited large scatter.
The LI-COR IRGAs measure CO 2 density, and the measured flux signal F IRGA must be corrected for the air-density flux bias terms (F q , F T , and F P ) to obtain the correct CO 2 flux signal F c . The flux bias terms at different measurement positions are shown in Fig. 4. For the un-dried IRGA, F q exceeded F c by an order of magnitude (Fig. 4 top). For the whole data set, the average magnitude of the latent heat flux from the un-dried IRGAs was 36 W m −2 ; in contrast the average magnitude of the latent heat flux downstream of the dryer was 2.4 W m −2 . The application of the diffusion dryer therefore reduced F q on average by 93 %. This is comparable to Miller et al. (2010), who found a reduction by 97 %. A similar effective reduction was found for F T (Fig. 4 bottom), when compared with the open-path measurement by the sonic anemometer. The reduction of F T is due to heat exchange of the sample air with the 20 m-long inlet tubing and does not depend upon the drying. F P (Fig. 4 bottom) is much smaller than F q and F T , but of the same magnitude as F c . F P cannot be reduced physically and needs to be measured accurately (Miller et al., 2010). The wind speed measurement was taken on the ship's main deck and is corrected for air-flow distortion (Popinet et al., 2004) and normalised to standard conditions (10 m height and neutral stability). This wind speed was used to calculated the bulk fluxes with the TOGA COARE 3.0 algorithm. All direct EC fluxes are measured at the bow mast using the Csat3 sonic anemometer and the IRGA in the science container on the foredeck.
The flux measurements of all four CP IRGAs, as presented in Fig. 3, have been corrected for the air-density bias fluxes by calculating the CO 2 mixing ratio. However, even after this correction was applied, the un-dried IRGA CO 2 fluxes showed erratic behaviour. The difference in the CO 2 flux measurements from the un-dried and dried IRGAs is plotted in Fig. 5. The variance of the flux data from wetA and wetB increased proportionally with the latent heat flux and became an order of magnitude larger than that from dryA or dryB. There was no apparent correlation between the differences in the CO 2 fluxes F and the bias fluxes caused by the pressure and temperature fluctuations (F T and F P ).
It has to be pointed out that the primary flux measurements from the two un-dried sensors agreed with the measurements from the dried IRGAs during periods with very low latent heat flux (Hl ≤ 7 W m −2 ). These periods are marked as shaded areas in Figs. 2 and 3. The limit of 7 W m −2 was chosen so that the envelope of the bias was approximately two times the scatter observed at Hl ≈ 0 W m −2 . Figure 6 shows scatter plots of the flux measurements from wetA and wetB against those from dryB for (Hl ≤ 7 W m −2 ) and of dryA against dryB for the whole data set. A linear regression of the dryA vs. dryB for the full data set gave a slope of 1.09 ± 0.01 with a R 2 = 0.96. For wetA and wetB, regression was performed over the restricted data set (Hl ≤ 7 W m −2 ) and gave slopes of 0.88 ± 0.15 with R 2 = 0.36 and 0.93 ± 0.06 with R 2 = 0.78, respectively.  the full data set. The magnitude of the latent heat flux is used as colour code. Linear regression gave a slope of −0.17 ± 0.8 for wetA vs. dryB and +0.7 ± 0.2 for wetB vs. dryB, respectively, both with very low R 2 values. On average, the effect of the bias was to reduce the CO 2 flux, even changing the sign.

Application of the PKT correction to the flux measurements from the un-dried IRGAs
The PKT correction, as presented by Prytherch et al. (2010a), was applied to the x cm measured by the two un-dried analysers, and the results were evaluated against the unbiased measurements of the dried IRGAs. Figure 3 (bottom) shows the PKT-corrected fluxes (F PKT c ) as well as the results from Eq. (7), which is derived in Sect. 4 and presents a simplified version of the PKT correction that also provides an output when the PKT correction does not converge. The results of Eq. (7) are not used in the evaluation of the PKT correction results; that is, intervals that were rejected by the PKT correction are excluded from the analysis.
Scatter plots in Figs. 7 and 8 show the correlation between the flux measurements form the un-dried IRGAs and the fluxes from dryB before (left) and after the application of the PKT correction to the un-dried measurements (right). For low latent heat flux, the PKT correction increases the scatter of the initially well-correlated measurements and also rejects a large part of the results. For wetA, the PKT correction reduces the large range of scatter, but does not improve the correlation with the dryB fluxes. For wetB, which shows a weaker bias, the PKT correction even reduces the correlation with the dryB flux estimates from 0.7 ± 0.2 to 0.4 ± 0.2.
The average raw flux estimates from the four CP IR-GAs and from the PFT-corrected un-dried IRGAs are shown in Table 2. The average was taken over the 161 intervals, where PKT results were available for both undried gas analyser, and over three subsets, which were based on the magnitude and sign of the latent heat flux Atmos. Chem. Phys., 14, 3361-3372  The average flux estimates of the two dried IRGAs agreed within 1 % for the whole cruise and for each of Subset 1 and Subset 3. For Subset 2 the agreement was within 3 %.

Analysis of the PKT correction
To investigate the unsatisfactory results of the PKT correction (cf. Sect. 3.2), we will now analyse the correction algorithm in detail.
The PKT method Prytherch et al. (2010a) is based on the assumption that the ratio of the variations of two quantities (e.g. CO 2 and relative humidity) is equal to the ratio of their vertical fluxes: Prytherch et al. (2010a) derived Eq. (4) from the Monin-Obukhov similarity theory, assuming that the scalar profiles of the two non-dimensionalised quantities are equal. The correction algorithm can be summarised as follows: first, the variations of x c that are dependent on RH are removed from the measured signal x cm with a third-order polynomial fit to the x cm and RH time series: where a n are the polynomial coefficients determined by the fit. A first-step CO 2 flux F c , and then used with Eq. (4) to get a first approximation of ∂ x c ∂ RH . The CO 2 mixing ratio is then adjusted using the following quantity: Here, the relative humidity flux RH w was substituted with loop typically converges within less than 10 steps). Equations (4)-(6) are taken from the Matlab code in the Supplement of Prytherch et al. (2010a). We found that the loop can be replaced by one simple equation: where In order to show this, we re-write Eq. (6) by replacing the adjusted mixing ratio x Equation (8) and is used to compute x (j +1) c via Eq. (8). However, if Eq. (9) is inserted into the convergence criterion (F (j ) c − F (j −1) c → 0) and solved for F (j −1) c , we find that the loop will terminate at F PKT c given by Eq. (7). The results of the loop agree with Eq. (7) within the tolerance |F (j ) c − F (j −1) c | ≤ 0.04 mol m −2 yr −1 , which is used by Prytherch et al. (2010a) to determine that the loop has converged. In Fig. 9 the results from Eq. (7) and the PKT loop are plotted over the 1 : 1 correspondence line. A significant advantage of Eq. (7) is that it always provides a result, whereas the PKT loop does not always converge. In Fig. 3 (bottom)  PKT correction algorithm lead to a reduced range of scatter in the PKT results when compared to the results of Eq. (7). Prytherch et al. (2010a) validated the PKT method by applying it to the sensible heat flux (F T s ) as calculated from the measured speed of sound temperature (T s ). We followed this analysis and show our results in Fig. 10, which can be directly compared to Fig. 2 in Prytherch et al. (2010a). The average of the flux, calculated from the detrended sonic temperature (F (0) T s ), yields approximately one half of the flux signal. The PKT flux, which is equal to the product of the detrended flux and β, correlates with the standard EC sensible heat flux. The factor 0.5 in Eq. (7) comes from the same factor Eq. (6), which was originally inserted to reduce the step width and improve the convergence of the iteration and was not expected to change the result of the PKT correction (J. Prytherch, review comments). In order to illustrate the influence of this factor, the results of a PKT correction with a factor of 0.75 are shown in Fig. 10. Here β ≈ 4 and the PKT results are ≈ 4 × F (0) T s and ≈ 2 × H s.

Discussion
The good agreement between the dried and un-dried CP systems for low latent heat fluxes (cf. Sect. 3.1) supports the findings of Miller et al. (2010) that application of a diffusion dryer does not alter the CO 2 flux signal, but avoids contamination of the sensor optics and significantly reduces the magnitude of the necessary air density correction.
The magnitude of the scatter in the CO 2 fluxes from the un-dried CP systems increases with the latent heat flux (Fig. 5). These results are similar to results reported for OP IRGAs (LI-COR 7500) (e.g Kondo and Osamu, 2007;Lauvset et al., 2011;Prytherch et al., 2010b), which showed an overestimation of the CO 2 flux magnitude when compared to common bulk formulae. In this study, on the other hand, the bias reduced the CO 2 flux on average. Kondo and Tsukamoto (2012) simultaneously deployed OP (LI-COR 7500) and CP (LI-COR 7000) sensors to measure CO 2 fluxes in conditions with low air-sea CO 2 gradient (12 µatm < pCO 2 < 42 µatm) and large latent heat fluxes (70 W m −2 ≤ Hl ≤ 140 W m −2 ). The EC CO 2 flux estimates from both OP and CP IRGAs were an order of magnitude higher than expected using the Sweeney et al. (2007) parameterisation and diverged increasingly for higher latent heat fluxes. We therefore assume that the bias observed in the fluxes from the un-dried CP has the same origin as the biases observed in the OP measurements cited above. Our measurements also indicate that the bias can be different for each individual IRGA unit. Equation (7) explains why the PKT correction produces unsatisfactory flux results: the PKT-corrected flux is simply a product of the flux signal, which was calculated from the CO 2 mixing ratios after detrending against the relative humidity, and the term β ≈ 2 that depends solely on water vapour and relative humidity fluctuations. The ratios of the detrended fluxes of the two un-dried IRGAs to the CO 2 flux measured by the dryB and the factor β are plotted in Fig. 11 as a function of the latent heat flux. The parameter β shows a large scatter for low Hl but converges to 2 for Hl > 50 Wm −2 . The ratio of the detrended fluxes to the fluxes measured by the sensor dryB ((F 0 c ) · (F c ) −1 ) is on average close to 1 when latent heat flux is small, but exhibits large scatter. For Hl > 50 Wm −2 the value of F 0 c becomes much smaller ⋅(F (dryB) ) −1 Fig. 11. Ratio of the detrended CO 2 fluxes F 0 c from wetA and wetB as used for the PKT correction to the CO 2 flux calculated from dryB (purple +, blue +). Two values of the same sample interval are connected with a grey line; the factor β = 1 − 0.5 as in Eq. (7), calculated from the latent heat flux and relative humidity, as measured by wetB, (grey •). The PKT-corrected fluxes are the product of F 0 c and β. The black lines indicate the ratios zero and one. than F c ; this leads to the observed underestimation by the PKT-corrected fluxes.
The PKT correction appears to correct the latent heat flux bias in the sonic sensible heat flux because the flux calculated from the detrended sonic temperature yields on average approximately one half of the flux signal and is then multiplied with β ≈ 2. However, this does not prove that the PKT correction can successfully remove the bias in the measured CO 2 fluxes.

Conclusions
Measurements of the air-sea CO 2 flux over the open ocean were conducted with four IRGAs, two of which had the water vapour fluctuations removed with a membrane dryer (Miller et al., 2010). The flux results from the dried and un-dried sensors agreed with each other during periods of very low latent heat flux, demonstrating that the membrane dryer does not alter the CO 2 flux signal. With increasing latent heat flux, the CO 2 flux measurements from the un-dried sensors showed large bias and scatter. This is similar to earlier studies (Kondo and Osamu, 2007;Lauvset et al., 2011;Prytherch et al., 2010a). In this study the bias flux was positive (on average), leading to a net reduction of the downward CO 2 flux.
The PKT correction reduced the scatter in the flux measurements from the un-dried gas analysers from 1000 to 100 % of the flux signal. However, the PKT-corrected fluxes showed only a weak correlation with the flux measurements Atmos. Chem. Phys., 14, 3361-3372, 2014 www.atmos-chem-phys.net/14/3361/2014/ from the dried gas analysers. A detailed analysis of the PKT algorithm was performed, which revealed that the loop in the PKT correction can be replaced by a single equation. The PKT-corrected flux was shown to be a product of the de-trended CO 2 flux and a factor that depends solely on the latent heat flux and relative humidity. The PKT method cannot be used to retrieve the true CO 2 from the measured signal since detrending to remove the bias also removes most of the CO 2 flux information. Conclusions made based on PKT-corrected CO 2 flux measurements should be treated with care. The results support the conclusions of Miller et al. (2010) that the order-of-magnitude bias in the measured CO 2 fluxes can be removed when the sample air is dried. The authors therefore strongly recommend the use of the closed-path IR-GAs with a diffusion dryer as presented by Miller et al. (2010) for EC flux measurements over the open ocean.